Nuclear Power Plant Design and Analysis Codes: Development, Validation, and Application 9780128181904, 0128181907

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NUCLEAR POWER PLANT DESIGN AND ANALYSIS CODES

Woodhead Publishing Series in Energy

NUCLEAR POWER PLANT DESIGN AND ANALYSIS CODES Development, Validation, and Application Edited by

JUN WANG XIN LI CHRIS ALLISON JUDY HOHORST

Woodhead Publishing is an imprint of Elsevier The Officers’ Mess Business Centre, Royston Road, Duxford, CB22 4QH, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom Copyright © 2021 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-12-818190-4 (print) ISBN: 978-0-12-818191-1 (online) For information on all Woodhead Publishing publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Candice Janco Acquisition Editor: Maria Convey Editorial Project Manager: Leticia M. Lima Production Project Manager: Anitha Sivaraj Cover Designer: Matthew Limbert Typeset by MPS Limited, Chennai, India

Contents 3.5 Summary 72 References 72

List of contributors ix

I

4. Multiphysics coupling plan

Map of code development

Miao Gui and Xingang Zhao

4.1 Introduction 75 4.2 Multiphysics coupling methods 76 4.3 Current status of research in multiphysics coupling 82 4.4 Conclusion 93 References 93

1. Road map Lin Sun, Xiaomeng Dong, Xin Li, Jun Wang and Kaya G. Mondry

1.1 1.2 1.3 1.4 1.5 1.6

Overview 3 Fuel codes 5 System code 6 Subchannel analysis code 10 Computational fluid dynamics code 12 Coupled multiscale thermal-hydraulics codes 14 1.7 Emerging methods for NPPs 16 References 18

II Physics and fuels codes 5. Nuclear physics deterministic code Tengfei Zhang

2. Guidance of nuclear power plant code development

5.1 Nuclear data processing codes 97 5.2 Cross section generation codes 99 5.3 Whole-core computational codes 109 References 115

Xianping Zhong

2.1 Nuclear power plant code 23 2.2 Code development examples 27 2.3 Source code 42 References 53

6. Nuclear physics probability code: OpenMC Jiankai Yu

3. Nuclear engineering software quality assurance

6.1 Introduction to Monte Carlo method 123 6.2 Recently developed Monte Carlo codes 124 6.3 Typical methodologies in OpenMC 125 6.4 Usage of OpenMC 130 6.5 Verification and validation 135 6.6 Summary 137 References 137

Xinghe Ni

3.1 3.2 3.3 3.4

Introduction 55 Software development life cycle 58 Software quality 64 Software quality assurance for nuclear engineering 68

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III Fuels and sub-channel codes 7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions Bowen Qiu and Jun Wang

7.1 Objectives, relations, and limitations 141 7.2 Code structures and physical models 143 7.3 Assessments 152 7.4 Summary 158 References 159

10. Subchannel codes: CTF and VIPRE-01 Xingang Zhao

10.1 Introduction and CTF code overview 235 10.2 CTF assessment: Motivation and work scope 237 10.3 VIPRE-01 code overview 238 10.4 CTF assessment: Flow mixing 238 10.5 CTF assessment: Pressure drop 243 10.6 CTF assessment: Void fraction 249 10.7 Summary 255 References 257

IV Thermal-hydraulic codes

8. The TRANSURANUS fuel performance code A. Magni, A. Del Nevo, L. Luzzi, D. Rozzia, M. Adorni, A. Schubert and P. Van Uffelen

8.1 Introduction: General overview of the TRANSURANUS code 161 8.2 TRANSURANUS code structure 162 8.3 Application to water reactor conditions 168 8.4 Preliminary assessment against fast reactor conditions 186 8.5 Conclusions and future code developments 198 Nomenclature 200 References 201

9. Two fuel performance codes of the PLEIADES platform: ALCYONE and GERMINAL B. Michel, I. Ramie`re, I. Viallard, C. Introini, M. Lainet, N. Chauvin, V. Marelle, A. Boulore, T. Helfer, R. Masson, J. Sercombe, J.C. Dumas, L. Noirot and S. Bernaud

9.1 General overview of the PLEIADES fuel software environment 207 9.2 ALCYONE fuel performance code for GEN II and III 210 9.3 GERMINAL fuel performance code for GEN IV 224 9.4 Conclusion and prospects 231 Acknowledgment 231 References 231

11. System-level code TRACE Anil Gurgen

11.1 Features of TRACE 261 11.2 Constitutive equations of TRACE 263 11.3 Validation of TRACE 274 References 275

12. Nuclear thermal hydraulics with the AC2 system code package Andreas Wielenberg and Christine Bals

12.1 The system thermal-hydraulic code ATHLET 277 12.2 COntainment COde SYStem thermal-hydraulic module THY 298 12.3 Quality assurance measures 305 12.4 Outlook and summary 305 Nomenclature 306 References 307

13. Development and application of System Analysis Module from the user’s view Yukun Zhou, Alejandro Perez and Jun Wang

13.1 Introduction 313 13.2 Software development 314 13.3 Verification and demonstration 13.4 Integration and coupling 330 References 332

319

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14. Mechanism-based codes for severe accident analysis

17. Engineering-level system code for severe accident analysis: MELCOR

Luteng Zhang

Tangtao Feng, Jun Wang, Xin Li, Ryan Dailey and George Vayssier

14.1 COPRA code 333 14.2 IVRASA code 345 14.3 Thermal EXplosion Analysis Simulation code 349 14.4 MOCO code 352 14.5 DETAC code 356 References 359

V Severe accident codes 15. Severe accident analysis with AC2 Andreas Wielenberg, Sara Beck, Thorsten Hollands, Liviusz Lovasz, Holger Nowack, Claus Spengler, Martin Sonnenkalb and Andreas Schaffrath

15.1 The severe accident code ATHLET-CD for invessel phenomena 363 15.2 Severe accident analysis for containment phenomena with Containment Code System 378 15.3 Quality assurance measures 389 15.4 Outlook and summary 390 Nomenclature 391 References 392

16. Integral severe accident codes: IMPACT/SAMPSON Marco Pellegrini

16.1 16.2 16.3 16.4

Introduction 397 SAMPSON main modules 398 3D containment modules 405 Application of the SAMPSON code to the Fukushima Daiichi nuclear power plant accident 410 16.5 Advantages and disadvantages in the use of SAMPSON 414 References 414

17.1 17.2 17.3 17.4 17.5

Introduction 417 Quality control 420 Capabilities and limitations 427 MELCOR version update history 429 Demonstration problems: Experiments for validation 430 Reference 434

VI Noval CFD methods 18. Moving Particle Semi-implicit method Zidi Wang, Guangtao Duan, Seiichi Koshizuka and Akifumi Yamaji

18.1 Introduction 439 18.2 Moving Particle Semi-implicit method 440 18.3 Application to nuclear engineering 446 18.4 Conclusion 458 Reference 458

19. Lattice Boltzmann method code Shimpei Saito and Hui Cheng

19.1 Introduction 463 19.2 Lattice Boltzmann multiphase models 464 19.3 Summary 476 References 476

VII Special or new direction 20. Code for nuclear materials Jianqi Xi

20.1 Electronic structure calculations in nuclear materials 483 20.2 Molecular dynamics simulations in nuclear materials 486

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20.3 Mesoscale modeling in nuclear materials field 489 References 492

21. Nuclear power plant cybersecurity Fan Zhang

21.1 Introduction 495 21.2 Cybersecurity differences of instrumentation and control system and information technology system 496 21.3 Cyber-incidents in the history of the nuclear industry 497 21.4 Regulations 499 21.5 Cyberattack detection research using machine-learning algorithms 503 21.6 Conclusion 510 Acknowledgment 511 References 511

22. Artificial neural network introductions Jing Zhang and Guanghui Su

22.1 What is artificial neural network 515 22.2 Theory of artificial neural network 516 22.3 Artificial neural network applications in T/H problem 522 References 537

23. New direction of nuclear code development: artificial intelligence Lianshan Lin and Xing Wang

23.1 Introduction 543 23.2 A brief history of artificial intelligence 544 23.3 Artificial intelligence research in nuclear power industry in the 1980s 547 23.4 Recent application of artificial intelligence in nuclear power plant code 548 References 550

24. Temporal data mining in nuclear site monitoring and in situ decommissioning Z.J. Sun and A. Duncan

24.1 Introduction 553 24.2 Theoretical: Frequent episode and discovery algorithms 554 24.3 Computational: Application of TDMiner 558 24.4 Experimental: In situ decommissioning Sensor Network Test Bed and data collection 571 24.5 Data analysis and discussions 574 24.6 Conclusion and future work 580 References 580

Index 583

List of contributors M. Adorni

Miao Gui School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi, P.R. China Anil Gurgen Department of Nuclear Engineering, North Carolina State University, Raleigh, NC, United States T. Helfer CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

Senior Scientist, Brussels, Belgium

Christine Bals Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany Sara Beck Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany S.

Bernaud CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

Thorsten Hollands Gesellschaft fu¨r Anlagenund Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany C. Introini CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

A. Boulore CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France N.

Chauvin CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

Seiichi Koshizuka Department of Systems Innovation, The University of Tokyo, Tokyo, Japan

Hui Cheng Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, P.R. China

Lainet CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France Xin Li Faculty of Science and Engineering, Waseda University, Shinjuku City, Tokyo, Japan M.

Ryan Dailey Department of Engineering Physics, University of Wisconsin Madison, Madison, WI, United States A.

Del Nevo ENEA, FSN-ING-SIS, Brasimone, Camugnano, Italy

CR-

University,

Lianshan Lin Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, United States

Guangtao Duan Department of Systems Innovation, The University of Tokyo, Tokyo, Japan

Liviusz Lovasz Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany

J.C. Dumas CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

L. Luzzi Politecnico di Milano, Department of Energy, Nuclear Engineering Division, Milan, Italy

A. Duncan Material Sciences and Technology, Savannah River National Laboratory, Aiken, SC, United States

A. Magni Politecnico di Milano, Department of Energy, Nuclear Engineering Division, Milan, Italy

Tangtao Feng Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States

V.

Xiaomeng Dong Shenzhen Guangdong Province, China

ix

Marelle CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

x

List of contributors

R.

Masson CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

Martin Sonnenkalb Gesellschaft fu¨r Anlagenund Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany

B.

Michel CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

Claus Spengler Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany

Kaya G. Mondry Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States Xiamen

Guanghui Su Shaanxi Key Lab of Advanced Nuclear Energy and Technology, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, P.R. China

L. Noirot CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

Lin Sun Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States

Holger Nowack Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany

Z.J. Sun Department of Health Physics and Diagnostic Science, University of Nevada Las Vegas, Las Vegas, NV, United States

Marco Pellegrini Department of Nuclear Engineering and Management, The University of Tokyo, Tokyo, Japan

P. Van Uffelen European Commission, Joint Research Centre, Directorate for Nuclear Safety and Security, Karlsruhe, Germany

Alejandro Perez Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States

George Vayssier Eindhoven University Technology, Eindhoven, Netherlands

Xinghe Ni College of Energy, University, Xiamen, P. R. China

Bowen Qiu Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States I.

Ramie`re CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

D. Rozzia Belgian Nuclear Research Centre (SCK.CEN), Mol, Belgium Shimpei Saito Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan Andreas Schaffrath Gesellschaft fu¨r Anlagenund Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany A.

J.

Schubert European Commission, Joint Research Centre, Directorate for Nuclear Safety and Security, Karlsruhe, Germany Sercombe CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

of

I. Viallard CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France Jun Wang Department of Engineering Physics, University of Wisconsin Madison, Madison, WI, United States Xing Wang Department of Nuclear Engineering, Pennsylvania State University, State College, PA, United States Zidi Wang Nuclear Safety Research Center, Japan Atomic Energy Agency, Ibaraki, Japan Andreas Wielenberg Gesellschaft fu¨r Anlagenund Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany Jianqi Xi Department of Materials Science and Engineering, University of WisconsinMadison, Madison, WI, United States Akifumi Yamaji Cooperative Major in Nuclear Energy, Waseda University, Tokyo, Japan Jiankai Yu Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA United States

List of contributors

xi

Fan Zhang Department of Nuclear Engineering, The University of Tennessee, Knoxville, TN, United States

Xingang Zhao Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States

Jing Zhang Shaanxi Key Lab of Advanced Nuclear Energy and Technology, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, P.R. China

Xianping Zhong Department of Engineering Physics, Tsinghua University, Beijing, China

Luteng Zhang Chongqing University, Chongqing, China; Xi’an Jiaotong University, Shaanxi, China Tengfei Zhang School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China

Yukun Zhou Xi’an Jiaotong University, Xi’an, P.R. China; Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States

C H A P T E R

1 Road map Lin Sun1, Xiaomeng Dong2, Xin Li3, Jun Wang1 and Kaya G. Mondry1 1

Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States 2Shenzhen University, Guangdong Province, China 3Faculty of Science and Engineering, Waseda University, Shinjuku City, Tokyo, Japan

1.1 Overview Nuclear reactors and power plants are such complicated and heterogeneous systems that they require complex physical and mathematical models to give a precise and clear description of their operation and accident characteristics. Till now, the development of nuclear thermalhydraulic analyses has evolved from initial coarse one-dimensional (1D) system codes such as RELAP5 [1], RETRAIN [2], CATHARE [3], and MARS [4] to finer revised component-scale codes COBRA [5], RELAP5-3D, VIPRE [6,7], and local-scale codes Fluent [8], CFX [9], and Star-CCM [10]. There is no doubt that the above codes are still in state of the art; they have been widely used in the nuclear industry for operation simulation, safety analyses, and even severe accident phenomena analyses. However, the above codes have their rooftops. System codes are 1D, which can save calculation cost and are suitable for transient accident simulation, but they cannot give an accurate description of local features [such as pressurized thermal shock, three-dimensional (3D) coolant mixing in reactor pressure vessel lower plenum, boron dilution and distribution in reactor pressure vessel]. While the local-scale computational fluid dynamics (CFD) codes could provide detailed 3D features, but they are too time-consuming to simulate large-scale problems and not suitable for transient system analysis. Besides, the component-scale investigations such as subchannel codes COBRA and 1D 2D (two-dimensional) combined RELAP5-3D [11] are somehow compromised solutions between the above two classes of codes. Not only does thermal-hydraulics code come across these problems, so does neutron kinetics solution code. The calculation costs surge dramatically as the precision grows from fuel assemblies (FAs) to pin-by-pin. To conquer these problems, researchers have developed a compromised solution between costs and accuracy, the coupled codes, which are mainly made up of multiphysics and multiscale coupled codes [12 14]. However, the coupled codes are not an easy way to success but face tons of challenges [15,16].

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00001-2

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Copyright © 2021 Elsevier Ltd. All rights reserved.

4

1. Road map

Meanwhile, the computational reactor physics has also made a huge progression from nodal expansion methods [17] solving simplified few-group neutron diffusion equation to the deterministic method of characteristics [18,19] and stochastic Monte Carlo method [20] that are widely utilized in neutron transportation calculation. All the above thermal-hydraulics and neutron kinetics progression provide the groundwork for further coupling T-H and N-K analyses. The reason why we need coupled analyses is that the stand-alone T-H or N-K codes cannot give a precise description of the strong coupling phenomena. For instance, among some transient operation conditions such as reactivity insertion [control rods (CRs) insertion or withdraw] and accident conditions such as main steam line break (MSLB), the major phenomena will cause coupled T-H and N-K features and feedbacks; meanwhile, the key operating parameters of the reactor core will present nonuniform 3D features. The most famous coupled codes platforms deserve to the Consortium for the Advanced Simulation of Light Water Reactors (CASL) [21] and European Reference Simulation Platform for Nuclear Reactors (NURESIM) [22]. The CASL project aims at providing leading-edge modeling and simulation capabilities to improve the performance of currently operating light-water reactor (LWR) [23], and it has developed and tested Virtual Environment for Reactor Applications [24], which can simulate the operation of an entire reactor down to the characteristics of a single fuel rod, significantly exceeding the resolution of industry tools. On the European side the NURESIM platform incorporates the latest progress in core physics, two-phase thermal hydraulics, and fuel modeling, which includes multiscale and multiphysics features, especially for coupling core physics and thermal-hydraulics models for reactor safety. For our group’s work, we mainly concern about the RELAP5-coupled neutron kinetics codes currently and RELAP5-coupled CFD codes in the future work. The RELAP5/N-K-coupled codes could trace back to the last century. Jackson et al. developed a dimensionally adaptive, automatic switching algorithm for RELAP5/PANBOX [25] coupled code to switch between 3D, 1D, and point N-K models during a transient calculation. In the following years a series of studies focus on coupled RELAP5 and PARCS codes [26] had been carried out. Anis Bousbia-Salah applied the codes for the Peach Bottom Turbine Trip 2 Experiment [27]. Tomasz Kozlowski verified the codes by the OECS MSLB coupled code benchmark [28]. The coupled codes were also used for the VVER-1000 coolant trip benchmark [29] and transient benchmark [30] validation, the results of which were in a reasonable agreement with experimental data and code-to-code comparison. Other RELAP5-coupled N-K codes such as SIMTRAN [31] and DYN3D [32] have also been presented, which successfully validated MSLB Nuclear Energy Agency benchmark and V1000CT-1 benchmark, respectively. In most recent studies the coupled RELAP5 and N-K codes have improved the calculation precision and efficiency, they have also been extended into wider applications. Costa et al. [33] coupled RELAP5 and PARCS, and simulations of out-of-phase instabilities in a BWR obtained by assuming a hypothetical continuous CR bank withdrawal are being presented. Del Novo and Martelli [34] coupled RELAP5-3D and 3D neutron kinetic analysis code against the test shutdown heat removal tests (SHRT-17), which aims at improving simulation capabilities in the fast reactor. In Wu and Kozlowski’s study [35], Monte Carlo reactor physics code Serpent coupled with RELAP5 has been developed, which

I. Map of code development

1.2 Fuel codes

5

demonstrated power features of UO2 and MOX assembly benchmark. Remarkably, an innovative convergence criterion based on statistical uncertainty has been investigated to achieve the desired precision. Furthermore, Garcia-Fenoll et al. [36] have developed code RELAP5/PARCS, TRACE/PARCS coupled code. A CR drop real plant transient with access to the experimental data was used to validate the codes, and the error is acceptable. Above all, through the literature, there exist several key problems in coupled code development. To be specific, ways of coupling (internal or external coupling), spatial mesh mapping, time-step algorithms, coupling numeric (explicit, semiimplicit) are required to be handled properly to guarantee the accuracy and calculation efficiency. Ever since then, a number of researchers have devoted themselves to coupling codes development and application, especially coupled CFD with N-K codes. Jewer et al. [37] developed an immersed body method to model a typical pressurized-water reactor (PWR) FA using coupled FETCH neutron transport code and CFD FETCH code, the coupling between them was through nuclear cross section dependence. Vyskocil and Macek [38] developed the coupling interface between CFD code Fluent and system code Athlete internally coupled with neutron kinetics code DYN3D, simulating the complex transients such as opening a steam dump to the atmosphere of VVER-1000. Chen et al. [39] coupled CFD code with the N-K model and the pin thermal model, applied to describe unprotected transient overpower accident of a liquid metal cooled fast reactor. Ge et al. [40] developed the Temporal and Spatial Neutronics Analysis Module in CFD code Fluent based on user-defined functions (UDFs), the feasibility and accuracy have been demonstrated by 2D-IAEA, 2D-TWIGL, and 2D-LRA benchmark problems. Grahn et al. implemented a coupling between 3D neutron kinetic core model DYN3D [41] and the CFD software ANSYS CFX [42] and Trio_U [43], the test cases covered mini and full core geometries, CR movement, and partial overcooling transients, even including MSLB of PWR. Vasconcelos et al. [44] developed the fine mesh coupled N-K/T-H framework mainly using open-source CFD software OpenFOAM and reactor core analysis code milonga, the concept was applied to model the behavior of a TRIGA-IPR-R1 reactor fuel pin in steady-state mode. Most of the mentioned work concentrated localscale T-H phenomena by utilizing the CFD codes. On the other side, to analyze transient reactor physics feedback characteristics, neutronic codes solving diffusion equations have been adopted due to the calculation cost. The presented coupled codes were normally verified and validated by the existing benchmark problems, typically involving rod-type fuel element, square FA, and loop-type PWR. However, there lacks related research on different types of reactors, FAs, and fuel elements.

1.2 Fuel codes The US Nuclear Regulatory Commission (NRC) conducted an objective of the reactor safety research program that is the ability to accurately calculate the performance of LWR fuel during both long-term steady state and various operational transients and hypothetical accidents, and also the NRC has sponsored an extensive program of analytical computer code development to achieve this objective, both in-pile and out-pile experiments to generate the data necessary for development and verification of the computer codes.

I. Map of code development

6

1. Road map

1.2.1 FRAPCON/FRAPTRAN The fuel performance analysis code, FRAPCON, has been developed for the US NRC by Pacific Northwest National Laboratory for calculating steady state, which means that power and boundary condition changes are sufficiently slow, fuel behavior at high burnup (up to burnup of 62 GWd/MTU). The corresponding transient fuel performance analysis code, FRAPTRAN, is an analytical tool that calculates LWR fuel rod behavior when power or coolant boundary conditions, or both, are rapidly changing. FRAPTRAN can simulate the transient behavior of a single rod independently, but the input parameters such as the initial cladding outer diameter and cladding irradiation swelling should be manually entered by users.

1.2.2 TRANSURANUS TRANSURANUS, written in Fortran95 language, is a computer code for the thermal and mechanical analysis of fuel rods irradiated in nuclear reactors [45]. The TRANSURANUS code consists of a clearly defined mechanical mathematical framework in which physical models can easily be incorporated, which enables it so able to deal with a wide range of different irradiation situations, for example, normal, off-normal, and accidental conditions [design-basis accidents (DBAs) such as reactivity-initiated accident or loss of coolant accident]. The timescale of the problems to be treated may range from milliseconds to years, and the spatial scale is also within a very wide range since physical phenomena occurring at the mesoscale of the fuel grain (such as the fission gas behavior) are brought into play at the engineering scale of the integral fuel pin.

1.2.3 GERMINAL The GERMINAL code [46] is dedicated to sodium fast reactor (SFR) fuel pin behavior under normal and abnormal operating conditions. The GERMINAL’s computational scheme is based on the generic algorithm of the PLEIADES platform with a local-scale model based on the 1D axisymmetric geometrical assumption. The SFR multiphysics couplings are based on specific models of fuel behavior under high fast neutron flux and high-temperature conditions. Among these physical aspects, fuel restructuring, fuel pellet fragments relocation, and oxide-cladding joint formation are included. Advanced modeling is under development for thermochemical aspects with a CALPHAD-type thermodynamic computation coupled with the multiphysics algorithm and for the pellet to cladding gap closure coupled with fuel restructuring and central hole formation.

1.3 System code System codes are mostly based on 1D models of lumped parameters. They are mainly used to simulate the thermal-hydraulic characteristics of nuclear systems. The coarse node modeling method is adopted for the computational node, and the number of nodes is typically required to be controlled between 10 and 1000. The system model is homogenized, and the basic momentum, energy, and mass conservation equations are used to obtain the

I. Map of code development

1.3 System code

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common characteristics of each thermal-hydraulic node parameter. Detailed calculations for fuel element channels, such as CR characteristics and density variations of individual subchannels, cannot be obtained using this model. The smallest control volume is also the whole or a part of the core. System analysis codes are normally used for transient and safety analysis of LWRs. The most widely used system codes include ATHLET, RELAP5, RELAP5-3D, CATHARE, and TRAC.

1.3.1 ATHLET ATHLET is developed by GRS and could predict and analyze various transient accident processes in nuclear power plants, such as small or medium breaks and large loss of coolant accidents. ATHLET has been coupled with the 3D neutron kinetic model DYN3D to calculate the boiling-water reactor (BWR) turbine reference. ATHLET’s program structure is highly modular, allowing a single implementation of different physical modules. The code consists of several basic modules that calculate the different phenomena involved in the operation of the nuclear power plant, including thermal hydraulics, heat transfer, neutron kinetics, basic control simulation model, and numerical integration method. The remaining independent models (such as process models that are self-adjusted over time) can be coupled to the ATHLET via a general interface without changing their code structure. ATHLET can choose different models to simulate coolant flow behavior. The current basic model is the five-equation model.

1.3.2 RELAP5 RELAP5s was developed by the Idaho National Laboratory (INL) and sponsored by the US Department of Energy (DOE), the US NRC, the Program Application and Program, and the International RELAP5 User Group. This is a widely used thermalhydraulic system code for analyzing various transient conditions in the LWR. This calculation procedure is based on the solution of six partial differential equations that are calculated using the semiimplicit finite difference method. Code modeling coupled the reactor coolant system and loss of coolant and operational transients such as anticipated transients without scram, loss of off-site power, loss of feedwater, and loss of flow. Use a general modeling approach to simulate multiple thermal-hydraulic systems. Control systems and equipment in the two-loop system can also be modeled, such as reactor control, steam turbines, condensers, and feedwater systems.

1.3.3 RELAP5-3D The latest version of the RELAP5-3D is a highly versatile program that can include steam, liquid, noncondensable gases, and nonvolatile solutes in the calculation of thermalhydraulic transients. The RELAP5-3D program applies a separate phase and unbalanced models in a two-phase flow system and uses a fast, semiimplicit numerical algorithm to save time in transient calculations. The mathematical model of the system uses a very efficient code structure. The RELAP-3D can use a 3D thermal-hydraulics general model or a

I. Map of code development

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1. Road map

porous media model in selected areas of the Nuclear Power Plant (NPP). Besides, this version incorporates the NESTLE-3D neutron kinetic model.

1.3.4 CATHARE CATHARE is a system analysis program developed directly for PWR. CATHARE is similar to RELAP5, uses different numerical solution methods, and requires the user to create an input card for different structures. Besides, the code can simulate the containment. CATHARE is modular; the primary and secondary systems of any PWR can be modeled by assembling several different modules. 0D, 1D, 3D modules can be used. All modules can be connected to walls, heat exchangers, and fuel rods. A 2D heat transfer is used to calculate core behavior during reflooding. The remaining submodules are used to calculate neutron flux, pump speed, heat exchangers, etc. All models use a two-fluid model to calculate a gas liquid two-phase flow in which four kinds of noncondensable gases could be mixed. The thermal and mechanical energy imbalances of each phase are described by mass, energy, and momentum equations.

1.3.5 TRAC TRAC-PF1, the original TRAC, is a thermal-hydraulics software developed by Los Alamos National Laboratory (LANL) in the mid-1970s, mainly used for the analysis of PWR. The software uses six equations, two-fluid models, and various reactor transients can be accurately modeled, so TRAC-PF1 is considered one of the most advanced software available today. The program can handle noncondensable gases in the steam field and can also process insoluble materials in the liquid. The TRAC-PF1 has 3D thermal-hydraulic analysis capabilities and is the best estimated system code for transient analysis procedures. The TRAC-PF1/MOD2 version of the code uses six equations, two-fluid models, finite difference equations combined with 3D fluid dynamics, and 1D balanced device modeling to solve general problems in 1D, 2D, and 3D computational capabilities and two-phase coolant transient conditions. Both the rod and the plate fuel types contain a 2D fluid heat transfer treatment. The rod portion provides for power generation and heat transfer to the coolant. The six equations that represent the two-phase flow condition, combined with the primary and secondary system components and the control system, enable TRAC-PF1/MOD2 version 5.4 to accurately simulate severe and normal transients. TRAC-BF1 is the system code for thermal-hydraulic optimization of BWRs. The twofluid model can be solved for 1D or 3D systems, and the program is modularized.

1.3.6 MELCOR MELCOR is a fully modular, engineering-level reactor simulation program that calculates the progression of serious accidents in LWRs [47]. It was initiated by the US NRC and developed by Sandia National Laboratories for risk assessment for second-generation nuclear power plants. A broad spectrum of severe accident phenomena in both BWR and PWR, respectively, can be handled in MELCOR within a unified framework [48]. This

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consists of the thermal-hydraulic response of the reactor’s primary coolant system, the reactor cavity, the containment, and the confinement buildings. In addition, accident scenarios are fully simulated, including loss of coolant (core uncovering), core heat-up, fuel degradation, and core material melting and relocation. Later portions of accident simulation are possible as well, including core concrete attack and hydrogen production, transport, and combustion, as well as fission product release and transport behavior. MELCOR can also be applied to analyze beyond DBA that contains the estimation of severe accident source terms and their sensitivities, and uncertainty analysis [49].

1.3.7 Modular Accident Analysis Program The Modular Accident Analysis Program (MAAP) is a computer code that simulates the response of LWR power plants during severe accidents. Given a set of initiating events and operator actions, MAAP can predict the plant’s response as the accident progresses. The code is used to predict the timing of key events (e.g., core recovery, core damage, core relocation to the lower plenum, vessel failure); evaluate the influence of safety systems, including the impact of the timing of their operation; evaluate the impact of operator actions; predict the magnitude and timing of fission product releases; and investigate uncertainties in severe accident phenomena. MAAP results are primarily applied to determine probabilistic risk assessment (PRA) Level 1 and 2 success criteria, and accident timing to support human reliability analyses. They are also used for equipment qualification applications, the determination of fission product large early release frequencies, integrated leak rate test evaluations, emergency planning and training, simulator verification, analyses to support plant modifications, generic plant issue assessments (e.g., significance determination), and other similar applications.

1.3.8 System Analysis Module Under the Nuclear Energy Advanced Modeling and Simulation program of the US government, the System Analysis Module (SAM) is developed by Argonne National Laboratory to execute system-level modeling and simulation for the next-generation advanced reactors, for example, SFR, lead-cooled fast reactor, fluoride salt cooled high-temperature reactor, and molten salt reactor [50 53]. To achieve the capabilities of fast running, high fidelity, and whole plant transient analyses, SAM employs the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework and the Portable, Extensible Toolkit for Scientific Computation solvers to satisfy the requirement of linear and nonlinear calculations. Dozens of new thoughts and numerical methods have been adopted in SAM code. Object-oriented C11, finite element method (FEM), and linear/nonlinear solvers are utilized to fulfill the code requirement. High-order spatial discretization schemes, fully implicit and high-order time integration schemes, and advanced solution methods, that is, the Jacobian-free Newton Krylov (JFNK) method, are incorporated to develop accurate and computationally efficient models in this code. In addition, the flexible interface and coupling SAM with other tools provide more potential for users to solve multiscale and multiphysics problems.

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1.4 Subchannel analysis code The subchannel model divides the cross section of the core FA, and the coolant flows path from the inside to the outside into subchannels and establishes the mass, momentum, and energy conservation equations of the subchannel transient process analysis, considering the adjacent subchannels. The mixture of coolant mass and momentum is connected in parallel to each subchannel and is gradually pushed from the inlet to the outlet along the axial direction of the core, thereby obtaining the mass flow rate and enthalpy of the coolant at different heights of each subchannel, and then calculating the temperatures at different heights on the fuel element. For subchannel analysis the FA needs to be divided into several parallel subchannels that are connected. When subchannels are separated, the distribution of core power is mainly considered, and a plurality of adjacent fuel rods with similar power distribution in one FA can be considered as a subchannel. For subchannel analysis in the entire reactor core, adjacent FAs with similar power distributions are usually divided into one channel, and the number of divided subchannels is determined according to the precision of calculation analysis. A method of radially concentric annular division, the concentric annular division method, defines an annular space in which an FA with similar circumferential powers is defined as a circular subchannel, whereby each subchannel in the middle has only two subchannels adjacent to the inner and outer sides. The solution process is relatively simple, and the calculation speed is faster. It is worth mentioning that when the subchannel analysis method is applied to the entire core analysis, it is assumed that there is a uniform condition through a set of unclear subchannels due to the existence of the lateral flow. Besides, in the full core calculation, the formation of a large number of void fractions in the higher power zone causes a large pressure drop, causing the flow in these zones to drop, with significant flow redistribution along the length of the assembly. Therefore necessary corrections to the inlet flow distribution are required in the calculation. Generally, the inlet pressure distribution is known. After setting the initial inlet flow distribution, the inlet flow is corrected according to the calculated outlet pressure distribution to meet the conditions of uniform outlet pressure.

1.4.1 COBRA The COBRA code was developed by the Pacific Northwest Laboratory. The first version of COBRA-I was released in 1967 and the revised versions have been updated ever since, such as COBRA-II and COBRA-III. The COBRA-IIIC, published in 1973, uses an advanced lateral momentum equation. Later versions will not only be able to calculate the flow distribution between the BWR but also in the lateral cross-mixing model, the Beus two-phase turbulent flow mixing model, and the Weisman lateral momentum model are added. Besides, the fuel rod model, such as MATPRO, is added. The air gap thermal resistance between the cladding and the gas mixture in the fuel gap can be considered. The COBRA code is used for thermal-hydraulic analysis with lateral flow between adjacent subchannels for single-phase and homogeneous flow calculations. The PWR core is divided into one or several channels per component for the departure from nuclear boiling ratio analysis of the LWR.

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1.4.2 HAMBO The HAMBO code was introduced in 1978 by the New England Power Systems Northeast Equipment Company. It belonged to the MIT Energy Laboratory Power Program for subchannel procedures for steady state and transient thermal-hydraulic analysis of BWR FAs. The HAMBO code uses the same subchannel definition as COBRA-II and can consider single- and two-phase flow, and it can include thermal mixing between subchannels due to turbulent mixing and steering lateral flow as well as turbulent mixing and lateral momentum exchange caused by flow. Besides, the HAMBO code also includes the lateral resistance effect of the lateral flow, which can take into account the arbitrary arrangement of the fuel and the coolant path, the pressure loss caused by the positioning device, the radial, and axial heat flux distribution. The user can also input various empirical relationships.

1.4.3 FLICA The FLICA code is a 3D two-phase flow thermal-hydraulic subchannel analysis program for reactor core developed in France in 1967. The code uses a separate flow model to determine single- or two-phase flow in a separation channel. A uniform slip flow model is used within the range, and the gas calculation model used in the program calculates the fluid to a dry vapor state. This code can be used to process closed or interconnected subchannels. The code also includes neutron coupling effects and can take into account the coupling of one or more recirculation lines with associated branches.

1.4.4 THINC The THINC code is a hydraulic analysis code for the PWR developed by Westinghouse in the United States in the 1970s. In its first version, THINC-I uses the parallel pressure drop between FAs to calculate the flow mixing between adjacent FAs. In the following version, THINC-II calculates the cross-flow mixing of adjacent subchannels using equal axial pressure gradients for all subchannels. In the latest version, THINC-IV, the new technique is used to simplify the lateral momentum equation, which reduces the nonlinear coupling of the momentum equation, so that the lateral momentum equation can be solved jointly with the axial momentum equation and the continuity equation to obtain a uniform velocity field. The procedure for the generation of the void fraction is divided into three phases: (1) in the highly subcooled zone, use the Moller relationship; (2) in the low subcooled zone, use the modified Weisman relationship or use modified Pauling relationship; (3) when the liquid reaches the saturation temperature, consider all the additional heat for generating steam and calculate the pressure drop according to the assumption of the uniform flow.

1.4.5 MATRA The MATRA code is a subchannel analysis program developed by the Korea Atomic Energy Research Institute, and its basic framework is based on the COBRA code. The current MATRA program is primarily used for the analysis of PWRs and improvements to heavy metal liquid reactors and supercritical water reactors are underway.

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1.4.6 CTF CTF is a modernized and improved version of the legacy subchannel code, COBRA-TF, which is jointly developed and maintained by Oak Ridge National Laboratory (ORNL) and North Carolina State University. The development of CTF in CASL has been primarily focused on improving the predictive code capabilities for normal reactor operating conditions in both PWRs and BWRs. It solves discretized forms of two fluid, six equations for mass, momentum, and energy conservation for the liquid and vapor fields, mass and momentum equations for the droplet field, and an energy equation for solid structures, for a total of nine equations. CTF includes a wide range of thermal-hydraulics (T-H) models crucial to accurate LWR safety analysis, including, but not limited to, flow regime dependent two-phase heat transfer, interfacial drag, and heat transfer, droplet breakup, and quench-front tracking.

1.4.7 VIPRE VIPRE-01 was developed on the strengths of the COBRA series of codes by Battelle Pacific Northwest Laboratories for the Electric Power Research Institute (EPRI) to help evaluate LWR core T-H parameters and safety limits in normal and assumed accident conditions. Unlike CTF, VIPRE-01 calculates single- and two-phase flow velocity, pressure, and thermal energy fields and fuel rod temperatures by solving the finite difference equations for mass, energy, and momentum conservation for an interconnected array of channels assuming incompressible thermally expandable mixture flow. The conservation equations are solved with no time step or channel size restrictions for stability. Empirical models are included to account for vapor/liquid slip in two-phase flow.

1.5 Computational fluid dynamics code Due to the rapid improvement of computer performance and CPU computing power in recent years, microscale simulation calculations have become easier. The application of CFD procedures to provide detailed 3D information for the flow in nuclear power plants is a very advantageous tool in today’s engineering analysis. However, large-scale CFD calculations for systems require high computer processing power and high-performance computing hardware. Currently, the flow field analysis codes generally used include CFX, Fluent, TransAT, and Star-CD.

1.5.1 CFX CFX was developed by AEA Technology of the United Kingdom and currently has massive global users in the aerospace, energy, and petroleum industries. Unlike most CFD software, CFX uses an FEM in addition to the finite volume method. The FEM guarantees the numerical accuracy of the conservation characteristics of the finite volume method. In the application of the turbulence model, in addition to the commonly used turbulence

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model, CFX first used advanced turbulence models such as large eddy model (LES) and detached eddy simulation (DES). CFX is the first commercial software to develop and use fully implicit multigrid coupling solution technology. This solution technique avoids the need for the traditional algorithm to repeat the iterative process. Momentum equations and continuity equations, combined with its multigrid technology, CFX’s computational speed, and stability are better than traditional methods. Besides, CFX’s solver achieves excellent scalability in a parallel environment. CFX’s various physical models include compressible and incompressible flow, coupled heat transfer, heat radiation, and other issues. It also has practical models for the number of complex phenomena such as cavitation, solidification, porous media, phase-to-phase mass transfer, and dynamic and static interference. CFX provides users with different levels of user interface programs such as USER FORTRAN, allowing them to add their physical models. The preprocessing module of CFX is ICEM CFD that can realize the automatic handling of the boundary layer grid.

1.5.2 Fluent Fluent is currently the most popular commercial CFD software package in the world, and it can be used in industries related to fluids, heat conduction, and chemical reactions. It has a variety of physical models, advanced numerical algorithms, and powerful pre- and post-processing capabilities. And using multiple solving methods and multigrid acceleration convergence technology, Fluent can achieve the best convergence speed and solution accuracy. Flexible unstructured grids and solution-based adaptive grid techniques and proven physical models enable Fluent to turbulent flow, heat transfer and phase change, chemical reaction and combustion, multiphase flow, rotating machinery, material processing, fuel cells, etc. Fluent is suitable for a wide range of advanced physical models such as computational fluid flow and heat transfer models (including natural convection, steady and transient flow, laminar flow, turbulent flow, compressible and incompressible flow, periodic flow, rotation flow and time-dependent flow, etc.); phase transition model, discrete phase transition model, multiphase flow model, etc.; and with the significant improvement of computer capabilities, Fluent has incorporated large eddy simulation (LES) into its standard modules and developed more efficient detached eddy simulation (DES). For the flow characteristics of each physical problem, there is a numerical solution suitable for it. Users can choose the explicit or implicit differentiate method to achieve the best calculation speed, stability, and precision. Fluent also provides wall functions and enhanced wall treatments to handle flow problems near the wall.

1.5.3 TransAT ASCOMP’s software package TransAT can simulate most forms of multiphase flow. It is a multiphase thermal-hydraulic calculation tool developed specifically for high-density and high viscosity ratio liquid liquid multiphase flow [computational multiphase fluid

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dynamic (CMFD)]. TransAT simulates lubrication processes, phase separation, capillary and Marangoni flow processes, and ultrathin film flow. The IST/BMR technology of TransAT can reduce the shortcomings of traditional grids, eliminating the traditional judgment of aspect ratio, cell extension, and distortion in traditional grid technology. TransAT can simulate large-, medium-, and small-scale problems, including 2D and 3D, two-phase flow characteristics of thermal hydraulics. The phase transition process and the conjugate heat transfer phenomenon were studied using the interface tracking method (VOF and level set method).

1.5.4 STAR-CD STAR-CD is a general fluid analysis software developed by the Imperial College of the United Kingdom and the CD-adapco Group, which was established in the United Kingdom in 1987. Based on the finite volume method, STAR-CD is suitable for incompressible and compressible calculations, thermodynamic calculations, and non-Newtonian calculations. It has three modules: preprocessing, solver, and postprocessor. It combines modeling, solving, and postprocessing with all physical models and algorithms in a software package with a friendly graphical user interface. STAR-CD’s preprocessor has strong CAD modeling capabilities, and it has a good interface with current popular CAD/CAE software for efficient data processing. With a variety of meshing techniques (such as the extrusion method, multiblock method) and local grid refine the technology, it has a self-adaptive function for the quality of the grid. STAR-CD has certain advantages in the ability to apply complex computing areas. It handles the problem of slip mesh and can be used for flow field calculations in multistage turbomachines.

1.6 Coupled multiscale thermal-hydraulics codes 1.6.1 Multiphysics Object-Oriented Simulation Environment The MOOSE developed at INL represents this alternative path for nuclear reactor simulation [54]. MOOSE, the program that was begun in 2008 at INL, is a parallel computational framework developed to solve all systems in a fully coupled manner [55]. In MOOSE the physical problems are generally solved as a system of fully coupled nonlinear partial differential equations (PDEs), and the JFNK method is implemented as a parallel nonlinear solver. MOOSE utilizes a modular approach, where the fully coupled multiphysics applications can be created following the same strict coding convention standard. Different from the traditional codes, these MOOSE-based physics software packages are often referred to as “applications” because they are not stand-alone codes but parts of the same “code” running at the MOOSE framework.

1.6.2 Consortium for the Advanced Simulation of Light Water Reactors To enhance the multiphysics modeling and simulation (M&S) capabilities for the commercial nuclear power generation and thus improve economic competitiveness and safety

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of the nuclear energy, the CASL was established as the first Energy Innovation Hub of the DOE of the United States in 2010 [56]. Integrated and advanced multiphysics coupling methods were developed to solve the multiphysics problems in nuclear systems, including radiation transport, thermal hydraulics, fuel performance, and corrosion chemistry. CASL project had been granted a 10-year lifetime, Phase 1 period from 2010 to 2015 and Phase 2 from 2015 to 2019. A unique consortium partnership has been built by CASL, which includes four DOE national laboratories [ORNL (lead consortium member), INL, LANL, and Sandia National Laboratory], three universities (Massachusetts Institute of Technology, University of Michigan, and North Carolina State University), and three industrial organizations (Electric Power Research Institute, Tennessee Valley Authority, and Westinghouse Electric Corporation).

1.6.3 Other coupled codes Although the CFD application described earlier can give a detailed local 3D distribution of key parameters, it is faced with the inability to simulate large-scale problems or transient analysis due to computational cost and time-consuming. To overcome these difficulties the researchers developed a compromise approach between computational accuracy and solution time—coupling methods that primarily combine different multiscale codes. For thermal-hydraulic calculations the 1D system analysis code is usually coupled with 3D CFD codes. Andersson et al. [57] used a system analysis code coupled with a CFD code to analyze the dissipation process of turbulence intensity in the reactor. Martelli et al. [58] coupled RELAP5/MOD3.3 with Fluent and simulated the normal operation and loss of flow of the NACIE (Natural Circulation Experiment) experimental loop, which is in good agreement with the experimental results and the separate simulation results. Jeong et al. [4] coupled the system code RELAP5 with the subchannel code COBRA-TF based on the modularization idea to form a brand new thermal-hydraulic analysis code MARS. The coupling code is solved by the semiimplicit method. The “dynamic memory allocation” method is adopted, which involves the exchange of information between the solving matrices of the subroutines, which is a strong coupling solution. Weaver et al. [59 62] carried out a series of coupling research work between RELAP5-3D and CFX, developed a general coupling program PVMEXEC, which enables RELAP5-3D coupled with other codes through parallel virtual machine (PVM) interface. The coupling calculation is performed using a semiimplicit method. Based on the above, Aumiller [61,62] developed coupled codes with RELAP-3D and CFDs-FLOW3D (predecessor of CFX) through the explicit method, simulating the Edwards pipeline blowdown experiment; the results had a good agreement with experiment results, RELAP5 calculation results, and CFD stand-alone calculation results. Anderson [63,64] coupled the very high-temperature reactor system model based on RELAP5-3D with the outlet chamber established by Fluent to perform detailed calculation and analysis of the flow field in the outlet chamber. Guelfi et al. [65] developed the NEPTUNE multiscale coupled simulation platform. The NURESIM [66] simulation platform for multiscale, multiphysics coupling calculations has been developed in Europe. Yan [67,68] compiled the RELAP5-3D code as a dynamic-link

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library (DLL) and programmed the main control code and the coupling interface through the Fluent UDF. The reactor core was modeled using a porous medium model and a point reactor kinetics model. The coupled code is applied to the simulation of the AP1000 nuclear steam supply system and the modular high-temperature gas-cooled reactor; the simulation results are beneficial to improve the reactor design based on conservative models. Li et al. [14] of Xi’an Jiaotong University conducted a preliminary study on the coupling of Fluent and RELAP5/MOD3.1, using Fluent’s UDF-coupled RELAP5 DLL, and using the Edwards pipeline blowdown experiment to verify the coupled code. Furthermore, a simplified analysis was performed, a cubic pressure vessel with two loops, one of which has a short-transient problem with a sudden change in coolant temperature. In summary, for the multiscale coupling method of system program and CFD code, the coupling interface of PVM or custom function programming is mainly used to realize the explicit or semiimplicit coupling calculation. However, the problems on computational stability, convergence, 1D and 3D code coupling boundary condition processing, and computational errors caused by different program physical models have yet to be solved to improve the calculation accuracy of the coupled code. Besides, nuclear reactor cores have strong neutronic/thermal-hydraulic coupling effects.

1.7 Emerging methods for NPPs Apart from the system codes and subchannel codes, there are still some emerging methods and codes for the thermal-hydraulic problems of NPPs. After 10 years’ development of new theory and concepts, they have been introduced into the nuclear power area and attracted much attention from the researchers. Despite the lack of validations, they have the potential methods to be very useful for the various kinds of problems in NPPs. These emerging methods include projection-based particle method (PPM), lattice Boltzmann method (LBM), NPP firewall system, artificial neural network (ANN), and temporal data mining (TDM).

1.7.1 Projection-based particle method The PPM [69,70], both including incompressible smoothed particle hydrodynamics (SPH) and moving particle semiimplicit, solves a pressure Poisson equation using HelmHoltz Leray decomposition and application of Chorin’s projection method [71]. Comparing with weakly compressible SPH (wcSPH), PPMs generally have higher accuracy for pressure and volume conservation [72]. Improving computational efficiency and performance of PPMs is extremely important for large-scale scientific and engineering simulations [73 75]. Due to the Lagrangian nature of the particle methods, such as SPH or incompressible SPH, the pattern of data access and computation are unknown until the application’s runtime. This often leads to poor temporal and spatial data accesses and insufficient usage of a memory hierarchy. As multilevel memory hierarchies are still going to be deployed in computing architectures for the foreseeable future, sorting algorithms are critical techniques to increase application data locality.

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Particle sorting is to rearrange an array of particles in the desired order. For particle methods the sorting implementation is to rearrange the particle basic data arrays, including particle index, coordinates, velocities, and pressure, so that the neighboring particles are close in their computer memory space. The sorting will not change any value of the particle physical data arrays, such as the particle coordinates contrast with particle regularization methods (e.g., shifting). It has already been shown that sorting particles can produce up to 20% performance improvement in wcSPH applications [76].

1.7.2 Lattice Boltzmann method In the 1980s the LBM has been developed to describe the characteristic length that is lower to micron and nanometer. The main point of LBM is the transform from the continuum model to the discrete model. Breaking the framework of the traditional method, LBM shows a new perspective that uses mesoscopic kinetic equations to describe the fluid flow. It has several advantages when compared with other macroscopic CFD methods based on the Navier Stokes equations. For instance, it is easy to incorporate mesoscale physics, such as interfacial breakup or coalescence and easy to program and parallelize. The applicability of boundary conditions is wider than the traditional methods, and no grid is required for the calculation. Moreover, the computational cost for simulating realistic fluid flows is reasonable when compared with microscopic particle based methods (e.g., molecular dynamics).

1.7.3 Cybersecurity system The number of industry-targeted cyberattacks is increasing, together with complexity. Understanding the start-of-the-art for cybersecurity in NPPs is essential for improving the cybersecurity of these facilities. The survey of the history of past cyber incidents reveals that current strategies may not be enough to keep up with both the progress made in digitalization as well as the increasing sophistication and growing attack surfaces that come from this progress. In addition, the conscientious cybersecurity expert must take into account not just the direct technical perspective but also those perspectives held by both government bodies and regulators. Other than applying the required or recommended measures by regulators, adopting new machine learning techniques are promising to enhance cybersecurity for industrial concerns. However, the lack of available data is a significant issue for both model development and evaluation. Machine learning models can only learn as much information as the data contain, and it is, therefore, hard to develop a good model when the data are not sufficient. Moreover, most research related to cyberattacks is not evaluated independently of the research itself and is usually taken in the context of the research being conducted, as there is not a single standard data set that researchers can utilize. So there is a need for a universal data set for cyberattacks on industrial systems; it would be beneficial if there were such a data set made universally available for model development and evaluation.

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1.7.4 Artificial intelligence and artificial neural network Along with the development of artificial intelligence, the ANN has been widely applied in the thermal-hydraulic problem of nuclear engineering, especially the heat transfer characteristics. ANN abstracts the neural network of the human brain on information processing, thus different networks form in according to different connection modes [77]. ANN works as an operational model, including numerous nodes (or neurons) connected. ANN is a nonlinear system that has higher fault tolerance and larger storage. Nonlimiting is another advantage for ANN, which can be applied to associative memory. Besides, instability gives the ANN the ability to autonomous learning. At last, the nonconvexity of ANN can deliver a few equilibrium states for the system. With given input parameters and the training process, ANN based on different neural networks has been used in the prediction of critical heat flux, heat transfer coefficient, the onset of nucleate boiling, characteristic points of the boiling curve, and so on. Results show good agreements with experimental data, which show that the ANN method is pretty suitable for the mechanism study of thermal-hydraulic problems.

1.7.5 Temporal data mining TDM [78] refers to the extraction of implicit, nontrivial, and potentially useful abstract information from large collections of temporal data. Temporal data are sequences of a primary data type, most commonly numerical or categorical values and sometimes multivariate or composite information. TDM is an active and rapidly evolving area in big data science. The concepts and algorithms of TDM have been applied to nuclear site monitoring and in situ decommissioning (ISD) research. Since all the data collected from the nucleardecommissioning sites are time-, age-, and development stage specific, they are ideal for TDM analysis to validate system performance and reveal unknown patterns of material failure, liquid leaking, and radiation field changing. An application of TDM method in ISD test bed by Savannah River National Laboratory shows TDM techniques, and corresponding codes are effective tools to validate ISD performance, and the frequent episodes found in the data stream not only showed the daily cycle of the sensor responses but also established the response sequences of different types of sensors, which was verified by the actual experimental setup. Some abnormal patterns may have the potential for prediction of system failures.

References [1] C. Allison, G. Berna, R. Chambers, et al., SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPRO—a library of materials properties for light-water-reactor accident analysis, DT Hagrman, NUREG/CR-6150, EGG2720, 1993, pp. 4 234. [2] J. Mcfadden, M. Paulsen, G. Gose, et al., RETRAN-02: a program for transient thermal-hydraulic analysis of complex fluid flow systems, EPRI NP-1850 CCM, 1981, pp. 1 4. [3] F. Barre, M. Bernard, The CATHARE code strategy and assessment, Nucl. Eng. Des. 124 (3) (1990) 257 284. [4] J.-J. Jeong, K. Ha, B. Chung, et al., Development of a multi-dimensional thermal-hydraulic system code, MARS 1.3.1, Ann. Nucl. Energ. 26 (18) (1999) 1611 1642. [5] C. Stewart, C. Wheeler, R. Cena, et al., COBRA-IV: The Model and the Method, Pacific Northwest Labs, 1977.

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[6] C. Stewart, J. Cuta, S. Montgomery, et al., VIPRE-01: A Thermal-Hydraulic Code for Reactor Cores, Electric Power Research Inst.; Pacific Northwest Lab, Palo Alto, CA; Richland, WA, 1989. [7] J.M. Kelly, C.W. Stewart, J.M. Cuta, VIPRE-02—a two-fluid thermal-hydraulics code for reactor core and vessel analysis: mathematical modeling and solution methods, Nucl. Technol. 100 (2) (1992) 246 259. [8] U. Rohde, T. Ho¨hne, S. Kliem, et al., Fluid mixing and flow distribution in a primary circuit of a nuclear pressurized water reactor—validation of CFD codes, Nucl. Eng. Des. 237 (15 17) (2007) 1639 1655. [9] T. Ho¨hne, E. Krepper, U. Rohde, Application of CFD codes in nuclear reactor safety analysis, Sci. Technol. Nucl. Install. 2010 (2010) 1 8. [10] J.N. Cardoni, Nuclear reactor multi-physics simulations with coupled MCNP5 and STAR-CCM 1 , 2011. [11] J. Wang, W.X. Tian, Y.H. Tian, et al., A sub-channel analysis code for advanced lead bismuth fast reactor, Prog. Nucl. Energ. 63 (2013) 34 48. [12] A. Bousbia-Salah, F. D’auria, Use of coupled code technique for best estimate safety analysis of nuclear power plants, Prog. Nucl. Energ. 49 (1) (2007) 1 13. [13] A.G. Mylonakis, M. Varvayanni, N. Catsaros, et al., Multi-physics and multi-scale methods used in nuclear reactor analysis, Ann. Nucl. Energ. 72 (2014) 104 119. [14] W. Li, X. Wu, D. Zhang, et al., Preliminary study of coupling CFD code FLUENT and system code RELAP5, Ann. Nucl. Energ. 73 (2014) 96 107. [15] K. Ivanov, M. Avramova, Challenges in coupled thermal-hydraulics and neutronics simulations for LWR safety analysis, Ann. Nucl. Energ. 34 (6) (2007) 501 513. [16] P.J. Turinsky, D.B. Kothe, Modeling and simulation challenges pursued by the Consortium for Advanced Simulation of Light Water Reactors (CASL), J. Comput. Phys. 313 (2016) 367 376. [17] P.J. Turinsky, R.M. Al-Chalabi, P. Engrand, et al., NESTLE: few-group neutron diffusion equation solver utilizing the nodal expansion method for eigenvalue, adjoint, fixed-source steady-state and transient problems, EG and G Idaho, 1994. [18] M. Eklund, M. Alamaniotis, H. Hernandez, et al., Method of characteristics a review with applications to science and nuclear engineering computation, Prog. Nucl. Energ. 85 (2015) 548 567. [19] J. Weisman, A. Tentner, Application of the method of characteristics to solution of nuclear engineering problems, Nucl. Sci. Eng. 78 (1) (1981) 1 29. [20] J.F. Briesmeister, MCNPTM—A General Monte Carlo N-Particle Transport Code. Version 4C, LA-13709-M, Los Alamos National Laboratory, 2000, p. 2. [21] DOE, Consortium for Advanced Simulation of LWRs—A Project Summary, 2011, p. 18. [22] C. Chauliac, J.-M. Aragone´s, D. Bestion, et al., NURESIM a European simulation platform for nuclear reactor safety: multi-scale and multi-physics calculations, sensitivity and uncertainty analysis, Nucl. Eng. Des. 241 (9) (2011) 3416 3426. [23] J. Gehin, CASL NRC Commissioner Technical Seminar, Oak Ridge National Laboratory, 2012, p. 41. [24] A.T. Godfrey, VERA Core Physics Benchmark Progression Problem Specifications, Oak Ridge National Laboratory, 2014. [25] C.J. Jackson, D.G. Cacuci, H.B. Finnemann, Dimensionally adaptive neutron kinetics for multidimensional reactor safety transients—I: new features of RELAP5/PANBOX, Nucl. Sci. Eng. 131 (2) (1999) 143 163. [26] H.G. Joo, D. Barber, G. Jiang, et al., PARCS: a multi-dimensional two-group reactor kinetics code based on the nonlinear analytic nodal method, PARCS Manual Version (1998) 2. [27] A. Bousbia-Salah, J. Vedovi, F. D’auria, et al., Analysis of the Peach Bottom Turbine Trip 2 Experiment by coupled RELAP5-PARCS three-dimensional codes, Nucl. Sci. Eng. 148 (2) (2004) 337 353. [28] T. Kozlowski, R.M. Miller, T.J. Downar, et al., Consistent comparison of the codes RELAP5/PARCS and TRAC-M/PARCS for the OECD MSLB coupled code benchmark, Nucl. Technol. 146 (1) (2004) 15 28. [29] A. Bousbia Salah, J. Vedovi, F. D’auria, et al., Analysis of the VVER1000 coolant trip benchmark using the coupled RELAP5/PARCS code, Prog. Nucl. Energ. 48 (8) (2006) 806 819. [30] S. Espinoza, V. Hugo, M. Bo¨ttcher, Investigations of the VVER-1000 coolant transient benchmark phase 1 with the coupled system code RELAP5/PARCS, Prog. Nucl. Energ. 48 (8) (2006) 865 879. [31] J.M. Aragone´s, C. Ahnert, O. Cabellos, et al., Methods and results for the MSLB NEA benchmark using SIMTRAN and RELAP-5, Nucl. Technol. 146 (1) (2004) 29 40. [32] S. Kliem, Y. Kozmenkov, T. Ho¨hne, et al., Analyses of the V1000CT-1 benchmark with the DYN3D/ATHLET and DYN3D/RELAP coupled code systems including a coolant mixing model validated against CFD calculations, Prog. Nucl. Energ. 48 (8) (2006) 830 848.

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[33] A.L. Costa, C. Pereira, W. Ambrosini, et al., Simulation of an hypothetical out-of-phase instability case in boiling water reactor by RELAP5/PARCS coupled codes, Ann. Nucl. Energ. 35 (5) (2008) 947 957. [34] A. Del Nevo, E. Martelli, Validation of a three-dimensional model of EBR-II and assessment of RELAP5-3D based on SHRT-17 test, Nucl. Technol. 193 (1) (2016) 1 14. [35] X. Wu, T. Kozlowski, Coupling of system thermal hydraulics and Monte-Carlo code: convergence criteria and quantification of correlation between statistical uncertainty and coupled error, Ann. Nucl. Energ. 75 (2015) 377 387. [36] M. Garcia-Fenoll, C. Mesado, T. Barrachina, et al., Validation of 3D neutronic-thermalhydraulic coupled codes RELAP5/PARCSv2.7 and TRACEv5.0P3/PARCSv3.0 against a PWR control rod drop transient, J. Nucl. Sci. Technol. 54 (8) (2017) 908 919. [37] S. Jewer, A.G. Buchan, C.C. Pain, et al., An immersed body method for coupled neutron transport and thermal hydraulic simulations of PWR assemblies, Ann. Nucl. Energ. 68 (2014) 124 135. [38] L. Vyskocil, J. Macek, Coupling CFD code with system code and neutron kinetic code, Nucl. Eng. Des. 279 (2014) 210 218. [39] Z. Chen, X.-N. Chen, A. Rineiski, et al., Coupling a CFD code with neutron kinetics and pin thermal models for nuclear reactor safety analyses, Ann. Nucl. Energ. 83 (2015) 41 49. [40] J. Ge, D. Zhang, W. Tian, et al., Steady and transient solutions of neutronics problems based on finite volume method (FVM) with a CFD code, Prog. Nucl. Energ. 85 (2015) 366 374. [41] U. Rohde, S. Kliem, U. Grundmann, et al., The reactor dynamics code DYN3D—models, validation and applications, Prog. Nucl. Energ. 89 (2016) 170 190. [42] A. Grahn, S. Kliem, U. Rohde, Coupling of the 3D neutron kinetic core model DYN3D with the CFD software ANSYS-CFX, Ann. Nucl. Energ. 84 (2015) 197 203. [43] A. Grahn, A. Gommlich, S. Kliem, et al., Simulation of an MSLB scenario using the 3D neutron kinetic core model DYN3D coupled with the CFD software Trio_U[J], Nucl. Eng. Des. 315 (2017) 117 127. [44] V. Vasconcelos, A. Santos, D. Campolina, et al., Coupled unstructured fine-mesh neutronics and thermalhydraulics methodology using open software: a proof-of-concept, Ann. Nucl. Energ. 115 (2018) 173 185. [45] K. Lassmann, A. Schubert, P. Van Uffelen, et al., Copyrightr 1975-2014 TRANSURANUS Handbook, Institute for Transuranium Elements, Karlsruhe, 2014. [46] M. Lainet, B. Michel, J.-C. Dumas, et al., GERMINAL, a fuel performance code of the PLEIADES platform to simulate the in-pile behaviour of mixed oxide fuel pins for sodium-cooled fast reactors, J. Nucl. Mater. 516 (2019) 30 53. [47] D.L. Luxat, D.A. Kalanich, J.T. Hanophy, et al., MAAP-MELCOR crosswalk phase 1 study, Nucl. Technol. 196 (3) (2016) 684 697. [48] T. Sevo´n, A MELCOR model of Fukushima Daiichi Unit 1 accident, Ann. Nucl. Energ. 85 (2015) 1 11. [49] L. Fernandez-Moguel, A. Rydl, T. Lind, Updated analysis of Fukushima Unit 3 with MELCOR 2.1. Part 2: fission product release and transport analysis, Ann. Nucl. Energ. 130 (2019) 93 106. [50] R. Hu, L. Zou, G. Hu, SAM User’s Guide, Argonne National Lab. (ANL), Argonne, IL, 2019. [51] R. Hu, SAM Theory Manual, Argonne National Lab. (ANL), Argonne, IL, 2017. [52] R. Hu, T. Fanning, T. Sumner, et al., Status Report on NEAMS System Analysis Module Development, Argonne National Lab. (ANL), Argonne, IL, 2015. [53] K. Bradley, NEAMS: The Nuclear Energy Advanced Modeling and Simulation Program, Argonne National Lab. (ANL), Argonne, IL, 2013. [54] D.R. Gaston, C.J. Permann, J.W. Peterson, et al., Physics-based multiscale coupling for full core nuclear reactor simulation, Ann. Nucl. Energ. 84 (2015) 45 54. [55] D. Gaston, C. Newman, G. Hansen, et al., MOOSE: a parallel computational framework for coupled systems of nonlinear equations, Nucl. Eng. Des. 239 (10) (2009) 1768 1778. [56] R. Szilard, H. Zhang, D. Kothe, et al., The Consortium for Advanced Simulation of Light Water Reactors, Idaho National Laboratory (INL), 2011. [57] R. Andersson, B. Andersson, F. Chopard, et al., Development of a multi-scale simulation method for design of novel multiphase reactors, Chem. Eng. Sci. 59 (22 23) (2004) 4911 4917. [58] D. Martelli, N. Forgione, G. Barone, et al., Coupled simulations of the NACIE facility using RELAP5 and ANSYS FLUENT codes, Ann. Nucl. Energ. 101 (2017) 408 418. [59] W.L. Weaver, The application programming interface for the PVMEXEC program and associated code coupling system, CiteSeerX, 2005.

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[60] W.L. Weaver, E.T. Tomlinson, D.L. Aumiller, A generic semi-implicit coupling methodology for use in RELAP5-3D (c), Nucl. Eng. Des. 211 (1) (2002) 13 26. [61] D.L. Aumiller, E.T. Tomlinson, W.L. Weaver, An integrated RELAP5-3D and multiphase CFD code system utilizing a semi-implicit coupling technique, Nucl. Eng. Des. 216 (1 3) (2002) 77 87. [62] D.L. Aumiller, E.T. Tomlinson, R.C. Bauer, A coupled RELAP5-3D/CFD methodology with a proof-ofprinciple calculation, Nucl. Eng. Des. 205 (1 2) (2001) 83 90. [63] N. Anderson, Y. Hassan, R. Schultz, Analysis of the hot gas flow in the outlet plenum of the very high temperature reactor using coupled RELAP5-3D system code and a CFD code, Nucl. Eng. Des. 238 (1) (2008) 274 279. [64] N.A. Anderson, Coupling RELAP5-3D and Fluent to Analyze a Very High Temperature Reactor (VHTR) Outlet Plenum, Texas A&M University, 2006. [65] A. Guelfi, D. Bestion, M. Boucker, et al., NEPTUNE: a new software platform for advanced nuclear thermal hydraulics, Nucl. Sci. Eng. 156 (3) (2007) 281 324. [66] D. Bestion, D. Lucas, H. Anglart, et al., Multi-scale thermalhydraulic analyses performed in Nuresim and Nurisp projects, in: 2012 20th International Conference on Nuclear Engineering and the ASME 2012 Power Conference, 2012, pp. 581 590. [67] Y. Yan, Development of a Coupled CFD—System-Code Capability (With a Modified Porous Media Model) and Its Applications to Simulate Current and Next Generation Reactors, University of Illinois at UrbanaChampaign, 2012. [68] Y. Yan, Coupled CFD—system-code simulation of a gas cooled reactor, Int. Conf. Math. Comput. Methods Appl. Nucl. Sci. Eng. (2011). [69] R. Fair, X. Guo, T. Cui, Particle sorting for the projection based particle method, Eng. Anal. Bound. Elem. 109 (2019) 199 208. [70] S. Koshizuka, Y. Oka, Moving-particle semi-implicit method for fragmentation of in-compressible fluid, Nucl. Sci. Eng. 123 (3) (1996) 421 434. [71] A.J. Chorin, Numerical solution of the Navier Stokes equations, J. Math. Comput. 22 (1968) 745 762. [72] H. Gotoh, A. Khayyer, H. Ikari, T. Arikawa, K. Shimosako, On enhancement of in-compressible SPH method for simulation of violent sloshing flows, Appl. Ocean Res. 46 (2014) 104 115. [73] H. Gotoh, A. Khayyer, On the state-of-the-art of particle methods for coastal and ocean engineering, Coast. Eng. J. 60 (1) (2018) 79 103. [74] S. Yeylaghi, B. Moa, P. Oshkai, B. Buckham, C. Crawford, ISPH modelling for hydro-dynamic applications using a new MPI-based parallel approach, J. Ocean Eng. Mar. Energ. 3 (1) (2017) 35 50. [75] A. Khayyer, H. Gotoh, Y. Shimizu, Comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in ISPH context, J. Comput. Phys. 332 (2017) 236 256. [76] J.M. Domnguez, A.J.C. Crespo, M. Gmez-Gesteira, J.C. Marongiu, Neighbour lists in smoothed particle hydrodynamics, Int. J. Numer. Methods Fluids 67 (12) (2011) 2026 2042. [77] Yao, A review of evolutionary artificial neural networks, Int. J. Intell. Syst. 8 (1993) 539 567. ¨ zsue, Encyclopedia of Database Systems, 2009. Springer. [78] L. Liu, M.T. O

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C H A P T E R

2 Guidance of nuclear power plant code development Xianping Zhong Department of Engineering Physics, Tsinghua University, Beijing, China

2.1 Nuclear power plant code Nuclear power plant is a highly complex-of-complex system and it requires a profound understanding of reactor systems not only the basic knowledge in mathematics, physics, and chemistry but also the professional knowledge in thermodynamics, heat transfer, fluids, electricity, instrument and control, materials, chemical engineering, mechanicals, nuclear physics, reactor theory, and radiation protection [1]. Scientific research on nuclear power plants is a highly challenging task. Experimental research, theory analysis, and numerical analysis are the main research methods for nuclear power plant system. Experimental research is the most reliable way of inquiring information/knowledge about physical processes. We can use full-scale equipment for experimental research to predict the operating characteristics of the same kind of equipment. But, in most cases, full-scale experiments of nuclear power systems require high capital expenditure. An alternate feasible method is to perform the similar experiments on reduced-scale equipment, and the results obtained from these experiments must be extrapolated to full-scale equipment. However, the general law for such extrapolation is often unavailable, and the reduced-scale equipment does not always reflect the physical phenomenon of full-scale equipment. In many cases, it is difficult to perform experimental measurements, and such measurements have a certain degree of errors that come from a variety of sources. In addition, many experiments related to nuclear power systems have not been performed due to safety concerns. Theory analysis usually refers to the process of abstracting physical problems into mathematical models (described by a set of equations) and solving them analytically. Reactor physics and thermal-hydraulic problems are usually described by a set of ordinary differential or partial differential equations. Thermal-hydraulic equations also contain a large number of empirical correlations. Mostly, a small portion of these differential

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00002-4

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2. Guidance of nuclear power plant code development

equations have analytical solutions. These analytical solutions often contain special functions with infinite series as well as transcendental functions. Therefore it is still a very difficult task to collect information from these analytical solutions. Numerical analysis refers to the process of using computer codes to simulate and analyze physical phenomena. It has the advantages of low cost and wide prediction range, which makes up for the lack of experimental research and theory analysis. Nowadays, with the development of numerical algorithms and rapid improvement of computer performance, numerical analysis has become another popular research method besides experimental research and theory analysis. Nuclear power plant code is the binary product created by converting the governing equations describing the physical phenomena of nuclear power plant into algebraic equations and using appropriate numerical algorithms to solve these algebraic equations.

2.1.1 Code classification Nuclear power plant code is useful for various aspects such as reactor type research, nuclear power plant design and approval as well as the formulation of nuclear power plant operation, regulations, and emergency planning. There are many kinds of nuclear power plant codes, which can be roughly classified into the following six types. 1. Nuclear power plant system analysis code This code has a neutron dynamics model with reactivity feedback. It can simulate primary and secondary coolant systems of nuclear power plants as well as components such as pressurizer, steam generators, pumps, valves, and fuel rods. It can analyze the system response of a nuclear power plant during loss-of-coolant accident and operating transient, which is the most important type of code for nuclear power plant accident analysis. Such codes include RETRAN series [2], RELAP series [3], and TRAC series codes [4,5]. 2. Reactor core analysis code This code is also called subchannel analysis code, which takes the results calculated by the system analysis code as boundary conditions. Considering the uneven heating of the fuel element in the core as well as the mass, momentum, and energy exchange between adjacent flow channels, it can calculate the flow field and enthalpy field of the open fuelassemblies reactor core, the core temperature, cladding surface temperature, and DNBR. Such codes include ASSERT [6], SUBCHAN [7], and COBRA series codes [8]. 3. Fuel element analysis code This code analyzes the shape of the fuel element facing damage under accident conditions, which also takes the results of system analysis code as boundary conditions. The code provides various heat transfer models such as the thermal radiation model, which can simulate the changes in the gap between the cladding and the pellet, the swelling, and rupture of the fuel element as well as blockage of the flow channel. Such codes include FRAP-T6 [9] and TOODEE2/MOD3 [10]. 4. Reactor physics analysis code This code is used for the analysis of reactor criticality, fuel consumption as well as reactivity accident. Coupling the three-dimensional neutron dynamics code and the

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three-dimensional thermal-hydraulic analysis code to perform high-precision reactor core analysis is very time-consuming. Therefore one-dimensional reactor physics code which has been verified by the three-dimensional code is usually adopted when largescale calculations are performed. Such codes include MPACT [11], RMC [12], and TRIPOLI [13]. 5. Containment thermal-hydraulic analysis code This code analyzes the thermal-hydraulic phenomena in the containment vessel when the pipelines of the primary or second circuit are ruptured and a large amount of coolant is sprayed into the containment vessel. Such codes include HYDRAGON [14], CONTEMPT-LT/028 [15], CONTAIN series [16], and PCCSAC/PCCSAP series codes [17,18]. 6. Radiological consequence analysis code This code describes the transport of radioactive materials within the reactor system, their release to the environment, and their dispersion in the atmosphere. It can also calculate the radiation dose exposed to the personnel. Such codes include CRAC [19] and COSYMA [20].

2.1.2 Code development process Code development is not a one-time event. The entire development process will be full of a large number of unit testing, verifications, validation, and version iterations. Depending on the complexity of the problem and the needs of the customer, the entire code development period can take up to a year or even decades. Code development process is briefly summarized in the following and illustrated schematically in Fig. 2.1: 1. Abstract physical process into physical models, which are generally expressed by ordinary differential equations or partial differential equations. There is a type of highly abstract models that can describe a wide range of physical problems. This type of model has a wide range of applications, such as computational fluid dynamics models expressed by Navier
Stokes equations [21] and reactor physics models expressed by three-dimensional neutron transport equations [22]. Another type of models based on the characteristics of the research object can only describe the research object itself, and its equations may contain a large number of empirical correlations related to the research object. This type of model has a narrow range of applications, such as nonequilibrium multiregion pressurizer models [23
25] and natural-circulation U-tube steam generator models [26
28]. 2. In some cases, first, the differential equations of the physics models need to be converted into integral equations. Then, according to the characteristics of the differential/integral equations, a suitable numerical format is selected to convert these equations into algebraic equations of unknown variables. Finally, a reasonable numerical algorithm is selected to solve the algebraic equations. 3. If the code is a large-scale program composed of many modules, each module needed to be verified after it has been developed. This process is also called unit testing. After all the unit testing are completed, the entire code needs to be verified. If the modules or the entire code cannot pass the verification, developers should go back to step 1 or 2 to

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2. Guidance of nuclear power plant code development

FIGURE 2.1 Process of nuclear power plant code development.

fix the bugs. The most reliable reference for verification is experiment data, if any is available. The simulation results of other widely accepted codes as well as analytical solutions of physical equations under specific conditions (if any is present) can be used as supplementary verification references. 4. If the code does not meet the customer’s needs, developers should go back to step 1 to supplement the related functions. This step is also called validation. 5. In the process of using the code, if the code is found to be insufficient or has bugs, the developer should go back to step 1 or 2 to fix the bugs or supplement the related functions.

2.1.3 Code development skills The author believes that in order to develop a good nuclear power plant program, the following skills must be grasped: 1. Mastering the ability of model development Selecting or deriving an appropriate model to describe the physical process of reactor system is the key to the code development. Wrong physical model will make the code meaningless and will mislead the users. Therefore developers need a deep foundation

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in the basic theory of nuclear power systems and strong model development capabilities. 2. Familiar with common numerical calculation algorithms The equations of the physical model are usually transformed into algebraic equations of unknown variables. These equations can only be solved correctly as long as a suitable numerical algorithm is selected. Therefore developers need to master the common calculation algorithms of ordinary differential equations, partial differential equations, and algebraic equations [29,30]. 3. Mastering a programing language Computer programing languages can be divided into machine languages, assembly languages, and high-level languages. Most of the nuclear power plant codes are written in high-level languages, such as Fortran, C11, and C#. Fortran was widely adopted in the development of nuclear power plant codes in the 20th century. Programing languages have their own characteristics; the choice of code development language should depend on project requirements and programing language characteristics. Programing languages are interlinked; beginners who master one of them can quickly master other programing languages. In addition, developers should be familiar with the knowledge of data structures and algorithms [31] as well as design patterns [32], which will help develop stable and efficient nuclear power plant codes. It should be emphasized that the abovementioned skills are not something that can be mastered at one time. Developers need to keep thinking and training in the process of code development in order to gradually improve and master the above skills. In view of the fact that this book is an entry-level reading and due to space limitations, the following contents will only introduce the development process of lumped parameter models for the reactor and pressurizer of pressurized water reactor (PWR). Readers can have a comprehensive understanding of code development from these contents.

2.2 Code development examples 2.2.1 Reactor Fig. 2.2 shows a simplified reactor structure of a typical PWR. The reactor consists of a reactor core, core support structures, a pressure vessel, and control rod drive mechanisms. The reactor core is composed of fuel rods with exactly the same geometry and mechanical structure and is located below the center of the reactor pressure vessel. Fuel rods are components that generate nuclear fission and release heat. Water, as coolant from outside of the pressure vessel, flows downward through the annular channel between the hanging basket and the inner wall of the pressure vessel and then turns 180 degrees from the lower part of the pressure vessel and flows upward into the core. When the coolant flows through the core, it absorbs the released heat of the fuel rods, and finally, it flows out of the pressure vessel from the top of the core. The reactor coolant acts as a neutron moderator as it flows into the core. The reactor of modern PWR generally has an inlet water temperature of about 300 C, an outlet water temperature of about 330 C, and an internal pressure of 15.5 MPa.

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FIGURE 2.2 Simplified reactor structure of a typical PWR. PWR, Pressurized water reactor.

FIGURE 2.3 Lumped parameter model of reactor.

2.2.1.1 Model development Fig. 2.3 shows a lumped parameter model of the reactor, which divides the reactor into three control volumes—a lower chamber, a core, and an upper chamber. The lower chamber is a combination of the space below the core in the pressure vessel and the annular channel, which is connected to the reactor inlet (i.e., the cold leg); the upper chamber is the space above the core in the pressure vessel, which is connected to the reactor outlet (i.e., the hot leg). 2.2.1.1.1 Reactor core

When the reactor is operating, the fuel pellets in the fuel rods undergo a fission reaction. The energy produced by the fission is converted into thermal energy of the fuel rod and is carried away by the coolant flowing through the fuel rod. In addition, when the state of the core changes (such as the movement of the control rod or the temperature change in the coolant or fuel rod), the reactivity of the core changes accordingly, which in turn changes the temperature distribution of the core. It can be seen that the reactor core

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has complex reactor physics and thermal-hydraulic phenomena. Here, the reactor model is divided into three submodels: a neutron dynamics model, a reactivity feedback model, and a thermal-hydraulic model. The structure of a real reactor is complex. To fully simulate the physical phenomena of the reactor core, the reactor physics model must use three-dimensional neutron dynamics equations and the thermal-hydraulic model must use two-phase fluid dynamics equations and a large number of empirical correlations, which is beyond the scope of this chapter. As a simplification, the reactor physics model in this chapter is described by six groups of delayed neutron point reactor dynamic equations, which are usually used to develop system-level codes; the thermal-hydraulic model is described by lumped parameter heat transfer equations. Six groups of delayed neutron point reactor dynamic equations are as follows 8 6 X > dn ρ 2 β > > 5 n 1 λi Ci > < dt Λ i51 (2.1) ði 5 1; 2; . . . ; 6Þ ; > dCi βi > > 5 n 2 λ C > i i : dt Λ where n is relative neutron density; ρ is reactivity; Λ is average neutron generation time; β is total delayed neutrons fraction; β i is fraction of delayed neutrons in ith group; λi is decay constant in ith group; Ci is the relative concentration of delayed neutron precursor nucleus in ith group. Lumped parameter heat transfer equations are as follows 8   dTf > > 5 2 U1 A1 Tf 2 Tc 1 P0 n Mf Cpf > > dt > > > > <   dTc 5 U1 A1 Tf 2 Tc 1 W1 Cp1 ðTcin 2 Tcout Þ ; ρ1 V1 Cp1 (2.2) dt > > > > > 1 > > Tc 5 ðTcin 1 Tcout Þ > : 2 where Tf and Tc are the temperature of fuel rod temperature and core coolant, respectively; Tcin and Tcout are the coolant temperature of core inlet and core outlet, respectively; P0 is the steady-state operating power of the core; U1 is the heat transfer coefficient between fuel rod and core coolant; A1 is the heat transfer area between fuel rod and core coolant; Mf is the mass of fuel rod; Cpf and Cp1 are the constant-pressure specific heat capacity of fuel rod and core coolant, respectively; ρ1 is the core coolant density; V1 is the core volume; W1 is the mass flow rate of core coolant. In a broad sense, the core reactivity feedback includes short- (temperature effect) and mid-long-term feedback (neutron poison effect, fuel consumption, and conversion). When simulating fast transients in a reactor, it is sufficient to consider only temperature feedback. Temperature feedback refers to the behavior of core reactivity caused by temperature changes in fuel rod or core coolant. The expression is as follows   ρ 5 ρex 1 αf Tf 2 Tf0 1 αc ðTc 2 Tc0 Þ;

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(2.3)

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2. Guidance of nuclear power plant code development

where ρex is the external reactivity; αf and αc are the temperature feedback coefficients of fuel rod and core coolant, respectively; Tf0 and Tc0 are the steady-state temperature of fuel rod and core coolant, respectively. Combing Eqs. (2.1)
(2.3) gives 8 2 3   6 > X > α T 2 T dn ρ 2 β α ð T 2 T Þ f f f0 > c c c0 5 > 4 ex 5 1 n 1 1 λi C i > > > dt Λ Λ Λ > i51 > > > > dCi β > > > 5 i n 2 λi C i < dt Λ (2.4) ði 5 1; 2; . . . ; 6Þ ; > dTf P0 U1 A1 U1 A1 > > > 5 n2 Tf 1 Tc > > dt Mf Cpf Mf Cpf Mf Cpf > > > > > U1 A1 1 2W1 Cp1 dTc U1 A1 2W1 > > > 5 Tf 2 Tc 1 Tcin > : dt ρ1 V1 Cp1 ρ1 V1 Cp1 ρ1 V1 Tcout 5 2Tc 2 Tcin :

(2.5)

Eq. (2.4) is the governing equation of the core. 2.2.1.1.2 Lower and upper chamber

The heat source does not exist in the lower and upper chamber, and they can buffer the temperature changes from the cold leg and the core, respectively. It is assumed that the coolant in the lower and upper chamber is incompressible. The energy conservation equation for the lower chamber is dTlc Wl 5 ðTin 2 Tcin Þ: dt ρlc Vlc

(2.6)

The energy conservation equation for the upper chamber is dTuc Wl 5 ðTcout 2 Tout Þ: dt ρuc Vuc

(2.7)

Assuming the control volume outlet temperature is decided by the donor control body temperature, one can get Tcin 5 Tlc ;

(2.8)

Tout 5 Tuc ;

(2.9)

where Tlc , ρlc , and Vlc are the coolant temperature, coolant density, and volume in the lower chamber, respectively; Tuc , ρuc , and Vuc are the coolant temperature, coolant density, and volume in the upper chamber, respectively; Tin and Tout are the coolant temperature at inlet and outlet of pressure vessel, respectively. 2.2.1.2 Numerical scheme Rewriting Eq. (2.4) into matrix form, one can get

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dx 5 Fx 1 b; dt

where 2





ρex 1 αf Tf 2 Tf0 6 Λ 6 6 6 1 αc ðTc 2 Tc0 Þ 2 β 6 6 Λ 6 6 6 β1 6 6 Λ 6 6 6 β2 6 6 F56 Λ 6 ^ 6 6 β6 6 6 Λ 6 6 6 P0 6 6 M 6 f Cpf 6 6 4 0

(2.10)

 T x 5 n; C1 ; C2 ; . . .; C6 ; Tf ; Tc ;

λ1

λ2

?

λ6

(2.11) 3 0

2 λ1 2 λ2 & 2 λ6 2

U1 A1 Mf Cpf

U1 A1 ρ1 V1 Cp1  T 2W1 b 5 0; 0; 0; 0; 0; 0; 0; 0; Tcin : ρ1 V1

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7; 7 7 7 7 7 7 7 7 7 U1 A1 7 7 Mf Cpf 7 7 U1 A1 1 2W1 Cp1 7 5 2 ρ1 V1 Cp1 0

(2.12) (2.13)

Eq. (2.10) is a rigid equation and the fourth-order explicit Runge
Kutta method [29] is used to solve it. C# source code for this method can be seen in Section 2.3. Eqs. (2.6) and (2.7) are both first-order ordinary differential equations and Euler’s method [29] is used to solve them. 2.2.1.3 Verification It is difficult to obtain experiment data related to reactor physics. Therefore a comparison of the reactor model with other codes is conducted for verification. Naghedolfeizi [33] proposed a reactor model based on a single-group delayed neutron point reactor dynamic equations. He selected a typical Westinghouse four-loop PWR as the research object and gave the simulation results of the reactor at the step increase in external reactivity and reactor inlet temperature. The design parameter of this reactor can be seen in Refs. [33,34]. The comparison between this model and the work of Naghedolfeizi is as in the following subsections. 2.2.1.3.1 Steady-state results

First, the submodels of reactor physics and reactivity feedback in this code are turned off. Then, keep the reactor inlet coolant temperature and core power constant and run the

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code. Finally, the code will obtain a steady-state solution after being run for a while. The steady-state value of the temperature at reactor outlet calculated by this model is 590.601K and that given by Naghedolfeizi was between 592 and 593K [33]. The calculated results of the two models differ by about 2K, which supports the reliability of the thermal-hydraulic submodel developed in this chapter. 2.2.1.3.2 Transient results

After the steady-state solution is obtained, the neutron dynamics and temperature feedback submodels of this code are turned on to simulate the reactor response under the step increase of reactivity and reactor inlet temperature, respectively, and the results are compared with the work of Naghedolfeizi. Figs. 2.4 and 2.5 show the changes in core normalized power reactor and reactor outlet temperature by introducing a step reactivity of 0.1β, respectively. The introduction of external reactivity leads to a rapid rise in core power, which causes the temperature of fuel rods and core coolant to rise rapidly. Due to the negative temperature feedback of fuel rod and the core coolant, the core power quickly drops and finally stabilizes. The reactor outlet temperature rises as the core power increases and then stabilizes as the core power stabilizes. The core power and reactor outlet temperature increase of this model are larger than those of Naghedolfeizi, reflecting the conservativeness of this model. The physical parameter changes of the two models are consistent, which supports the reliability of the model developed in this chapter. Figs. 2.6 and 2.7 show the changes in core normalized power reactor and reactor outlet temperature by introducing a step reactor inlet temperature of 5.5K, respectively. An increase in the reactor inlet temperature causes a rise in the temperature of the core coolant. Due to the negative temperature feedback of the core coolant, the core power

FIGURE 2.4 Change in core normalized power by introducing a step reactivity of 0.1β.

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33 FIGURE 2.5 Change in reactor outlet temperature by introducing a step reactivity of 0.1β.

FIGURE 2.6 Change in core normalized power by introducing a step reactor inlet temperature of 5.5K.

decreases rapidly, which in turn causes the fuel rod temperature to decrease rapidly. Due to the negative temperature feedback of the fuel rod, the decline in core power is suppressed, and finally, the core power becomes stable. The reactor outlet temperature increases with the reactor inlet temperature, decreases with the core power, and finally

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FIGURE

2.7 Change in reactor outlet temperature by introducing a step reactor inlet temperature of 5.5K.

stabilizes as the core power stabilizes. Both models have the same change trend and amplitude of physical parameters, which supports the reliability of the model developed in this chapter.

2.2.2 Pressurizer Pressurizer is one of the key devices of PWR. It can maintain system pressure during steady-state operation of a PWR, buffer the fluctuations of system pressure and primary circuit coolant volume during operating transients, and provide over (low) pressure protection in the event of an accident. In normal operation the pressurizer can be divided into a vapor lump and a liquid lump based on the liquid
vapor interface (water level). The vapor lump is connected to the cold leg of the reactor coolant through a spray line; the liquid lump is connected to the hot leg of the reactor coolant through a surge line. The temperature change in the coolant of the primary circuit will result in reactor coolant flowing into or out of the pressurizer through the surge line. When the reactor coolant flows into the pressurizer, the spray will be activated to condense the steam to provide a buffer space for the inflowing water, and the electric heater may be turned on to maintain the liquid lump at saturated state (see Fig. 2.8A). When reactor coolant flows out of the pressurizer, the electric heater will be activated to generate steam to prevent the pressure drop due to the departure of water and the sudden expansion of steam (see Fig. 2.8B). Drastic pressure changes of the pressurizer may cause the liquid and vapor lumps to evaporate and condense,

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FIGURE 2.8 Operating mechanism of pressurizer: (A) insurge and (B) outsurge.

respectively, which further affect the pressure of the pressurizer. It can be seen that complex two-phase flow phenomena occur in the pressurizer. Development of a pressurizer model that can accurately predict the pressure and water level changes of the pressurizer is essential for the simulation of the reactor system.

2.2.2.1 Model development An improved nonequilibrium multiregion pressurizer developed by Zhong et al. [25] is briefly introduced here. The pressurizer is divided into m liquid control volumes and n vapor control volumes based on the liquid
vapor interface. The liquid control volumes 1 to m 2 1 belongs to the liquid layer and vapor control volumes 1 to n 2 1 belongs to the vapor layer. The mth liquid control volume and nth vapor control volume are considered as in saturated state, forming the saturated layer (see Fig. 2.9). Assumptions that are made in this model include: 1. 2. 3. 4. 5. 6. 7. 8.

Each control volume has the same averaged uniform cross-sectional area. Each control volume has the same pressure. Each control volume has the averaged uniform specific enthalpy at each time step. Spray droplets and their attached condensation droplets are already in saturated state before they reach the liquid
vapor interface. Time for spray droplets reaching the liquid
vapor interface is neglected. Mass exchange at the liquid
vapor interface is a result of bubbles rise and droplets fall. Delay time for bubble rise and droplet fall to the liquid
vapor interface is neglected. Wall condensation and boiling are neglected.

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FIGURE 2.9 Schematics of nonequilibrium multiregion model developed by Zhong et al.

9. Work and gravitational potential energy of each control volume are neglected. 10. Positive direction of the liquid control volume is upward and positive direction of the vapor control volume is downward. 2.2.2.1.1 Governing equations

As for liquid volume iði 5 1; 2; . . . ; m 2 1Þ in the liquid layer, based on mass conservation and energy conservation, one can get    d ρl;i VL =m (2.14) 5 Wl;i21 2 Wl;i 2 Wbe;l;i ; dt    d ρl;i hl;i 2 p VL =m (2.15) 5 Wl;i21 h~l;i21 2 Wl;i h~l;i 2 Wbe;l;i hsg 1 Qh;l;i 1 Qtc;l;i ; dt where p is the pressure of the pressurizer; VL is the liquid volume of the pressurizer; Wx;i ðx 5 l; vÞ is the mass flow between control volumes i and i 1 1; h~x;i is the specific

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enthalpy of flow between control volumes i and i 1 1; Wbe;l;i is the bulk evaporation mass rate of liquid control volume i; Qh;l;i is the heat absorption rate of liquid control volume i from electric heater. Qtc;x;i is the Fourier thermal conductivity absorption rate of control volume i from adjacent control volume(s). Taking the surge line as the 0th liquid control volume, the mass flow rate between the 0th and 1st liquid control volumes is expressed as Wl;0 5 Wsu ;

(2.16)

where Wsu is the mass flow rate in the surge line. The specific enthalpy of flow between control volumes in the liquid layer is determined by the donor control volume, therefore

h~l;i 5





hsu ; Wl;0 . 0 ; hl;1 ; Wl;0 , 0

(2.17)

hl;i ; Wl;i . 0 ði 5 1; 2; . . . ; m 2 1Þ: hl;i11 ; Wl;i , 0

(2.18)

h~l;0 5

As for vapor volume iði 5 1; 2; . . . ; n 2 1Þ in the vapor layer, based on mass conservation and energy conservation, one can get    d ρv;i ðVT 2 VL Þ=n (2.19) 5 Wv;i21 2 Wv;i 2 Wbc;v;i 2 Wsc;v;i ; dt    d ρv;i hv;i 2 p ðVT 2 VL Þ=n 5 Wv;i21 h~v;i21 2 Wv;i h~v;i 2 Wbc;v;i hsf 2 Wsc;v;i hsg 1 Qtc;v;i ; (2.20) dt where VT is the total volume of the pressurizer; Wbc;v;i is the bulk condensation mass rate of vapor control volume i; Wsc;v;i is the vapor condensation of vapor control volume i by spray droplets. Similarly, take the pressure relief and safety valve be the 0th vapor control volume, and the mass flow between the 0th and the 1st is expressed as Wv;0 5 Wrsv ;

(2.21)

where Wrsv is the mass flow of pressure relief and safety valve. The specific enthalpy of flow between control volumes in the vapor layer is determined by the donor control volume, therefore h~v;0 5 hv;1 ð_Wv;0 5 Wrsv < 0Þ;  hv;i ; Wv;i . 0 h~v;i 5 ði 5 1; 2; . . .; n 2 1Þ: hv;i11 ; Wv;i , 0

(2.22) (2.23)

As for the saturated layer, based on mass conservation and energy conservation, one can get

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     d ρsf VL =m 1 ρsg ðVT 2 VL Þ=n dt

5 Wbe;sum 1 Wbc;sum 1 Wl;m21 1 Wv;n21 1 Wsp 1 Wsc;sum ; (2.24)

d



     ρsf hsf 2 p VL =m 1 ρsg hsg 2 p ðVT 2 VL Þ=n dt

5 Wbe;sum hsg 1 Wbc;sum hsf ~ 1 Wl;m21 h~l;m21 1 W  v;n21 hv;n21 1 Wsp 1 Wsc;sum hsf 1 Qtc;l;m 1 Qtc;v;n ; (2.25)

where Wbe;sum is the total bulk evaporation mass rate from liquid layer; Wbc;sum is the total bulk condensation mass rate from vapor layer; Wsp is the spray mass flow rate; Wsc;sum is the total vapor condensation mass rate by spray droplets. 2.2.2.1.2 Empirical correlations Bulk evaporation and condensation During the drastic change in the pressure of the pressurizer, a part of the liquid water in the liquid lump will flash (i.e., bulk evaporation) and a part of steam in the vapor lump will suddenly condense (i.e., bulk condensation). It is assumed that the phenomena of bulk evaporation and condensation come from bubble rise and condensate fall. Assuming that the mass rate of bulk evaporation is dependent on the velocity of bubble rise, one can get

Wbe;l;i 5 ρsg αl;i AVbr;l;i ;

(2.26)

where α is the void fraction; A is the cross-sectional area of the pressurizer; Vbr is the rising velocity of bubbles, which can be determined by Gunther
Kreith correlation [35,36], that is,   8 > g ρsf 2 ρsg d2b > > > ; LLa , db > < c1 μsf (2.27) Vbr 5 ;   !0:25 > > > g ρ 2ρ σ sf sf sg > > ; LLa > db : c2 ρ2 sf

where c1 is a constant related to the type of liquid and its value is between 2/9 and 3/9. c2 is a constant and determined to be 1.18 based on experiment data. db is the bubble rising diameter. σ is the surface tension. LLa is the Laplace length and is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σsf  : LLa : 5 (2.28) g ρsf 2 ρsg

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Assuming that the bubble rising diameter db is equal to the bubble departure diameter in the boiling saturated liquids, which can be determined by Cole
Rohsenow correlation [37], that is, db 5 cCR Ja1:25

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi σsf  ; g ρsf 2 ρsg

(2.29)

where cCR is determined by the type of liquid and is equal to 1.5E 2 4 for water. Ja is the Jakob number, which is defined as Ja: 5

ρsf Cpsf Tsf : ρsg hfg

(2.30)

Ignoring the delay time of bubble rise, the mass rate of bubbles entering into the saturated layer is equal to the sum of the mass rate of bulk evaporation in all liquid volumes of the liquid layer, that is, Wbe;sum 5

m21 X

Wbe;l;i :

(2.31)

i51

Assuming that the mass rate of bulk condensation is dependent on the velocity of condensate fall, one can get   Wbc;v;i 5 ρsf 1 2 αv;i AVcf;v;i ;

(2.32)

where the falling velocity of condensate droplets Vcf is an empirical constant. Ignoring the delay time of condensate fall, the mass rate of condensate droplets entering into the saturated layer is equal to the sum of the mass rate of bulk condensation in all vapor volumes of the vapor layer, that is, Wbc;sum 5

n21 X

Wbc;v;i :

(2.33)

i51

The homogeneous-fluid model [36] is adopted in the liquid and vapor layer, then the void fraction of the control volume is decided by 8 1 > > 0 1; 0,x,1 > > > > ρsg 1 < @ A (2.34) ; α 5 1 1 ρsf x 2 1 > > > > 1; x>1 > > : 0; x > > ; for single phase < @h (2.39) rh 5 v fg > > ; for two phase; > : hfg

rp 5

8 > > > > >
dvfg vfg dhfg dv dh sf sf > @x A2 @x A; > 1 1 > > : dp dp hfg dp dp

(2.40) for two phase;

where v is specific volume and vfg is defined by vfg : 5 vsg 2 vsf :

(2.41)

By expanding Eqs. (2.14), (2.15), (2.19), (2.20), (2.24), and (2.25), one can obtain a set of 2ðm 1 n 2 1Þ equations as BX 5 C;

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(2.42)

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41

where the coefficient matrix BAℝ2ðm1n21Þ 3 2ðm1n21Þ ; the constant vector CAℝ2ðm1n21Þ 3 1 ; the solution vector XAℝ2ðm1n21Þ 3 1 and is defined by  dp dVL dhl;1 dhl;2 dhl;m21 dhv;1 dhv;2 dhv;n21 ; ; ; ;...; ; ; ;...; ; X: 5 dt dt dt dt dt dt dt dt (2.43) T Wl;1 ; Wl;2 ; . . . ; Wl;m21 ; Wv;1 ; Wv;2 ; . . . ; Wv;n21 : Eq. (2.42) is solved by the Gauss
Jordan elimination with partial pivoting [36]. C# source code for this method can be seen in Section 2.3. 2.2.2.3 Verification The verification reference of this model is the experiment data of two groups of Shippingport loss-of-load experiments [38]. One experiment was initiated from a reactor power level of 74 MW(e), reduced to 10 MW(e), and then to 0. The other was initiated from a reactor power level of 105 MW(e), reduced to 35 MW(e), 10 MW(e), and then to 0. The imbalance of the power and load in the primary circuit resulted in the temperature change of the reactor coolant, which further causes the combination of insurge, outsurge, spray actuation, and heater cycling in the pressurizer. The experiment conditions can be seen in Refs. [38,39]. In this simulation, (1) because the geometry and location of the electric heater are unknown, it is assumed that the electric heater power is evenly distributed into each

FIGURE 2.10 Experiment data and mesh-independent simulations of pressure transients due to loss-of-load from 74 MW(e).

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FIGURE 2.11

2. Guidance of nuclear power plant code development

Experiment data and mesh-independent simulations of pressure transients due to loss-of-load

from 105 MW(e).

control volume of liquid layer; (2) the model empirical coefficients are set as c1 5 2=9 and Vcf 5 5:0 m=s. After testing the model, it is learned that when the number of vapor control volumes and liquid control volumes reach 250 and higher, respectively, the simulation results are independent of the number of control volumes [25], that is, mesh-independent solutions can be obtained. Figs. 2.10 and 2.11 show the comparison of the experiment data and the meshindependent simulations of pressure transients of the loss-of-load from 74 and 105 MW(e), respectively. It can be seen that the absolute errors between the simulation results and experiment data are less than 0.5 MPa, which supports the reliability of the pressurizer model developed in this chapter.

2.3 Source code C# source code for fourth-order explicit Runge
Kutta method and Gauss
Jordan elimination with partial pivoting is shown in the following subsections.

2.3.1 Fourth-order explicit Runge
Kutta method Source code in ExplicitRungeKutta4Order.cs

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2.3.2 Gauss
Jordan elimination with partial pivoting Source code in GlobalFunAndVar.cs

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Source code in MatrixAugmented.cs

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References [1] J. Yu, Fundamental Principles of Nuclear Engineering, Tsinghua University Press, 2016. [2] M.P. Paulsen, et al., RETRAN-3D—a program for transient thermal-hydraulic analysis of complex fluid flow systems, in: NP-7450, vol. 1, 1996, p. 4. [3] I. N. Laboratory, RELAP5-3D Code Manual Volume I: Code Structure, System Models and Solution Methods, 2012. [4] N.M. Schnurr, R.G. Steinke, V. Martinez, J.W. Spore, TRAC-PF1/MOD2 Code Manual. Volume 2, User’s Guide, 1992. [5] J.A. Borkowski, et al., TRAC-BF1/MOD1: An Advanced Best-Estimate Computer Program for BWR Accident Analysis, Model Description. 1992. [6] R.A. Judd, et al., ASSERT-4 User’s Manual, 1984. [7] Y. Jiyang, W. Songtao, J. Baoshan, Development of sub-channel analysis code for CANDU-SCWR, Prog. Nucl. Energy 49 (4) (2007) 334
350. [8] C.L. Wheeler, C.W. Stewart, R.J. Cena, D.S. Rowe, A.M. Sutey, COBRA-IV-I: An Interim Version of COBRA for Thermal-Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements and Cores, 1976. [9] L.J. Siefken, G.A. Berna, V.N. Shah, FRAP-T6: a computer code for the transient analysis of oxide fuel rods, Nucl. Eng. Des. 88 (3) (1985) 341
355. [10] W. Nuclear Regulatory Commission DC (USA), Office of Nuclear Reactor Regulation, TOODEE 2: A Two Dimensional Time Dependent Fuel Element Thermal Analysis Program, 1975. [11] B. Kochunas, B. Collins, D. Jabaay, T.J. Downar, W.R. Martin, Overview of development and design of MPACT, in: Proceedings of M&C 2013, Sun Valley, ID, 2013. [12] K. Wang, et al., RMC—a Monte Carlo code for reactor core analysis, in: SNA 1 MC 2013—Joint International Conference on Supercomputing in Nuclear Applications 1 Monte Carlo, 2014, p. 6020. [13] E. Brun, et al., Overview of TRIPOLI-4r version 7 continuous-energy Monte Carlo transport code, in: Proceedings of the Internal Conference ICAPP, vol. 2011, 2011. [14] X. Zhang, J. Yu, T. Huang, G. Jiang, X. Zhong, M. Saeed, An improved method for hydrogen deflagration to detonation transition prediction under severe accidents in nuclear power plants, Int. J. Hydrogen Energy 44 (21) (2019) 11233
11239. [15] D.W. Hargroves, L.J. Metcalfe, L.L. Wheat, G.F. Niederauer, C.F. Obenchain, CONTEMPT-LT/028: a computer program for predicting containment pressure-temperature response to a loss-of-coolant accident, 1979. [16] K.K. Murata, D.C. Williams, R.O. Griffith, R.G. Gido, E.L. Tadios, F.J. Davis, et al., Code manual for CONTAIN 2.0: a computer code for nuclear reactor containment analysis, in: Sandia Natl. Lab. Albuquerque, NM, Prep. US Nucl. Regul. Comm. NUREG/CR-6533, SAND97-1735, 1997. [17] J. Yu, B. Jia, PCCSAC: a three-dimensional code for AC600 passive containment cooling system analysis, Nucl. Sci. Eng. 142 (2) (2002) 230
236. [18] R. Li, J. Yu, Development of PCCSAP-3D Code for Passive Containment: Models of Noncondensable Gases, Aerosols and Fission Products, 2013. [19] L.T. Ritchie, J.D. Johnson, R.M. Blond, Calculations of Reactor-Accident Consequences, Version 2 CRAC2: Computer Code User’s Guide, 1983. [20] G.N. Kelly, Cosyma: A New Programme Package for Accident Consequence Assessment, Commission of the European Communities (CEC), 1991. [21] W. Malalasekera, H.K. Versteeg, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, Pearson Prentice Hall, 2007. [22] W.M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2018. [23] S. Min Baek, H. Cheon No, I.Y. Park, A nonequilibrium three-region model for transient analysis of pressurized water reactor pressurizer, Nucl. Technol. 74 (3) (1986) 260
266. [24] A.N. Nahavandi, S. Makkenchery, An improved pressurizer model with bubble rise and condensate drop dynamics, Nucl. Eng. Des. 12 (2) (1970) 135
147. [25] X. Zhong, et al., Development of an improved non-equilibrium multi-region model for pressurized water reactor pressurizer, Ann. Nucl. Energy 126 (2019) 133
141. [26] D. Gal, D. Saphier, E. Elias, A DSNP movable boundary U-tube steam generator, Nucl. Technol. 95 (1991) 64
76.

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[27] L.N.F. Guimara˜es, N. da Silva Oliveira Jr., E.M. Borges, Derivation of a nine variable model of a U-tube steam generator coupled with a three-element controller, Appl. Math. Model. 32 (2008). [28] A. Hoeld, A theoretical model for the calculation of large transients in nuclear natural-circulation U-tube steam generators (Digital code UTSG), Nucl. Eng. Des. (1978). [29] E. Su¨li, D.F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press, 2003. [30] W.F. Ames, Numerical Methods for Partial Differential Equations, Academic Press, 2014. [31] T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to Algorithms, MIT Press, 2009. [32] E. Gamma, Design Patterns: Elements of Reusable Object-Oriented Software, Pearson Education India, 1995. [33] M. Naghedolfeizi, Dynamic Modeling of a Pressurized Water Reactor Plant for Diagnostics and Control, University of Tennessee, Knoxville, TN, 1990. [34] J.D. Freels, An Investigation of High Order and Low Order Dynamic Modeling of a Complete Pressurized Water Reactor Nuclear Power Plant, University of Tennessee, Knoxville, TN, 1979. [35] F.C. Gunther, F. Kreith, Progress report, Jet Propuls. Lab. Calif. Inst. Technol, 1950. [36] J. Lyu, Y. Wu, Z. Li, Q. Song, R. Yang, Gas-Liquid Two-Phase Flow and Boiling Heat Transfer, Science Press, Beijing, 2017. [37] R. Cole, W.M. Rohsenow, Correlation of bubble departure diameter for boiling of saturated liquids. Chem. Eng. Prog. Symp. Ser. 65 (1969) 211
213. https://doi:10.1016/j.ijheatmasstransfer.2011.04.007. [38] J.A. Redfield, V. Prescop, S.G. Margolis, Pressurizer performance during loss-of-load tests at Shippingport: analysis and test, Nucl. Appl. 4 (3) (1968) 173
181. [39] Z. Sun, (in Chinese) Nuclear Power Equipment, Harbin Engineering University Press, 2004.

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C H A P T E R

3 Nuclear engineering software quality assurance Xinghe Ni College of Energy, Xiamen University, Xiamen, P. R. China

3.1 Introduction Keeping nuclear safety is the first essential duty for developing nuclear power. With the development and application of digital instrument and control systems, more and more professional software systems or tools are used in nuclear power plant design, analysis, and operation activities [1 3]. High-quality software products used in the nuclear industry can help us guarantee or even improve the safety performance of the nuclear power system. Different from the tangible industrial product produced by the factory worker, the software is something bodiless product produced by the programer. What manufacturers pursue is to make superior quality, to satisfy user requirements (URs), and to acquire benefits. People are interested in product quality, and spontaneously software quality is one crucial issue. However, software products are different from tangible industrial products. It is high complexity, invisibility, and defect detecting limited in the development phase that brings difficulties and highly professional challenges into the quality assurance of software. In the IEEE definition [4,5], software quality assurance (SQA) is (1) a planned and systematic pattern of all actions necessary to provide adequate confidence that an item or product conforms to establish technical requirements (2) and a set of activities designed to evaluate the process by which the products are developed or manufactured. Sometimes, lacking high-quality software may mean loss of money, health, safety, and even life. Software defects are incredibly costly. A 2002 study by the US National Institute of Standards and Technology estimated that software defects cost the United States $59.5 billion a year [6,7]. Think about what the global amount would be. The study also confirmed that more than one-third of the losses (i.e., $22.2 billion) could have been avoided with a little testing. There are some distressing cases caused by software quality defects, as listed in Table 3.1.

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00003-6

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3. Nuclear engineering software quality assurance

TABLE 3.1 Summary of important events caused by software errors. Event

Time

Risk/damage

Reason

Mars climate orbiter disintegration

1999/9

More than 300 million dollars lost The disunity of unit systems in flight control software

Ariane 5 launch failure

1996/6

About 500 million dollars lost

Mismatch of critical variables’ byte

Missile attack on Zahran base

1991/2

28 soldiers died and more than 100 others wounded

A tiny millisecond delay in the system clock, and error accumulation by running for a long time

False reports of missile attack

1980 and Come close to warfare 1995

False alarm from the feedback system

Therac-25 medical accelerator incident

1985 87

At least three people died

Without independent V&V, and a fatal defect of high energy operating mode

Panama medical accelerator incident

2000

At least five people died

Treatment planning software had a wrong preset procedure

Indonesian Lion Air JT610 air crash

2018/10

189 people died

A design defect in MCAS

Ethiopian Airlines ET302 Air crash

2019/3

157 people died

A design defect in MCAS

MCAS, Maneuvering characteristics augmentation system; V&V, verification and validation.

Mars Climate Orbiter was launched in December 1998 and then was disintegrated in the Mars atmosphere in September 1999. The root cause is that the metric unit was employed in the software of the flight control system, while the British Unit was usually used by the ground control team [8,9]. The difference of the unit system resulted in 100 km deviation of orbit navigation. Ariane 5 launch vehicle was developed from previous Ariane 4. The maiden voyage of Ariane 5 was on June 4, 1996. Unfortunately, since blast-off to tipping self-destruction, it was only 30 seconds. The cause was that a section code in previous Ariane 4 was simply copied to Ariane 5 [10]. Unfortunately, a key velocity variable in the section code is 16 bits floating point, but the variable in Ariane 5 needs 64 bits [11]. During the First Gulf War in February 1991, an Iraqi Scud missile accurately hit the US base at Zahran in Saudi Arabia, killing 28 American soldiers and wounding more than 100 others. A later investigation [12] found that a simple computer bug had disabled the base’s Patriot antimissile system and prevented it from intercepting Scud missiles in the air. At that time the Patriot antimissile system responsible for defending the base had been working for 100 hours continuously, and every hour of operation, the clock in the system would have a tiny millisecond delay, which was the root of this failure tragedy. Because of software bugs, World War ever was on the verge of breaking out. In 1980, North American Air Defense Command reported several missile attacks on the United States. It was later confirmed that this was a circuit fault of the feedback system, but the system software did not consider the false alarm caused by the fault problem [13]. It happens that there is a similar case in 1995 [14], the radar and satellite networks of Russia reported an American missile invasion. But officials’ instincts told them it was a false alarm. Soon afterward, it turned out to be a false alarm.

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Therac-25 medical accelerator incident was happened in Canada, causing patients to receive excessive radiation doses from 1985 to 1987 [15]. The Therac-25 is built on an operating system developed without independent verification and validation (V&V), and a fatal defect of high-energy operating mode cannot be eliminated. Another incident involving excessive doses of radiation occurred in 2000 in Panama City [16,17]. It is since treatment planning software had a wrong preset procedure. An Indonesian Lion Air Boeing 737 Max-8 passenger plane gone missing and crashed about 13 minutes after taking off from Jakarta, Indonesia, on October 29, 2018. All 189 people were killed. On March 10, 2019, an Ethiopian Airlines Boeing 737 Max-8 crashed 6 minutes after takeoff. All 157 people died. The interval between the two air crashes on a new plane type was only 5 months that had alarmed the airline industry [18]. As we know, the higher the aircraft’s nose, the greater the angle of attack. According to aerodynamics, if the angle of attack exceeds a specific range, the aircraft would face the risk of stall. The Boeing 737 Max-8 series equips with an automatic stall-prevention system, that is, Maneuvering Characteristics Augmentation System (MCAS) [19]. By design, once the plane’s angle of attack sensor data shows the sign of stall, the MCAS system can automatically take over without the pilot’s intervention and plunge the plane’s nose down into mitigating the risk of stall. In practice, however, if the plane’s angle of attack sensor is not calibrated correctly and is deficient in determining the stalled status of the plane, then the wrong information of attack angle may be provided to the MCAS. Once the MCAS is started, due to the design defects in the priority problem, the MCAS continuously controls the plane, which can make the plane fall. Black box data shows that MCAS repeatedly lowered the plane’s nose of the two flights before their crash [19]. On April 4, 2019, Boeing Former President and CEO Dennis A. Muilenburg acknowledged that “with the release of the preliminary report of the Ethiopian Airlines Flight 302 accident investigation, it’s apparent that in both flights, the Maneuvering Characteristics Augmentation System, known as MCAS, activated in response to the erroneous angle of attack information.” Most software defects may only cause some minor problems. However, according to the events mentioned previously, the software for spacecraft control system, flight control system, military equipment system, and medical equipment system, as well as the other software related to human life and industrial safety (e.g., nuclear power system), should never cause major disasters to people’s lives and property due to software defects. A rigorous, effective, and successful SQA can avoid fatal defects in software. It is the planned and systematic action to provide confidence that the software product meets established technical requirements. A life cycle for software, module, or model development contains the following phases [5], that is, initial planning, requirements definition, software design, coding, software testing, installation, and acceptance. At the start of each project, an SQA plan is completed by the project manager or principal investigator [20]. During each development phase, specific products are developed. These products are evaluated, approved, and controlled. Usually, documents are reviewed, and codes are tested. And then, software is finally approved if test results meet acceptance criteria. Reviewing and testing are the primary manners of V&V activities [21]. Verification is a process of ensuring that products developed in a phase meet the requirements defined by the previous phases. Validation is a process of testing software and evaluating results to

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demonstrate that the software meets its requirements as defined in the software requirements specifications (SRS). To sum up, SQA always includes, in addition to code quality, the quality of the procedures, the documentation, and the necessary software data.

3.2 Software development life cycle The software development life cycle (SDLC) is an essential concept in the field of software engineering. It is also called the software life cycle [22] that refers to the structural framework of all the processes, activities, and tasks of software development. Furthermore, the life of software always has two essential characteristics. The first is the sequential development process for a functional unit or one software, whereas the other is the iterative update for a prototype or a previous test version or an earlier release version. There are various SDLC models used for software development, and some typical SDLC models or methodologies have been summarized by previous researchers. These models or methodologies are also referred to as software development process models. As listed in Table 3.2, SDLC models or methodologies include the sequential model (e.g., waterfall model, V-model, and W-model), the iterative methodology (e.g., incremental model, prototype evolution model, rapid prototype model, spiral model, fountain model, rapid application development (RAD) model, and component assembly model), the unified process methodology, the agile development methodology (ADM) (e.g., scrum, extreme programing, feature-driven development, adaptive software development, dynamic system development methods, crystal family methods), and the lean development methodology (LDM). No matter what these SDLC models are, a realistic SDLC always includes one group of basic processes or many groups of essential subprocesses [e.g., requirements analysis (RA), design, coding, and testing]. SDLC has another higher level idea that is regarded as the system development life cycle [53,54]. The concept of the system development life cycle can apply to a system composed of software and/or hardware. Waterfall model is a software development model initially proposed by Winston W. Royce in 1970 [23]. It represents the oldest, simplest, and most structured methodology. The model is essentially a linear sequential model. As shown in Fig. 3.1, it includes several phases of planning, requirements definition, general design (GD), detailed design (DD), implementation, testing, operation, and maintenance. Each stage depends on the outcome of the previous stage, and all stages run sequentially. The model does not work well when flexibility is required. Nevertheless, this model already made a milestone contribution, and it is that it provides basic phase disciplines for the development of any software function unit. Just as Lavoisier first described carbon in the first list of elements, and then the questions of how carbon atoms constitute diamond, graphite, graphene, and amorphous carbon that should be revealed and explained by other later researchers. In Fig. 3.2, a modified waterfall model is described with more detailed phases of implementation and testing. The implementation phase is made up of two substages, that is, components coding (CC) and components integration (CI). The testing phase includes four substages, that is, unit testing, integration testing, system testing, and acceptance testing. If the unit testing is required, it must be set into the stage between CC and CI.

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TABLE 3.2 SDLC models or methodologies proposed by researchers [23 52]. Category

Time

Model or methodology

Sequential model

1970

Waterfall model

1986

V-model

1993

W-model

The 1950s

Iterative method

1971

Incremental model

1980

Prototype evolution model (i.e., prototyping)

1982

Rapid prototype model (i.e., rapid prototyping)

1988

Spiral model

1990

Fountain model

1991

RAD

1996

Component assembly model

1998

RUP

2004

EUP

2006

EssUP

The 1990s

Scrum

Iterative methodology

Unified process methodology

Agile development methodology

XP PP FDD Adaptive software development Dynamic system development methods Crystal family methods Lean development methodology

The 2000s

Kanban

Agile-lean development methodology

The 2000s

Scrumban

EssUP, Essential unified process; EUP, enterprise unified process; FDD, feature-driven development; PP, pragmatic programing; RAD, rapid application development; RUP, rational unified process; XP, extreme programing.

A modified waterfall model in Fig. 3.2 is proposed to emphasize testing activities. For the sake of assuring software quality through testing activities, Paul Rook (1986) [24] had suggested the V-model that evolved from the waterfall model. The V-model can be regarded as a variant from the modified waterfall model shown in Fig. 3.2. The V-model is also viewed as a software testing model (STM). As displayed in Fig. 3.3, a system project plan is generated before starting the development phase. Testing plans (i.e., procedures, cases, and criteria) are written for subsequent testing activities before CC. Acceptance testing plan (ATP) comes from URs. System testing plan (STP) is generated

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FIGURE 3.1 Classical waterfall model.

Planning

Requirements definition

General design

Detailed design

Implementation

Testing Operation and maintenance

FIGURE 3.2 A modified waterfall model.

Planning Requirements definition General design

Detailed design Components coding Unit testing

Implementation

Components integration Testing

Integration testing System testing Acceptance testing Operation and maintenance

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Planning

Operation and maintenance

User requirements

Acceptance testing

Requirements analysis

System testing

General design

Integration testing Components integration Detailed design

Unit testing

Components coding

FIGURE 3.3 V-model.

during the phases of RA and GD. Integration testing plan (ITP) is produced from two phases, that is, GD and DD. Unit testing plan (UTP) is made from the DD phase. Unit testing is used to checking the quality of CC and part of DD. Integration testing is employed to verify the quality of CI and part of GD and the rest of DD. System testing is used for validating the quality of RA and verifying the quality of the rest of the GD. Acceptance testing is employed to validate the quality of URs. The main shortcoming of V-model is that testing activities come into work after CC. Thus initial mistakes in the early phases (i.e., URs, RA, GD, and DD) are not discovered until later testing. The V-model does not explicitly address early testing and fails to embody the principle of “Early and Continuous Software Testing.” To solve the previous limitation of V-model, a W-model was developed by Paul Gerrard (1993) from Evolutif Company [25]. As seen in Fig. 3.4, the W-model is made up of two V-type parts. The left V-type section describes software development processes, while the right one defines software testing processes. The testing activities are carried out synchronously in each development stage of the software. There are stil other important STMs, such as H-model and X-model, that mainly emphasize software testing activities and put little attention to the software development life cycle. Therefore we do not discuss too much about them in this chapter. Usually, actual software development projects rarely follow the linear sequence. Before the establishment of a software system, it is difficult to determine a set of complete, accurate, consistent, and effective URs based on the RA by user and developer. First, user demand is variable. Second, URs are vague. Third, communication difficulties between

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User requirements

UR V&V acceptance test plan Delivery

Requirements analysis

RA V&V system test plan Execution

General design

System testing

GD V&V integration test plan Components integration

Detailed design

Acceptance testing

Integration testing

DD V&V unit test plan

Unit testing Components coding

FIGURE 3.4 Classical W-model.

users and developers. Hence, the SDLC model of overall predefining requirements cannot adapt well to the changing situation of URs. For the sake of solving the limitation of sequential models, various iterative methodologies are proposed, such as the iterative method, incremental model, prototype evolution model, rapid prototype model, spiral model, fountain model, RAD, and component assembly model. In the iterative methodologies, each development cycle produces an incomplete but executable version or prototype of the software. The first iteration implements an incomplete set of the software requirements, and each subsequent version adds more requirements or function modules. The later iteration contains a relatively complete set of requirements. The earliest iterative method had been around since the late 1950s, which was employed in the US Air Force SAGE program led by H. D. Benington [26 28]. In this chapter the software prototype is essentially considered as the transitional software version. Prototyping methods were classified into three types, that is, exploratory prototyping, experimental prototyping, and evolutionary prototyping. Exploratory prototyping is used

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during the RA phase of development to clarify URs, identify desired features, and explore the feasibility of various scenarios. It is mainly aimed at the situation that the development goal is vague, and both the user and the developer are inexperienced in the project. The requirements of the user are clarified through the development of prototypes. Experimental prototyping is mainly used in the design stage to assess whether the implementation scheme is suitable and can be realized. For a complicated system, if we are not sure about the design scheme, this prototype can be used to verify the correctness of the design scheme. Evolutionary prototyping is mainly used to submit a prototype system to the user early, which either contains the framework of the system or contains the main functions of the system and then expands the prototype system into the final software system after the user’s approval. It extends the idea of prototyping to the whole process of software development. The incremental model [29] is divided into different function modules, and each stage completes a specific function. The iterative model divides an SDLC into several stages according to the degree of performance and function refinement. The functions of each stage are improved and enhanced in the iterative model. Thus the iterative model is suitable for projects with unclear requirements and high architectural risks, while the incremental model is suitable for projects with relatively clear requirements and stable architecture. In 1988 Barry Boehm published the spiral model [35]. This model adopts an iterative method to develop the software system. Each cycle consists of four phases: requirements definition, risk analysis, engineering implementation, and review. Spiral model combines the waterfall model and rapid prototype model, which highlights the risk analysis ignored by other models. It allows developers and users to understand the risk of evolution of each iteration cycle, and then to make a proper response, so it is suitable for the large, complex, and high-risk system. Fountain model is proposed by Henderson and Edwards in 1990 [36]. The word fountain itself embodies the characteristics of iteration and no-gap. No-gap means there is no apparent boundary between activities, such as analysis, design, and coding. RA and design are performed before coding, during which functions are added to allow the system to evolve. Fountain model often iterates several times in a part of the system, with the associated objects inserted into the progressive system in each iteration. Because of the introduction of object concepts, phase activities are only expressed by object classes and relationships, which makes the fountain model easier to achieve iterative and seamless activities and makes the development process naturally to include reusing. The fountain model is mainly used for software development projects adopting object-oriented technology. RAD is first proposed by James Martin in 1991 [37]. It is a structured development approach that attempts to generate systems without significant loss of quality quickly. This approach is now widely used in advanced IT communities around the world. RAD’s goal is to build business software that meets URs in a short period of 60 90 days. RAD uses the fourth-generation language instead of the traditional third-generation programing language and makes extensive use of existing or newly created reusable components to construct the entire application system quickly. However, RAD is generally used only for information system development. RAD is not suitable for systems that cannot be modularized appropriately, systems that require high performance, systems that need to adjust component interfaces, and systems with high technical risk. Component assembly model [38] came from the modularization idea. The whole system is modularized, which makes full use of software reusing and improves the efficiency of

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software development. Nevertheless, the lack of general structural standards of component assembly is of high risk. It is not easy to coordinate between component reusability and system efficiency. Because of overreliance on components, component quality can affect the quality of the final software product. Unified process is first proposed by Rational Software Company in 1998, as known as the rational unified process (RUP) [39 41]. Essential unified process [42,43] is a lightweight unified process that can be used as a method for agile development (i.e., agile unified process). Hence, the unified process is often seen as one of the methods of agile development by some expert programers. But here, the unified process is considered as equal methodology as agile development. ADM has been around since the early 1990s. On February 11 13, 2001, “manifesto for agile software development” was emerged by 17 top experts in software engineering [47]. Even though they, respectively, represent different software development methodologies, the common values have been suggested by them. The first value is “individuals and interactions over processes and tools.” The second value is “working software over comprehensive documentation.” The third value is “customer collaboration over contract negotiation.” The fourth is “responding to change over following a plan.” Furthermore, they have proposed 12 principles of ADM. The critical characteristics of ADM are (1) to satisfy the customer, (2) to welcome changing requirements, (3) early and continuous delivery, (4) business people and developers must work together, (5) face-to-face conversation, and so on. It means process flexibility, quick response, active cooperation, and active exchange. The agile methodology produces ongoing release cycles, each version featuring small incremental changes from the previous version. At each iteration cycle the product is tested. The agile methodology helps teams identify and address small defects in projects before they evolve into more significant problems. Teams can also engage business stakeholders and get their feedback throughout the development process. LDM is inspired by lean manufacturing practices and principles that came from the Toyota Motor Corporation since the 1950s [51]. The lean principles encourage creating better flow in work processes and developing a continuous improvement culture. The lean principles are (1) eliminate waste, (2) amplify learning, (3) make decisions as late as possible, (4) deliver as fast as possible, (5) empower your team, (6) embed quality in the process, and (7) optimize holistically. The Kanban is the primary method or tool to carry out the lean development. The Kanban system was first created and used by Toyota. Some experts classify the LDM as one of the ADM. It is not reaching a consensus. In this chapter, LDM is considered as another methodology different from ADM. The Scrumban method was introduced by Corey Ladas in his book “ScrumBan” [52]. It is a more robust method combining the best of agile (i.e., Scrum) and lean (i.e., Kanban). It can be seen as a representative method for Agile-lean development methodology (ALDM). ALDM is a matter of course, evolved from the uniting of ADM and LDM.

3.3 Software quality What is software quality? What and how many attributes or factors are used to define software quality? In 1977 McCall built a model that tried to use a series of attributes to describe software quality [55 58], as shown in Fig. 3.5. Subsequently, Boehm (1978) proposed a similar

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FIGURE 3.5 McCall model (1977).

model [55,59,60], as described in Fig. 3.6. The McCall model had considered quality factors from developer views and user views. The Boehm model put more attention to maintainability. Geoff Dromey suggested another similar model [55,61,62]. His model was made up of three parts. The first part is the product attributes that influence quality. The second part is the high-level quality factors. The third part is the means of linking the product attributes with the quality factors. In 1992 Grady first proposed the FURPS model [55,63 65], and then it was extended to FURPS 1 by Rational Software Company [39,40,66]. The FURPS model includes functionality, usability, reliability, performance, and supportability. On the basis of the models mentioned previously, ISO/IEC 9126 was issued in 1991 [67]. In 2001 ISO/IEC 9126:1991 was replaced by ISO/IEC 9126:2001 [67]. ISO/IEC 9126 quality model (i.e., ISO/IEC 9126-1) mainly describes the internal quality, external quality, and use quality. This model consists of 6 quality attributes and 27 quality factors, as listed in Table 3.3. The quality attributes include functionality, efficiency, usability, reliability, maintainability, and portability.

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FIGURE 3.6 Boehm model (1978). TABLE 3.3 Attributes and factors of software quality model in ISO/IEC 9216:2001 [67]. Functionality

Efficiency

Usability

Suitability

Time behavior

Accuracy Interoperability

Reliability

Maintainability

Portability

Understandability Maturity

Analyzability

Adaptability

Resource utilization

Learnability

Fault tolerance

Changeability

Installability

Efficiency compliance

Operability

Recoverability

Stability

Coexistence

Security

Attractiveness

Reliability compliance

Testability

Replaceability

Functionality compliance

Usability compliance

Maintainability compliance

Portability compliance

ISO/IEC 9126 had been widely used by software engineering and made a tremendous and historical contribution. With the accumulation of practical experience and in-depth understanding, in 2011, ISO/IEC 9126:2001 was replaced by ISO/IEC 25010:2011 [68]. ISO/IEC 25010 is a part of the systems and software quality requirements and evaluation (SQuaRE) series of International Standards. The SQuaRE is based on two related multipart international standards: ISO/IEC 9126 (software product quality) and ISO/IEC 14598 (software product evaluation). It is due to the fact that quality characteristics and associated measures can be useful not only for evaluating a systems and software product but also for defining quality requirements, that is, the uniting of ISO/IEC 9126 and ISO/IEC 14598 that forms a complementary set of standards. Furthermore, both ISO/IEC 9126 and ISO/IEC 14598 have common normative, referential, and functional roots.

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The SQuaRE series of International Standards consists of the following divisions [68]: 1. 2. 3. 4. 5. 6.

Quality management division (ISO/IEC 2500n), Quality model division (ISO/IEC 2501n), Quality measurement division (ISO/IEC 2502n), Quality requirements division (ISO/IEC 2503n), Quality evaluation division (ISO/IEC 2504n), SQuaRE extension division (ISO/IEC 25050 ISO/IEC 25099).

ISO/IEC 25010 has 8 quality attributes (in contrast to 6 quality attributes in ISO/IEC 9126), and 31 quality factors. Compared to ISO/IEC 9126, “security” and “compatibility” are added as main attributes in ISO/IEC 25010, as shown in Table 3.4. It indicates that software compatibility and security have been appreciated by people with the increasing complexity and widespread application of software products. Furthermore, the quality factors in ISO/IEC 25010 are more detailed than those in ISO/IEC 9126. It manifests that people have already got a more profound understanding of the quality factors of software products during the past decade. Besides, as described in Table 3.5, ISO/IEC 25010 has considered the quality of user views. It reveals that user experience and satisfaction have been put more attention by development teams due to commercial purpose and market competition in the past decade. As listed in Table 3.4, functional suitability is the degree to which a product or system provides functions that meet stated and implied needs when used under specified conditions [68]. It includes functional completeness, functional correctness, and functional appropriateness. Performance efficiency is the performance relative to the amount of resources used under stated conditions [68]. It contains time behavior, resource utilization, and capacity. Usability is the degree to which a product or system can be used by specified users to achieve specified goals with effectiveness, efficiency, and satisfaction in a specified context of use [68]. It includes six factors, that is, appropriateness recognizability, learnability, operability, user error protection, user interface esthetics, and accessibility. TABLE 3.4 Attributes and factors of software quality model in ISO/IEC 25010:2011 [68]. Functional suitability

Performance efficiency

Usability

Reliability

Maintainability Portability

Compatibility

Security

Functional completeness

Time behavior

Appropriateness recognizability

Maturity

Modularity

Adaptability

Coexistence

Confidentiality

Functional correctness

Resource utilization

Learnability

Availability

Reusability

Installability

Interoperability Integrity

Functional appropriateness

Capacity

Operability

Fault tolerance

Analyzability

Replaceability

User error protection

Recoverability Modifiability

User interface esthetics

Testability

Accessibility

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Accountability

Authenticity

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TABLE 3.5 Attributes and factors of software quality in use suggested in ISO/IEC 25010:2011. Quality in use Effectiveness

Effectiveness

Efficiency

Efficiency

Satisfaction

Usefulness Trust Pleasure Comfort

Freedom from risk

Economic risk mitigation Health and safety risk mitigation Environmental risk mitigation

Context coverage

Context completeness Flexibility

Reliability is the degree to which a system, product, or component performs specified functions under specified conditions for a specified period of time [68]. It is made up of four factors, that is, maturity, availability, fault tolerance, and recoverability. Maintainability is the degree of effectiveness and efficiency with which a product or system can be modified by the intended maintainers [68]. It consists of modularity, reusability, analyzability, modifiability, and testability. Portability is the degree of effectiveness and efficiency with which a system, product, or component can be transferred from one hardware, software, or other operational or usage environment to another [68]. It includes adaptability, installability, and replaceability. Compatibility is the degree to which a product, system, or component can exchange information with other products, systems, or components and/or perform its required functions while sharing the same hardware or software environment [68]. It is composed of coexistence and interoperability. Security is the degree to which a product or system protects information and data so that persons or other products or systems have the degree of data access appropriate to their types and levels of authorization [68]. It consists of five factors, that is, confidentiality, integrity, nonrepudiation, accountability, and authenticity. Software product quality models provide a high-level overview of what needs to be considered in product design and development. Nowadays, ISO/IEC 25010 software quality model is widely adopted by software development teams.

3.4 Software quality assurance for nuclear engineering SQA is a systematic and planned set of actions necessary to provide adequate confidence that the software development process or the software maintenance process

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conforms to establish technical requirements as well as the managerial requirements of keeping the schedule and operating within the budgetary confines [20,69,70]. SQA makes the development and maintenance processes visible and traceable to software project managers. It verifies requirements compliance by testing, reviewing, and auditing software products and development activities [20,69 71]. This requires the SQA team to work together with the development team at the beginning of the project to establish plans, standards, and processes. The idea of total quality management has been employed for SQA, which conforms to the principle of “the sooner defects are found, the sooner they are corrected, the more economical the project” in software engineering. The critical characteristics of SQA include (1) systematic and planned activities (i.e., overall process), (2) independent review mechanism, (3) objectively verify that software products and development efforts follow appropriate standards and procedures as well as requirements, (4) require a thorough testing effort, (5) visible and traceable documental records, (6) duly inform relevant groups and individuals about SQA results, and so on. The SQA job itself is challenging. It requires the SQA team to know about software engineering, software development, industry background, mathematical statistics, project management, quality management. People skills are also needed for the SQA job. To some extent the independent full-process SQA review mechanism is a product of the waterfall model in the early time. With the development of modern software development technology (i.e., iterative methodologies and ADM), the SQA review mechanism is quietly changing. This change is from full-process SQA to part-time SQA throughout the process. The part-time SQA is also allowed to use in the capability maturity model integration model. Why did this change? Whether it is XP, RUP, or other advanced SDLC methodologies, the software prototype is first generated and then incrementally developed until it is complete. In this pattern, requirements and design defects are identified and fixed early in each iteration, quality is built into the architecture and process, and project cost and schedule are guaranteed. At this point, will independent full-process SQA cease to exist? In fact, some specific industries or special projects still need it, such as the nuclear power industry, mainly to ensure the effectiveness of process execution and the objectivity of evaluation. The V-model is recommended by safety standards such as IEC 61508, IEC 62278, EN 50126, and EN 50128 for safety-related systems [72,73]. As discussed in Section 3.2, W-model evolved from V-model to assure V&V for the early phases. Hence, at present, W-model is the most rigorous SDLC option for independent full-process SQA for safety-related software or system development, such as nuclear power engineering software and reactor safety protection system. In this section, W-Model is employed to introduce an implementation framework of QA of nuclear power engineering software.

3.4.1 Implementation framework As shown in Fig. 3.7, the W-model is looking as a double-V model. The first V describes the basic procedures of software development mostly conducted by the development team. At the same time, the second V emphasizes the corresponding V&V activities mainly conducted by the SQA team. Each necessary software development phase has its V&V activities.

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User requirements

UR V&V Acceptance test plan

Acceptance testing Requirements analysis

RA V&V system test plan System testing

General design

GD V&V integration test plan Integration testing

Detailed design

DD V&V unit test plan

Components coding

Unit testing

FIGURE 3.7 Modified W-type model used for SQA of nuclear power engineering. SQA, Software quality assurance.

In the initial phase, URs are proposed; at the same time, the corresponding acceptance test plan (ATP) is put forward. And then, the V&V activities for URs are carried out by the SQA team. Usually, the URs V&V is implemented by means of expert review. In the requirements definition phase, the development team analyses URs, and then the SRS and the most part of the STP are compiled. Subsequently, the V&V activities for RA are carried out. The RA V&V is also executed by way of expert review. In the software design phase, the software design and implementation document is written out. The most part of the ITP and a little part of STP are made by the development team in GD phase. And then, the UTP and a little part of ITP are made by the development team in the DD phase. Usually, the relevant V&V activities for GD and DD are still carried out by the method of expert review. After the DD phase the work of CC is implemented. Unit testing is the corresponding V&V activity, and UTP has been made from the design phase. After the CC phase, the task of CI is executed. The integration testing is the corresponding V&V activity, and ITP has been made from the design phase too.

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After the CI phase the execution phase of the software product is carried out. System testing is a relevant V&V activity. The most part of STP came from the RA phase and a little from GD phase. After the system testing phase, the procedure of software development shifts into the delivery phase. If the results of acceptance testing conform to ATP and acceptance criteria, then the official version of the software product is delivered to the user.

3.4.2 Verification and validation Elements of SQA are listed in Table 3.6. It indicates that V&V activities are core actions of SQA, and the key means of V&V activities are documental review and program testing. Usually, each phase of SDLC has its special review documents, that is, review checklists or testing reports. For an identical review task, different V&V team has different review checklists due to different experience them own. The testing activities should have suitable test matrixes (i.e., test cases) and corresponding assessment criteria. Requiring a thorough testing effort is one of the key characteristics of SQA. It means that the review items in the checklists and test cases in the test matrixes must cover all situations if possible. Besides, while some physical mechanisms or operational mechanisms are unclear in a physical or functional model, sensitivity analysis (SA) and uncertainty analysis (UA) are two useful methods to evaluate the performance bounds of interesting variables or models. Basing on the results of SA and UA, the performance or quality of a model (i.e., a subroutine or a module) and even software can get a much more comprehensive V&V. Nevertheless, there are always some situations that we cannot realize. Therefore what we can do is to follow the existing standards in the world and the ripe experience from expert teams. TABLE 3.6 Elements of software quality assurance (SQA). Life cycle

Development products

Initial planning

V&V activities

System project plan, SQA plan

Management review

Requirements definition

URs

Acceptance test plan, UR review checklists

UR review

RA

SRS, STP Part1, RA review checklists

RA review

Program design

GD

General SDID, STP Part2, ITP Part1, GD review checklists

GD review

DD

Detailed SDID, ITP Part2, UTP, DD review checklists

DD review

Components coding

Module or subroutine source code, unit testing report

Source code review, unit testing

Components integration

System source code, integration testing report

Source code review, Integration testing

Execution

System testing report

System testing

Delivery

Acceptance testing report

Acceptance testing

Coding activities

DD, Detailed design; GD, general design; RA, requirements analysis; SDID, software design and implementation document; SRS, software requirements specifications; UR, user requirement.

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3.5 Summary This chapter is devoted to introducing the foundational knowledge of SQA, which can be referred to as the development and maintenance of nuclear power engineering software. In this chapter, we have discussed several significant events due to software defects, they tell us that some defects in software would be fatal, so SQA is a vital job for safetyrelated system development. Then, we have introduced various SDLC models and different software quality factors. Even though an excellent software product should theoretically have a good performance on every quality factor, considering application requirements and budget constraints, not the entire group of quality factors must be focused during software development processes. The W-model is recommended for the quality assurance of nuclear engineering software due to two reasons. The first reason is that nuclear power engineering software emphasizes functional suitability and reliability. The second reason is that the W-model has a distinct and traceable phase characteristics, and V&V activities are rigorously defined in the W-model.

References [1] IAEA, IAEA Technical Reports Series No. 384. Verification and Validation of Software Related to Nuclear Power Plant Instrumentation and Control, 1999. [2] IAEA-Tecdoc-1565, Validation Procedures of Software Applied in Nuclear Instruments, 2007. [3] IEC 60880-2006, Nuclear Power Plants—Instrumentation and Control Systems Important to Safety—Software Aspects for Computer-Based Systems Performing Category A Functions, 2006. [4] IEEE Std610.12-1990, IEEE Standard Glossary of Software Engineering Terminology, Corrected Edition, 1991. [5] D. Galin, Software Quality Assurance From Theory to Implementation, Pearson Education, 2004. [6] J.D. Strate, P.A. Laplante, A literature review of research in software defect reporting, IEEE Trans. Reliab. 62 (2) (2013) 444 454. [7] W.E. Wong, A. Bertolino, V. Debroy, et al., Teaching software testing: Experiences, lessons learned and the path forward, in: 24th IEEE-CS Conference on Software Engineering Education and Training, CSEE&T 2011, May 22 24, 2011, Waikiki, Honolulu, HI, Proceedings, IEEE, 2011. [8] D. Isbell, M. Hardin, J. Underwood, NASA jet propulsion laboratory, mars climate orbiter team finds likely cause of loss, NASA News Release, September 30, 1999. [9] A.G. Stephenson, L.S. LaPiana, D.R. Mulville, et al., MCO MIB. Mars Climate Orbiter Mishap Investigation Board Phase I Report, 1999. [10] J.L. Lions, ARIANE 5 Flight 501 Failure Report by the Inquiry Board, Paris, 1996. [11] J.M. Jazequel, B. Meyer, Design by contract: the lessons of Ariane, Computer 30 (1) (1977) 129 130. [12] R. Wanderer, Just a second, ETC: A Review of General Semantics, 48 (3) (1991) 318 319. [13] G. Hart, B. Goldwater, Recent False Alerts from the Nation’s Missile Attack Warning System: Report of Gary Hart and Barry Goldwater to The Committee on Armed Services, United States Senate, 1980. [14] G. Forden, P. Podvig, T.A. Postol, False alarm, nuclear danger, IEEE Spectr. 37 (3) (2000) 31 39. [15] N.G. Leveson, C.S. Turner, An investigation of the Therac-25 accidents, Computer 26 (1993). [16] S. Vatnitsky, L.P. Ortiz, J. Izewska, et al., The radiation overexposure of radiotherapy patients in Panama 15 June 2001, Radiother. Oncol. 60 (3) (2001) 237 238. [17] C. Borra´s, Overexposure of radiation therapy patients in panama: problem recognition and follow-up measures, Rev. Panam. Salud Pu´blica 20 (2 3) (2006) 173 187. [18] T. Heine, An analysis of Boeing’s image repair efforts. ,https://www.suu.edu/hss/comm/masters/capstone/thesis/heine-t.pdf., 2019. [19] P. Johnston, R. Harris, The Boeing 737 MAX SAGA: lessons for software organizations, Softw. Qual. Prof. 21 (2019). [20] NUREG-1737, Software Quality Assurance Procedures for NRC Thermal Hydraulic Codes, 2000.

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[21] IEEE Std1012-2016, IEEE Standard for System and Software Verification and Validation, 2016. [22] R. Singh, International standard ISO/IEC 12207 software life cycle processes, Softw. Process: Improv. Pract. 2 (1996) 35 50. [23] W.W. Royce, Managing the development of large software systems, in: IEEE WESCON, IEEE, 1970. [24] P. Rook, Software Reliability Handbook, 1990. Elsevier Science Inc. [25] P. Gerrard, A Unified Approach to System Functional Testing, 1993. [26] R.R. Everett, C.A. Zraket, H.D. Benington, SAGE—a data processing system for air defense, IEEE Comput. Soc. 5 (1983). [27] R.R. Everett, C.A. Zraket, H.D. Benington, SAGE: a data-processing system for air defense, in: Papers & Discussions Presented at the December, Eastern Joint Computer Conference: Computers With Deadlines to Meet, ACM, 1957. [28] H.D. Benington, Production of large computer programs, Ann. Hist. Comput. 5 (4) (1983) 350 361. [29] H.D. Mills, Software development, IEEE Trans. Softw. Eng. 2 (4) (1976) 265 273. [30] H.E. Keus, Prototyping: a more reasonable approach to system development, ACM SIGSOFT Softw. Eng. Notes 7 (5) (1982) 94 95. [31] S.M. Feather, Mappings for rapid prototyping, ACM SIGSOFT Softw. Eng. Notes 7 (5) (1982) 17 24. [32] P.R. Hanau, D.R. Lenorovitz, A Prototyping and Simulation Approach to Interactive Computer System Design, 17th Design Automation Conference, Minneapolis, MN, USA, 1980, pp. 572 578. Available from: https://doi.org/10.1109/DAC.1980.1585304. [33] C. Heitmeyer, C. Landwehr, M. Cornwell, ACM Press the workshop—Columbia, Maryland (1982.04.19 1982.04.21), in: Proceedings of the Workshop on Rapid Prototyping, The Use of Quick Prototypes in the Secure Military Message Systems Project, 1982, pp. 85 87. [34] M.A. Stavely, ACM press the workshop—Columbia, Maryland (1982.04.19 1982.04.21), in: Proceedings of the Workshop on Rapid Prototyping, Models as Executable Designs, ACM SIGSOFT Softw. Eng. Notes 7, 1982, 167 168. [35] B.W. Boehm, A spiral model of software development and enhancement, Computer 21 (5) (1988) 61 72. [36] S.B. Henderson, J.M. Edwards, The object-oriented systems life cycle, Commun. ACM 33 (9) (1990) 142 159. [37] J. Martin, RAD cycle in manageable phases, PC Week Asia, 1992. [38] J.Q. Ning, A component-based software development model, in: COMPSAC’96—20th Computer Software and Applications Conference, Seoul, Korea, IEEE, 1996. [39] I. Jacobson, G. Booch, J. Rumbaugh, The Unified Software Development Process, Addison Wesley, 1999. [40] P. Kruchten, The Rational Unified Process: An Introduction, Addison Wesley, 2000. [41] A. Anwar, A review of RUP (rational unified process), Int. J. Softw. Eng. 5 (2014). [42] S. Ambler, J. Nalbone, M. Vizdos, Enterprise Unified Process, The Extending Rational Unified Process, 2005. Prentice Hall Press. [43] A. De Nicola, M. Missikoff, R. Navigli, A proposal for a unified process for ontology building: UPON, Comput. Sci. (3588) (2005). [44] I. Jacobson, P.W. Ng, I. Spence, The Essential Unified Process—A Fresh New Start, 2006. Doctor Dobbs Journal. [45] G.K. Hanssen, F.O. Bjørnson, H. Westerheim, Tailoring and introduction of the rational unified process, in: P. Abrahamsson, N. Baddoo, T. Margaria, R. Messnarz (Eds.), Software Process Improvement, EuroSPI 2007, Lecture Notes in Computer Science, vol. 4764, Springer, Berlin, Heidelberg. [46] Y. Hui, Y. Yan, W. Quanyu, C. Zhiwen, Compare essential unified process (EssUP) with rational unified process (RUP), in: 2015 IEEE 10th Conference on Industrial Electronics and Applications (ICIEA), Auckland, 2015, pp. 472 476. [47] Agile Manifesto, ,http://www.agilemanifesto.org/., 2001. [48] P. Abrahamsson, et al., Agile Software Development Methods: Review and Analysis, vol. 478, VTT Publication, 2002. [49] M.A. Khan, A. Parveen, M. Sadiq, A method for the selection of software development life cycle models using analytic hierarchy process, in: 2014 International Conference on Issues and Challenges in Intelligent Computing Techniques (ICICT), IEEE, 2014. [50] K. Beck, Extreme programming: a humanistic discipline of software development, in: International Conference on Fundamental Approaches to Software Engineering, ACM, 1999.

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[51] D.I.K. Sjoberg, A. Johnsen, J. Solberg, Quantifying the effect of using Kanban versus scrum: a case study, IEEE Softw. 29 (5) (2012) 47 53. [52] C. Ladas, Scrumban—Essays on Kanban Systems for Lean Software Development, 2009. Modus Cooperandi Press. [53] R.G. Sabale, A.R. Dani, Comparative study of prototype model for software engineering with system development life cycle, IOSR J. Eng. (2012). Available from: https://doi.org/10.9790/3021-02722124. [54] ID Network, QuickStudy: System Development Life Cycle, Computerworld, 2002. [55] D. Samadhiya, S.-H. Wang, D. Chen, Quality models: role and value in software engineering, in: 2010 Second International Conference on Software Technology and Engineering, 2010, pp. 320 324. [56] J.A. McCall, P.K. Richards, G.F. Walters. Factors in software quality: concept and definitions of software quality, in: RADC-TR-369, vol. I, RADC AFSC, Griffis Air Base, New York, 1977. [57] J.P. Cavano, J.A. McCall, A Framework for the Measurement of Software Quality, ACM, 1978. [58] G.F. Walters, J.A. McCall, Software quality metrics for life-cycle cost-reduction, IEEE Trans. Reliab. 28 (3) (1979) 212 220. [59] B.W. Boehm, Software engineering—as it is, in: Proceedings of the Fourth International Conference on Software Engineering, IEEE Press, 1979. [60] B.W. Boehm, J.R. Brown, M. Lipow. Quantitative evaluation of software quality, in: Second International Conference on Software Engineering, 1976, pp. 592 605. [61] R.G. Dromey, A model for software product quality, IEEE Trans. Softw. Eng. 21 (2) (1995) 142 162. [62] R.G. Dromey, Cornering the Chimera [software quality], IEEE Softw. 13 (1) (1996) 33 43. [63] R.B. Grady, Practical Software Metrics for Project Management and Process Improvement, 1992. PrenticeHall Inc. [64] R.B. Grady, Practical results from measuring software quality, Commun. ACM 36 (11) (1993) 62 68. [65] R.B. Grady, Measuring and managing software maintenance, Softw. IEEE 4 (5) (1987) 35 45. [66] A.-O. Fahad, A. Ali, Towards customized smart government quality model, Int. J. Softw. Eng. Appl. 9 (2018) 41 50. [67] ISO/IEC 9126, Software Product Evaluation—Quality Characteristics and Guidelines for Their Use, International Organization for Standardization, Geneva, 2001. [68] ISO/IEC25010, Systems and software engineering—Systems and software Quality Requirements and Evaluation (SQuaRE)—System and software quality models, International Organization for Standardization, 2011. [69] NUREG/BR-0167, Software Quality Assurance Program and Guidelines, 1993. [70] NUREG/CR-4640, Handbook of Software Quality Assurance Techniques Applicable to the Nuclear Industry, 1987. [71] NRC, Inspection manual/procedure 35710, in: Quality Assurance Inspection of Software Used in Nuclear Applications, 2018. [72] M.S. Durmu¸s, et al., Enhanced V-model, Informatica (42)(2018) 577 585. [73] IEC 61508, Functional Safety of Electrical/Electronic/Programmable Electronic Safety-Related Systems, IEC, 2010.

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C H A P T E R

4 Multiphysics coupling plan Miao Gui1 and Xingang Zhao2 1

School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, Shaanxi P.R. China 2 Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States

4.1 Introduction Numerical simulation method is an important way to predict the various physical phenomena in nuclear reactor system and plays a key role on both the reliability of design and the improvement in safety of nuclear reactor. However, when it comes to nuclear reactor analysis, the complexity of those archetypal multiphysics phenomena makes it an extremely challenging problem. Multiphysics can be defined as solving two or more physical models simultaneously in order to resolve interdependent nonlinearities between the models [1]. In a light water reactor (LWR) system, the simulations under steady state and transient conditions are an exceptionally complex multiphysics task with the interacting multiple physical principles occurring simultaneously, involving microstructural evolution of materials, plasticity, creep, neutronics product and transport, conjugate heat transfer, nucleate boiling, and others [2]. Traditionally, all the involved physical phenomena in nuclear reactor are analyzed separately by using some extensively validated and verified simulation codes, but the interacting of multiphysics is usually described in a simplified way. For example, the static-critical neutronics behavior in reactor core is usually analyzed either solving the steady-state eigenvalue form of the neutron transport equation in a deterministic way or simulating the corresponding physics in a stochastic (Monte Carlo) way, with the thermal-hydraulic (T-H) conditions fixed. Meanwhile, the T-H behavior of the reactor core is analyzed using a variety of T-H solvers and codes in various levels, including system level, subchannel, and computational fluid dynamics (CFD), while in this case the neutronics conditions (power distribution) are regarded as known. However, neutronic and T-H phenomena are strongly bonded in the reactor core analysis. The distribution of the neutron flux can determine the heat source of the thermal hydraulics, simultaneously the T-H parameters feedback to the neutronics calculation through neutron cross sections [3]. Even if only

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00004-8

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the neutronic flux and T-H phenomena are considered, these two strongly bonded sections will vary by several orders of magnitude resulting from some nonlinear interdependencies. This interrelation indicates that the accurate analysis of nuclear reactor needs the simulation conjointly considering all the relevant multiphysics phenomena occurring in the entire nuclear reactor system. In recent years the continuously increasing computer power in combination with the new more advanced numerical methods allows the performance of more detailed and hence more complex calculations, which makes multiphysics simulations of nuclear reactor systems are a rapidly growing field of interest. Based on the mature development of the state-of-the-art single-physics simulation codes in the past decades, the multiphysics coupling shows the great importance to solve the multiphysics problems when modeling an operating nuclear reactor. Multiphysics coupling can be defined as that two or more single-physics codes that have been coupled together to simulate a multiphysics system, with information transferred between each codes during the solution process. In view of this the coupling work can be carried out based on preexisting computation codes that are embedded as individual components to information through a limited set of interfaces and is operated using generic functionalities. It is beneficial to making use of the past results achieved in nuclear simulations and greatly reducing programming effort. Since entering the 21st century, worldwide efforts have been made to develop high-fidelity multiphysics coupling simulation for nuclear reactor design and safety analysis. In addition, multiphysics coupling is also proposed as a hot topic at the Generation IV International Forum to meet the need for sophisticated codes capable of performing both multiphysics and multiscale analysis of the GENIV reactors [4]. The main motivation of this chapter is to introduce the current status of the multiphysics coupling method and work in nuclear reactor analysis and help the readers to know the main perspectives in these fields. In the second section, some mainstream multiphysics coupling methods are summarized. In the third section, it presents some influential existing works in these fields. Finally, in the last section, the future challenges and developments are discussed.

4.2 Multiphysics coupling methods 4.2.1 Operator splitting methods The purpose of the multiphysics coupling methods is to combine the multiphysics problems, which are obtained by numerical solvers of the separate sets of partial differential equations (PDEs) of the different physical phenomena of interest, into one single solution scheme [5]. In such segregated configuration the different sets of PDEs cannot be solved simultaneously, because each set of PDEs is to be applied as the boundary condition to the other one. To overcome this problem, operator splitting (OS) methods were developed as a tool employed to solve numerically PDEs describing multiphysical phenomena with different nature. The first OS method was proposed by Chorin in his projection method to solve the incompressible nonstationary Navier
Stokes equations by decoupling the pressure and velocity fields and solving them iteratively within one single time step [6]. An OS method generally follows the “divide-and-conquer” strategy, where the set of PDEs of the multiphysical problem is split into several simpler subproblems. Each subproblem represents a particular physical phenomenon, such as convection, diffusion,

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and boiling, and can be discretized independently. Hence, the corresponding numerical algorithms can be individually defined as a sequence of solutions for each of the subproblems. After one-time step iteration on a subproblem, the partial solutions of this subproblem are regarded as the new estimation of the boundary conditions and derivatives of the other subproblem. That is to say, in most OS method, an explicit coupling of the physics codes is performed, in which solution is exchanged between each physics’ field at every time step as only the boundary conditions of the other physics. The general scheme of the OS method can be concluded in the following [7]: 1. A small time step(s) is selected to divide the whole time interval into subintervals of equal duration. 2. On each subinterval the time-dependent problems are consecutively solved, each of which involves only one physical problem. 3. The next time subinterval then follows. It should be noted that the different physics problems involved in the multiphysics simulation are connected through the initial conditions. The first problem is solved by the first operator and the original initial condition, and then the solution of the first problem at the end point of the time subinterval is applied as initial condition of the second one. A typical neutronic/T-H coupling problem solved by OS method is illustrated in Fig. 4.1 [4]. The main advantage of this OS method for multiphysics coupling of nuclear reactor is that the already developed and validated codes can be employed to solve each part of the original multiphysics field separately, and very limited modifications in these codes are required to implement the coupling scheme. This can lead to a very efficient way with the effort required significantly lower. As a result, most of the existing code coupling work on nuclear reactor system applies the OS coupling method. On the other hand, a significant drawback of the OS coupling method is that the inconsistent treatment is employed to deal with the nonlinear terms owing to the explicit treatment of the coupling terms. This coupling method is generally referred to as “weak coupling” due to the fact that the solution of the one of the coupled codes is treated as the input of the other one without converging the nonlinear terms over the time step, which induces the numerical

FIGURE 4.1 A typical OS method scheme used in a neutronic/T-H coupling problem [4]. OS, Operator splitting; T-H, thermal-hydraulic.

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instability. It has been proved that the OS method is first-order temporal accuracy in time because of the first-order transfer of nonlinearities resulting from the explicit treatment of the coupled terms. In order to eliminate this inaccuracy, smaller time step is required for the convergence of the solution, which results in a large CPU time use as well as computational costs.

4.2.2 Jacobian-free Newton
Krylov methods Since the traditional OS method used in nuclear reactor multiphysics modeling has limitation in the improvement of numerical stability and accuracy, it is a logical place that some new coupling techniques are attempted. As a result, a methodology, the Jacobianfree Newton
Krylov (JFNK) method, that is an approximation of the original Newton method trying to alleviate the problem of the calculation of the “expensive” Jacobian matrix is developed for multiphysics coupling in nuclear reactor modeling [8]. The JFNK method is a modern fully implicit method of solving nonlinear systems of equations, which can achieve a tight convergence tolerance without splitting or linearization error, as shown in Fig. 4.2 [9]. This method significantly differs from the traditional OS methods. It is based on a nonlinear iterative method (Newton method) applied to a residual equation res(u) 5 0 of the all set of multiphysics PDEs, in which each Newton step is solved iteratively using a linear decomposition on a Krylov vector base. This JFNK method uses the Newton and Krylov methods to solve a given set of nonlinear equations effectively and accurately. Each time step of the JFNK method is composed by three main parts: the “external” Newton iteration, the “internal” Krylov iteration, and the preconditioning part. According to [8], an extra globalization method is often employed outside of the Newton part. Recently, owing to the advantages of this method, nuclear technology has been oriented in using the JFNK method in multiphysics coupling [4]. A simple calculation process of JFNK method is shown in Fig. 4.3. First, a system of the nonlinear equations is transformed into the form of a residual equation, and A Newton iterative is then formulated to reduce the residual, making it into a linear one. Generally, the major drawback of the Newton iterative method is that the calculation of the Jacobian matrix for each element by using analytic techniques or discrete derivatives is a computationally intensive procedure, which can also introduce errors [4]. Therefore, in the JFNK method, the nonlinear iteration is not calculated directly, which means that the Jacobian matrix is neither

FIGURE 4.2 Scheme for an implicit coupling of the neutronics and the thermal hydraulics [9].

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FIGURE 4.3 Simplified flowchart of the JFNK method [4]. JFNK, Jacobian-free Newton
Krylov.

formed nor inverted at each iteration step. Instead, the Krylov iteration method is applied to minimize the residual r within each Newton iteration. The main feature of Krylov methods making the JFNK methods suitable for use is that only matrix
vector needed to product and the “expensive” creation of the Jacobian matrix can be avoided. In addition, the preconditioning process is usually implemented, aiming to reduce the number of Krylov iterations, improve the numerical efficiency of the JFNK method, minimize the storage of Krylov vectors, and reduce physical memory computational cost. Preconditioning is a process that approximates the inverse of the Jacobian matrix. A good preconditioner P should lead to eigenvalues of JP21, which are sufficiently clustered. This leads to the minimization of Krylov iterations needed until convergence is achieved. The main advantage of JFNK is that it substitutes the construction of the Jacobian matrix by the calculation of the effect of the Jacobian matrix on a vector, which makes it possible to use the implicit nonlinear iterative method for multiphysics coupling in nuclear reactor modeling, with higher accuracy than OS method. However, when a JFNK method was used

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for the coupling of two distinct codes, quite extensive modification would be applied on their source codes in order to calculate the required residuals, which creates more work.

4.2.3 Approximate block Newton methods When the JFNK method is applied for coupling, the residuals of all the variables of the coupled sets of PDE should be formed and recorded simultaneously at each step of the Newton iterations, and all the equations should be reassembled into one single set of PDEs [5]. When it comes to coupling existing codes by the JFNK method, significant modifications of the codes are requisite unless the solvers are already based on JFNK methods. Hence, another coupling methodology, referred to as approximate block Newton (ABN) methods, is proposed for the purpose of modularity and simpler implementation. The ABN method can be treated as a modified and approximate version of the JFNK method, which aims to eliminate the features of the JFNK method that make its implementation in the coupling of different solvers difficult or even impossible [3]. The original idea of ABN method was proposed by Chan [10], to derive an approximate Newton method for solving the coupled nonlinear problem based on the solvers of each subproblem. In this method, different solvers for coupling can be considered as black-box solvers, which is significantly beneficial to inherit from the development and the validation work made on these existing solvers. After years of development, various of derivation and description of ABN methods have been presented, but any ABN method is developed on the basis of the same strategy that the coupling problem is rewritten to a Newton solution procedure with only iterations of the original solvers, that is fixed-point iteration, needed. Based on the topic of this section, only one ABN method, referred to as ABN-J method, will be introduced here. The coupling procedure of ABN-J method is formulated as follows [5]:
 n11 5 F xn11 xk11 k ;y (4.1)
 n11 yk11 5 G x; ykn11 k 5 1; 2; . . . where F and G are two solvers, with one-time step for variables x and y advanced and coupled variables y and x used as parameters, respectively. It should be noted that variables at the previous time step, xn and yn, which are also arguments of solvers, are omitted in the previous expressions. The coupling problem can be rewritten to a residual form, as shown in the following:
 
 f
x; y 5 x 2 F
x; y 5 0 g x; y 5 y 2 G x; y 5 0 then a Block-Newton method can 0 @f B @x B B @g @ @x

be constructed out of it: 1 @f     @y C f C Δx 52 @g C Δy g A @y

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(4.2)

(4.3)

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because the derivatives of f and g may not be available in the black-box coupling process, one approach that left-precondition the system by using the Jacobian inverses of the subproblems is applied in order to eliminate the need of computing the Jacobian blocks, shown as follows: 0

@f 21 B @x B B B @ 0

10 0 21 1 @f @f @f 0 C B @x  C @x @y CB B C Δx CB 52B B @g @g C B @g21 C @ A Δy A @ 0 @x @y @y

1 0 C  C f C 21 C g @g A @y

(4.4)

Eq. (4.4) can be reconstructed by a Gauss elimination method: 

I C 0 S



Δx Δy

 52

  q r

(4.5)

where C 5 ð@f=@xÞ21 ð@f=@yÞ, S 5 I 2 ð@g=@yÞ21 ð@g=@xÞC, q 5 ð@f=@xÞ21 f, r 5 ð@g=@yÞ21 g 2 ð@g=@yÞ21 ð@g=@xÞq. The advantage of Eq. (4.5) is that the update in Δy can be solved separately and can be contained in the equation of Δx to solve the entire coupling system at each Newton iteration [5]. Meanwhile, it should be noted that the “the coupling-derivatives”, that is, the partial derivatives of f and g in the direction of their coupled variables, in expressions of C, S, and r, make it difficult to be solved. To get around this problem, two approximations are made [5]: 1. Taylor expansion is used to express “the coupling-derivatives” of f and g in the expressions of S, C, and r. 2. SΔy 5 2 r is not solved by Δy directly but using a Newton
Krylov method. Therefore the action of S and C on a Krylov vector v is approximated as follows [11]: 8  21 @f 


1  @f 21
@f > > v Cv 5 @x f x; y 1 εv 2 f x; y > < @y ε @x > > > : Sv 5 v 2



@g @y

21 @g @x

Cv  v 1




1  @g 21
g x; y 2 εCv 2 g x; y @y ε

(4.6)

and then r can be expressed by taking q as the increment for the Taylor expansion of g in the direction of x:   21  21 
 @g @g @g r5 g2 q  g x 1 q; y @y @x @y

(4.7)


21 expressions of Cv, Sv, and r, with only terms in the form of @f=@x f or
The new 21 @g=@y g, can be approximated using F and G by means of a Newton iteration in

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Eq. (4.2). Meanwhile, according to Eq. (4.1), the variables x and y at iteration k 1 1 are approximated by one fixed-point iteration of F and G, respectively [5]: 8 
21

 @f > > x 5 x 2 x ; y f xk ; y 5 F xk ; y k k < k11 @x (4.8) 
21

 > @g > y 5 G x; y 5 y 2 x; y g x; y : k11 k k k k @y This substitution in ANB method is not always accurate, since the x and y arguments of f and g in Eqs. (4.6) and (4.7) are not always taken at the same location as those of their respective derivative inverses [5]. However, the error of Cv and Sv caused by this substitution can be estimated by ε. Simultaneously, the error of r is commensurate with the shift q, which also tends to 0 as the solution converges. From the above the ABN-J method can be decomposed as follows [5]: For each time step For each Newton iteration i
 1. Compute q 5 xi 2
F xi ; yi 2. Compute G 5 G xi ;
yi  3. Compute r 5 yi 2 G xi 1 q; yi 4. Solve SΔy 52 r for Δy for a given tolerance using a GMRES method, with:  


 1 @f 21
f xi ; yi 1 εv 2 f xi ; yi Cv 5 ε @x  


 1 @g 21
Sv 5 v 1 g xi ; yi 2 εCv 2 g xi ; yi ε @y
 5. Compute yi11 5 yi 1 Δy and xi11 5 F xi ; yi11 6. Check for convergence End Newton iteration End time step It can be seen that the ABN methods can divide a large system into some smaller blocks, resulting in inverting a smaller matrix compared to that of the JFNK methods. Meanwhile, the conservations of the “black-box” nature of the solvers coupled by the ABN methods are attractive. For the implementation of an ABN-J method into existing codes, creating a functionality should be created to perform a single iteration of the outer convergence loop of a solver and the result is reformulated as a fixed-point problem [5].

4.3 Current status of research in multiphysics coupling 4.3.1 Neutronic and thermal-hydraulic code-to-code coupling As LWRs have been developed for some decades, many attempts in coupling neutronic and T-H codes have been made to perform more accurate numerical simulation of LWRs. Here some typical examples are presented.

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In Aghaie et al. [12] a package named IRTRAN for steady state and transient analysis of pressurized water reactors (PWRs) was developed by coupling the neutronic modules WIMS and CITATION and a reactor kinetics equation solver along with the RELAP5/3.2 T-H module. In order to assess the accuracy of IRTRAN results, the drop of a control rod transient case was calculated. In addition, the reactivity coefficients of Bushehr Nuclear Power Plant that is a VVER-1000 were simulated. The obtained transient results agreed well with the published data. Davis et al. [13] present an external multiphysics coupling work to predict the hydrogen distribution in fuel cladding by coupling the subchannel code COBRA-TF (CTF) to the neutronic code DeCART and a fuel performance code BISON. In their work a 4 3 4 array of fuel rod bundle with zircaloy cladding developed with DeCART was modeled in CTF. The power distribution was calculated by DeCART and was used as for input in CTF. Also, in order to calculate temperature and stress distributions in the cladding, coolant temperature distribution from CTF and power distribution from DeCART were used in BISON. In Ellis et al. [14], Purdue Advanced Reactor Core Simulator code, which solves the steady state and time-dependent, multigroup neutron diffusion and transport equations in orthogonal and nonorthogonal geometries, was coupled by an implicit steady-state solution method to the T-H system code TRACE, which aims to analyze large/small break loss-of-coolant accidents (LOCAs) and system transients in LWRs. In addition, an implicit steady-state solution used to couple these two codes for solving an implicit transient problem was also described in detail. In Grahn et al. [15] an code coupling work between the three-dimensional (3D) neutron kinetics core model DYN3D and the commercial, general-purpose CFD software ANSYS-CFX was presented. During the coupling, parts of the T-H calculation were replaced by CFX in order to better simulate the 3D coolant redistribution in reactor core, while the heat transfer from the fuel into the coolant was still calculated by DYN3D. In the CFX calculation the reactor core region was simulated based on the porous body approach. Besides, the performance of code coupling was verified by comparing test case results with reference solutions of the DYN3D stand-alone version. The test cases covered mini and full-core geometries, control rod movement, and partial overcooling transients [15]. Leppa¨nen et al. [16] published an article to introduce the 4-year numerical multiphysics (NUMPS) project at VTT Technical Research Centre of Finland, which aims at develop high-fidelity computational methods for nuclear reactor analysis. In the NUMPS project a continuous-energy Monte Carlo code Serpent was externally coupled with a multiphase CFD code PORFLO. In addition, two lightweight solvers, COSY and FINIX, were internally coupled to Serpent at source code level. Kozmenkov et al. [17] reported another neutronic and a T-H codes coupling for analyzing complex transient problems. DYN3D, known as one of the best estimated 3D neutron kinetics codes for the calculation in LWRs, was coupled with a widely applied T-H system code ATHLET. According to Kozmenkov et al. [17], three different methods for coupling were presented: the external, the internal, and the parallel. Once the external coupling implemented, all the physical phenomena in the core were calculated by DYN3D, while the rest of reactor systems was simulated by ATHLET. When the internal coupling option implemented, the thermal hydraulics of the core was obtained by ATHLET and only the neutron kinetics part was calculated by DYN3D. Finally, in the parallel mode, the thermal

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hydraulics in core was calculated by the coupled code in the same iteration loop of the code system. In Daeubler et al. [18] an internal coupling between the Monte Carlo reactor physics code Serpent 2 and the subchannel code SUBCHANFLOW was developed. This coupling work utilized the universal multiphysics interface introduced in Serpent recently. Thereafter, the developed coupled code Serpent 2/SUBCHANFLOW was verified and compared to an external coupling of the Monte Carlo tool TRIPOLI4 and SUBCHANFLOW as well as the internally coupled code MCNP5/SUBCHANFLOW. Simulation results of all codes showed a good agreement.

4.3.2 NURESAFE European project The NURESAFE European project is being developed since 2005, which aims at developing an integrated simulation platform to support safety analysis and future nuclear reactor design and a high level of expertise in the proper use of the most recent simulation tools within Europe [19]. This project must integrate the dynamic 3D coupling of codes simulating the various physics problems into a common multiphysics and multiscale simulation scheme, which contribute to enhance the prediction capability of the computations used for safety demonstration of the current LWRs and the design of innovative LWRs [20]. In NURESAFE, emphasis has been given in the implementation of the latest advances in core physics, two-phase thermal hydraulics and fuel modeling. The coupling method applied in the NURESAFE project is the OS method, mainly because of the low implementation effort. The NURESIM software platform employs not only higher fidelity methods and innovative CFD methods, but also an integrated multiphysics environment in an open-source software, named SALOME, which can provide a generic user-friendly interface and can facilitate the coupling of codes in a heterogeneous distributed environment as well as the interoperation between CAD modeling and codes. Besides, another open-source software named URANIE is developed as a toolbox for uncertainty quantification, sensitivity analysis, and model calibration. To achieve the objectives and to demonstrate the predictive capability of the software platform of NURESIM, the NURESIM implementation strategy comprises four steps. First, physical models and computational tools with enhanced predictive capacity are developed. Second, these tools are integrated in the SALOME software platform to get a standardized environment with the multiphysics and multiscale functionalities. Third, tools for simulation of some challenging reactor problems or “situation targets” is developed and run. These challenging “situation targets” that were selected based on the required coupling between different disciplines include five categories: advanced boron dilution modeling, PWR main steam line break, boiling water reactor (BWR) anticipated transient without scram, LOCA in PWR, and BWR T-H scenarios Finally, a methodology for verification and validation is implemented [20]. The roadmap of NURESAFE European project is shown in Fig. 4.4. It can be seen that three successive projects constituted the whole NURESAFE European project. The NURESIM project established the basic architecture of the platform and a first prototype of a truly integrated multiphysics simulation environment. The NURISP project was a consolidation of the platform together with an extension of the simulation capabilities toward

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85 FIGURE 4.4 The NURESAFE roadmap [19].

higher resolution both in space and time. The NURESAFE project showed the extended capabilities of the platform, demonstrated the readiness of the tool for industrial safety applications, and established the platform as a reference European tool [20]. The NURESAFE project was carried out through four subprojects focusing on software development and validation [20]. The first subproject, that is, multiphysics applications involving core physics, developed the coupled models of neutronics and thermal hydraulics and carried out the analysis of mains steam line break and BWR anticipated transient without scram. The second one, multiscale analysis of core thermohydraulics, was to develop new CFD models for LWR core analysis and to implement these models in the NURESIM codes. The third one, multiscale and multiphysics applications of thermal hydraulics, was focused on three challenging problems, that is, the LOCA, the pressurized thermal shock, and BWR T-H applications. The last one, software platform, was to integrate the models and software developed by other three subprojects into the SALOME software. The NURESIM simulation platform included a set of the state-of-art codes involving core physics, thermal hydraulics, and fuel thermo-mechanics, which were integrated in the SALOME open-source software by using a common data structure, generic functions, and preprocessing and postprocessing functions. As shown in Fig. 4.5, the NURESIM platform currently includes one neutronics deterministic spectral code for cross section generation, one neutronics and radiation propagation Monte Carlo code, three complementary core kinetics codes, three complementary T-H subchannel codes, two complementary T-H system codes, three complementary CFD codes, one sensitivity and uncertainty quantification software, and two fuel thermo-mechanics codes. Owing to the standardized tools used by most of the NURESIM software, the interoperability and comparison between different codes become much easier. By this way, both regulators and industry using different codes can benefit from all the generic platform features. In the further future, the NURESAFE project will continue to share common views, methods, and tools of numerical analysis of nuclear reactors and federate a team of toplevel experts from many European countries and institutions, which helps to strengthen nuclear safety within Europe [20].

4.3.3 Multiphysics Object-Oriented Simulation Environment The modeling approach of most multiphysics coupling work introduced in Section 4.3.1 can be referred to as code coupling, where disparate physics codes are loosely coupled together through data passing interfaces. In this case, each physics code is solved separately and the solutions are passed back and forth. However, multiphysics in nuclear reactor system is exceptionally complex, and the nonlinear interdependencies between different physics can vary by several orders of magnitude. It presents further difficulties and complications for the

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FIGURE 4.5 The NURESIM platform, at the end of the NURESAFE project until January 2016 [20].

abovementioned code coupling approach to orchestrate the solution processes of multiple, individual codes running at different time and length scales [2]. Hence, another multiphysics modeling approach, to employ a “cohesive” framework with all physics problem modeled at a common software design, is applied recently. The Multiphysics Object-Oriented Simulation Environment (MOOSE) developed at Idaho National Laboratory (INL) represents this alternative path for nuclear reactor simulation [2]. MOOSE, began in 2008 at INL, is a parallel computational framework developed to solve all systems in a fully coupled manner [21]. In MOOSE the physical problems are generally solved as a system of fully coupled nonlinear PDEs, and the JFNK method is implemented as a parallel nonlinear solver. MOOSE utilizes a modular approach, where the fully coupled multiphysics applications can be created following the same strict coding convention standard. Different from the traditional codes, these MOOSE-based physics software packages are often referred to as “applications” because they are not stand-alone codes but parts of the same “code” running at the MOOSE framework. People are allowed to create new MOOSE-based applications. Since 2011 more than 60 MOOSE-based applications and over 58,000 MOOSE framework
built package downloads had been created by researchers from both national and international laboratories and universities.

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Since all the MOOSE-based applications are created under the MOOSE framework software quality paradigm, tight coupling of MOOSE-based applications at different space and time scales can be a relatively straightforward process by multiscale approach, named “MOOSE MultiApps and Transfers.” The MOOSE MultiApps and Transfers systems can give the flexibility to run both tightly coupled and loosely coupled modeling among MOOSE-based applications. The main function of MultiApp system is the creation, spatial positioning, and execution control of multiple applications. The MultiApp hierarchy for multicoupling applications is shown in Fig. 4.6 [2]. It can be seen that there is always a “main” application at the top level and a hierarchy of MultiApps beneath it. Each single application allows one or more MOOSE (or external) applications to run simultaneously in parallel. Each subsidiary application, called a “subapp,” can be considered as an independent solve. To achieve cohesive coupling, solution field transfers are performed among all of the MultiApps through Transfers system to build up more complex simulations. Transfers are responsible for in-memory movement of solution information, including parallel communication due to domain decomposition. Besides, MOOSE provides a custom transfer way to improve the flexibility in the algorithms written to perform data transformation among MultiApps. The combination of the MultiApp and Transfer systems makes MOOSE an excellent coupling platform. Another great advantage of MOOSE is the existing widely used codes that can be utilized for multiphysics coupling in an efficient manner. A method, named “MOOSEwrapped apps,” has been developed to add a minimal application programmer interface (API) to the external codes, as if they are MOOSE based, in fact, a “cohesive-like” manner [22]. The wrapping process starts through the creation of a standard MOOSE-based application, and then linking in the external application, built as a library underneath the new skeleton MOOSE-based application. Once the application construction completed, a few interfaces must be extended to provide MOOSE with the hooks it needs to interact with the external application. The complete set of objects for providing the full MOOSE API is housed within the MOOSE-wrapped application and provides the cohesive-like interface FIGURE 4.6 Depiction of the MultiApp system [2].

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for coupling with other MOOSE-based and MOOSE-wrapped applications. The two main objects should be extended are the “ExternalProblem” and “ExternalMesh.” Here, the first is a wrapper for the idea of execution control and the interface for syncing solution information from the external application to MOOSE’s in-memory mesh data structures. The second is the object holding the external spatial information of applications and acting as a map for the underlying solution data stored in the “ExternalProblem.” Once these two objects exist, an application can interact with other MOOSE-based and MOOSE-wrapped applications through two-way, in-memory and loose coupling. In addition, in order to execute more advanced schemes, two methods, named the “backup” and “restore,” are implemented, which is designed to save and restore application states so that the same starting criteria are used when the applications resolving at each iteration. It should be noted that these two methods are only needed by tightly coupling schemes. Finally, a custom TimeStepper object is defined to compute the time step sizes for the external applications and to define the behavior of dealing with failed solves or convergence criteria. It is believed that MOOSE provides a new and computationally efficient pathway to deal with the multiphysics problems in both the nuclear field and the broader scientific community. MOOSE fundamentally alters the process of the development of complex multiphysics tools. Rather than the code-to-code coupling methods, multiple smaller individual simulations can be conducted under a general framework and then be linked together by using the “MultiApps and Transfers” systems. Also, new information from any length scale can be incorporated seamlessly and the main simulation can rerun to reflect any changes [2]. MOOSE is expected to evolve rapidly owing to these advantages.

4.3.4 Consortium for the Advanced Simulation of Light Water Reactors In order to enhance the multiphysics modeling and simulation (M&S) capabilities for the commercial nuclear power generation, and thus improve economic competitiveness and safety of the nuclear energy, the Consortium for the Advanced Simulation of Light Water Reactors (CASL) was established as the first energy innovation hub of the Department of Energy (DOE) of the United States in 2010 [23]. Integrated and advanced multiphysics coupling methods were developed to solve the multiphysics problems in nuclear systems, including radiation transport, thermal hydraulics, fuel performance, and corrosion chemistry. CASL project had been granted a 10-year lifetime, Phase 1 period from 2010 to 2015 and Phase 2 from 2015 to 2019. An unique consortium partnership has been built by CASL, which includes four DOE national laboratories [Oak Ridge National Laboratory (lead consortium member), INL, Los Alamos National Laboratory, and Sandia National Laboratory]; three universities (Massachusetts Institute of Technology, University of Michigan, and North Carolina State University); and three industrial organizations (Electric Power Research Institute, Tennessee Valley Authority, and Westinghouse Electric Corporation) [24]. In addition, over a dozen additional institutions and universities provide key contributions to CASL. More than hundreds of technical reports have been produced by the CASL staff composed by over 200 individuals since 2010 [25]. To develop CASL’s M&S capabilities, a challenge problem approach has been established according to the long standing issues on M&S of nuclear reactor. The M&S technology of individual physics has been developed first and then integrated to provide the

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FIGURE 4.7 Challenge problems selected by CASL [25]. CASL, Consortium for the Advanced Simulation of Light Water Reactors.

multiphysics M&S capabilities for solving these “challenge problems” [25]. Fig. 4.7 presents the “challenge problems” focused during the Phase 1 of CASL. All “challenge problems” selected by CASL focus on the current operating nuclear reactors, especially the PWRs. It can be seen that the in-core phenomena attract significant concern, including radiation transport, isotopic depletion, thermal hydraulics, fuel performance, and chemistry [25]. Each of the “challenge problems” needs a specific combination of physics, spatial and temporal resolution, and level of coupling/feedback among components [26]. One of primary missions of CASL is to achieve tighter integration and to couple these single phenomena within a unified multiphysics environment to solve the above “challenge problems,” by means of rigorous numerical methods. For this purpose, CASL has developed a collection of M&S tools, referred to as the Virtual Environment for Reactor Applications (VERA). VERA is composed by integrating and interfacing software together with a series of adapted or refactored physics components to model the specific multiphysical phenomena in a coupled way. In general, VERA is neither a specific framework nor a single-system code traditionally employed in nuclear fields. Instead, VERA combines capabilities of those together to solve the specific nuclear solutions and provides an extensible software environment where analytical applications and tools can be developed and established in the next few decades. VERA mainly consists of four elements: physics components, numerical tools for solving coupled-physics problems, drivers that execute the individual and coupled components, and the infrastructure to develop high-quality software in a collaborative environment [26]. Based on VERA, CASL has developed a sequence of coupled tools and applications for solving challenge problems in nuclear reactor systems. In addition, some existing advanced simulation tools, such as Bison [27] and

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COBRA-TF [28], can be also leveraged in VERA. Therefore VERA can contain the software components developed with multiple programming languages (primarily FORTRAN and C11), user interfaces, build systems, and quality assurance practices [26]. CASL has developed a core simulator (CS), referred to as the VERA-CS, to simulate the in-core behavior of commercial LWRs, which can integrate the lower fidelity applications and components to provide a high-resolution full-core modeling capabilities for neutronics, fuel performance, thermal hydraulics, and some other specific chemical and mechanical phenomena. VERA-CS can also provide the initial and boundary conditions for a number of the high-fidelity analyses of “challenge problem.” For the simulation of PWR, M&S technology of the currently utilized industry CS is compared to that of CASL’s VERA-CS in Table 4.1. It should be noted that the aim of VERA-CS is not to replace the existing industry-class CS, but to provide higher fidelity M&S capabilities shown in Table 4.1 when required. VERA is designed following the “environment” approach, which has the advantage for reducing the barriers to integrating existing physics components, because the internal data structures should not be affected [26]. A conceptual architecture of VERA with component packages is shown in Fig. 4.8. VERA was allowed to develop the multiple problemspecific “driver codes” to solve specific multiphysics problems, since multiple means of coupling are required for solving the “challenge problems.” As a result, general-purpose tools for multiphysics coupling have been developed in VERA, that is, a flexible noninvasive method for solving coupled nonlinear equations and a general tool for transferring data between physics components [26]. TABLE 4.1 Comparison of currently utilized industry-class core simulators (CSs) and Consortium for the Advanced Simulation of Light Water Reactors’ Virtual Environment for Reactor Applications (VERA)-CS. Physics model

Industry practice

VERA-CS components

Neutron transport power

3D diffusion (core), 2 energy groups (core), 2D transport on single assembly

3D transport, 23 1 energy groups

Power distribution

Nodal average with pin power reconstruction methods

Pin-by-pin, either homogenized or explicitly modeled

Xenon/ samarium

Nodal average with correction

Pin-by-pin, either homogenized or explicitly modeled

Depletion

Infinite-medium cross sections, quadratic burnup correction, Pin-by-pin with actual core history corrections, spectral corrections, reconstructed pin conditions exposures

Reflector models 1D cross section models

Actual 3D geometry

Thermal hydraulics

1D assembly-averaged

Subchannel with cross-flow

Fuel temperatures

Nodal average

Pin-by-pin 2D or 3D

Fuel performance

Empirically based models for key performance phenomena

Science-based models for key performance phenomena

Target platforms Workstation (single processing core)

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1000
300,000 processing cores

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FIGURE 4.8 Diagram of conceptual architecture of VERA with component packages. VERA, Virtual Environment for Reactor Applications.

Advanced parallel mathematics solver libraries, such as PETSc, Hypre, and Trilinos, can be utilized by a driver code to solve a set of steady state or transient, linear or nonlinear, systems of equations. However, these solvers often have different requirements and constraints. To alleviate this an existing lightweight environment for multiphysics coupling named the Lightweight Integrating Multiphysics Environment (LIME) is leveraged by VERA and is redesigned and integrated into Trilinos, known as physics integration kernels (PIKE). LIME and PIKE can help one physics component to identify what it can provide, and what needs to get from some other components. A variety of coupling methods from OS to JFNK can be also used by these lightweight frameworks. LIME was employed as the initial basis for noninvasive multiphysics coupling in VERA, which was specifically designed to integrate the existing tools and components for modeling the multiphysics problems in nuclear systems. The key high-level software written by C11 and interface provided by LIME is used to couple the multiple physics codes into a single-executable coupled code multiphysics simulation tool. When creating a new multiphysics application

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though LIME, physics codes are needed to support a minimal software interface, and more invasive coupling requires more interface support for the additional data dependencies [26]. According to the original structure of these physics codes, some refactoring may be required. PIKE is a latest released open-source software library for developing multiphysics coupling applications within Trilinos, which can provide basic interfaces and utilities for supporting the code-to-code multiphysics coupling. As to more invasive couplings (JFNK) and acceleration techniques such as Anderson acceleration, PIKE can also be employed in combination with the Thyra abstraction layers and the NOX nonlinear solver packages in Trilinos [29]. In addition, VERA developed a new data transfer tool, referred to as the Data Transfer Kit (DTK), to facilitate solution transfer between different physics components [28]. Since some independently developed software operating on geometrically defined regions instead of traditional mesh can be allowed to use in VERA, the strict requirements cannot be imposed on defined tools for data transfer. Therefore DTK can provide multiple accuracy and constraint-enforcement algorithms for solution transfer from one spatially decomposed physics codes or components to another without requiring the physics component to have any knowledge of the other physics components [26]. DTK can also support the service of both overlapping volume domain transfers and nonconforming surface transfers. Based on the knowledge of the geometric or mesh data along with the location of the data, DTK can build an optimal MPI communication pattern to transfer field variables among different components [26]. One of the main features of VERA is to use common input and output file to drive and couple all the different physics codes’ components, since different separate codes are developed with its own format specification [29]. Using a common input file can ensure all the codes working from a single set of simulation parameters so that errors caused by inconsistent inputs for different codes can be significantly reduced. In addition, users can only need to understand a single syntax rather than multiple inputs for multiple physics codes. In VERA the common input is implemented as a single ASCII input file, resolved by a processor into a consumable intermediate format. The input files use a modular approach to describe all the physical reactor objects, and each object can be described independently of each other and rely on very little global information [26]. The input files also include the description of the reactor state point such as power, flow, and depletion. Meanwhile, VERA’s common output is a binary HDF5 (hierarchical data format) file commonly utilized for scientific data storage and I/O. In the HDF5 format, data can be easily viewed and modified by software tools such as HDFView [26]. Another distinctive aspect of VERA is the development of the Tribal Build, Integrate, and Test System (TriBITS) [30], a coherent, unified method to build applications for various platforms and support for extensive automated testing [26]. TriBITS can help the CASL developers work in a range of development and sync models. The primary repositories of TriBITS at ORNL behind the laboratory firewall contain a multitude of unit, nightly, and weekly tests to ensure the performance of individual components and coupled multiphysics codes. In the future, CASL work will aim at extending the coupled drivers and components to additional nuclear reactor types, including BWRs and small modular reactors. Besides, CASL team will keep working on the improvement of the accuracy and efficiency for all the individual and coupled multiphysics codes [26]. CASL VERA is not only a capability demonstration,

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but also an industry tool for accurate and robust simulations of real operating nuclear reactors. CASL provides a modeling environment where applications and tools for design and analysis of nuclear reactors can be developed and deployed in the next decades.

4.4 Conclusion In this chapter, multiphysics coupling simulations of nuclear reactor systems are reviewed. On the one hand, the mainstream methods of multiphysics coupling are demonstrated. The fundamental theory and coupling scheme of OS methods, JFNK methods, and ABN methods are summarized and presented. On the other hand, some significant works on neutronic and T-H codes coupling, and large research project, including NURESAFE European project, MOOSE plan, and CASL project, are reviewed. This chapter helps the readers have a better understanding on the worldwide current status of multiphysics coupling research.

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3106, 2019. [23] CASL, 2015, Consortium for Advanced Simulation of Light Water Reactors (CASL) (WWW Document). Available from: ,http://www.casl.gov/.. [24] P.J. Turinsky, W.R. Martin, Special issue on the “Consortium for Advanced Simulation of Light Water Reactors Research and Development Progress”, J. Comput. Phys. 334 (2017) 687
688. Available from: https://doi.org/10.1016/j.jcp.2017.01.028. [25] P.J. Turinsky, D.B. Kothe, Modeling and simulation challenges pursued by the Consortium for Advanced Simulation of Light Water Reactors (CASL), J. Comput. Phys. 313 (2016) 367
376. Available from: https:// doi.org/10.1016/j.jcp.2016.02.043. [26] J.A. Turner, K. Clarno, M. Sieger, R. Bartlett, B. Collins, R. Pawlowski, et al., The Virtual Environment for Reactor Applications (VERA): design and architecture, J. Comput. Phys. 326 (2016) 544
568. Available from: https://doi.org/10.1016/j.jcp.2016.09.003. [27] J.D. Hales, R.L. Williamson, S.R. Novascone, G. Pastore, B.W. Spencer, D.S. Stafford, et al., BISON theory manual—the equations behind nuclear fuel analysis, BISON Release 1.1, INL/EXT-13-29930, Rev. 1, 2014. [28] R.K. Salko, M.N. Avramova, CTF Theory Manual, Pennsylvania State University, 2014. [29] S. Hamilton, M. Berrill, K. Clarno, R. Pawlowski, A. Toth, C.T. Kelley, et al., An assessment of coupling algorithms for nuclear reactor core physics simulations, J. Comput. Phys. 311 (2016) 241
257. Available from: https://doi.org/10.1016/j.jcp.2016.02.012. [30] R. Bartlett, TriBITS developer guide and reference, Milestone Report, CASL Technical Report: CASL-U-20140075-b, Oak Ridge National Laboratory, Oak Ridge, TN, 2014.

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5 Nuclear physics deterministic code Tengfei Zhang School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China

5.1 Nuclear data processing codes 5.1.1 NJOY The nuclear data evaluations are widely employed in reactor physics simulations by providing the origins of nuclear data that can be used to describe the behaviors of neutrons inside nuclear power plants. The most well-known physics representations of the data are generally encoded in a computer-readable format called ENDF (evaluated nuclear data file) [1]. Although the ENDF libraries can be useful in their original formats, they are often converted into forms more feasible for applications, such as neutron transport calculations using multigroup transport or Monte Carlo methods. The NJOY Nuclear Data Processing System [2,3] is developed for this purpose. The NJOY code comprises a set of main modules, each performing a predefined processing task. Utilizing these modules, NJOY can be assembled in flexible ways depending on different application purposes. For nuclear engineering applications, several important modules are listed as follows: NJOY is the master module that directs and groups the rest modules for descriptive purposes. RECONR reconstructs pointwise (energy-dependent) cross sections from ENDF resonance parameters, using user-specified interpolation schemes. It allows for different resonance treatment models such as Single-Level Breit Wigner, Multilevel Breit Wigner, Adler Adler, Reich Moore (RM), Hybrid R-Function, Reich Moore Limited, energy-independent unresolved, and energy-dependent unresolved representations [4]. Fig. 5.1 presents a typical total cross section for 235U reconstructed from an ENDF evaluation data library. BROADR deals with the Doppler broadening of pointwise cross sections, using the kernel broadening method. UNRESR computes effective self-shielded pointwise cross sections in the unresolved energy range.

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FIGURE 5.1 A typical cross section reconstructed from an ENDF evaluation using RECONR with the smooth, resolved, and unresolved energy regions. ENDF, Evaluated nuclear data file. Source: Reprinted with permission from R.E. MacFarlane, A.C. Kahler, Methods for processing ENDF/B-VII with NJOY, Nucl. Data Sheets 111 (12) (2010) 2739 2889 [5]; r2010 Published by Elsevier Inc.

THERMR deals with cross sections and scattering distributions for free or bound scatterers in the thermal energy range. GROUPR generates self-shielded multigroup cross sections, group-to-group scattering matrices from pointwise input. ERRORR computes multigroup covariance matrices based on uncertainty data from ENDF library. CCCCR produces multigroup cross section data for the CCCC standard interface files such as ISOTXS, BRKOXS, and DLAYXS. MATXSR formats multigroup data for the MATXS material cross-section interface file, which works in combination with the TRANSX (transport cross section) code to construct libraries for different particle transport codes. ACER prepares libraries in ACE format for continuous-energy Monte Carlo codes, typically, the MCNP code. The ACER module is supported by several subsidiary modules for different classes of the ACE format. WIMSR generates cross section libraries for the assembly codes WIMSD and WIMSE. PURR is used to produce unresolved-region probability tables for the MCNP continuous-energy Monte Carlo code.

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The typical workflow of data in NJOY can be illustrated as follows. The first step is normally to generate a “point-ENDF” (PENDF) file. An ENDF file is read by RECONR, and a common energy grid is thus produced for all reactions (the union grid) such that all cross sections can be attained within a specified tolerance by linear interpolation. By this means a PENDF file is generated containing pointwise cross sections. The PENDF data are then Doppler-broadened by the BROADR module. After that, PURR reads the Dopplerbroadened PENDF data and writes self-shielded cross sections and probability tables onto a new PENDF file, which can be subsequently used for Monte Carlo methods. THERMR reads this PENDF file and produces pointwise cross sections in the thermal range. The scattering matrices also need to be accounted in this process. One important application of the resulting PENDF file is to use ACER to prepare cross section libraries in ACE format for the MCNP code [6]. Another common application of the PENDF file is to use GROUPR to convert the pointwise cross sections into multigroup libraries, namely, the “groupwise-ENDF” (GENDF) data. The weighting neutron spectrum used to homogenize the cross sections can either utilize the Bondarenko approximation or be obtained by solving the neutron slowing-down equation. Particularly, the MATXSR module reformats GENDF data for neutrons, photons, and charged particles into the MATXS format, which is used as input to the TRANSX code [7]. TRANSX can produce libraries for a variety of particle transport codes such as ANISN [8], DIF3D [9], and PARTISN [10]. Another possible function of the full PENDF file is to use the module ERRORR to produce covariance matrices for use in sensitivity and uncertainty analysis [11].

5.2 Cross section generation codes 5.2.1 Winfrith improved multigroup scheme The Winfrith improved multigroup scheme (WIMS) is one of the most famous and versatile software packages employed for neutronics calculations [12 16]. The code goes through a long development history stretching back over 50 years. The early version of WIMS, WIMSD [17], focuses on thermal reactors, including light water moderated, heavy water moderated, and graphite moderated designs. During the years, WIMSD has gradually evolved into a standard tool for reactor physicists worldwide and is still among the most often employed software until now [18 20]. With the success of WIMSD, an upgraded version, WIMSE [21], was developed in the context of UK work in support of high-temperature reactors, introduced a more modular structure, advanced resonance shielding capabilities, and a capability for three-dimensional (3D) calculations. Since then, continuous researches on WIMS have been maintained which result in a horde of the WIMS code system. For simplicity, here WIMS9 [22] is selected as a representative example. In WIMS9, the neutron flux distribution can be solved using either a 69-group, or a refined 172-group nuclear data library, with a series of solution options such as 1D or 2D (one- or two-dimensional) collision probability method, the method of characteristics (MOCs), the 1D or 2D SN method, and the Monte Carlo method [4]. The resonance capture can be treated with the equivalence model [22] while allowing for a fine group calculation

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at lower resonance energies to more accurately describe interactions between resonances. In addition, it also includes a subgroup model [23] that enables accurate calculations for a wide range of geometries types. A general depletion module BURNUP is employed to treat all burnup problems. Despite the wide variations of code versions, the legacy WIMS codes focused on 2D calculations. Feasible geometries with WIMS include single pin, cluster of pins on square pitch, hexagonal cluster of pins, cluster of rings of pins, particulate fuel in graphite matrix, and plate fuel. Recently, with the growing computing power, the WIMS code has been equipped with whole-core calculation capability, by including a 3D MOCs solver with reflective and oncethrough tracking methods to analyze problems of varying size and complexity [24]. A timedependent neutron flux solver along with thermal-hydraulic (T-H) modeling capability has been incorporated to allow steady-state and transient coupled calculations [25].

5.2.2 CASMO-4 CASMO-4 is a multigroup 2D lattice code developed by Studsvik Scandpower, dedicated mainly to boiling water reactor and pressurized water reactor (BWR and PWR) assemblies or simple pin cells [26]. The code handles the geometry consisting of cylindrical fuel rods of varying composition in a square pitch array, with allowance for fuel rods loaded with gadolinium, erbium, integral fuel burnable absorber, burnable absorber rods, cluster control rods, in-core instrument channels, water gaps, and cruciform control rods in the regions separating fuel assemblies. Reflector/baffle calculations and simple fuel storage rack calculations can also be performed with CASMO-4 [27,28]. CASMO-4 incorporates the direct microscopic depletion of both fuel rods and burnable absorbers. A predictor corrector approach is used, which reduces the number of burnup steps required with satisfactory accuracy. This is particularly important when burnable poison rods are involved [29]. For each burnup step, two calculations are performed. The depletion is simulated first using the spectra at the start of the step, and then using the spectra at the end of the step after another spectrum calculation [30]. Number densities are averaged from these two calculations and used as starting values for the next burnup step. CASMO-4 treats resonance calculation using the equivalence theory [4] by establishing the equivalence relation of tabulated effective resonance integrals for each resonance absorber in each resonance group to the particular heterogeneous problem. The fuel selfcollision probability is derived from rational approximations. Dancoff factors [31] are employed to account for the shadowing effect caused by heterogeneous pin-cell distribution. Neutron energies cover the range from 0 to 10 MeV, and the resonance region is defined to exist between 4 and 9118 eV. The calculation flow of CASMO-4 starts with 70-group collision probability calculations of different pin-cell types, for example, pins containing fuel of different enrichment [30]. This procedure is typically named “microgroup calculations.” For absorbing materials, calculations are carried out in a supercell manner, that is, modeling the absorber rod surrounded by coolant and a buffer region representing the surrounding fuel pins. A 40-group 2D calculation with the fuel bundle model is then performed using pin-cell homogenized cross sections, which named “macro-group calculation.” The solution from this calculation

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yields neutron spectra for the final energy condensation of cross sections for use in the 2D transport calculation. The data generated in the previous steps constitute the input to the heterogeneous, 2D MOC transport calculation, normally performed in eight energy groups, which gives the eigenvalue and the associated flux distribution. Leakage effects are accounted using a fundamental mode buckling calculation. Reflector calculations are easily performed and discontinuity factors are calculated at the assembly boundaries and for reflector regions. CASMO-4E can be viewed as a variation of CASMO-4 with extended modeling capability. When modeling of more realistic problems is required, CASMO-4E can be utilized to simulate arbitrary arrangements of multiple fuel assemblies or generalized fuel storage rack calculation [32 34].

5.2.3 HELIOS HELIOS is a powerful tool developed by Studsvik Scandpower for lattice depletion calculations in general 2D geometry [35 42]. The latest HELIOS code employs the MOC to solve the neutron transport equation, while one distinguished feature of the legacy HELIOS codes (such as HELIOS-1.7) is that transport calculations are performed by the current-coupling-collision probability method that allows for a flexible geometrical modeling. “The transport method of HELIOS is called the CCCP method, since it is based on current coupling and collision probabilities (first-flight probabilities) . . . the system to be calculated consists of space elements that are coupled with each other and with the boundaries by interface currents, while the properties of each space element its responses to sources and in-currents are obtained from collision probabilities” [43]. HELIOS builds the geometric system from the smallest unit named “structure” and forms the final system by connecting a series of intermediate geometric components. HELIOS comprises mainly of three executable codes: AURORA, HELIOS, and ZENITH. AURORA is responsible for reading, processing, and saving the user’s input. The processed information is written into a HERMES database for retrieval by HELIOS and/or ZENITH. For each case, HELIOS retrieves the input information from HERMES database and executes the calculations specified therein. HELIOS undertakes the neutronics simulations and generates outputs written into a consistent database for reuse and further processing by ZENITH. As a representative example, in Helios-1.7, three different data libraries are available: 190/48 neutron/gamma groups, 112/18 neutron/gamma groups, and 45/18 neutron/ gamma groups [43]. The subgroup method is employed to treat the resonance calculation [44]. To handle the interaction of resonance isotopes, the resonance isotopes are grouped into resonance sets and treated one by one while neglecting the rest sets. Critical buckling search is performed as a correction to the obtained neutron spectrum whereby yielding the criticality spectrum. As an alternative option, the user can add an amount of a 1/v absorber or a constant absorber. The depletion of isotopes is simulated by first linearizing burnup chains and then solved with the Laplace transformation method [45]. To reduce computational costs, the predictor corrector scheme is included to better capture the depletion process while allowing for larger burnup steps [46].

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5.2.4 APOLLO2 The APOLLO2 spectral transport code is developed at the Commissariat a` l’Energie Atomique et aux Energies Alternatives (CEA) and is widely used for cross section generation and transport calculations, including a large range of applications in reactor physics, criticality safety studies, and fuel cycle analysis [47]. The code is utilized as an integrated component for multigroup cross section generation of other CEA and third-party industrial software packages and it is also used for benchmarking and educational activities [48 56]. APOLLO consists of a number of independent modules, each of which aiming at a specific task (e.g., geometry constructions, resonance calculations, collision matrix generations, and performing external iterations) and can be used as a symbolic operator that acts on input data to create output data. This greatly clarifies the flow of the code and enhances the readability of the user input information. The external multigroup cross section libraries in APOLLO2 are in APOLIB format [57]. These libraries contain temperature-dependent infinite-dilution cross sections and associated self-shielding data, fission yields, decay constants, and delayed neutron data. The data may come from any ENDF in ENDF format such as JEF, JEFF, ENDF/B, and JENDL. The standard APOLIB multigroup libraries have 99, 172, and 281 groups, respectively, along with gamma source and gamma flux calculation capability using a 94-group gamma library with 99, 172, or 281 group neutron to 94 gamma production cross sections associated to the neutron libraries. The depletion library contains 127 fission products without pseudo products. In addition to the external multigroup library, in APOLLO2 space-dependent multigroup reaction rates are obtained by solving a simplified elastic slowing-down equation in fine structure, obtained for one resonant isotope diluted in nonresonant isotopes [58]. Use of Dancoff factors is avoided since space-dependent interference effects can directly be accounted by a full collision probability description. Moreover, the code can treat stochastic dispersions of grains in homogeneous matrices by the double heterogeneity technique for both the collision probability method and the method of long characteristics and has the capability to carry out leakage calculations for mutually interacting assemblies [59]. APOLLO2 flux solvers are based on a wide range of transport calculation methods, either on the collision probability method (CPM)—full CPM, interface current techniques (ICT) and simplified ICT (multicell methods)—or on the finite differences and transverse nodal Sn method, and short and long characteristics (MOC) methods. APOLLO2 solvers cover the 1D and 2D geometries, both in rectangular and in hexagonal [50,57,60,61]. Besides these main components, there are a number of tools to perform depletion calculations, perturbation reactivity analysis and first-order perturbation analysis, on-the-fly tabulations of mathematical functions, constructors for geometries and internal objects used by the code, and many more. Leakage corrections are introduced to account for the macroscopic variation of the flux in the critical core.

5.2.5 Standard Reactor Analysis Code The SRAC (Standard Reactor Analysis Code) system is designed to permit overall neutronics calculations for any type of thermal reactors [62]. This code covers microscopic

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library compilation, macroscopic constant generation, and cell and core calculations, including burnup and fuel management [63 66]. The group cross-section library of SRAC has been processed from the JENDL-3.2-based evaluated nuclear data. The library, named the Public Library, consists of public fast, public thermal, and public resonance cross sections. The energy group structure of the current Public Library consists of 107 groups (48 groups for thermal and 74 for fast energy ranges, with 12 overlapping groups) and more than 300 nuclides, covering the energy range from 1e25 eV to 10 MeV. Most of the macroscopic cross-section data are processed by the collision probability method cell calculations [67]. PIJ (collision probability method code) performs transport calculation, and three kinds of resonance integral methods are provided: narrow resonance (NR) approximation, intermediate resonance approximation, and direct calculation with hyperfine neutron energy group performed by the PEACO routine [68]. Using this routine, the interaction of resonances can be accurately treated. It should be noted that in SRAC a doubly heterogeneous system can be solved by successive cell calculations since smearing and/or collapsing of macroscopic cross sections is carried out separately. For the NR calculations, Dancoff correction factors required in the interpolation of the self-shielding factors of resonance nuclides are also considered for each constituent nuclide for the lattice cell, which contains a resonant nuclide in two materials with different composition. SRAC is capable of dealing with over 10 different geometries, such as 1D slab geometry, 1D cylinder geometry, 2D square cell, 2D hexagonal cell, square fuel assembly, and annular assembly with annular arrays of pin rods. The available transport methodologies include 1D SN, 2D SN, collision probability method, and the diffusion method. Moreover, the P1 or B1 approximations based on the fundamental mode approximation is available for collapsing the multigroup cross sections into few group ones after smearing the multigroup cross sections [62]. The function BURN performs burnup calculations by a series of procedure to yield a neutron spectrum by a selected method, to get one-group effective cross sections and to calculate generation and incineration rates at each burnup step. The reaction rate calculation function REACT provides the spatial distribution of microscopic or macroscopic reaction rate and spectrum indices by neutron flux obtained with a selected code.

5.2.6 DRAGON4 The computer code DRAGON4 results from a concerted effort made at Ecole Polytechnique de Mont´real [69]. It contains a collection of models that can simulate the neutron behavior of a unit cell or a fuel assembly in a nuclear reactor. All functions that characterize a lattice cell code are accounted, including interpolation of microscopic cross sections supplied by standard libraries, resonance self-shielding calculations in multidimensional geometries, multigroup and multidimensional neutron flux calculations that can take into account neutron leakage, transport transport or transport diffusion equivalence calculations, as well as the editing of condensed and homogenized nuclear properties for reactor calculations, isotopic depletion calculations [70 73]. In DRAGON4 the transport equation can be solved by a variety of algorithms: the collision probability method, the MOCs, the diffusion method, the SPN method, and the

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discrete ordinates method. Particularly, the SYBIL option is used to solve the integral transport equation using the collision probability method for simple 1D geometries (either slab, cylindrical, or spherical) and the interface current method for 2D Cartesian or hexagonal assemblies. The EXCELL option solves the integral transport equation using the collision probability method for general 2D geometries and for 3D assemblies [74]. The MCCG option solves the integral differential transport equation using the long characteristics method for general 2D and 3D geometries. DRAGON4 utilizes the same tracking procedures that are compatible with both CPM and MOC. For resonance treatments, models based on the generalized Stamm’ler method and the subgroup method are implemented in DRAGON4. B0 model and B1 model can be employed to account for the leakage effect. An equivalence method based on the superhomogenization (SPH) method is available. The lumped depletion matrix system containing the nonsaturating isotopes is solved using either a fifth-order Cash Karp algorithm or a fourth-order Kaps Rentrop algorithm, taking care to perform all matrix operations in sparse matrix algebra [69,72,75]. The execution of DRAGON4 is arranged in a modular manner via the GAN generalized driver. DRAGON4 can access directly microscopic cross-section libraries in the standard formats such as DRAGLIB [76], MATXS [7], WIMS-D4 [77], WIMS AECL [78]. The macroscopic cross section can also be read in DRAGON4 via the input data stream, which is very useful for few groups’ benchmarking exercises.

5.2.7 AEGIS The AEGIS code is a lattice physics code developed by Nuclear Engineering Ltd. in cooperation with Nagoya University and Nuclear Fuel Industries, Ltd. [79]. The AEGIS code aims at preparing cross section sets dedicated for the SCOPE2 code [80], a 3D pin-bypin core analysis simulator developed by Nuclear Fuel Industries, Ltd. In AEGIS the conventional “pin-cell” calculations for spatial homogenization and energy condensation are abandoned to reduce uncertainties and increase accuracy. By this means large-scale calculations, such as for a whole core, can be carried out with a consistent lattice physics computation model [80 82]. The AEGIS code uses two different types of cross section libraries: the multigroup cross section library and the ultrafine group cross section library. The multigroup cross section library employs cross sections of various nuclides in relation to temperature and background cross section. While the ultrafine group cross section library is incorporated for the resonance calculation [83,84], it is also permitted to use the equivalence theory for the preparation of effective microscopic cross sections. AEGIS adopts 172-group or 281-group multigroup library structure generated through the cross section processing code NJOY. A total of 43 heavy nuclides and 305 other nuclides, including 193 fission products, are included in the library. Anisotropic scattering cross sections up to the P3 component can be selected for light nuclides, structural nuclides, and major heavy nuclides. For a more accurate resonance modeling, the ultrafine group structure employs 32,000 groups with the neutron energy range from 10 MeV to 0.1 eV, with explicit consideration of temperature dependencies. To mitigate the cross section condensation error by the ultrafine

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computations, an SPH method dedicated for energy is also adopted. Besides, the positiondependent effective cross sections are evaluated through the Dancoff factor estimated with the neutron current method [79]. MOC is used for the assembly transport calculation due to its efficiency for handling a large and complicated geometry. Various numerical techniques are adopted for the efficient execution of assembly transport calculations such as the ray tracing method, the acceleration technique [based on the generalized coarse mesh rebalance (GCMR) method], and the polar angle quadrature set. The burnup chain employed in the AEGIS code consists of 28 heavy nuclides and 193 fission products, which covers both U-Pu and Th-U cycles [85]. Lumped fission products are avoided since fission products are treated in a detailed manner. In order to accurately handle the detailed burnup chain that has short-lived nuclides, a Krylov subspace method is adopted [86]. Besides, the projected predictor corrector method, which reduces discretization error resulted from using a constant reaction rate during a burnup step, is also developed and implemented in the AEGIS code.

5.2.8 SCALE The SCALE code system is developed and maintained by the Oak Ridge National Laboratory in the United States, serving as a multipurpose code for nuclear safety analysis and reactor design [87]. It contains numerous sets of codes with a broad range of functions and capabilities; thus it has been widely employed in lattice calculations for a series of reactor types [41,88 90]. SCALE includes both continuous energy and multigroup ENDF/B-VI cross-section libraries. The multigroup library is a 238-group general-purpose criticality safety library with the same energy group structure as the 238-group ENDF/B-V library in SCALE [91]. The resonance self-shielding in the unresolved resonance range is treated with the BONAMI code based on the Bondarenko method [92]. The resolved resonance treatment modules CENTRM (Continuous-Energy Transport Module) and PMC (Pointwise Multigroup Converter) provide a rigorous approach for generating problem-dependent multigroup cross sections. CENTRM performs a 1D discrete ordinates calculation to generate a continuous-energy spectrum for a unit cell using pointwise cross-section data. Neutron spectra are typically constructed on a grid of 30,000 40,000 energy points tailored to the macroscopic cross-section energy structure for the mixtures in the problem geometry. PMC employs the continuous-energy flux and cross sections from CENTRM to generate problem-dependent multigroup cross sections. These methods provide a rigorous crosssection treatment that explicitly handles effects from overlapping resonances, fissile material in the fuel and surrounding moderator, anisotropic scattering, and inelastic level scattering. Doubly heterogeneous cells can be addressed by applying CENTRM/PMC resonance calculations for the low-and high-level heterogeneities in sequence [93 95]. In SCALE, depletion calculations are performed with the ORIGEN code [96]. The most up-to-date version of ORIGEN, ORIGEN-S, tracks 1119 individual fission products generated in the fuel during irradiation, 129 actinides, and 698 isotopes associated with structural and/or activation components [93,95]. It is also worthwhile to mention that the advanced sensitivity and uncertainty analysis capabilities are achieved by the TSUNAMI

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code, which contains a number of codes that were developed primarily to assess the area of applicability of benchmark experiments for use in criticality code validations [97]. Problem-dependent cross-sectional weighting, resonance self-shielding with CENTRM/ PMC, 2D unstructured-mesh transport calculations with NEWT [98], or 2D depletion calculations through coupling of NEWT and the ORIGEN-S point depletion code can be performed by the TRITON code integrated in SCALE [94]. In addition, the TRITON control module also can perform 3D depletion calculations using the KENO Monte Carlo transport code [99] along with the ORIGEN-S code.

5.2.9 PARAGON The PARAGON code is primarily consisted of four basic modules: resonance selfshielding, flux solver, leakage correction, and depletion. The PARAGON code provides accurate angular treatment and geometry modeling flexibilities, based on collision probability and interface current coupling methods [100]. Compared to its predecessor PHOENIX-P [101], PARAGON can model exact cell geometry representations and enable descriptions of multiple rings and regions within the fuel pin and the moderator cell geometry. PARAGON facilitates performing whole-core modeling, 2D baffle/reflector modeling, and rack-type calculations for spent fuel pools [102,103]. The code is based on the collision probability and the interface current coupling method, using ENDF/B-VI as the source of the basic evaluated data. The library consists of 70 neutron energy groups along with 48 gamma groups generated with the NJOY code. The Space-Dependent Dancoff Method resonance self-shielding method is adopted in PARAGON [104]. This method allows for the treatment of the multiregion resonance capability inside pins, which is essentially necessary to describe the plutonium buildup at the periphery of the fuel rod. B1 theory is employed to compute the multigroup diffusion coefficients and the multigroup critical spectrum flux. For the depletion calculation, PARAGON conducts the Laplace transform method through linearizing the isotopic depletion chains [105].

5.2.10 Bamboo-Lattice Bamboo-Lattice is a lattice code developed at Xi’an Jiaotong University designed to meet different requirements ranging from engineering application, scientific research, and nuclear force education of PWR cores [106]. The code is established based on the purpose of eliminating empirical corrections embedded in legacy lattice codes, allowing for applications to different PWR designs. The multigroup cross section library was processed in combination of NJOY, NRSC package [107], and Python scripts based on ENDF/VII.0. Three energy group structures are available in the code, including the WIMS-D-69, WIMS-D-172, and SHEM-361 group structures. For the resonance calculation the subgroup method is employed to enable flexible geometric treatment [108]. The 2D steady-state multigroup neutron transport equation is solved with the assembly-modular MOC, with consideration of water gaps. A two-level coarse mesh finite difference (CMFD) scheme is adopted to accelerate outer iterations. The Chebyshev Rational Approximation Method is employed to solve the depletion

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FIGURE 5.2 Workflow of the Bamboo-Lattice code. Source: Reprinted with permission from Y. Li, B. Zhang, Q. He, D. Wang, H. Wu, L. Cao, et al., Development and verification of PWR-core fuel management calculation code system NECP-Bamboo: Part I Bamboo-Lattice, Nucl. Eng. Des. 335 (2018) 432 440; r2018 Elsevier.

equation accurately and efficiently [109]. In addition, the improved Trajectory Transmutation Approximation method has also been implemented as another option to solve the pure decay depletion equations analytically [110]. The workflow of BambooLattice is shown in Fig. 5.2.

5.2.11 MC2-3 Fast rectors are characterized with distinct nuclear characteristics from thermal reactors, making much of the assumptions employed in traditional light-water reactor (LWR) analysis methods not applicable. For instance, the scattering resonances of intermediate atomic mass nuclides result in the strongly jagged structure of fast reactor spectrum, and the lack of 1/E spectrum for the calculation of heavy isotope resonance absorption requires detailed modeling for slowing-down calculations. The hard neutron spectrum peaked in the keV and MeV range makes it important to model anisotropic scattering, inelastic scattering, (n,2n) reaction, and unresolved resonance self-shielding. The long mean free path due to small absorption cross sections in fast region implies global coupling of the core and requires exact whole-core depletion calculations [111]. These reasons motivated a distinct philosophy of physics analysis tools with tailored methodologies for fast reactors. The MC2-3 code is a multigroup cross section generation code for fast reactor analysis [112]. This code originates from the legacy fast reactor analysis code MC2-2, which had been extensively used for over three decades [113]. The improved spectrum calculation methods were integrated with the 1D cell calculation capabilities of the SDX code. The MC2-3 code solves the consistent P1 multigroup transport equation utilizing nuclear data from ENDF/B data files to attain the neutron spectrum for generating multigroup neutron cross sections [114]. The code allows for the modeling of homogeneous medium, or a heterogeneous slab, or cylindrical unit cell problem in ultrafine (B2000) or hyperfine (B400,000) group levels. Anisotropic inelastic scattering to P1 is introduced on the ultrafine group basis.

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Pointwise cross sections are reconstructed with Doppler broadening at specified isotopic temperatures in the resolved resonance range [4]. In the hyperfine group calculation mode, the pointwise cross sections are directly utilized, while for the ultrafine group calculation, self-shielded cross sections are obtained by the numerical integration of the pointwise cross sections using the NR approximation. Although the NR approximation shows substantial deviations from the hyperfine group solution in a few tens of the electron-volt energy ranges, the neutron population in these low energy ranges is very small in fast reactors, and thus the errors introduced in the ultrafine group cross sections by the NR approximation make no significant impact on global calculations. As an alternative, the hyperfine group calculation can be employed. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. MC2-3 performs transport calculation using the collision probability method in 1D slab geometry and cylindrical geometry. To account for high-order scattering source, a 1D MOC solution scheme can also be utilized. The ultrafine group calculation can also be performed with 2D whole-core models to generate region-dependent broad-group cross sections [114]. This treatment makes it possible to account for more realistic region-to-region leakage effect in actual core configurations. The fundamental mode spectrum calculation is also feasible in MC2-3, by which the critical buckling is determined in an iterative manner until the multiplication factor k converges to unity. The code has been validated against abundant fast reactor designs and proven to be one of the most state-of-the-art tools for the analysis of fast nuclear reactors.

5.2.12 ECCO The ECCO code contains several different neutron cross section libraries derived from the JEF-3.1 nuclear data evaluated files, that is, the 1968-group library with 112 nuclides, the 33-group library with 446 nuclides, including pseudo fission products, the 172-group library with 389 nuclides in XMAS energy group scheme [115,116]. These libraries are generated by processing the JEF-3.1 files with the NJOY and CALENDF codes [117]. Probability tables are included for the main 37 resonant nuclides. The 172-group library in XMAS energy scheme may be used for thermal spectrum calculations. The ECCO code adopts the subgroup method to treat resonance self-shielding effects, which is particularly suitable for calculations involving complex heterogeneous structures. The self-shielded parameters are generated by combining a slowing-down treatment in 1968 groups with the subgroup method within each fine group. Flux calculations in heterogeneous geometry are performed by means of the collision probability method [118]. For reference purposes, ECCO treats nuclides in different ways. For important nuclides the heterogeneous geometry in ultrafine groups is employed; while for less important nuclides, broad-group libraries with 33 or 172 groups are used. In these calculations the fine group plus subgroup schemes have been set up to represent accurately the reaction thresholds and the resonances in a wide range of situations. The geometrical modeling capabilities of ECCO include 1D (slab or cylindrical: exact collision probabilities); 2D (rectangular lattice of cylindrical and/or square pins within a

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square tube, hexagonal lattice of cylindrical pins within a hexagonal wrapper: approximate collision probabilities by Roth and double step methods); and 3D (slab with the sides of the boxes and the tube described explicitly: approximate collision probabilities). Three main classes of flux solvers are available: finite difference diffusion solvers can be used in any geometry: 1D (slab, cylindrical, spherical); 2D (RZ, R-theta, rectangular lattice XY, hexagonal lattice); and 3D (rectangular lattice XYZ, hexagonal-Z). Finite difference SN transport calculations can be performed with BISTRO code in 1D geometry (slab, cylindrical, spherical) and several 2D geometries (RZ, XY) [119].

5.3 Whole-core computational codes 5.3.1 SIMULATE-3 SIMULATE-3 is a two-group 3D core calculation code developed by Studsvik Scandpower for the analysis of both PWRs and BWRs [120,121]. The code is based on the QPANDA neutronics model [122], which employs fourth-order polynomial representations of the intranodal flux distributions in both the fast and thermal groups. SIMULATE-3 is generally utilized along with the CASMO-4 code [27,28,123,124], through the cross-section linking code TABLES-3. With TABLES-3 the user can create cross-section models that are designed for fuel management, core follow, reload analysis, or special projects. It generates a master binary library consisting of partial cross sections for use by SIMULATE-3. The partial cross sections can each be a function of up to three variables such as exposure, fuel temperature, moderator temperature, control rod, and enrichment. SIMULATE-3 is characterized by the ability of performing pin power reconstruction [125], the explicit representation of the reflector region, the easy-to-use free format input, the easy-to-use binary cross-section library, the expanded cross-section modeling capabilities, the automatic geometry expansion, etc. The code allows for a variety of calculations modes, such as depletion in two or three dimensions, 1/8, 1/4, 1/2 or full core, reload shuffling, including reinsertion of discharged fuel, reactivity coefficient calculations, control rod worth, including shutdown margin, dropped and ejected rod in two or three dimensions, xenon transients, and criticality searches [33,126,127].

5.3.2 ANC9 ANC9 is the latest version of the ANC multidimensional PWR core neutronics simulator [128,129]. It is an accurate and efficient 3D core neutronics simulator built on years of experience in nodal simulation. Embedded within the NEXUS code system [130], ANC9 is viewed as the next-generation Westinghouse core design system. It is designed to support a wide range of PWRs currently under operation. ANC9 capabilities include the once-through cross-section methodology, node-wise tracking of core depletion parameters and isotopes, corrections of control rod cusping effects for accurate differential rod worth predictions, T-H modeling by integrating T-H codes, axial homogenization model, explicit modeling of spacer grids, B-10 depletion during cycle burnup, modeling of in-core detectors, and automated sequences for most

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reload design applications. Besides, ANC9 is integrated with the BEACON core monitoring system [131], which allows automation of core predictive and monitors calculations, fuel shuffling checks, boron concentration searches, control rod position, power level, and axial offset, as long as a wide variety of user-selectable edits for the display of desired results. ANC9 also includes neutron kinetics capabilities. Therein, the time-dependent solution is based on the stiffness confinement method, which is designed to efficiently and accurately solve the time-dependent equations during core reactivity transients [132,133].

5.3.3 PANTHER PANTHER is a modern code developed over the past 10 years at E´lectricite´ de France by a team driven by the challenge and responsibility for improving the performance of its own nuclear reactor plant. PANTHER provides a general-purpose whole-core calculation capability based on multigroup neutron diffusion and core T-H models for thermal reactor analysis. The development dates back to 1986, led by CEGB with contributions from the UKAEA. The code can be applied to the analysis of PWR, AGR, MAGNOX, VVER, RBMK, and BWR [134 136]. PANTHER imports few-group nuclear data from the lattice code WIMS [19]. The interface is openly defined and accepts data from other lattice codes. PANTHER allows a comprehensive range of calculations, including steady-state performance, fuel management, safety transient analysis, and operational support, including online core follow calculations. Neutron kinetics calculation in zero-dimensional, 1D, 2D, or 3D rectangular or hexagonal assemblies can be performed using either the analytic nodal method (ANM) or finite difference method. The numerical iteration used for the two methods is essentially the same, while in the nodal method the node-to-node coupling coefficients are periodically updated through the iteration by solving subsidiary 1D nodal equations for each direction. The steady-state solution is accelerated with the Chebyshev polynomial method [137]. Based on the diffusion solvers, transient problems can be solved with an exponential transformation method to the temporal variable, allowing the use of large time steps. PANTHER has been designed in modular form. Each of the basic elements of the reactor calculation is executed by a separate module called by the user. PANTHER has its own easy-to-use interface by which the user controls the execution of modules and the data flow between them. Full links with RELAP enable integrated 3D whole plant kinetics calculations to be performed [138].

5.3.4 Purdue Advanced Reactor Core Simulator PARCS known as Purdue Advanced Reactor Core Simulator is designed to predict the dynamics response of the BWR and PWR, pressurized heavy water reactor, and pebble bed reactor to reactivity changes such as control rod movement or change in temperature/ fluid conditions in the reactor core [139 141]. PARCS was developed by gathering advanced methods modeling each physical phenomenon and making numerous improvements over the existing methods to treat the spatial kinetics calculations [20,142,143]. PARCS employs the theta method with exponential transformation and a second-order analytic precursor integration technique for the

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temporal discretization. The temporal discretization scheme allows sufficiently large time step sizes even in severe transients involving superprompt critical reactivity insertion [144]. For the spatial discretization the efficient nonlinear nodal method is performed consisting of solving repetitively the CMFD problems and the local two-node problems with a Krylov subspace method. Both the nodal expansion method (NEM) and the ANM can be used to obtain the two-node solution. For some applications such as the MOX fuel loaded reactor core, an SP3 kernel was chosen for both the fine mesh (pin-by-pin) finite difference and nodal NEM discretization. A hexagonal multigroup nodal diffusion kernel was also implemented in PARCS based on the Triangular Polynomial Expansion Method to handle nonorthogonal geometries such as VVER. For modeling more accurately the control rod movements, a control rod cusping correction method is included by solving a three-node problem for the intranodal flux using the fine mesh finite difference method. The cross section formalism is accounted for with the GENPMAXS code, by considering control rod insertion, fuel temperature, moderator temperature, moderator density, and soluble boron concentration. Utilizing this code, some well-known lattice physics codes are compatible with PARCS, such as TRITON [94], HELIOS [43], and CASMO [30]. In addition, a series of models are employed for the purpose of fuel cycle analysis, such as the critical boron concentration search, adjoint calculation and reactivity edits, decay heat modeling, treatments to iodine/xenon/promethium/samarium poisons, and point kinetics. T-H feedback effects are also available either by using a simplified T-H solution method or by coupling commercial T-H codes [20,140,145].

5.3.5 DONJON4 DONJON4 is a full-core simulation code designed on solution techniques of the neutron diffusion or SPN equation [146]. The DRAGON4 modules are used in combination with DONJON4 code to provide the macroscopic cross-section libraries and to perform microdepletion calculations [71]. The TRIVAC solver modules are used to perform the spatial discretization of the reactor geometry and to provide the numerical solution according to the user-selected numerical procedure [147]. The DONJON4 code is divided in modules, each of which performs particular tasks. The DONJON4 modules are first designed for the reactor full-core modeling in 3D Cartesian geometry. These modules are built around the reactor fuel lattice specification corresponding to the common design features of CANDU reactors. DONJON4 allows several different types of full-core calculations and can be used to determine some important core characteristics, such as the power and normalized flux distributions over the reactor core [71,73,148]. The cross sections for each material are essentially recovered from the reactor database, obtained from the lattice calculations using DRAGON4 code. The produced extended macrolib is subsequently used to obtain the numerical solution, using TRIVAC modules. TRIVAC, the main full-core lux solver, is based on diffusion theory and simplified PN Raviart Thomas finite elements in Cartesian 1D/2D/3D geometry and hexagonal 2D/3D geometry [147]. Space time kinetics problems can be solved with the theta method. In addition, DONJON4 is equipped with the capability of performing reactor’s fuel map management, device management, including solid rods and liquid zone controllers. Besides, a simplified T-H

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module is implemented where the reactor is represented as a collection of independent channels with no cross-flow between them based on a two-fluid homogeneous model.

5.3.6 DYN3D The reactor dynamics code DYN3D is a 3D best estimate tool for simulating steady states and transients of LWRs and has been developed at the Helmholtz-Zentrum DresdenRossendorf, Germany, and its predecessor organizations for more than 20 years [149]. The code is undergoing continuous development with respect to the improvement of physical models and numerical methods. Abundant efforts have been expended to couple DYN3D to different T-H codes and fuel performance codes, rendering it to be an advanced simulation tool for transients in LWRs and innovative reactor designs [143,150 156]. The neutron kinetics model comprises the solution of the 3D two-group or multigroup neutron diffusion equations or simplified transport equations applying nodal expansion methods, which is specific for the geometry of fuel assemblies [157]. Cartesian as well as hexagonal fuel assembly geometries are treated [150]. To ensure the mesh refinement capability also for hexagonal problems, a trigonal-geometry approach is also incorporated. Concerning transient processes, time integration over a time step is performed with the help of an implicit difference scheme and exponential transformation. Adjoint flux and reactivity calculation are accounted. DYN3D includes an intrinsic T-H model for one- and two-phase flow in the reactor core and a fuel rod model. Besides, fuel cycle analysis taking into account fuel element shuffling operations is also permitted in DTYN3D. To model the poison-related reactor dynamics, in particular xenon oscillations, the balance equations for the 135Xe, 149Sm, 135I, and 149Pm concentrations are solved [158]. Moreover, a model for calculating the space-dependent decay heat power derived from the operational history as well as during the transient is also integrated in DYN3D. In terms of modeling the complex processes in nuclear power reactors occurring during transients, the close interaction between neutron kinetics and thermal hydraulics has to be modeled adequately. For this purpose, DYN3D can be coupled with a series of code systems for multiphysics simulations, such as the system code ATHLET [159 162] or RELAP5 [160,162], the subchannel code SUBCHANFLOW, the CFD code ANSYS CFX, and the fuel performance code TRANSURANUS [151,163 165].

5.3.7 Bamboo-Core As the core calculation component of the Bamboo code system developed in Xi’an Jiaotong University, a fuel management calculation code Bamboo-Core provides a series of functions required by fuel management calculation [166,167]. Compared with existing PWR core codes, its features can be summarized by the following: (1) the generalized cross section parameterization module provides an opportunity for users to design their own parameterization form and (2) the variational nodal method (VNM) is employed as the neutron diffusion solver in PWR core calculation. The 3D continuous nodal flux distributions can be obtained once the VNM solution is be obtained. For the parameterization of neutron cross sections, a code named NECP-Lilac is developed [168]. The code holds a flexible choice of fitting options, thus there is no limitation on the type and the number of few-group constants and state parameters. The control rod

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113 FIGURE 5.3 he workflow of Bamboo-Core. Source: Copied with permission from W. Yang, H. Wu, Y. Li, J. Yang, L. Cao, Development and verification of PWR-core fuel management calculation code system NECPBamboo: Part II Bamboo-Core, Nucl. Eng. Des. 337 (2018) 279 290 r2018 Elsevier.

cusping effect is readily handled using the heterogeneous capability of VNM [169]. The predictor corrector quasistatic method is incorporated for dynamics calculations. A T-H feedback is accounted by solving the 1D mass and energy conservation equations within each single channel. The workflow of Bamboo-Core is shown in Fig. 5.3.

5.3.8 SCOPE2 The SCOPE2 code is the core simulator corresponding to the AEGIS code based on the pin-by-pin calculation method [170]. It adopts a tabulated cross section library, which

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is prepared from the results of the AEGIS calculation [80,81,171]. SCOPE2 is based on the pin-wise homogenization along with fine mesh calculation scheme, which significantly increases the computational resolutions. SPH methods (also known as SPH factors) are generally employed to enhance the cross section homogenization accuracy [172]. SCOPE2 is established on a 9-energy group structure to perform 3D pin-by-pin calculation with SP3 nodal transport theory [81]. Red/black iterative solver with a fine-grained parallel mode as well as one-group GCMR method is employed to accelerate the prohibitive computation processes resulted from fine-grained spatial meshing [173]. Reconstruction of cross sections from tabulation using a variety of indexes is allowed. Quarter assembly-wise closed channel model or thermal mixing model between subchannels is implemented. The SCOPE2 code is designed and implemented for the use in reload core design; it must give the solution within reasonable computing time. In order to accomplish the requirements, a number of acceleration techniques are adopted, including parallel computing. Parallel computing is established based on the MPI (Message Passing Interface). SCOPE2 runs on any parallel environments where a MPI implementation is available such as Linux-powered PCs or parallel supercomputers [174].

5.3.9 DIF3D/VARIANT/REBUS DIF3D VARIANT is the main toolkit developed at Argonne National Laboratory tailored to the 2D or 3D neutronics analysis of fast reactor cores based on the finite difference method or the VNM [9,175,176]. The nodal option of DIF3D solves the multigroup steady-state neutron diffusion equation in 2D and 3D hexagonal and Cartesian geometries. VARIANT solves the multigroup steady-state neutron diffusion and transport equations in 2D and 3D Cartesian and hexagonal geometries using the VNM [177 179]. The transport approximations allow complete spherical harmonic expansions up to order P99. Eigenvalue, adjoint, fixed source, gamma heating, and criticality (concentration) search problems are permitted. Anisotropic scattering is treated, and although primarily designed for fast reactor problems, up-scattering options are also included [114]. REBUS is a system of codes designed for the analysis of fast reactor fuel cycles [180]. Two basic types of analysis problems are solved: (1) the infinite-time, or equilibrium, conditions of a reactor operating under a fixed fuel management scheme and (2) the explicit cycle-by-cycle, or nonequilibrium, operation of a reactor under a specified periodic or nonperiodic fuel management program. REBUS will handle both equilibrium and nonequilibrium problems using a number of different core geometries, including triangular and hexagonal mesh by utilizing the DIF3D VARIANT solvers. Other features include fully automatic restart capability, no restrictions on number of neutron energy groups, and general external cycle with no restrictions on number of external feeds, reprocessing plants, etc. Microscopic cross sections are permitted to vary as a function of the atom density of various reference isotopes in the problem as appropriate for soft spectrum systems. The transmutation equations are solved by the matrix-exponential technique [45]. The isotopes to be considered in the burnup equations, as well as their transmutation reactions, are specified by the user.

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5.3.10 European Reactor Analysis Optimized calculation System To achieve the challenging technology goals set by the GENERATION IV International Forum in the sustainability, safety, and reliability fields, the European Reactor Analysis Optimized calculation System (ERANOS), has been developed and validated with the aim of providing a suitable basis for reliable neutronics calculations of current, as well as advanced fast reactor cores [181]. The latest version of the ERANOS code and data system, ERANOS 2.1, contains all of the functions required for reference and design calculations of liquid-metal fast reactor cores (as well as blankets, reflectors, and shields), with extended capabilities for treating advanced reactor fuel subassemblies and cores, accelerator-driven systems and gas-cooled fast reactors. The ERANOS code system was developed to answer the needs of both industrial and R&D organizations [182 186]. The ERANOS is a code system written in a modular structure to allow incorporation of the recent research and development innovations. Among the modules involves the aforementioned ECCO code for the generation of neutron cross sections. Here, for core and shielding calculation codes, 1D/2D/3D diffusion, or the 1D/2D SN transport code BISTRO [119], or 2D/3D TGV/VARIANT code [178,187] can be utilized. A kinetics driver named KIN3D has been developed using the TGV/VARIANT module and is integrated into ERANOS [188]. An isotopic point depletion code MECCYCO is included for direct and adjoint calculations and sensitivity calculations. Special procedures for control rod homogenization, sensitivity and perturbation calculations, representative analysis, intranodal homogeneous flux reconstruction, and shielding calculations are also allowed. The ERANOS code system is examined with the VENUS-F facility by comparing with the Serpent code the core reactivity for different critical reactor core configurations. As shown in Section 5.3.2, the accuracy of ERANOS is comparable to the Monte Carlo method, confirming the code package to be a powerful to for the modeling of fast reactors.

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[164] A. Grahn, S. Kliem, U. Rohde, Coupling of the 3D neutron kinetic core model DYN3D with the CFD software ANSYS-CFX, Ann. Nucl. Energy 84 (2015) 197 203. [165] L. Holt, U. Rohde, M. Seidl, A. Schubert, P. Van Uffelen, R. Macian-Juan, Development of a general coupling interface for the fuel performance code TRANSURANUS tested with the reactor dynamics code DYN3D, Ann. Nucl. Energy 84 (2015) 73 85. [166] B.N. Liang, H.C. Wu, Y.Z. Li, Adaptive expansion order for diffusion variational nodal method, Ann. Nucl. Energy 117 (2018) 114 130. [167] W. Yang, H. Wu, Y. Li, J. Yang, L. Cao, Development and verification of PWR-core fuel management calculation code system NECP-Bamboo: Part II Bamboo-Core, Nucl. Eng. Des. 337 (2018) 279 290. [168] Y. Li, S. Gao, H. Wu, L. Cao, W. Shen, PWR few-group constants parameterization analysis, Prog. Nucl. Energy 88 (2016) 104 117. [169] Y.P. Wang, H.C. Wu, Y.Z. Li, Comparison of two three-dimensional heterogeneous variational nodal methods for PWR control rod cusping effect and pin-by-pin calculation, Prog. Nucl. Energy 101 (2017) 370 380. [170] M. Tatsumi, A. Yamamoto, H. Nagano, K. Sengoku (Eds.), PWR core tracking using a next-generation core calculation code, SCOPE2, in: Proceedings of the International Conference Global Environment and Advanced Nuclear Power (GENES4/ANP2003), Paper. [171] M. Tatsumi, Y. Ohoka, N. Sugimura, A. Yamamoto, Verification of the AEGIS/SCOPE2 in-core fuel management system, 2008. [172] A. Yamamoto, M. Tatsumi, Y. Kitamura, Y. Yamane, Improvement of the SPH method for pin-by-pin core calculations, J. Nucl. Sci. Technol. 41 (12) (2004) 1155 1165. [173] Yamamoto A, Acceleration of response matrix method using cross-section scaling, Nucl. Sci. Eng. 147 (2) (2004) 176 184. [174] T. Masahiro, Y. Akio, Performance of a fine-grained parallel model for multi-group nodal-transport calculations in three-dimensional pin-by-pin reactor geometry, 2003. [175] Derstine K, DIF3D: A Code to Solve One-, Two-, and Three-Dimensional Finite-Difference Diffusion Theory Problems, Argonne National Lab., 1984. [176] T. Taiwo, H. Khalil, An Improved Quasistatic Option for the DIF3D Nodal Kinetics Code, Argonne National Lab., IL, 1991. [177] E.E. Lewis, G. Palmiotti, Simplified spherical harmonics in the variational nodal method, Nucl. Sci. And. Eng. 126 (1) (1997) 48 58. [178] G. Palmiotti, E. Lewis, C. Carrico (Eds.), Variant: variational anisotropic nodal transport, in: Proceedings of the International Conference Mathematics and Computations, Reactor Physics, and Environmental Analyses, 1995. [179] M. Smith, N. Tsoulfanidis, E. Lewis, G. Palmiotti, T. Taiwo, Higher order angular capabilities of the VARIANT code, Trans. Am. Nucl. Soc. 86 (2002) 321. [180] B. Toppel, User’s Guide for the REBUS-3 Fuel Cycle Analysis Capability, Argonne National Lab., 1983. [181] J.M. Ruggieri, J. Tommasi, J. Lebrat, C. Suteau, D. Plisson-Rieunier, C. De Saint Jean, et al. (Eds.), ERANOS 2.1: international code system for GEN IV fast reactor analysis, in: Proceedings of the International Congress on Advances in Nuclear Power Plants, ICAPP06, Reno, 2006. [182] K. Sugino, G. Rimpault, Analyses of the JUPITER fast reactor experiments using the ERANOS and JNC code systems, in: JAITMoAiRP, Mathematics, Millennium CitN, 2000, pp. 7 12. [183] K. Allen, T. Knight, S. Bays, Benchmark of advanced burner test reactor model using MCNPX 2.6.0 and ERANOS 2.1, Prog. Nucl. Energy 53 (6) (2011) 633 644. [184] L. Monti, T. Schulenberg, Coupled ERANOS/TRACE system for HPLWR 3 pass core analyses, 2009. [185] A. Talamo, Y. Gohar, G. Aliberti, Y. Cao, D. Smith, Z. Zhong, et al., MCNPX, MONK, and ERANOS analyses of the YALINA Booster subcritical assembly, Nucl. Eng. Des. 241 (5) (2011) 1606 1615. [186] M. Sarotto, A. Kochetkov, A. Kra´sa, G. Bianchini, V. Fabrizio, M. Carta, et al., The neutronic modelling of the VENUS-F critical core experiments with the ERANOS deterministic code (FREYA EU FP7 project), Ann. Nucl. Energy 121 (2018) 626 637. [187] J. Ruggeri, F. Malvagi, R. Boyer, TGV: a coarse mesh 3 dimensional diffusion-transport module for the CCRR/ERANOS code system. CEA DRNR-SPCI-LEPh-93-209. 1993 Feb. [188] G. Rimpault (Ed.), The ERANOS data and code system for fast reactor neutronic analyses, in: Proceedings of the International Conference PHYSOR, Seoul, South Korea, October 7 10, 2002.

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C H A P T E R

6 Nuclear physics probability code: OpenMC Jiankai Yu Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA United States

6.1 Introduction to Monte Carlo method The determination of reactor core neutronic characteristics is the first step and the basis of all successive procedures in the complete nuclear power plant design and analysis. In general, the neutronic analysis of reactor core is performed via solving neutron transport equation. However, it is not easy to solve the neutron transport equation, due to the complexity coupled with time, space, direction, and energy. There are two general ways to solve it, including deterministic and probability (also unknown as Monte Carlo) methods. Of which, deterministic method discretizes neutron transport equation via time, space, direction, and energy. This method replies on coordinate system, energy grid, which could save computation time, however, introduces major approximation in computation accuracy. However, Monte Carlo method solves the neutron transport equation via simulating the neutron behavior from birth to death, which makes it easy to process the details of the neutron transport, including continuous energy, arbitrary geometry, and even all possible nuclear reactions. The drawback of Monte Carlo method lies in computation efficiency and the statistical uncertainty introduced by probability theorem. Deterministic method has been widely used in nuclear industry due to the high efficiency. However, with the development of high-performance computers, and the increasing demand of advanced nuclear application system, that is, next generation nuclear power plant, Monte Carlo method has been recently rapidly developed. Therefore, this chapter only focuses on the Monte Carlo neutron transport methodologies and their implementations in OpenMC code.

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6.2 Recently developed Monte Carlo codes Table 6.1 describes a brief summary of some recently developed Monte Carlo reactor physics codes, that is, MCNP [1], MC21 [2], Serpent [3], and OpenMC [4]. MCNP is a general-purpose Monte Carlo N-Particle code that can be used for not only neutron but also photon, electron, and coupled neutron/photon/electron transport, which is the pioneer in Monte Carlo neutron transport code development. It utilizes the point-wise continuous-energy nuclear data library (called “ACE”), constructive solid geometry (shortly “CSG”) description of nuclear application system with arbitrary three-dimensional (3D) geometric configuration. Those methodologies are still widely used in many other Monte Carlo codes. In addition, MCNP has been also developing to reach the latest version MCNP6, which is the improved combination of MCNP5 and MCNPX based on the advanced programming features. The MC21 code is a continuous-energy Monte Carlo neutron (and photon) transport code for the calculation of the steady-state spatial distributions of reaction rates in 3D nuclear system, which is intended to support the large-scale problem-solving. It also applies the CSG to describe the model and has great capability in large numbers of tallies with high efficiency. Serpent is a continuous-energy Monte Carlo reactor physics burnup calculation code. It uses a universe-based geometry model to describe the complicated structures, which is similar to CSG, but more user-friendly. Serpent has been widely used in more than 100 universities and research organizations all over the world.

TABLE 6.1 Summary of Monte Carlo codes. Codes

Organizations

Countries

MCNP

Los Alamos National Laboratory

United States

MC21

Bettis and Knolls Atomic Power Laboratory

United States

Serpent

VTT Research Center of Finland

Finland

OpenMC

Massachusetts Institute of Technology

United States

Shift [5]

Oak Ridge National Laboratory

United States

KENO [6]

Oak Ridge National Laboratory

United States

COG [7]

Lawrence Livermore National Laboratory

United States

RMC [8]

Tsinghua University

China

McCARD [9]

Seoul National University

Korea

MCS [10]

Ulsan National Institute of Science and Technology

Korea

MVP [11]

Japan Atomic Energy Agency

Japan

Monk [12]

Atomic Energy Authority

United Kingdom

TRIPOLI [13]

CEA

France

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OpenMC is the only one open-sourced Monte Carlo neutron transport code that is served as a simulation tool for large-scale advanced nuclear system based on highperformance computing platforms. Many features benefit from the advanced software engineering techniques. It also adopts CSG and CAD representation to model the complex geometry. The point-wise nuclear data library is based on a native HDF5 format other than ACE itself. In addition, all input files are prepared in XML format, making it very friendly for beginners. Finally, the development of Python API treats neutron transport as an independent solver, which makes it easy to be coupled with depletion calculation, as well as multiphysics feedback. Other codes have also been developed recently to satisfy the increasing demands of design and analysis of advanced nuclear application systems. This section does not discuss in detail their features. However, some typical reference papers are provided to the person who is interested.

6.3 Typical methodologies in OpenMC This section depicts certain typical and important features and corresponding methodologies in OpenMC code. The typical flow to simulate one neutron history can be arranged like this: sampling neutron from source, random walk through geometry, sampling reaction if collision happens, sampling secondary particle if fission-related reaction happens. If the history of one neutron terminates, all necessary tallies will be collected.

6.3.1 Random number generator There are many applications of random number generators (RNGs) in the whole random walk tracking of a particle. Hence, the performance of RNG plays one of the most important roles in the complete Monte Carlo simulation. The commonly used RNG utilizes the linear congruential algorithm to generate the pseudorandom number:




Si11 5 Si g 1 c mod2m ; ri11 5

(6.1)

Si11 ; 2m

(6.2)

where r is the random number, S is the seed, g is the multiplier, c is adder (or increment), and 2m is the modulus. This is the most robust algorithm that has been tensely examined over a few decades. TABLE 6.2 Some values of random number generator. Code MCNP MCNP5 OpenMC

Modulus 48

2

63

2

63

2

Period

Multiplier 5

63

(Varies)

1

63

2,806,196,910,506,780,709

1

2 2 2

19

Increment

46

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0

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As shown in Table 6.2, RNG in MCNP has the period of 246 with the stride of 152,917, and therefore it could simulate 4:6 3 106 histories without repeated random number. However, the RNG in MCNP5 extends the capability to .109 particles simulation.

6.3.2 Computational geometry The computation geometry is to tell the code that where the particle is located and how far the distance is from particle to the surface or boundary. In general, there are two major ways to describe the computational geometry in the Monte Carlo codes, including CSG in MCNP and body geometry in KENO. The principle of CSG is to construct the model by using surfaces with the operators of intersection, union, and complement. Take an example as shown in Fig. 6.1, the modeling starts from pin cells to fuel assemblies and finally constructs 3D model of the full-core configuration. However, the basic idea of body geometry is to construct the target model via some predefined basic bodies, including cylinder, sphere, cones, cuboid, hex-prisms, planes, rhomboids, and wedges with the operators of rotation, truncation, and intersection. Fig. 6.2

FIGURE 6.1 Constructive solid geometry modeling from fuel pin to fuel assembly and full core.

FIGURE 6.2 Body geometry modeling of single fuel pin.

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shows the body geometry modeling of a single fuel pin via the combination of two cylinders and one cuboid to present fuel pellet, cladding, and coolant.

6.3.3 Random walk The solution of Monte Carlo neutron transport originates from hundreds of millions of independent simulations of each neutron particle. Therefore the complete history of neutron is usually called random walk. The random walk in Monte Carlo is composed of those procedures according to the time sequence of a neutron particle from birth to death (from generation to disappearance). Those procedures contain sampling from initial source, sampling the flight distance, sampling collision nuclide, sampling reaction, sampling the energy, and direction of secondary particle if the reaction with neutron production occurs. In random walk the neutron was born at the specific location with given energy and direction, in which location, energy, and direction are sampled from initial neutron source or prestored neutron source from previous generation of random walks. Once the neutron particle travels through a homogeneous material, the distance to the next possible collision will be sampled according to the macroscopic total cross section of the material based on flight path sampling method. If a collision occurs, the specific nuclide within the material will be sampled. Once the nuclide is determined, the specific reaction for the nuclide is sampled. In most Monte Carlo random walk, due to no secondary neutron particle produced from disappearance reactions (e.g., photon or alpha particle production reactions), there is no need to track those reactions. However, the exception is that one needs to explicitly track photons so as to accurately evaluate the effect of gamma heating. In that case the coupled neutron and photon transport is applied. In nuclear physics, fission is considered as one of absorption reactions together with other disappearance reactions. However, Monte Carlo treats it as kind of inelastic scattering reaction, since fission produces secondary neutron after collision. Those secondary neutrons are sampled from the corresponding secondary particle angleenergy distribution in nuclear data library. That information, including the average number of prompt and delayed neutrons, and the outgoing energy and direction for secondary neutrons, are stored for next generation of random walk instead of being tracked just like the neutrons sampling from elastic and inelastic scattering. This is how the fission bank method treats it in OpenMC code. Note that the generation concept only applies in eigenvalue mode of Monte Carlo neutron transport simulation, other than fixed-source mode of simulation.

6.3.4 Tallies and statistics Tallies are one of three major components in Monte Carlo simulation together with geometry and physics. Of which, geometry determines those items like that: the cell is the neutron currently in; the cell will the neutron come in next; the distance to the boundary and the boundary condition. Physics tells one that as follows: the possibility for the occurrence of a collision, the nuclide of the material that collides with neutron particle, and the exiting energy and direction of secondary neutron if nondisappearance reaction occurs. Therefore the tallies contain such item like that: tallies of events of interest during random walk, accumulation of the score and squares of those above-tallied events after the

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completion of each random walk, and the final statistics of mean value and standard deviations after the completion of all random walks. In mathematics, suppose that one has the quantities of interest R(x), complying to the probability density function f(x), where x is the independent random variable. Hence, the expected value and the variance of the R(x) can be expressed like this: ð μ 5 RðxÞfðxÞdx (6.3) ð σ 5

R2 ðxÞfðxÞdx 2 μ2

2

(6.4)

In Monte Carlo tallies and statistics the estimation of expected value is the summation of all tallies score instead of integral as follows: R

N 1X Rðxj Þ N j51

(6.5)

According to the central limit theorem, in the case of large number N, the probability density function of R is approaching a Gaussian distribution. In Monte Carlo simulation, if the number of random walks is large enough, the mean value is equal to expected value. Consequently, given the tallied scores of interests in random walks xj , the mean value, variance, and the variance of the mean can be expressed like that: x5 σ2 5

N 1X xj N j51

(6.6)

1 XN 2 x 2 x2 j51 j N

(6.7)

σ2 N

(6.8)

δ2x 5

To make the tallies more flexible, tally bin is utilized to extend the tallied score for different events in difference phase space. Those can be range of energies, interval of time, specified cells, surfaces and the range of directions, the specified nuclides, reactions, and so on. Any tally in OpenMC can be expressed in the following to maximize the flexibility for user to specify it, ð ð ð X 5 dr dΩ dEfðr; Ω; EÞψðr; Ω; EÞ; (6.9) Ð Ð Ð where dr dΩ dE is the filter, which can be specified on user’s demands. Those can be filter in OpenMC: the universe in CSG description, material, cell, cell that neutron is born, crossing-surface, user-defined mesh, precollision and postcollision energy, polar angle and azimuthal angle in spherical coordinate, and the cosine of the change-in-angle caused by a scattering event. In addition, f ðr; Ω; EÞ in Eq. (6.9) is the tallied score. Those can be scored in OpenMC: flux, reaction rate for any reaction cross section stored in nuclear data library, higher scattering moments, and surface currents.

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Flux tally is the most important one in neutronic analysis of reactor core. There is more than one way to estimate flux tally during Monte Carlo simulation, including track-length and collision. They are expressed in the following equations: 1 X φ5 (6.10) all particles dj wj WV flights in cell 1 X 1 (6.11) φ5 all collision Σt wj WV in cell wheredj is the track-length, wj is the weight of neutron, W is the total starting weight assigned for neutron at the beginning of random walk, V is the cell volume, and Σt is the macroscopic total cross sections. Finally, figure of merit (also known as FOM) might be obtained in some Monte Carlo code to evaluate the quality of the tallied score of interest. It can be calculated as follows: FOM 5 δ5

1 ; δ T 2

δx ; x

(6.13) (6.14)

where T is the Monte Carlo simulation time and δ is the standard deviation or relative error as expressed in Eq. (6.14).

6.3.5 Eigenvalue calculation Criticality safety or steady-state neutronic analysis of nuclear reactor core is classic eigenvalue problem. Hence, the eigenvalue problem will be solved by power iteration in Monte Carlo neutron transport. Instead of inner and outer iterations method in deterministic code, the power iteration procedure for Monte Carlo is like that: 1. 2. 3. 4. 5.

Guess initial k-eigenvalue (k-effective) and neutron flux. Random walk for N particles in one generation (or batch). Compute new k-eigenvalue and statistic neutron flux. Repeat the steps from 2 to 3 until k-eigenvalue and neutron flux have converged. Compute generation averaged k-eigenvalue and neutron flux.

In most of Monte Carlo codes, there are three means to estimate k-eigenvalue, including track-length estimator, collision estimator, and absorption estimator, respectively. They are expressed in the following equations: P all flights wj dj υΣf ktrack2length 5 (6.15) W P wj ðυΣf =Σt Þ kcollision 5 all collisions (6.16) W

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P kabsorption 5

all absorptions wj ðυΣf =Σa Þ

W

(6.17)

where W is the total weight starting each generation (or batch) and υΣf and Σa are macroscopic neutron production cross section and absorption cross section.

6.3.6 Fixed-source calculation Instead of eigenvalue calculation, alternative Monte Carlo simulation named fixedsource calculation is commonly used in solving fixed-source problem, that is, the subcritical nuclear system with external neutron source, or the time-dependent problem of nuclear reactor core. To simulate fixed-source problem, there is no more concept of generation. All random walks start from the given neutron source, including point source or source with spatial distribution. The procedure is like that: 1. 2. 3. 4.

Sample neutron from given source. Random walk until the neutron disappears. Repeat the steps from 1 to 2 until neutron flux has converged. Compute particle averaged neutron flux.

Surely, there is no more k-eigenvalue in such calculation mode. However, the neutron flux and related scores of interests would be tallied during the simulation.

6.4 Usage of OpenMC This section illustrates how to use the basic capabilities of OpenMC code, including the preparation work, the definition of geometries, materials, and control parameters. In addition, the simulation and how to extract basic results information are also stated.

6.4.1 Preparation To prepare the running of OpenMC code, the installation based on Ubuntu 18.04 is taken as an example: 1. Install all necessary compiler and tools for the compilation of C11 source code. 2. Install Python and all necessary packages. Anaconda is recommended to simplify the installation. 3. Clone source code from GitHub (https://github.com/openmc-dev/openmc.git). 4. Compile and build the source code. 5. Install Python API for OpenMC. 6. Configure environment variables for OpenMC executable code. Detailed introduction to the installation can be referred to OpenMC documentation website (https://docs.openmc.org/en/latest/index.html).

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6.4.2 Data library OpenMC adopts native HDF5 format to store and present all nuclear data libraries. Pregenerated HDF5 libraries can be found at https://openmc.org. The temperature sets of the nuclear data libraries cover 0K, 293.6K, 600K, 900K, 1200K, and 2500K. If one needs to simulate the system at other temperatures, the windowed multipoles based on-the-fly Doppler broadening method is highly recommended to use. Once the nuclear data library is ready, environment variable “OPENMC_CROSS_SECTIONS” to explicitly present the absolute path of the “cross_sections.xml” file included in the nuclear data library.

6.4.3 Geometry definition The sequence to define the geometry is described as follows: Define surfaces. Define cells using surface and operators that apply to surfaces. Group cells together into a universe if possible, and embed that universe inside another cell. Group cells together into a universe if possible, and repeat that universe in a lattice arrangement, and then embed the universe inside another cell. 5. Assign materials to cells. 1. 2. 3. 4.

Fig. 6.3 shows an example of a pressurized water reactor (PWR) fuel pin geometry definition via XML format input file. Note that all input files in XML format in this section refer to example suite of OpenMC source code on Github.

6.4.4 Material definition It is simple to define materials in XML input file. Take an example as shown in Fig. 6.4, all materials pile up without any order. Each material data block contains identification number, density value and unit, and all the nuclides included with name and atomic ratio.

6.4.5 Tally definition To define the tallies, one should define the filter first. Cell, mesh, energy can be used as filter in OpenMC. Once again, take the fuel pin as example just shown in Fig. 6.5, mesh and energy are used as filter, and flux, fission reaction rate, and fission production reaction rate have been tallied as score.

6.4.6 Settings definition Other parameters, which are not defined in geometry or material, are defined in settings input file. Those are simulation mode, number of batches, inactive and active batches, and the number of particles simulated in each batch. Moreover, the definition of source distribution, and the mesh used in entropy estimation are also included in settings definition. Fig. 6.6 shows the example for a fuel pin.

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FIGURE 6.3 Example of fuel pin geometry definition.

6.4.7 Plots definition Besides, plots definition is needed when the user is interested in plotting geometry of the modeling. Sometimes, it works to help check the possible error existed in geometry definition. This part of input file contains the basis, color filling mode and the origin, and width and pixels of the plotting. Fig. 6.7 displays the example of plotting definition for a fuel pin. To activate the plotting mode of OpenMC running, the parameter “ 2 p” is needed in command line input like this “openmc 2 p.” Fig. 6.8 displays the top view of fuel pin geometry that is generated by using the plots definition as shown in Fig. 6.7.

6.4.8 Simulation in serial and parallel OpenMC is developed as the tool for high-fidelity simulation based on highperformance computing platform. One can benefit from the computer with multiple cores, threads, or clusters, when OpenMC is ran in parallel mode other than default serial model. OpenMC supports shared-memory parallelism (OpenMP) and distributed-memory parallelism (MPI).

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FIGURE 6.4 Example of material definition for a fuel pin geometry.

FIGURE 6.5 Example of tallies definition for fuel pin.

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FIGURE 6.6 Example of settings definition for fuel pin.

FIGURE 6.7 Example of plotting definition for a fuel pin.

However, the OMP_NUM_THREADS environment variable is used to determine the number of threads to be specified in OpenMP. Also, one can specify it by following command line “openmc 2 s 8.” To run MPI parallel, either OpenMPI or MPICH, should be installed as the prerequisites, which is called using command line like this “mpiexec 2 n 8 openmc.” Apparently, the hybrid uses of OpenMP and MPI are allowed via command line like this “mpiexecc 2 n 8 openmc 2 s 8.”

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FIGURE 6.8 Top view of fuel pin geometry configuration.

6.4.9 Output description As the results of OpenMC simulation, the “tallies.out,” “summary.h5,” and “statepoint. #.h5” will be created. Of which, the first file is an ASCII file presenting the mean and standard deviation of the mean for user-defined tallies. The second one is an HDF5 file containing a complete description of the geometry and materials in the modeling. The last one is also an HDF5 file, including the complete results of the simulation, which is mainly used to visualize or postprocess simulated results. Moreover, it is necessary to be loaded in the restarting calculation.

6.4.10 Python API Plenty of Python API have been developed based on OpenMC, which make it much easier for the user to prepare input file, run the simulation, and postprocess the simulated results. Table 6.3 lists the Python API for OpenMC, which provides most of necessary functions in nuclear reactor application.

6.5 Verification and validation The Monte Carlo performance benchmark that is proposed by Hoogenboom et al. [14] has been utilized to verify OpenMC for the capability of full-core modeling and simulation. This model is composed of 241 typical PWR fuel assemblies, and each assembly has the layout of 17-by-17 lattice of fuel pins, including 24 guide tubes and one instrumentation tube. Totally 34 different isotopes are included in this model, covering major actinides, minor actinides, and typical fission products. Top view of the quarter core of this benchmark is displayed in Fig. 6.9.

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TABLE 6.3 List of Python API for OpenMC. openmc

Basic function in handling nuclear data, geometry modeling, materials definition, tallies constructing, geometry plotting, simulation settings, and postprocessing of results

openmc. model

Model building for borated water, fuel pin, hexagonal prism and rectangular prism, and TRSIO particle modeling

Openmc. deplete

Advanced function to run OpenMC coupled depletion

Openmc. mgxs

Advanced function to generate multigroup cross section

Openmc.data

Tools for the nuclear data preparation

Openmc.lib

Binding python to C/C11 function defined by OpenMC shared library

FIGURE 6.9 Top view of quarter core of Monte Carlo Performance Benchmark.

This comparison between OpenMC and MCNP has shown a good agreement based on the same set of cross sections libraries. This chapter also analyzes the tally efficiency in the case of 289-by-289-by-100 mesh in Cartesian coordinate for this full-core model. The effective calculation rate can be kept as normal as 4957 neutrons per second [4]. The Benchmark for Evaluation And Validation of Reactor Simulations (BEAVRS) has been released by Computational Reactor Physics Group at MIT (Massachusetts Institute of Technology) in 2013 [15]. Later on, the revised versions have been released in 2016 [16] and 2018 [17], respectively. The current version is 2.0.2 that provides specifications and measured results for two complete fuel cycles. This full-core model contains 193 fuel assemblies, and each assembly has 17-by-17 configuration for 264 fuel rods and 24 guide tube and one instrumentation tube. The top view of geometric configuration is illustrated in Fig. 6.10. The full-core model at hot-zero-power state has been simulated by OpenMC and compared to the results of MC21 and measured data. The comparison results have proven that

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References

FIGURE 6.10

137 Top view of full core of BEAVRS

benchmark.

OpenMC can be applied in the analysis and design of 3D PWR realistic problems with high fidelity [18].

6.6 Summary This chapter first depicts brief introduction to Monte Carlo neutron transport method and recently developed Monte Carlo codes. Then, taking OpenMC as an example, some important methods are explained, including RNG, computational geometry, random walk, tallies and statistics, and eigenvalue and fixed-source calculation modes. Successively, advanced features implemented in OpenMC are described based on an example of a fuel pin. Those cover the definitions for geometry, materials, tallies, settings, plotting, running simulation in parallel, and postprocessing of simulated results. Posterior to that the advanced features based on Python API is briefly introduced, the previous verification work of the OpenMC application in realistic 3D PWR full-core analysis has been briefly discussed.

References [1] X-5 Monte Carlo Team, MCNP—A General Purpose Monte Carlo N-Particle Transport Code, Version 5, LAUR-03 1987, Los Alamos National Laboratory, 2003. [2] T.M. Sutton, T.J. Donovan, T.H. Trumbull, P.S. Dobreff, E. Caro, D.P. Griesheimer, et al., The MC21 Monte Carlo Transport Code, No. LM-06K144, Knolls Atomic Power Laboratory (KAPL), Niskayuna, NY, 2007. [3] J. Leppa¨nen, M. Pusa, T. Viitanen, V. Valtavirta, T. Kaltiaisenaho, The serpent Monte Carlo code: status, development and applications in 2013, Ann. Nucl. Energy 82 (2015) 142150. [4] P.K. Romano, B. Forget, The OpenMC Monte Carlo particle transport code, Ann. Nucl. Eng. 51 (2013) 274281. [5] T.M. Pandya, S.R. Johnson, T.M. Evans, G.G. Davidson, S.P. Hamilton, A.T. Godfrey, Implementation, capabilities, and benchmarking of Shift, a massively parallel Monte Carlo radiation transport code, J. Comput. Phys. 308 (2016) 239272.

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[6] B.T. Rearden, M.A. Jessee, SCALE Code System. No. ORNL/TM--2005/39-V-6.2, Oak Ridge National Laboratory (ORNL), 2016. [7] T.P. Wilcox Jr., COG: A Particle Transport Code Designed to Solve the Boltzmann Equation for DeepPenetration (Shielding) Problems: Volume 1: User’s Manual, No. M-221-1, Lawrence Livermore National Lab., CA, 1989. [8] K. Wang, Z. Li, D. She, Q. Xu, Y. Qiu, J. Yu, et al., RMC—a Monte Carlo code for reactor core analysis, in: SNA 1 MC 2013—Joint International Conference on Supercomputing in Nuclear Applications 1 Monte Carlo, EDP Sciences, 2014, p. 06020. [9] H.-J. Shim, B.-S. Han, J.-S. Jung, H.-J. Park, C.-H. Kim, McCARD: Monte Carlo code for advanced reactor design and analysis, Nucl. Eng. Technol. 44 (2) (2012) 161176. [10] H. Lee, W. Kim, P. Zhang, M. Lemaire, A. Khassenov, J. Yu, et al., MCS—a Monte Carlo particle transport code for large-scale power reactor analysis, Ann. Nucl. Eng. 139 (2020) 107276. [11] T. Mori, K. Okumura, Y. Nagaya, Status of JAERI’s Monte Carlo code MVP for neutron and photon transport problems, Advanced Monte Carlo for Radiation Physics, Particle Transport Simulation and Applications, Springer, Berlin, Heidelberg, 2001, pp. 625630. [12] V.S.W. Sherriffs, MONK—A General Purpose Monte Carlo Neutronics Program, No. SRD-R--86, UKAEA Safety and Reliability Directorate, 1978. [13] J.C. Nimal, T. Vergnaud, TRIPOLI: a general Monte Carlo code, present state and future prospects, Prog. Nucl. Energy 24 (13) (1990) 195200. [14] J.E. Hoogenboom, W.R. Martin, B. Petrovic, The Monte Carlo performance benchmark test-aims, specifications and first results, in: International Conference on Mathematics and Computational Methods Applied to, vol. 2, 2011, p. 15. [15] N. Horelik, B. Herman, B. Forget, et al., Benchmark for evaluation and validation of reactor simulations (BEAVRS), v1.0.1, in: Proceedings of the International Conference Mathematics and Computational Methods Applied to Nuclear Science and Engineering, 2013. [16] N. Horelik, MIT Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS), Version 2.0, MIT Computational Reactor Physics Group, Massachusetts Institute of Technology, 2016. [17] N. Horelik, MIT Benchmark for Evaluation and Validation of Reactor Simulations (BEAVRS), Rev. 2.0.2, MIT Computational Reactor Physics Group, Massachusetts Institute of Technology, 2018. [18] D.J. Kelly, N.A. Brian, P.K. Romano, B.R. Herman, N.E. Horelik, B. Forget, Analysis of Select BEAVRS PWR Benchmark Cycle 1 Results Using MC21 and OPENMC, No. JAEA-CONF2014-003, 2015.

II. Physics and fuels codes

C H A P T E R

7 FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions Bowen Qiu and Jun Wang Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States

7.1 Objectives, relations, and limitations 7.1.1 Objectives of the two codes Accurate calculation of the fuel rods behaviors of light-water reactor (LWR) under longterm steady states, operational transients, or accident conditions is the objective of the nuclear regulatory commission’s (NRC’s) ongoing program on reactor safety research [1]. To achieve this purpose the NRC sponsored a series of programs for computer code development, as well as in- and out-pile experiments for code validations [2]. FRAPCON and FRAPTRAN codes are developed under this background for steady-state and transient simulations, respectively. The performance analysis code, FRAPCON, was developed by the Pacific Northwest National Laboratory (PNNL) for the US NRC and is used to simulate steady state, which means that the power history and boundary conditions change very slowly, behaviors of the single fuel rod in pressurized water reactor or boiling water reactor under high burnup conditions (can up to 62 GWd/MTU) [1]. The code has been modified since the first version in 1997, FRAPCON-3 v1.0 [3], and then eight big updates have been released: FRAPCON-3 v1.1, FRAPCON-3 v1.2, FRAPCON-3 v1.3, FRAPCON-3 v1.3, FRAPCON-3.2, FRAPCON-3.3, FRAPCON-3.4, and FRAPCON-3.5. After a lot of code rewriting, FRAPCON-4.0 was released. FRAPCON-4.0 represents a major advance in the modernization of the FORTRAN language used by the code. All the subroutines have been merged into the module, and the old syntax has been removed. In general, the modified code is more readable and has a clearer program structure than previous versions.

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00007-3

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions

The corresponding transient performance analysis code, FRAPTRAN, is a fuel rod performance analysis code for LWR simulation when power history or boundary conditions rapidly change, such as LOCA, RIA, or operation transient conditions [4]. It is the successor to the previous FRAP-T (Fuel Rod Analysis Program-Transient) code that was developed in the 1970s
80s [5,6]. The latest version, FRAPTRAN-2.0, was also rewritten recently, and its code structure and subroutines are completely modularized for being more readable and maintainable [7]. Obviously, FRAPTRAN is a companion code to the FRAPCON code [1], it can read the output file calculated by FRAPCON in normal operation, such as burnup, fission gas release fraction, and internal gas pressure. Through the comprehensive application of these two codes, the whole process of the in-pile behavior of a single fuel rod can be simulated from normal operation condition to a specific transient condition. In addition, FRAPTRAN is also an independent simulation tool when several kinds of necessary information are provided by the user, such as initial geometry parameters and cladding irradiation swelling.

7.1.2 Relations Although the two codes can be used independently, the transient fuel performance code, FRAPTRAN, and the steady-state fuel performance code, FRAPCON, are closely related in two ways: (1) the material property modules and fundamental assumptions of the two codes are barely the same, except thermohydraulic model or fission gas release model, and (2) FRAPCON can create an initialization file that can be read by FRAPTRAN to initialize the burnup-dependent parameters in FRAPTRAN before a transient analysis as shown in Fig. 7.1.

FIGURE 7.1 Relations FRAPCON and FRAPTRAN.

Input card

FRAPCON

Steady-state simulation

Steady state/transie nt

Read the final state

FRAPTRAN

Transient simulation

Add boundary conditions

Steady-state output

Transient output

III. Fuels and sub-channel codes

between

7.2 Code structures and physical models

143

7.1.3 Limitations The simulation functions of the two codes are relatively comprehensive, but they are not intended to replace more professional codes, the models of which are more accurate. For example, subchannel codes (such as CPBRA or VIPRE) [8] are still preferred even through CHF correlations are modeled by FRAPCON/FRAPTRAN. Besides, the two codes have their own inherent limitations as follows: 1. Material limitations: The two codes are limited to modeling three kinds of pellets include UO2, MOX, and UO2—10 wt.% Gd2O3 in zirconium alloy cladding with a gas gap under light- and heavy-water reactor conditions [1,4]. Other kinds of fuel rod or coolant cannot be modeled unless relevant models are modified. Therefore further model changes are necessary to accommodate them, not only the MATPRO physical database but also the mechanical model. Furtherly, the model of fission gas release also needs to be modified. Besides, since the codes are established based on the experimental correlations, which means that the code is not validated beyond the specific temperature range and the calculation will stop if melting temperature is reached. 2. Direction limitation of heat flow: The heat flows in axial and hoop direction are not considered in thermohydraulic model, this assumption is valid and usually applied in fuel rod performance analysis code for typical fuel rod. 3. Time step limitation: Although thermohydraulic and mechanical models in FRAPCON code can accurately perform their functions involve time steps low to 0.001 day [1], the fission gas release model cannot because these models are established based on sufficiently slow data up to 50 days. However, the fission gas release code in FRAPTRAN code can calculate fuel behavior under transient condition involved time step of a few minutes or less. 4. Cladding strain limitation: The cladding strains calculated by mechanical models, which assume that the fuel rod is axisymmetric and axial constrains are inexistent in FRAPCON/FRAPTRAN code, are limited in 5%. 5. Inaccuracy: The calculated cladding strains are overpredicted by FRAPCON-4.0 up to high burnup even through the code can predict the hard contact stress exactly. Because of the limitation of experimental data, the code will generate inaccuracy on cladding strain at very high burnup. It should be noted that overestimation occurs in the physical property model of the cladding strain hardening. Besides, the oxidation thickness on cladding outer surface is underestimated according to Baker
Just model.

7.2 Code structures and physical models Fig. 7.2 presents the model order of FRAPCON and FRAPTRAN for steady-state and transient calculation. The specific order of these two models is different. Relevant models will be introduced briefly in the following sections.

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Initialization

Initialization

FIGURE 7.2 Model order of FRAPCON (A) and FRAPTRAN (B) calculations [1,4].

Gap temperature difference criterion < – 1%

Gas pressure difference criterion < – 1%

Temperature distribution (transient)

Temperature distribution

Plenum temperature disribution

Mechanical deformation

Mechanical deformation

Fission gas release and internal pressure (transient)

Fission gas release, internal pressure, and void volume

Oxidation at high temperature

Cladding ballooning

New time step New time step

(A)

(B)

7.2.1 Thermohydraulic models Assumption and limitations of models used in the two codes for temperature calculation are summarized as follows: 1. Only the radial direction of heat transfer of the axisymmetric fuel rod is considered in 1.5-D codes due to the large length-to-diameter ratio. 2. The constant boundary conditions remain constant at a certain time step. 3. The fuel rod is assumed as a circular cylinder. Since steady-state thermal equations are used in FRAPCON code while transient equations are used in FRAPTRAN code, the order to calculate thermal behaviors of the fuel rod under steady-state and transient conditions is different to a certain extent as shown in Fig. 7.3.

III. Fuels and sub-channel codes

7.2 Code structures and physical models

FRAPCON

FRAPTRAN

Local coolant conditions

Local coolant conditions

Cladding temperature

Heat generation of pellets

Gap heat conductance

Gap heat conductance

Pellet temperature distribution

Surface temperature

145

FIGURE 7.3 Comparison of thermal models in FRAPCON and FRAPTRAN [1,4].

Temperature distributions

7.2.1.1 Coolant conditions FRAPCON calculates coolant temperatures using the single-channel model that is closed under steady-state condition. Correlation is presented in the following equation: ðz  Tc ðzÞ 5 Tin 1 0

 πDo qvðzÞ dz Cp GAf

(7.1)

where Tc ðzÞ is the coolant temperature at z elevation (K), Tin is the inlet temperature (K), qvðzÞ is the surface heat flux (W/m2), Cp is the specific heat (J/kg/K),G is the mass flow rate (kg/m2/s), Af is the channel area (m2), and Do is the cladding diameter (m). Therefore pressure, mass flux, and inlet enthalpy are all necessary elements for calculating local coolant condition. Besides, the local pressure on cladding outer surface indispensable decides the cladding condition. These coolant conditions should be provided by a professional thermal-hydraulic code for FRAPTRAN calculation. 7.2.1.2 Cladding temperature and heat generation After the coolant condition is confirmed, the outer surface temperature of the cladding can be decided according to the flow pattern (single-phase forced convection heat transfer or boiling heat transfer). For avoiding convergence problem the heat transfer coefficient of these two patterns from coolant to cladding outer surface will be calculated both and the minimum one will be used [9]. Then the local temperature of the cladding outer surface and the temperature distribution of the whole cladding can be obtained. For FRAPTRAN code, heat is continually generated in pellets. Since the reactor physics model does not exist in FRAPTRAN code, heat generation history shall be provided by relevant code. It should be noted that the decay heat model in FRAPTRAN code developed by the American Nuclear Society (ANS) can calculate the decay heat generation [10], and therefore no external input file is needed if the reactor is scrammed and not fission heat is generated in an accident.

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7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions

7.2.1.3 Gap heat conductance The models of gap heat conductance used in FRAPCON and FRAPTRAN are the same. The fuel-cladding gap conductance model consists of three terms: radiation heat transfer, heat conductance through gas, and contact heat transfer [11] when pellet-cladding mechanical interaction occurs. Among them the contact heat transfer model is based on empirical equations depended on the ratio of contact stress, cladding Meyer hardness, thermal conductivity, and surface roughness of the pellet and cladding. It should be noted that the jump distance term accounts for the temperature discontinuity caused by incomplete thermal accommodation of gas molecules is also considered in the gap heat conductance model. This phenomenon occurs because gas molecules that leave the surfaces of the fuel and the cladding cannot fully exchange energy with neighboring gas molecules, resulting in nonlinear temperature gradient near surfaces. 7.2.1.4 Pellets temperature distributions The steady-state heat transfer fundamental equation in FRAPCON is shown in the following equation: ðð ððð 


kðT; xÞ r TðxÞ n ds 5 Q_ x dV (7.2)



V

S

-

2

where s is the surface of the control volume (m ), k is the thermal conductivity (W/m/K), n is the surface normal unit vector, V is the control volume (m3), and x- is the space coordinates (m). Accordingly, the transient heat transfer equation in FRAPTRAN is shown in the following equation: ð ð ð @T dV 5 krTds 1 qv dV ρCp (7.3) @t s

V

V

The finite difference method is applied in both FRAPCON and FRAPTRAN to calculate Eqs. (7.2) and (7.3), respectively. Therefore the radial grid division of the pellet at a certain axial node is performed as shown in Fig. 7.4.

Pell et c enter line

δml

δmr

2

2

m-1 δml

m

δmr

m+1

Pell et out er s urface

FIGURE 7.4 Radial meshes division of the pellet. ml and mr are the distances between nodes to the left and right of point m. The first node is the pellet center at a certain node, and the last node is on the outer pellet surface. It should be noted that the division lengths of radial nodes are not the same, which consistent with the radial power distribution. The closer to the outer surface, the denser the meshes are divided for edge effect. The thermal conductivity and heat source items to the left and right of node m are represented by KML and KMR, Sml and Smr. In the space between m and m 2 1 and m 1 1, the thermal conductivity and heat source items are assumed to be constant.

III. Fuels and sub-channel codes

7.2 Code structures and physical models

FIGURE 7.5

Spring

147

Energy flow in plenum model.

Cladding

Natural convection

Conduction and radiation Gas

Natural convection

7.2.1.5 Plenum gas temperature model and energy storage model In order to calculate the internal pressure of the fuel rod, the temperature of all the gas volumes in the fuel rod must be obtained, respectively. In fact, about 40%
50% internal gas of the fuel rod is in the plenum, which is usually at the top but sometimes at the fuel bottom. It is usually assumed that the temperature of the gas in the plenum is 5.6K higher than that of local coolant, which is just a rough estimation. Another method will be more comprehensively and complexly as shown in Fig. 7.5 that the heat exchange between all the components by natural convection [12], conduction, or radiation is considered. The heat storages of pellet and cladding are calculated separately in FPRACON code, the specific correlation is as shown in Eq. (7.4). For a certain axial node the total heat storage of the pellet or cladding is obtained by summing up the heat storage of each radial ring. Ð Ti PI i51 mi 298K Cp ðTÞdT (7.4) Es 5 m where Es is the stored energy (J/kg), mi is mass of ring segment i (kg), Ti is the temperature of ring segment i (K), Cp ðTÞ is the specific heat evaluated (J/kg/K), and m is the total mass of the axial nodes (kg).

7.2.2 Mechanical models Highly coupling of each model in FRAPCON/FRAPTRAN determines that the accuracy of mechanical models is significant for the reliability of the whole code through effecting models of other physical fields, such as heat transfer, gas pressure, and fission gas release. Besides, significance obviously is there for failure behavior of fuel rod under accident conditions. As mentioned earlier, deformation analysis is limited as small deformation

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7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions

includes stress, strain, and displacement of the cladding. Following physical phenomena are considered in the analysis: 1. The elastic and plastic deformation, thermal expansion, creep behavior, and irradiation growth are taken into account for cladding analysis. 2. The thermal expansion, swelling, densification, relocation, and hot press behavior are taken into account for pellet analysis. 3. Internal gas pressure. “FRACAS-I” model, which is solved with finite difference method, is applied not only in FRAPCON code but also in FRAPTRAN code. This mechanical model is a kind of pellet rigid model, which means that the displacement of the fuel outer surface will apply a driving force to the cladding deformation when fuel-cladding gap close and hard contact occurs. But the cladding deformation never has a feedback to the deformation of the fuel. Relevant fundamental assumptions of cladding deformation in FRACAS-I model are listed as follows [13]: Incremental theory of plasticity [14]. Prandtl
Reuss flow rule. Isotropic work hardening. Thick wall cladding (thick wall approximation formula is used to calculate stress at the midwall). 5. If fuel and cladding are in contact, no axial slippage occurs at fuel cladding interface. 6. Bending strains and stresses in cladding are negligible. 7. Axisymmetric loading and deformation of cladding.

1. 2. 3. 4.

Accordingly, relevant fundamental assumptions of pellet deformation in FRACAS-I model are listed as follows: 1. Thermal expansion, swelling, and densification are the only sources for fuel deformation. 2. No resistance to expansion of fuel. 3. No creep deformation of fuel. 4. Isotropic fuel properties. There are two situations that need to be considered separately when deformation analysis of fuel rod is performed, the first occurs when no contact happened between the cladding and the fuel, which is called the “open gap.” In this situation, it can be assumed as a problem of a cylindrical shell hypothesis with internal and external pressures that have already been obtained. The cladding stress in hoop and axial direction can be calculated by Eq. (7.5), but the stress in radial direction is ignored in this model: 8 r i Pi 2 r o Po > > σ 5 > > < θ t (7.5) 2 ri Pi 2 r2o Po > > > σ 5 > : z r2o 2 r2i

III. Fuels and sub-channel codes

7.2 Code structures and physical models

149

where σ is the cladding stress (MPa), θ and z are the hoop and axial direction, r is the radius of cladding (m), The subscript “i” and “o” means inner and out, respectively, and P is the pressure (MPa). Refer to the shell theory, further cladding strain in three directions can be obtained via the following equation: 8 ðT ðσθ 2 vσz Þ > p p > 1 ε 5 1 dε 1 αθ dT ε > θ θ θ > > E T0 > > > ðT > < ðσz 2 vσθ Þ p p 1 εz 1 dεz 1 εz 5 αz dT E > T0 > > > ðT > > 2 vðσθ 1 σz Þ p p > > 1 ε ε 5 1 dε 1 αr dT > r r r : E T0

(7.6)

where ε is the cladding strain, v is the Poisson ratio, superscript P means plastic and ÐT α dT is the thermal expansion in this time step (%). Therefore the cladding effective T0 θ stress can be obtained by the following equation:  1  σe 5 pffiffiffi ðσθ 2σz Þ2 1 σ2z 1 σ2θ 2

(7.7)

Therefore the stress status and the total effective plastic strain, dεp , can be determined via compared with the strain
stress curve of the cladding material. Furtherly, the additional plastic strain in the three directions can be calculated via Prandtl
Reuss rule. In the second case the fuel and the cladding have come into contact, which is caused by thermal expansion, relocation of the pellet and cladding creep due to high coolant pressure. Since the outward cladding stress on inner surface is unknown, the following steps need to be performed for each time step. 1. Values of additional cladding plastic strain in three directions are assumed. Then, the total effective plastic strain can be computed from Eq. (7.8), and the effective stress is obtained from the stress
strain curve. 2. Refer to Eq. (7.6), corresponding stresses in hoop and axial direction can be obtained. However, the stresses cannot be obtained directly, combined with geometric equations, Eq. (7.6) can be translated to Eq. (7.8) as shown in follows: 8 9 8 9 > > >



ðT ðT = > < = 1  uðri Þ 1 1 < p νt t p p 11 2 1 σz 1 εr 1 dεr 1 αdT 2 εθ 1 dεθp 1 αdT 5 σθ 1 ν > > 2 2r > 2r 2ν r : ; > : ; E T0

(7.8)

T0

Furtherly, combined with the second equation of Eq. (7.6), Eq. (7.8) can be translated to matrix form as shown in the following equation: 

A11 A12 A21 A22



   σθ B 5 1 σz B2

III. Fuels and sub-channel codes

(7.9)

150

7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions

where νt A11 5 1 1 2r ; t  A12 5 ν 2ν 2 1 ;

A21 5 2 ν; A22 5 1;  n o n o ÐT ÐT p p p p B1 5 E uðrri Þ 1 Et ε 1 dε 1 αdT 2 E ε 1 dε 1 αdT ; r r θ θ T0 T0 4r  Ð p p T B2 5 E εz 2 Eεz 1 dεz 1 T0 αdT Therefore the cladding stress in hoop and axial direction can be calculated via the following equation: 8 B1 A22 2 B2 A12 > > > σθ 5 A A 2 A A < 11 22 12 21 (7.10) B2 A11 2 B1 A21 > > σ 5 > : z A11 A22 2 A12 A21 3. New values of additional cladding plastic strain in the three directions can be calculated via Prandtl
Reuss rule. 4. Compared the new additional cladding plastic strains with the assumed ones, the process will continue until they reach convergence. 5. Once the convergence is reached, the contact stress can be obtained via the following equation: Pint 5

tσθ 1 r0 P0 ri

(7.11)

where Pint is the contact stress (MPa), t is the cladding thickness (m). Besides, many other factors that affect the mechanical performance of the cladding are taken into account in FRAPCON or FRAPTRAN code. For example, in FRAPCON code, cladding creep is a significant factor that cannot be ignored during a long-term process. The method of solution described for the time-independent plasticity calculations can also be used for time-dependent creep calculations. The only change required to extend the method of successive elastic solutions to allow consideration of creep is to rewrite the Prandtl
Reuss flow rule as follows: 8 > p > > > dεθ 5 > > > > > > < p dεz 5 > > > > > > > p > > dε 5 > : r

c 3 ε_ c Δt V_ Δt ðσθ 1 σz 1 σr Þ Sθ 1 2 σe 9 σm c 3 ε_ c Δt V_ Δt ðσθ 1 σz 1 σr Þ Sz 1 2 σe 9 σm c 3 ε_ c Δt V_ Δt ðσθ 1 σz 1 σr Þ Sr 1 2 σe 9 σm

III. Fuels and sub-channel codes

(7.12)

7.2 Code structures and physical models

151

7.2.3 Internal gas response and fission gas release The internal gas pressure in fuel rod is calculated by applying the complete gas law to the multivolume region of the fuel rod. The volumes contained in FRAPCON and FRAPTRAN include the plenum volume, gap, pellet crack due to thermal stress, pellet porosity, roughness of pellets and cladding, and interface volume between cladding and pellet when pellet-cladding mechanical interaction occurs. Therefore the equation of the internal pressure can be obtained by the following equation: P5 

Vp =Tp



MR              P N  1 n51 Vg =Tg 1 Vch =Tch 1 Vcr =Tcr 1 Vdsh =Tdsh 1 Vpor =Tpor 1 Vrf =Trf 1 Vi =Ti

(7.13) where P is the internal gas pressure (Pa); M is the moles of gas; R is the gas constant, which is 8.34 J/(mole K); N is the number of axial nodes; n is the axial node index; Vp ; Tp are the plenum volume and temperature, respectively; Vg ; Tg are the nodal gap volumes and corresponding temperatures; Vch ; Tch are the central hole volumes and corresponding temperatures; Vcr ; Tcr are the crack volumes and corresponding temperatures; Vdsh ; Tdsh are the dish volumes and corresponding temperatures; Vpor ; Tpor are the porosity volumes of the pellet and corresponding temperature; Vrf ; Trf are the roughness volumes and corresponding temperatures; and Vi ; Ti are the nodal interface volumes and corresponding temperatures. The method to obtain the temperature of upper plenum has been introduced earlier, other parameters of each area in Eq. (7.13) can be obtained as follows: 1. The gap temperature is the average temperature of the inner cladding surface temperature and the outer pellet surface temperature. 2. The temperature of the center hole of pellet if exists is the fuel centerline temperature. 3. The crack temperature is the mean temperature between pellet surface and temperature at the local ring. 4. The temperature of the fuel porosity is the average temperature of the whole pellet. 5. The temperature in pellet dish is the average temperature of the whole pellet. 6. The temperature of cladding and fuel roughness is as same as that of gap. Krypton, xenon, nitrogen, which are released from the lattice of pellets due to being trapped in fabrication, and helium are all taken into account for fission gas release calculation in the fission gas release model of FRAPCON/FRAPTRAN code. There are four models for selection in FRAPCON code, including ANS-5.4 [15], ANS-5.4 (2008), the modified Forsberg
Massih model [16], and the FRAPFGR model developed by PNNL [1]. Although the ANS-5.4 model is good at simulating the release behavior of short-lived radioactive gas nuclides, while the FRAPFGR model is good at initializing the transient gas release, Forsberg
Massih model is better than the two models mentioned earlier in fission gas release under steady-state condition and also used in FRAPTRAN code. To calculate the fission gas release fraction, the mole of total fission gas release needs to be calculated first. After the burnup of the pellet nodes is determined, the total fission gas production at each axial node can be calculated by correlations. The grain size of the pellet grows with the temperature and the burnup of the pellets, which can be predicted by the

III. Fuels and sub-channel codes

152

7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions

rate equation. Once the grain size reached the release criterion, whether the grain of the pellet will release the fission gas can be calculated. For a single pellet grain the calculation of the fissionable gas release is essential to solve a spherical equation of the gas diffusion equation as shown in the following equation: 2

dC d C 2dC 5D 1 (7.14) 1 φgas dt dr2 rdr



where C is the gas concentration (%), t is the time (s), r is the pellet radius (m), φgas is the mole of released fission gas (mole). Combined with the boundary condition, Massih also provided the solution of Eq. (7.14) as shown in the following equation: 8Ða Ðτ 4πr2 Cðr; tÞdr 5 0Kðτ 2 τ 0 Þφ > 0 >  e ð2τ0 Þdτ 0 > > 2 2 3 X > exp 2n π τ =a 8a 4 > > >K5 < n51 n2 π (7.15) > φgas > > ; φ 5 > > > e D > > : τ 5 Dt where D is the diffusion coefficient.

7.3 Assessments 7.3.1 FRAPCON A total of 137 postirradiation examined fuel rods are used to assess the integral functions of FRAPCON code, which include 92 fuel rods under steady-state operation condition with high burnup and 45 fuel rods under power ramp condition at End of Life. These assessments were conducted to ensure that the code could predict key performance parameters of fuel rod in LWR at the range of limited operation conditions. The key parameters consist of fuel temperature distributions, deformation of cladding and pellets, fission gas release fraction, internal gas pressure, void volume in the fuel rod, and the cladding corrosion thickness. The assessments of fuel rod thermal behavior in FRAPCON are summarized and presented in Fig. 7.6, which included UO2, MOX, and UO2
Gd2O3 if classified by pellet materials. The similar summary of assessments for fission gas release behavior is presented in Fig. 7.7. The assessment files are classified as steady-state and power-ramp conditions. The summary of internal rod void volume assessments is presented in Table 7.1. The accuracy of the internal void volume prediction of the fuel rod is significant in the internal gas pressure calculation along with the fission gas release prediction that mentioned earlier. The change in the fuel rod void volume with burnup is primarily due to the combined effects of cladding creep, fuel swelling, and axial cladding growth.

III. Fuels and sub-channel codes

7.3 Assessments

153

FIGURE 7.6 Assessments of fuel rod centerline temperature: (A) UO2 beginning of life, (B) UO2, (C) MOX, and (D) UO2
Gd2O3 [2].

FIGURE 7.7 Fission Gas Release assessment under steady-state (A) condition and (B) power-ramp condition [2].

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7. FRAPCON and FRAPTRAN codes: Fuel rod performance analysis codes under normal and accident conditions

TABLE 7.1 Assessment of FRAPCON code on internal void volume [2]. BOL void volume (in.3)

EOL void volume (in.3)

Reactor

Rod

Burnup (GWd/MTU)

Measured

Calculated

Measured

Calculated

BR-3

36-I-8

61.5

NA

0.645

0.508

0.678

BR-3

111-I-5

48.6

NA

0.648

0.516

0.608

BR-3

24-I-6

60.1

NA

0.646

0.491

0.614

ANO-2

TSQ002

53.0

1.55

1.55

1.086

1.069

Oconee

15309

49.5 to 49.9

2.14

2.14

1.6 to 1.72

1.573

BOL, Beginning of life; EOL, end of Life.

1.0

Experiment FRAPCON

FIGURE 7.8 Summary of assessments on rod-average hoop strain [2].

Hoop strain (%)

0.8

0.6

0.4

0.2

0.0 IRRMP16IRRMP18

GE2

GE4

GE6

GE7

AN1

AN8

PK1/1

PK1/3

PK2/1

PK2/3

PK2/S

PK4/1

PK4/2

PK6/1

PK6/2

Fuel rod

The ability of FRAPCON code to simulate hoop strain under power ramp conditions is assessed through a database consisting of 29 rods under power-ramp condition at burnup from 18 to 76 GWd/MTU and ramp terminal levels from 30 to 52 kW/m. The assessment results are summed up and presented in Fig. 7.8 that shows that FRAPCON-4.0 will overpredict the measured hoop strain generally.

7.3.2 FRAPTRAN FRAPTRAN code is assessed with a variety of cases that consists of 43 transient or postirradiation examined integral assessment data. These data can be classified by Loss of Coolant Accident (LOCA) program or Reactivity Initiated Accident (RIA) program.

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7.3.2.1 RIA condition What the fuel rod performance analysis concerned under RIA condition in these assessments conclude cladding hoop strain, failure time, and fission gas release, which are shown in Fig. 7.9, Tables 7.2 and 7.3, respectively. The assessment of residual cladding hoop strain under RIA condition is assessed with 13 integrated fuel rods that have UO2 and MOX pellets from the CABRI and NSRR cases. Fig. 7.9 presented that FRAPTRAN provides reasonable analysis on permanent hoop strain that has error less than 2% compared with experimental data. However, according to the assessment data from the NSRR rods, obvious underprediction occurs when the measured uniform strains are greater than 2%. FIGURE 7.9 Residual cladding strain assessments of FRAPTRAN [2].

Pridicted permanent cladding hoop strain (%)

8

NSRR CABRI CABRI MOX

7 6 5 4 3 2 1 0 0

1

2

3

4

5

6

7

8

Measured permanent cladding hoop strain (%)

TABLE 7.2 Assessment of FRAPTRAN code predictions on failure time in RIA cases [2]. Failure

Max enthalpy (cal/g)

Test

Measured

Predicted

Reported

Predicted

NA1

Failed at 0.074 s

Failed at 0.07919 s

114

120

NA2

Not failed

Not failed

199

209

NA3

Not failed

Not failed

124

126

NA4

Not failed

Not failed

85

83

NA5

Not failed

Not failed

108

108 (Continued)

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TABLE 7.2 (Continued) Failure

Max enthalpy (cal/g)

Test

Measured

Predicted

Reported

Predicted

NA6

Not failed

Not failed

133

148

NA7

Failed at 0.405 s

Failed at 1.095 s

138

148

NA8

Failed at 0.5318 s

Failed at 0.5241 s

98

96

NA9

Not failed

Not failed

197

234

NA10

Failed at 0.456 s

Failed at 0.4479 s

98

96

CIP0
1

Not failed

Not failed

91

97

FK1

Not failed

Not failed

116

117

GK1

Not failed

Not failed

93

91

HBO1

Failed

Not failed

73

73

HBO5

Failed

Not failed

80

80

HBO6

Not failed

Not failed

85

85

MH3

Not failed

Not failed

67

67

O12

Not failed

Not failed

108

107

TS5

Not failed

Not failed

98

98

VA1

Failed

Failed at 0.0089 s

133

132

VA3

Failed

Not failed

122

121

RT1

Not failed

Not failed

142

139

RT2

Not failed

Not failed

115

114

RT3

Not failed

Not failed

138

135

RT4

Not failed

Not failed

125

120

RT5

Not failed

Not failed

146

143

RT6

Not failed

Not failed

153

150

RT7

Not failed

Not failed

134

125

RT8

Failed

Not failed

164

152

RT9

Failed

Not failed

165

155

RT10

Failed

Not failed

164

152

RT11

Failed

Not failed

188

181

RT12

Not failed

Not failed

155

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TABLE 7.3 Assessment on peak cladding residual strain. Case

Measured failure time

Predicted failure time

MT-1

60
95 s

61 s

MT-4

52
58 s

27 s

MT-6A

58
64 s

31 s

LOC-11C rods 1 and 4

Not failed

Not failed

LOC-11C rods 2

Not failed

12.1 s

LOC-11C rods 3

Not failed

24.5 s

TREAT rod 16 and 17

30.3
37.5 s

26.5 s

IFA-650.5

179 s

169 s

IFA-650.6

525 s

419 s

IFA-650.7

247 s

152 s

FIGURE 7.10 Comparison

20

between predicted and measured fission gas release under RIA condition in CABRI and NSRR cases [2].

Cabri NSRR

18 16

Predicted FGR (%)

14 12 10 8 6 4 2 0 0

2

4

6

8

10

12

14

16

18

20

Measured FGR (%)

The 33 cladding failure assessment data, which consists of UO2 and MOX fuel, are from CABRI, NSRR, and BIGR. These predictions and experimental data are compared and listed in Table 7.2. The predicted and measured maximum enthalpy are listed and compared in the table as well. The 10 nonfailed assessment data of fission gas release under RIA condition are from CABRI and NSRR cases and presented in Fig. 7.10. The code predictions for these tests

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FIGURE 7.11 Assessment of oxide thickness at peak nodes [2].

40

Oxidation thickness (Pm)

35

FRAPTRAN (nonprotective) Data FRAPTRAN (protective)

30 25 20 15 10 5 0 IFA-650.6

IFA-650.5

IFA-650.7

Fuel rod

utilized the grain boundary gas inventory as predicted by the FRAPFGR model in FRAPCON-4.0.

7.3.3 Loss of Coolant Accident condition 10 full-length fuel rods for LOCA assessment from NRU, PBF, TREAT, and Halden reactors were used in FRAPTRAN assessment to verify the accuracy of the code in pressurized water reactor, boiling water reactor, and VVER. The various parameters that represent key in-pile behaviors of reactors in these assessments consist of temperature distribution, cladding ballooning, cladding residual strain, internal gas pressure, oxidation thickness, and rupture time. Table 7.3 lists the measured and predicted cladding residual strain at peak nodes in LOCA condition. The oxidation thickness prediction at high-temperature under LOCA condition was assessed with experimental data from three rods, including IFA-650.5, IFA-650.5, and IFA650.7, and presented in Fig. 7.11. As recommended by user manuals, Cathcart
Pawel model is used for these three cases.

7.4 Summary This report briefly introduced a set of 1.5-D fuel performance analysis codes, FRAPCON and FRAPTRAN, which were developed by PNNL for NRC. After a series of big update, FRAPCON-4.0 and FRAPTRAN-2.0, the latest versions for now, are rewritten modularly. The calculation of the code is fast, highly robust, and well assessed, and they are great tools for

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References

159

evaluating the steady-state or transient performance of the fuel. Besides, they can help to understand some experimental phenomena or guide-specific experiments roughly. However, due to fundamental assumptions of the two codes, the axial and hoop heat transfer are ignored. Besides, the radial cladding stresses are also ignored due to the plane strain hypothesis. These disadvantages limit their further application compared with 3D codes, such as BISON. Further modifications are still needed before the codes are applicated in other reactors with different geometry fuels or other forward position fields, such as plate-type fuel and accident tolerant fuel.

References [1] K.J. Geelhood, W.G. Luscher, FRAPCON-3.5: a computer code for the calculation of steady-state, thermalmechanical behavior of oxide fuel rods for high burnup, NUREG/CR-7022, Washington, Pacific Northwest National Laboratory, U.S. Nuclear Regulatory Commission, 2014. [2] K.J. Geelhood, W.G. Luscher, FRAPTRAN-2.0: integral assessment, Pacific Northwest National Laboratory, PNNL-19400, 2016, p. 2. [3] G.A. Berna, C.E. Beyer, K.L. Davis, D.D. Lanning, FRAPCON-3: a computer code for the calculation of steady-state, thermal-mechanical behavior of oxide fuel rods for high burnup, NUREG/CR-6534, Vol. 2, PNNL-11513, Vol. 2, Pacific Northwest National Laboratory, Richland, WA, 1997. [4] K.J. Geelhood, W.G. Luscher, C.E. Beyer, et al., FRAPTRAN 2.0: a computer code for the transient analysis of oxide fuel rods, Pacific Northwest National Laboratory (PNNL), NUREG/CR-7023, Richland, WA, 2016, p. 1. [5] L.J. Siefken, C.M. Allison, M.P. Bohn, S.O. Peck, FRAP-T6: a computer code for the transient analysis of oxide fuel rods, NUREG/CR-2148 (EGG-2104), EG&G Idaho, Inc., Idaho Falls, ID, 1981. [6] L.J. Siefken, V.N. Shah, G.A. Berna, J.K. Hohorst, FRAP-T6: a computer code for the transient analysis of oxide fuel rods, NUREG/CR-2148 Addendum (EGG-2104 Addendum), EG&G Idaho, Inc., Idaho Falls, ID, 1983. [7] K.J. Geelhood, W.G. Luscher, FRAPCON-4.0: a computer code for the calculation of steady-state, thermalmechanical behavior of oxide fuel rods for high burnup, Washington, Pacific Northwest National Laboratory, U.S. Nuclear Regulatory Commission, 2015. [8] C.W. Stewart, J.M. Cuta, J.M. Kelly, K.L. Basehore, T.L. George, S.D. Montgomery, D.S. Rowe, VIPRE-01: a thermal-hydraulic code for reactor cores, Vo1. 1-4, Rev. 4, NP-2411-CCM, Electric Power Research Institute, Palo Alto, CA, 1998. [9] W.H. Jens, P.A. Lottes, Analysis of Heat Transfer, Burnout, Pressure Drop, and Density Data for HighPressure Water. ANL-4627, Argonne National Laboratory, Argonne, IL, 1951. [10] G.J. Scatena, G.L. Upham, Power Generation in a BWR Following Normal Shutdown on Loss-of Coolant Accident Conditions. NEDO-10625, General Electric Co., San Jose, CA, 1973. [11] N. Todreas, G. Jacobs, Thermal contact conductance of reactor fuel elements, Nucl. Sci. Eng. 50 (1973) 283. [12] W.H. McAdams, Heat Transmission, 34th ed., McGraw-Hill Book Company, Inc, New York, 1954. [13] A. Knuutila, Improvements on FRAPCON-3/FRAPTRAN Mechanical Modeling, VTT-R-11337-06.VTT, Finland, 2006. [14] A. Mendelson, Plasticity: Theory and Applications, The MacMillan Company, New York, 1968. [15] W.N. Rausch, F. Panisko, ANS54: a computer subroutine for predicting fission gas release, NUREG/CR1213, PNL-3077, Pacific Northwest Laboratory, Richland, WA, 1979. [16] K. Forsberg, A.R. Massih, Diffusion theory of fission gas migration in irradiated nuclear fuel UO2, J. Nucl. Mater. 135 (1985) 140
148.

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C H A P T E R

8 The TRANSURANUS fuel performance code A. Magni1, A. Del Nevo2, L. Luzzi1, D. Rozzia3, M. Adorni4, A. Schubert5 and P. Van Uffelen5 1

Politecnico di Milano, Department of Energy, Nuclear Engineering Division, Milan, Italy ENEA, FSN-ING-SIS, CR-Brasimone, Camugnano, Italy 3Belgian Nuclear Research Centre (SCK.CEN), Mol, Belgium 4Senior Scientist, Brussels, Belgium 5European Commission, Joint Research Centre, Directorate for Nuclear Safety and Security, Karlsruhe, Germany 2

8.1 Introduction: General overview of the TRANSURANUS code TRANSURANUS is a computer program, written in Fortran95 programing language, for the thermal and mechanical analysis of fuel rods irradiated in nuclear reactors [1]. It was originally developed at the Institute for Transuranium Elements (ITU), now Joint Research Centre (JRC) Karlsruhe [2
6], and is used worldwide by universities, research centers, technical safety organizations, safety authorities, and industry. The TRANSURANUS code consists of a clearly defined mechanical
mathematical framework into which physical models can easily be incorporated, being so able to deal with a wide range of different irradiation situations, for example, normal, off-normal and accidental conditions [design basis accidents (DBAs), such as RIA (reactivity-initiated accident) or LOCA (loss of coolant accident)]. The timescale of the problems to be treated may range from milliseconds to years, and the spatial scale also is very wide, since physical phenomena occurring at the mesoscale of the fuel grain (like the fission gas behavior) are brought into play at the engineering scale of the integral fuel pin. The code relies on a comprehensive built-in material data bank for oxide, mixed oxide (MOX), carbide and nitride fuels, zircaloy and steel claddings, and several different coolants (light water, liquid sodium, liquid potassium, helium, liquid lead, and lead
bismuth). It can be employed in two different modes—in deterministic or statistical mode—allowing for assessing the impact of experimental and model uncertainties via incorporation of a Monte Carlo (MC) technique. TRANSURANUS is a fast and reliable tool thanks to the mathematical methods and solvers implemented in the code, which support the modification and extension of the code and guarantee numerical stability. It is a

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00008-5

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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8. The TRANSURANUS fuel performance code

flexible tool, easy to handle with different graphical user interfaces (GUIs) for input and output handling on both Windows and Unix platforms, and exhibits very fast running times (of the order of the minute for a deterministic run, of the hour for a statistical run, depending on the complexity of the irradiation history and on the number of desired runs). The development and assessment of the code are rigorously carried out and organized in three steps [7,8]. The first is the verification step, consisting in comparing the calculations performed by the code, with exact (analytical) solutions, available in many special simple cases. The verification step is followed by an extensive validation of separate models incorporated in the fuel performance code (FPC), performed against separate-effect data. The inclusion of each new model in the code should respect the “nonregression” principle, that is, the code should be verified and validated against the complete validation matrix, so to make sure to achieve an effective advancement in the code development. Finally, in the third step the assessment is completed by integral validation against fuel rod experimental data, as well as by benchmark activities consisting in code-to-code evaluations. Hence, fundamental is the participation in international benchmarks involving other FPCs, organized for example by the International Atomic Energy Agency (IAEA) [9
11] or the OECD/NEA (Organization for Economic Co-operation and Development/Nuclear Energy Agency) [12]. In the following, details about the structure and features of the TRANSURANUS FPC are given, pointing out the most recent developments and the still open issues. The main models allowing for the thermal
mechanical analysis and for the fission gas behavior prediction will be introduced and explained. Then, in Section 8.3, examples of application and validation of the code against water reactor irradiation conditions are presented. Up to now, TRANSURANUS has been indeed mostly developed to deal with thermal reactor conditions, taking advantage of a large validation database available [13]. Section 8.4 contains the preliminary assessment of the code against new generation, fast reactor (FR) applications, highlighting the need for future improvements of the code, in order to deal with extreme conditions of very high neutron flux in the core, high fuel temperatures and linear heat rates (LHRs). The conclusions of the chapter focus on the still-open challenges in fuel performance modeling and simulation, knowing that performance codes are continuously developed and improved with more and more accurate models of physical phenomena to get the best possible fuel behavior predictions as more and better experimental data become available.

8.2 TRANSURANUS code structure TRANSURANUS is referred to as a “1.5-D” code, meaning that the thermal and mechanical analysis of the fuel rod under irradiation is performed along the radial dimension, according to the chosen radial discretization, and then the solved radial profiles are coupled between different axial slices of the fuel column (the number of which can be selected on input). The code exploits the cylindrical symmetry of the simulated system (the nuclear fuel rod) and differs from other 3-D FPCs, for example, BISON [14
16] and ALCYONE [17]. TRANSURANUS is able to deal with both normal and transient operation (up to accident) conditions. The code allows the user to simulate the behavior of the entire fuel rod structure (fuel column, cladding, coolant, eventual surrounding structure) or of only a part of it, such as in the simulation of a cladding tube burst or an oxidation test. In the case of an analysis

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including the cladding the mechanical interaction between fuel and cladding (pellet-cladding mechanical interaction, PCMI) could play an important role and it is considered by the code, while the chemical interaction (pellet-cladding chemical interaction) is at present neglected [7]. The main fuel behavior models implemented in the code regard densification and relocation, restructuring, central void formation, cracking, creep and plasticity, grain growth, high burn-up structure (HBS) formation and evolution, fission gas and helium diffusion in and release from the fuel pellet, fuel-to-cladding gap conductance, and lastly radial redistribution of oxygen, fission products and actinides. Instead, the main property models (for fuel and cladding) regard elastic parameters, stresses and strains, thermal conductivity, specific heat, density, and solidus
liquidus (melting) temperatures, while viscosity, density, Nusselt number, boiling temperature and pressure, specific heat, thermal conductivity, and enthalpy are considered for the coolants. The TRANSURANUS code structure reflects the structure of the fuel rod system, which requires: • • • •

the analysis of the fuel rod behavior at different times along the irradiation history; the analysis of the different sections or slices at a specific time; the loop structure to obtain converged solutions of the various nonlinear problems; and driver programs for the various models of properties/phenomena. Consequently, the whole code is designed in levels, which are organized as follows:

• Level 1 is the main level, which drives the time loop for analyzing the fuel rod behavior. • Level 2 drives the analysis of the fuel rod behavior in the axial sections or slices, performing the axial coupling between them. • Level 3 drives the analysis of the fuel rod behavior in a single section or slice, employing both explicit and implicit (including iteration loops) models, searching for convergence within the explicit and implicit models. All the abovementioned properties and models, corresponding to different blocks of the code structure, are presented in Sections 8.2.1
8.2.3. The basic assumptions and models can be summarized as follows: Thermal analysis: steady-state and transient analysis, phase changes included, tackled with advanced numerical solution technique (fast and stable). Mechanical analysis: TRANSURANUS solves the basic constitutive equations under equilibrium conditions, checking the strain compatibility. One-dimensional radial and axial mechanical analyses are superimposed, semianalytical solutions are obtained by effective numerical algorithms. Physical models: All the significant physical models are included, that is, models for thermal and irradiation-induced densification of fuel, swelling due to solid and gaseous fission products, fission gas diffusion and release, fuel and cladding creep and plasticity, pellet cracking and relocation, oxygen and plutonium redistribution, nuclide evolution and fuel composition changes, volume changes during phase transitions, formation and closure of the central void and treatment of axial friction forces. Every solution is verified in the TRANSURANUS code by comparison with exact solutions. Numerical tests prove the numerical robustness of the solution for specific simple

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cases for which an analytic solution is available. Referring to the thermal analysis, suitable cases consist in constant radial power distribution or assumed constant power density and material properties (thermal conductivity, density, specific heat at constant pressure). Instead, mechanical models, including the treatment of creep and plasticity, are verified against steady-state creep processes characterized by constant stress distributions (valid only for small deformations), or plastic flows in a thick-walled cylinder [7,18].

8.2.1 Thermal analysis The calculation of temperatures in a fuel rod is one of the primary goals of fuel element modeling. The accuracy of these calculations influences temperature-dependent physical phenomena such as fission gas diffusion and release, fuel restructuring, creep and thermal expansion. The nonlinear thermal problem must be solved by applying numerical techniques guaranteeing numerical reliability (stability) and a low computational cost. The axial symmetry and the assumption of small axial temperature variations, compared to the radial ones, are always exploited to simplify the mathematical formulation of the thermal problem. The thermal analysis of an integral fuel rod is performed by TRANSURANUS superimposing the one-dimensional radial and axial energy conservation equations. The energy equation (heat conduction equation) is solved for the fuel, cladding and structure under a quasi-steady-state approximation within cylindrical rings (exploiting the cylindrical symmetry of the pin system). The thermal analysis of the coolant considers the mass, momentum and energy conservation equations, solved employing a combination of finite difference and finite element methods, which makes the solution extremely accurate, and considers coolant phase changes (melting, boiling). The heat transfer coefficient between fuel and cladding (gap conductance) is calculated by the URGAP model [19] and depends on the gap width, the contact pressure, the filling gas pressure and composition, and on the surface characteristics of cladding and fuel. Various model options for the gap conductance are implemented in the TRANSURANUS code, for different conditions and filling material (i.e., vacuum, sodium, different gases and gas mixtures), taking into account fuel-cladding material pairings, gap closure conditions and gas accommodation coefficients. A new gap conductance model has been recently developed, based on Charles and Bruet data [20]. This model always considers a contact pressure term between fuel and cladding and is currently under testing and validation. As for the heat transfer between the fuel rod and the coolant, the code accounts for the different heat transfer regions encountered when liquid is flowing along a vertical heated tube, depending on the temperature [21,22]. Correlations are implemented for singlephase convective heat transfer (useful for the lower part of the fuel rod), nucleate boiling and saturated boiling, for different kinds of coolant [light water, helium, liquid metals such as sodium, lead, bismuth, lead
bismuth eutectic (LBE)] [7]. In TRANSURANUS the applied iteration scheme for solving the nonlinear thermal analysis problem is the Newton
Raphson one, fully described in Ref. [23]. A thorough time step control (obtained by limiting the increments of temperature) is needed, in order to find a reasonable compromise between numerical accuracy and effort, the uncertainties inherent in the thermal analysis and the consequences of physical processes.

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8.2.2 Mechanical analysis The mechanical analysis consists of the calculation of stresses, strains and the corresponding fuel rod deformations. TRANSURANUS computes the solution by applying the principal conditions of equilibrium and strain compatibility together with constitutive relations [3,4] (dynamic forces are not treated). The code works on the following assumptions: • The geometric problem is of one-dimensional, plane and axisymmetric nature, that is, the axial deformation is constant across the radius (generalized plane strain condition). • The elastic constants E (Young’s modulus of elasticity) and ν (Poisson ratio) are constant within a cylindrical ring. • The elastic strain vectors are all expressed via stress
strain relationships, through E and ν. • All volume changes due to different nonelastic processes (e.g., densification, swelling, creep, cracking) are expressed via strains. The assumptions, together with the strain compatibility equations and the equation of radial equilibrium, lead to the classical semianalytical solution of the problem (so-called since the strains must be evaluated numerically by integral operation). The optimal solution is computed subdividing each radial coarse zone into fine zones, allowing for numerical integration. It is thus a variable multizone concept, since any discretization can be chosen as input. To deal with nonlinearities, for example, the behavior of creep (of fuel and cladding) as a function of stress, TRANSURANUS relies on both explicit and implicit numerical techniques. As for the treatment of plasticity, if the stress is above the yield stress and if the material (fuel or cladding) has sufficient possibilities for plasticization, stresses can be relaxed by flow of material [3,7]. Cracking is treated as an extension of plastic flow, since the material will crack if the rupture strain is reached [3,24]. In the case of fuel-cladding contact the friction force model consists of a superposition of one-dimensional radial and a one-dimensional axial treatment [7,25]. The basic mechanical assumptions are: • Generalized plane strain condition in the axial direction, • Axial strains are determined from an axial equilibrium balance. The URFRIC model, implemented in TRANSURANUS, includes in the calculation of friction forces all the different modes of interaction between fuel and cladding. The nonlinear system of equations is solved by an iterative fast algorithm [25], in order to avoid significant increases of the computational costs. Fuel axial deformation is of particular interest for fast breeder reactor (FBR) fuel accident analyses, since the axial deformation of the fuel is one important reactivity feedback mechanism and impacts on the cladding failure.

8.2.3 Fission gas behavior modeling Among the physical models, fission gas release (FGR) and swelling is a fundamental topic to be covered in fuel rod performance analyses, for different reasons [26]:

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1. The fission gases xenon and krypton degrade the thermal conductivity of the pin filling gas (normally helium), decreasing the gap conductance and thus enhancing fuel temperatures. Enhanced fuel temperatures may further increase FGR and may cause an unstable thermal feedback when the gap is large enough. 2. The release of fission gases increases the inner pin pressure, which may limit the lifetime of a fuel rod, since the inner pressure should never exceed the coolant pressure under normal operation conditions [LWR (light water reactor)-simplified design limit]. 3. The fuel swelling due to gaseous fission products retained in the fuel pellets may lead to enhanced PCMI, especially during power transients. 4. The release of radioactive gases from the fuel column to the pin free volume decreases the safety margin of a nuclear plant. Various isotopes of the fission gases xenon and krypton are created inside the fuel grains by fission events and decay processes. Since their solubility in UO2 is very low, they tend to leave the fuel pellet after diffusion processes or to precipitate into intra- and intergranular bubbles. Details about the basic gas mechanisms leading to FGR and swelling, occurring in oxide nuclear fuels (UO2 and MOX), are provided and explained in Refs. [26
33]. Many gas-related phenomena (e.g., intragranular and grain boundary diffusion, trapping and resolution by both intra- and intergranular bubbles, bubble migration and interconnection, grain boundary sweeping, burst release, HBS) are currently treated by the TRANSURANUS code, in the form of simplified or mechanistic (i.e., physics-based) models [7]. A mechanistic model for fission gas behavior, allowing for the consistent calculation of both FGR and gaseous swelling by describing the population of bubbles both inside the fuel grains and along the grain boundaries, has been developed in Ref. [31] and is implemented in TRANSURANUS [30,31,34]. The extension of Speight’s model [35], considering the contribution of bubble mobility to the gas transfer to grain boundaries, is also available in TRANSURANUS. Different correlations are implemented in the code (LWR version, under extension for FBR conditions) for the various gas behavior parameters, for example, the (effective) diffusion coefficient [36
38], the bubble trapping and resolution rates (for a detailed study about the gas trapping and resolution mechanisms, see Refs. [28,39
41]). While the solution of the effective intragranular gas diffusion equation is analytical under constant conditions (i.e., constant temperature and fission rate) [7,38,42], numerical algorithms must be applied to solve the equation under transient (i.e., time-varying) conditions. The algorithms currently available in TRANSURANUS are the FORMAS [43,44], the URGAS one [45] and the more recently developed POLYPOLE2 [46]. Intergranular fission gas behavior is considered in TRANSURANUS based on the concept of grain boundary saturation, according to which, at a specific saturation concentration, a network of interconnected bubbles has formed and allows the release of gas atoms from the grain boundaries into the rod free volume [47]. The intergranular bubble dynamics is governed by the mechanical equilibrium pressure of the gas. Indeed, grain-face bubbles can grow in size (or shrink) by absorption (or emission) of vacancies generated on the grain boundaries, to reach the equilibrium pressure (typically, this process corresponds to an overpressure relaxation). The vacancy absorption rate is proportional to the bubble over- pressure with respect to equilibrium, according to the Speight and Beere model [48]. The intergranular bubble evolving size may lead

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to bubble intersection and merging into larger but fewer bubbles (i.e., reduced bubble number density and increased average bubble size), forming paths leading to fission gas release from the fuel stack. During abrupt power variations, micro- and macrocracking may also occur, providing an additional (burst) gas release contribution, which can be accounted for in TRANSURANUS [31,47]. The treatment of the grain growth phenomenon (and associated grain boundary sweeping) is also implemented in the code, according to the model of Ainscough et al. [49]. Helium surely plays an important role among gases in nuclear fuel: it can diffuse, be trapped by or resoluted from bubbles (according to characteristic coefficients and rates) and it can cause the helium embrittlement issue in the cladding. Being emitted in alpha decay processes [besides ternary fission and the (n,α) reaction on oxygen], its treatment is particularly important for MOX fuels, under both irradiation and storage conditions. In order to simulate its behavior in the fuel, both a helium intragranular and intergranular transport models are implemented in TRANSURANUS [7], complemented by a model describing the absorption in the fuel of the filling helium contained in the rod free volume [7,50,51].

8.2.4 The TRANSURANUS burn-up module A nuclide analysis allows to describe the actinide transport (together with appropriate models for redistribution) and concentration evolution across the fuel pellet during irradiation, impacting on the microstructure of the fuel and hence on its thermal and mechanical performance. At each fuel radial and axial position the burn-up module allows to calculate the fraction of fissile material burnt (i.e., the local burn-up), the build-up and fission rates of the higher Pu isotopes, the build-up of actinides and fission products. In turn, the radial redistribution of the fuel fissile material determines the radial power density distribution, which is the source term for the temperature calculations, and the radial burn-up distribution, from which the local concentrations of fission products such as Kr, Xe, Cs, and Nd are obtained. The TRANSURANUS burn-up module (called TUBRNP [52,53]) consists in the Bateman’s set of equations for the most relevant actinide isotopes [26,54]. Each equation includes, in principle, absorption, capture, fission, and decay contributions, each one described by a proper microscopic, one-group effective cross section. The Bateman’s system of equations is solved incrementally, meaning that for each average burn-up increment a new radial power density profile is calculated, from which the radial burn-up profile is updated. The local concentrations of Kr, Xe, Cs, and Nd are obtained by multiplying the local burn-up increment by the appropriate fission yields. As for helium production, three main sources are considered, under irradiation conditions of both UO2 and MOX fuels: alpha decays of actinides (238Pu, 241Am, 242Cm, and 244Cm are currently considered), (n,α) reactions on oxygen, ternary fissions of actinides. The TRANSURANUS-LWR burn-up model has been verified against a large LWR database of spent fuel measurements by electron-probe microanalysis, for burn-up between 21 and 102 MWd/kgHM. The TRANSURANUS-FBR burn-up model is an extension of the LWR model, including the modeling of plutonium and americium radial redistributions [55]. The same burn-up equations are also used to describe the evolution of burnable

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absorbers in the fuel, for example, gadolinia (Gd2O3) or zirconium diboride (ZrB2), which are options for UO2 irradiated in LWR conditions.

8.2.5 Material conservation equations In the TRANSURANUS code the material conservation, for each species inside each volume of a fuel pellet, is guaranteed by the basic equation of material transport [26], focusing on the radial material transport in cylindrical geometry. The governing equation is solved by a finite difference technique, assuming as boundary condition that the fuel is a closed system with null material flux at the extreme nodes. As for actinide redistribution, TRANSURANUS includes models describing the behavior of plutonium and americium across the pellet radius, in FR conditions (PUREDI and AMREDI, for Pu and Am redistribution, respectively [56]). The main mechanisms of Am and Pu transport are solid-state transport by thermal diffusion and vapor transport by pores and cracks (evaporation-condensation process) [26,57
59]. The actinide redistribution model is coupled with the Pu and Am evolutions calculated by TUBRNP and considers the effect of the oxygen-to-metal ratio on the diffusion coefficient (oxygen redistribution is calculated by the OXIRED model [60]).

8.3 Application to water reactor conditions The verification of the structure and models implemented in the TRANSURANUS FPC and the code validation have up to now focused on LWR fuel, due to the availability of a large experimental database built over years of dedicated tests and commercial operation of LWRs. For each type of LWR fuel (UO2, Gd-doped UO2, and MOX), submodules and models of the code are validated against separate-effect experimental data, when possible, but fundamental is the integral verification of the FPC under normal operating conditions, transient conditions, and DBAs, e.g., LOCA). The code validation matrix relies to a large extent on two main experimental sources of data, namely, the OECD Halden Reactor Project (HRP) [61] and the International Fuel Performance Experiments database of the IAEA and the OECD/NEA [13]. The validation matrix for LWR conditions comprehends UO2, Gd-doped UO2, and MOX fuels irradiated in PWR (pressurized water reactor), BWR (boiling water reactor), HBWR (Halden Boiling Water Reactor), and WWER (water
water energetic reactor) environments, up to a burn-up ranging from 15 to around 100 MWd/kgHM. An overview of the main integral experimental data used for verification and validation of the TRANSURANUS code for LWR fuel is reported in Table 8.1. Among these irradiation experiments, the application of TRANSURANUS in simulating power ramp tests from the PWR Super-Ramp irradiation experiment is presented in the following section as an example. The showcase framework is complemented by an example of safety analysis application of the code, on the Atucha-II Nuclear Power Plant (NPP) under accidental large break-LOCA (LB-LOCA) conditions. More recent results for LOCA were obtained in the frame of the coordinated research project Fuel Modeling under Accident Conditions (FUMAC) of the IAEA [62,63], and in the ESSANUF (European Supply of Safe Nuclear Fuel) Project, as outlined in Section 8.3.3.

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8.3 Application to water reactor conditions

TABLE 8.1 Overview of the main integral experimental data used for the verification and validation of the TRANSURANUS code for LWR oxide fuels [7,13,61]. Experiment

Fuel type

Number of rods

Reactor

Burn-up (MWd/kgHM)

Contact

UO2

3

PWR and Siloe

23

Osiris

UO2

4

PWR, Osiris

23
50

HBEP

UO2

28

BR3

60
65

IFA 429

UO2

3

HBWR (PWR)

60

IFA 432

UO2

5

HBWR (BWR)

30
34

IFA 503.1,2

UO2

15

HBWR (WWER, PWR)

15
26

IFA 504

UO2

4

HBWR

50

IFA 508

UO2

1

HBWR

17

IFA 515

UO2, (U,Gd)O2

6

HBWR

96

IFA 533

UO2

1

HBWR

2

PWR, HBWR

52

IFA 534 IFA 535.5,6

UO2

4

HBWR

43

IFA 597.3

UO2

3

BWR, HBWR

52

IFA 633

MOX, UO2

6

HBWR

43

IFA 636.1,2

UO2, (U,Gd)O2

4

HBWR

30

IFA 650.2,3,4

UO2

3

PWR, BWR

0, 82, 92

IFA 651.1,2

MOX

2

HBWR

32

IFA 663

Zry, M5, E110, Zirlo

HBWR

(9000 h of irradiation)

IFA 681

UO2, (U,Gd)O2

6

HBWR

20
30

IFA 597.4,5,6

MOX

2

HBWR

32

Kola3

UO2

32

WWER-440 and MIR

46
48

Risoe-1

UO2

11

HBWR, DR3

32

Risoe-2

UO2

15

HBWR, DR3 (BWR)

27
42

Risoe-3

UO2

16

HBWR, DR3

13
46

Regate

UO2

1

PWR and Siloe

47

SOFIT-1

UO2

12

WWER-440 and MIR

10

Super-Ramp

UO2

28

PWR, R2

33
45

Tribulation

UO2

19

BR3, BR2

20
51

DOE WG-MOX

WG-MOX

9

ATR

20
50

PRIMO

MOX

1

BR3 and Osiris

30 (Continued)

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8. The TRANSURANUS fuel performance code

TABLE 8.1 (Continued) Experiment

Fuel type

Number of rods

Reactor

Burn-up (MWd/kgHM)

OMICO

UO2, MOX

4

BR2

10
15

M501, M502

SBR-MOX

8

PWR

35
55

Zaporoshye

UO2

22

WWER-1000

42
51

Novovoronezh

UO2

15

WWER-1000

47

FUMEX-I

UO2

6

PWR, HBWR

16
55

ATR, Advanced Test Reactor; BWR, boiling water reactor; HBEP, High Burn-Up Effects Programme; HBWR, Halden Boiling Water Reactor; IFA, instrumented fuel assembly; LWR, light water reactor; MIR, Multi-loop Reactor; MOX, mixed oxide; OMICO, Oxide Fuels
Microstructure and Composition variations; PRIMO, PWR Reference Irradiation of MOX fuels; PWR, pressurized water reactor; SBR, short binderless route; WG, weapons-grade; WWER, water
water energetic reactor.

8.3.1 Assessment against the pressurized water reactor Super-Ramp irradiation experiment The aim of the Super-Ramp irradiation experiment was to study the pellet-cladding interaction (PCI) and to investigate the failure propensity of LWR fuel rods during power ramps [64
67]. The experimental database includes 28 PWR rods and 16 BWR rods (KWU or W type), belonging to 6 groups of rods (groups PK1, PK2, PK4, PK6 for KWU rods, groups PW3, PW5 for W rods) with different designs, irradiation history and materials, all tested under high ramp rates. The rods were base-irradiated in the KK Obrigheim (KWU pins) or BR-3 (W pins) power reactors, with time-averaged ratings in the range 14
26 kW/m [67]. The ramp tests were carried out in the R2 research reactor at Studsvik, Sweden [67,68]. The final burn-up ranges from 33 to 45 MWd/kgU. Pre-, during-, and postirradiation examinations, both nondestructive and destructive, were performed, providing suitable experimental data useful for code validation. The Super-Ramp Project is part of the International Fuel Performance Experiments database [13]. Fabrication details about the fuel pellets and KWU/W rods of the Super-Ramp database are shown in Table 8.2, while details about the base-irradiation of the KWU and W rods can be found in Refs. [66
68]. The power ramping of the experimental fuel rods was performed in the loop-type R2 reactor at Studsvik, whose general data are collected in Table 8.3. The power ramp consisted in a conditioning phase (from the end of the base irradiation until the power ramp phase, performed increasing the linear rating with slow rates until 25 kW/m are reached, and then holding the power at this value for 24 hours), a fast ramping phase from the conditioning level to the ramp terminal level (RTL), and a holding phase at RTL of 12 hours, before reactor shutdown. The scheme of the power ramping phases performed in the R2 Studsvik reactor is shown in Fig. 8.1. In the following, examples of validation of the TRANSURANUS code against the PWR Super-Ramp database is showcased, focusing on relevant figures of merit under PCI/stress-corrosion cracking conditions. Comparisons between experimental data and simulation results are performed for the fuel burn-up (Fig. 8.2), the cladding outer corrosion (Fig. 8.3), the fission gas release (Fig. 8.4), the cladding average hoop stress and gap size (Fig. 8.5), and the pin failure predictions (Fig. 8.6).

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8.3 Application to water reactor conditions

TABLE 8.2 PWR Super-Ramp project: test matrix of the experimental UO2 fuel rods, including as-fabricated features [66,67]. Variable

PK1

PK2

PK4 (Gd)

PK6

PW3

PW5

Number of rods

5

5

4

5

5

4

Burn-up (average at axial PPN, MWd/kg)

33
36

41
45

33
34

34
37

28
31

32
33

LHR (average at axial PPN, kW/m)

19
26

17
25

18
25

20
27

12
19

9
21

He fill pressure (bar)

22.5

22.5

22.5

22.5

13.8

13.8

UO2 stack length (mm)

311

318

314

315

982

977

Overall rod length (mm)

388

390

390

390

1135

1136

Diametral gap (μm)

197

145

169

146

165

165

Outer diameter (mm)

10.76

10.75

10.77

10.74

9.51

9.51

Inner diameter (mm)

9.31

9.28

9.28

9.29

8.35

8.35

Wall thickness (mm)

0.73

0.74

0.74

0.73

0.58

0.58

Base irradiation

Rod variables

Cladding variables

Pellet variables Initial

235

3.2

3.31

3.19

2.99

8.26

5.74

Outer diameter (mm)

U content (wt.%)

9.11

9.14

9.11

9.14

8.19

8.19

Inner diameter (mm)
















2.17

Ratio length/diameter

1.25

1.24

1.19

1.21

1.63

1.66

Density (g/cm )

10.36

10.34

10.30

10.42

10.32

10.40

Grain size (average, μm)

6.0

5.5

5.5

22

10.5

16.9

3

LHR, linear heat rate; PPN, peak power node.

TABLE 8.3 PWR Super-Ramp project: general data about the R2 Studsvik research reactor [66,67]. Power

50 MW (thermal)

Control rods

6 Cd
U rods

Moderator—coolant

H2O

Thermal neutron flux

2.4 1014 n/cm2/s

Reflector

Be and D2O

Fast (.1 MeV) neutron flux

 2.5  10

Fuel material

U2Si3Al

Primary coolant flow

1300 kg/s

Fuel enrichment

19.75%

Coolant inlet temperature

30 C
40 C

Loading

B12 kg 235U

Type of fuel element

MTR

14

n/cm2/s

Maximum neutron flux in experimental positions

MTR, Material Testing Reactor.

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8. The TRANSURANUS fuel performance code

70 LHR peak axial position

60 RTL=[35,50] kW/m

Hold time at RTL: 12 h (not for all rods)

LHR (kW/m)

50 40 30

Conditioning level CL 25 kW/m

20

Hold time at CL: 24 h

10 dR/dt=[360,660] kW/(m*h) 0 Time (h)

FIGURE 8.1 PWR Super-Ramp project: outline of the ramping phases.

46

Calculated burnup (MWd/kgU)

44

PK2-2

PK2-1

PK2-3

42

PW5-3

+5%

PK1-S

40

PK2-S

PW5-1 PW5-2 PK2-4 PW5-4 PW3-4

38

PW3-1

–5%

PK6-1

36

+10% PW3-S PK6-3 PK6-4

34

PK6-2 PK6-S

–10%

PK1-1 PK1-3 PK1-2 PK4-2 PK4-1

32

PK4-3 PK1-4

30

PK4-S

28 28

30

32

34

36

38

40

42

44

46

Measured burnup (MWd/kgU)

FIGURE 8.2 PWR Super-Ramp experimental data versus TRANSURANUS v1m1j09 results: burn-up at the end of the irradiation.

The analysis of the simulation results (referring in particular to pin failure, Fig. 8.6) leads to the following considerations: • The experimental failure thresholds of the groups PK1, PK2, and PK4 are close to or above the RTL limit (50 kW/m), for burn-up values between 30 and 45 MWd/kgU.

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8.3 Application to water reactor conditions

Calculated outer oxidation layer (µm)

70 65

5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

60 55 50 45 40 35 30

PW5-3 B PW3-4

–50%

PW5-3 T

–50%

0

25 20

PW5-3 I

0.5

1

1.5

2

2.5 PK4-3

15 10

3

3.5

4.5

5

PK2-2

PK2-4

PK6-3

PK1-2

5 0

4

PK4-S

0

5

10

15

20

25 30 35 40 45 50 Measured outer oxidation layer (µm)

55

60

65

70

FIGURE 8.3 PWR Super-Ramp experimental data versus TRANSURANUS v1m1j09 results: cladding outer oxidation layer.

50

40

+8%

Calculated FGR (%)

+50%

PK2-3

–8%

30 PK2-2 PK4-3 PK1-4

20

PK1-3

PK1-2 PK2-S

PK4-2

PK2-1

–50% PK1-1 PK4-S

10 PK6-3 PK6-2 PW3-3

PK2-4 PK4-1

PK6-S

PW3-2

0 0

10

20 30 Measured FGR (%)

40

50

FIGURE 8.4 PWR Super-Ramp experimental data versus TRANSURANUS v1m1j09 results: fission gas release analysis.

• The behavior of Super-Ramp pins of group PK2, which is characterized by the lowest fuel-cladding gap width and highest burn-up, is predicted with the worst accuracy. • The presence of Gadolinia in the fuel (group PK4) shows a negligible influence in the rod failures, both experimentally and from TRANSURANUS simulations.

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8. The TRANSURANUS fuel performance code 90

150

200

80 70

100

60 50

50 40 0

30 20

–50

LHR (kW/m)//gap width (Pm)

CALC gap width in peak LHR position

Cladding average hoop stress (MPa)

Cladding average hoop stress (MPa)

CALC clad avg. hoop stress in peak LHR position LHR axial peak power

70 CALC clad avg. hoop stress in peak LHR position LHR axial peak power CALC gap width in peak LHR position

60

150

50 100 40 50 30 0

20

–50

10

10 –100

0 0

2500

5000

7500

10,000 12,500

15,000

17,500

0

–100 21,020

20,000 22,500

LHR (kW/m)//gap width (Pm)

200

21,030

21,040

21,050

21,060

21,070

21,080

Time (h)

Time (h)

(A) Overall

(B) Zoom on ramp phase

21,090

21,100

FIGURE 8.5 PWR Super-Ramp experiment, rod PK1/1: cladding average hoop stress, gap size and linear heat rate, as a function of time, predicted by TRANSURANUS v1m1j09 [(A) overall irradiation, (B) zoom on ramp phase]. 80

Full symbols indicate failure

TU threshold for PW3

RTL (kW/m)

70

TU threshold for PK4

60

TU threshold for PK1

PK1 EXP PK4 EXP PW3 EXP PK1 TU reference PK4 TU reference PW3 TU reference

PK2 EXP PK6 EXP PW5 EXP PK2 TU reference PK6 TU reference PW5 TU reference

TU threshold for PW5

50

40

PK1/S

TU threshold for PK6 TU threshold for PK2

30 28

30

32

34

36 38 Burnup (MWd/kgU)

40

42

44

46

FIGURE 8.6 PWR Super-Ramp experiments versus TRANSURANUS v1m1j09 results: predictions of SuperRamp pin failures in terms of ramp terminal level and burn-up.

• The large fuel grain size (group PK6) causes a reduction of the RTL threshold limit, which was observed in the experiment equal to 44 kW/m at about 35 MWd/kgU. The TRANSURANUS simulations qualitatively reproduce this effect, even though they underestimate this threshold by about 10 kW/m. • The remedy cladding and annular pellets studied (groups PW3 and PW5) have no effect on the cladding failures. The experimental data evidenced a failure threshold of 37.5 kW/m for a burn-up from 35 to 42 MWd/kgU. The TRANSURANUS simulations reveal that the calculated threshold is beyond the experimental one, especially for group PW3.

III. Fuels and sub-channel codes

8.3 Application to water reactor conditions

175

8.3.2 Application to the safety analysis of the Atucha-II Nuclear Power Plant 8.3.2.1 Overview of the Atucha-II Nuclear Power Plant Atucha-II is a pressurized heavy water reactor (pressurized heavy water reactor, both cooled and moderated by heavy water) designed by Siemens, in operation since 2016 in Argentina, with nominal electric power of 745 MWe [69]. The reactor core is composed of 451 fuel bundles placed in vertical fuel channels, each one containing a fuel assembly (FA) with 37 fuel rods. The moderator and coolant circuits are connected through the bypass in the lower plenum and the upper plenum of the reactor pressure vessel (RPV). The coolant flows in two loops with U-Tube steam generators, while the moderator circuit is a four-loop system connecting, upstream and downstream, the moderator tank. Four horizontal U-Tube exchangers remove the heat from the moderator system and preheat the feed water. The Atucha-II fuel rod consists of a 5.3 m long stack of UO2 pellets, surrounded by a Zircaloy-4 cladding tube, including compensation pellets in Al2O3, supporting tube and compression spring. All fuel rods are internally pre-pressurized in order to reduce the compressive cladding stresses and creep-down, caused by the high coolant pressure. Helium is used as pressurizing gas, to guarantee an inert inner environment with good heat transfer from fuel to cladding. The plant is operated with an on-power refueling, performed when the equilibrium burn-up is reached. Each FA is moved three times during its in-core lifetime, until the discharge burn-up is reached. 8.3.2.2 Atucha-II large break
loss-of-coolant accident transient The double-ended guillotine break LOCA (DEGB-LOCA or 2A-LOCA) constitutes the “historical” event for the design of emergency core cooling systems in water-cooled reactors and it is primarily analyzed in vessel-equipped NPPs. It assumes that the largest pipe connected with the RPV can break, so that two end-breaks are generated, typically at the RPV side and at the main coolant pump side. In the case of Atucha-II, the 2A-LOCA transient belongs to the category of selected-beyond DBA events [70
72]. A peculiarity of the Atucha-II design is the positive void reactivity coefficient, which is a characteristic in common with other heavy water-moderated reactors that utilize natural uranium as a fuel. This implies that after a large break - loss-of-coolant accident (LB-LOCA) event, the fission power peak at the very beginning of the transient is controlled by the void formation in the core channels, and then by the pressure wave propagation from the break. Indeed, the moderator is still liquid and its flash is delayed with respect to the coolant, making the LOCA event also a RIA event. The analyses presented in what follows are limited to the first 10 seconds of the LOCA transient (starting at the end of the base irradiation for each assembly), because the power excursion and the cladding heat-up occur during this time span [70,73]. Several additional analyses, including the fuel rod long-term behavior, were performed in order to investigate the worst LOCA event in Atucha-II. For more details, see Ref. [70]. Specific acceptance criteria for design basis accidents in the Atucha-II NPP are reported in Table 8.4. In addition to these, a limit extent of fuel failure up to 10% has been considered as reference, in accordance with German licensing regulations [74].

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8. The TRANSURANUS fuel performance code

TABLE 8.4 Atucha-II specific acceptance criteria for design basis accidents (DBAs) [69,71]. Safety parameter

Acceptance criterion for the DBA

Fuel temperature

Tmax , Tmelt for 90% of pellet cross section at hot spot

Fuel enthalpy (for RIA)

Average fuel hot-spot enthalpy , 180 cal/g for irradiated fuel

Heat transfer cladding-coolant

DNB is admissible, except for the cases listed latera

Cladding temperature

Tclad , 1200 C (Tclad , 650 C in the cases listed latera)

Cladding integrity (for LOCA)

Limited loss of integrity (admissible maximum local oxidation , 17%)

Core-wide oxidation (for LOCA)

Maximum hydrogen generation H2 , 1% of H2,total

Operation of pressurizer safety valves

Challenge admissible

Reactor coolant system pressure

ASME code level C service limit (P , 1.2pdesign)

Secondary side pressure

ASME code level B service limit (P , 1.2pdesign)

Containment pressure

Maximum pressure , design pressure

Permissible dose

Calculated doses below 10CFR50.67 limits: 0.25 Sv for total effective dose equivalent (0.05 Sv in control room)

a

DNB and high cladding temperature are not admissible during events with potential primary medium release outside the containment: (1) SG tube or moderator cooler tube rupture (with emergency mode), (2) long-term loss of main heat sink, due to SG or moderator cooler tube leakage (operational leakages), (3) main steam line rupture outside containment with SG or moderator tube leakage, (4) break of an instrument in the annulus.

DNB, departure from nucleate boiling; LOCA, loss of coolant accident; RIA, reactivity-initiated accident; SG, steam generator.

TABLE 8.5 Atucha-II failed assemblies, represented by the average fuel pins (at the equilibrium burn-up, in the reference core). Assembly no.

Time (s)a

BU/BUmax

PCT/PCTmax

LHR/LHRmax

467_AB11

2.75

0.572

1

0.960

327_AF33

3.02

0.528

0.971

1

267_AK22

5.13

0.931

0.960

0.914

267_BL21

5.32

0.870

0.960

0.914

a

From the beginning of the LOCA, starting at the end of the base irradiation. BU, burn-up; LHR, linear heat rate; LOCA, loss of coolant accident; PCT, peak-cladding temperature.

The 2A-LOCA transient calculations start when each fuel rod reaches the reference equilibrium burn-up (8 MWd/kgU maximum). The fuel performance analyses are carried out using the “v1m1j08” version of the TRANSURANUS code, simulating a single fuel rod representative of one out of the 37 included in each of the 451 FAs, placed at different radial positions in the reactor core. The analyses herein discussed focus on the average fuel pin of each assembly. Input parameters for the TRANSURANUS analysis are obtained from RELAP-3D code calculations, employing a detailed thermal-hydraulics nodalization coupled with 3D-neutron kinetics boundary conditions [75]. The list of the failed assemblies is reported in Table 8.5. The table highlights the time of failure (from the beginning of the LOCA transient), the burn-up value at the beginning of the LOCA, the cladding temperatures (PCT) and LHR values (relative to their maximum values)

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8.3 Application to water reactor conditions 1

2

3

4

5

6

7

8

9

10 11

12 13

14

15 16

17

18

19

20 21

BG

22

23

277

BF

265

BE

257

BD

528

BC

528

BB

518

BA

512

BL

512

AK

521 517

511 503

AH

510

502

AG AF 495

496 489

501

AD

493 493

487

AC

488

AB 482 AA

486

480

AL

472 473

LK

474

LH

470

464

469

463 464

LF

460

462

455

451

453

LE

459

450

452

LD

436

426

426

427

431

421 424

429

2

3

4

5

6

7

8

9

10 11

12 13

14

15 16

17

18

19

20 21

41

42

43 44

45

384

400

408

367

400

385

393

405

388

401 404

410

376 385

394

386

398

AH

343

AD

348

AC

350 356

357

AL LK

363 372

LH

373

LG

373

LF

379

LE

389

LD

389

LC

397

LB

403

LA

414

23

24

AB AA

378 380

AF AE

364

371

381

AG

349

354 354

371

382

390

347

362

377

342

362

368

377

388 395

396

369

AK

341 340

354 355

361

370

340

346

335 334

333

340

355 355

370 376

387

401

408

367

384 392

345

361

331

339

BL

325 332

330

339

352 359

367

375

339

345

324

330

BA

325

323

329

338

352 360

375

392

402

345 353

384

400 402

408

344

323

321

BB

316 315

322

329 328

BC 314

312

320

338

BD

313

320

319 327

360 375

392

409

416 415

22

40

307

312

311

337

351

383

409 409

416

344

366

391

407

412

414

1

38 39

313

311

319

327

308

304

319

336

358

399

411

416 422

LA

399

411

421

344

374 391

407

413

420 423

37

306

305

304

310

318

303

310

310

299

303 302

301

326

365

296

301

301

309

250

411

419

36

BE 297

295 294

300

317

406

411

419

35

BF

294

293

391

411

418

33 34

298

289

294

293

250

418

419

427

430

LB

425

32

289

287 287

286

293

250

288

287

286

250 417

425

426

428 428

437

432

31

291 290

288 280

250

250

432

433 433

434 435

LC

439

433

250

284 281

280

278 250

432

282

279

250

456 448

440

440

442

483 465

440

441

442 438

449

443

444

483

30

BG

279

271

251

292

272

266

504

285

280

271

259

283

274

267

251 513

457 449

449

443

445 446

458 450

451

447

458

251

497

475 466

267

28 29

281

271 271

259

522 505

483 476

458

459

452

484

466

252

490

273

268

27

275 275

268

260

523

499 492

477

468

461

454

484

467

260

514

275

268

25 26

277 276

269

262

252

514

499

262

523

506

491

477 478

468

462

498

484 478

478 469

471

LG

485 479

479

523

506

269

260 252

514

506

491

261

525

515

269 263

253

526

509

494 494

254

526

500

264 261

524

515

507

494

524

509

500

493

479 481

516

256 255

527 516

508

501

AE

529 520

519

510

258

270

24

25 26

27

28 29

30

31

32

33 34

35

36

37

38 39

40

41

42

43 44

45

FIGURE 8.7 Failure of Atucha-II fuel assemblies predicted by TRANSURANUS code, at the equilibrium burnup, in the reference core (accounting for shuffling). The failed assemblies, colored in black, correspond to assemblies number 267 and 327, located in burn-up zone 4, and to assembly number 467 in burn-up zone 3 (zone 1: light blue, zone 2: light orange, zone 3: blue, zone 4: orange, zone 5: green, zone 6: light green).

at the pin failure. The fuel rod from assembly 467_AB11 is assumed to fail because it exhibits the maximum PCT after about 2.75 seconds from the beginning of the LOCA. The failure of assemblies 267_AK22 and 267_BL21 is predicted due to plastic instability, just after the cladding temperature peak, during the quench phase of the LOCA (i.e., after about 5 seconds from the beginning of the LOCA). The assembly 327_AF33 is predicted as failed during the cladding heat-up (i.e., after about 3 seconds from the beginning of the LOCA). Fig. 8.7 reports in black the failed FAs, represented by the average fuel rods, for each core burn-up zone (highlighted with different colors in Fig. 8.7). Fig. 8.8 shows the trend, as a function of time, of the fuel pellet outer radius, the cladding inner radius, the contact pressure between fuel and cladding, and of the gap and coolant pressure of the average pin representative of the assembly 267_BL21 (which fails after B5 seconds from the beginning of LOCA). The fuel and the cladding are in contact at the beginning of the LOCA transient, and the contact pressure shows a maximum value above 12 MPa. The rod equivalent stress and the burst stress, together with the creep strain, are depicted in Fig. 8.9 as a function of time. The burst stress is a decreasing function of temperature, up to pin failure. The rod fails due to plastic instability, when the sum of the effective plastic strain and the effective creep and swelling strains exceeds the safety limits. The overall behavior of the cladding outer radii as a function of burn-up, for all the rods of Atucha-II FAs, is shown in Fig. 8.10. Generally higher values are predicted at lower burn-up, with the maximum value exhibited by the failed average 267_BL21 rod

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6.00

14

RBI slice 3 RHI slice 3 Contact P Gap P Coolant P

10

8 5.90 6

Pressure (MPa)

Radius (mm)

5.95

12 Cladding failure due to plastic instability

4 5.85 2

5.80 0

1

2

3

4

5

6

7

8

0 10

9

Time (s)

FIGURE 8.8 Average rod of assembly 267_BL21, slice #3: outer fuel (“RBI”, blue) and inner cladding (“RHI”, red) radii, contact (green), gap (black), and coolant (brown) pressures as a function of time.

500

3

450 Equivalent stress Burst stress Creep strain

350

2.5

2

300 250

1.5

200

Creep strain (%)

Average stress in the cladding (MPa)

Strain limit

400

1

150 100

0.5

50 0 0

1

2

3

4

5 Time (s)

6

7

8

9

0 10

FIGURE 8.9 Average rod of assembly 267_BL21, slice #3: equivalent stress, burst stress and creep strain as a function of time.

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8.3 Application to water reactor conditions

6.54 Zones 1, 4, and 5

272_BA24

6.53

Zones 2, 3, and 6 327_AF31

6.52 467_AB11

Radius (mm)

6.51

267_AK22

6.50 6.49 6.48 6.47 6.46 Nominal cladding radius

6.45 6.44 0

1

2

3

4 5 Burn-up (MWd/kgU)

6

7

8

FIGURE 8.10 Overall cladding outer radius behavior, of all the pins of Atucha-II FAs, as a function of fuel burn-up. The result for rod 267_BL21 (around 7.58 mm) is not reported.

(not reported in the figure, failed due to plastic instability, as shown in Fig. 8.8). Notwithstanding the low burn-up, the rod 272_BA24 exhibits the highest cladding strain, due to the maximum cladding temperature and LHR it was subjected to.

8.3.3 Application to water
water energetic reactor conditions The third and important reactor type for which the TRANSURANUS code has been developed and commercially applied is the Russian type VVER, with Westinghouse as the industrial partner. The most recent developments were carried out in the frame of the EU (European Union)-funded Project ESSANUF [76], with the main objective of contributing to the security of nuclear fuel supply by developing an alternative nuclear fuel design, as well as licensing methods and methodologies, for the Russian-designed PWR VVER-440 operated in the EU and neighbouring countries. The TRANSURANUS fuel performance code has been selected for the fuel rod design analyses as well as for the DBA analyses. To this end, specific material properties for fuel and cladding have been implemented, and new generic models for inner cladding oxidation, breakaway oxidation and hydrogen uptake have been developed. Moreover, the capabilities of the TRANSURANUS code for Monte Carlo probabilistic analyses have been extended to cover fission gas behavior in the fuel and oxidation rates of the cladding. To support the best estimate as well as conservative safety analyses of PWR and VVER fuel elements, specific Westinghouse proprietary extensions of TRANSURANUS have been focused on: • fuel material properties covering swelling, fission gas diffusion and athermal FGR coefficients in UO2;

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8. The TRANSURANUS fuel performance code

• cladding material properties covering effective creep rates, irradiation growth as well as corrosion layer growth for both Zircaloy-4/Duplex and optimized ZIRLOTM; • specific correlations developed for analyses of DBA conditions between 600 C and 1200 C. They include effective cladding creep strain at high temperatures, as well as cladding burst stress and burst strain. In addition, models for outer and inner cladding oxidation, oxide spalling and hydrogen uptake have been developed and implemented in the code, in the framework of the ESSANUF Project. The high-temperature cladding oxidation model is based on a simple recursive formula for parabolic kinetics which is appropriate to model both the mass gain and the oxide layer growth under transient (temperature-varying) conditions. The following kinetics equation is incorporated for the outer cladding oxidation throughout the simulation and for inner cladding oxidation starting at the time of burst: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 Xn 5 fsp Xsp 1 (8.1) Xn21 2fsp Xsp 1 Kn2 dtn where X is the oxide layer thickness, f represents the oxide fraction (ratio between the clean metal surface area and the total reaction surface area), the indexes n and n 2 1 refer to the current and previous time steps, respectively, dt is the time step. K is the actual reaction rate of cladding oxidation and Ki is calculated as a function of the temperature through an Arrhenius relation. The recent model extension covers the effect of breakaway oxidation or oxide spalling by the quantities Xsp and fsp. The extended cladding oxidation model has also benefited from the coordinated research project of the IAEA on Fuel Modeling under Accident Conditions (FUMAC), aiming at comparing fuel performances predicted by different codes under DBA conditions with a focus on LOCAs. Fig. 8.11 shows the simulation of the inner and outer cladding oxide layers in two LOCA experiments with preirradiated UO2 fuel that were performed (B)

(A) 0.020

0.015

Oxide thickness (mm)

Oxide thickness (mm)

0.020

Outer surface

0.010 Time of burst

0.005

0.015 Outer surface Assumed time of spalling

0.010

0.005

Time of burst

Inner surface

Inner surface

0

0 0

800 600 400 200 Time after onset of blow-down (s)

0

800 600 400 200 Time after onset of blow-down (s)

FIGURE 8.11 Simulated outer and inner oxide layer thickness (mm) after the onset of the blow-down in two LOCA tests of FUMAC: (A) irradiated VVER fuel and (B) irradiated PWR fuel without as well as with oxide spalling (dashed, arbitrarily assumed time of spalling).

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8.3 Application to water reactor conditions

181

at the Halden reactor and are part of the FUMAC exercise. The figure also illustrates the effect of oxide spalling starting at the same arbitrary time point for both the inner and outer cladding surfaces. The most recent extension of TRANSURANUS includes the simulation of the integrated hydrogen uptake during normal operating conditions. To this end, the following formulae taken from Ref. [77] have been implemented: κ2 ð1 2 e2sκ3 Þ FðsÞ 5 κ1 1 sκ3 (8.2) s 2ro cH 5 A ðro 2 ri Þ ðro 1 ri Þ where F(s) is the hydrogen pickup fraction in the cladding, s is the corrosion layer thickness, cH is the integrated hydrogen uptake, ri and ro are the cladding inner and outer radii, respectively. A, κ1, κ2, κ3 are the model parameters. The following parameters were obtained from a fit to data of the total hydrogen pickup fraction in oxidized Zy-2 and Zy-4 published in Ref. [78]: A 5 28940 ppm, κ1 5 0.0584, κ2 5 0.329, κ3 5 0.114 μm21. For evaluating the amount of hydrogen in the metal part (Fig. 8.12), all data points were reduced by a constant value of 2.215%. This reduction corresponds to the typical absorption of 1000 ppm atoms H/atoms Zr in ZrO2 [79], or to a solubility of 0.0005 mol H/mol ZrO2. The latter value is derived from an extrapolation of data from Ref. [80] to typical cladding operating temperatures (300 C
350 C). In order to simulate the cladding hydrogen uptake under DBA conditions, the present correlation for normal operation conditions needs to be combined with an analogous model for high cladding temperatures, e.g., the stand-alone hydrogen uptake model developed for Zr1%Nb [81] that separately considers steam oxidation and steam starvation

FIGURE 8.12 Hydrogen pickup fraction in the metal part of Zy-2 and Zy-4 cladding versus oxide thickness according to Refs. [77,78,80].

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8. The TRANSURANUS fuel performance code

conditions (or H2 rich environment). This code extension is carried out in the frame of the R2CA European Project [82]. The extended code validation has been based on two major sources: (1) an extensive database of Westinghouse consisting of pool-side measurements and postirradiation examinations (PIEs) for a large number of commercial and experimental fuel rods, as well as separate-effect tests representing a wide range of conditions and (2) data of on-line measurements in specific test FAs of the HRP. This extended validation covers best estimate code predictions of fuel rod internal pressures, fission gas release, oxide layer thickness, fuel central temperatures, cladding burst as well as high-temperature oxidation. For illustration, conservative predictions of fuel temperatures are summarized as well. The comprehensive validation database maintained at Westinghouse Electric Sweden contains a wide variety of experimental data for different quantities of interest, for example, fission gas release, oxidation thickness, hydrogen content, rod growth and cladding creep. A large number of on-line fuel temperature, fuel elongation and rod internal pressure measurements in different experimental fuel rods are also compiled from the HBWR. In addition, there are separate-effect test data on Optimized ZIRLOTM cladding performance under accident conditions. In what follows, the analysis is focused on a systematic comparison of measured and calculated (best estimate) values for fission gas release, rod internal pressure, oxide layer thickness, and fuel central temperatures under normal operating conditions. In order to cover DBA conditions the analyses of cladding burst and high-temperature oxidation data are addressed too. First of all, the irradiation history and the fission gas release (FGR) of commercial PWR fuel rods and Halden experimental rods have been simulated with the extended TRANSURANUS version (TU-WSE: TransUranus-Westinghouse Sweden Electric). The relative FGR measured by PIE and the calculated best estimate data are compared in Fig. 8.13, also presenting the relative errors of the best estimate analysis as a function of the rod burn-up. The corresponding rod internal pressures at the reference temperature of 298.15 K were also confirmed to be in good agreement with measured values without deviations with increasing burn-up [76]. 8 y=x PWR data HRP data

Relative error on FGR (c-m)/m

Calculated FGR (%)

50

10

1

0.1 0.1

1

10

50

6 4 2 0 –2 –4 –6 –8

0

Measured FGR (%)

Rod burnup (a.u.)

FIGURE 8.13 Comparison of measured and calculated (best estimate) FGR data (left) and relative error of best estimate FGR computation as a function of the rod burn-up (right: c, calculated; m, measured).

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183

60 y=x Maximum Average

40

20

0 0

20 40 Measured oxide thickness (µm)

60

Absolute error on oxide thickness (c-m) (µm)

Calculated oxide thickness (µm)

8.3 Application to water reactor conditions

30 20

Maximum Average

10 0 –10 –20 –30 0

Rod burnup (a.u.)

FIGURE 8.14 Comparison of measured and calculated ZrO2 thickness (left) and absolute error of best estimate computations as a function of the rod burn-up (right: c, calculated; m, measured) for optimized ZIRLO rods irradiated in PWRs.

In a second step, the Westinghouse PWR database containing data of rod average and local maximum oxide thickness, measured on Optimized ZIRLO rods across a range of rod burnup, was considered for comparison with calculated values (corresponding to the best estimate model parameters, Fig. 8.14). The scatter of the data is relatively large since PIEs had been carried out by different techniques and evaluation methodologies. The absolute differences between measurements and simulations confirm that there is no bias or trend dependency on fuel rod burn-up. The statistical analysis reveals a mean residual difference of only 20.14 μm and a root mean square deviation of 4.34 μm, which mainly represents the scatter of the experimental data. In a third step, the independent evaluation of the fuel temperature computations, compared with in-pile test data, was performed. It is the most complex and most important part of the code validation, since the fuel thermal performance is influenced by burn-up dependent fuel properties and by several physical phenomena like pellet and cladding deformations, fission gas release or corrosion. TRANSURANUS fuel temperature computations have been validated against data from twenty-four Halden test rods (Table 8.6), irradiated in five different assemblies up to a maximum burn-up of B60 MWd/kgU. The test rods covered UO2, (U,Gd)O2 and doped fuels with wide ranges of 235U enrichments (2.8
10 wt.%), Gd contents (2
8 wt.%), and grain sizes (6
56 μm). The Halden test rods in Table 8.6 have been simulated with the TRANSURANUS code version implementing the best estimate material properties and models for Westinghouse PWR fuels with either Zy-4 cladding or Zr1%Nb cladding. The parameters of the fuel densification model have been fitted to the fuel stack elongation data normalized to hot standby conditions (i.e., zero power and the coolant temperature of B235 C, to represent isotropic deformation). The fuel stack elongation measurements usually indicated negligible densification of the Gd-doped fuels and this is represented by zero porosity changes in the densification model.

III. Fuels and sub-channel codes

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8. The TRANSURANUS fuel performance code

TABLE 8.6 Main fuel characteristics of the simulated Halden test rods, in the framework of the ESSANUF Project. Fuel type

Fuel vendor

Number of rods

Enrichment (wt.%235U)

Grain size (μm)

Burn-up (MWd/kgU)

UO2

BNFL

3

7.98

10

57

UO2, Gd-doped

ENUSA

3

3.95
4.25

6
13

40

UO2, Gd-doped

TVEL

6

3.6
10

11
26

54

UO2, Cr-doped

Westinghouse GNF Framatome

6

4.7
4.95

12
56

30

UO2, Gd-doped

ENUSA

6

2.8
4.7

7
11

56

BNFL, British Nuclear Fuel Ltd; ENUSA, Empresa Nacional del Uranio, SA; GNF, Global nuclear fuel; TVEL, Russian nuclear fuel company (Russian abbreviation).

FIGURE 8.15 (A) Comparison of UO2 and (U,Gd)O2 fuel center temperatures measured in the Halden reactor and calculated by means of TRANSURANUS best estimate models and (B) relative error of best estimate fuel central temperature computations as a function of the rod burn-up (c, calculated; m, measured).

The calculated best estimate and the measured fuel centerline temperatures, for all simulated rods under steady-state operating conditions, are compared in Fig. 8.15A, indicating the data of the UO2 and the (U,Gd)O2 fuel rods with different markers. The accuracies of the temperature computations for the UO2 and for the (U,Gd)O2 rods are very similar, with a slightly larger standard deviation in the case of the Gd-doped fuels (9.8% vs 7.1%). Fig. 8.15B represents the relative errors of the best estimate computations as a function of the rod burn-up. From these results, two main trends can be identified. The first is a slight overestimation of the fuel centerline temperatures, noticeable mainly above B20 MWd/kgU rod burn-up. This general trend can be observed for both types of test rods, that is, with either thermocouples or expansion thermometers. The second trend is a systematic underestimation of the temperature of the Gd-doped fuel at beginning of life (BoL), below B4 MWd/kgU, and an overestimation above 6
7 MWd/kgU. This behavior was associated with the limitations of

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8.3 Application to water reactor conditions

(A)

(B) 0.05

1.0 n = 2,602,018 = 27 °C = 72 °C

0.03

0.6 0.5

0.02

0.4 0.352

0.3 0.01

6 Probability density

0.7 Frequency

7

6 Best estimate Conservative

5

0.8 Cumulative frequency

0.04

8

0.9

5

= 0 .0 2 9 = 0.0 8 0

4

4

3 = 0.2 9 8 = 0.1 8 9

3

2

2

0.2 0.1

0 –400 –300 –200 –100

0

100

200

300

0 400

1

1 0 –1.0 –0.8 –0.6 –0.4 –0.2

Calculated - measured fuel temperature (qC)

0

0.2

0.4

0.6

0.8

1.0

0

Relative error on fuel temperature (c-m)/m

FIGURE 8.16 Statistics of the residuals in fuel center temperature computations by TRANSURANUSWestinghouse Sweden Electric for UO2 and (U,Gd)O2 rods irradiated in the Halden reactor: (A) absolute errors of best estimate predictions; (B) relative errors of best estimate and conservative predictions (c, calculated; m, measured).

the TRANSURANUS burn-up model (TUBRNP) in the simulation of the so-called onion burning of the Gd isotopes from the periphery to the center of the fuel pellet [83]. This problem can be addressed by prescribing the radial power profiles as boundary conditions for the TRANSURANUS simulations, calculated by detailed neutron transport computations such as SERPENT [84], for instance. Although the inaccurate modeling of the radial power distribution at low burn-up strongly contributes to the deviation of the simulated fuel temperatures, it is important to consider further effects, as the uncertainty of the fuel rod power (derived from neutron detector signals and neutron-physics calculations). The distribution of the residuals (i.e., differences between calculated and measured fuel central temperatures) for all the simulated fuel rods is presented in Fig. 8.16A, indicating a reasonably small general overestimation of the fuel centerline temperature, by 27 C. The statistics of the relative errors on the fuel temperature computations are presented in Fig. 8.16B. The best estimate results are here compared to the statistics of the conservative (worst case) simulation of fuel central temperatures, which is part of the Westinghouse fuel design methodology. The mean percentage error of the best estimate analyses is 2.9% with a standard deviation of B8%. As expected, the mean percentage bias (30%), as well as the standard deviation (19%) of the conservative analyses, is much larger than the corresponding values of the best estimate approach. The TRANSURANUS code has also been used in the ESSANUF Project to simulate fuel performance under accident conditions, in order to verify the acceptance criteria and to calculate rod failures during DBAs, which is important for fuel licensing. Cladding ballooning, burst and steam oxidation are the key phenomena for DBA simulations. The corresponding models have been verified against standard and Optimized ZIRLO separate-effect test data: 1. tube burst tests with as-received and prehydrided cladding tubes in the temperature range of 600 C
1200 C, 2. isothermal steam oxidation tests in the temperature range of 1100 C
1300 C.

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8. The TRANSURANUS fuel performance code

250

200 Calculated burst time (s)

FIGURE 8.17 Comparison of burst times measured in separate effect tests of standard and Optimized ZIRLO tubes and calculated by TRANSURANUSWestinghouse Sweden Electric.

Std. ZIRLO Opt. ZIRLO Opt. ZIRLO (hydrided) y=x

150

100

50

0

0

50

100

150

200

250

Measured burst time (s)

The cladding burst tests have been simulated at prescribed rod internal pressure and temperature boundary conditions. Since the burst tests were carried out in steam environment, the cladding oxidation and the consequent thinning of the metallic tube wall have also been calculated by means of the Cathcart
Pawel oxidation correlation [85]. The mechanical deterioration due to the hydrogen uptake has been simulated with the relevant mechanical model given in Ref. [86]. The evaluation of the simulations has been based on the case-by-case comparison of the calculated and the measured times from the test initiation (i.e., start of temperature increase) until the rod burst. Fig. 8.17 shows calculated and measured burst times for standard and optimized ZIRLO claddings and indicates adequate predictions for as-received as well as for prehydrided specimens. The accuracy of the burst time predictions has been judged through the statistics of the residuals and the relative errors [76] as well. The results indicate a slight overprediction of the burst time for the as-received specimens by 7.8%, which is still within the experimental uncertainties. No bias was observed for the burst time of the prehydrided specimens. The standard deviation of 9.4% is comparable to the standard deviations of the relative errors of former burst analyses on Zircaloy and Zr1%Nb cladding tubes. For performing the validation of the high-temperature oxidation simulations, isothermal steam oxidation tests, carried out at 1100 C, 1200 C, and 1300 C with open tube specimens of standard and optimized ZIRLO, have been simulated with TRANSURANUS [76]. While at temperatures of 1100 C and 1200 C the Baker
Just kinetic correlation leads to conservative predictions also for ZIRLO claddings, at 1300 C the model slightly underpredicts the measured Equivalent Cladding Reacted ratio (not shown here).

8.4 Preliminary assessment against fast reactor conditions Since its inception, the TRANSURANUS code was developed for fast reactor (FR) fuels. Hence, it contains not only materials properties for MOX fuels, carbides, nitrides,

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8.4 Preliminary assessment against fast reactor conditions

TABLE 8.7 Overview of the main integral experimental data used for the preliminary verification and validation of the TRANSURANUS code for fast reactor oxide fuels. Experiment

Fuel type

Number of rods

Reactor

Burn-up (MWd/kgHM)

SUPERFACT-1

MOX (MA)

4

PHENIX

45
62

L5, L6

MOX

4

SILOE

1

HEDL P-19

MOX

19

EBR-II

1

SPHERE

MOX (MA)

1

HFR

45

B11

MOX (MA)

3

JOYO

1

B14

MOX (MA)

4

JOYO

1

B8-HAM

MOX (MA)

1

JOYO

15

NESTOR-3

MOX

1

PHENIX

80

RAPSODIE-I

MOX

2

RAPSODIE

100

RAPSODIE-II

MOX

3

RAPSODIE

100

DFR-455

MOX

1

DFR

50

HEDL, Hanford Engineering Division Laboratory; MA, minor actinide; MOX, mixed oxide.

various coolants and cladding materials but also specific FR models such as the radial migration of oxygen and actinides in oxide fuels, the central void formation, etc. Nevertheless, the focus of the developments shifted to LWR fuels since the end of the 1980s. Some interest in FR fuels was triggered again when Euratom joined the Gen-IV forum in 2003. The current section therefore provides an overview (Table 8.7) of the integral experiments used for the preliminary verification and validation of TRANSURANUS for FR oxide fuels. The total number of cases for FBR MOX fuel is much less in comparison with the verification cases for LWR fuels shown in Table 8.1. Two examples of modeling developments specific for FR conditions are provided in Section 8.4.1. Then, the code assessment against the HEDL (Hanford Engineering Division Laboratory) P-19 irradiation experiment and its application to the preliminary design of the lead-cooled ALFRED (Advanced Lead-cooled Fast Reactor European Demonstrator) Generation IV case study are presented in Sections 8.4.2 and 8.4.3, respectively. Indeed, TRANSURANUS is currently applied for the design of fuels for accelerator-driven systems (ADSs) [87] and Generation IV FRs. Additional validation works are ongoing in the frame of international benchmarks organized by the Expert Group on Innovative Fuels (EGIF) of the NEA [88], the technical working group on fuel performance and technology of the IAEA, and the EU H2020 Project INSPYRE [89].

8.4.1 Development of TRANSURANUS for fast reactor conditions This section focuses on two phenomena, relevant for MOX fuel under irradiation in FR conditions, which are modeled in the code and employed for FR and Generation IV irradiation simulations. Recent advancements have been introduced in TRANSURANUS

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8. The TRANSURANUS fuel performance code

concerning the plutonium radial redistribution and fuel central void formation models, explained in what follows. Other improvements related to FR MOX behavior modeling in TRANSURANUS are planned, regarding, for example, MOX thermal conductivity, melting temperature and stoichiometry evolution under irradiation up to high burn-up. 8.4.1.1 Plutonium redistribution model In hypo-stoichiometric MOX fuel for FBRs, plutonium migrates towards the central, high-temperature region of the fuel pellet. Consequently, fuel thermal properties, such as the thermal conductivity and the melting temperature, are sensibly affected, resulting in a restriction of the safety margins for power uprating in potential commercial FRs [26]. Several PIEs and out-of-pile experiments indicated that plutonium migration is promoted by two main mechanisms [57]: (1) solid-state thermal diffusion; (2) vapor transport by migrating pores (which also contributes to the formation of the central void). The TRANSURANUS model for Pu redistribution (PUREDI, described in Refs. [6,7]), has been recently refined in order to include the effects of oxygen-to-metal ratio, burn-up and their feedback [90], and further extended to account for the effect of vapor transport [56]. Indeed, plutonium migration is modeled in the code considering that thermal diffusion occurs simultaneously with vapor transport via pores in the fuel and that actinides can migrate only along the radial coordinate, assuming axial symmetry and neglecting axial concentration gradients. A correction factor according to Ref. [91] is applied to the diffusion coefficient, to account for the hypo-stoichiometry of the fuel. The Neumann boundary conditions, imposing zero flux of Pu at both the fuel outer and inner radius, ensure that the mass balance of Pu is preserved during migration. The solution of the Pu migration governing equation is obtained by means of a finite difference scheme, described in Ref. [90]. The model applies for the different Pu isotopes present in the fuel (238Pu, 239Pu, 240Pu, 241Pu, 242Pu). The herein described model for plutonium redistribution in MOX fuels is implemented in the LFR (lead fast reactor)-oriented version of TRANSURANUS and has been applied to the analysis of the ALFRED fuel pin performance. 8.4.1.2 Formation and closure of the fuel central void The fuel pellets usually feature as-fabricated porosity, corresponding to approximately 5%
10% of the pellet volume. When the fuel is heated up, the steep thermal gradient may cause the as-fabricated porosity in the hot region of the fuel to start migrating toward the centerline, with the consequence that a central void develops when pores reach the axis of the fuel rod. This phenomenon is relevant for FBR conditions, due to characteristic higher linear ratings and fuel temperatures. The algorithm employed by TRANSURANUS to deal with the formation of the fuel central void divides the fuel into two distinct regions—an outer region, which cannot contribute to the formation of a central void, and an inner region, in which volume changes may affect the central void. The boundary between both regions is the radius r b (see Fig. 8.18). It is assumed in TRANSURANUS that the hoop and radial strain increments can contribute to the fuel central void formation, determining a fractional increase in volume.

III. Fuels and sub-channel codes

8.4 Preliminary assessment against fast reactor conditions

189

r1

Zone j

Zone i

Zone 1

Central void

FIGURE 8.18 Schematic representation of the two fuel radial regions, employed by TRANSURANUS to deal with the formation of the central void. The inner region may contribute to the formation of the central void.

ri

ri+1

rj

rb

Also, it is further assumed that if only part of the fuel volume change can be accommodated by the central void, the other part contributes to fuel swelling. The option for the central void formation is recommended to be used for FR performance analyses, adopting the appropriate FBR model for pore migration and densification. Nevertheless, TRANSURANUS is currently under testing and verification for all the FBR irradiation conditions, in order to allow for a correct mechanical analysis during central void formation, affected by fuel melting, creep, and swelling.

8.4.2 Assessment against the HEDL P-19 irradiation experiment The purpose of the HEDL P-19 experiment, performed in the 1970s in the EBR (Experimental Breeder Reactor)-II reactor, was to investigate the effect of the asfabricated fuel-cladding gap (ranging from 0.086 to 0.25 mm) on the linear power needed to cause incipient fuel melting [92]. The employed fuel was (25% PuO2
75% UO2) MOX fuel. The experiment consisted of a subassembly containing 19 encapsulated pins, representative of the FFTF (Fast Flux Test Facility) fuel design. The main design data of the pins from the HEDL P-19 database can be found in Table 8.8, while the EBR-II axial linear power profile, normalized to the peak power value, and the irradiation history at the peak power node (PPN) are plotted in Fig. 8.19 (left and right, respectively). The HEDL P-19 experiment aimed at simulating fast start-up situations typical of FBRs. Indeed, irradiation started with a slow power ramp, after which a steady power level (conditioning phase) was kept for an hour. The reactor power was then rapidly ramped with a 15% increase, keeping the maximum power for 10 minutes and then scramming the reactor, to quench the fuel structure. Apart from data about the linear power resulting in incipient fuel melting (i.e., the power-to-melt, affected by the uncertain effects of molten fuel relocation and central void formation), other outcomes of interest from the experiment were the fuel restructuring radii, the residual gap widths and the radial extent of melting at the peak power position, obtained from PIEs [92
94].

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TABLE 8.8 Main design data of the HEDL P-19 fuel pins [92]. Rod ID

2

3

5

6

7

8

13

20

24

25

26

27

28

30

33

35

Gap size (μm)

99

127

72.5

49.5

79

122

99

123

127

101.5

76

51

43

89

62.5

91.5

Density (% TD)

90.75

92.4

90.75

90.75

92.4

90.75

90.75

90.75

92.4

92.4

92.4

92.4

92.4

92.4

90.75

90.75

Clad OD (mm)

5.84

6.35

5.84

5.84

6.35

5.84

5.84

5.84

6.35

6.35

6.35

6.35

6.35

6.35

5.84

5.84

Fuel

25% PuO2
75% UO2

Cladding

AISI 316 stainless steel (20% cold-worked)

Filling gas

98% He, 2% Ar at 1 bar

O/M

1.96

Active fuel length

343 mm

Na inlet temperature

371 C

Max LHR (kW/m)

54.5

64

55.1

54.1

Melting

X

X

56.1

56.1

66.6

53.8

54.5

54.1

64.6

66

66.9

66.9

67.9

65.6

X

X

X

X

X

X

X

X

X

X

X

HEDL, Hanford Engineering Division Laboratory; LHR, linear heat rate; OD, outer diameter; TD, theoretical density.

FIGURE 8.19 Normalized power axial profile (left) and power history at the peak power node (right) during the HEDL P-19 irradiation experiment [92].

The following analysis focuses on two selected pins from the HEDL P-19 irradiation experiment—P-19-2 and P-19-5 (melted and unmelted at the end of irradiation, respectively). Calculations are performed with the “v1m1j12” version of the TRANSURANUS code. The results herein presented are obtained employing the Van Uffelen
Schubert thermal conductivity correlation for MOX fuel [1], while the melting temperature has been fixed equal to the value experimentally measured and reported on the HEDL P-19 kind of fuel, that is, 3035K. The analysis is focused on interesting figures of merit from an engineering point of view, for which experimental data are available (reported in Ref. [92]). The evolution of the predicted fuel central temperature, at the peak power position, is given in Fig. 8.20 (black lines). The temperature profile calculated by the code gradually increases with the LHR, reaching the fuel melting temperature at the conditioning phase. During the fast ramp, predicted temperatures exceed the melting point for both

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191

FIGURE 8.20 Fuel centerline temperature as a function of time, at the peak power node (black line) and at other fuel axial nodes (gray lines), for the selected HEDL P-19 rods (left: P-19-2, right: P-19-5).

FIGURE 8.21 Fuel-to-cladding gap radial size at end-of-life, at different axial positions, for the selected HEDL P-19 rods (left: P-19-2, right: P-19-5).

the P-19-2 and P-19-5 rods, reaching maximum values of 3220 C and 3122 C, respectively (both at the PPN). Nevertheless, experimental analyses showed that rod P-19-5 did not suffer melting at all, indicating that TRANSURANUS provides conservative predictions. No in-pile temperature measurement has been performed during the HEDL P-19 campaign; therefore a direct comparison between predicted temperatures and experimental measurements is not possible. TRANSURANUS was able to capture the experimental gap widths from PIEs, especially for rod P-19-2, employing the standard relocation model [7,95], as shown in Fig. 8.21. This relocation model generally resulted in the best predictions of the gap size, also for the other rods of the HEDL P-19 database. Instead, the code significantly underpredicts the HEDL P-19 central void size at the end of irradiation, as can be noticed from Fig. 8.22.

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FIGURE 8.22 Fuel inner radius at end-of-life, at different axial positions, for the selected HEDL P-19 rods (left: P-19-2, right: P-19-5).

FIGURE 8.23 Columnar grain radius at end-of-life, at different axial positions, for the selected HEDL P-19 rods (left: P-19-2, right: P-19-5).

However, the large uncertainty on the measured fuel inner radius, due to molten fuel relocation, must be considered. The columnar grain growth, from experimental records, started when the linear power increased above 36 kW/m, after 8 hours of irradiation. TRANSURANUS was able to predict the end-of-life fuel restructuring with minor deviations (Fig. 8.23), since the predicted radius is only slightly lower (about 0.1
0.2 mm) than the experimental PIE value. Finally, as shown in Fig. 8.24, TRANSURANUS was able to accurately simulate the molten radius of rod P-19-2. As for rod P-19-5, the code predicted melting, while the experimental PIE showed that this rod did not experience fuel melting during the irradiation history (i.e., the melting radius should be zero). In this, the code confirms its conservative predictions. TRANSURANUS generally provides conservative predictions as far as the fuel melting behavior is concerned, as confirmed by the analysis of the axial front of melting. Nevertheless, the reasons for this overprediction of fuel

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FIGURE 8.24 Fuel melt radius at end-of-life, at different axial positions, for the selected HEDL P-19 rods (left: P-19-2, right: P-19-5).

melting should be thoroughly investigated by checking its sensitivity to the various phenomena that occur in the fuel under irradiation, and to the different ways of modeling them. This is in line with recent findings in the frame of the benchmark organized by the NEA-EGIF [88].

8.4.3 Application to the safety assessment of the ALFRED reactor ALFRED is a small-size (300 MWth) pool-type lead fast reactor (LFR). It is one of the main current Generation IV nuclear reactor concepts, together with ASTRID (sodium fast reactor), MYRRHA (accelerator driven system, LBE-cooled), and various molten salt reactor (MSR) concepts. The main reactor specifications, according to the preliminary concept layout, can be found in Ref. [96]. The ALFRED core [97] is composed of 171 wrapped hexagonal FAs, each one containing 127 fuel pins arranged on a triangular lattice. The fuel considered for ALFRED is made by annular U
Pu MOX pellets, with different plutonium content according to the radial zone in the core. As far as the cladding is concerned, a steel from the 15-15Ti class has been selected, because already licensed for other liquid metal-cooled FRs (e.g., Phenix, Superphenix). Details about the as-fabricated fuel pin design parameters are collected in Table 8.9 [97,98]. The herein presented analysis focuses on two different coolant channels of the ALFRED reactor, that is, the average channel (AC) representative of the average core conditions, and the hot channel (HC) representative of the most critical conditions achieved in the core in terms of power history. This channel is characterized by the highest linear power, which decreases from the beginning to the end of life. The ALFRED power history, considered in this analysis, is calculated by means of the deterministic code ERANOS and shown in Fig. 8.25 [97]. The main results from the ALFRED AC and HC simulations are presented in what follows. For each outcome, the compliance with the associated ALFRED design limit is checked. These limits are reported in Table 8.10, to be intended as preliminary indications, useful in the phase of ALFRED conceptual design. The engineering figures of merit herein

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TABLE 8.9 ALFRED design parameters of as-fabricated fuel pins. Fuel pin design specification Fuel type

MOX

Cladding type

AIM1

Coolant type

Lead

Fuel enrichment as Pu/(Pu 1 U), inner zone (wt.%)

21.7

Fuel enrichment as Pu/(Pu 1 U), outer zone (wt.%)

27.8

Fuel density (% TD)

95

O/M (/)

1.97

Rod filling gas

He

Initial filling pressure (MPa)

0.1

Upper plenum volume (mm )

B30000

Upper plenum length (mm)

120

Fuel active length (mm)

600

Lower plenum length (mm)

550

Cladding outer diameter (mm)

10.5

Cladding inner diameter (mm)

9.3

Fuel pellet outer diameter (mm)

9

Fuel pellet inner diameter (mm)

2

Initial fuel-cladding gap width (μm)

150

Pin pitch (mm)

13.86

3

MOX, mixed oxide; TD, theoretical density.

(A)

(B) Slice

30

20

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

40

HC power history AC power history

Linear power (kW/m)

Average linear power (kW/m)

40

30

20

AC BoC AC EoC HC BoC third cycle HC EoC third cycle

10

0

0 0

500

1000

1500

2000

0

100

200

300

400

500

600

Axial position (mm)

EFPD

FIGURE 8.25 Power histories for ALFRED average and hot channel as a function of (A) equivalent full power days (EFPD) and (B) axial position (BoC, beginning of cycle).

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TABLE 8.10

Preliminary design limits for the ALFRED case study.

Limited quantity

Proposed limit

Reference



, 2000 C

Peak fuel temperature

[99]



Peak-cladding temperature

, 550 C

[99]

Plenum pressure

, 5 MPa

[99]

Cladding relative diameter variation (ΔD/D)

, 3%

[100]

Cladding swelling strain

, 5%

[101]

Thermal creep strain (1)

, 0.2%

[100]

Thermal creep strain (2)

, 1%

[101]

Total creep strain

, 3%

[101]

CDF

, 0.2
0.3

[100]

Cladding plastic strain

, 0.5%

[102]

a

a

The CDF is a pin lifetime parameter that considers the linear accumulation of damage and it is calculated as the ratio between each time interval and the current time-to-rupture [103]. CDF, cumulative damage function.

(A)

(B)

ALFRED AC | slice 14 | z = 337.5 mm

ALFRED HC | slice 14 | z = 337.5 mm 0.03

1000 0.01 500 Fuel inner temperature Fuel outer temperature Gap conductance

0

0

2

4

6

8

0

0.03

2000 Temperature(°C)

0.02 1500

Gap conductance (W mm–2/K–1)

Temperature(°C)

2000

2500

0.02 1500 1000 0.01 500 0

Fuel inner temperature Fuel outer temperature Gap conductance

0

2

4

6

8

Gap conductance (W mm–2/K–1)

2500

0 10

Burn-up (at.%)

Burn-up (at.%)

FIGURE 8.26 Inner and outer fuel temperature, and gap conductance evolution versus burn-up for (A) AC and (B) HC reference case.

considered are the fuel, cladding and coolant temperatures, fission gas release, gap dynamics, stresses and strains in the cladding. Fig. 8.26 shows the fuel temperature evolution during irradiation for both the average and the hot channels, together with the evolution of the gap conductance, for a mid-column fuel slice. The maximum fuel temperature is well below the design limit (2000 C) for the AC. On the other hand, for the HC the maximum temperature is close to 2200 C (anyway far from fuel melting) and located in the middle of the first-year cycle (i.e., at B1 at.% burn-up). As for the cladding and the coolant temperatures, the maximum temperature is reached by the HC

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(B)

(A) ALFRED AC | slice 24 | z = 587.5 mm

ALFRED HC | slice 24 | z = 587.5 mm

600

550

Temperature(°C)

500

550

500

450

450

Cladding inner temperature Cladding outer temperature Coolant temperature

Cladding inner temperature Cladding outer temperature Coolant temperature

400

400 0

2

FIGURE 8.27

4 Burn-up (at.%)

6

8

8

(A)

(B) ALFRED HC | slice 14 | z = 337.5 mm

100

10

60

1.0

40

0.5

20

0

0 2

4

6

8

Internal pressure (MPa)

80

1.5

100

2.5

Fractional FGR (%)

Internal pressure (MPa)

4 6 Burn-up (at.%)

ALFRED AC | slice 14 | z = 337.5 mm

Internal pressure Fractional FGR

0

2

Coolant and cladding temperature evolution for (A) AC and (B) HC reference case.

2.5

2.0

0

Internal pressure Fractional FGR

2.0

80

1.5

60

1.0

40

0.5

20

0 0

2

4

6

8

Fractional FGR (%)

Temperature(°C)

600

0 10

Burn-up (at.%)

Burn-up (at.%)

FIGURE 8.28 Fission gas release and internal pressure as a function of burn-up for (A) AC and (B) HC reference case.

at the beginning of the irradiation, at the top of the fuel active length (Fig. 8.27). In addition, the outer cladding temperature is acceptable, since it is close to the design limit of 550 C (set to limit the lead corrosion of the cladding steel) only at the beginning of the irradiation. The integral fission gas release (FGR) is 32% for the AC and 32.4% for the HC. The fractional FGR (defined as the fraction of fission gas released with respect to the total quantity produced), along with the pin internal pressure, is shown in Fig. 8.28 for the mid-column slice already considered in Fig. 8.26. Due to the fuel higher temperature, the fractional FGR in the HC is greater compared to the AC, reaching B70% maximum at 2 at.% burn-up. Due to this relatively small amount of fission gas released, the internal pressure remains below the preliminary limit of the 5 MPa during all the power cycles, both in AC and HC situation. The relative low values reached by the internal pressure suggest a potential increase of the design initial helium filling pressure (fixed at 0.1 MPa), with a beneficial effect on the gap conductance and hence on the

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8.4 Preliminary assessment against fast reactor conditions

(B)

(A) 150

ALFRED HC | slice 14 | z = 337.5 mm

150

4.75

4.75

4.70

4.60 50

Gap width Fuel outer radius Cladding inner radius

Gap width (Pm)

4.65

Radius (mm)

Gap width (Pm)

4.70 100

4 Burn-up (at.%)

6

4.60 50

Gap width Fuel outer radius Cladding inner radius

0

8

2

4 6 Burn-up (at.%)

4.55

4.50 10

0

4.50 2

4.65

4.55

0 0

100

Radius (mm)

ALFRED AC | slice 14 | z = 337.5 mm

8

FIGURE 8.29 Cladding inner and fuel outer radius, and gap width evolution as a function of burn-up for (A) AC and (B) HC reference case.

(A)

(B)

ALFRED AC | slice 14 | z = 337.5 mm

ALFRED HC | slice 14 | z = 337.5 mm

500

500

200

100

0 0

2

4

6

8

400

Contact pressure (MPa)

300

Equivalent stress (MPa)

Equivalent stress Contact pressure

400 Contact pressure (MPa)

Equivalent stress (MPa)

Equivalent stress Contact pressure

300

200

100

0 0

Burn-up (at.%)

2

4

6

8

10

Burn-up (at.%)

FIGURE 8.30 Contact pressure between fuel and cladding, along with the radially averaged equivalent stress in the cladding for (A) AC and (B) HC reference case.

fuel temperature, keeping the same initial gap width and initial plenum height as in the standard design [98,103,104]. The evolution of the gap size and of cladding and outer fuel radii, as a function of burn-up, are shown in Fig. 8.29. The gap size dynamics is mostly driven by pellet deformation, due to the progressive fuel swelling. In the AC the closure happens at a burn-up of 5 at.% (i.e., between the second and the third year of irradiation). On the other hand, the HC, which is subject to the highest LHR, shows an anticipated gap closure at a burnup of 4 at.% (i.e., at the end of the second year of irradiation). Consequently, a stronger fuel-cladding mechanical interaction (FCMI) is observed in the HC, leading to the worsening of the clad performance (i.e., higher stress, see next Fig. 8.30). The results of the mechanical analysis, in terms of radially averaged cladding hoop stress during irradiation, are reported in Fig. 8.30. No issues regarding the cladding stress are

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8. The TRANSURANUS fuel performance code

observed until the gap is open, since both the internal pressure and the thermal stresses are quite low. When the gap closes and a fuel-cladding contact pressure starts, the stress undergoes a sharp increase, reaching at the end of the irradiation 160 and 430 MPa for the AC and the HC case, respectively. As expected, due to the anticipated gap closure, the cladding stress in the HC is much higher than the AC one and close to the yield strength. The stress relaxation due to thermal creep is not enough to avoid a little plastic strain in HC, which is in any case very low (below the design limit of 0.5%, Table 8.10). Therefore, while the AC presents no issues, the HC high-stress levels deserve particular attention, since thermal creep strain, due to the high stress induced by FCMI, could be a serious issue for the cladding.

8.5 Conclusions and future code developments The TRANSURANUS code is continuously under development, verification and validation, benefiting from the collaboration between different partners of the so-called TRANSURANUS network (including research centers, universities, safety authorities, nuclear industry players). Independent verification and validation procedures are essential to promote the inherent quality of the code. The code relies on a wide validation matrix composed of experimental databases mainly about UO2 fuel irradiated in LWR conditions, but also models describing physical processes and specific behavior of FR MOX are already implemented in the code and under testing against available data from integral FR irradiation experiments. In this chapter, the general structure and main features of TRANSURANUS have been presented, followed by showcases of application of the code, both as integral validation against irradiation experiments (power transients in LWR, WWER and FR conditions) and safety evaluations on oxide fuel behavior for different reactor concepts (a heavy water reactor and a liquid metal-cooled fast reactor). The satisfactory predictive capabilities of TRANSURANUS prove that, as well as fast, it is also reliable; indeed, it is one of the most widespread and applied FPCs. The herein presented analyses allow to affirm that TRANSURANUS can be successfully used not only to simulate base-irradiation or transient conditions but also to predict failures during DBAs such as LOCAs, even though there is a need to extend the validation against these kind of integral tests. In light of some of these observations, a number of activities have been launched recently. First of all, in line with the general tendency to increase the level of detail in modeling embedded in dedicated analysis codes, the mechanistic model for fission gas behavior has been further developed with features for grain boundary cracking and HBS formation [34] and is now available in the stand-alone SCIANTIX code [105], which is coupled to TRANSURANUS and also being coupled to other different FPCs (e.g., GERMINAL [106]). As for fission gas release, the grain boundary sweeping, as an additional mechanism for FGR driven by grain growth, has been recently incorporated in the TRANSURANUS code, along with a semiempirical model for grain boundary cracking during rapid power variations [107]. Hence, a consistent model for the gas release and gaseous swelling is available, predicting FGR with an accuracy considered satisfactory for FPCs (i.e., the ratio of most measured to computed values is below a factor of two) [108]. The second trend is to couple the TRANSURANUS code with various other simulation tools. On one hand, the code coupling aims at the multiphysics simulation of an experimental setup

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199

or a full reactor core, such as the recent coupling of the TRANSURANUS code with SERPENT and also with SUBCHANFLOW. Such a code coupling could enable to take into account the sensitivity of the calculated inner pin pressure to the axial temperature distribution of the cladding during a LOCA transient, which is provided as input by thermal-hydraulic codes. More recently, an effort has also been initiated to couple the TRANSURANUS code with the OFFBEAT code for a local multidimensional analysis [109], which would be required for a detailed understanding of pellet-cladding interaction and fuel cracking, for instance. On the other hand, there is a trend to couple the FPC with simulation tools that deal with smaller (meso-) scales such as the SCIANTIX code mentioned above or the MFPR-F code [110], which currently describes not only the fission gas behavior but also volatile and non-volatile fission products and their chemical interactions in the fuel and with the cladding inner surface. The third activity is also in line with a general trend, namely, to consider more and deep uncertainty and sensitivity analyses. The most relevant capabilities for statistical analyses of fuel performance simulations were established in the early versions of the TRANSURANUS code [111]. Applying the Monte Carlo technique, already the first code versions allowed statistical variations of a large number of input quantities to be simulated according to normal (Gaussian) distributions. More recently, the TRANSURANUS package has been extended with a Python module [112]. Combined with the built-in MC generator, it can be used for the first-level statistical analyses of the output and input variable distributions. The TUPython extension has a GUI and enables to determine the time-dependent input and output uncertainties and to plot the probability distributions of the variables. The sensitivity of a selected output against a selected input can be quantified with the time-dependent Pearson’s and Spearman’s rank correlation coefficients. Data export is possible for further mathematical analyses in different statistical softwares. Furthermore, there is of course the need to acquire and implement more experimental data. This is particularly required for new accident tolerant materials that are being studied worldwide. However, it is also pivotal for MOX fuel during FR transients, at extended burn-up. This would help in developing improved models for the fuel and cladding behavior (e.g., the models for creep and plasticity, which are under revision together with the gap conductance model) in all the possible different irradiation conditions. This is also necessary in view of the much more limited number of integral data available for these fuel types (compare for instance Tables 8.1 and 8.7). Finally, the further developments and verification of TRANSURANUS by its users also consider Gd-doped UO2 fuels and concern the model for H-uptake during accident conditions, as well as the integral verification of LOCA (useful to correctly simulate DBA scenarios), fission gas and He release in MOX (for both LWRs and FRs) and cladding creep under storage conditions. Moreover, the focus is also on developing thermochemistry capabilities that are currently missing in TRANSURANUS, in order to allow the simulation of fission products compounds forming in the fuel and their effect on the fuel-cladding gap evolution and properties (since their release from the fuel leads to the formation of a fuel outer oxide layer, usually called JOG, whose dynamics is currently very little understood). These topics are and will be tackled in the framework of ongoing and future European Projects, OECD
NEA benchmarks and working groups, as well as international collaborations.

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Nomenclature AC ADS ALFRED AMREDI americium redistribution BoL BWR CDF DBA DEGB DFR EBR ECR EGIF ENEA EoL EPMA ESSANUF EU FA FBR FCMI FFTF FGR FPC FR FUMAC GUI HBS HBWR HC HEDL HFR HRP IAEA IFPE INSPYRE ITU JRC LB LBE LFR LHR LOCA LWR MC MOX MSR MTR MYRRHA

average channel accelerator-driven system Advanced Lead-cooled Fast Reactor European Demonstrator ASTRID Advanced Sodium Technological Reactor for Industrial Demonstration. beginning of life boiling water reactor cumulative damage function design basis accident double-ended guillotine break dual fluid reactor experimental breeder reactor equivalent cladding reacted ratio Expert Group on Innovative Fuels Agenzia nazionale per le nuove tecnologie, l’energia e lo sviluppo economico sostenibile end of life electron probe micro-analysis European Supply of SAfe NUclear Fuel European Union fuel assembly fast breeder reactor fuel-cladding mechanical interaction Fast Flux Test Facility fission gas release fuel performance code fast reactor Fuel Modelling under Accident Conditions. graphical user interface high burn-up structure Halden Boiling Water Reactor hot channel Hanford Engineering Division Laboratory high flux reactor Halden Reactor Project International Atomic Energy Agency International Fuel Performance Experiments Investigations Supporting MOX Fuel Licensing in ESNII Prototype Reactors Institute for Transuranium Elements Joint Research Centre large break lead
bismuth eutectic lead fast reactor linear heat rate loss of coolant accident light water reactor Monte Carlo mixed oxide Molten Salt Reactor material testing reactor Multipurpose hYbrid Research Reactor for High-tech Applications

III. Fuels and sub-channel codes

References

NEA NPP OECD OXIRED PCCI PCI PCMI PCT PHWR PIE PPN PTM PUREDI PWR RIA RPV RTL SCC SFR SG TU-WSE WWER (or VVER)

201

Nuclear Energy Agency nuclear power plant Organization for Economic Co-operation and Development oxygen redistribution pellet-cladding chemical interaction pellet-cladding interaction pellet-cladding mechanical interaction peak-cladding temperature pressurized heavy water reactor postirradiation examination peak power node power-to-melt plutonium redistribution pressurized water reactor reactivity-initiated accident reactor pressure vessel ramp terminal level stress corrosion cracking sodium fast reactor steam generator TransUranus-Westinghouse Sweden Electric water
water energetic reactor

References [1] K. Lassmann, A. Schubert, P. Van Uffelen, C. Gyori, J. van de Laar, TRANSURANUS Handbook, Copyright r 1975
2014, Institute for Transuranium Elements, Karlsruhe, 2014. [2] K. Lassmann, A. Moreno, The light-water-reactor version of the URANUS integral fuel-rod code, Report Junta de Energia Nuclear 397, 1977. [3] K. Lassmann, URANUS—a computer programme for the thermal and mechanical analysis of the fuel rods in a nuclear reactor, Nucl. Eng. Des. 45 (1978) 325
342. [4] K. Lassmann, H. Blank, Modelling of fuel rod behaviour and recent advances of the TRANSURANUS code, Nucl. Eng. Des. 106 (1988) 291
313. [5] K. Lassmann, C. Ronchi, G.J. Small, The development of fuel performance models at the European institute for transuranium elements, J. Nucl. Mater. 166 (1
2) (1989) 112
119. [6] K. Lassmann, TRANSURANUS: a fuel rod analysis code ready for use, J. Nucl. Mater. 188 (C) (1992) 295
302. [7] European Commission, TRANSURANUS Handbook, 2017. [8] P. Van Uffelen, et al., Verification of the TRANSURANUS Fuel Performance Code—An Overview, In: Proceedings of 7th International Conference on WWER Fuel Performance, Modelling and Experimental Support, September 17-21, Albena Congress Center, Bulgaria, 2007, pp. 305-320. [9] P. Van Uffelen, A. Schubert, J. van de Laar, V. Di Marcello, Final Report for the FUMEX-III Exercise With the TRANSURANUS code, 2013. [10] L. Luzzi, G. Pastore, P. Van Uffelen, Contribution of the Politecnico di Milano to the FUMEX-III Project, IAEA-TECDOC-1697, 2011. [11] R. Calabrese, FUMEX III Project (Improvement of Computer Codes Used for Fuel Behaviour Simulation)— ENEA Contribution, 2012. [12] OECD/NEA, State-of-the-Art Report on Multi-scale Modelling of Nuclear Fuels, 2015. [13] OECD/NEA, International Fuel Performance Experiments (IFPE) database, 2017. https://www.oecd-nea. org/science/wprs/fuel/ifpelst.html. [14] J.D. Hales, et al., BISON Theory Manual: the equations behind nuclear fuel analysis, Tech. Rep. INL/EXT-1329930, Rev. 1, Idaho Falls, ID, 2014. [15] J.D. Hales, S.R. Novascone, B.W. Spencer, R.L. Williamson, G. Pastore, D.M. Perez, Verification of the BISON fuel performance code, Ann. Nucl. Energy 71 (2014) 81
90.

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[16] R.L. Williamson, et al., Validating the BISON fuel performance code to integral LWR experiments, Nucl. Eng. Des. 301 (2016) 232
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4, 2013. [100] IAEA, Structural Materials for Liquid Metal Cooled Fast Reactor Fuel Assemblies—Operational Behaviour, IAEA Nuclear Energy Series No. NF-T-4.3, 2012. [101] NEA, Fuels and materials for transmutation, OECD/NEA No. 5419, 2005. [102] F. Vettraino, L. Luzzi, ADS-demo fuel rod analysis report, ENEA-DT-SBD.00033 Technical Report, 2001. [103] L. Luzzi, S. Lorenzi, D. Pizzocri, A. Aly, D. Rozzia, A. Del Nevo, Modeling and Analysis of Nuclear Fuel Pin Behavior for Innovative Lead Cooled FBR, Report ENEA RdS/PAR2013/022, 2014. [104] A. Aly, D. Rozzia, A. Del Nevo, L. Luzzi, D. Pizzocri, Supporto alla progettazione del combustibile nucleare per il reattore LFR, Report ENEA RdS/PAR2014/194, 2014. [105] D. Pizzocri, T. Barani, L. Luzzi, SCIANTIX: a new open source multi-scale code for fission gas behaviour modelling designed for nuclear fuel performance codes, J. Nucl. Mater. 532 (2020) 152042. [106] M. Lainet, B. Michel, J.C. Dumas, M. Pelletier, I. Ramie`re, GERMINAL, a fuel performance code of the PLEIADES platform to simulate the in-pile behaviour of mixed oxide fuel pins for sodium-cooled fast reactors, J. Nucl. Mater. 516 (2019) 30
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22, 2020.

III. Fuels and sub-channel codes

C H A P T E R

9 Two fuel performance codes of the PLEIADES platform: ALCYONE and GERMINAL B. Michel, I. Ramie`re, I. Viallard, C. Introini, M. Lainet, N. Chauvin, V. Marelle, A. Boulore, T. Helfer, R. Masson, J. Sercombe, J.C. Dumas, L. Noirot and S. Bernaud CEA, DES, IRESNE, DEC, Cadarache F-13108, Saint-Paul-Lez-Durance, France

9.1 General overview of the PLEIADES fuel software environment 9.1.1 Architecture and generic tools for fuel performance codes The PLEIADES software environment is a simulation framework allowing the development of fuel performance codes dedicated to specific nuclear systems [Pressurized Water Reactor (PWR), Sodium Fast Reactor (SFR), and Material Testing Reactor (MTR)], experimental devices, and advanced fuel modeling. This platform is based on the C11 language. The kernel of the platform, called the architecture, provides generic tools for multiphysics algorithms, data exchange (SALOME [1]), multidimensional thermomechanical solver (Cast3m finite element code [2]), and the link with fuel databases. User-friendly interfaces are available for pre- and postprocessing within SALOME. The development method in the PLEIADES platform is based on a continuous integration process based on Jenkins. Thanks to this process, an automatic nonregression test database can be run after each commit in the version control system. The PLEIADES software environment provides also the open-source MFront tool [3] for the implementation and storage of all the material properties and behavior laws. This tool includes a common numerical library to solve nonlinear differential constitutive equation systems associated with the mechanical behavior. ALCYONE and GERMINAL are the fuel performance codes of the PLEIADES platform, devoted, respectively, to PWR and SFR fuel rod type concepts. For these two codes, a

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00009-7

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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9. Two fuel performance codes of the PLEIADES platform: ALCYONE and GERMINAL

qualification status, based on verification, validation, and uncertainties, is provided to the users for their studies. ALCYONE and GERMINAL codes validation is based on various experimental programs including irradiations in French power nuclear reactors (see Refs. [4
7]). Simulation results and modeling are also discussed in the framework of several international programs [8
11].

9.1.2 Multiphysics computational scheme for fuel rod type geometries 9.1.2.1 Algorithm For fuel rod type geometries, a generic multiphysic computational scheme is proposed in the PLEIADES platform. Main features of this computational scheme are illustrated in Fig. 9.1. A time incremental formulation where a set of fixed point coupling resolutions at different scales or stages are achieved to compute the multiphysic fuel rod behavior for each time step. These fixed point algorithms are block Gauss
Seidel algorithms where each model is called sequentially within a convergence loop. Acceleration algorithms [12] are commonly used to fasten the slow linear convergence of the standard fixed point iterations. The time marching can be a priori given or automatically adjusted during the calculation. Two main scales are considered, respectively, named “global” and “local.” At the local scale a recursive coupling algorithm is also possible to compute physical state variables involving a multi scale approach (see for instance Section 9.2.2.6 with the microscopic and macroscopic square finite element approach implemented in ALCYONE). 9.1.2.2 Global scale This scale describes the behavior of the whole fuel rod with a fixed point algorithm between the axial discretization in slices and the 0D models for the uniform state variables

FIGURE 9.1 PLEIADES generic computational scheme for fuel rod type geometries.

III. Fuels and sub-channel codes

9.1 General overview of the PLEIADES fuel software environment

209

in the fuel rod. These state variables can be, for instance, fuel rod internal pressure or total fission gas release (FGR). 9.1.2.3 Local scale The local scale describes the multiphysic behavior of one slice composed of a stack of pellets and associated piece of cladding. The slice behavior is derived from an axial homogenization assumption where a single pellet located in the middle of the axial slice is represented. Different geometrical assumptions can be used to describe the local behavior from one-dimensional (1D) axisymmetric up to a two-dimensional (2D) or three-dimensional (3D) representation of one or several pellet fragments (see Fig. 9.1). The local state variables are stored and computed with fields associated to a mesh representing the pellet, the gap, and the cladding. In the multiphysics coupling scheme at local scale two types of models can be called: spatial models (e.g., thermic and mechanic) or point models (fission gas behavior, simplified neutronic model, swelling, etc.). The spatial thermal and mechanical equilibria are solved with the Cast3M finite element code. Point models are usually based on nonlinear ordinary differential equation (ODE) systems. These constitutive equations are derived from a multiscale description of the physicochemistry of irradiation. Among these point models, a Calphad Solver [13] is also available, in the PLEIADES environment, in order to assess the thermodynamic equilibrium under irradiation. 9.1.2.4 Software implementation The fuel rod computational scheme is implemented thanks to the coupling tools provided by the PLEIADES architecture. These tools are generic functions describing fixed point algorithms illustrated in Fig. 9.1. Among these generic tools, we can have for instance: • global coupling, global Model: to describe physical coupling at the fuel rod scale • local coupling, local model: to describe the physical coupling at the slice scale • objects linked to the fixed point convergence assessment: convergence criterion, acceleration algorithm, and prediction algorithm • time step evaluation functions (available as a model methods) for the automatic management of the time marching: time step prediction and time step subdivision (in case of nonconvergence).

9.1.3 Verification process and quality control for the fuel performance codes of the PLEIADES platform The verification process is based on the software quality control and on the unit and integral nonregression tests. Verification is performed after each commit in the version control system thanks to the Jenkins tool. Nonregression verifications are achieved through a comparison between two text files (the reference and the new one) structured under a multicolumn format. Relative, absolute, or mixed error criteria can be selected for each pair of columns. All the process, test execution and comparison, is automatized with a script file located in each folder containing the input files and the reference results of a verification test.

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210

9. Two fuel performance codes of the PLEIADES platform: ALCYONE and GERMINAL

9.1.3.1 Software quality control In the PLEIADES software environment, programing rules are recommended for the different languages available in the platform. An automatic verification of the use of these programming rules in the source code can be done with the tools Cpplint and Clang-Tidy. In order to check the fraction of the source code covered by the nonregression tests, opensource codes GCOV and LCOV are available in the platform. This verification can also be done with an automatic process through the Jenkins tools and a code coverage report is available at the end. 9.1.3.2 Unit nonregression tests These tests are possible thanks to a unit computational scheme called “SKEL” provided by the PLEIADES software environment. With “SKEL” each physical model can be executed separately with all the input data defined in an “xml” file. So, a unit test can be done for a single time step with a “global scale” model or a “local scale” model (see Sections 9.1.2.2 and 9.1.2.3). For the “local scale,” it can be either a point model or a spatial model. For a complete verification of nonlinear models the source code coverage tool can help to select enough time steps. In the case of unit verification tests the reference results can be derived from an analytical solution or from a reference computation with another code. Experimental results of unit tests are not used at the verification stage but are used for the separate effect validation with the fit of some material parameters. 9.1.3.3 Integral nonregression tests These tests are achieved with a complete execution of the fuel performance code. These integral nonregression tests are composed of a representative sample of the validation data base. This representative sample has to be defined according all the computational schemes implemented in the fuel performance code (see source code coverage in Section 9.1.3.1) and in order to cover the entire validation domain. In the case of integral verification tests the reference results refer to a previous validated version of the fuel performance code. The reference results have to be updated when the computationexperiment comparison is improved.

9.2 ALCYONE fuel performance code for GEN II and III 9.2.1 General presentation The ALCYONE [14] code is dedicated to the modeling of the in-reactor behavior of PWR fuel rods during normal (base irradiation) and off-normal (power ramps and accidental situations) operating conditions and incorporates several calculation schemes (Table 9.1). A 1D reference scheme, based on a 1D axi-symmetric description of the fuel element associated to a discrete axial decomposition of the fuel rod in stacked independent fuel slices, is used to study the behavior of the complete fuel rod. A 2D scheme that describes pellet-cladding interaction (PCI) at the mid-pellet (MP) plane of a pellet fragment is available to assess precisely stress concentration in the cladding near a pellet crack tip [15]. A 3D model of the complete pellet fragment and overlying cladding is also

III. Fuels and sub-channel codes

TABLE 9.1

Computational schemes available in the ALCYONE fuel performance code.

Loading conditions

Local model Modeling dimension

Neutronic Thermohydraulic

Nominal and power ramp

Standard

Prodhel

1D 2D (r, theta) 3D

RIA LOCA Nominal and power ramp

1D homogenized twophase flow

Fission gas Thermic Mechanic behavior Cast3M

CARACAS

1D two phase flow and post-DNB 1D

convection and radiation heat transfer

Advanced 1D

1D homogenized twophase flow

1D, One-dimensional; 2D, two-dimensional; 3D, three-dimensional.

MARGARET

He behavior Thermodynamic RACHEL

Open Caphad

212

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of interest when detailed studies of PCI are required [16]. Moreover, two advanced schemes (MARGARET and RACHEL) for UO2 and MOX fuels can be used in 1D. MARGARET [17] is an advanced gas model, which describes more precisely gas diffusion and gas release in the fuel, and RACHEL is a model dedicated to helium release. Finally, transient schemes are used to simulate accidental situations with the activation of specific models and constitutive laws. One of the key features of ALCYONE is the integration of a thermochemical model, which is very useful to predict cladding failure during PCI power ramps.

9.2.2 Physical models 9.2.2.1 Isotopic vector evolution and nuclear reactions products The isotopic vector evolution and nuclear reactions products, including fission, are computed with a 1D axisymmetric neutronic model [18]. This model consider an assumption of a one group of energy homogenization based on a conservation principle of the mean nuclear reaction rate in the pellet as a function of the pellet. The input of this model are the linear power and the one energy group mean cross section both given by a multigroup neutronic computation including the Boltzmann transport equation at assembly scale or core scale. Outputs of the PRODHEL model are the power density and the nuclear reactions products concentration as a function of the radius and time. This model includes all the data to compute Helium production in the reactor core or under storage. 9.2.2.2 Fission gas behavior and helium release The fission gas models in ALCYONE represent all the physical and microstructural evolution of the fuel induced by fission gases under different irradiation conditions, including nominal, transient, and accidental loadings. They have been developed with a large experimental database which gather post irradiation examination and in situ measurement results for base irradiations up to high burn up, power ramp tests and annealing tests [19
22]. The model constitutive equations, based on a mean spherical grain assumption for the diffusion process, are defined with a set of state variables that represent the fission gas behavior according all the mechanisms identified through postirradiation examination [21], separate effect experiments [23], and simulation [24]. Microstructure evolution and fission gas localization assessment includes the fundamental features of fission gas behavior, among which are gas creation, diffusion, precipitation in fuel grains, gas resolution from bubbles, growth and coalescence of gas bubbles at grain faces, grain growth, as well as steady-state and transient gas release. For intra- and intergranular behaviors description the physical state variables are the bubble density, bubble size, gas concentration in bubbles, and dissolved in the fuel lattice. These state variables give an accurate description of the microstructure radial gradient induced by irradiation. More complex microstructure evolutions such as the precipitation zone are achieved through a bimodal bubble radius population in MARGARET [17]. The main difference between the two approaches is the nanometric bubbles precipitation. A physical mechanism of precipitation is represented in MARGARET whereas CARACAS approach is based on experimental quantified data. The High Burn Structure zone development is also

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described with a continuous transition thanks to an heterogeneous approach including a partially restructured state [17,25]. A specific model of intergranular fragmentation due to over pressurized intergranular bubbles has been developed in both approaches for LOCA conditions. The partial derivatives equations, associated to the intragranular diffusion, are solved with a finite volume method. A complete ODE system is then built with the discretized finite volume system and all the balance equations used to describe fission gas behavior. The number of state variables is adjusted depending on the irradiation condition in order to optimize the number of unknown. A continuous transition between different irradiation conditions (for instance steady state and accidental conditions) can be obtained through a dynamic evolution of the size of the ODE system and appropriate initialization process. FGR and fuel swelling assessments have been compared to experimental results for a large data base devoted to the integral validation of the ALCYONE fuel performance code. RACHEL provides an integrated modeling of helium behavior during nominal and transient irradiations of the fuel. The model takes into account helium diffusion with trapping and resolution from intra- and intergranular cavities described by the fission gas model CARACAS. Contrary to fission gases, helium is slightly soluble in the fuel, then diffusion and infusion between intragranular dissolved He, intergranular dissolved He, and free volume are modeled too. Furthermore, a sizeable collection of helium-release measurements, at the end of irradiations, allows calibration and validation of RACHEL model. 9.2.2.3 Thermochemical analysis and corrosive fission products release Chemistry of volatile fission products (FP), such as cesium Cs, iodine I, and tellurium Te, is of some importance with regards to PCI failures of the cladding by iodine stress corrosion cracking (I-SCC) [26] in transient conditions (class 2 power ramp). A realistic thermo-chemical-mechanical modeling of PCI/I-SCC is now possible thanks to the sophisticated models integrated in the PLEIADES/ALCYONE fuel performance code. In particular, the multiphysics coupling scheme of PLEIADES includes the neutronics model PRODHEL [18], the inert FGR model MARGARET [17], and the OpenCalphad (OC) thermochemical solver [13] which enables one to estimate the FPs inventory and to describe precisely their chemical association and their migration/release in gaseous form from the fuel during irradiation. The three main steps of this thermochemical calculation can be detailed as follows: • The first step is to calculate at each node of the Finite Element mesh the FPs inventory with PRODHEL from a 1D radial neutron model using one-group burn up
dependent cross-sectional data. The neutronics model PRODHEL considers the chains of actinides (U, Pu, Am, Cm, and Np) and the FPs (Xe, Kr, Cs, Rb, I, Br, Te, Se, Mo, Tc, Ru, Rh, Pd, Sr, Ba, Y, La, Nd, Pm, Eu, Gd, Ce, Pr, Nb, and Zr). Overall, it includes 199 isotopes of FPs and 23 isotopes of actinides. Only isotopes having a significant impact on the isotopic inventory are considered, namely, those with neutronics cross sections above 0.1 barn. For the sake of simplification of the equilibrium calculations, actinides and FPs having similar behavior are grouped according to chemical families (e.g., inert fission gas, volatile FPs, stable oxides, metallic FPs, actinides, and FPs in solid solution in UO2) with one representative element for each of them.

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FIGURE 9.2 Assessment of the gaseous species amount for the CsI chemical compound during a power ramp transient in ALCYONE.

• The second step is to calculate at each node of the Finite Element mesh the local chemical equilibrium state of the FPs from the inventory provided by the model PRODHEL. For this purpose an extensive thermodynamics database containing all the phases and chemical species that are likely to form in the fuel in a gaseous, solid, or liquid states is required, such as the Thermodynamics of Advanced Fuels
International Database (TAF-ID) [27,28]. In PLEIADES the OC thermochemical solver is used to calculate the equilibrium state at constant pressure and temperature by minimizing the Gibbs energy under mass balance constraint and, for phases with ions, under an additional charge balance constraint [13]. The outputs are the concentrations of all the phases and species formed at equilibrium: fluorite phase, gaseous species, condensed species, metallic precipitates, and liquid phases) (see illustration in Fig. 9.2), the oxygento-metal ratio in the bulk but also in the fluorite phase, the chemical potentials of each element and thermodynamic properties such as the heat capacity. • The third step is to take into account the transport of the FPs and their release from the fuel. A reasonable estimate of FPs release can be obtained in simulations of power ramp by considering that only the gas species formed in the fuel are released, showing, therefore, the importance of fuel thermochemistry. To avoid a complex coupling with the inert Fission Gas model MARGARET, an FP gas species release rate proportional to the inert FGR from grain faces has proved to give good results [29]. • In recent years, another phenomenon of importance for fuel thermodynamic equilibrium calculations has been integrated in the PLEIADES/ALCYONE [29,30]: oxygen thermodiffusion. In fact, oxygen radial redistribution in the fuel driven by the thermal gradient strongly modifies local thermochemical equilibria at the pellet center and leads to the release of a large amount of gaseous cesium which, in turn, can limit PCI failure propensity by reacting with iodine in the free volume of the fuel rod [31].

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9.2.2.4 Crack extension modeling in fuel 9.2.2.4.1 Macroscopic scale

Crack extension at macroscopic scale is considered in the fuel in order to assess stress relaxation and pellet fragment relocation induced by the material rupture. In ALCYONE crack-extension assessment is included in the nonlinear finite element mechanical model through two different aspects: a direct description of the pellet fragment with a mesh and a smeared crack model [32,33] based on a continuum damage approach. The first aspect concerns only 2D and 3D models where primary cracks, occurring the first power increase, are explicitly meshed with appropriate boundary conditions. The smeared crack model is used in 1D, 2D, and 3D in order to describe crack initiation and growth depending on the stress and strain states evolution under irradiation. 9.2.2.4.2 Microscopic scale

Crack extension at microscopic scale is considered in the fuel in order to assess grain boundary separation involved in FGR or a pellet over fragmentation process under accidental loading. In ALCYONE microcracks extension are introduced in the fission gas model through a simplified equation depending on the macroscopic mechanical state and on the stable fission gases pressure. These simplified models are derived from experimental results and from 3D full field computation achieved with the “reference volume element” application of the PLEIADES platform. 9.2.2.5 Heterogeneous mechanical behavior For heterogeneous Pu content microstructures, homogenized mechanical models are available in ALCYONE. Initially formulated to model the fuel behavior during normal operating conditions (see Refs. [34,35]), this work has been extended to model the fuel behavior during off-normal operating conditions [36]. For these models the computational scheme enables a two-scale coupling formulation between gaseous swelling and nonlinear mechanical behavior [37]. The homogenized mechanical model provides macroscopic and microscopic stress
strain states according heterogeneous gaseous swelling and heterogeneous creep properties of the material. The microscopic stress state can then be used through the coupling formulation to assess heterogeneous gaseous swelling. 9.2.2.6 Multidimensional and multiscale analysis The multidimensional analysis proposed in the ALCYONE is based on a continuous formulation at the pellet fragment scale for the thermal and the mechanical behaviors coupled with the same multiphysic equations than the ones derived for the 1D fuel performance codes. The computational scheme available [14] is a single pellet approach where boundary conditions for the coolant temperature and fuel rod internal pressure are given by a preliminary 1D computation. An illustration of the elementary finite element mesh used for the 3D model is given in Fig. 9.3. In this approach, each pellet fragment is represented with a simplified “piece of cake” type geometry, and mechanical interaction between the pellet and the cladding and with other pellet fragments is taken into account with unilateral contact conditions. Thanks to this elementary 3D model, several pellet

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z

(P, x1, y1) Mid pellet plane

y1

UP–UC= cste when the gap is closed

Uz =UP

P

FIGURE 9.3 3D finite element mesh for PCI: symmetries and boundary conditions. PCI, Pellet-cladding interaction.

Uz =UC Cladding inner surface

C A

x1

y0

0

Uz ≥ 0 Uz=0 (0, x0, y0) Inter-pellet plane

Symmetry condition on plane (0, r0, z)

Unilateral contact with friction

Uy ≥ 0

D B

r0

x0

fragments can be represented in order to study a fraction of the pellet or a small stack of pellet fragments. The thermomechanical problem is solved with the Cast3M finite element code for a general continuous formulation presented here after. 9.2.2.6.1 Thermal model

Temperature distribution through the fuel element is computed according to the conservation energy principle given by:


5 div λ  gradT   @T @t

p Cp



1 pv

(9.1)

with T the temperature, ρ the density, cp the heat capacity, λ the thermal conductivity, and pv the nuclear power density in the fuel. The heat transfer through the pellet-to-cladding gap is derived from a Robin boundary condition (see Eq. 9.2) prescribed on the pellet external surface and cladding internal surface and added to the thermal stiffness matrix. The equivalent heat transfer coefficient h depends on: the local radial gap size, the gas composition in free volumes, the contact pressure, and interface contact roughness for a closed gap.



Φ 5 h ðTclad 2 Tpellet Þ

(9.2)

with h the equivalent heat transfer coefficient of the gap, Tclad the cladding internal surface temperature, and Tpellet the pellet external surface temperature.

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9.2.2.6.2 Mechanical model

Mechanical state of the fuel element is computed with the static equilibrium and its boundary conditions (see Eq. 9.3) integrated according a weak formulation with the Finite Element method. 8 5 < div σ 5 0 in Ω 5 ~ ~ imp on @ΩT such as; @Ω - @Ω 5 [ and @Ω , @Ω 5 @Ω (9.3) σ n5Σ T u T u : mec ~ ~ u 5 U imp on @Ωu where @ΩT and @Ωu are external surfaces with Neuman and Dirichlet boundary conditions, respectively. In addition to this equilibrium principle, the nonlinear behaviors of the pellet and the cladding are taken into account through several mechanical models with a generic formulation based on the Hooke law and an additive formulation to compute the elastic strain rate as de difference between the total strain rate and all inelastic strain rates (see Eq. 9.4).  tot  5 5 5 _ _ th 5_ ir 5_ plast 5_ creep 5_ crack _ σ 5 E: ε 2ε 2ε 2ε 2ε 2ε (9.4) 5

tot th the total strain rate, 5 where E is the Hooke fourth order tensor, 5 ε_ ε_ the thermal expan5 ir plast the plastic strain rate, sion strain rate, 5 ε_ ε_ the irradiation volumetric strain rate, 5 5 _ε creep the creep strain rate, and 5 _ε crack the inelastic strain rate induced by cracks extension. The constitutive Eq. (9.4) lead to a nonlinear ODE system. In Alcyone and Germinal these equations are implemented with MFront. In the case of the Alcyone 3D computational scheme the following inelastic strains are introduced:

• isotropic thermal expansion in the pellet and anisotropic thermal expansion in the cladding • isotropic densification induced by irradiation and mechanical compressibility in the pellet • isotropic swelling induced by irradiation defects and gaseous FP in the pellet • anisotropic swelling induced by irradiation defects in the cladding • isotropic creep strain in the pellet, including three main contributions: athermal irradiation-induced creep, thermal creep1 induced by void diffusion, and thermal creep (see footnote 1) induced by dislocation motion2 • crack strain in the pellet based on a smeared crack model [32,33] • anisotropic thermal creep strain in the cladding including irradiation damage effects • anisotropic plasticity strain in the cladding under high strain rate loading.

1

Irradiation acceleration coefficient is prescribed to thermal creep to represent activation energy due to fission spikes.

2

At high strain rate ( . 0.1 s21) the dislocation creep model is equivalent to a plastic behavior with no strain rate sensitivity.

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FIGURE 9.4 Computational scheme with the multiscale square finite element algorithm in ALCYONE.

9.2.2.6.3 Pellet-to-cladding gap model

The pellet-to-cladding gap is described with a finite element mesh based on joint elements for the thermal exchange and on solid-to-solid unilateral contact conditions for the mechanical behavior. The nonlinear mechanical solution gives the contact status opened or closed, with the gap size or the mechanical pressure, respectively, for all the nodes describing the gap. Then the thermal exchange coefficient through the gap (h in Eq. 9.2) can be assessed with the gap radial size as a function the circumferential and the axial positions. Thanks to the multiphysic convergence loop the contribution of the nonuniform gap size to the pellet temperature and to the pellet-to-cladding mechanical interaction can be computed. 9.2.2.6.4 Multiscale analysis

The ALCYONE multidimensional computational scheme includes also the finite element square multiscale approach [38] proposed as a generic algorithm in the PLEIADES architecture (see Section 9.1.2.1). In this approach, a 3D finite element model of a Representative Volume Element can be used to assess the nonlinear mechanical behavior at the microstructure scale. This multiscale computational scheme, illustrated on Fig. 9.4, is used for heterogeneous MOX fuel and can be extended to any kind of fuel heterogeneities.

9.2.3 3D simulation results and integral validation of the ALCYONE code The mechanisms leading to pellet-cladding gap closure and ridge formation in the cladding during base irradiations and power ramp tests can be schematically decomposed as described later. 9.2.3.1 Base irradiation During the first power increase the thermal gradient and associated fuel fragmentation are at the origin of the hourglass shape of the pellet (see Fig. 9.5). The consequence is a reduction of the gap at the interpellet (IP) plane (see Fig. 9.5A). Then, during the power hold period the fuel element dimensions will change due to the following phenomena: • densification and solid swelling in the pellet and • cladding creep under a compressive stress state

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FIGURE 9.5 Pellet cladding gap closure and cladding ridging mechanisms under base irradiation: (A) hour glass shape at the end of the first power increase and (B) complete gap closure during the second cycle.

The competition between these geometrical changes leads to a gap decrease with mainly two steps of PCI: • low interaction stage with a gap partially closed in the vicinity of the inter pellet plane and • strong interaction stage with a gap entirely closed and a significant contact pressure level (see Fig. 9.5B). During the interaction period the pellet hourglass shape is printed in the cladding because of its inelastic strains due to material creep under external pressure loading. Moreover, the cladding diameter decrease can also tend to reduce the extent of pellet hourglass magnitude, thanks to stress relaxation due to irradiation-induced creep in the pellet fragment. Through this analysis, it appears that the magnitude of cladding primary ridges at the end of base irradiation is the result of the competition between cladding and pellet creep. The development of a highburn up structure in the pellets with pronounced gas-swelling can smooth the radial deformation of the cladding after base irradiation (see Ref. [9]). 9.2.3.2 Power ramp test The behavior of fuel rods during ramp testing depends on many factors: the geometry of the fuel pellet (height/diameter ratio of the pellet, dish volume, chamfer dimensions, etc.), the power history (maximum power, increase of power, power rate, duration of holding period, etc.), the thermomechanical behavior of fuel and cladding (burn up of the pellet, thermal expansion of the fuel pellet, cladding creep and plasticity, fuel creep, etc.), and fission gas swelling in the fuel pellet (see Fig. 9.6). The diameter increase of the cladding during power ramp is driven by the thermal expansion of the pellet and by fission gas swelling if the temperature of the pellet is high enough. The contribution of gas swelling can be important particularly if the holding period is long ( . 20
30 minutes) or if the fuel rod has a high burn up. Cladding expansion during ramp testing is first induced at IP level due to the hourglass of the pellet resulting from the thermal gradient (see Fig. 9.6A) but soon it is compensated by dish filling due to creep and fission gas swelling of UO2. If the height/diameter ratio of the pellet is large ( . 1.5), the impact of the dish filling on the creep strain accommodation at the MP plane will be small. Radial expansion will, therefore, be maximum at MP level since dish filling will limit radial expansion at IP level (see Fig. 9.6B). This is the reason why the MP ridges observed

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FIGURE 9.6 Pellet viscoplasticity and cladding ridging mechanisms under power ramp test: (A) primary ridge increase at the beginning of the power transient and (B) impact of viscoplasticity at the end of the power transient.

9.54

FIGURE 9.7 3D calculated and measured ridges after base irradiation and ramp testing showing the important development of the mid-pellet ridge during ramp testing. 3D, Three-dimensional.

After ramp test

External diameter (mm)

9.52 9.5 9.48 Inter-pellet level

Mid pellet level

9.46 9.44 9.42

After base irradiation

9.4 0.14

0.16

Measure Simulation

0.18

0.2

0.22

Axial level (m)

in the database can reach significant values (30 μm) and often exceed their IP counterparts by a factor 2 or 3, see Fig. 9.7. This is not the case with pellets of smaller height/diameter ratio (B1) as was shown with ALCYONE 3D in reference [9] since dish filling has, in this case, consequences on the deformation of the MP plane due to axial creep. Hourglass-induced strains remain, therefore, predominant in this configuration leading mainly to IP ridges. The integral validation of the ALCYONE code is based on around 340 study cases, presented in Table 9.2, with input data and postirradiation examination results stored in the CRACO experimental data base. An illustration of the computation/measurement comparisons obtained for the integral validation of the 1D computational scheme of ALCYONE is given in Figs. 9.8
9.10 (see Ref. [5]). As shown in these figures, simulation results are well correlated to experiments for a large range of irradiation conditions. Computation-experiment gaps, generally centered on the perfect agreement curve, have been identified for the whole application domain and can be used to provide a conservative assessment or an uncertainty analysis.

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9.2 ALCYONE fuel performance code for GEN II and III

TABLE 9.2 Study cases used for the integral validation of ALCYONE. Fuel

Cladding

Irradiation conditions

Computational scheme

Number of study cases

UO2/MOX

Zy4/M5

Nominal up to 80 GWd/t

Standard 1D

124

UO2/MOX UO2

Zy4/M5

PCI power ramp

37

Analytical experiments

8

Nominal up to 80 GWd/t

1D 1 MARGARET FGM

MOX

40 47

UO2

PCI power ramp

MOX

Nominal

22 1D 1 RACHEL HGM

PCI power ramp

10 2

UO2

Zy4/Zirlo

LOCA

1D standard

2

UO2/MOX

Zy4/M5

Nominal

2D and 3D standard

41

1D and 3D

10

PCI power ramp UO2/MOX

Zy4/M5/Zirlo

RIA

1D, One-dimensional; 2D, two-dimensional; 3D, three-dimensional; PCI, pellet-cladding interaction.

FIGURE 9.8 Fraction gas release (left) and cladding external diameter variation (μm) (right) at the end of base irradiation: ALCYONE 2.0 versus measures.

The integral validation of the ALCYONE 3D computational scheme has been done with three main types of experimental data: residual cladding ridges at the end of irradiation [39], pellet cracks density [40], and residual dishing volume [41]. An illustration of the simulation/ experiment comparison is given on Fig. 9.11 for the pellet ridges at the end of base irradiation.

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FIGURE 9.9 Fuel (left) and cladding (right) elongation at the end of base irradiation: ALCYONE 2.0 versus measures.

FIGURE 9.10 External corrosion thickness (left) and internal pressure (bar) (right) at the end of base irradiation: ALCYONE 2.0 versus measures.

The validation is still qualitative, but it gives important insights to understand the competition between different phenomena involved in the PCI. Pellet dish filling validation is illustrated on the Fig. 9.12 with a simulation/experiment comparison given for various power-ramp test conditions. Thanks to this comparison, the influence of the pellet thermal creep law can be clearly understood. In Ref. [41] an inverse engineering method is proposed to fit the material parameters of the fuel irradiated creep law with the fuel dish filling measurement.

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FIGURE 9.11 Calculated and measured heights of interpellet ridges at the end of base irradiation.

FIGURE 9.12 Calculated and measured dish filling after a power ramp test.

Fuel pellet radial crack pattern evolution and associated 3D simulations are illustrated on Fig. 9.13. Simulation and experiment are compared on the Fig. 9.14 as a function of the burn up. In reference [40] the number of cracks measurement was used to fit the pellet-tocladding friction coefficient. Thanks to this inverse method, the crack density increase assessment as a function of the burn up is in good agreement with experimental values.

9.2.4 International benchmarks The ALCYONE code has been benchmarked in the framework of several international program such as the SCIP project [9], the IAEA Concerted Research Project FUMAC [42], or the NEA Working Group Fuel Safety [43].

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FIGURE 9.13 Irradiation history and pellet radial crack pattern evolution under normal and off-normal operating conditions.

FIGURE 9.14 Calculated and measured number of radial cracks in the fuel pellet as a function of the fuel rod mean burn up.

9.3 GERMINAL fuel performance code for GEN IV 9.3.1 General presentation The GERMINAL code [7] is dedicated to SFR fuel pin behavior under normal and offnormal operating conditions. The GERMINAL’s computational scheme is based on the generic algorithm of the PLEIADES platform (see Section 9.1.2) with a local scale model based on the 1D axisymmetric geometrical assumption. The SFR multiphysics couplings are based on specific models of fuel behavior under high temperature and high fast neutron flux conditions (see Fig. 9.15). Among these physical aspects (all detailed in reference [7]), fuel restructuring, fuel pellet fragments relocation, and oxide-cladding joint [Joint Oxyde Gaine (JOG)] formation are briefly described in the following section. An advanced

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Global resoluons needed by the local resoluons to come Simplified thermal-hydraulics of coolant channel Determines the boundary condions for the local thermal analyses to come: cladding outer temperature in each axial slice. N.B. Preliminary resoluon for a staonary analysis only. For a transient analysis, coupled resoluon with fuel pin thermal analysis. Local resoluons Loop on axial slices Neutronics Calculaon of average Oxygen to Metal rao in fuel slice (burn-up dependent) Local convergence loop Thermal analysis of fuel and cladding Coupled with coolant thermal-hydraulics for a transient analysis Thermally acvated fuel physical processes Oxygen radial migraon with specific update frequency Fuel irradiaon shrinkage Fuel swelling (gas and solid swelling) Fuel pellet fragments relocaon Gaseous and volale fission products behavior Includes “Joint Oxyde-Gaine” formaon. Mechanics of fuel and cladding Oxygen potenal calculaon with specific update frequency Major acnides radial redistribuon with specific update frequency Fuel restructuring: porosies radial migraon and central hole formaon with specific update frequency Global resoluons needing the previous local resoluons Plenum gas composion and pressure Fuel column axial relocaon Cladding internal and external corrosion Fuel column compression spring reacon

FIGURE 9.15 GERMINAL multiphysics computational scheme for one step [7].

modeling is under development for thermochemical aspects with a CALPHAD type thermodynamic computation coupled with the multiphysics algorithm and for pellet-to-cladding gap closure coupled with fuel restructuring and central hole formation

9.3.2 Physical models 9.3.2.1 Fuel restructuring Fuel restructuring and associated central hole formation are due to high temperatures and steep radial thermal gradients occurring in SFR fuel pins—around 5000 C/cm in normal operating conditions [44]. The mass transfer inside fuel modifies the microstructure of the material and leads to geometry changes at the pellet scale. The driving physical process is pore migration toward the fuel center, activated both by the high temperatures and their radial gradient. Pore migration is due to an evaporation
condensation mechanism [45], where oxide molecules evaporate from the hottest free surface of a pore or a microcrack, then diffuse through

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the gaseous phase and finally condense on the coolest free surface. Pore migration by vapor transport leads to form columnar grains along the way of the pores toward the pellet center, where the coalescence of the pores results in a central hole. This phenomenon usually happens at the beginning of irradiation—fresh fuel is the most reactive—but it is essentially depending on operating conditions that will fix the temperatures and their radial gradient [44,46,47]. A temperature threshold around 1800 C
2000 C is usually considered for the activation of the mechanism. It may also happen later in irradiation, as a consequence of an increase of reactor power or fuel-to-clad gap reopening due to irradiation-induced swelling of clad material. In GERMINAL the radial pore migration is described by the following advection equation:
 @p 1 @ rvp p 52 (9.5) @t r @r where p is the fractional porosity 3 porosity volume ratio (dimensionless) and vp is the average pore velocity (m/s). The average pore velocity is derived from a microscopic model of the actinides vapor mass transfer through helium in a spherical pore [44]. In GERMINAL, Eq. (9.5) is solved from a finite volume integration method. The initial condition is a radially uniform porosity in the fuel pellet. The contribution of free volumes induced by the pellet fragmentation is derived from the relocation strain and added, at each time step, to the total porosity. The central hole radius is deduced from the radial porosity versus time profile, corresponding to the upper bound of the domain where the porosity ratio is equal to one. The resolution of fuel restructuring also verifies the integral condition of mass conservation along the pellet radius, at all times. 9.3.2.2 Gap closure and relocation model The fuel thermal power removal depends greatly on the heat-transfer coefficient in the pellet-to-cladding gap. At first order, this coefficient can be defined as the ratio of the average thermal conductivity coefficient of the gas mixture to the gap thickness. Heat conduction through solid
solid contact between pellet and cladding represents a contribution that is lowered when compared to that in a PWR fuel rod, since the fuel
clad mechanical interaction is itself lowered as a consequence of a low external pressure (coolant pressure) in an SFR. Hence, the gap size influences considerably the heat exchange between the fuel and the cladding and, consequently the fuel temperature changes. During irradiation the gap, initially filled with helium, is polluted by the FGR, leading to a decrease in the average thermal conductivity of the gap. This degradation of the gas mixture thermal conductivity is compensated by the gap size reduction, which finally induces a fuel temperature decrease. Then, in order to have a good assessment of the fuel maximum temperature at the beginning of life, the gap size effect on the thermal power removal has to be described in the multiphysics coupling. In GERMINAL the gap closure mechanism is described by a fuel fragments relocation model [7] combined with the pellet and cladding mechanical equilibrium. The fragments radial relocation is modeled with a uniform free strain in the plane ðr; θÞ, according to the 1D axisymmetric geometrical assumption (local scale).

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In the current version of GERMINAL an empirical formulation (see details in [7]) has been proposed in order to accurately describe the relocation displacement as a function of the thermal gradient in the pellet. The parameters of this relocation model have been fitted with an indirect validation of the maximal fuel temperature based on experimental measurements of the central hole radius and the restructured zone radius. Thanks to this model a good simulation/experiment agreement is obtained for solid and annular pellets under a large range of linear heat rates. Recently, a new relocation model has been proposed in order to replace in the end the empirical formulation with physics-based constitutive equations. This formulation, presented in Ref. [48], considers two mechanisms to explain the relocation displacement: • displacement increase of a fragmented pellet compared to an unfragmented pellet and • radial displacement induced by the volume increase of the columnar grains zone. The first mechanism is described by the mechanical equilibrium of a fragmented pellet compared to that of an unfragmented one. The second mechanism corresponds to the volume increase of the fuel restructured zone, resulting from the mass redistribution of the material that was originally located in the central hole. It is derived from a balance equation ensuring the mass conservation during the crack porosity migration contributing to the central hole formation. 9.3.2.3 Joint Oxyde Gaine formation and interaction with thermomechanical behavior At high temperature the volatile FP (Cs, Te, and I) do not form stable compounds that would enable them to remain in the hot regions of the pellets. As they behave more or less like gas, a fraction of them migrates down the thermal gradient and condensates in the colder area at the periphery of the pellets in order to form a new phase called the “Joint Oxyde Gaine” (JOG [44]). In the current version of GERMINAL, a JOG model based on the Cs release is proposed [7]. The Cs release is correlated to the stable FGR, itself derived from a single grain diffusion model. In this model the diffusion coefficient consists of two terms, including a thermal activation effect and an irradiation activation effect [7]. The equivalent thickness of fully dense JOG is estimated as the product of the released quantity of volatile FP and an average molar volume representative of the elements entering into the JOG composition. In order to assess the real thickness of the JOG, a coupling with mechanical modeling has to be considered. If the pellet-to-cladding gap is greater than the equivalent JOG thickness, the JOG is assumed to be porous and its thickness is equal to the gap size. When the gap size is lower than the fully dense JOG equivalent thickness, the pellet-to-cladding contact condition is changed into a minimum gap condition, accounting for the initial gap size decreased by the fully dense JOG equivalent thickness. The pellet radius will then decrease under an accommodation process if some free volumes induced by pellet fragmentation (assessed with the radial relocation model described in Section 9.3.2.2) are still available. The formation of the JOG layer has also a significant impact on the heat transfer in the pellet-to-cladding gap and modifies consequently the fuel maximal temperature.

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9. Two fuel performance codes of the PLEIADES platform: ALCYONE and GERMINAL

Some developments are in progress in order to improve the JOG composition assessment. In this new formulation the Calphad solver [13] available in the PLEIADES platform is used to compute the thermodynamic equilibrium in the pellet and in the pellet-to-cladding gap. The computational scheme under development has the following features: • an estimation of the quantities of FP available in the fuel [18]; • a thermodynamic data base [27], including any chemical compounds which are likely to be involved in the JOG formation; • a thermodynamic solver [13] to compute the inventory of the multiphase and multicomponent system as a function of the radius in the pellet and in the pellet-tocladding gap; • a simplified assessment of the release into the fuel-to-clad gap of gaseous chemical compounds available in the pellet; and • an estimation of the JOG thickness and composition based on the thermodynamic equilibrium in the pellet-to-cladding gap. First results have been obtained from this this new computational scheme and compared to experiments as presented in Ref. [49].

9.3.3 Validation and application for fuel design 9.3.3.1 Validation Manufacturing features and irradiation conditions of fuel subassemblies and pins are stored in the BREF reference database together with postirradiation examination fuel pins results. BREF is the validation experimental database for fast reactor fuels. It gathers data from several thousands of characterized pins irradiated in sodium-cooled fast reactors, including a wide range of fuel element features. Experimental results come mainly from irradiations achieved in the Rapsodie, Phenix, PFR, and CABRI reactors, and also from other experimental facilities in the framework of international collaboration (see Section 9.3.4. Manufacturing and irradiation conditions data are used as input data for the GERMINAL code. The calculated output data are then compared to PIE results available in the database. The integral validation of the GERMINAL code is based on a selection of more than 100 fuel pins with different geometrical configurations and irradiation conditions. A large range of parameters was then able to be tested in the GERMINAL code through this experimental data base, including the following ones: solid or annular pellets, homogeneous or heterogeneous fuel column, pellet composition (plutonium content and oxygen-to-metal ratio) and cladding material. The application field derived from the integral validation is given in Table 9.3 extracted from Ref. [7]. An illustration of the validation results as given in Ref. [7] is proposed in Fig. 9.16. The latter graph shows an overall good agreement between experiments and simulation with some discrepancies for few experiments under low power operating conditions. Some improvements are expected with new developments focused on experiments irradiated at intermediate power level [50].

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9.3 GERMINAL fuel performance code for GEN IV

TABLE 9.3 Application field for the GERMINAL fuel performance code. Fuel Material

(U, Pu)O22X, (U, MA)O2, UO2

Pellet geometry

Solid/annular

Pellet φext

[4.2-12.2] mm

Pellet φint

[0-2.5] mm

Initial Pu/M

[0-45]%

Initial MA/M

[0-21]%

As-fab. O/M

[1.926-1.999]

As-fab. density

[85-98] %Dth

Cladding φext

[5.1-28.0] mm

Materials

Austenitic steels: 316a, cold work 15 2 5 Ti and AIM1 Inconel 706, Nimonic PE16 EM12, HT9

Fuel pin Types

Homogeneous Axial heterogeneous

Operating conditions Power transients (CRWA, TOP)b

Normal operating conditions Linear heat rate

[50-590] W/cm 

LHR max. (RIA)

-1300 W/cm

Clad nominal temp.

[550-700] C

Pmax/Pn (Top)

-26.3

Damage

[0-155] dpa

Coolant temp.

-900 C

Burn up

[0-23.7] at.%

a

Tempered 316, cold work 316, cold work 316 Ti. b Control Road Withdrawal Accident Transient Over Power.

MA, Minor actinides, Np and/or Am.

FIGURE 9.16 Illustration of the validation of GERMINAL.

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9. Two fuel performance codes of the PLEIADES platform: ALCYONE and GERMINAL

9.3.3.2 Fuel design for the ASTRID project The GERMINAL fuel performance code has been used in the framework of the conceptual design of the ASTRID fuel subassemblies [51]. The aim of this analysis was to check that the design criteria (maximal temperatures, mechanical constraints, clad swelling, etc.) are met in nominal and incidental transient conditions (CRW, etc.). A statistical analysis has also been proposed [52] to assess the number of pin failures during a severe accident.

9.3.4 International benchmarks 9.3.4.1 NEA expert group on innovative fuels In the framework of the NEA Expert Group on Innovative Fuels group, fuel performance codes have been benchmarked with seven irradiations under normal operating conditions [53]. The following codes are compared: CEPTAR (JAEA, Japan), FEMAXI-FBR (KIT, Germany), GERMINAL (CEA), and TRANSURANUS (JRC-Karlsruhe) for oxide fuels; ALFUS (CRIEPI, Japan) and MACSIS (KAERI, Korea) for metal fuels. As an output of the benchmark conclusions were drawn in order to identify common understanding as well as discrepancies that require further investigation and developments. For oxides fuels analysis of the results from calculations (FGR, temperatures, fuel restructuring, and axial elongation) shows some discrepancies between the different codes. One of the most noticeable disagreements between the codes concerns the temperature predictions. This was attributed to the calculations performed on the gap size evolution, the gap heat conductance, and the evaluation of the fuel thermal conductivity. Improvement on models is, therefore, recommended to increase the accuracy of codes. In addition, the analysis revealed that the presence of a low content of MA in the fuel does not appear to be causing any significant differences in the codes calculations. 9.3.4.2 ESFR-SMART In the ESFR-SMART European project code-to-code comparisons are provided for the computation of a fuel pin of an oxide core of 3600 MWTh with 15/15 TiCW cladding. The objective of this benchmark is to compare fuel performance code results regarding the design analysis of the fuel pins. The results, obtained with all the fuel performance codes, have been used to set a 2D correlation for the heat conductance with respect to fuel burn up and fuel rating [54]. 9.3.4.3 CEA-JAEA collaboration A cross-comparison between CEPTAR and GERMINAL was performed as benchmark calculations by both sides in accordance with the Fuel R&D collaboration objective. The latter is to improve the code validation database and to develop new fuel models. Irradiation experiments, selected for the benchmark calculations, are: Two JOYO experiments devoted to measure the in-pile fuel center temperature and the power-to-melt Two Phenix experiments devoted to solid and annular pellet under burn up levels of 11 and 9 at.%, respectively. The results analysis has revealed similarities and differences between the two codes.

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References

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9.3.4.4 INSPYRE European project In the framework of the INSPYRE project the GERMINAL fuel performance codes is benchmarked with TRANSURANUS and MACROS through some computation/experiment and code-to-code comparisons [55]. The main objective of this benchmark is to test new models and material properties derived from the basic research achieved in the INSPYRE project. For GERMINAL significant improvement are expected for the modeling of stable fission gas behavior, especially thanks to the implementation of the SCIANTIX module [56] in the GERMINAL code.

9.4 Conclusion and prospects After 15 years of development the fuel performance codes ALCYONE and GERMINAL of the PLEIADES platform are fully operational for a use at an industrial stage. They offer standard and advanced multiphysic computational schemes with possible 1D
2D
3D and multiscale approaches. The PLEIADES software architecture used some open-source generic tools such as SALOME or MFront. The development and verification process have proven its flexibility and its robustness thanks to a continuous integration methodology. Fuel modeling and its validation with ALCYONE and GERMINAL capitalize results and knowledge of irradiation programs conducted for more than 40 years in PWR and SFR. These two codes have been benchmarked in the framework of various international collaborations, for which they have contribute to improve the understanding of fuel behavior under irradiation. For several years the objectives have been focused on a detailed multiscale description in link with a separate effect approach in order to have a complete understanding of the mechanisms and the physical properties governing the fuel element behavior in the reactor core. These improvements, requiring small scale simulations, smart experiments, and high performance computations, will be the key for a better understanding, including uncertainties, needed for a safe and innovative design.

Acknowledgment This work has been done in the framework of a cooperative program between CEA, EDF, and FRAMATOME.

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124. [48] M. Temmar, B. Michel, I. Ramiere, N. Favrie, Multi-physics modelling of the pellet-to-cladding gap closure phenomenon for SFR fuel performance codes, J. Nucl. Mater. 529 (2020) 151909. [49] K. Samuelsson, J.-C. Dumas, B. Sundman, M. Lainet, An improved method to evaluate the Joint-OxydeGaine formation in (U, Pu)O2 irradiated fuels using the Germinal V2 code coupled to Calphad thermodynamic computations, EPJ Nuclear Sci. Technol. 6 (2020), https://doi.org/10.1051/epjn/2020008. [50] I. Munoz-Viallard et al., Overview of axially heterogeneous PAVIX 8 fuel pin irradiation in PHENIX within the framework of the French GEN IV development program, in: Conference Proceeding Paper 29755, GLOBAL 2019, Seattle, WA, September 22
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C H A P T E R

10 Subchannel codes: CTF and VIPRE-01* Xingang Zhao Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, United States

10.1 Introduction and CTF code overview Subchannel analysis has been used extensively to evaluate core-wide thermal fluid behavior in light-water reactors (LWRs). As illustrated in Fig. 10.1, it provides a higher degree of physical modeling and more detailed local (pin-level) information than lumped analysis approaches. Although not being able to offer resolutions as fine as a high-fidelity computational fluid dynamics (CFD) solver, subchannel codes allow for a relatively fast and reasonably accurate estimation of the flow, enthalpy, and void distributions in an LWR. Jointly developed and maintained by Oak Ridge National Laboratory and North Carolina State University, CTF is a modernized and improved version of the legacy subchannel code, COBRA-TF (Coolant Boiling in Rod Arrays—Two Fluids) [2]. CTF has been adopted for use in the Consortium for Advanced Simulation of Light Water Reactors (CASL) in support of its challenge problems (Fig. 10.2) through the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). CASL is one of the first innovation hubs initiated in 2010 by the US Department of Energy (DOE) to bridge research, engineering, and industry. 1 Since then, activities related to CTF have included implementing software quality assurance measures, implementing new * Note: This chapter was excerpted from and revised upon the PhD thesis of Xingang Zhao, author of this chapter. The reuse permission was granted by the Massachusetts Institute of Technology (MIT), which owns the copyright of Dr. Zhao’s thesis, on November 27, 2019. The authorization to use the copyrighted material also applies to any future editions, revisions, or translations (in whatever language published) and to mechanical and electronic storage on any carrier. 1

CASL website: https://www.casl.gov/.

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00010-3

235

Copyright © 2021 Elsevier Ltd. All rights reserved.

236

FIGURE 10.1

10. Subchannel codes: CTF and VIPRE-01

Subchannel modeling philosophy at pin-level resolution [1].

FIGURE 10.2 CASL challenge problems [4]. CASL, Consortium for Advanced Simulation of Light Water Reactors.

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237

closure models and user features, performing verification and validation testing, establishing and supporting a CTF user group, 2 and integrating the code into the VERA-CS environment for coupled applications [3]. The development of CTF in CASL has been primarily focused on improving the code predictive capabilities for normal reactor operating conditions in both pressurized-water reactors (PWRs) and boiling-water reactors (BWRs), as well as for the departure from nucleate boiling (DNB) margin and the crud-induced power shift analysis. Like COBRA-TF, CTF is based on a two-fluid, three-field (vapor, continuous liquid, and entrained liquid droplets) modeling approach [5]. It solves discretized forms of six equations for mass, momentum, and energy conservation for the liquid and vapor fields, mass and momentum equations for the droplet field, and an energy equation for solid structures, for a total of nine equations. CTF includes a wide range of thermal-hydraulic (T/H) models crucial to accurate LWR safety analysis including, but not limited to, flow regime dependent two-phase heat transfer, interfacial drag and heat transfer, droplet breakup, and quench-front tracking. Due to its extensive array of reactor T/H modeling capabilities for single- and two-phase flow in LWR geometries, CTF has found wide use in modeling of rod bundle transient analysis and whole-vessel loss-of-coolant accident (LOCA) analysis.

10.2 CTF assessment: Motivation and work scope Accurate determination of flow distribution, pressure drop, and void content is crucial for predicting margins to thermal crisis (i.e., DNB for PWRs and dryout for BWRs) and ensuring more efficient plant performance. In preparation for the intended applications, CTF has been validated [6] against data from experimental facilities comprising the General Electric (GE) 3 3 3 bundle [7], the BWR full-size fine-mesh bundle tests (BFBT) [8], the Risø tube [9], and the PWR subchannel and bundle tests (PSBT) [10]. To address the issues with limited experimental data and their ineluctable measurement uncertainties, code-to-code verification provides an effective and reliable approach to assess the single- and two-phase capabilities of CTF. The well-established subchannel code VIPRE01 (Versatile Internals and Component Program for Reactors; EPRI), licensed by the US Nuclear Regulatory Commission (NRC), is selected to generate a baseline set of simulations for the targeted tests. The solution parameters will be compared to CTF results. The CTF flow mixing models are assessed in Section 10.4 via single-phase (including a two-channel flow split verification problem and single-phase GE 3 3 3) and two-phase (GE 3 3 3) flow cases. The single- and two-phase BFBT pressure drop tests are simulated in Section 10.5, as well as the Risø tube cases, to evaluate CTF’s capability to predict pressure gradients. Finally, Section 10.6 will focus on the predicted void fraction solutions against BFBT and PSBT void data.

2

Current CTF code users include members of academia, nuclear vendors, utilities, and regulatory institutions.

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10. Subchannel codes: CTF and VIPRE-01

10.3 VIPRE-01 code overview VIPRE-01 was developed on the strengths of the COBRA series of codes by Battelle Pacific Northwest Laboratories for the Electric Power Research Institute (EPRI) to help evaluate LWR core T/H parameters and safety limits in normal and assumed accident conditions. VIPRE-01 MOD-01 was accepted by the US NRC for PWR licensing applications. VIPRE-01 MOD-02 is an improved and updated version of VIPRE-01 MOD-01 and was developed to address, in particular, issues related to generic BWRs. This up-to-date version of VIPRE-01 MOD-02 (MIT license, through agreement with EPRI) was benchmarked and qualified for both PWR and BWR applications [11]. Unlike CTF, VIPRE-01 calculates single- and two-phase flow velocity, pressure, and thermal energy fields and fuel rod temperatures by solving the finite-difference equations for mass, energy, and momentum conservation for an interconnected array of channels assuming incompressible thermally expandable mixture flow. The conservation equations are solved with no time step or channel size restrictions for stability. Empirical models are included to account for vapor/liquid slip in two-phase flow.

10.4 CTF assessment: Flow mixing 10.4.1 Two-channel single-phase flow split problem This preliminary verification problem consists of two unheated channels connected by a gap of 3.1 mm wide, corresponding to the typical gap value of a PWR channel. The goal is to verify the single-phase flow redistribution length in CTF. The two channels are provided with the same boundary conditions and differ in flow area only, which leads to a lateral pressure gradient: Channel 2 has a hydraulic diameter twice that of Channel 1 (see Fig. 10.3). The turbulent mixing (TM) (i.e., interchannel flow mixing due to turbulence, usually assumed to cause a lateral enthalpy flux without any associated net mass flow [12]) model is disabled so

FIGURE 10.3

Layout of two-channel flow split problem.

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239

FIGURE 10.4 Predicted normalized mass flux profile versus analytical solution in the two-channel system.

that wall friction becomes the only cross-flow driver. The McAdams’ friction correlation [5] is used throughout this chapter. An analytical solution was derived to determine the theoretical flow split considering the two channels to be in mechanical equilibrium (at which point the frictional pressure drop is the same in both channels, and the cross-flow ceases). The CTF versus VIPRE-01 (and the analytical equilibrium) axial flow profiles are compared in Fig. 10.4. The normalized mass flux is defined as the relative difference between local and inlet mass flux. As can be seen, the agreement is essentially perfect between the two codes: both predict the ideal flow split at B7 m from the inlet. Salko et al. [13] addressed the concern of the flow redistribution length being excessively long for this verification case, yet this result shows that the prediction by CTF is well in line with a commercial subchannel tool (i.e., VIPRE-01).

10.4.2 General Electric 3 3 3 benchmark The GE 3 3 3 bundle is a classic BWR-like electrically heated 9-rod test facility that is used for assessing interchannel flow mixing and energy redistribution. The exit mass flux and quality measurements were performed for individual channel types (inner, side, and corner channels) using an isokinetic flow splitter measurement technique. The subchannel layout is shown in Fig. 10.5. Detailed bundle geometry and operating conditions can be found in the original report of Lahey et al. [7]. The bundle was uniformly heated both axially and radially for diabatic tests; the power level, mass flux, and inlet subcooling varied from case to case (4 test cases for single-phase flow and 13 for two-phase flow). Six sets of pin-type spacer grids were employed to hold the rods. 10.4.2.1 Single-phase flow benchmark This study was conducted to evaluate the capability of CTF to correctly predict singlephase flow distribution. The four unheated test cases (1B, 1C, 1D, 1E) were simulated with CTF and VIPRE-01. Mass flow rate is the only parameter that varies (increases) from case 1B to 1E. Predicted exit mass fluxes are compared against measurements in Fig. 10.6. The TM cross-flow model in both codes is a simple turbulent diffusion approximation for which the user is required to specify the single-phase TM coefficient β. A constant value

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10. Subchannel codes: CTF and VIPRE-01

FIGURE 10.5 GE 3 3 3 cross-sectional view and subchannel layout (I: inner, S: side, C: corner).

FIGURE 10.6 Predicted versus measured exit mass flux for GE 3 3 3 single-phase cases. GE, General Electric.

of β 5 0.007 is used here (and throughout this chapter unless otherwise specified) in accordance with previous assessments [14] using the Kumamoto University 2 3 3 facility data [15]. It is noticeable that VIPRE-01 and CTF solutions agree well with each other and both match experimental results closely for inner and side channels, having the relative rootmean-square error (rRMSE) values very close to or less than the reported measurement uncertainty ( 6 2%). The corner channel predictions deviate more from the measured data (rRMSE is close to 10% with both codes). 10.4.2.2 Two-phase flow benchmark Based on the single-phase flow benchmark, this study aimed to evaluate the impact of unique CTF modeling features comprising the two-phase TM enhancement and the void drift (VD) mechanism. The latter feature was introduced to describe the tendency of a vapor phase within the liquid phase along the interconnected channels to redistribute itself according to a certain equilibrium void distribution [12]. VD models are not currently

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FIGURE 10.7 Predicted versus measured exit mass flux for GE 3 3 3 two-phase cases with (A) cTM and noVD and (B) ReTM and VD. cTM, Constant TM coefficient (0.007) in VIPRE-01; ReTM, Reynolds number dependent TM model in VIPRE-01; noVD, no 2-Φ TM enhancement and VD disabled in CTF (1-Φ TM coefficient 5 0.007); VD, 2-Φ TM enhancement and VD enabled in CTF (1-Φ TM coefficient 5 0.007).

available in VIPRE-01, and the code user manual [16] suggested that the same TM model used in single-phase flow be used in two-phase flow for lack of a thorough understanding of the underlying physics. Unlike VIPRE-01, CTF includes the Lahey Moody model [17] for estimating VD, in which the default scaling weight factor Ka 5 1.4 is used.3 Note that the Lahey Moody VD model cannot be directly implemented in VIPRE-01 because it may only be applied with an equal-volume TM model (whereas VIPRE-01 uses an equal-mass TM model). It was recently modified and made applicable to VIPRE-01, showing reasonable validation results [18]. In addition, experimental evidence [5,19] showed a higher TM rate in two-phase flow compared to the single-phase rate. The TM rate was found first to increase with increasing steam quality (due to the increased turbulent fluctuations as a result of the liquid bubble interaction) until reaching its maximum around the slugannular regime transition point and then decrease dramatically to the level of single-phase flow TM in annular-mist flow. Faya et al. [20] quantified this enhancement effect with a two-phase multiplier ΘM based on the Beus model [21], and it was implemented in CTF. Its maximum value was set to 5.0 [5]. The publicly available data for a total of 13 two-phase flow measurement points are compared with the simulation results. Initially, cases were run with VD disabled and with a constant TM coefficient (β 5 0.007, no two-phase enhancement) in CTF. The same grid loss coefficients as provided in the original reference [7] were applied in both codes. Fig. 10.7A shows that under this configuration, the CTF and VIPRE-01 mass fluxes were visually and statistically similar, closely matching experimental data for the inner and side channels 3

The default (recommended) scaling factor (Ka ) value of 1.4 was picked using a “view-graph norm” by fitting with data from three experiments, including GE 3 3 3. It was found [35] that the calculated VD results had little sensitivity to Ka as long as this parameter was in the range of [1.2, 1.6].

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10. Subchannel codes: CTF and VIPRE-01

(rRMSE  5%), although with larger scatter than single-phase cases. The corner channel was poorly predicted (rRMSE . 20%), as most data points were substantially underestimated. When both two-phase TM enhancement and VD were enabled, the CTF solutions were significantly improved and agreed better with the measurements (see Fig. 10.7B), in particular for the corner channels: corner rRMSE is half of the value with the noVD configuration. However, most corner mass fluxes were still considerably underpredicted, requiring search and implementation of more robust (e.g., flow regime dependent) TM and VD models. Furthermore, the corner channel hydraulic diameter (B7 mm) was significantly smaller than that of a typical BWR bundle (11 12 mm), based on which the standard flow mixing models were developed. Therefore models derived from the data of a tight lattice bundle (or a small-diameter tube) would be deemed better qualified for this channel type. The comparison in Fig. 10.7B is also performed by employing a Reynolds number related TM (ReTM) model in VIPRE-01, as recommended by Brynjell-Rahkola et al. [22]. ReTM was included in VIPRE-W (the Westinghouse version of VIPRE-01), and the code package was validated against BFBT data. Fig. 10.7 reveals that while the VIPRE-01 results with ReTM slightly outperformed those with constant TM (cTM), ReTM on its own was unable to improve corner predictions to a more significant extent for these cases. In Fig. 10.8, similar results were generated for the exit equilibrium quality inside each channel type with a reverse trend as compared to mass flux comparison: corner channel quality tended to be overestimated by both codes. Using the same flow mixing model (i.e., β 5 0.007, no 2-Φ enhancement and no VD; see Fig. 10.8A), the corner channel discrepancy between CTF and VIPRE-01 became more dramatic when the outlet flow was in the annular-mist regime. According to the void-based flow regime map in CTF [5], flow regime is annular-mist when the calculated local void fraction is greater than 0.8.

FIGURE 10.8 Predicted versus measured exit equilibrium quality for GE 3 3 3 two-phase cases with (A) cTM and noVD and (B) ReTM and VD. cTM, Constant turbulent mixing; GE, General Electric; ReTM, Reynolds number dependent turbulent mixing; VD, void drift.

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10.5 CTF assessment: Pressure drop 10.5.1 Boiling-water reactor full-size fine-mesh bundle tests pressure drop benchmark These experiments were conducted by the Nuclear Power Engineering Corporation (NUPEC) at the BFBT facility in Japan, where a BWR-type electrically heated 8 3 8 rod assembly design was adopted. The benchmark specifications are documented by Neykov et al. [8]. Tests from Phase II (critical power benchmark), Exercise 0 (steady-state pressure drop) of the BFBT were simulated for this study. They covered both single-phase (series P7, 10 published points) and two-phase (series P6, 22 published points) pressure drop measurements. The assembly type C2A, having a nonuniform axial (cosine shape) and radial power distribution, was used for all test cases. Its cross-sectional view, along with the layout of other assembly types (which will be used in Section 10.6.1), is depicted in Fig. 10.9, showing 60 heater rods and one large central guide tube with no water. The pressure tap locations are shown in Fig. 10.10.

FIGURE 10.9

BFBT bundle channel layout. Within the “unheated pins,” black pins represent guide tubes and gray pins represent heater rods that were shut off for particular assembly configurations; “unheated channels” include both inside-unheated-rod and near-unheated-rod channels. BFBT, Boiling-water reactor full-size finemesh bundle tests. Source: Adapted from R.K. Salko, A.J. Wysocki, B.S. Collins, M. Avramova, C. Gosdin, Development and assessment of CTF for pin-resolved BWR modeling, in: Proceedings of the International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering (M&C), 2017.

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10. Subchannel codes: CTF and VIPRE-01

FIGURE 10.10 BFBT bundle pressure tap axial locations [8]. BFBT, Boiling-water reactor full-size fine-mesh bundle tests

FIGURE 10.11 BFBT predicted-to-measured singlephase pressure drop ratio. BFBT, Boiling-water reactor fullsize fine-mesh bundle tests.

10.5.1.1 Single-phase flow benchmark In an unheated vertical upflow bundle, the pressure drop comprises wall friction, gravity, and form loss (introduced by the presence of spacer grids). Note that the reported BFBT experimental results did not account for gravitational pressure loss; therefore this term was subtracted from the predicted total loss for different pressure tap locations. This study assessed the wall friction (McAdams’ correlation) and grid form loss (Shiralkar and Radcliffe’s approach [14]) models in both codes. Fig. 10.11 shows that the predicted and measured pressure gradients agreed closely (with VIPRE-01 slightly outperforming CTF), although most pressure taps were underpredicted except for T1 and T3. The relative discrepancy between the measured and the

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10.5 CTF assessment: Pressure drop

TABLE 10.1 Boiling-water reactor full-size fine-mesh bundle tests two-phase pressure drop relative rootmean-square error values. Pressure tap no.

T1 (%)

T2 (%)

T3 (%)

T4 (%)

T5 (%)

T6 (%)

T7 (%)

T8 (%)

T9 (%)

All (%)

VIPRE-01

15.7

18.9

9.0

12.7

12.4

11.7

8.4

0.6

8.6

11.9

CTF

9.5

7.8

24.1

11.6

6.9

5.6

4.9

0.7

6.4

10.6

predicted results for dpT9, which covered the entire bundle with 7 grids, was smaller than all tap statistics (rRMSE or MAPE—mean absolute percentage error). The taps with the largest sources of error were T2, T5, T6 (one grid span), and T7 (three grid spans). The reported measurement error for bundle-averaged pressure drop is 1% and predictions fall outside this uncertainty range. Sensitivity studies on single-phase friction and form loss correlations may help further improve the statistics. 10.5.1.2 Two-phase flow benchmark The traditional means of modeling the effect of two-phase flow on the frictional pressure loss is the use of a two-phase friction multiplier. In VIPRE-01 the default and recommended EPRI correlation was selected for this study. The EPRI correlation was based on the analytical homogeneous model and incorporated mass flux dependence observed in some adiabatic steam-water vertical upflow data [11,23]. In CTF the Wallis multiplier [24], defined as one over the liquid volumetric fraction squared, was applied on the liquid wall drag. The form loss due to spacer grids was calculated with the Romie multiplier [11] in VIPRE-01, while it was determined separately for each phase in CTF [5]. Table 10.1 summarizes the two-phase pressure drop rRMSE values for all nine pressure taps. The results were more scattered than single-phase cases (see Fig. 10.11). The two codes resulted in similar overall statistics, with CTF marginally outperforming VIPRE-01. However, the discrepancies at certain tap locations were significant. The largest disagreement with the experiments was from taps T1 T4, located at the upper part of the bundle (i.e., relatively high quality/void). Several tap pressure drops were rearranged, and the full suite of comparison plots for all taps is presented in Fig. 10.12. On one hand, VIPRE-01 consistently underestimated one or more grid spans and slightly overestimated the bare bundle sections. This observation is consistent with the ones previously reported in the literature [22,25]. On the other hand, CTF tended to overpredict the two-phase pressure drops, especially for tap T3 (Fig. 10.12C) and the two upper bare (i.e., no grid) bundle sections— T3 T1 (Fig. 10.12D) and T4 T2 (Fig. 10.12F)—which were severely overestimated by CTF. The two-phase friction multiplier and the liquid vapor interfacial drag model are called into question and will be addressed in Section 10.5.2.

10.5.2 Risø round tube benchmark The Risø experimental facility [9] enabled study of upward flow through a vertical cylindrical pipe, either unheated or with a constant heat flux applied over a specified section of the pipe. Previous work performed at CASL [26] concluded that the effect of heating and tube diameter on CTF’s pressure drop prediction was negligible. Hence, only the adiabatic

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10. Subchannel codes: CTF and VIPRE-01

FIGURE 10.12 Predicted versus measured BFBT pressure drop: (A) dpT1 (1 grid), (B) dpT2 (1 grid), (C) dpT3 (1 grid), (D) dpT3-dpT1 (0 grid), (E) dpT4 (1 grid), (F) dpT4 dpT2 (0 grid), (G) dpT5 (1 grid), (H) dpT6 (1 grid), (I) dpT7 (3 grids), (J) dpT7 dpT6 (2 grids), (K) dpT8 (1 grid), and (L) dpT9 (entire bundle, 7 grids). BFBT, Boiling-water reactor fullsize fine-mesh bundle tests.

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FIGURE 10.13 Risø adiabatic tube: (A) predicted versus measured pressure drop per unit length and (B) predicted-to-measured dP/dz ratio versus equilibrium quality.

(i.e., preheated to a desired constant thermodynamic quality throughout the pipe) test section Risø 10 (tube inner diameter 5 10 mm, length 5 9 m, and exit pressure 5 7 MPa) was selected for this work to serve as a separate-effect benchmark. Impacts of flow mixing and spacer grids were eliminated, and most cases fell within the annular-mist flow regime (i.e., void fraction .0.8). A wide range of mass fluxes (from 500 up to 3000 kg/m2 s) was covered by a total of 26 data points. Pressure gradients were measured by the electric differential pressure transducers with a claimed accuracy of 6 0.5 kPa. Fig. 10.13 confirms the dramatic overprediction tendency of CTF observed in the BFBT bare bundle sections. Moreover, as quality (or void fraction) increases, such overprediction becomes more pronounced. It can be noticed that VIPRE-01 also predicts higher than measured pressure gradients but to a much smaller extent than CTF (at high quality in particular). The void-based Wallis wall friction multiplier used in CTF was derived from horizontal laminar annular flow and showed reasonable approximation for turbulent annular flow. However, no assessment was available for vertical flow, and no formulation for other flow regimes was provided by Wallis [24]. In the TRACE4 V5.0 theory manual [27], the Wallis multiplier was validated and agreed well with vertical air-water data when the void fraction was higher than 82% (TRACE also uses the Wallis multiplier in annular flow). Another set of data covering void fraction ranging from 10% to 90%—the adiabatic steamwater tests of Ferrel McGee—was also included [27], and a modified multiplier was obtained to better fit Ferrel McGee measurements. As compared to Wallis, the modified formulation has a lower exponent in the denominator (1.72 vs 2.0 in Wallis) and is being 4

The TRAC/RELAP Advanced Computational Engine (TRACE) is the latest in a series of advanced best estimate reactor systems codes developed by the US NRC for analyzing steady-state and transient neutronic/thermal-hydraulic behaviors in LWRs.

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10. Subchannel codes: CTF and VIPRE-01

used in TRACE for the bubbly/slug flow regime. The Risø high void ( . 80%) test cases were also recently simulated with TRACE [28], and close agreement was found between CTF and TRACE: the pressure drop was significantly overpredicted in annular flow (where both codes apply the Wallis multiplier). Besides the two-phase wall friction multiplier, pressure drop overprediction may also result from the use of an inadequate interfacial drag model. In the current version of CTF the interfacial drag in annular-mist flow regime depends on the nature of the liquid film (stable or unstable). An unstable film has large waves that will increase the pressure drop and cause a higher friction factor. The interfacial friction factor is taken as the maximum of the unstable film friction factor (Henstock and Hanratty model [29]) and five times the stable film friction factor (Wallis model [24]). The Henstock and Hanratty model was developed with low-pressure air-water data from 30- to 35-mm-diameter tubes, and its applicability beyond this range is unclear. In addition, such a criterion not only would trigger discontinuity at the stable-unstable film boundary but also tend to overestimate the interfacial drag and therefore the pressure drop. As illustrated in Fig. 10.14, by disabling the Henstock and Hanratty model (i.e., the unstable film friction factor) and switching the denominator exponent of the Wallis wall friction multiplier from 2.0 to 1.72— referred to as “CTF-new” in Fig. 10.14—the predicted pressure drop’s agreement with the high void data was considerably improved. Furthermore, as a result of the finding of CTF pressure drop overestimation, a physics-based interfacial drag modeling package has been implemented in the code by the CASL team. Based on Lane [30], this package relies on local closure terms, including the film thickness (in the case of annular flow), a two-zone interfacial friction factor, an entrainment inception point, an entrainment suppression point (which serves as demarcation between the stable and unstable film regimes in annular flow), and modification of the transition criterion between annular-mist and churn-turbulent flow FIGURE 10.14 Risø predicted-to-measured dP/dz ratio versus void fraction: sensitivity study.

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FIGURE 10.15 Risø tube pressure drop predicted by CTF using Lane’s interfacial drag model [28].

regimes. More details regarding the theory and implementation of the package can be found in Salko et al. [28] and Lane’s dissertation [30]. According to Fig. 10.15 (from Fig. 28 in Salko et al. [28]), despite some unresolved code stability issues (several test cases failed to reach convergence in CTF), the accuracy of pressure drop prediction for the Risø tests is clearly improved with the new package. Further improvement on the flow regime detection logic and an extended validation test matrix is desired.

10.6 CTF assessment: Void fraction 10.6.1 Boiling-water reactor full-size fine-mesh bundle tests void benchmark Tests from Phase I (void distribution benchmark), Exercise 1 (steady-state subchannel grade benchmark) of BFBT were modeled for this study. These tests measured 15 sets of published void fraction data referring to 5 assembly types (0 1, 0 2, 0 3, 1, and 4) as presented in Fig. 10.9. Their operating conditions are summarized in Table 10.2. While the assembly types 0 1, 0 2, and 0 3 had uniform axial and radial heating, they differed in that some heater rods were shut off in assembly 0 2 (two nonheated rods) and 0 3 (seven nonheated rods). Assembly type 1 employed the same geometry as assembly 0 1, yet it applied a nonuniform axial (cosine shape) and radial power profile. Assembly type 4 (uniform axial power distribution) had the same geometry as assembly C2A that was used in Section 10.5.1 for the pressure drop benchmark. X-ray computed tomography (CT) measurements were made above the end of the heated length of the facility to determine the high-resolution outlet void distribution. These measurements were averaged on a percoolant-channel basis so they could be used for subchannel code validation exercises. Table 10.3 recapitulates the VIPRE-01 and CTF outlet void solutions in terms of the mean error (error 5 predicted value 2 measured value) and the standard deviation of error for all data, as well as for each assembly and channel type (corner, side, inner, near

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TABLE 10.2 Boiling-water reactor full-size fine-mesh bundle tests void benchmark test conditions. Assembly type

Test number

P (MPa)

_ (t/h) m

hsub;in (kJ/kg)

Q_ (MW)

0 1

0011-55

7.18

54.03

52.6

1.90

0011-58

7.17

54.90

51.0

3.51

0011-61

7.21

54.79

50.9

6.44

0021-16

7.19

54.85

54.0

1.91

0021-18

7.17

54.90

49.8

3.51

0021-21

7.18

54.90

51.4

6.45

0031-16

7.18

54.96

52.4

1.92

0031-18

7.18

54.79

50.0

3.52

0031-21

7.17

54.90

49.4

6.45

1071-55

7.19

54.61

52.8

1.92

1071-58

7.16

55.07

50.3

3.52

1071-61

7.20

54.65

51.8

6.48

4101-55

7.20

54.59

52.9

1.92

4101-58

7.15

54.58

50.6

3.52

5101-61

7.18

54.65

52.5

6.48

0 2

0 3

1

4

TABLE 10.3 Boiling-water reactor full-size fine-mesh bundle tests void benchmark results: mean error and standard deviation (SD). Mean error ( ) Assembly type No. of tests

SD ( )

0 1

0 2

0 3

1

4

all

All

3

3

3

3

3

15

15

VIPRE-01 All channels

0.02

0.03

0.03

0.02

0.01

0.02

0.01

Corner

0.03

0.04

0.03

0.02

0.08

0.04

0.04

Side

0.04

0.04

0.03

0.02

0.01

0.03

0.02

Inner

0.02

0.02

0.02

0.01

0.00

0.01

0.01

nNH

0.03

0.04

0.05

0.03

0.05

0.04

0.01

iNH

0.00

0.05

2 0.01

2 0.01

0.01

0.03 (Continued)

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TABLE 10.3

(Continued) CTF (2-Φ TM enhancement and VD: on)

All channels

0.05

0.06

0.06

0.04

0.03

0.05

0.02

2 0.01

2 0.01

2 0.04

2 0.08

0.01

2 0.02

0.05

Side

0.04

0.04

0.02

0.00

2 0.01

0.02

0.03

Inner

0.05

0.05

0.04

0.05

0.04

0.05

0.02

nNH

0.06

0.12

0.13

0.07

0.10

0.10

0.04

iNH

0.02

0.16

0.26

0.00

0.11

0.12

Corner

CTF (2-Φ TM enhancement and VD: off) All channels

0.05

0.06

0.06

0.04

0.03

0.05

0.02

2 0.03

2 0.03

2 0.05

2 0.07

0.01

2 0.03

0.04

Side

0.03

0.03

0.02

0.01

0.00

0.02

0.02

Inner

0.06

0.06

0.06

0.05

0.04

0.06

0.02

nNH

0.05

0.09

0.11

0.06

0.08

0.08

0.03

iNH

2 0.01

0.05

0.14

2 0.01

0.04

0.07

Corner

nonheated—nNH, and inside nonheated—iNH; see Fig. 10.9). Both codes applied the same wall friction correlation and form loss coefficient (0.94) as suggested in VIPRE-W [22] since the latter code matched data well within the quoted experimental uncertainty of 6 0.03. It can be concluded that VIPRE-01 marginally outperformed CTF and matched the measurements more closely. The bundle-averaged (i.e., averaged on all channels) data were slightly overestimated by both codes, as well as individual channel types except for corners (which were mostly underestimated by CTF). For the inner channels and channels surrounded by one or more unheated pins (i.e., nNH and iNH), CTF behaved poorly as compared to VIPRE-01, especially in slug flow (i.e., void fraction between 0.2 and 0.5, according to the CTF flow regime map) where the CTF overprediction became more remarkable [3], and for assembly types 0 2 and 0 3 in which large flow and enthalpy gradients were expected around the nonheated rods. For this benchmark, CTF seemed to struggle with nonperipheral channels even more when 2-Φ TM enhancement and VD were enabled.

10.6.2 Pressurized-water reactor subchannel and bundle tests void benchmark The NUPEC PSBT data were released following the success of the BFBT benchmark. Specifications were detailed by Rubin et al. [10]. The Phase I (void distribution benchmark) steady-state test cases were selected for this study. Data from both Exercise 1 (single subchannel) and Exercise 2 (5 3 5 bundle) were modeled. The reported void

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252

FIGURE 10.16

10. Subchannel codes: CTF and VIPRE-01

PSBT void benchmark: single subchannel layout [10]. PSBT, Pressurized-water reactor subchannel

and bundle tests.

measurement uncertainties were 6 0.03 for a single subchannel5 and 6 0.04 for a region-averaged bundle. 10.6.2.1 Single subchannel benchmark The object was to evaluate void modeling using CTF with no bias from interchannel flow mixing and spacer grids. As shown in Fig. 10.16, four uniformly heated channel types were included in this benchmark: inner, inner next to a guide tube, side, and corner (denoted as test series S1, S2, S3, and S4, respectively). Channel-heated length was equal to 1.555 m. Outlet pressure ranged from 4.9 to 16.6 MPa, mass flux from 494 to 3072 kg/m2 s, and experimental channel-averaged void (at 1.4 m from the channel bottom where the void fraction was measured by means of a CT scanner) from 0.003 to 0.83. The Organisation for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) released PSBT benchmark results [31] in which various subchannel/system/CFD codes were evaluated, including VIPRE-01 by CSA (Computer Simulation & Analysis, Inc.)6 and F-COBRA-TF (French version of COBRA-TF) by AREVA. The void results extracted from NEA’s work, along with CTF and replicated VIPRE-01 solutions, are summarized in Fig. 10.17. Replicated VIPRE-01 used the same closure models as instructed by CSA [31] and their results essentially agreed with each other. CTF yielded consistently higher void fraction solutions as compared to the measured data and the other codes with similar scatter (i.e., standard deviation). In addition, Fig. 10.18 plots the VIPRE-01 versus CTF axial void profile for Test Point 1222 in 5

The masking effect of the CT measurement technique on void fraction was studied by the OECD NEA [31]. Because of low fidelity of the current CT scan technology, some near-wall void might have been masked, leading to lower measured void fraction than in reality. Depending on the assumptions, the CT scanner would not show any void until the actual void content reached 3.8% 7.8%. Along with concerns on shifting of the CT image, it was therefore suggested that a total experimental uncertainty of B 6 0.062 (vs 6 0.03 as claimed) would be deemed more reasonable.

6

CSA, the code custodian for VIPRE-01, was recently acquired by Zachry Group.

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FIGURE 10.17 PSBT single subchannel void fraction by test series: (A) mean error and (B) standard deviation of error. PSBT, Pressurized-water reactor subchannel and bundle tests.

FIGURE 10.18 PSBT single subchannel axial void profile for S1.1222. PSBT, Pressurized-water reactor subchannel and bundle tests.

Test Series 1 (S1.1222). While both codes predicted similar onset of nucleate boiling (ONB) points, CTF had a faster void fraction increase along the channel in the subcooled boiling region. In VIPRE-01 the subcooled steam quality is calculated using a profile-fit model (Levy or EPRI [11]), and the effect of phase slip is accounted for in the void fraction model (EPRI drift-flux model by default). In CTF a different methodology is adopted. Bubbles are assumed to exist as long as the wall surface temperature exceeds the bulk saturation temperature, and the code relies on the near-wall vapor condensation model of Hancox and

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FIGURE 10.19

10. Subchannel codes: CTF and VIPRE-01

PSBT void benchmark: bundle channel layout [10]. PSBT, Pressurized-water reactor subchannel

and bundle tests.

Nicoll [32] to recondense away the generated vapor. Whether or not the near-wall condensation is adequately capturing the net vapor generation rate in subcooled boiling as well as how the Hancox Nicoll model should be interpreted require further investigation, along with extended validation work and code stability analysis. 10.6.2.2 Rod bundle benchmark As shown in Fig. 10.19, the PSBT 5 3 5 rod bundle test consisted of three assembly types: B5 (uniform axial heating), B6 (cosine shape axial heating), and B7 (cosine shape axial heating with one central thimble rod). Gamma-ray transmission measurements were made at three axial locations: the lower at 2216 mm, the middle at 2669 mm, and the upper at 3177 mm. Seventeen spacer grids were used on each bundle. The CSA VIPRE-01 solutions were collected from the NEA report [31]. The predicted versus the measured regionaveraged (average of four central subchannels) void fraction results for each test series are presented in Fig. 10.20. While most high void fraction ( . 0.5) data points fell within the reported measurement uncertainty ( 6 0.04), both codes tended to overpredict bubbly/slug flow void content (mostly at the lower elevation in the bundle, which was in line with the NEA report findings [31]).

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255

FIGURE 10.20 Predicted versus measured region-averaged void fraction for PSBT bundle test series (A) B5, (B) B6, and (C) B7 with VIPRE-01 (CSA) and CTF. PSBT, Pressurized-water reactor subchannel and bundle tests.

10.7 Summary This chapter aimed to assess the single- and two-phase capabilities of the subchannel code CTF by validating with an extensive database and benchmarking with the commercial code VIPRE-01. Relevant solution parameters were compared between the two codes and against targeted measurements. A comparison of the key fluid flow and heat transfer closure models between CTF and VIPRE-01 within the scope of this work is summarized in Table 10.4. It can be concluded that the CTF prediction of single-phase

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TABLE 10.4 CTF versus VIPRE-01: key fluid flow and heat transfer closure models. Closure term

CTF model

VIPRE-01 model

Turbulent mixing

Constant 1-Φ coefficient and 2-Φ enhancement (Beus) Lahey Moody

Constant coefficient or Reynoldsdependent correlation

Void drift 1-Φ pressure drop 2-Φ pressure drop 1-Φ heat transfer

Wall friction (McAdams’ or user-defined) and form loss Wallis multiplier

EPRI multiplier (default) Dittus Boelter (or user-defined)

Subcooled boiling void and Two-fluid modeling Thom [33] (or Chen [34]) plus Hancox Nicoll heat transfer Saturated boiling heat transfer Saturated boiling heat transfer

EPRI drift flux (default) Thom (or Chen)

Thom (or Chen)

flow distribution is consistent with the experimental (or analytical) solution and VIPRE-01. The single-phase and low-void two-phase pressure drop predictions tend to agree closely with the experimental data. The two-phase flow distribution in inner and side subchannels is also well predicted with the inclusion of the two-phase TM and VD models in CTF. However, this study has revealed that CTF tends to consistently overpredict void content, especially in subcooled boiling and when the void fraction is lower than 0.5. The code also predicts higher than measured two-phase pressure drop in medium-to-high void regions, and the corner subchannel mass flux is considerably underpredicted. These observations have led to the conclusion that the key closure terms in the greatest need of improvement comprise: 1. liquid vapor interfacial friction in medium-to-high void regions (churn/annular flow), 2. subcooled boiling heat transfer mechanism, and 3. flow mixing in subchannels having a significantly smaller than typical LWR hydraulic diameter. Due to uncertainties in whether the near-wall vapor condensation is adequately capturing the net vapor generation rate in subcooled boiling as well as in how the Hancox Nicoll model should be interpreted, detailed investigation will be conducted in the future along with extended validation work on void fraction and code stability analysis. In addition, a physics-based interfacial friction modeling package has been implemented in CTF at CASL, and improved pressure drop solutions have been generated for the Risø tests. Future work should include revising the flow regime detection logic and implementing other advanced/mechanistic closure models in CTF to further improve its accuracy and robustness.

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References

257

References [1] J.C. Gehin, CASL: Consortium for the Advanced Simulation of Light Water Reactors, CASL-U-2015-0137-000, 2015. [2] M.J. Thurgood, J.M. Kelly, T.E. Guidotti, R.J. Kohrt, K.R. Crowell, COBRA/TRAC—a thermal hydraulics code for transient analysis of nuclear reactor vessels and primary coolant systems, NUREG/CR-3046, PNL-4385, 1983. [3] R.K. Salko, A.J. Wysocki, B.S. Collins, M. Avramova, C. Gosdin, Development and assessment of CTF for pin-resolved BWR modeling, in: Proceedings of the International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering (M&C), 2017. [4] P.J. Turinsky, D.B. Kothe, Modeling and simulation challenges pursued by the Consortium for Advanced Simulation of Light Water Reactors (CASL), J. Comput. Phys. 313 (2016) 367 376. [5] R.K. Salko, M. Avramova, CTF theory manual, CASL-U-2016-1110-000, 2016. [6] X. Zhao, K. Shirvan, R.K. Salko, A.J. Wysocki, Validation and benchmarking of CTF for single- and twophase flow, in: Proceedings of the 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), 2017. [7] R. Lahey, B. Shiralkar, D. Radcliffe, Two-phase flow and heat transfer in multirod geometries: subchannel and pressure drop measurements in a nine-rod bundle for diabatic and adiabatic conditions, GEAP-13049, AEC Research and Development Program, 1970. [8] B. Neykov et al., NUPEC BWR full-size fine-mesh bundle test (BFBT) benchmark, volume I: Specifications, NEA/NSC/DOC(2005)5, OECD Nuclear Energy Agency, 2006. [9] J. Wurtz, An experimental and theoretical investigation of annular steam-water flow in tubes and annuli at 30 to 90 bar, Risø Report No. 372, Risø National Laboratory, 1978. [10] A. Rubin, A. Schoedel, M. Avramova, H. Utsuno, S. Bajorek, A. Velazquez-Lozada, OECD/NRC benchmark based on NUPEC PWR subchannel and bundle tests (PSBT), volume I: Experimental database and final problem specifications, NEA/NSC/DOC(2010)1, OECD Nuclear Energy Agency, 2010. [11] C.W. Stewart et al., VIPRE-01: a thermal-hydraulic code for reactor cores. Volume 1: Mathematical modeling, NP-2511-CCM-A, Vol. 1, Rev. 4.3, Pacific Northwest National Laboratory, 2011. [12] T.M. Conboy, Assessment of Helical-Cruciform Fuel Rods for High Power Density LWRs (PhD Thesis), MIT, 2010. [13] R.K. Salko, M. Gergar, C. Gosdin, M. Avramova, CTF void drift validation study, CASL-U-2015-0320-002, 2015. [14] R.K. Salko et al., CTF validation and verification, CASL-U-2016-1113-000, 2016. [15] M. Sadatomi, A. Kawahara, K. Kano, Y. Sumi, Single- and two-phase turbulent mixing rate between adjacent subchannels in a vertical 2 3 3 rod array channel, Int. J. Multiphase Flow 30 (5) (2004) 481 498. [16] C.W. Stewart et al., VIPRE-01: a thermal-hydraulic code for reactor cores. Volume 2: User’s manual, NP2511-CCM-A, Vol. 2, Rev. 4.4, Pacific Northwest National Laboratory, 2011. [17] R. Lahey, F. Moody, The Thermal-Hydraulics of a Boiling Water Nuclear Reactor, American Nuclear Society, 1977. [18] J.Le Corre, Experimental investigation and modeling of void drift in modern BWR fuel designs, in: Proceedings of the 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), 2017. [19] M. Zimmermann, Development and Application of a Model for the Cross-Flow Induced by Mixing Vane Spacers in Fuel Assemblies, Karlsruhe Institute of Technology, 2015. [20] A. Faya, L. Wolf, N.E. Todreas, Canal User’s Manual, MIT Energy Laboratory, 1979. [21] S.G. Beus, A two-phase turbulent mixing model for flow in rod bundles, WAPD-TM-2438, Bettis Atomic Power Laboratory, 1971. [22] K. Brynjell-Rahkola, J. Le Corre, C. Adamsson, Validation of VIPRE-W sub-channel void predictions using NUPEC/BFBT measurements, in: Proceedings of the 13th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-13), 2009. [23] D.G. Reddy, S. Sreepada, A. Nahavandi, Two-phase friction multiplier correlation for high-pressure steamwater flow, EPRI Report NP-2522, Electric Power Research Institute, 1982. [24] G. Wallis, One-Dimensional Two-Phase Flow, McGraw-Hill, 1969.

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[25] J. Le Corre, K. Brynjell-Rahkola, C. Adamsson, Steady-state Void, Pressure Drop and Critical Power BFBT Benchmark Analysis and Results with VIPRE-W/MEFISTO, Westinghouse Electric Sweden AB, 2009. [26] A.J. Wysocki, R.K. Salko, Validation of CTF droplet entrainment and annular/mist closure models using Risø steam/water experiments, CASL-U-2016-1080-000, 2016. [27] U.S. Nuclear Regulatory Commission, TRACE V5.0 Theory Manual, 2012, pp. 175 184. [28] R.K. Salko, M.-O.G. Delchini, X. Zhao, D.D. Pointer, W. Gurecky, Summary of CTF accuracy and fidelity improvements in FY17, CASL-X-2017-1428-000, 2017. [29] W.H. Henstock, T.J. Hanratty, The interfacial drag and the height of the wall layer in annular flows, AIChE J. 22 (6) (1976) 990 1000. [30] J. Lane, The Development of a Comprehensive Annular Flow Modeling Package for Two-Phase Three-Field Transient Safety Analysis Codes (Ph.D. thesis), Pennsylvania State University, 2009. [31] OECD Nuclear Energy Agency, International benchmark on pressurized water reactor sub-channel and bundle tests. Volume II: Benchmark Results of Phase I—Void Distribution, NEA/NSC/R(2015)4, 2016. [32] W.T. Hancox, W.B. Nicoll, A general technique for the prediction of void distributions in non-steady twophase forced convection, Int. J. Heat Mass Transfer 14 (9) (1971) 1377 1394. [33] J.R.S. Thom, W.M. Walker, T.A. Fallon, G.F.S. Rising, Boiling in subcooled water during flow up heated tubes or annuli pumps, in: Symposium on Boiling Heat Transfer in Steam Generating Units and Heat Exchangers, 1965. [34] J.C. Chen, A correlation for boiling heat transfer to saturated fluids in convective flow, BNL-6672, Brookhaven National Laboratory, 1962. [35] A. Faya, L. Wolf, N.E. Todreas, Development of a method for BWR subchannel analysis, MIT-EL 79-027, MIT Energy Laboratory, 1979.

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C H A P T E R

11 System-level code TRACE Anil Gurgen Department of Nuclear Engineering, North Carolina State University, Raleigh, NC, United States

11.1 Features of TRACE The Transient Reactor Analysis Code/Reactor Excursion and Leak Analysis Program (TRAC/RELAP) Advanced Computational Engine (TRACE) is a modernized thermalhydraulic (TH) code that combines and extends the capabilities of NRC’s four safety system codes (TRAC-P, TRAC-B, RELAP5, and RAMONA) into one computational tool. The TRAC was developed at Los Alamos National Laboratory to simulate postulated accidents and transients in pressurized water reactors (PWRs). With the same modeling approach, boiling water reactor (BWR) version of the code was developed later at Idaho National Laboratory. The RELAP is a tool for analyzing loss of coolant accident (LOCA) in PWRs and BWRs and was developed at Idaho National Laboratory. TRACE code combines both PWR and BWR predictive capabilities of these codes and able to analyze LOCAs and system transients. TRACE is a best estimate TH code, and it is the NRC’s flagship TH modeling and safety analysis tool by replacing RELAP and TRAC. TRACE has been designed to perform the best estimate analyses of LOCAs, operational transients, and other accident scenarios in LWRs. The first validated version of TRACE5.0 was released in 2007 [1
3]. For the rest of the chapter, TRACE5.0 will be mentioned as TRACE. TRACE takes a component-based approach to model a reactor system in which each component represents a piece of physical equipment in the flow loop (Fig. 11-1). The components are a combination of numerical cells at which fluid, conduction, and kinetic equations are averaged and solved. Reactor hydraulic and thermal components of TRACE include: • PIPEs: The PIPE component models the coolant flow in a 1D tube, channel, duct, or pipe. The PIPE components can be connected to other PIPEs or BREAK/FILL components to complete the flow of the fluid in a reactor system. • PLENUMs: The PLENUM component models the TH of a volume that connected to an arbitrary number of 1D hydraulic components.

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11. System-level code TRACE

FIGURE 11.1 An example PWR plant model in TRACE with associated PIPEs, FILLs, BREAKs, PUMPs, VALVEs, and PRIZER [5]. TRACE, Transient Reactor Analysis Code/Reactor Excursion and Leak Analysis Program (TRAC/RELAP) Advanced Computational Engine.

• PRIZERs: The PRIZER component models the PWR pressurizer, which maintains the coolant pressure of the primary coolant system. • PUMPs: The PUMP component models the interaction of the system fluid with the reactor pumps. The framework of pump models is based on homologous curves that are supplied through pump parameters and fluid conditions. • HEATRs: The HEATR component models the feedwater heaters or steam condensers, which may play important roles in the modeling of balance of plant. • VALVEs: The VALVE component models various types of valves associated with LWRs. TRACE allows modeling 13 different types of valves. • VESSEL: The VESSEL component models an LWR vessel and its associated internals with a 3D geometry. • FILLs: The FILL component models an imposed coolant flow at any 1D hydraulic component junction. • BREAKs: The BREAK component models an imposed pressure boundary condition to 1D hydraulic components. The boundary is applied to one cell away from its adjacent component. • HTSTRs: The HTSTR component models the heat transfer of fuel elements and structural elements. The heat transfer mechanisms of HTSTRs are conduction, convection, and gap-gas radiation.

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• POWER: The POWER component models the heat generation of thermal elements and supplies power to HTSTRs. The power is determined either from a user-specified table of powers, initial power, point kinetics calculation, or 3D transient neutronics calculation. TRACE adopts the one-dimensional two-fluid six-equation model in which the mass, momentum, and energy balance equations for liquid and vapor phases are established separately. The area average allows the representation of space in one-dimension, and the six equations are represented in differential form with time and one dimension as independent variables. The partial differential equations that describe the two-phase flow and heat transfer are solved with a finite volume approach with a semiimplicit time-differencing scheme. The two-fluid model has two interfaces, the interface between two phases and the interface between the fluid and wall. There are heat, mass, and momentum transfers between the two phases, and there are heat and momentum transfers between the fluid and wall. The basic modeling approach of TRACE for transient two-phase flow is using flow regime
dependent correlations of the interfacial heat, momentum, and energy transfer processes. Such nonhomogeneous, nonequilibrium modeling allows simulating important flow phenomena such as counter-current flow and critical flow explicitly. Solution strategy of TRACE is solving partial differential equations that model twophase flow with independent time and space and system-dependent physical properties. Initial and boundary conditions specify the problem domain, and the solution is integrated forward in time over the spatial domain of the problem. TRACE’s computing time is highly problem-dependent and affected by the total number of mesh cells, time step size, and gradients of evaluated neutronic and TH phenomena. TRACE can use the stability-enhancing two-step numerics in hydraulic components, which allows the benefit of large time steps in transients by allowing material Courant limit to be exceeded [4].

11.2 Constitutive equations of TRACE 11.2.1 Conservation equations Two-fluid equations of TRACE consist of separate mass, momentum, and energyconservation equations for liquid and gas phases. The following time and volume-averaged equations define the one-dimensional two-fluid model of TRACE where l is liquid phase and g is gas phase. • Mass equation for liquid and gas phases ~l  @½ð1 2 αÞρl  @½ð1 2 αÞρl V 1 52Γ @t @x @ðαρg Þ @t

1

@ðαρg V~g Þ @x

5Γ

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• Momentum equation for liquid and gas phases ~l  @ðð1 2 αÞρ V ~~ @½ð1 2 αÞρl V l l Vl Þ ~i 1 5 2 ð1 2 αÞrP 1 ~ fi 1 f~ g 2 ΓV wl 1 ð1 2 αÞρl~ @t @x @½αρg V~g  @t

1

@ðαρg V~g V~g Þ @x

~i g 1 ΓV 5 2 αrP 2 ~ fi 1 f~ wg 1 αρg~

• Energy equation for liquid and gas phases h i
 2 ~ 2 @ ð1 2 αÞρ ðe 1 P=ρ 1 V =2Þ V l l l l l @ ð1 2 αÞρl ðel 1 Vl =2Þ 1 @t @x   ~l 2 Γh0 l 1 ~ ~l g V fi 1 f~ 5 qil 1 qwl 1 qdl 1 ð1 2 αÞρl~ V wl h i h i @ αρg ðeg 1 Vg 2 =2Þ @ αρg ðeg 1 P=ρg 1 Vg 2 =2ÞV~g 1 @t @x   0 g V~g 1 Γh v 1 2~ fi 1 f~ 5 qig 1 qwg 1 qdl 1 α~ V~g wg









For some transient scenarios the gas phase may contain vapor and noncondensable gases. For example, air from the containment or nitrogen gas from the accumulator tanks can leak into the primary coolant. In these scenarios the vapor and noncondensable gas are treated as a gas mixture, and all components of the gas mixture are assumed to be moving at the same velocity and same temperature. As a result, single momentum and single energy equation are used for the gas mixture, but separate mass equations are used for each component of the gas mixture. Similarly, it is possible to follow the concentration of boric acid by additional mass conservation equation to the liquid. In this condition the concentration of boric acid is assumed to be too small that the mass of liquid is not changed in momentum and energy equations. TRACE considers three distinct classes of two-phase flow regimes: (1) the pre-CHF flow regime that consists of bubble/slug and annular/mist regimes, (2) the horizontal stratified flow regime for horizontal or inclined components, and (3) the post-CHF flow regime that encompasses inverted flow regimes that occur when wall temperature is too large for liquid
wall contact. The TRACE pre-CHF flow regime map is based on mass flux and void fraction and consists of dispersed bubble, cap/slug bubble, interpolation region, and annular mist regions. Post-CHF flow regime map of TRACE is based on superficial gas velocity and void fraction and consists of inverted annular, interpolation region, dispersed flow, inverted slug, and transition between dispersed flow and inverted slug. TRACE uses lookup tables for the CHF prediction. This method is accurate, but it requires a lot of experimental data, and it does not allow extrapolations out of the domain covered by data. TRACE has mechanistic models for each flow regime and closure relations. The details of these models can be viewed in TRACE manuals.

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11.2.2 Closure equations The source terms of conservation equations require eight closure relations. They are: • • • • • • • •

interfacial mass-transfer rate (Γ) interface to gas heat transfer (qig ) interface to liquid heat transfer (qil ) wall-to-gas heat transfer (qwg ) wall-to-liquid heat transfer (qwl ) shear at the phase interface (fi ) wall shear force to gas (fwg ) wall shear force to liquid (fwl )

TRACE adopts fully empirical approach in closure relations. In fully empirical approach, experiments are carried out to represent the real world in the interested range of parameters. An equation-based model then uses parameters to represent the physics of the problem and fits the experimental data using statistical analysis. 11.2.2.1 Interfacial mass-transfer rate The interfacial mass-transfer rate can be defined as the sum of mass transfer rates from interfacial heat transfer and subcooled boiling. The interfacial mass transfer due to interfacial heat transfer is calculated with a simple thermal-energy balance at jump condition. Γi 5

qig 1 qil ðh0 v 2 h0l Þ

Interfacial mass-transfer rate due to subcooled boiling is calculated considering forced convection and pool boiling conditions. It is given by 00 0

Γsub 5

fsub ðq}NB 2 q}FC ÞAw hv;sat 2 hl

11.2.2.2 Interface to gas heat transfer The interfacial heat transfer to gas per unit volume is calculated by qig 5

Pv hig αi ðTsv 2 Tv Þ P

hig is the gas heat transfer coefficient at the liquid/gas interface and αi is the interfacial area per unit volume. In TRACE, hig and αi values are calculated separately for each flow regime. For preCHF bubbly flow regime, αi has the values between 0:3 and 0:5 and interpolated based on the value of mass flux. For bubbly flow regime, hig is constant and has a value of 1000 W=m2 K. In cap/slug bubble regime, αi is calculated using hydraulic diameter of the channel and the interfacial area per unit volume value of bubbly flow regime. hig is again constant and has a value of 1000 W=m2 K in cap/slug bubble regime. In annular mist regime, αi is calculated considering the void fraction and hydraulic diameter. hig is calculated using Dittus
Boelter correlation in this regime.

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In stratified flow regime, αi is calculated by dividing the width of stratified two-phase interface to the flow area. hig calculation in stratified flow regime is not documented. In post-CHF inverted annular regime, αi is calculated using the void fraction and hydraulic diameter of the channel. hig is calculated assuming laminar convection in a thin film. In inverted slug film regime, αi is calculated considering the diameter of ligament and void fraction. hig calculation in this regime is not documented. Finally, in dispersed flow regime, αi is calculated using Sauter mean diameter and void fraction. hig is calculated with the assumption that liquid side heat transfer resistance is much smaller than the gas side. 11.2.2.3 Interface to liquid heat transfer The interfacial heat transfer to liquid per unit volume is calculated by qil 5 hil αi ðTsv 2 Tl Þ where hil is the liquid side heat transfer coefficient at the liquid/gas interface. It must be noted here that for both liquid and gas side, αi calculations are the same; therefore αi models are not documented here. In pre-CHF bubbly flow regime, hil between liquid and bubble interface is modeled using the Ranz
Marshall correlation [6]. The same correlation is also used for cap/slug bubble regime. For the annular mist regime, there are two regions, the film region and droplet region. The heat transfer coefficient in film side is power-law weighted combination of laminar and turbulent heat transfer coefficients. For laminar regime the condensation correlation of Kuhn et al. [7] is used. For the turbulent regime, single-phase forced convection heat transfer correlation of Gnielinski [8] is used. For the droplets in the mist, Kronig and Brink [9] model is used. In stratified flow regime, hil is based on the data from a series of condensation experiments conducted at Northwestern University [10,11]. In post-CHF inverted annular regime, hil is calculated with the assumption of liquid interface Nusselt number equals to 100. This value is determined considering FLECHTSEASET high flooding rate tests. In inverted slug film regime a model that modifies the dispersed droplet model considering the increase in heat transfer coefficient due to large droplets is used. In this model an increase as a factor of 4 is assumed. Finally, in the dispersed flow regime, hil calculation is not documented since the most crucial interfacial heat transfer process is at the gas side since it limits the steam superheat, thereby directly affecting the peak clad temperature. During condensation the heat transfer is usually between the interface and the subcooled liquid. hil is calculated using Sklover and Rodivilin correlation [12] considering the effects of noncondensable gases. 11.2.2.4 Wall-to-gas heat transfer The wall heat transfer to gas is calculated with the extended Newton’s law of cooling to thermal nonequilibrium qwg 5 hwg αw ðTw 2 Tg Þ hwg is the wall-to-gas heat transfer coefficient and αw is the heated surface area per volume of fluid. Wall heat transfer models are grouped into five regimes in TRACE code. Pre-CHF

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heat transfer models for wall
liquid convection, nucleate boiling, and subcooled boiling. Critical heat flux model calculates the maximum heat flux in the nucleate heat transfer regime. Minimum film boiling (MFB) temperature models the region where wall
liquid contact does not occur. Post-CHF models the transition and film boiling heat transfer. And finally, condensation heat transfer models for film condensation. In TRACE, it is assumed that only one phase is in contact with the wall. hwg is nonzero only when only gas phase is in contact with wall. Similarly, in pre-CHF regime, wall-togas heat transfer is zero, and wall-to-gas heat transfer is enabled after CHF point. CHF model of TRACE is 1995 AECL-IPPE CHF look-up table [13], which provides a continuous estimate of CHF over a wide range of conditions. An iterative solution to TCHF using the balance q00NB ðTCHF Þ 5 q00CHF calculates the CHF temperature point. Another important point in the boiling curve is the MFB temperature. This point shows that the wall superheat is high enough to prevent any liquid
wall interaction. In TRACE, this point also shows the quench temperature while cooling the wall at which liquid
wall interaction begins and increases the heat transfer. MFB temperature is denoted with Tmin , and TRACE uses Groeneveld
Steward correlation [14] to calculate it. When wall temperature exceeds TCHF , post-CHF heat transfer models are activated. The post-CHF heat transfer regimes in TRACE are transition boiling and film boiling. If the wall temperature is below Tmin , the heat transfer regime is transition boiling and if wall temperature is above Tmin , the heat transfer regime is film boiling. The transition boiling regime provides an intermediate regime between the nucleate boiling regime where there is liquid
wall interaction and film boiling regime where there is no liquid
wall interaction. In transition boiling regime, an interpolation approach is adapted. Similar to CHF point that has q00CHf and TCHF , heat flux at Tmin is calculated using the balance q00FB ðTmin Þ 5 q00min . The interpolation approach is based on finding the transition boiling heat flux based on the wall temperature interpolating between heat fluxes and temperatures of CHF and MFB points. Interpolation weighting factor, wf TB , represents the fractions of q00CHF and q00min in q00TB . hwg in transition boiling regime is then equal to the weighted  wall-to-gas heat transfer coefficient in film boiling regime and can be denoted as 1 2 wf TB hwg;FB . The film boiling regime consists of three different regimes. They are inverted annular, dispersed flow and inverted slug film boiling regimes. Inverted annular film boiling is the regime where liquid phase is significantly subcooled and a thin vapor film separates the hot wall and the subcooled liquid. In TRACE, inverted annular film boiling regime persists for void fractions up to 60% and wall-to-gas heat transfer coefficient is calculated using the laminar theory. In this regime, hwg equals to the ratio of vapor thermal conductivity and the vapor film thickness. When the void fraction is greater than 90%, the flow regime is dispersed flow film boiling. In this regime, two primary components of wall heat transfer are forced convection to superheated vapor and thermal radiation to liquid droplets. The convective heat transfer to superheated vapor is the same as the single-phase liquid convection heat transfer with enhancements due to the presence of the dispersed droplets. The last film boiling regime considered in TRACE is inverted slug film boiling regime. In TRACE, inverted slug film boiling regime is considered a transitional regime between inverted annular film boiling and dispersed flow film boiling. Interpolation is applied using a weighting function, wf . Then the hwg in inverted slug film boiling regime is interpolated as hwg 5 wf hwg;IAFB 1 ð1 2 wf Þhwg;DFFB .

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11.2.2.5 Wall-to-liquid heat transfer The wall heat transfer to liquid is calculated with the extended Newton’s law of cooling to thermal nonequilibrium. qwl 5 hwl αw ðTw 2 Tl Þ hwl is the wall-to-liquid heat transfer coefficient. Since only one phase is assumed to be in contact with the wall in TRACE, pre-CHF regime is dominated by the liquid phase. The wall heat transfer coefficient for single-phase liquid equals to the maximum value of heat transfer coefficients of laminar convection, turbulent convection, and natural convection. For laminar convection a constant Nusselt number of 4.36 is used to calculate the heat transfer coefficient. For turbulent convection, Gnielinski [15] correlation is used. For natural convection the correlations for both laminar and turbulent regimes [16] are used, and a maximum of the two values is used to ensure continuity. These correlations are for tube geometry, and for the core region of the vessel, TRACE uses Weisman correlation [17], which is developed for rod bundle. The other flow regimes for pre-CHF region are two-phase forced convection, subcooled nucleate boiling and nucleate boiling. Two-phase forced convection is the regime when the fluid is two-phase and the wall temperature is below the onset of nucleate boiling temperature. In this regime, TRACE applies a multiplier to the single-phase heat transfer correlations to account for two-phase effects. The enhancement factor is calculated based on the study of Rezkallah and Sims [18], which corrects the liquid Reynolds number so that it is based on the actual liquid velocity rather than the superficial liquid velocity. As the wall temperature increases, it gets close to the onset of nucleate boiling temperature. Onset of nucleate boiling temperature is calculated in TRACE using model of Basu et al. [19]. When the wall temperature exceeds the onset of nucleate boiling temperature, the heat transfer regime can be either nucleate boiling or subcooled nucleate boiling. When the bulk liquid temperature is above saturation temperature, the heat transfer regime is nucleate boiling and TRACE uses Chen correlation [20] is a combination of forced convection and pool boiling heat transfers. When the wall temperature exceeds the onset of nucleate boiling temperature, but the bulk liquid temperature is subcooled, the heat transfer regime is subcooled nucleate boiling. In subcooled nucleate boiling regime, TRACE uses nucleate boiling heat transfer coefficient correlations, and the difference in mass transfer rate per unit volume is added due to subcooled boiling, and there is a vapor-generation rate. In transition boiling regime, hwl has two components. The first component is nucleate boiling part of the transition boiling, and it is assumed that this heat flux is entirely transmitted to the liquid phase and denoted with hwl;TB . The second component is the film boiling part of the transition boiling, and the heat flux of this component is shared between liquid and gas phase. The combination of these components of hwl is denoted as hwl;TB 1 ð1 2 wf TB Þhwl;FB . In film boiling regime, when the void fraction is below 0.6, the heat transfer regime is inverted annular film boiling regime. In this regime, wall-to-liquid heat transfer is a combination of interfacial heat transfer from vapor film and radiation heat transfer from the wall. Interfacial heat transfer from vapor film is calculated by adding an enhancement factor,

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which is a function of vapor film thickness and proposed by Cachard [21]. In dispersed flow film boiling regime the heat transfer mechanism from wall to water droplets is due to thermal radiation. In inverted slug film boiling regime the same interpolation process is applied to hwl as, hwl 5 wf hwl;IAFB 1 ð1 2 wf Þhwl;DFFB . During condensation, heat transfer occurs in a two-step process, whereby heat is removed from the two-phase interface by interfacial heat transfer and from subcooled liquid to the wall. Interfacial heat transfer was discussed in previous sections, and for the liquid-to-wall heat transfer, TRACE calculates wall
liquid Nusselt number using a powerlaw weighting of values for laminar and turbulent film flow. For laminar flow the empirical correlation of Kuhn et al. [22], and for turbulent film flow, Gnielinski [23] correlation was implemented in TRACE. 11.2.2.6 Shear at the phase interface The shear at the phase interface is calculated by   ~l ÞV~g 2 V ~l  fi 5 Ci ðV~g 2 V Ci is the interfacial drag coefficient. Along with the phasic wall drag coefficients, all the drag models are dependent on flow regime. It is possible to classify flow regimes for interfacial drag as pre-CHF regime, which consists of bubbly/slug and annular/mist regimes, stratified regime, and post-CHF regime which encompasses the inverted flow regimes. Pre-CHF flow regime consists of dispersed bubble, slug flow, Taylor cap bubble, and annular/mist regimes. In bubbly/slug flow regime, TRACE uses a drift flux
based model with different correlations for pipes and rod bundles. Such a drift flux based model uses the traditional drift velocity approach with modifications considering slip factor. For pipes, bubbly/slug flow regime is divided into two flow regimes, dispersed bubbly flow and slug/Taylor cap bubbly flow. For the dispersed bubbly flow, correlation of Ishii [24] and for cap/slug regime, correlation of Kataoka and Ishii [25] were implemented. For rod bundles, Bestion [26] drift flux model was implemented in TRACE code for the whole bubbly/slug flow regime. Annular/mist flow regime of the pre-CHF regime is treated as a superposition of interfacial drag on a liquid film and entrained droplets. Interfacial drag model for films and droplets are implemented, and in addition to that, an entrainment model is also needed to determine the fraction of liquid flowing as droplets. A weighting scheme then used to combine the individual contributions. For liquid film, Asali
Hanratty correlation [27] is used. For entrainment models, TRACE code uses Ishii
Mishima [28] correlation for geometries with small hydraulic diameters and Steen
Wallis entrainment correlation [29] for large diameter pipes. For droplets the drag coefficient is calculated with the correlation of Ishii and Chawla [30]. Finally, the drag forces at the gas-droplet and gas-film interfaces are superposed considering the relative velocities between the phases. In stratified flow regime, there are five different assumed flow regimes in TRACE code. In stratified smooth regime the two phases flow separately with a relatively smooth interface. In stratified wavy regime the interface is disturbed due to increased gas velocity and waves travel in the direction of flow. In plug/slug flow regime a further increased gas velocity causes waves at the interface to form a slug that is propagated with the high

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velocity. In annular regime, higher gas velocity results in the formation of a gas core with a liquid film around the periphery of the pipe. And finally, in dispersed bubble regime, gas bubbles tend to travel in the upper half of the pipe due to low liquid velocity. It must be noted here that in some of these flow regimes, TRACE uses the vertical flow model for the flow with the same physics. For example, dispersed bubble and annular flow regimes of stratified flow are calculated using the bubbly/slug and annular/mist correlations that were implemented for vertical flow. Differences that may occur due to horizontal flow in these regimes are neglected. Stratified smooth regime is explicitly considered in interfacial friction for stratified flow; on the other hand, stratified wavy and plug/slug flow regimes are treated as transition regimes to nonstratified flow. For stratified flow, TRACE code calculates the Ci using the interfacial friction factor that is calculated by applying a correction factor to single-phase wall drag friction factor for the gas phase. For the transition regime to nonstratified flow, TRACE code applies a weighting factor to weight the contributions to interfacial drag from the stratified and nonstratified flow regimes. Post-CHF regime consists of inverted annular, inverted slug, and dispersed flow. For inverted annular regime, Ci is calculated using interfacial friction factor and two interfacial friction factors are calculated in this regime. TRACE calculates the smooth flow friction factor, and wavy flow friction factor then calculates the interfacial friction factor using a power-law weighting of two calculated friction factors. In inverted slug regime, Ci is calculated using the drag coefficient corrected for multiparticle effects, and Richardson and Zaki correlation [31] is used for the drag coefficient with multiple particles. For the dispersed flow a similar approach using drag coefficient with multiple particles was adopted. The differences between inverted slug and dispersed flow regimes are the models for droplet diameters, droplet drag coefficients, multiple particle effects, and entrained fraction. 11.2.2.7 Wall shear force to gas The wall shear force to gas is calculated by     fwg 5 2 Cwg V~g V~g  where Cwg is the gas wall drag coefficient. TRACE assumes that only one of the phasic wall drag coefficients has a nonzero value. In bubbly/slug and annular/mist flow regimes, Cwg is zero and all the wall drag is applied to the liquid phase. In TRACE, wall drag models are applied in four specific flow regimes. They can be listed as single-phase regime, pre-CHF regimes, horizontal stratified flow, and post-CHF regimes. In single-phase gas flow the gas wall drag coefficient is calculated based on friction factor of the flow and for friction factor, Churchill formula [32] is used. As mentioned previously, the gas wall drag coefficient is zero in pre-CHF regime. In horizontal stratified flow regime the friction factor is calculated by f 5 0:046=Re0:2 for turbulent flow and f 5 16=Re for laminar flow. Gas Reynolds number is calculated considering the hydraulic diameter of the gas flow. In post-CHF regime, wall drag coefficient is calculated for inverted annular and dispersed flow regimes. In inverted annular regime, TRACE treats this regime as a direct inverse analog to the annular flow regime. Two-phase multiplier is calculated with

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1=ð12αÞ2 and the friction factor is calculated with Churchill formula. In dispersed flow regime, an empirical model is developed by Pfeffer et al. [33]. In post-CHF regime, inverted annular regime is applied for void fractions less than 60%, and dispersed flow regime is applied for void fractions higher than 90%. For intermediate values a linear interpolation scheme based on weighting factor is used. 11.2.2.8 Wall shear force to liquid The wall shear force to liquid is calculated by

  ~l V ~l  fwl 5 2 Cwl V

Cwl is the liquid wall drag coefficient. In single-phase liquid flow the same approach to single-phase gas flow is used, which calculates the friction factor using Churchill formula. In pre-CHF regime a two-phase multiplier and a two-phase friction factor are used for both bubbly/slug and annular/mist flow regimes. In bubbly/slug flow regime, TRACE uses a void fraction based two-phase multiplier model. The model first calculates the twophase multiplier using 1=ð12αÞ1:75 for upflow and 1=ð12αÞ1:8 for downflow. Then a nucleate boiling correction factor is applied based on Ferrell and Bylund [34] data. In annular/ mist flow regime, two-phase multiplier equals to 1=ð12αÞ2 and the friction factor is a power-law combination of laminar and turbulent values. Laminar part equals to 16=Re and turbulent part is calculated using Haaland’s approximation [35] to the Colebrook equation. In horizontal stratified flow regime, TRACE uses the same approach for both liquid flow and gas flow. In post-CHF regime, wall
fluid shear only effective for gas phase and Cwl is zero.

11.2.3 Heat conduction equations In addition to the closure models in hydrodynamics, heat-conduction equations are used to calculate heat distribution in reactor structure materials. TRACE uses the general heat conduction equation with Fourier’s law of conduction. The conduction equations have the following form: ρcp

@T 5 r ðkrTÞ 1 q000 @t



The conduction equation is converted into finite-difference equations by applying the integral method, and TRACE has finite-difference equations for cylindrical and slab geometries. The material properties, density, ρ, specific heat, cp , and thermal conductivity, k, are defined for Zircaloy as cladding, mixed-oxide as fuel, and stain steel as structural materials. For the fuel rod gap gas, TRACE has option to use helium, argon, xenon, hydrogen, and nitrogen. The thermal conductivity of the gap gas mixture is calculated using MATPRO correlations [36]. Thermal conductivity of the gas mixture is also calculated when there is a contact between fuel and cladding, and TRACE code can calculate this condition. The fuel-cladding gap conductance is a function of gap-gas conductance, fuel-cladding contact resistance, and fuel-cladding thermal radiation.

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One critical phenomenon of fuel rod is cladding oxidation. Zirconium undergoes an exothermic chemical reaction with water and forms zirconium oxide as a result. Zirconium oxide properties are different from zirconium-based allows; therefore solution to conduction equation changes with the formation of zirconium oxide and generation of heat. The reaction rate is slow at normal operating conditions, but in accident conditions, the reaction rate is rapid with high-temperature steam. The rate of reaction is given by the Arrhenius equation, and TRACE calculates the zirconium oxide thickness for each time step and adds the chemical energy as a heat source to conduction equation. q000 is the heat generation rate per unit time and it has two components in TRACE. The first one is fission power and TRACE code allows to specify fission power as a constant or a table or calculated from a point kinetics model or from a simulation of 3D transient neutronics. 3D transient neutronics simulation is possible when TRACE is coupled with Purdue Advanced Reactor Core Simulator (PARCS) code [37]. The second component of the q000 is the decay heat power and TRACE uses 1979 [38] and 1994 [39] ANS decay heat standards. The heat generated in fuel rods needs to be transferred into the coolant fluid. In order to couple THs and reactor structure, Newton’s law of cooling is used. Newton’s law of cooling calculates the energy exchange between structure material and coolant fluid. Wall to fluid heat transfer mechanisms were discussed in previous sections. The coupling algorithm of TRACE code is implicit in terms of wall temperature, liquid and vapor phase temperatures, and explicit in terms of the heat transfer coefficient. Wall heat transfer coefficient for the current time step is calculated using the wall temperature and liquid and vapor phase temperatures at the previous time step. The current wall temperature and liquid and vapor phase temperatures are then calculated using the conduction and energy balance equations to complete the continuous energy calculation.

11.2.4 Other models In addition to field equations, TRACE code has some special models to improve predictive capability. These models can be listed as critical flow models, countercurrent flow models, form loss models, pump models, pressurizer models, and steam separator models. 11.2.4.1 Critical flow Critical flow is an important phenomenon that can affect the flow rate of fluid when the velocity of fluid flow exceeds the velocity of sound. In this case, acoustic signals can no longer propagate upstream, and mass flow rate becomes independent of the downstream conditions. A further reduction in the downstream pressure will not change the mass flow rate. In operation of nuclear power plant, there are cases where the presence of critical flow can play an important role. One big example is the conditions of LOCA, where highpressure coolant and low-pressure containment can create a critical flow condition. TRACE uses critical flow models at cell edges and compares them with the momentum solutions to predict critical flow presence. If critical flow is present in the cell edge, the velocities and pressure derivatives are adjusted with the models. TRACE has three

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separate regimes for critical flow. They are subcooled-liquid critical flow, two-phase critical flow, and single-phase critical flow regimes. In subcooled-liquid regime, TRACE uses a modified version Burnell model [40], which considers the Bernoulli equation. In two-phase regime, TRACE uses a model which is an extension of a model developed by Ransom and Trapp [41]. This model is described by overall continuity equation, two-phase momentum equations, mixture energy equation, and inert-gas continuity equation. In single-phase vapor regime, critical flow model is based on isentropic expansion of an ideal gas. A calculational sequence assures the continuity of the critical flow model in TRACE. 11.2.4.2 Countercurrent flow Countercurrent flow can be defined as the two-phase flow regime in which the working fluids flow in opposite directions. One of the important interactions between these fluids is drag at which drag force acts opposite to the relative motion of the one fluid with respect to the other fluid. Then the countercurrent flow limitation (CCFL) can be defined as the scenario at which one of the fluids exerts large drag to other fluid and causes distortion in other fluid’s flow. If the exerted drag is large enough, CCFL can cause blockage in the flow of other fluid. In nuclear power plants, CCFL can occur in hot leg entrance of the steam-generator inlet plenum in reflux-condensation and in reactor vessel during blowdown as ECCS liquid is attempting to fill the downcomer. Also during reflood, CCFL can occur at a tie plate, where the upflow of steam distorts the fallback of liquid. TRACE uses a relation between gas flux, liquid delivery, abscissa intercept, and slope for CCFL model and requires user to supply correlation constants, which can be developed from experimental data. 11.2.4.3 Form loss In steady-state single-phase pipe flow, wall drag and gravity head are two critical factors in pressure gradient calculation. TRACE also has models for pressure gradient that can be activated based on the flow area or components. Pressure losses at flow area changes, pipe bends, flow through orifice, tee, or manifold are calculated based on a form loss factor, K, which is calculated separately for each loss mechanism. The pressure loss has the following form ΔPBρK

V2 2

11.2.4.4 Pump models Pump model of TRACE defines the interaction of system fluid with a centrifugal pump. Pressure gradient across the pump is calculated as a function of fluid flow rate and fluid properties using pump
curve correlations. The pump component in TRACE is identical to pipe component with a single difference at which a motion equation is applied for the cell interface. Pump head modeling in TRACE is based on the standard homologous curves approach. Several sets of built-in curves allow user TRACE to calculate pump head as a function of volumetric flow and pump speed.

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11.2.4.5 Pressurizer model Pressurizer component of TRACE can model the effect of pressurizer heaters and sprays by manipulating the energy deposited into or extracted from the liquid in pressurizer component. Based on how much the top-most pressure deviates from a user-defined set point, energy is added to or removed from pressurizer to return the pressure to the desired set point. Energy is added or removed linearly between zero and a user-defined maximum power of heaters and sprays. 11.2.4.6 Steam separators model Steam separators are essential components in nuclear plant to ensure that the steam entering the turbine is dry. Steam separators are modeled with a tee-shaped pipe using suitable functions for separators. Basically, two-phase liquid
gas mixture enters to separator and exits as liquid and gas at separate exits. If the separation is not perfect, small amount of liquid can be found at exit bulk gas flow. Separator model of TRACE consist of a control cell that is connected to flow junctions and uses a special solution of the field equations considering the prescribed separator performance. Separator model of TRACE consists of an analytical model that solves the field equations based on void fraction and flow quality relation, and a mechanistic model to simulate physical processes occurring inside the separator.

11.3 Validation of TRACE TRACE is designed to provide realistic predictions of plant behaviors for a variety of hypothetical accidents and transients [42]. In order to achieve this goal, TRACE is assessed against suitable experimental data. TRACE should be able to perform adequately for many physical processes, and these physical processes are identified in Phenomena Identification and Ranking Tables (PIRT). Considering the modeling requirements of LWRs and PIRT, TRACE assessment is performed for fundamental tests, separate effects tests, and integral effects tests. Fundamental tests are basic tests that are used to assess the capability of TRACE on TH interactions at the fundamental level. These tests provide information on specific models and correlations. For example, solution of heat conduction, predicting motion of water level, predicting motion of interface between liquid and gas, predicting adiabatic two-phase upflow, predicting horizontal two-phase flow, predicting pressure drop due to wall friction, predicting flooding and counter-current flow, and predicting interfacial shear model for adiabatic steam
water flows are some applied fundamental tests to TRACE. Separate effect tests are tests that are designed to provide detailed information on individual system components under the expected ranges of postulated accidents and transients. TRACE models are assessed against separate effect tests, and it is reported that TRACE performance on critical break flow is reasonable, on ECC bypass is reasonable to excellent, on blowdown heat transfer is reasonable, on reflood heat transfer is reasonable to excellent, on mixture level swell is moderate to excellent, on CCFL and flooding is reasonable to excellent, on condensation is reasonable, and on steam generator hydraulics is overpredicting important physics.

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Integral effects tests are tests that are designed to produce, to the extent possible, overall reactor TH behavior under the expected ranges of postulated accidents and transients. TRACE models are assessed against PWR large break integral facilities, PWR small break integral test facilities, and BWR integral test facilities. It is reported that the overall large break test performance of TRACE is reasonable. However, TRACE is overpredicted cladding temperatures in cylindrical core test facility and gravity reflood in slab core test facility. This error was attributed to lack of spacer grid models in reflood package, poor prediction of entrainment process, and sensitivity to condensation in the loops and downcomer. For overall small break test performance, it is reported that a reasonable agreement was obtained for most cases between TRACE and experimental results. Most differences were reported to be related to break flow. For overall BWR integral test performance a general agreement was reported between TRACE and measurements.

References [1] USNRC, TRACE V5.0 Theory Manual: Field Equations, Solutions Methods, and Physical Models, Washington, DC, 2008. [2] USNRC, TRACE V5.0 User’s Manual Volume 1: Input Specification, Washington, DC, 2008. [3] USNRC, TRACE V5.0 User’s Manual Volume 2: Modeling Guidelines, 2008. [4] USNRC, TRACE V5.0 Assessment Manual: Main Report, 2008. [5] G. Anil, S. Koroush, Estimation of coping time in pressurized water reactors for near term accident tolerant fuel claddings, Nucl. Eng. Des. 337 (2018) 38
50. [6] E. Ranz, W.R. Marshall, Evaporation from droplets: part I and part II, Chem. Eng. Prog. 48 (141
146) (1952) 173
180. [7] S.Z. Kuhn, V.E. Schrock, P.F. Peterson, Final Report on U.C. Berkeley Single Tube Condensation Studies, UCB-NE-4201. U.C. Berkeley, CA, 1994. [8] G. Gnielinski, New Equations Flow Regime Heat and Mass Transfer in Turbulent Pipe and Channel Flow, 1976. [9] R. Kronig, J. Brink, On the theory of extraction from falling droplets, Appl. Sci. Res A2 (1950) 142
154. [10] I.S. Lim et al., Cocurrent Steam/Water Flow in a Horizontal Channel, NUREG/CR2289, 1981. [11] H.J. Kim, Local properties of countercurrent stratified steam-water flow, NUREG/CR-4417, 1985. [12] G.G. Sklover, M.D. Rodivilin, Condensation on water jets with a cross flow of steam, Teploenergetika 23 (1976) 48
51. [13] D.C. Groeneveld, et al., The 1995 look-up table for critical heat flux in tubes, Nucl. Eng. Des. 163 (1996) 1
23. [14] J.C. Steward, D.C. Groeneveld, Low-quality and subcooled film boiling of water at elevated pressures, Nucl. Eng. Des. 67 (1981) 259
272. [15] V. Gnielinski, New equations flow regime heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359
368. [16] J.P. Holman, Heat Transfer, fifth ed., McGraw-Hill Book Co., Inc., New York, 1981. [17] J. Weisman, Heat transfer to water flowing parallel to tube bundles, Nucl. Sci. Eng. 6 (1959) 78
79. [18] K.S. Rezkallah, G.E. Sims, An examination of correlations of mean heat transfer coefficients in two-phase two-component flow in vertical tubes, in: AIChE Symposium Series, 83 (257), 10 1 -114, 1987. [19] N. Basu, G.R. Warrier, V.K. Dhir, Onset of nucleate boiling and active nucleation site density during subcooled flow boiling, J. Heat Transfer 124 (2002) 717
728. [20] J.C. Chen, A correlation for boiling heat transfer to saturated fluids in convective flow, in: Sixth National Heat Transfer Conference, Boston, 1963. [21] F. de Cachard, Development, implementation, and assessment of specific closure laws for inverted-annular film-boiling in a two-fluid model, NURED/IA-0133, 1996. [22] S.Z. Kuhn, V.E. Schrock, P.F. Peterson, Final report on U.C. Berkeley single tube condensation studies, UCB-NE-4201, August 1994.

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[23] V. Gnielinski, New equations flow regime heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359
368. [24] M. Ishii, One dimensional drift-flux model and constitutive equations for relative motion between phases in various flow regimes, ANL-77-47, 1977. [25] I. Kataoka, M. Ishii, Drift flux model for large diameter pipe and new correlation for pool void fraction, Int. J. Heat Mass Transfer 30 (1987) 1927
1933. [26] D. Bestion, Interfacial friction determination for the 1-D six equation two-fluid model used in CATHARE code, European Two-Phase Flow Group Meeting, Marchwood, 1985. [27] C. Asali, T.J. Hanratty, P. Andreussi, Interfacial drag and film height for vertical annular flow, AIChE J. 31 (6) (1985) 895
902. [28] M. Ishii, K. Mishima, Droplet entrainment correlation in annular two-phase flow, Int. J. Heat Mass Transfer 32 (10) (1989) 1835
1845. [29] G.B. Wallis, Phenomena of liquid transfer in two-phase dispersed annular flow, Int. J. Heat Mass Transfer 11 (1968) 783
785. [30] M. Ishii, T.C. Chawla, Local drag laws in dispersed two-phase flow, ANL-79-105, December 1979. [31] J.F. Richardson, W.N. Zaki, Sedimentation and fluidisation, Part I, Trans. Inst. Chem. Eng 32 (1954) 35
53. [32] S.W. Churchill, Friction factor equations spans all fluid flow regimes, Chem. Eng. 84 (1977) 91
92. [33] R. Pfeffer, S. Rossetti, S. Lieblein, Analysis and correlation of heat transfer coefficients and friction factor data for dilute gas-solid suspensions, NASA TN D-3603, September 1966. [34] J.K. Ferrell, D.M. Bylund, Low pressure steam-water flow in a heated vertical channel, Final Report Volume II on a Study of Convection Boiling Inside Channels, North Carolina State University, Dept. of Chemical Eng., 1966. [35] S.E. Haaland, Simple and explicit formulas for the friction factor in turbulent pipe flow, J. Fluids Eng 105 (1983) 89
90. [36] D.L. Hagerman, G.A. Reymann, R.E. Mason, MATPRO Version 11: A Handbook of Material Properties for Use in the Analysis of Light Water Reactor Fuel Rod Behavior, EG&G Idaho, Inc. Report TREE-1280, Rev. 2, (NUREG/CR-0479), August 1981. [37] H.C. Joe, D. Barber, G. Jiang, T.J. Downar, PARCS, A Multi-Dimensional Two-Group Reactor Kinetics Code Based on the Nonlinear Analytic Nodal Method, PU/NE-98-26, September 1998. [38] American National Standard for Decay Heat Power in Light Water Reactors, American Nuclear Society publication ANSI/ANS-5.1, 1979. [39] American National Standard for Decay Heat Power in Light Water Reactors, American Nuclear Society publication ANSI/ANS-5.1, 1994. [40] J.W. Burnell, Flow of boiling water through nozzles, orifices and pipes, Engineering 164 (1947) 572
576. [41] V.H. Ransom, J.A. Trapp, The RELAP5 choked flow model and application to a large scale flow test, ANS/ ACME/NRC International Tropical Meeting on Nuclear Reactor Thermal-Hydraulics, 799
819, 1980. [42] USNRC, TRACE V5.0 Assessment Manual: Main Report, 2008.

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C H A P T E R

12 Nuclear thermal hydraulics with the AC2 system code package Andreas Wielenberg and Christine Bals Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany

By the Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) (Wielenberg, A.; Hollands, T.; Reinke, N.; Scho¨ffel, P.; Spengler, C.; Steinhoff, T.; Weyermann, F.; Sonnenkalb, M., Schaffrath, A.) The AC2 code suite integrates the thermal-hydraulic system codes ATHLET (Analysis of Thermal Hydraulics of LEaks and Transients), ATHLET-CD, and COCOSYS (COntainment COde SYStem) for the analysis of nuclear reactors at normal operation, for anticipated operational occurrences (AOOs), design basis accidents (DBAs), and analyses of design extension conditions (DECs) up to severe accidents (SAs) with radionuclide releases to the containment respectively the environment. AC2 allows the integral simulation of plant behavior considering the interaction between the cooling circuit and the containment with state-of-the-art methods. Its recent release is AC2 2019 [1]. Here, the ATHLET code, version 3.2, for nuclear thermal hydraulics in the reactor cooling circuit up to the start of core degradation is described in Section 12.2. We then discuss the thermal-hydraulic module THY of COCOSYS, version 3.0, in Section 12.3. Importantly, the thermal-hydraulic models in ATHLET and COCOSYS form the basis for ATHLET-CD and COCOSYS extending AC2 for accident scenarios. In Section 12.4 we discuss the common quality assurance (QA) approach for AC2 codes and in Section 12.5 we give a brief outlook and summary. Further description of the AC2 code suite and COCOSYS models for SA scenarios is given in Chapter 15 in the part on severe accident codes in this book.

12.1 The system thermal-hydraulic code ATHLET 12.1.1 Introduction The thermal-hydraulic computer code ATHLET is being developed by the GRS for the analysis of normal operation, AOOs, DBAs, and DECs up to the start of core degradation.

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One important aim of the continuing code development is to cover the whole spectrum of design basis and SAs (without core degradation) for pressurized-water reactors (PWRs), boiling-water reactors (BWRs), small modular reactors (SMRs), and future Gen-IV reactors with one single code. Its current version is ATHLET 3.2 [1,2]. ATHLET is written in FORTRAN. The software structure is highly modular. The code is composed of four basic modules (see Fig. 12.1) for the calculation of the different phenomena relevant to the operation of a nuclear power reactor [1]: • Thermo-fluid-dynamics (TFD) for the conservation equations and most constitutive models, • Heat transfer and heat conduction (HECU) for computing heat conduction and phenomena related to heat transfer, • Neutron Kinetics (NEUKIN) for adopting point kinetics and providing an interface to external 3D NEUKIN codes, and • General Control Simulation Module (GCSM) for the simulation of Instrumentation & Control (I&C), measurements, component and component actions and overall simulation control. Other independent modules (e.g., large models with own time-advancement procedure) can be flexibly coupled without structural changes in ATHLET. In order to extend simulation capabilities of ATHLET by user-provided correlations, plug-in interfaces are prepared. Advanced numerical methods with rigorous error control ensure the high quality of numerical results.

FIGURE 12.1

ATHLET code structure and couplings. ATHLET, Analysis of Thermal Hydraulics of LEaks and

Transients.

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ATHLET has been developed and validated to be applied for all types of DBA and DEC without core degradation. The range of applicability particularly covers light-water reactors (LWRs) such as PWR, BWR, water
water energetic reactor (WWER), and the Russian graphitemoderated, pressure-tube reactor design “reaktor bolshoy moshchnosti kanalny” (RBMK). The available working fluids are light and heavy water, where transition between subcritical and supercritical fluid states is enabled. In addition, helium, sodium, lead, lead
bismuth eutectic, and molten salts can be simulated. These working fluids aim at the investigation of future Gen-IV reactor designs, which are still subject to further code development and validation. The outline of this section is as follows. In 19,752.2 we give a brief overview of the history of ATHLET development. We present the modeling approach and basic governing equations solved in Section 12.2.3. Section 12.2.4 provides an overview of code extension implemented for the simulation of specific, for example, next-generation nuclear reactor designs. The methodology and current state of validation is described in Section 12.2.5. We treat couplings for multiphysics, multiscale analyses in Section 12.2.6, and discuss ATHLET’s scope and limits of application in Section 12.2.7.

12.1.2 History of Analysis of Thermal Hydraulics of LEaks and Transients development ATHLET was created by combining its predecessor codes DRUFAN and ALMOD in 1988 [3]. The development of both predecessor codes at GRS started in the 1970s. DRUFAN was used to calculate mainly loss-of-coolant accident (LOCA) scenarios in the primary system of water-cooled reactors. DRUFAN 01 in 1979 was based on a four-equation model allowing thermal nonequilibrium conditions [4,5]. DRUFAN 02 included a relative velocity model, a mixture-level tracking model for vertical geometries, and allowed for mechanical nonequilibrium conditions [6,7]. ALMOD was used to calculate transients like loss of heat sink or pump failures [8] with a three-equation model and a drift-flux approach. The first ATHLET version, ATHLET MOD1, was completed in 1988. It used the nonequilibrium fluid dynamics and mixture-level tracking from DRUFAN as well as the common integration method FEBE, the control simulation module GCSM, and the heat conduction and heat transfer module HECU [9]. Highlights of the further development of ATHLET are depicted in Fig. 12.2. The initial development progress was quite fast. ATHLET version 1.0E introduced a fiveequation model with separate energy balance equations for gas and liquid phase in 1991 [10]. ATHLET 1.1 from 1993 included a first six-equation model from the FLUT code based on a two-fluid model with separated balance equations for the two phases and considered thermal and mechanical nonequilibrium conditions to calculate the mass, momentum, and energy exchange between water and steam [11]. This model was further elaborated and complemented with improved interfacial friction and condensation models and extended to noncondensable (NC) gases [12]. Similarly, radiation heat transfer and boron transport were added [13,14]. A large factor in improving stability was increased control over the Jacobian matrix and its updates. The possibility to simulate a complete LOCA process within ATHLET led to increased international interest in the code. ATHLET was now being developed for both Windows and

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FIGURE 12.2

12. Nuclear thermal hydraulics with the AC2 system code package

Timeline of ATHLET development. ATHLET, Analysis of Thermal Hydraulics of LEaks and

Transients.

UNIX systems, with over 20 external users in Germany and nearly 30 users abroad, mainly in Europe and Asia. ATHLET 1.2, which included a T-junction model, was released in 1998 [15] with further improvements for the simulation of WWER-type reactors like a specific heat transfer correlation for horizontal heat exchangers. The code version 1.2C from November 2000 included a first implementation of coupling between ATHLET and COCOSYS. In 2003 ATHLET 2.0A was released. It included further improvements to the models for condensation, mass, and energy transfer at the phase interface and allowed cross-connection objects. The latter enabled the simulation of cross flows to better represent multidimensional flow behavior in huge components such as the reactor pressure vessel. Also, this was the first version accompanied by the complete code documentation: a user’s manual, a programmer’s manual, one volume on validation, and other on the applied models and methods [16]. Since then, ATHLET and ATHLET-CD were released jointly with the same version number. ATHLET 2.1A from 2006 extended the parameter range for water to supercritical pressures, including the calculation of material properties and heat transfer correlations. As well as general improvements to different models, this version introduced a model to simulate the clogging of pipes [17]. The models for supercritical fluid and sump strainer clogging were further improved in ATHLET 2.2A, released in 2009. It also allowed consideration of fuel burnup for NEUKIN and introduced additional material properties for UO2 and Pu/U mixed oxide [18] and established a coupling to the CFD code ANSYS CFX. The next major release was ATHLET 3.0 in 2012, which introduced the new working fluids heavy water, liquid lead, sodium, helium, and lead
bismuth eutectic. This version also added the option to utilize 2D or 3D momentum equations as well as the possibility to simulate pebble bed reactors. In addition, new models for spray condensation and

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turbines were implemented [19,20]. ATHLET 3.1A from 2016 implemented a model for axial heat transfer in heat conduction objects (HCOs), improved the 3D momentum models, and added an option to use cylindrical coordinates. Turbine models were further improved, and argon was added as a new NC gas. This version also introduced the plugin technique to allow for easier coupling with external modules [21,22]. More than 50 organizations hold a license for ATHLET 3.1. Since 2016 many efforts were spent on an improved code coupling and the plug-in concept was further enhanced and several new plug-in interfaces were made available in ATHLET, enabling the user to extend ATHLET capabilities by using their own models or correlations, for example, for material properties, heat transfer, or critical heat flux (CHF) calculation [2]. Further improvements were implemented with a view to advanced GenIII/III 1 LWRs, SMRs, and also Gen-IV reactor designs with a specific focus on passive safety systems [23]. These developments are included in the most recent version of ATHLET, version 3.2, which was released in June 2019 as part of the software package AC2 2019. It also introduced supercritical CO2 and molten salts as working fluids and now offers the Numerical Toolkit (NuT), which allows access to alternative numerical solvers to speed up calculations.

12.1.3 Modeling basis 12.1.3.1 Thermal-hydraulic field equations The TFD module of ATHLET offers two different sets of thermal-hydraulic model equations for the simulation of the fluid-dynamic processes. On the one hand a six-equation model with fully phase-separated conservation equations for liquid and vapor mass, energy, and momentum is available. On the other hand a five-equation model with separate conservation equations for liquid and vapor mass and energy and a mixture momentum equation can be employed. The five-equation model is supplemented by a drift-flux-model to account for mechanical nonequilibrium. It also includes a mixture-level tracking model to resolve stratification processes in vertical components. It is important to note that both equation systems can be used in parallel for different components of the system to be simulated. For example, the five-equation model with mixture-level tracking may be employed in the pressurizer, accumulators, and upper head while all other parts of the primary system use the six-equation model. The TFD module of ATHLET employs a modular network approach for the description of the thermal-hydraulic system. A given system configuration can be simulated by combining basic fluid-dynamic elements, so-called TFD objects (TFO), and specific component models. The numerical discretization of the TFO results in the representation of the fluiddynamic domain by a set of control volumes (CVs). The spatial discretization of the field equations is performed on the basis of a finite-volume staggered-grid approach. The phase mass and energy equations are solved within the CVs and the momentum equations are solved along junctions that connect the centers of adjacent CVs. 12.1.3.1.1 The six-equation model

The six-equation model is based on fully phase-separated conservation equations for mass momentum and energy. The solution variables used in ATHLET are pressure p,

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phase temperatures Tl and Tv , vapor mass quality x, and the phase volumetric flows. ~ k ρk w ~k Þ 5 ψk or in integrated form Starting point is the continuity equation ð@=@tÞðαk ρk Þ 1 rðα balanced across a CV n X @mk _ k;in 2 m _ k;out 1 5m ðΨi-k 2 Ψk-i Þ @t i51

P Considering the definition of the vapor mass fraction x 5 mv = ni51 mi and inserting the integrated continuity equation yields the ordinary differential equation (ODE) for the vapor mass fraction  Pn Pn  @x ð@mv =@tÞ i51 ðmi Þ 2 mv i51 @mi =@t 5 :  Pn 2 @t i51 mi





The sum on the right side of the previous equation considers all components existing in the fluid: liquid, vapor, NC gases, etc. The differential equations for the phase temperatures are derived from the integrated energy equation in terms of the specific enthalpy h " !#     v2k;CV v2k  v2k  @ mk @p _ k hk 1 _ k hk 1 m k hk 1 1m 2  5 ℝEk  2m @t 2 ρk @t 2  2 



in

out

The right-hand side ℝEk of this equation contains source terms due to heat supply from structures, heat flow through phase interface, enthalpy flow by phase change, as well as external heat sources S (e.g., pump) and can be expressed as ð ℝEk 5

q_ w-k dV 1 1

n ð X i51

n ð X



ð q_ i-k dV 2 q_ k-i dV

i51

     ð ð 1 1 vi ~ vk ~ ψi-k hi 1 ~ v i dV 2 ψk-i hk 1 ~ v k dV 1 SEk dV 2 2





In the energy balance equations the potential energy contribution and the dissipation energy are neglected. By inserting the total differential of the enthalpy as function of the state variables p and T and considering the definition of the specific heat capacity at constant pressure, one gets the ODE for the phase temperature, and by considering the definition of the specific heat capacity at constant pressure, one finally gets the ODE for the phase temperature  ! @Tk 1 Ek 1 1 @hk  @p 5 1 2  cp;k mk cp;k ρk @t @t @p T







k

where Ek is given by     v2k  v2k  @mk _ k hk 1 _ k hk 1 Ek 5 m  2m  2 2 in 2 out @t



v2 hk 1 k;CV 2

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  @ vk;CV 1 ℝEk 2 mk vk;CV @t

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The differential equation for the pressure is derived from the postulation, that the volume V of a CV is constant in time. Introducing the specific volume vi of component i this yields     n n  X X @V @ @mi @vi  @Ti @vi  @p 5 50 1 mi 1 ð m i vi Þ 5 vi @t @t @t @Ti p @t @p Ti @t i51 i51





Substituting the time derivative of the phase temperature by the previously derived differential equation and rearranging the formula results in @p ℤ1 52 @t ℤ2 with

  n  X @mi @vi  Ei 1 vi @t @Ti p cp;i i51       n X @vi  1 @vi  @hi  ℤ2 5 mi 1 v 2 i @p Ti cp;i @Ti p @p Ti i51



ℤ1 5







The differential momentum conservation equation in vector form is shown in the following equation:     @ αk ρk v~k 1 r αk ρk v~k  v~k 5 pintf grad ðαk Þ 1 ~ g f fric;intf;k 1 αk ρk~ @t   n  X 5  ~k;Ext 2r αk p I 1 ~ ψi-k v~i 2 ψk-i v~k 1 S f fric;wall;k 1





i51 5

where  denotes the tensor product and I the unit matrix. The terms on the right-hand f fric;intf;k is the interfacial side are: pintf grad ðαk Þ is the pressure force on interfacial area, ~   shear force, αk ρk~ g is the gravitational force,r αk p 5 I is the pressure force at CV bound Pn  ~ ary, f is the wall friction and form losses, ψ v~i 2 ψ v~k is the change of



i51

fric;k

i-k

k-i

~k;Ext is the external forces (e.g., pump). momentum due to phase transition, and S Additional contributions such as the virtual mass force are not considered here. Assuming constant pressure within one CV for both phases and at the interface and substituting the continuity equation times the phase velocity, the momentum equation can be given by

αk ρ k

 @ @ðv~k Þ 1 αk ρk ðv~k rÞv~k 5 2 αk grad p 1~ f fric;intf 2 αk ρk~ g sinðγ Þ @t @s " # n  n  X X   ~k;Ext 1~ f fric;k 1 ψi-k v~i 2 ψk-i v~k 2 v~k ψi-k 2 ψk-i 1 S





i51

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  Assuming constant flow area in time @A=@t 5 0 , the integration along a flow path s between two CV centers results in the 1D ODE for the phase volumetric flow: 2 ð~ ð ð ð f fric;intf @ ð uk A Þ 1 6 @uk @p 6 Ð 5 ds 2 g ρk sinðγ Þds ρk 4 2 ρk uk @s ds 2 @s ds 1 @t αk ðsÞ A ds



ðs Þ

1

ðsÞ

0

ðsÞ

1

ð ð~ ð n X f fric;k ψk-i uk C B ψi-k ui ds 1 ds 2 dsA @ αk αk αk i51

ðsÞ

ðsÞ

0

2

ðsÞ

ðs Þ

3

1

ð ð ð~ n X ψk-i uk C S k;Ext 7 B ψi-k uk ds 2 dsA 1 ds7 @ 5 α α α k k k i51 ðs Þ

ðs Þ

ðsÞ

12.1.3.1.2 The five-equation model

The five-equation model solves phase-separated equations for mass and energy. Compared to the six-equation model, its main difference is having only one ODE for mixture momentum balance based on the mixture density ρm 5 αρV 1 ð1 2 αÞρL , mixture velocity wm , and the relative phase velocity (slip) wr . The last term is calculated with the flooding based drift-flux model [24,25] with area-averaged superficial velocity j , void

fraction hαi, and drift flux jVL as

jVL C0 2 1

j 1 wr 5 hαið1 2 hαiÞ 1 2 hα i The phase distribution parameter C0 is derived from geometry dependent (pipe, bundle, or annulus) correlations in flow maps for vertical and horizontal flow respecting countercurrent flow limitation. 12.1.3.1.3 3D model

ATHLET provides a 3D extension of the 1D six-equation model described previously. Key element of the 3D model is a multidimensional implementation of the momentum equation, where the convective term is treated as follows: 1 @wx @wx @wx 1 wy 1 wz B @x @y @z C C B B @w @wy @wy C C B y C 1 wy 1 wz w ~ rÞ w ~5B ðw B x @x @y @z C C B C B @ w @wz 1 w @wz 1 w @wz A x y z @x @y @z 0

wx



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The 3D model equations are available in both Cartesian and cylinder coordinates. The selection is made on the basis of the problem-specific geometry input. The 3D model can be applied together with a mixture-level tracking model. This feature improves the 3D simulation of large water pools, for example, of passive safety systems. 12.1.3.1.4 Noncondensable gases

The multicomponent model of ATHLET provides the possibility to simulate different gaseous components as well as nitrogen dissolved in liquid in addition to the working fluid. This applies to all current working fluids except helium and CO2. Fluid properties for the following NC gases are implemented: air, argon, helium, hydrogen, nitrogen, oxygen, and one userdefined gas. NC are treated as ideal gases so that an ideal mixture of several NC, including water and sodium vapor, can be simulated. Thus NC mixture enthalpy is the mass-weighted P sum of constituent enthalpies hg 5 Xg;i hg;i , as is isobaric specific heat capacity cp;g : Transport properties are calculated following the model used in SCDAP [26]. NC are assumed to be in thermal and dynamic equilibrium with the vapor phase (if present). The same holds for nitrogen solutes in liquid, where maximum solubility depends on total and partial pressure. The presence of NC is considered in wall friction and drift model via mixture properties. For bulk condensation of vapor the condensation rate is reduced due to accumulation of gas and restricted by the saturation pressure of vapor at prevailing temperature. The heat transfer coefficient (HTC) for condensation (based on Refs. [27,28]) is modified as  rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    μV min 2;1 1 2:88 1025 Re1:18 HTCk;nc 5 HTCk min 1:3 ;1 2 C N V 100ρV DCN





with

D5





0:00013 Ti1:75 ; p

where CN denotes NC concentration and Ti the average between liquid and vapor temperature. Finally, evaporation at the interfacial area is considered via volatilization with mass exchange rate of ΓVOT 5 0:01ðTL 2 TVS Þ α ð1 2 αÞ; introducing the vapor saturation temperature TVS , which may be below the saturation temperature TS depending on NC partial pressure. Irrespective of that (and similarly for nonboiling working fluids), a simple heat transfer model ensures that liquid and gas temperatures do not drift apart too much. If zirconium oxidation is simulated, the release of hydrogen and the consumption of steam are considered as source or sink term in the according balance equations. 12.1.3.2 Constitutive equations 12.1.3.2.1 Working fluid properties

ATHLET’s two-phase working fluids are light and heavy water as well as sodium, the nonboiling working fluids are lead, lead
bismuth eutectic, molten salts and two userdefined fluids, and finally helium and supercritical CO2. The main water
steam properties package is based on the IAPS-84 formulation [29]. Values are estimated by local interpolation with a nonequidistant optimized grid relative

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to the saturation line. To ensure consistency at the saturation line, properties for vapor and liquid as functions of p and T are approximated relative to saturation values, that is,       f p; T 5 fsat p 1 Δf p; T 2 Tsat ðT 2 Tsat Þ      f p; T 5 fsat ðT Þ 1 Δf p 2 psat ; T p 2 psat   and consistency of derivatives df p; T 5 dp@p f 1 dT@T f imposed. Interpolation on the grid is bicubic. For coexisting phases the properties are continued in the overheated/subcooled region  by extrapolation at the saturation line, for example, fL ðp; Tsat 1 ΔTÞ 5 fsat ðpÞ 1 Δf p; ΔTÞΔT, where necessary derivatives are calculated analytically. The subcritical water package operates in the range between 1 Pa and 22 MPa, liquid temperatures from 240  C to 371.85  C, and vapor temperatures from 2270  C to 6000  C; however, the more extreme values are outside the range of physical validity and are estimated, for example, assuming ideal gas to enhance program stability. For supercritical pressure up to 100 MPa and below 1000  C, the values are based on IAPWS-IF97 [30] where the approximation uses the pseudocritical line. For heavy water, enthalpy and specific volume are multiplied with suitable factors. Liquid metal properties are defined in the range between 10 Pa and 10 MPa with liquid temperatures between the respective melting temperature and up to boiling temperature 210 K. For sodium the vapor temperature is at most 2000 K. Properties are evaluated using polynomials from Ref. [31] and for sodium from Refs. [32,33]. Liquid salts are all nonboiling and properties between 100 Pa and 2 MPa with temperatures between the melting temperature and up to boiling temperature minus10 K at 0.1 MPa are derived with polynomials taken mainly from Refs. [34,35]. The implementation for supercritical CO2 is based on Ref. [36], whereas helium gets ideal gas properties and additional partial derivatives @p ν and @T ν. 12.1.3.2.2 Interfacial shear

Interfacial shear forces are determined in ATHLET based on a flow pattern map. For horizontal flows, Skorek’s modification of the Wallis correlation is used for stratified flow [37] and for slug flows Ishii’s correlation [38], while wavy flow is approximated as a transition between both correlations weighted by the fraction of nonstratified flow, and for dispersed droplet a correlation by Ishii [38] is applied. The transition criteria for the flow patterns are for stratified—stratified wavy transition the modified form of Jeffreys’ sheltering hypothesis [39] and for wavy—slug transitions the Taitel and Dukler formulation [40]. For the onset of liquid entrainment in a vertical bundle a specific ATHLET correlation is used and for other geometries a modified TRAC correlation [41]. For vertical flows a correlation based on ATHLET’s flooding-based drift-flux model is employed for nondispersed flow. Ishii’s correlation is used for dispersed droplet flow, where the transition is predicted with a correlation by Taitel et al. [42]. 12.1.3.2.3 Wall friction and form losses

Form loss coefficients ξ 5 ζ=A2 associated with fixtures and fittings in pipes or geometry changes generally are input by the user [although for the latter ATHLET assumes as minimum pressure loss ξmin 5 ð1=A2i Þ 2 ð1=A2j Þ]. Form losses are then computed via

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Δpform;k 5 0:5ξk Rk A2 vk jvk j, where phase-specific form losses are calculated in the sixequation model and the mixture flow and density are used in the five-equation model. Wall friction losses are computed analogously with a Darcy
Weisbach friction factor λ and a two-phase multiplier Cφ either distributed on both phases or at suitable mixture values following pwall;k 5 0:5

λk Rk Cφ ðAvk ÞjAvk j 5 kk ðRk Avϕ ÞjRk Avk j: DH A2

For laminar flow the friction factor for pipes is determined using Hagen
Poiseuille λk 5 64=Rek (with Rek $ 500) and for turbulent flow the Colebrook equation [43] is used with r as absolute roughness and with a preset value on the right side to prevent iteration   ! 1 r 6:81 0:9 pffiffiffiffiffi 5 2log 1 : 3:7DH Rek λk The two-phase multiplier following the Martinelli
Nelson [44] model is adapted for ATHLET computing friction losses separately for vapor and liquid with  0:571  0:143 νL ηL 12x pcrit 2 p and a 5 1 1 1:53 Xtt 5 x pcrit νV ηV !1:75a

11Xtt 1=a 1 1:75a 1:75 a Cφ;L 5 ð12xÞ and C 5 11X x1:75 φ;V tt Xtt 1=a and the overall loss coefficient is interpolated over the enthalpy quality x between 0 and 1. The pressure drop due to wall friction and form losses are calculated under assumption of the homogenous flow and for the six-equation model distributed between gas and liquid phase proportionally to the void fraction. 12.1.3.2.4 Interfacial heat and mass transfer

Interfacial mass transfer rate is split into bulk evaporation/condensation ΨVol and structure surface evaporation/condensation ΨF . For the latter, HTC values are determined with the HECU models and transferred to mass flows. In addition, the mass transfer at mixture levels is calculated. For the bulk processes, ATHLET has models for four scenarios: overheated and subcooled vapor and overheated and subcooled liquid. Bulk mass transfer for the first three cases is predicted with a model by Wolfert [45,46], adapted from bubble mass transfer models by Sideman [47] and, for overheated liquid, by Plesset and Zwick [48] complemented by a volatilization term. For condensation in a subcooled liquid, a direct condensation model is used based on an energy balance at the steam
water interface of area Aint, where ΨVol 5

 1  HTCL Aint ΔTL;subcool : Δhvap

The HTC value is determined based on surface renewal theory following an approach by Hobbhahn [49]. The surface area depends on the flow regime, and the model considers

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bubbly flow, annular and annular mist flow, stratified and horizontal plug flow or water level. These are used to calculate bubble sizes depending on the overall energy dissipation rate E. Using the iteratively determined penetration depth δ, if sffiffiffiffiffiffiffi λ ν 1=4 21 # 0:92979; ZL 5 δ Rcp E the HTC is determined as HTCL 5 0:4

qffiffiffiffiffiffiffiffiffiffi    1=4 λRcp E=ν 1 1 2exp ð2 2Z21 L Þ

and otherwise via a modified film condensation model. 12.1.3.3 Heat conduction and heat transfer The heat conduction and transfer package (HECU) discretized  solves  a one-dimensional   heat equation for solid structures, that is, @T=@t 5 λ=cp R r2 T 1 1=cp R W with W as rate of heat generation. Assuming that heat flow rates  between temperature layers of a structure are related to heat resistances via Qj11 5 Rj11 Tj11 2 Tj , this is discretized as     dTj 1 1 1 1 1 5 Tj21 2 1 Tj11 1 Wj Vj Tj21 1 cp;j Rj Vj Rj Rj Rj11 Rj11 dt For the further calculation of Rj for each layer, the basic geometry such as plate, cylinder, or sphere is considered and there are specific models for, for example, fuel rods or TRISO particles as well. Importantly, a HCO inherits its basic nodalization from the (one or two) TFOs it is connected to, with a positive integer number of (axial) levels between these boundaries and then for each a number of (radial) HCO layers resulting in the separate heat control volumes with constant shape in time. In each HCO, up to three material zones plus gaps with a specific HTC can be modeled. For each level the radial conduction problem is solved with a separate integration procedure with error control. Axial heat conduction within an HCO can be activated by the user and is solved as an explicit contribution to the integration scheme. Importantly, fuel rods are represented by HCOs and are therefore assigned to specific CVs. Several fuel rods and their compositions can be defined, with rod power determined by the NEUKIN module. For point kinetics the axial power profile for each rod is input by the user and kept constant in time. HECU also models heat transfer at the surfaces of HCOs considering single- and twophase flow conditions, including CHF, minimum film boiling (MFB), quench front progression, evaporation, and condensation. Fig. 12.3 gives an overview of the logic HECU uses to determine the appropriate correlations depending on the temperature difference between the wall and the fluid, the enthalpy quality of subcooled water (and overheated steam), and the void fraction for two-phase conditions. In all regions, several correlations are available in principle, and users may override the HECU selection logic by specific inputs or provide their own correlation via a plug-in. Important correlations are McAdams for free [50] and Dittus
Boelter for forced convection to liquid and vapor [51]

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FIGURE 12.3 HECU heat transfer logic for water. HECU, Heat transfer and heat conduction.

and the modified Chen correlation for nuclear boiling [52]. A bundle factor according to Inayatov [53] is applied to these types of correlations. In small regions, smooth interpolation of correlation results for the different flow regions (subcooled—two-phase and two-phase—superheated) is performed, also to increase numerical stability. And in the transition boiling region, the HTC is calculated as an interpolation between the nucleate and film boiling results. The CHF temperature defined as minimum wall temperature for initiation of departure from nucleate boiling or dry-out is determined using a set of CHF correlations. The transition toward stable film boiling or back from film boiling toward transition boiling is decided on the basis of correlations for MFB temperature and maximum rewetting temperature, respectively [54]. A quench front model for bottom and top reflooding is also available. Condensation for turbulent film is computed with modified Dobson and Chato correlation [55] in horizontal tubes and with Carpenter and Colburn [52] else. For other fluids, this heat transfer logic is adapted (e.g., there are yet no correlations for CHF or departure from nucleate boiling available for sodium) and there are special heat transfer correlations, for example, for supercritical water, liquid metal working fluids, and helium considering specific geometries (e.g., bundle or pebble bed). In some cases, however, the correlations implemented for water are used with other working fluid materials data irrespective of the range of validity (e.g., Dittus
Boelter).

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Finally, HECU also includes a radiation heat transfer model between HCOs connected to one TFO (at high void fractions) assuming gray body radiation following Stephan
Boltzmann law. The net energy flow can then be determined by solving 2 3 N N X X QRad;i 5 Ai 4 Ej ϕi;j 2 Ei 5with Ei 5 εi σTi4 1 ð1 2 εi Þ Ej ϕi;j j51

j51

with user inputs for emissivities εi und view factors ϕi;j . 12.1.3.4 Neutron kinetics The NEUKIN module describes nuclear power generation. Within ATHLET a standard point kinetics is implemented that calculates the fission power generation. For standard cases the following effective equation system for the energy increment within the integration step Δt is solved h Δt i ΔE 5 ½P0 1 S0 τ 0 eτ0 2 1 2 S0 Δt with

τ0 5

NG X L β i Yi;0 ; S0 5 ; β ðΔk0 2 1Þ βðΔk 0 2 1Þ i51

  Yi 5 Yi;0 1 λi ΔE 2 Yi;0 Δt

with

Yi 5

γLλi R0 ðtÞ : Ci ; Δk0 5 β βi

The subscript 0 refers to the values at the start of the integration step, and the subscript i to the delayed neutron group, of which 6 are assumed, L denotes the neutron generation time, γ the factor relating power to neutron flux, R(t) the total reactivity, β the (total) delayed neutron fraction, and C its concentration. The system is solved with separate numerics; the time step is the FEBE time step or the maximum NEUKIN time step, whichever is smaller. For prompt criticality conditions, different approximations are used. The model considers reactivity contributions from fuel temperature, coolant temperature, coolant density, boron concentration, solid moderator temperature, and external reactivity (e.g., control rods) provided by a GCSM signal R 5 RTf 1 RTc 1 RRc 1 RB 1 RTm 1 Rext ðtÞ Reactivity contributions for the core are derived by volume weighted, and also neutron flux weighted (with exponent k usually 1) contributions from the respective CVs to which fuel rod heat control volumes are assigned, for example, for coolant density feedback X    1 Rpc 5 P R pci VCV;i nki k i VCV;i ni i







External reactivity changes, for example, due to control rod movement or reactor scram are given by a GCSM signal. The fission power is complemented by the decay heat calculated by ATHLET. The module NEUKIN also offers a generic interface for coupling of 3D neutronic models (see Section 12.2.6). Thus local power changes and feedbacks can be simulated.

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12.1.3.5 General control and simulation GCSM provides for the simulation of safety class and operational I&C system of a reactor, the activation and control of components such as pump, valves or whole connecting systems, the processing of model results such as temperatures or water levels, and the setting of boundary conditions. The module comes with the basic controllers for analog process control and logic controllers and includes specialized library models for diverse applications such as simplified simulation of heat exchangers. GCSM separates between process signals (i.e., most of the system variables calculated in the code), special models (e.g., decay heat calculation), and control elements. These include switches, adders, integrators, functions such as multiplication, function generators using tables for interpolation, as well as logical controllers such as AND. This allows building complex control structures for describing balance-of-plant systems. Even fluiddynamic (support) systems (e.g., steam line, condensate system) can be modeled in a very simplified way (quasi stationary approach) saving computational effort. GCSM output can be fed back to model in the form of hardware actions (e.g., valve cross-sectional area, control rod position) or boundary conditions (e.g. temperature, heat, and mass sources). GCSM comes with its own explicit time integrating method, which might impose a GCSM time integration constant smaller than the TFD time step. Usually, GCSM signal blocks are strongly coupled to the TFD integration, that is, GCSM signals will be determined for the intermediate steps in the FEBE time advancement with detection of signal discontinuities, adaption of step size, Jacobian updates, and overall numerical error control. 12.1.3.6 Numerical approach and new Numerical Toolkit The thermal-hydraulic field from Section 12.2.3.1 and the closure relations  equations  constitute a system of ODEs f t; y which gives rise to an initial value problem of the form   y0 ðtÞ 5 f t; y ; yðt0 Þ 5 y0 ; where y0 is a suitable initial value computed by ATHLET’s steady-state calculation (SSC), see Section 12.2.3.7. Numerical time integration is performed in the FEBE module, which implements an extrapolation ansatz based on Euler’s method. A combined approach of explicit and linearly implicit integration (forward Euler, backward Euler) is available [56]. However, for the  sake  of stability, purely linearly implicit integration is performed in general. Thus, at tn ; yn and for given integration step size h and iAN, the corresponding Euler increments @yi;k and approximation yei are computed via ! j
1 X @fn h ; j 5 0; . . . ; i
1; hi 5 ; ðI
hi J Þ δyi;j 5 hi f tn 1 j hi ; yn 1 δyi;k 1 h2i i @t k50



yei 5 yn 1 @yi;0 1

   1 @yi;i21:

The matrix J approximates the Jacobian @fn =@y and is determined by finite differences. Its quality is closely monitored by FEBE’s control logic and it is partially or fully updated if deemed necessary. Since Euler’s method is of consistency order 1, extrapolation provides a convenient way to increase the order of the overall method. In FEBE extrapolated approximations of up to order 3 are recursively computed by means of the

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Aitken
Neville algorithm, see, for example, Hairer et al. [57]. As shown in Fig. 12.4, this results in a tableau of approximations Tq;p where p indicates the order of consistency w.r.t.   the real value y tn 1 h;y0 . Due to the increasing order of the tableau values, local error estimates of orders 1 and 2 are readily available by taking differences. This is exploited by the overall step size control in a staggered fashion. A first-order error estimate based on T2;2 2 T2;1 is computed. If the   specified error bounds are already met, T2;2 is set as final approximation to y tn 1 h;y0 . Otherwise, all the remaining tableau values are computed and T3;3 2 T3;2 serves as a basis for an error estimate of order 2. If the error bounds are met, T3;3 is used to proceed the integration, if not Jacobian updates and/or step size corrections are applied. Step size correction and prediction are governed by the classical dead-beat controller H0 110, see for example, So¨derlind [58]. With default options FEBE utilizes ATHLET’s block sparse matrix package FTRIX to handle the repeated computation and (partial) updates of the Jacobian approximation J. FTRIX performs sufficiently well for small- up to mid-scale problems. For large or complex problems with a considerable amount of cross-connections, the user may alternatively activate the AC2 -component NuT to enhance ATHLET/CD’s linear algebra performance significantly, see Ref. [59]. The toolkit offers easy access to dedicated open-source libraries for numerical computations. The corresponding software architecture is given in Fig. 12.5. It makes use of ATHLET’s plug-in mechanism and is of minimally invasive design. The FIGURE 12.4 FEBE extrapolation scheme and tableau determination.

FIGURE 12.5

Software architecture of the Numerical Toolkit. NuT, Numerical Toolkit.

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library PETSc [60] provides scalable and optimized data structures to store the matrix J as well as preconditioned Krylov subspace methods to solve the above stated linear systems. In addition, an internal interface to the direct sparse solver MUMPS [61] is available. For efficient and fast fill-in reduction MUMPS utilizes the algorithms of METIS [62], (Sca) LAPACK is involved to access standardized basic linear algebra operations. For ease of use the user of NuT may choose from a list of predefined solver presets. Due to scalable data structures and algorithms using NuT in a multicore environment may greatly improve the performance for (very) large problems and puts AC2 in a good spot to handle future problems of higher complexity appropriately. The selection of NuT and the assignment of processor cores are conveniently done via the general AC2 -GUI. 12.1.3.7 Steady-state calculation Generally, user inputs for initial and boundary conditions will be neither fully consistent nor complete. To preclude spurious transients, misleading results or even run termination, ATHLET starts with a SSC. The SSC basically follows the so-called priority chains that order ATHLET TFOs and predicts steady-state solutions employing a four-equation model with drift flux. Importantly, the SSC automatically adjusts user inputs, particularly pressure losses, pump speeds, heat exchanger power, separator effectiveness, or initial reactivities within certain bounds, thus involving all ATHLET modules. This problem is then iterated until a converged consistent solution is found or the calculation fails.

12.1.4 Specific models for certain reactor designs 12.1.4.1 Critical discharge models For break mass flow computation, apart from limiting each junction velocity to sonic velocity, ATHLET offers the homogeneous equilibrium model and the Moody model following Ref. [63] and the specific 1D model CRD1D based on Ref. [64]. The latter calculates the critical mass flux in the break plane considering the thermal nonequilibrium of the fluid, the discharge geometry, and hydraulic parameters. It applies a four-equation model with closure laws taken from ATHLET, a simple slip velocity correlation and an enhanced evaporation rate for flashing in turbulent flow. The CDR1D model is applicable for LWR and also for helium. 12.1.4.2 Boron tracking model ATHLET comes with a boron tracking model for H3BO3. Its main assumptions are that one species is transported dissolved in the liquid phase of water only, without any influence on the thermal hydraulics. Concentrations CB are specified in ppm where the (solute) mass is MB;sol 5 1026 CB ML and solute mass flows over a junction analogously GB;j 5 1026 CB;j GL;j . A profile transport model, where the concentration profile is shifted spatially with an interpolation method based on liquid mass flows, is the recommended option for boron transport to reduce numerical diffusion. The boron deposition model uses a table for maximum boron solubility versus fluid temperature and all excess boron plates out immediately on structures. Redissolution, if allowed, is also immediate.

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ATHLET keeps track of the respective boron masses. For reactivity feedback the boron concentration is computed as XB 5 106

MB;sol 1 MB;dep : ML 1 MV 1 MNC

The H3BO3 can be replaced by any (boron) species. There are built-in solubility tables for H3BO3 (aq) and hydrated zinc borate and the possibility for a user-supplied table. Importantly, the boron feedback coefficient in NEUKIN needs to take into account the different content of 10B in the species defined in this model. 12.1.4.3 Gas-cooled reactor models For pebble beds in gas-cooled reactors, ATHLET includes the models from Ref. [65] for pressure loss through a pebble bed, and [66] for the Nusselt number. Moreover, the fuel modeling allows defining pebble-shaped fuel and a pebble bed, and there is a model for estimating TRISO particles’ temperatures. NEUKIN includes options for considering necessary moderator feedbacks. Moreover, ATHLET comes with a specific compressor model for He and its multistage steam turbine model is also applicable for helium. These models have been applied successfully to some test cases [67].

12.1.5 Validation The ATHLET validation matrices and the corresponding simulation cases are documented in the ATHLET validation report [68], which is available on the GRS website. An excerpt of the validation matrices for LWR design is shown in Table 12.1. In addition, the validation matrices for SMR and passive safety systems were developed in the last years [69
71] and are also documented in the ATHLET validation report [68]. Over the last three decades with at least one version of ATHLET, 61 single and combined effect tests for LWR, 88 PWR experiments, 18 BWR experiments, and 33 WWER experiments are covered by 2018 [72]. Overall, validation of ATHLET 3.2 prior to release shows good agreement to the experimental data and better results than previous code versions or at least the same quality of results. The validation demonstrated that improvements of several code and model weaknesses identified based on user feedbacks from prior versions are effective [72]. In the following one validation case (5% cold leg break test, ROSA-IV LSTF Run SB-CL18) is briefly described, for details see Ref. [68]. The LSTF (Large-Scale Test Facility) is a 1/48 volumetrically scaled model of a Westinghouse-type 3423 MWth four-loop PWR. The LSTF has the same major component elevations as the reference PWR to simulate the natural circulation phenomena, and large loop pipes to simulate the two-phase flow regimes and phenomena of significance in an actual plant, but with only two loops. Both the initial steady-state conditions and the test procedures were designed to minimize the effects of LSTF scaling compromises on the transients during the test. Summarizing the comparison of the ATHLET calculation with the experimental results, it can be stated that, in general, the calculated parameters show a good, some of them

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TABLE 12.1 Summary of integral tests for western light-water reactors (excerpt) used for Analysis of Thermal Hydraulics of LEaks and Transients validation [68]. PWRs

BWRs

Small and Transients with Facility or plant Scale Large breaks medium breaks Transients loss of RHRS AM LOCAs Transients UPTF/TRAM

1:1

2

2

LOFT

1:50

2

3

LSTF

1:50

4

PKL

1:145 2

8

ROSA-III

1:424

5

1

FIST

1:642

2

1

German PWR Konvoi

1 0 3 7

3

5

3

German BWR Total

3 12

32

25

4

15

7

11

BWRs, Boiling-water reactors; LOCAs, loss-of-coolant accidents; LSTF, large-scale test facility; PWRs, pressurized-water reactors; UPTF, upper plenum test facility; TRAM, transient and accident management; LOFT, loss-of-fluid test facility; LSTF, large-scale test facility at ROSA; PKL, Prima¨rkreislaufversuchsanlage test facility; ROSA, rig of safety assessment facility; FIST, full integral simulation test facility.

FIGURE 12.6 LSTF SB-CL-18 pressure in pressurizer.

even excellent, agreement with the measurements. ATHLET is able to simulate all main phenomena for the SBLOCA scenario. The calculated primary side pressure agrees very well with the experiment with two exceptions (Fig. 12.6). In the early phase of the

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depressurization (20
60 seconds), the pressure drops too far for two reasons: the core is represented only by one inner and one outer channel. Since there is no hot channel simulation, the beginning of evaporation in the core is calculated late. The second reason is the overprediction of the heat flow to the secondary side in that time period, which can be derived from the too fast increase of the pressure on the secondary sides of the steam generators. The comparison of the densities in both the hot and cold legs of the two loops, as well as upstream of the break orifice shows that the calculation matches very well the measurement, with the exception of the liquid entrainment at the break nozzle, which is clearly underestimated by ATHLET (Fig. 12.7).

12.1.6 Code coupling Several 3D codes for rectangular and hexagonal core geometries have been successfully coupled to ATHLET with the NEUKIN interface, for example, QUABOX/CUBBOX, TORTTD, PARCS [73], BIPR [74], or DYN3D [75]. ATHLET has also been successfully coupled to the CFD codes CFX and OpenFOAM [1]. Currently, the semi-implicit coupling schemes with underrelaxation have received increased attention [67], with further development ongoing. ATHLET can be extended by user-provided feature implementations to apply the code more individually. Two coupling approaches can be distinguished. One option for controlling the simulation is offered by using a controller code that invokes the shared library version of ATHLET. This library provides the main entry of ATHLET via an exported routine symbol and allows calling ATHLET as a subroutine. In this case the simulation process can be controlled in response to events. An event can be considered as a certain and named point in the simulation flow, like input done or end FIGURE 12.7

LSFT SB-CL-18 fluid density upstream of break orifice.

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of time step. These points have been made available as so-called hooks, at which a user might associate routines that instruct ATHLET what to do at this point before continuing the simulation. On the other hand, ATHLET can be extended by user-provided plug-ins, that is, separate shared libraries. ATHLET will register available plug-ins at startup and invoke them if the applied input file demands their use. Hashmaps, which include pointers to exported ATHLET variables, are accessible by both the user code and ATHLET. They enable intercode data transfer of, for example, physical field variables or GCSM controller states. Specific modules and macros have been prepared in order to facilitate implementing controller code or plug-ins. Interface modules contain the necessary initialization procedure, pointers to global variables, and service procedures as a complete package to be used in an ATHLET-extension. The described coupling technique can be flexibly applied to different applications. Generic plug-in interfaces are available for, for example, CHF correlations, working fluid properties, or BOP models.

12.1.7 Scope of application and limits ATHLET is applicable and well validated for analyses of operation and fault scenarios prior to core degradation for LWR designs (western PWR, WWER, BWR) and similar design with heavy water (e.g., Atucha NPP). It has also been qualified for RMBK. For (HWR) pressure tube reactors like CANDU, some specific models, which are related to the fuel elements, as well as recent experiences are missing. For such a design, ATHLET is broadly applicable to most scenarios; however, due to a lack of turbulence and fuel behavior models, subchannel analyses have limited validity. Similarly, for transients with pronounced 3D effects such as coolant mixing or stratification, predictiveness of ATHLET is limited, but coupling with suitable CFD model is a way for addressing these issues. Regarding passive safety systems, ATHLET has been successfully validated against several tests. However, systems with small driving forces, at low pressures or even near vacuum conditions, pose challenges to ATHLET and further validation and model improvements are needed. Regarding liquid metal and molten salt reactors, ATHLET has basic capabilities with some specific correlations available, so that at least transient scenarios can be calculated. Especially for sodium-cooled reactors, ATHLET has been successfully applied. Yet, systematic extended validation and further model improvements are still necessary. For gas-cooled reactors, there are similarly some specific correlations, for example, for pebble beds, so that transients are accessible, but scenarios with, for example, air ingress where chemical reactions become important are out of scope. Again, further validation and model improvement is needed. Finally, for supercritical water as working fluid, ATHLET has basic modeling capabilities, including transition between supercritical and subcritical states, but cannot reliably predict deteriorated heat transfer near the pseudocritical line due to a lack of sufficiently accurate correlations available for this phenomenon so far. Moreover, the validation base of ATHLET needs to be extended for such designs to identify further necessary improvements.

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12.2 COntainment COde SYStem thermal-hydraulic module THY The thermal-hydraulic computer code COCOSYS is being developed by the GRS for the analysis of containment behavior during AOOs, DBAs, DECs, and SAs in LWRs. COCOSYS consists of three main modules, see Fig. 12.8: • THY for containment thermal hydraulics, • AFP for aerosol and fission product behavior, and • CCI for corium
concrete interaction. COCOSYS can be coupled to ATHLET/ATHLET-CD for integral simulations of plant behavior. In this chapter the capabilities of the THY module of COCOSYS for AOO and DBA are briefly summarized. More information on COCOSYS and AC2 can be found in the respective section in the chapter of SA codes. In the following, Section 12.3.1 summarizes main steps in THY module development and Section 12.3.2 describes the modeling basis.

12.2.1 History of THY development The THY module is based on the code RALOC (RAdiolysis and LOcal gas distribution in Containments), which was developed for describing the gas behavior in the containment of LWR, especially with regard to hydrogen distributions in subcompartments of reactor containments. First descriptions of RALOC can be found in Refs. [76,77]. The code had been stepwise improved from a rather simple model to a sophisticated containment system code, which could be applied to various types of containments. In the late 1990s RALOC together with a few GRS codes for other relevant containment phenomena, which had been developed separately, were integrated into a first version of the COCOSYS [78]. For the further history of COCOSYS, see Chapter 15 on AC2 as a severe accidents code. For detailed investigation of 3D effects in subcooled containment water pools, COCOSYS can be coupled to the special coarse-grid CFD code CoPool developed by the Fraunhofer Institute for Industrial Mathematics ITWM. FIGURE 12.8 and coupling. COde SYStem.

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COCOSYS code structure COCOSYS, COntainment

12.2 COntainment COde SYStem thermal-hydraulic module THY

299

12.2.2 COntainment COde SYStem THY modeling basis The THY module applies a lumped-parameter approach for the discretization of containment compartments (Fig. 12.9). COCOSYS simulates energy and mass flow in buildings based on a network of CVs or zones interconnected with junctions. These junctions can represent real openings between rooms (CVs) or so-called virtual junctions between CVs subdividing a real physical volume. Stagnation gas properties are calculated in the zones and these (scalar) properties are used to calculate the mass flux inside junctions between zones. The simulation technique described next is a reasonable simplification for the prediction of low-speed gas flows. 12.2.2.1 Basic thermal-hydraulic equations The main THY zone models are an equilibrium and a nonequilibrium model, complemented by special models, for example, for pressure suppression systems. The nonequilibrium zone model is recommended, where the zone is subdivided into two parts: the atmosphere part, in which NC gases, liquid droplets (fog), and steam are assumed to be mixed homogeneously, and a sump part (if existing) specified by its own temperature and water mass (Fig. 12.10). At the water surface between both parts heat exchange by convection and condensation (or evaporation/boiling) is possible. For the equilibrium model the following equation is solved for each zone: m X X k51

j

Gk;j hk;j 1

X

q_ ex 5

m  X d k51

dt

ðMk hk Þ 2 Vk

 d pk ; dt

with k as index over all fluids (NC, steam, water), j as index over all junctions, G as mass flows in junctions, h as specific enthalpies (taken from the donor zone), and q_ ex as heat FIGURE 12.9 Network of zones and junctions based on discretized containment geometry.

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FIGURE 12.10

Principle concept of the nonequilibrium zone model.

flows from and to structures or sources. The right-hand side derivatives are computed analytically assuming saturation or superheating conditions. For the nonequilibrium model a separate equation for liquid water is added and the right-hand side derivatives are also calculated analytically: X

X

d d ðMW hW Þ 2 VW pW dt dt j Constitutive equations (e.g., for condensation/evaporation and heat transfer) provide the necessary closure relations. GW;j hW;j 1

q_ W;ex 5

12.2.2.2 Junction models In THY the gaseous and fluid flow is handled separately. Only the fog calculated by nonequilibrium zone models or air-carried water in equilibrium zone models is also transported by atmospheric junctions. No slip of water droplets (fog) is considered. THY provides models for standard atmospheric junctions, for which incompressible flows or (compressible) orifice flows can be specified. In addition, THY has special junction models for valves, rupture discs, flaps, etc. For the simulation of the liquid flow from one zone to another one several drainage junction models are available, including special models to simulate pump systems. A new junction type was implemented into the latest COCOSYS version to handle a combined flow of water and air between two connected zones. This is needed for the simulation of connected zones being completely filled by water. The basic atmospheric junction flow model is the transient momentum equation, based on conservation of kinetic energy. Assuming an incompressible flow through the junction j with a given cross section Aj and length lj (see Fig. 12.9), the resulting equation for the _ j of mass flow through that junction is derivative G !     ζj A j pjs 2 pje 1 gρΔzj 2 Gj Gj  G_ j 5 lj 2ρA2j where pjs is the pressure in the donor zone, and pje in the end zone of the junction. The term gρΔzj describes weight of the fluid column with Δzj as height difference between the

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start point and the end point of the junction j. The third term accounts for the pressure loss where the pressure loss coefficient ζ j consists of two parts: ζ j 5 ζ major 1 ζ minor The term ζ major is due to viscous effects and computed according to 8 64 lj > > > ; Re # 2300 ðlaminar flowÞ > < Re DH lj major ζ 5 fD 5 64 lj DH > > > ; Re . 2300 ðturbulent flowÞ > : 2300 DH The form losses described by ζ minor are due to changes in geometry. Values of this parameter for specific geometries can be found in engineering handbooks and are a user input value. 12.2.2.3 Fluid properties THY comes with its own properties package. Fluid properties for air, steam, liquid water, O2, N2, H2, CO, CO2, and He are calculated using approximating functions with reasonable accuracy for pressures up to 1 MPa and temperatures below 1200 K. Above 1200 K, different functions are used that take dissociation processes into account. Finally, derivations of most material properties are also performed analytically using suitable approximations, some liquid water and saturation properties and numerically evaluated. 12.2.2.4 Heat conduction, heat transfer, and interfacial heat transfer The walls, floors, and ceilings of the considered building and other components are represented by heat structure objects. For these the one-dimensional heat equation is solved, and specific correlations can be selected to simulate surface heat transfer. Plate-type as well as cylinder-type structures can be simulated. The initial temperature profile and the boundary conditions to the zones can be directly defined by the user. For heat conduction, COCOSYS uses a variant of ATHLET’s HECU module (Section 12.2.3.3). Interfacial heat and mass transfer models consider the related processes at surfaces (structures, water films, and water pools). For free and forced convection heat transfer, THY computes Nusselt numbers using the Churchill correlation for free convection with heat flow to the area above, and forced convection over a horizontal plate using the Pohlhausen correlation and the Gnielienski correlation [79]. Both contributions are combined using Churchill’s mixed convection approach for cocurrent flows [79]. The convection models need user-supplied, characteristic lengths for heat transfer surfaces, and THY then uses free and forced convection correlations for the different configurations as found, for example, in Ref. [79]. For steam condensation at cold structures, several different film condensation models are implemented. The basic approach follows Stefan’s law considering heat transfer

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through a water film, which is important especially for high steam concentrations (near _ cond obtained is 100%). The total condensation mass flux m    p 2 psat Tf p 1 _ cond 5 β m ln 2 p 2 psteam Rsteam T 1 2 n0 with the zone atmospheric pressure and the steam partial pressure p and psteam , film surface temperature Tf , the specific gas constant of steam Rsteam , the average temperature in
the thermal boundary layer T above the film surface, and the fog droplet density n0 . The coefficient β and the resulting HTC hcond due to condensation are determined via an analogy between dry heat transfer and wet heat transfer. The actual condensation of steam _ steam 5 ð1 2 n0 Þm _ cond and the volume condensation rate into the film is then calculated by m _ fog 5 n0 m _ cond . (fog formation rate) is the complement m Another model combines convection and condensation to further improve the code performance. In addition, two models are included for comparison taken from the WAVCO code [80]. Regarding radiation, one model describes structure to gas heat transfer and one In addition structure to structure heat transfer. Absorption of radiation heat by the gas is assumed to be significant for containment behavior, different to the conditions in the reactor circuit simulated by ATHLET. 12.2.2.5 Additional models The THY module allows simulating the distribution of gaseous species in the containment. For combustible gases, COCOSYS provides special combustion and recombination models. These models become relevant for SA analyses. 12.2.2.6 Numerical approach THY uses the integration package FEBE/FTRIX as does ATHLET, see Section 12.2.3.6, although with different adaptations and (yet) without the NuT library. For the HECU module, heat structures are usually also solved via the FEBE, with explicit or implicit coupling between structures and fluids. In addition, the package FEBE_HECU, which is a specially reduced version restricted to tridiagonal Jacobian matrices, can be used. This means that each node is coupled with maximum two other nodes (e.g., a node or layer in a 1D structure).

12.2.3 COntainment COde SYStem validation To keep the model basis at the state-of-the-art in science and technology continuous development parallel to thoroughly validating the code is required. The COCOSYS validation matrix covers all modules of COCOSYS and is described in the accompanying user manual [81]. Furthermore, prior to each release a suite of regression tests is performed and results are presented as part of the program documentation [81] too. COCOSYS is validated on a wide spectrum of tests performed in German or international test facilities (see Table 12.2). The tests performed in the former Battelle Model Containment and the former Heiß-Dampf-Reaktor as well as the ongoing tests in the THAI facility forms

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12.2 COntainment COde SYStem thermal-hydraulic module THY

TABLE 12.2 [77].

303

Summary of experiments used for validation of the THY module in COntainment COde SYStem

Phenomenon

Facility

Experiment

Thermal hydraulics

BMC

Rx4, C13, D3, D6, D17, F2, VANAM M3

HDR

T31.3, T31.5, E11.2, E11.4

THAI

TH-1, TH-2, TH-7, TH-9, TH-10, TH-13 (ISP-47), TH-14, TH-15, TH-17, TH-23, TH-27, TH-29, HM-1, HM-2

TOSQAN/ MISTRA

ISP-47 step 1 tests, MICOCO

PANDA

T9, T9bis, T17

BMC

PACOS P 3 1

HDR

E11.1

MISTRA

MASP0, MASP1, MASP2

PANDA

BC3, BC4, PC1, ISP-42 tests, A, D, E, and F

BC-V213

LB LOCA test 1, SLB-G02

GKSS

M1

MARVIKEN

M19, M24

THAI

WH-20

BMC

HYJET Jx2

Spray systems

Passive systems/ hydrodynamic

Jets and plumes

THAI

TH-7, TH-10, TH-13, HM-2

PANDA

OECD-SETH T9, T9bis, T17

BMC, Battelle Model Containment; HDR, Heiß-Dampf-Reaktor; THAI, Thermal hydraulics, Hydrogen, Aerosols and Iodine; TOSQAN, Test station for simulation and qualification in airborne conditions; MISTRA, Mitigation and stratification facility; PANDA, Passive Nachzerfallswa¨rmeabfuhr und Druck-Abbau Testanlage; BC: Bubble condenser test facility; GKSS, Gesellschaft fu¨r Kernenergieverwertung in Schiffbau und Schiffahrt mbH.

the backbone of the COCOSYS validation concerning thermal-hydraulic phenomena. In the beginning most of the tests were calculated knowing the experimental results already prior to the calculation, whereas nowadays a more ambitious approach is often followed where the calculations are performed without any knowledge about the experimental results. These socalled blind benchmarks prove to be the biggest challenge in qualifying the code. In such calculations both user experience and the quality of the model basis inside the code are checked without prior knowledge of the results. As one striking example, the calculation of the TH-27 experiment performed in the THAI facility operated by Becker Technologies GmbH is presented hereafter [82]. TH-27 was performed as the commissioning test for the extended, two-vessel THAI 1 test facility with a total free volume of almost 80 m3 . The experiment addresses the phenomena of gas

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mixing, steam condensation, stratification behavior of light gases, etc. under conditions resembling typical accident conditions, thus providing detailed insight into such phenomena and their interaction. The test is characterized by several phases where steam or helium (as a replacement for hydrogen) is injected and the walls of the vessels are heated up or cooled down to adjust defined thermal-hydraulic boundary conditions. The test lasted for almost 60 hours. The challenge of the double-blind benchmark was to generate an adequate model (e.g., numerical grid nodalization) and simulate a long-lasting transient without previous model calibration based on knowledge gained from earlier tests being performed in the facility. The experimental measurements allow quantifying transport mechanisms and flow conditions between the two vessels as well as inhomogeneities of the gas mixtures in the vessels. Already the double-blind calculation (green line Fig. 12.11) predicts the experiment (black line) remarkably well as shown for the example of pressure behavior in the facility over 60 hours. Only minor adaptations of the input data due to postexperimental analyses of the data were found to be reasonable leading to a slight improving for the open calculations (red line). All in all, COCOSYS demonstrates its high prediction quality.

3 Experiment COCOSYS open calculation COCOSYS blind calculation

Pressure p (bar)

2.5

2

1.5

1 0

10

20

30

Time t (h) FIGURE 12.11

THAI TH-27 pressure history.

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40

50

60

12.4 Outlook and summary

305

12.2.4 Scope of application and limits The scope of applications for COCOSYS THY and its limits are detailed in the respective section in chapter 15 of this book.

12.3 Quality assurance measures All codes in AC2 are subject to a strict QA with internal procedures leaning on definitions in and standards of ISO 9001 as well as of the IAEA Safety Standards (SSG-2) for deterministic safety analysis for nuclear power plants [83]. Specific QA plans are maintained, and code development and code validation activities are properly separated. For the development process a version control system is used. All bug fixes, changes, or development of new features and models are first done and verified and tested in separate development branches. Only after successful review and tests, changes are transferred to the main development branch or release branches. Prior to release, a set of regressions tests needs to be passed. Changes to the source code in the main branches are automatically checked by a continuous integration system [84]. This system compiles the source code and builds all executables. It then calls unit tests to verify single program routines and functions. Then, different sets of single effect and integral effect tests are triggered on different time scales and results are automatically compared to results of prior versions considered acceptable. In the case of failures or if acceptance bounds for results are exceeded, developers are alerted and can check for errors. A further essential element is the continuous validation of AC2. Each code (ATHLET, ATHLET-CD, and COCOSYS) is validated stand-alone and coupled with each other against a set of validation calculations, which should cover all models implemented in this code package. New experiments from various national and international test facilities are calculated and compared to the measurement values, where blind tests are prioritized to get an impression on the predictiveness of the code, and previous calculations are repeated by a separate working group. In addition, external partners are involved in the systematic validation of AC2 codes. This is complemented by user feedback, both from internal and external code users. User meetings for AC2 provide a forum for further exchange. Findings from validation and user feedback flow back into the AC2 development. These measures ensure the AC2 codes continue to be of the highest quality.

12.4 Outlook and summary We have briefly presented the main features of the thermal-hydraulic codes ATHLET for simulation of reactor system behavior and the THY module of COCOSYS for simulation of containment thermal hydraulics. Within AC2 , both codes can be coupled for integral analyses of plant behavior. ATHLET and COCOSYS can be reliably applied to LWR designs, including WWER, and have additional capabilities for gas-cooled reactors. For liquid metal and molten salt reactors, ATHLET has some basic capabilities.

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Both codes are actively developed and validated by GRS and its partners. The current main development lines strive at improving AC2 for the simulation of advanced LWR and particularly light-water-cooled SMRs with a focus on models and validation for passive safety systems with small driving forces, including heat pipes. The water properties of ATHLET are currently being updated in collaboration with Hochschule Zittau
Go¨rlitz to look-up tables of the IAPWS-97 formulation and will be applied for COCOSYS as well. In addition, coupling interfaces to CFD and computational structure mechanics codes (e.g., OpenFOAM) are being improved, where two-phase mass flow at the coupling interface is seen as a major challenge. Finally, some limited developments will be done on reactors with alternative working fluids (e.g., Gen-IV reactors), where concepts such as the Belgian MYRRHA with relevance to Germany will be prioritized.

Nomenclature A cp DH G h m; M n p _q R Re t T u; v; w V x X α β E λ μ ν ψ Ψ ρ ξ ζ

area (m2 ) isobaric-specific heat capacity [J/(kg K)] hydraulic diameter (m) mass flow (kg/s) specific enthalpy (J/kg) mass (kg) neutron flux (1/s), fog fraction ( 2 ) pressure (Pa) heat flow (W) heat resistance (K/W), reactivity (
) Reynolds number (
) time (s) temperature ( C) velocity (m/s) volume (m3 ) mass fraction (
), enthalpy quality (
) 2-phase parameter void fraction (
) delayed neutron fraction (
), fraction of dry to wet heat transfer ( 2 ) kinetic energy dissipation rate [J/(kg s)] specific heat conductivity [W/(m K)] dynamic viscosity (Pa s) kinematic viscosity (m2 /s) mass transfer rate (kg/m3 ) mass transfer (kg) density (kg/m3 ) form loss coefficient (1/m4) form loss coefficient (
)

Subscripts, superscripts cond e ex k

condensation recipient Zone external sources phase index

IV. Thermal-Hydrualic codes

References

L; l V; v Crit s Sat Vap W

307

liquid vapor critical donor zone saturation vaporization liquid water

Abbreviations AOO CV DBA DEC HCO HTC LOCA NC ODE SA TFO WWER

anticipated operational occurrence control volume design basis accident design extension condition heat conduction object heat transfer coefficient loss-of-coolant accident noncondensable (gas) ordinary differential equation severe accident thermofluid object water
water energetic reactor

References [1] A. Wielenberg, L. Lovasz, P. Pandazis, A. Papukchiev, L. Tiborcz, P. Scho¨ffel, et al., Recent improvements in the system code package AC2 2019 for the safety analysis of nuclear reactors, Nucl. Eng. Des. 354 (2019). Available from: https://doi.org/10.1016/j.nucengdes.2019.110211. [2] G. Lerchl, H. Austregesilo, A. Langenfeld, P. Scho¨ffel, D. von der Cron, F. Weyermann, ATHLET 3.2 User’s Manual GRS-P-1, vol. 1 Rev. 8, GRS, 2019b. [3] A. Forge, Comparison of Thermal-Hydraulic Safety Codes for PWR Systems, Graham & Trotman, London, 1988. 402 pp. [4] Gesellschaft fu¨r Reaktorsicherheit, Jahresbericht 1979, GRS, 1979. [5] M.J. Burwell, D. Enix, F. Steinhoff, K. Wolfert, DRUFAN-01/MOD1: User’s Manual, GRS-A-395, GRS, 1979. [6] G. Lerchl, W. Pointner, F. Steinhoff, DRUFAN-02: Stand der Entwicklung und Verifikation, GRS, 1985. [7] F. Steinhoff, Phasenseparation und Gemischspiegeldynamik bei instationa¨ren Zweiphasenstro¨mungen, Zugl.: Mu¨nchen, Techn. Univ., Diss., 1989, GRS-73, Ko¨ln, 1989, 147 pp. [8] R. Meißner, Einsatz des DWR-Anlagenmodells ALMOD zur Analyse spezieller Transienten, GRS-A-79, GRS, 1977. [9] Gesellschaft fu¨r Reaktorsicherheit, Jahresbericht 1988, GRS, 1988. [10] C. Bals, Aufteilung des HECU-Gesamtwa¨rmestroms auf die Einzelphasen Wasser und Dampf fu¨r die 2-Energie-Gleichungsoptionen von ATHLET, Technical Notice TN-MIS-91-1, GRS, 1991. [11] W. Pointner, Nachrechnung des ROSA III Versuchs Run 916 mit den Rechenprogrammen ATHLET und FLUT, GRS-A-1624, GRS, 1989. [12] V. Teschendorff, H. Austregesilo, C. Bals, G. Lerchl, W. Luther, P. Romstedt, et al., ATHLET-Entwicklung: Abschlußbericht, GRS, 1996. [13] A. Petry, A. Moskalov, Development of a Radiation Heat Transfer Model and its Coupling with the ATHLET-Code, Technical Note TN-PEA-94-2, GRS, 1994. [14] H. Austregesilo, Ein Vorschlag zur Modellierung des Borontransportes in ATHLET, Technical Notice TN-AUH-94-1, GRS, 1994. [15] V. Teschendorff, H. Austregesilo, G. Lerchl, C. Bals, A. Hora, A. Hoeld, et al., ATHLET-Weiterentwicklung, Abschlußbericht RS 828A, GRS 1997.

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7/26/2018, The American Society of Mechanical Engineers, New York, 2018.

IV. Thermal-Hydrualic codes

C H A P T E R

13 Development and application of System Analysis Module from the user’s view Yukun Zhou1,2, Alejandro Perez2 and Jun Wang2 1

Xi’an Jiaotong University, Xi’an, P.R. China 2Department of Engineering Physics, University of Wisconsin-Madison, Madison, WI, United States

13.1 Introduction Over the past five decades, numerous efforts have been devoted to developing code for safety analysis of nuclear reactor systems. Some well-known software, such as RELAP5 and CATHARE, has been widely used in the design and optimization of commercial nuclear power plants [1,2]. However, due to limitations on computing power, simulation method, and solution algorithm, only low-order numerical scheme and poor accuracy were revealed in the analysis of the reactor transient behavior. Yet, with new advancements in computer science and software development, advanced codes have been proposed with comprehensive abilities to model the thermal-hydraulic characteristic of two-phase flow, such as RELAP-7 and CATHARE-3 [3,4]. Under the Nuclear Energy Advanced Modeling and Simulation program of the US government, System Analysis Module (SAM) is developed by Argonne National Laboratory (ANL) to outline system-level modeling and simulation for advanced reactors [5
8]. This code employs the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework and its underlying meshing and finite element library (libMesh) [9,10]. Meanwhile, the linear and nonlinear Portable, Extensible Toolkit for Scientific Computation (PETSc) solvers are also applied to achieve high-fidelity calculations [11]. As a result, the program environment, numerical method, and physical models are enhanced to provide better experience and access for its users. Compared with the previous system analysis code for light-water reactor, SAM can be employed to predict the transient characteristics of sodium fast reactor (SFR), lead-cooled fast reactor, fluoride salt
cooled high-temperature

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00013-9

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reactor (FHR), and molten salt reactor, in which single-phase, low-pressure, hightemperature, and low Prandtl number fluids are used as coolants. During the development of SAM code, verification and examples have been widely performed based on the early experimental data and code-to-code comparisons [12,13]. All the results illustrate that SAM is capable of predicting the fluid dynamics and heat transfer responses within different advanced reactor systems. In addition, the coupling strategy between SAM and other external codes has also been well verified. Continuous effort is being made on the development of this modern system analysis tool that can support the design, operation, and licensing of advanced reactors in the future.

13.2 Software development Compared to the previous analysis tools, SAM is a modern system-level software with advanced program environment, numerical method, and physical models [14]. It provides the fast-running, high-fidelity, and whole-plant transient analysis capabilities for generation IV reactor systems. Based on the MOOSE framework and advanced software libraries, SAM absorbs a large amount of experience from modern code development practices. Objectoriented C11, finite element method (FEM), and linear/nonlinear solvers are utilized to fulfill the code requirement. High-order spatial discretization schemes, fully implicit and high-order time integration schemes, and advanced solution methods, that is, the Jacobianfree Newton
Krylov (JFNK) method, are incorporated to develop accurate and computationally efficient models in this code. In addition, the flexible interface and coupling SAM with other tools provide more potential for users to solve multiscale and multiphysics problems.

13.2.1 Structure As shown in Fig. 13.1, the structure of SAM software mainly consists of four parts. The fundamental physics models are used to describe the fluid flow and heat transfer behavior of single-phase coolant. Some associated physics modeling in the components is encapsulated as component classes to provide friendly user interactions. A similar FIGURE 13.1 Software structure of SAM [5]. SAM, System Analysis Module.

IV. Thermal-hydraulic codes

13.2 Software development

315

component-based modeling strategy can be found in RELAP-7, where the thermal-hydraulic analysis is conducted within the MOOSE framework. Moreover, a flexible coupling interface has also been developed in SAM to combine with the other higher fidelity or conventional simulation tools. Thus multiscale and multiphysics modeling can be achieved to take into account the three-dimensional (3D) effects on the evaluation of different transients or accident scenarios. The coupling capabilities between SAM and STAR-CCM 1 , SAS4A/ SASSYS-1 have been demonstrated in the simulations of the advanced burner test reactor the protected loss of flow transient. Integrations with the other advanced tools, such as Nek5000, PROTEUS, and BISON, are currently under development.

13.2.2 Models 13.2.2.1 Fluid dynamics One-dimensional (1D), single-phase incompressible but thermally expandable flow model is applied in SAM to describe the fluid dynamics. The mass, momentum, and energy equations are then closed by the state equations of fluid. After simplification and combination the conservative and nonconservative forms of governing equations are given in Eqs. (13.1) and (13.2), respectively. These equations are accordingly solved by the primitive variable
based FEM. @ρ @ðρuÞ 1 50 @t @z @ðρuÞ @ðρuu 1 pÞ f ρujuj 1 52ρ g2 @t @z De 2

(13.1)

@ðρHÞ @ðρuHÞ 1 5 qw @t @z ρ 5 ρðp; TÞ where t is the time; z is the axial coordinate in flow direction; ρ is the coolant density; u is the velocity; g is the acceleration due to gravity; p is the pressure; f is the friction coefficient; H is the enthalpy; De is the equivalent hydraulic diameter; k is the fluid thermal conductivity; and qw is the volumetric internal heat source. @ρ @ðρuÞ 1 50 @t @z @u @u @p f ρujuj 1 ρu 5 2 ρg 2 @t @z @z De 2 @T @T 1 ρCp u 5 qw ρCp @t @z

ρ

(13.2)

ρ 5 ρðp; TÞ where Cp is the specific heat. Furthermore, a 3D module and subchannel module are developed to simulate the thermal-hydraulic phenomena in the upper plenum, cold pool, and fuel assembly of SFR

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[15]. Expanding the velocity vector and the momentum equation in three coordinates and simplifying the energy conservation equation, the set of governing equations can be written in the conservative form (Eq. 13.3) or in the nonconservative form (Eq. 13.4). @ρ @ðρuÞ @ðρvÞ @ðρwÞ 1 1 1 50 @t @x @y @z @ρu @ðρuuÞ @ðρuvÞ @ðρuwÞ @p , 1 1 1 52 1 r τx @t @x @y @z @x



@ρv @ðρvuÞ @ðρvvÞ @ðρvwÞ @p 1 1 1 52 1r @t @x @y @z @y

 τ,y

@ρw @ðρwuÞ @ðρwvÞ @ðρwwÞ @p 1 1 1 52 1r @t @x @y @z @z



, τz

(13.3) 1 ρg

@ρh @ðρuhÞ @ðρvhÞ @ðρwhÞ 1 1 1 5 rðkeffrTÞ 1 qw v @t @x @y @z ρ 5 ρðp; TÞ where t is the time; x, y, z are the coordinates; ρ is the coolant density; u, v, w are the velocity vectors; g is the acceleration due to gravity; p is the pressure; T is the temperature; h is , the enthalpy; τx is the shear stress in x-axis direction and dependent on the velocity gradients and fluid properties, for Newtonian fluid, τ ii 5 2μð@vi =@xi Þ 2 ð2=3Þμr , v , and τ ij 5 τ ji 5 μðð@vi =@xj Þ 1 ð@vj =@xi ÞÞ; keff is the effective thermal conductivity, and keff 5 k 1 α, which accounts for both normal thermal conductivity and additional diffusivity due to turbulence and the use of coarse mesh; and qwv is the volumetric heat. @ρ @ðρuÞ @ðρvÞ @ðρwÞ 1 1 1 50 @t @x @y @z @u @u @u @u @p , 1 ρu 1 ρv 1 ρw 52 1 r τx ρ @t @x @y @z @x @v @v @v @v @p , 1 r τy ρ 1 ρu 1 ρv 1 ρw 5 2 @t @x @y @z @y @w @w @w @w @p , 1 ρu 1 ρv 1 ρw 52 1 r τ z 1 pg ρ @t @x @y @z @z





(13.4)



ρ

@h @h @h @h 1 ρu 1 ρv 1 ρw 5 rðkeffrTÞ 1 qw v @t @x @y @z

ρ 5 ρðp; TÞ

13.2.2.2 Heat transfer The heat structure model, describing the heat conduction inside solid and heat transfer between solid and fluid, can be simplified to 1D or 2D heat conduction problems in Cartesian or cylindrical coordinates. Temperature-dependent thermal conductivities and volumetric heat capacities are provided in tabular or functional forms. The heat transfer model predicts the

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temperature distributions in solid components (such as fuel pins or plates, heat exchanger tubes, pipes, and vessel walls) and calculates the heat flux conditions for fluid components. The governing equation is expressed in the form of Eq. (13.5). Besides, the convective and radiative heat transfer behavior at the solid surface is also considered in the SAM code. ρCp

@ðTÞ 2 rðkrTÞ 2 Qw 5 0 @t

(13.5)

where k is the solid thermal conductivity and Qw is the volumetric internal heat source in the solid. 13.2.2.3 Closure models The state equations of fluid are essential for the solution of governing equations. The fluid properties, depending on temperature and pressure, have been implemented in the SAM fluid equation of state model, as shown in Eq. (13.6). Meanwhile, the properties of sodium, air, FLiBe, and FLiNaK are directly offered by the code. ρ 5 ρðp; TÞ β 5 βðp; TÞ Cp k 5 kðp; TÞ Pr 5 μk

μ 5 μðp; TÞ (13.6)

H 5 Hðp; TÞ Cp 5 Cp ðp; TÞ Cv 5 Cv ðp; TÞ where ρ is the density; β is the thermal expansion coefficient; μ is the dynamic viscosity; Pr is the Prandtl number; H is the enthalpy; Cp is the specific heat at constant pressure; and Cv is the specific heat at constant volume. After reviewing the closure models used in many existing system codes and the available correlations in the literature, a subset of empirical correlations for convective heat transfer and wall friction coefficient has been implemented in SAM as available user options. Figs. 13.2 and 13.3 display the modeling options for convective heat transfer and wall friction factors, respectively. 13.2.2.4 Mass transport and reactor kinetics The mass transport model simulates the sources and transport of particles under extensive situations, such as tritium transport, delayed neutron precursor drift, and radioactive isotope transport for molten salt fueled or cooled systems. A general passive scalar transport model has been implemented in SAM to track any number of species carried by the fluid flow. Moreover, the point kinetics model and reactivity feedback model have also been developed and integrated to capture the characteristics of fuel axial expansion, core radial expansion, fuel Doppler, and coolant density reactivity [16]. These models have also been verified by several external tests. 13.2.2.5 Numerical schemes Since SAM is developed under the framework of MOOSE, a continuous Galerkin FEM is implemented to conduct the weak forms of governing equations. It uses an increasingly popular solution JFNK method to solve the equation system. The multilevel approach with outer Newton’s iterations (nonlinear solver) and inner Krylov subspace methods

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FIGURE 13.2

SAM modeling options for convective heat transfer [6]. SAM, System Analysis Module.

FIGURE 13.3

SAM modeling options for wall friction coefficient [6]. SAM, System Analysis Module.

(linear solver) are successfully employed in SAM to solve large nonlinear problems. One feature of JFNK is that all the unknowns are solved simultaneously in a fully coupled fashion. This solution scheme avoids the errors from operator splitting and is especially suitable for conjugate heat transfer problems in which heat conduction of solid is tightly coupled with fluid flow.

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13.2.3 Current capabilities The major modeling features of SAM can be summarized as follows: 1. 1D pipe networks represent the general fluid systems (modeling the coolant loops of reactors). 2. Flexible integration of fluid and solid components, model the complex and generic engineering system. 3. Pseudo-3D capability by physically coupling the 1D or 2D components in a 3D layout (modeling the heat transfer behavior of full core in SFR). 4. Safety analysis of pool-type reactor (tracking liquid volume level, analyzing cover gas dynamics, heat transfer between 0D pools, and fluid heat conduction). 5. Multidimensional flow model for thermal mixing and stratification phenomena. 6. General mass transport capability (tracking species carried by the fluid flow). 7. Coupling with different external codes (STAR-CCM 1 , SAS4A/SASSYS-1, Nek5000, and BISON).

13.3 Verification and demonstration 13.3.1 Spatial and temporal discretization To solve the 1D and single-phase transient flow model, high-order spatial and temporal discretization schemes have been adopted in SAM to assure the efficiency and accuracy of the solution method. The effects of different spatial and temporal discretization schemes are processed by modeling a core channel with uniform power distribution inside the fuel pin, as shown in Fig. 13.4. The fuel, gap, and cladding are distinguished by elements in different colors. Each element between two nodes represents a first-order element, and it becomes a second-order element when an extra node is added to the node center. FIGURE 13.4 Schematic of the spatial discretization of the core channel problem [7].

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Constant temperature and flow rate are applied in the inlet of the channel, and fixed material properties are assumed during the calculation. It can be seen from Fig. 13.5 that second-order finite elements would significantly increase the efficiency and accuracy of the simulation, even though only two radial elements were used for the fuel pellet region. Another test problem (a solid cylinder with homogenous heat inside and fixed surface temperature) also demonstrated the efficiency of using second-order finite elements. As shown in Fig. 13.6, the radial temperature distributions from different spatial discretization are compared. Evident errors can be found in the cases with first-order finite elements, while no errors are observed in the cases using second-order finite elements. Moreover, the numerical convergence rates of the high-order spatial and temporal discretization schemes have been verified by tests on natural convection cooling of a used fuel assembly. The fuel assembly, which is located in a large sodium pool, with the decay heat level is considered as 0.4% of the peak power. Equal pressure boundary conditions are assumed at the inside and outside of the top of the fuel assembly. Fig. 13.7 presents

FIGURE 13.5

Errors of fuel and coolant temperature predictions [7].

FIGURE 13.6

Temperature distributions of a heated pin rod [7].

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FIGURE 13.7 Spatial convergence for natural circulation flow rates and transient responses of PCT [7]. PCT, Peak cladding temperature.

the errors using different spatial discretization to predict the natural circulation flow rates and the transient responses of the peak cladding temperature. These strict verifications demonstrate that SAM code can be utilized to figure out various flow issues with high accuracy, efficiency, and minimal numerical diffusions.

13.3.2 Three-dimensional finite element flow model A 3D finite element flow model of SAM is developed to analyze the thermal mixing and stratification phenomenon in large enclosures of reactor systems [15]. This 3D flow model is based on solving the primitive variables in the conservative form of the governing equations. It should be noted that the streamline-upwind/Petrov
Galerkin and pressure-stabilizing/Petrov
Galerkin schemes are implemented to enhance the numerical stability of finite element analysis for incompressible flows. Therefore combined with the use of the JFNK solution method and high-order discretization schemes, this 3D fluid model is desirable for both efficient and accurate multidimensional flow simulations. Three CFD verification and validation (V&V) efforts have been performed to evaluate the laminar flow modeling capability of SAM. The demonstration includes the flow problem in a lid-driven cavity, the laminar flow in a channel of parallel plates, and the natural convection inside a cavity. The consistency between the analytical solutions and experimental data indicates that SAM can provide efficient and accurate simulation for the reactor safety analyses during transients by embedding this 3D flow model, as shown in Figs. 13.8
13.10. Continued developments will be focused on the closure model developments to capture the effects of turbulence and the use of coarse mesh in momentum and energy transport, and on additional code V&V tests.

13.3.3 Pseudo-three-dimensional full-core conjugate heat transfer The pseudo-3D full-core conjugate heat transfer modeling capability of SAM is outlined by a hexagon lattice with seven identical fuel assemblies, as shown in Fig. 13.11. In this

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FIGURE 13.8

Flow problem in a lid-driven cavity [15].

FIGURE 13.9

Flow in a channel of parallel plates [15].

FIGURE 13.10

Natural convection in a square cavity [15].

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FIGURE 13.11

Single-channel system SAM model and CFD model [17]. SAM, System Analysis Module.

FIGURE 13.12

Comparison of average axial temperature and wall temperature distributions [17].

323

model the highest power peaking factor of 1.5 is utilized in the center assembly, while the lowest power peaking factor of 0.5 is employed in assembly 6. The other assemblies have the same power peaking factor of 1. Moreover, uniform power distribution and the same inlet flow rate are assumed within each assembly. Both single-channel and two-region twochannel approaches are applied to confirm the code performance in predicting the duct wall temperature. Furthermore, code-to-code benchmark exercises were performed by the Reynolds Averaged Navier
Stokes-based CFD tool using the same model. The comparison clearly showed that the single-channel model would significantly overestimate the duct wall temperatures, while the two-region two-channel model agreed well with the CFD simulation results in the high-temperature gradients, high power, and high flow conditions, as shown in Fig. 13.12. The demonstration implied that SAM could efficiently and accurately model the interior assembly heat transfer characteristics and the duct wall temperatures in a 3D core lattice layout.

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13.3.4 EBR-II benchmark The experiments based on the EBR-II plant were conducted by ANL to validate the feasibility of passive safety in LMR. Among these efforts, unprotected loss of forced cooling flow test (SHRT-45R) and unprotected loss of heat rejection test (BOP-302R) were selected as benchmark tests to assure the performance and validity of SAM code. This demonstration mainly focused on the transient thermal-hydraulic responses of the primary coolant system throughout the accidents. The reactor power history and pump speed history were specified as input parameters, while the intermediate heat exchanger intermediate side inlet temperatures and mass flow rates were provided as boundary conditions. The core model and primary system model employed in SAM simulation are illustrated in Figs. 13.13 and 13.14, respectively. As shown in Figs. 13.15 and 13.16, the results by both tests show that there is a strong agreement between SAM simulation and EBR-II benchmark. For the SHRT-45R test the main transient responses of the primary loop flow, such as the Z-pipe inlet temperature and the intermediate heat exchanger primary inlet temperature, were captured by SAM. According to the BOP-302R test, the high- and low-pressure inlet plenum temperatures of SAM predictions were consistent with the test data under initial heat-up rates and the later pseudo-equilibrium states, implying that the thermal stratification phenomenon in the cold pool can be described by the simple two-volume cold pool model. All these results demonstrate the SAM performance of predicting the thermal-hydraulic responses in the primary coolant loop during SFR loss of flow and loss of heat sink transients.

FIGURE 13.13

EBR-II core model of SAM [7]. SAM, System Analysis Module.

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325 FIGURE 13.14 Primary coolant system model of SAM [7]. SAM, System Analysis Module.

FIGURE 13.15

Z-pipe and the intermediate heat exchanger primary inlet temperatures during SHRT-45R test [7].

13.3.5 Compact Integral Effects Test experiments The Compact Integral Effects Test (CIET) experimental loop is a test facility that is designed to reproduce the thermal-hydraulic response of FHRs under forced and natural circulation conditions. Three experiments of CIET include the transient heat transfer tests with power step changes under forced convection conditions, the natural circulation tests in coupled DRACS/DHX loops, and the frequency response tests in the heater, all

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FIGURE 13.16

13. Development and application of System Analysis Module from the user’s view

High- and low-pressure inlet plenum temperatures during BOP-302R test [7].

of which are selected to support the validation of SAM performance on fluid properties, pump behavior, conjugate heat transfer characteristic, and so on [18]. The SAM input model of CIET facility is displayed in Fig. 13.17. The simulation results produced strong consistency against the data of three distinctive series of experiments. For the experiment of a power step change, both temperature and mass flow prediction of SAM agree quite well with the experimental data, as plotted in Fig. 13.18. For the isolated DRACS and coupled DRACS
DHX natural circulation, the comparison between SAM, RELAP5-3D, and experimental results is shown in Fig. 13.19 with TTCHX, out of 40 C. SAM predicted results on natural circulation mass flow rates in DRACS loop and heater-DHX loop that are consistent with experimental data in all test cases. For the frequency domain test the results from SAM were very similar to the ones in the CIET experiment, both in terms of temperature magnitude and phase shift compared to the input signal, as shown in Fig. 13.20. Overall, the suitability of SAM for FHRs analysis applications is sufficiently validated by three sets of CIET experiments of distinctive characteristics. Furthermore, experimental data for loss of forced convection test are available for further validation of the SAM code.

13.3.6 Heat pipe modeling The heat pipe has been regarded as an ideal method to extract thermal power from a nuclear reactor. To model the heat transport behavior inside the heat pipe, two different models, 2D-RZ heat conduction and 3D
1D coupling, were developed in SAM code [19,20]. The vapor core of the heat pipe was simulated as a superconductor with high thermal conductivity and no heat loss was considered in the heat pipe. After the verification by a simplified thermal resistance model, these two modeling options were then exemplified by coupling the heat pipe with a prototype microreactor under both normal and offnormal conditions. Fig. 13.21 presents the temperature distributions of single- and sevencell models. These reasonable simulation results certified the capability of SAM to model the heat transport in the heat-pipe reactors.

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FIGURE 13.17

327

SAM input model for the CIET facility [18]. CIET, Compact Integral Effects Test; SAM, System

Analysis Module.

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FIGURE 13.18 Comparison between SAM results and power step-change experimental data [18]. SAM, System Analysis Module.

FIGURE 13.19 SAM and RELAP5-3D simulation results compared with CIET experimental data [18]: (A) Isolated DRACS natural circulation and (B) coupled DRACS
DHX natural circulation. 3D, Three-dimensional; CIET, Compact Integral Effects Test; SAM, System Analysis Module.

13.3.7 High-temperature gas reactor primary loop modeling The unit-cell approach and detailed ring model were applied in SAM code to simulate the primary loop of the modular high-temperature gas reactor (MHTGR) [21]. The first approach used representative geometry to approximate the fuel assembly, while the

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FIGURE 13.20

329

Fluid temperature at heater outlet of SAM results and experimental data [18]. SAM, System

Analysis Module.

FIGURE 13.21

Temperature distributions of the single- and seven-cell models [20].

second approach modeled all reactor core components (upper and lower plenum, coolant channels, heat structures, and heat exchanger and blower) as rings. Fig. 13.22 shows the different models of MHTGR primary loop. Two scenarios, including normal operating conditions and pressurized conduction cooldown (PCC) transient, were employed to perform the simulation. The results confirmed that the SAM code alongside the detailed ring model could accurately investigate the convection dominant in core heat removal during

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FIGURE 13.22 Unit-cell approach and detailed ring model of SAM for MHTGR primary loop [21]. MHTGR, Modular high-temperature gas reactor; SAM, System Analysis Module.

the normal operating conditions and conduction dominant heat removal during PCC transient. Moreover, the unit-cell approach is appropriate for convection dominant regime simulations due to its superior execution speed.

13.4 Integration and coupling For the practical engineering issues, multiscale and multiphysics analysis abilities are indispensable to evaluate different transients or accident scenarios. Through a flexible interface combined with SAM and other high-fidelity or conventional simulation tools, such as STARCCM 1 and SAS4A/SASSYS-1, data exchange and time synchronization can be achieved. The coupling strategy between SAM and those codes will be introduced in the following parts.

13.4.1 Implementation in the system code SAS4A/SASSYS-1 is a deterministic analysis tool utilized for various events or accidents of advanced liquid metal
cooled nuclear reactors. It contains a primary and intermediate system module, known as PRIMAR-4, which can represent complex arrangements of coolant system components. Since there are some limitations in data management, code structure, and user input of SAS4A/SASSYS-1, coupling with SAM effectively eliminates these shortcomings and makes the modeling process more flexible and extensible. The coupling strategy is meant to retain the full complement of core modeling capabilities

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FIGURE 13.23

331

Sequential two-way coupling scheme for a generic

time step [7].

of SAS4A/SASSYS-1 while using SAM for the primary, intermediate, and decay heat coolant systems. As shown in Fig. 13.23, a sequential two-way scheme is applied for coupling, in which each code drives its portion of the simulation and exchanges data at well-defined points. Besides, the SAS
SAM coupling interface has been verified by the Versatile Test Reactor program, with a strong agreement between the known analytical solutions and the transient behavior showed reasonable expectation [22].

13.4.2 Implementation in STARCCM 1 code Known as a widely used commercial CFD software, STARCCM 1 employs a finite volume formulation for the analysis of compressible and incompressible flow and heat transfer problems in nuclear reactor systems. The coupling strategy and the implementation of SAM alongside STAR-CCM 1 have been initially examined by a simple flow loop model under these three cases: steady state, flow transient, and temperature transient. Simulation results provided a proof-of-principle among the coupling of the two codes and have demonstrated the significance of the coupled code for 3D applications and how these effects can play an important role in the evolution of a given accident scenario. Furthermore, the multiscale coupling capability has also been demonstrated in the simulation of the advanced burner test reactor the protected loss of flow transient [23].

13.4.3 Implementation in other codes Moreover, continuous efforts have been made to achieve the coupling between SAM and Nek5000, PROTEUS, and BISON codes. Based on the spectral element method, Nek5000 supports two different formulations for the spatial and temporal discretization of the Navier
Stokes equations. It has been extensively verified and validated for several benchmark problems and has proven scalability to perform parallel computing in petascale grids. PROTEUS is a high-fidelity deterministic neutron transport code that can be applied for coupled calculations of thermal-hydraulic and structural mechanics. The coupling between PROTEUS and Nek5000 has been applied in SFR core simulations. BISON is a nuclear fuel performance code developed based on the MOOSE platform. With the ability to solve the fully coupled equations of thermal mechanics and species diffusion, the application scope of BISON ranges from fuel rods, TRISO particle fuel, and metallic rod to plate fuel. Since SAM is also developed under the MOOSE framework, the coupling between SAM and BISON is straightforward, utilizing the MOOSE MultiApp system.

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References [1] F. Barre, M. Bernard, The CATHARE code strategy and assessment, Nucl. Eng. Des. 124 (1990) 257
284. [2] G. Mesina, A history of RELAP computer codes, Nucl. Sci. Eng. 182 (2016) v
ix. [3] R.A. Berry, J.W. Peterson, H. Zhang, R.C. Martineau, H. Zhao, L. Zou, et al., Relap-7 Theory Manual, Idaho National Lab. (INL), Idaho Falls, ID, 2018. [4] P. Emonot, A. Souyri, J.L. Gandrille, F. Barre´, CATHARE-3: a new system code for thermal-hydraulics in the context of the NEPTUNE project, Nucl. Eng. Des. 241 (2011) 4476
4481. [5] R. Hu, L. Zou, G. Hu, SAM User’s Guide, Argonne National Lab (ANL), Argonne, IL, 2019, pp. Medium: ED. [6] R. Hu, SAM Theory Manual, Argonne National Lab (ANL), Argonne, IL, 2017. [7] R. Hu, T. Fanning, T. Sumner, Y. Yu, Status Report on NEAMS System Analysis Module Development, Argonne National Lab (ANL), Argonne, IL, 2015. [8] K. Bradley, NEAMS: The Nuclear Energy Advanced Modeling and Simulation Program, Argonne National Lab (ANL), Argonne, IL, 2013. [9] D. Gaston, C. Newman, G. Hansen, D. Lebrun-Grandie, MOOSE: a parallel computational framework for coupled systems of nonlinear equations, Nucl. Eng. Des. 239 (2009) 1768
1778. [10] B.S. Kirk, J.W. Peterson, R.H. Stogner, G.F. Carey, libMesh: a C11 library for parallel adaptive mesh refinement/coarsening simulations, Eng. Comput. 22 (2006) 237
254. [11] S. Abhyankar, J. Brown, E.M. Constantinescu, D. Ghosh, B.F. Smith, H. Zhang, PETSc/TS: a modern scalable ode/dae solver library, arXiv preprint arXiv 1806 (2018) 01437. [12] R. Hu, Preliminary SAM Assessment, Argonne National Lab (ANL), Argonne, IL, 2018. [13] R. Hu, Verification and Validation Plan for the SFR System Analysis Module, Argonne National Lab (ANL), Argonne, IL, 2014. [14] R. Hu, Y. Zhu, A. Kraus, Advanced Model Developments in SAM for Thermal Stratification Analysis during Reactor Transients, Argonne National Lab (ANL), Argonne, IL, 2018. [15] R. Hu, Three-dimensional flow model development for thermal mixing and stratification modeling in reactor system transients analyses, Nucl. Eng. Des. 345 (2019) 209
215. [16] G. Hu, G. Zhang, R. Hu, Reactivity Feedback Modeling in SAM, Argonne National Lab (ANL), Argonne, IL, 2019. [17] R. Hu, Y. Yu, A computationally efficient method for full-core conjugate heat transfer modeling of sodium fast reactors, Nucl. Eng. Des. 308 (2016) 182
193. [18] L. Zou, R. Hu, A. Charpentier, SAM Code Validation Using the Compact Integral Effects Test (CIET) Experimental Data, Argonne National Lab (ANL), Argonne, IL, 2019, pp. Medium: ED. [19] G. Hu, R. Hu, J.M. Kelly, J. Ortensi, Multi-Physics Simulations of Heat Pipe Micro Reactor, Argonne National Lab (ANL), Argonne, IL, 2019, pp. Medium: ED. [20] G. Hu, R. Hu, L. Zou, Development of Heat Pipe Reactor Modeling in SAM, 2019. [21] P. Vegendla, R. Hu, L. Zou, Multi-Scale Modeling of Thermal-Fluid Phenomena Related to Loss of Forced Circulation Transient in HTGRs, Argonne National Lab (ANL), Argonne, IL, 2019, pp. Medium: ED. [22] A.J. Brunett, T.Q. Hua, G. Hu, D. O’Grady, R. Hu, T.H. Fanning, et al., Integrated Simulation Capabilities for Analysis of Experiments in the Versatile Test Reactor, Argonne National Lab (ANL), Argonne, IL, 2019. [23] R. Hu, J. Thomas, E. Munkhzul, T. Fanning, Coupled system and CFD code simulation of thermal stratification in SFR protected loss-of-flow transients, Proc. ICAPP 2014 (2014) 6
9.

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C H A P T E R

14 Mechanism-based codes for severe accident analysis Luteng Zhang1,2 1 2

Chongqing University, Chongqing, China Xi’an Jiaotong University, Shaanxi, China

Several mechanism-based codes for severe accident (SA) analysis are developed based on mechanistic models concerning specific phenomena or processes during reactor SAs [1]. The mechanism-based codes can be integrated into advanced thermal-hydraulic systematic analysis programs for engineering-level simulation of the entire nuclear power system and accident scenario. In addition, the integration could provide boundary conditions and feedback results for further thermal-hydraulic analysis [2]. Here listed some typical mechanism-based codes for analysis of in-vessel and ex-vessel SA scenario.

14.1 COPRA code The reactor core may melt and relocate into the lower head forming corium pool with high-Rayleigh-number natural convection during SAs. Then the lower head wall was exposed to the direct thermal load from corium pool with high temperatures. The vessel wall would then go through of creep rupture or boiling crisis if the local heat flux surpassed the corresponding critical heat flux (CHF). The decay power in corium pool would threaten the integrity of reactor vessel, which was directly relevant to the problem of corium in-vessel retention (IVR). In order to avoid these failure mechanisms, the strategy of external reactor vessel cooling was designed to ensure the corium IVR. The corium pool behaviors were important characteristics for estimating the integrity or failure of pressure vessel wall [3]. The COPRA code [4,5] was developed for the behavior analysis of high-Rayleighnumber corium pool with heat and mass transfer based on the COPRA experiments [6,7]. As illustrated in Fig. 14.1, the calculation model based on COPRA facility was composed of four regions, including corium pool, solid crust, steel vessel wall, and upper air space.

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00014-0

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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FIGURE 14.1

Simulation regions for COPRA facility [4].

14.1.1 Governing equations The governing equations for the natural convection heat transfer in corium pool can be expressed as follows. The primary physical properties all changed in relation with temperature. However, the density was treated according to the Boussinesq assumption. Continuity equation: @ρ @ðρuÞ @ðρνÞ 1 1 50 @t @x @y

(14.1)

Momentum equation in x direction:

 @ðρuÞ @ðρuuÞ @ðρuνÞ @p @ @u @ @u 1 1 52 1 ηeff ηeff 1 1 Su @t @x @y @x @x @x @y @y Su 5



 Cm ηeff uð12fl Þ2 @ @u @ @ν ηeff ηeff 1 2 @x @x @y @x fl 3

(14.2)

(14.3)

Momentum equation in y direction:

 @ðρνÞ @ðρuνÞ @ðρννÞ @p @ @ν @ @ν 1 1 52 1 η η 1 1 Sν @t @x @y @y @x eff @x @y eff @y Sν 5



 Cm ηeff νð12fl Þ2 @ @u @ @ν ηeff ηeff 1 ρgβðT 2 Tref Þ 1 2 @x @y @y @y fl 3

(14.4)

(14.5)

The third parts in Eqs. (14.3) and (14.5) were the source terms introduced by the solidliquid mushy zone based on the porous medium theory. The last term in Eq. (14.5) was the source term introduced by buoyancy in gravitational direction based on the Boussinesq hypothesis.

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14.1 COPRA code

Energy equation:



 @ðρcp TÞ @ðρucp TÞ @ðρνcp TÞ @ @T @ @T 1 1 5 λt λt 1 1 ST @t @x @y @x @x @y @y ST 5 qν 2

@ @ @ ðρΔHÞ 2 ðρuΔHÞ 2 ðρνΔHÞ @t @x @y

(14.6) (14.7)

The enthalpy formation method [8] was taken into consideration to solve phase-change problems. In the case of solidification the internal heating qν in crust part was set to zero. The relationship between temperature and enthalpy followed the rule: h 5 cp T

(14.8)

14.1.2 Turbulence model Despite the high-Rayleigh-number natural convection with strong turbulence in the pool, the flow in the near-wall region slowed down with temperature approaching solidus point. The low-Reynolds-number kε turbulence model proposed by Chien [9] considered both the effects of turbulent viscosity and molecular viscosity, as well as the anisotropy energy dissipation. The corresponding governing equations were: 

    @ðρkÞ @ðρukÞ @ðρνkÞ @ ηt @k @ ηt @k 1 1 5 η1 η1 (14.9) 1 1 Sk @t @x @y @x @y σk @x σk @y 

    @ðρεÞ @ðρuεÞ @ðρνεÞ @ ηt @ε @ ηt @ε 1 1 5 η1 η1 (14.10) 1 1 Sε @t @x @y @x @y σε @x σε @y The turbulent dynamic viscosity and source terms were written as: 1

Cμ ρk2 ð1 2 e20:0115y Þ ηt 5 ε

(14.11)

Sk 5 Gk 2 ρε 1 Bk 1 D

(14.12)

Sε 5 C1 Gk f1

ε ε2 ε 2 C2 f2 1 C3 Bk 1 E k k k f1 5 1:0

(14.13) (14.14)

2

f2 5 1 2 0:22e2ðRe=6Þ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi     ρy2 @u=@x 1 @ν=@y 1 y 5 η

(14.15) (14.16)

The turbulent source term introduced by shear stress, buoyant force, and anisotropy dissipation was in form of: "

2
 # @u 2 @ν @u @ν 2 1 12 1 (14.17) Gk 5 ηt 2 @x @y @y @x

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Bk 5 2 βg

D52

ηt ε @T σt k @y

(14.18)

2ηk y2

(14.19) 1

E5

2 2ηεe20:5y y2

(14.20)

In order to better simulate the turbulent anisotropy caused by larger temperature gradient and density gradient in the near-wall region, dimensionless Ri number was introduced as in form [10]: Ri 5 2

Bk Gk

(14.21)

Based on the near-wall Ri, the turbulent dynamic viscosity and the turbulent temperature diffusion coefficient were modified as follows [11]: η0t 5

Cμ ρk2 1 ð1 2 e20:0115y fRi Þ ε

(14.22)

n h i o 1 fRi 5 0:5 1 1000 3 tanh 6:7ðy1 Þ2 e20:02y Ri 2 4:15 1 1

(14.23)

n h i o 1 σ0T 5 0:009 1 45 3 tanh 26:7ðy1 Þ2 e20:02y Ri 2 2:3 1 1

(14.24)

The previous equations were constructed together as the near-wall modified lowReynolds-number kε turbulence model to simulate the natural convection in the whole region of the corium pool.

14.1.3 Crust model The heat transfer from corium pool toward crust can promote crust melting and thickness decreasing. On the contrary, the heat transfer from crust toward vessel wall can accelerate crust growth and thickness increasing. Based on this, the heat balance equation of crust can be established as: 2ρcr ΔH

dδcr λw R 5 hdn ðTmax 2 Tint Þ 2 ðTwi 2 Two Þ Ro dt δw

Then the corresponding crust growth rate was obtained as:     λw =δw ðTwi 2 Two Þ R=Ro 2 hdn ðTmax 2 Tint Þ dδcr Rcr 5 5 ρcr ΔH dt

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(14.25)

(14.26)

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As for the two-phase mushy zone due to the noneutectic feature, the liquid fraction can be expressed linearly by the corresponding temperatures: 8 0 T # Tsol > > < T 2 Tsol Tsol , T , Tliq (14.27) fl 5 T 2 T sol > > liq : 1 T $ Tliq The mixture properties were calculated based on the liquid fraction:   Pmix 5 Psol 1 2 fl 1 Pliq fl

(14.28)

It was found that the phenomena of component diffusion and mass transfer occurred at crust front. The interface temperature was equal to the liquidus temperature relating to the local component concentration. Therefore the diffusion process will influence the interface temperature and the transient heat transfer behavior. The diffusion rate of K1 from corium pool toward crust was stronger than that of K1 apart from crust. On the contrary, more Na1 was diffused from crust to interface. Due to the diffusion difference for K1 and Na1, the crust interface was characteristized with depletion of K1 and enrichment of Na1. This phenomenon was more obvious during the transient stages with rapid crust formation, leading to lower interface temperature and stronger heat transfer [12]. It was assumed that the melt solidification was in quasisteady process with a planar interface front. The concentration in melt pool was uniform with dominant convection. However, the component in the interface boundary layer was mainly characteristized with diffusion. Then the local concentration varied linearly along crust growth direction. The component diffusion process can be described as [13]: DNa

d2 CNa dCNa 50 1 Rcr 2 dδ dδ

(14.29)

Given the boundary conditions as follows: CNa 5 CNa;p

δ 5 δd

(14.30)

CNa 5 CNa;int

δ50

(14.31)

ðCNa;int 2 CNa;cr ÞRcr 1 DNa

dCNa 50 dδ

δ50

(14.32)

Then the solution of Eq. (14.29) was obtained as: CNa;int 2 CNa;cr 5 eRcr δd =DNa CNa;p 2 CNa;cr

(14.33)

Based on the two dimensionless concentration ratios kcp and kci: kcp 5

CNa;cr CNa;p

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(14.34)

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kci 5

CNa;cr CNa;int

(14.35)

The Na1 concentration and corresponding liquidus temperature at the interface can be calculated from: h i CNa;int 5 CNa;p kcp 1 ð1 2 kcp ÞeRcr δd =DNa (14.36) 8 0:19 , CNa;int # 0:20 < 334:4 2 250:0CNa;int (14.37) Tint 5 Tliq 5 459:191 2 873:617CNa;int 0:20 , CNa;int # 0:21 : 336:458 2 261:354CNa;int 0:21 , CNa;int # 0:25 The reference values are recommended as [14]: CNa,p 5 0.2; kcp 5 0.45; DNa in range of 1.72 3 10291.97 3 1029 m2/s; δd in range of 0.10.5 mm.

14.1.4 Conduction model A narrow air gap was formed between the solidified corium crust and lower head wall. The gap thickness was set constant in the range of 0.10.5 mm. The convective heat transfer from corium pool was conducted through crust, gap, and wall in sequence, as illustrated in Fig. 14.2. It is assumed that the surfaces were approximately planar. When the heat transfer reached steady state, the conductive heat flux was constant as in dynamic equilibrium: λcr

Tint 2 Tcro Tcro 2 Twi Twi 2 Two 5 λgap 5 λw δcr δgap δw

(14.38)

The outside temperature was given in the boundary conditions and interface temperature was obtained in the component diffusion model. Then the boundary temperatures on both sides of gas gap can be calculated to be:         Tint = δcr =λcr 1 Two = δgap =λgap 1 δw =λw             Tcro 5 (14.39) 1= δcr =λcr 1 1= δgap =λgap 1 δw =λw

FIGURE 14.2 The conductive heat transfer in crust, gap, and wall [5].

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       Tint = δcr =λcr 1 δgap =λgap 1 Two = δw =λw             Twi 5 1= δcr =λcr 1 δgap =λgap 1 1= δw =λw

(14.40)

Given the boundary temperatures of crust and vessel wall, the temperature field in transient states can be obtained from: @Tcr @2 Tcr 5 λcr @t @δ2

 @Tw λw @ @Tw λw @ @Tw r ρw cp;w 5 1 2 @t r @r @r r @θ @θ ρcr cp;cr

(14.41) (14.42)

14.1.5 Radiation model It should be noted that the heat transfer in top air space was unneglectable due to the higher temperatures at top surface than the surrounding walls. For the enclosure domain of top space, the pool surface, upper lid downward surface, cooling curved wall surface, and other wall surfaces were marked as 14, respectively. The four-node equilibrium equations based on Kirchhoff law were established as: Ji 5 εi σTi 4 1 ð1 2 εi Þ

4 X

Jj Xi;j

(14.43)

j51

Qrad 5

Ebi 2 Ji 1 2 εi =εi Ai

The net radiation heat loss from top surface was then obtained as:   4 P 4 Eb1 2 ε1 σT1 1 ð1 2 ε1 Þ Ji X1;i Eb1 2 J1 i51 5 Qrad 5 ð1 2 ε1 Þ=ε1 A1 ð1 2 ε1 Þ=ε1 A1

(14.44)

(14.45)

The natural convection in the top confined air space was calculated from the following equations: 1=4 4 5 Nunc 5 0:212ðGrPrÞ1=3 1:0 3 10 # Gr5 # 4:6 3 10 (14.46) 0:061ðGrPrÞ Gr . 4:6 3 10 Then the heat loss by air natural convection was obtained as: Qnc 5 Aup hnc ðTmax 2 Tlid Þ

(14.47)

14.1.6 Code validation The code validation was performed with the transient simulation of COPRA experimental tests with molten salt. The temperature field and velocity distribution from experiment

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FIGURE 14.3 Temperature field from corium pool simulation [4].

FIGURE 14.4 Velocity distribution from corium pool simulation [4].

steady states and code simulations were shown in Figs. 14.3 and 14.4. There occurred with obvious thermal stratification in the pool with crust formation along curved side. The natural convection flow slowly moved upward and gradually transferred to the wall side at a lower speed and then slipped downward at a higher speed after cooling. The turbulences were stronger in the top and near-wall regions with direct cooling and more vortices. The pool temperature distribution along height from experiment and simulation was compared in Fig. 14.5. The data were in good agreement with increasing trend along pool height and flatted gradually in top part. The relatively stable temperature stratification in lower pool was caused by the smaller fluid velocity and stronger viscous effect. However, the temperature was approximately uniform in top with stronger turbulence and more intensified heat transfer. The comparisons of local heat flux at polar angle 40 degrees during entire transients were presented in Fig. 14.6. The calculated heat fluxes from both sides were in similar trend with model prediction, proving the validity of experimental measurements and code simulations. As shown in Fig. 14.7, the calculated steady distribution of heat flux

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341 FIGURE 14.5 Comparison of temperature distribution along pool height [4].

FIGURE 14.6 Comparison of transient local heat flux at polar angle 40 degrees [4].

along polar angles was basically consistent with the experimental data. The heat flux increased with polar angle and reached the maximum value near the pool top level due to radiation loss. The transient variation of crust growth rate at polar angle 40 degrees was compared with experimental data in Fig. 14.8. The positive values represented crust growth and the negative ones indicated crust melting. The crust increased rapidly at the initial stage of melt injection with the maximum growth rate of 60 μm/s. The crust thickness increased with decreasing power and the change rate stayed within 6 10 μm/s. During the second melt injection the crust was melted quickly by thermal shock at rate of 40 μm/s and then solidified again with rate of 20 μm/s.

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FIGURE 14.7 Comparison of heat flux distribution along polar angle [4].

FIGURE 14.8

Transient variation of crust growth rate at polar angle 40 degrees [4].

The transient evolution of corresponding liquidus temperature at crust interface from code simulation was presented in Fig. 14.9. Due to the rapid solidification at beginning, there occurred with obvious enrichment of Na1 at crust interface by diffusive mass transfer, leading to the lowest liquidus temperature of about 260 C. The power increase will lead to crust melting and Na1 concentration decrease, resulting in the increase of liquidus temperature and decrease of transient heat transfer. On the contrary, the power decrease will lead to crust growth and Na1 concentration increase, resulting in the decrease of liquidus temperature and increase of transient heat transfer. The crust thickness distribution in steady states at different power stages was compared as shown in Fig. 14.10. The decreasing trend along polar angle was opposite compared to

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FIGURE 14.9 Transient variation of liquidus temperature at crust interface [4].

FIGURE 14.10 thickness angle [4].

Comparison of crust distribution along polar

the heat flux distribution. Lifting the heating power can effectively reduce the crust thickness on the top, but it imposed little effect on the bottom crust. The insufficient heating at bottom part from experiment made it difficult to remelt the solidified thick crust to reversible state. Therefore the bottom crust was still thicker in T3 and T4 (even with higher heating powers) than that in T1. It should be noted that the parameters of crust-wall gap size and diffusive boundary layer thickness were key factors to influence crust behaviors. The calculated crust thickness distribution with different crust-wall gap sizes was compared in Fig. 14.11. Obviously,

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FIGURE 14.11 Effects of crust-wall gap size on crust thickness distribution [5].

FIGURE 14.12 Effects of diffusive boundary-layer thickness on interface temperature [5].

the crust thickness decreased with the increase of gap thickness. This was because the thermal resistance introduced by the increased gap thickness will compensate for the thermal resistance removed by the decreased crust thickness to achieve a new thermal equilibrium. In addition, the effects of diffusive boundary-layer thickness on interface temperature were studied and the results at polar angle 50 degrees were depicted in Fig. 14.12. The interface temperature deviation became larger with increased diffusive layer thickness due to the intensified process of component diffusion. The enlarged interface boundary provided conditions for stronger component diffusion, thus introducing more disturbance for the interface temperature and further heat transfer behavior.

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14.2 IVRASA code

14.2 IVRASA code RASPLAV and MASCA experiments with suboxidized prototypical corium indicated the possibility of corium pool stratification [15,16]. It was observed that the initial homogenous corium pool may separate into two layers with the oxide layer of UO2ZrO2 lying beneath the light metal layer of FeZr. Moreover, the suboxidized Zr may react with UO2 to form the heavy metal layer of U at bottom, leading to the formation of three-layer structure. As a result, the nonhomogeneous layer configurations will directly impose effect on the thermal loading along curved wall. The IVRASA code was developed for the analysis of multilayer corium pool behavior and IVR safety margin during SAs [17,18]. The point estimate method was employed for the modeling of steady state behavior of two-layer structure and three-layer structure corium pool. The schematic of the three-layer configuration was shown in Fig. 14.13.

14.2.1 Heat transfer model Oxide pool: Q_ o Vo 5 qvo;up Sup 1 qvo;dn Sdn

(14.48)

Q_ o Vo Sside 1 Sdn 1 Sup R0

(14.49)

qvo;dn 5

R0 5

Nuup Nudn

(14.50)

FIGURE 14.13 The schematic of the melt pool configuration [17].

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qvo; up 5

Q_ o Vo 2 qvo;dn ðSside 1 Sdn Þ Sup

The crust thickness was then obtained based on equation as:
 qvo;dn ðθÞ Q_ o δw ðθÞ qvo;dn ðθÞδw ðθÞ Q_ o δ2cr ðθÞ 1 δcr ðθÞ 1 1 Tw;o 5 0 2 To;m 1 2λcr λcr 2λw λw δw ðθÞ 5 λw

Tw;m 2 Tw;o   qvo;dn ðθÞ 1 Q_ o δcr ðθÞ=2

(14.51)

(14.52) (14.53)

δcr ðθÞ qvw ðθÞ 5 qvo;dn ðθÞ 1 Q_ o 2

(14.54)

Q_ l Vl 1 qvl;b Sl;b 5 qvl;t Sl;t 1 qvl;w Sl;w

(14.55)

Light metal layer:

λcr Q_ δcr;t 1 o δcr;t 2 h i 4 4 σ Tl;t 2 Ts;i     qvl;t 5 1=εl 1 ð1 2 εs ÞSl;t =εs Ss qvl;b 5 ðTo;m 2 Tbl Þ

qvl;w 5

 λw  Tw;m 2 Tw;o δw

 3 4 4 σ T 2 T s;i l;t δs   5 Ts;o 5 Ts;i 2 4 λs Ss =εl Sl;t 1 ð1 2 εs Þ=εs

(14.56)

(14.57)

(14.58)

2

   0:25 λs  4 Tw 5 Ts;o 2 Ts;i 2Ts;o δs σεs Tw 5

 λs δo  Ts;i 2 Ts;o 1 Tw;o λw δ s

(14.59)

(14.60) (14.61)

Heavy metal layer: Q_ h Vh 1 qvo;h Sdn 5 qvh;b Sh;b qvo;h 5

Sup Sdn

ð θh

(14.62)

qvo;dn ðθÞsinðθÞcosðθÞdθ

(14.63)

 λw  Tw;i 2 Tw;o δw

(14.64)

0

qvh;b 5

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The decay heat in the oxide pool and the heavy metallic layer was calculated in a simple way: Q_ o 1 Q_ h 5 Pdecay;t

(14.65)

  mU 270=238 Q_ h Vh 5 mUO2 Q_ o Vo

(14.66)

14.2.2 Heat transfer relationships The heat transfer relationships for light metal layer, oxide layer, and heavy metal layer were selected from typical experimental results. As for the oxide layer, ACOPO relation [19] and Mayinger relation [20] were used for upward and downward heat transfer. Nuup 5 1:95Ra00:18

(14.67)

Nudn 5 0:55Ra0 0:22

(14.68)

As for the metal layer, ChurchillChu relation [21] and GlobeDropkin relation [22] were used for sideward and upward/downward heat transfer. Nuup 5 h

0:15Ra1=3 11ð0:492=PrÞ

9=16

i16=27

Nudn 5 0:069Ra1=3 Pr0:074

(14.69)

(14.70)

The heat flux of CHF was selected from the experimental data of full-scale ULPU-V facility for AP1000 [23]: qCHF 5 0:49 1 3:02 3 1022 θ 2 8:88 3 1024 θ2 1 1:35 3 1025 θ3 2 6:65 3 1028 θ4

(14.71)

14.2.3 Benchmark and in-vessel retention analysis In order to verify IVRASA study, benchmark calculation results of IVRASA were compared with the UCSB data and INEEL data [23]. The variables reflecting the IVR margins such as heat flux and crust thickness were compared in Figs. 14.14 and 14.15, respectively. The heat flux results indicated that IVRASA, UCSB, and INEEL predictions differ slightly at the locations adjacent to ceramic pool. Obvious differences were observed at the locations near the metallic layer. The results indicated that the IVRASA heat flux prediction was larger than those from UCSB and INEEL, in which the INEEL prediction was the smallest. The oxide crust thickness predicted by IVRASA was the smallest while the INEEL prediction was the largest. In total, it can be seen from the comparisons that the IVRASA code correctly interpreted heat transfer equations in the UCSB and INEEL analyses.

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FIGURE 14.14 Comparison of IVRASA heat flux with UCSB and INEEL [17].

FIGURE 14.15 Comparison of IVRASA crust thickness with UCSB and INEEL [17].

The good agreement indicated the applicability and accuracy and the code was further applied to predict the IVR safety margin during SAs in AP1000. The calculation results of two-layer structure showed that the heat flux remained below the CHF. However, the heat flux at top side could exceed the CHF because of the focusing effect with thin metallic layer. It was reported that the CHF ratios of AP1000 predicted by IVRASA remained below unity. However, there were still uncertainties in input parameters, such as metallic melt

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mass. Due to the higher thermal conductivity in the metallic layer, the metallic mass significantly affected the magnitude of heat fluxes toward the vessel sidewall. If metallic melt mass was reduced, the excess of energy that came from the oxide pool and cannot be removed by radiation was focused toward the vessel wall, leading to the considerable thermal attack. This was the so-called focusing effect, which may be one of the most important challenges to the vessel integrity. It’s reported that the reduced metallic melt mass may affect the heat flux. The CHF ratio at metallic layer side approach unity for steel masses equal to 15,000 kg. The vessel failure may occur if the steel mass was below this value. Particularly, the CHF ratio could reach to 2.5 when the steel mass equals to 3000 kg, which was the minimum steel mass calculated by AP1000 case from MELCOR. The thin metal layer may finally lead to the vessel wall failure. The three-layer structure results suggested that the thermal failure at bottom location was highly unlikely, but the heat flux at light metal layer could be higher than two-layer case due to smaller thickness. The heat flux ratiosfrom calculations were well below the unity, indicating that the vessel wall cloud maintain integrity. Although IVRASA predicted that CHF ratios remained below unity for three-layer configuration, there were potential factors affecting heat loads in the heavy metallic layer, such as the intermetallic reactions, oxidation in the heavy metallic layer. However, there were few investigations on the impact of the intermetallic reactions and the oxidation in the heavy metallic layer. It was difficult to determine the quantitative analysis of the intermetallic reactions and the oxidation in the heavy metallic layer. There are limitations of IVRASA code without considering potential factors affecting thermal distribution, such as the complicated physicochemical reactions. In addition, the existing CHF correlation for IVR analysis based on 2D UPLU-V tests also introduced uncertainty in the safety analysis. These concerns still need further investigation.

14.3 Thermal EXplosion Analysis Simulation code The molten corium may poured out of the reactor vessel and then interact with coolant water in the in-vessel lower head or ex-vessel reactor cavity. The rapid heat transfer will occur in fuelcoolant interaction (FCI) companied with steam explosion due to rapid coolant evaporation forming high-pressure shock waves. During the process of mixing and associated jet breakup, there were three hydraulic mechanisms, including KelvinHelmholtz (KH) instabilities, RayleighTaylor (RT) instabilities, and boundary-layer stripping [24,25].

14.3.1 Basic assumption The Thermal EXplosion Analysis Simulation model (TEXAS) was developed in UWMadison for simulation of FCI and steam explosion [26,27]. The Eulerian field was used for the coolant liquid and vapor phases and the LaGrangian field was used for molten fuel in form of user-defined material volumes. The interchange of mass, momentum, and energy between phases of vapor and liquid was modeled with complete Eulerian

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two-fluid model. Besides, the constitutive relations and phase-change models were applied for interphase exchange. The LaGrangian fuel model considered the injected fuel to be particles of molten material with the characteristic size, velocity, and temperature. These parameters were tracked in relation to fuel particles that entered before and after others, allowing for easy modeling of the jet structure. The sizes of LaGrangian fuel particles were also allowed to decrease dynamically during the process of fuelcoolant mixing or fragmentation. Due to the instability introduced from the relative velocity between phases, this dynamic fuel fragmentation during mixing was treated with RT breakup as the key mechanism for this process. More complete subsequent models were included to account for the effects of KH instability effects as well as boundary-layer stripping. These models were also further extended to consider fuel solidification effects. The transition from fuelcoolant mixing to fuel fragmentation during explosion was incorporated into the code empirically based on an artificial pressure-trigger model. The pressure trigger or the calculated pressure rapid increase can be used as the trigger for the fuel fragmentation in a specific Eulerian cell. Therefore the TEXAS model was equipped with a rapid fuel fragmentation model based on film boiling collapse and subsequent coolant jet penetration causing fragmentation. The fragmentation model constant was theoretically estimated and validated against with KROTOS test data. The key assumption was that the fuel fragments were small enough to complete quench in the timescale of the explosion propagation and all energies were transferred into vapor production. In addition, the code was developed with a first-principle model to consider the oxidation of molten metallic fuel with the coolant vapor. This model helped to present reasonable agreement with experimental data [28].

14.3.2 Code validation The TEXAS code was validated with FARO, KROTOS, ZrEX, and UW-FCI experiments. Here listed the comparison of TEXAS-VI model results against with KS-2 and KS-4 test data, conducted at CEA in the KROTOS facility [29]. The continuous molten jet was injected into the test section in KS-2 test. As shown in Fig. 14.16, the melt leading front position predicted by TEXAS-VI was in good agreement with the experimental results before entering the water pool. And reasonable agreement was reached with the experimental results after entering the liquid pool. The steam volume in water pool during coarse mixing process was depicted in Fig. 14.17. This parameter was estimated in the experiment by the measurement of level swell of water pool. At the initial stage a small amount of melt particles at leading front were injected into the water pool quickly and fragmented rapidly. The steam volume increased rapidly although the heat released from melt particles at beginning was small. The mass of hightemperature melt particles entering the liquid pool increased later, leading to the increasing of heat transfer to the water pool and larger volume of steam. As noted in the figure, the prediction of TEXAS-VI was consistent with the reported experimental result. In the KS-4 simulation the high pressure-trigger gas was released at vessel bottom about 1.03 seconds after coarse mixing to trigger the steam explosion. Fig. 14.18 showed the comparison of the pressure measured at K1 pressure sensor and the values predicted by TEXAS-VI. The simulation results were slightly higher than

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FIGURE 14.16 Comparison of melt leading front position of KS-2 test [28].

FIGURE 14.17

Comparison of steam volume in water pool of KS-2 test [28].

test data and the predicted pressure wave propagation velocity was slower due to the higher prediction of steam. The steam explosion characteristics were successfully predicted by TEXAS-VI code. However, the code applicability to evaluate the effect of initial or boundary conditions on steam explosion, as well as the uncertainty analysis should be assessed in future.

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FIGURE 14.18

Comparison of K1 pressure sensor of KS-4 test [28].

14.4 MOCO code In some series of SAs, with the continuous thermal shock toward vessel wall until failure, the corium will be discharged into the reactor cavity and spread over the concrete basemat. Then the Molten Corium Concrete Interaction (MCCI) was occurred with concrete ablation. The molten materials are maintained at high temperature by decay heat and exothermal reaction, leading to concrete decomposition and ablation. A large amount of water vapor and carbon dioxide produced by concrete decomposition will react with metals and produce hydrogen and carbon monoxide. The combustible gases introduced additional risks of sudden over pressurization if ignited. In addition, the radioactive aerosols that evolve during core debris interactions can enhance radiological consequences of containment failure [30,31]. The MOCO was developed to investigate the heat transfer behavior and coolability mechanisms of MCCI progress in both axial and radial directions toward the basemat and sidewall concrete [32]. The crust generation and growth, as well as the concrete erosion and gas release, are important for the MCCI process. Cavity ablation depth, melt temperature, and gas release are the key parameters in the code calculation.

14.4.1 Chemical reaction model First, the basic conservation equations of mass and energy were solved. The mass conservation equation inside the molten corium pool was determined as: @m @mside @mbasemat @mcore 5 1 1 1 madd @t @t @t @t

(14.72)

As for the energy conservation equation, several heat sources or sinks were considered. The primary one was the decay heat from fission products. The other heat energy came from IV. Thermal-hydraulic codes

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the melt discharged following reactor pressure vessel (RPV) failure, chemical reactions between metallic corium components and concrete decomposition particles or gases, heat transfer to concrete, including slag heat sink, and heat transfer toward above atmosphere. The energy conservation equation inside the molten corium pool was determined as: @E 5 2 Qm 1 Qdec 1 Qht 1 Qox 1 Qde 2 Qc 2 Qent 1 Qrpν 1 Qadd @t

(14.73)

The parameters on the right side were the energy due to the change of corium mass, the decay heat, the heat transfer between corium and other parts, the oxidation heat in the corium, the decomposition heat from the concrete, the heat transfer to the solidified crust, the entrainment heat from the corium to upper crust, the heat introduced from RPV discharge, and the additional energy due to error from mass calculation, respectively. In prototypical reactor situations the melt composition was complicated ranging from fully oxide to fully metallic. And these two phases were assumed to be well mixed in the present model. Most part of the core inventory and concrete metals, as well as their corresponding oxides, were considered in the mass conservation equation. However, the mass equations for the solidified crust and fragmented particles were solved separately. And the material properties were also evaluated based on the calculated compositions in different regions. Due to the interaction between corium and concrete, the decomposition of concrete and the release of gases may occur with high-temperature heating. The decomposition reactions were involved inside the interaction, including: CaCO3 -CaO 1 CO2 2 177:82 kJ=mol

(14.i)

CaðOHÞ2 -CaO 1 H2 O 2 109:45 kJ=mol

(14.ii)

In addition, the metals in molten corium could react with the carbon dioxide and water vapor created from the decompose reactions, leading to the production of hydrogen and carbon monoxide. These exothermal reaction equations were also included: Zr 1 2H2 O-ZrO2 1 2H2 1 6:4 MJ=kg

(14.iii)

2Cr 1 3H2 O-Cr2 O3 1 3H2 1 2:4 MJ=kg

(14.iv)

Fe 1 H2 O-FeO 1 H2 1 5:1 MJ=kg

(14.v)

Zr 1 2CO2 -ZrO2 1 2CO 1 6:0 MJ=kg

(14.vi)

2Cr 1 3CO2 -Cr2 O3 1 3CO 1 2:0 MJ=kg

(14.vii)

Fe 1 CO2 -FeO 1 CO 2 0:4 MJ=kg

(14.viii)

Moreover, the chemical reactions between components of Zr and SiO2 were also considered and incorporated into code, such as: Zr 1 2SiO2 -ZrO2 1 SiðlÞ 1 1:9 MJ=kg

(14.ix)

Zr 1 2SiO2 -ZrO2 1 SiO 2 5:0 MJ=kg

(14.x)

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14.4.2 Concrete ablation model The MOCO code was able to perform calculations for the one-dimensional and twodimensional ablation problems. The concrete ablation depth heated with corium was calculated by several different models. The crust formation could occur between corium pool and surrounding concrete during ablation process. The initial heat-up phase at concrete surface, heat conduction toward concrete, dynamic growth, and failure of interfacial crust were considered in the code. This complete model was developed to calculate the transient behavior further to interpret the test results. The depth of concrete ablation was solved based on the thermal balance between concrete and crust as: ρΔe

@η dcr @Q @T ΔT 5 1 λcc 1 λcr @t @x dcr 2 @t

(14.74)

The surface area of melt pool top was simplified as the same of the basemat area for entire calculation time. The stratification of different phases in the corium pool was also considered. Both cases of porous or impervious crust were considered for the contact modeling between melt and concrete. The gases released from concrete were assumed to form the gas film to fully cover the concrete surface. The heat across the film was transferred by convection and radiation. For the axial direction the energy balance across the filmmelt interface was established as: q 5 hmelt ðTmelt 2 Tl Þ 5 hrad ðTl 2 Tdec Þ 1 hconν ðTl 2 Tdec Þ

(14.75)

14.4.3 Corium cooling model As for the situations with top flooding, the crust solidification and evolution at interface and other cooling mechanisms, such as bulk cooling, water ingression, melt eruption, and crust failure, were all considered in the code. In the early stage with flooded surface, only film boiling was modeled for top surface. The heat transfer rate from pool toward cooling was estimated from:
 kfilm ΔT qcool 5 ϕ 1 qrad;w (14.76) dfilm ϕ511

4:5j uter

(14.77)

where ϕ denoted the area enhancement due to gas sparging where j was the sparging rate and uter was the bubble terminal rise velocity. The crust formation was started with the contact between coolant and corium. The film boiling was existed until the stable crust was achieved. The dynamic growing process of crust was obtained before the stable crust completely formed. Then the other thermal mechanisms would play a key role in the following phase. The phenomenon of melt eruption through crust has been observed in experiments with prototypical materials. The entrained melt flowed across the top crust by sparging gases would increase the debris cooling rate greatly. The melt entrained into coolant was then quenched, leading to the formation of particle bed on the top crust. Generally, melt entrainment rate was considered to be proportional to the gas volumetric flowrate. Once the final crust thickness was reached, the crust upper surface was considered to be IV. Thermal-hydraulic codes

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fixed and the elevations of the crust bottom and the melt top were obtained. Then the melt and crust was assumed to separate when the two elevations were different. It was noted that the heat transfer resistance from melt to water was proportional to the crust thickness. Therefore the heat removed by coolant was limited by the ability of heat conduction across crust. The water ingression could enhance the cooling heat transfer, which should be conduction limited otherwise with the porous crust. The criterion for the onset of water ingression into crust was that the total heat flux at interface must be lower than the crust dryout. The dryout limit was evaluated taking into consideration of the countercurrent flow of noncondensable gases during MCCI process and the decay heat inside crust. The gas volumetric flowrate was estimated at the saturation point of coolant because the debris bed was assumed to be saturated during entire process.

14.4.4 Code validation The MOCO code was validated by comparisons with experimental results from fulloxide corium experiments as well as oxide/metal stratified corium experiments. The concrete ablation was fairly well predicted by the code in most cases. The CCI-2 experiment was characteristized with long-term 2D corium concrete interaction with top flooding [33]. The tests were conducted with limestone/common sand concrete and flooding water was poured into the cavity after 5 hours. The initial melt temperature and the structure temperature are 2150K and 750K respectively. The radial and axial ablation depths are compared with the test data in Fig. 14.19. The comparison indicates that the trend and magnitude of ablation depths agreed well with each other. The ablation rate began decreasing after flooding. The Bradley slag film heat transfer model was adopted for both lateral and axial calculation. Therefore both evolution of axial and radial ablation depth are identical. The comparison of melt temperature with CCI-2 experiment is shown in Fig. 14.20. In the early 5 hours with dry cavity, the calculation results were in good agreement with experimental data. However, the melt temperature FIGURE 14.19 Comparison of ablation depth with CCI-2 experiment [32].

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FIGURE 14.20 Comparison of melt temperature with CCI-2 experiment [32].

was underpredicted after flooding with stronger cooling. The results indicated that the heat transfer model needs further modification.

14.5 DETAC code Due to the zirconiumwater reaction and MCCI, a large amount of hydrogen can be produced and spread in the containment. The hydrogen will mix with the air and steam to generate a flammable mixture. It is possible to trigger hydrogen combustion, flame acceleration, deflagration-to-detonation transition, and finally detonation to happen, which may threaten containment integrity [34,35].

14.5.1 Mathematical model The DETAC code is used for the analysis of hydrogen detonation during SA [36]. Due to the rapid hydrogenair detonation process, the consideration of physical modeling effects such as molecular diffusion, turbulence, heat conduction, or viscosity is not necessary [37]. The mixture consisting of four gas components (hydrogen, oxygen, nitrogen, and vapor) was concerned here with the assumption that all components have the same velocity and temperature. The governing equations for the gaseous components are: @ρk 1 rðρk V Þ 5 wk @t

(14.78)

-

-@ðρ V Þ 1 rðρ V V 1 pÞ 5 0 @t h -i @E 1 r ðE 1 pÞ V 5 0 @t

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(14.79) (14.80)

357

14.5 DETAC code

The specific heat and enthalpy of kth gaseous component at constant pressure can be calculated by: cp;k 5

R ðAk1 1 Ak2 T 1 Ak3 T 2 1 Ak4 T3 1 Ak5 T 4 Þ Mk


 R Ak2 2 Ak3 3 Ak4 4 Ak5 5 T 1 T 1 T 1 T 1 Ak6 Ak1 T 1 hk 5 Mk 2 3 4 5

(14.81) (14.82)

It is time-consuming to solve a detailed set of chemical kinetic rate equations in conjunction with the three-dimensional unsteady fluid flow equations. Therefore simplified global-chemistry models were employed to investigate the characteristics of chemical energy release during hydrogen detonation. For the H2/O2/N2 system, it was assumed that the reaction between N2 and O2 was ignored due to the limited effect of NOx formation on the detonation propagation. The global-chemistry model was a single-step irreversible chemical reaction model with reaction rate given in Arrhenius form [38]: T . Tc Ar Tn e2Ea =RT kr 5 (14.83) T # Tc 0 Based on the physical models being calculated, the setup of boundary conditions will differ greatly. In the following simulation cases the heat convection between gases and wall was not considered because the detonation process was too rapid to minimize the effect of internal energy interaction.

14.5.2 Code validation The comparison between the experimental data and calculated results code for validation was shown in Fig. 14.21. The experiment of hydrogen detonation was carried out in 2.74 m long tube [39]. The code was further used to predict the H2airsteam detonation FIGURE 14.21 Comparison of pressure between code results and experimental data [36].

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FIGURE 14.22 The distribution of the monitoring points and ignition points [36].

FIGURE 14.23 The pressure history at the two sides of the internal wall [36].

in the compartments of boiling water reactor building, as shown in Fig. 14.22. Fig. 14.23 presented the pressure history at the two sides of the internal wall. The pressure at point 1 increased rapidly in a short time. This is because the detonation waves reached and collided with wall, leading to the reflection shock wave propagating in an opposite direction immediately. Then the pressure at point 1 decreased gradually over time due to the hydrogen consumption and lack of energy to sustain detonation. The pressure at other points displayed the same trend except that the time delay.

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References

359

References [1] B.R. Sehgal, Nuclear Safety in Light Water Reactors: Severe Accident Phenomenology, Elsevier Academic Press, England, 2011. [2] Y.P. Zhang, S.P. Niu, L.T. Zhang, S.Z. Qiu, G.H. Su, W.X. Tian, A review on analysis of LWR severe accident, J. Nucl. Eng. Radiat. Sci. 1 (2015) 041018. [3] L. Zhang, Y. Zhou, Y. Zhang, W. Tian, S. Qiu, G. Su, Natural convection heat transfer in corium pools: A review work of experimental studies, Prog. Nucl. Energy 79 (2015) 167181. [4] L. Zhang, Z. Ma, Y. Zhang, G.H. Su, W. Sun, S. Bu, et al., Experimental study and model development for the high-Rayleigh-number corium pool with heat and mass transfer, Int. J. Heat Mass Transfer 138 (2019) 304313. [5] L. Zhang, Z. Ma, Y. Zhang, G.H. Su, S. Bu, W. Sun, et al., Research on the non-eutectic phase-change dynamics with heat transfer and component diffusion, App. Therm. Eng. 156 (2019) 230236. [6] L. Zhang, Y. Zhang, Y. Zhou, G.H. Su, W. Tian, S. Qiu, COPRA experiments on natural convection heat transfer in a volumetrically heated slice pool with high Rayleigh numbers, Ann. Nucl. Energy 87 (Part 2) (2016) 8188. [7] Y.P. Zhang, L.T. Zhang, Y.K. Zhou, W.X. Tian, S.Z. Qiu, G.H. Su, et al., The COPRA experiments on the invessel melt pool behavior in the RPV lower head, Ann. Nucl. Energy 89 (2016) 1927. [8] V.R. Voller, C. Prakash, A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems, Int. J. Heat Mass Transfer 30 (1987) 17091719. [9] K.Y. Chien, Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model, AIAA J. 20 (1982) 3338. [10] M.M. Gibson, B.E. Launder, On the calculation of horizontal, turbulent, free shear flows under gravitational influence, J. Heat Transfer 98 (1976) 8187. [11] T.N. Dinh, R.R. Nourgaliev, Turbulence modelling for large volumetrically heated liquid pools, Nucl. Eng. Des. 169 (1997) 131150. [12] J.M. Seiler, G. Ratel, H. Cornbeau, X.Y. Gaus-Liu, F. Kretzschmar, A. Miassoedov, Transient refractory material dissolution by a volumetrically-heated melt, Nucl. Eng. Des. 280 (2014) 420428. [13] Y.P. Zhang, W.X. Tian, S.Z. Qiu, G.H. Su, Study effects of the kinetics of local composition diffusion on the melt pool coolability by developing a DBL-LIVE model, Prog. Nucl. Energy 90 (2016) 219228. [14] X. Gaus-Liu, A. Miassoedov, T. Cron, J. Foit, T. Wenz, S. Schmidt-Stiefel, Core melt solidification characteristics in PRV lower head—experimental results from LIVE tests, J. Eng. Gas Turbines Power 132 (2010) 102924. [15] V.G. Asmolov, V.F. Strizhov, Y.G. Degaltsev, RASPLAV final report—behavior of the corium molten pool under external cooling, OECD RASPLAV Project, Kurchatov Institute, Russia, 2000. [16] V.G. Asmolov, D.F. Tsurikov, MASCA project: major activities and results, in: Proceedings of MASCA Seminar, Provence, France, 2004. [17] Y.P. Zhang, S.Z. Qiu, G.H. Su, W.X. Tian, Analysis of safety margin of in-vessel retention for AP1000, Nucl. Eng. Des. 240 (2010) 20232033. [18] Y.P. Zhang, S.Z. Qiu, G.H. Su, W.X. Tian, A simple novel analysis procedure for IVR calculation in coremolten severe accident, Nucl. Eng. Des. 241 (2011) 46344642. [19] T.G. Theofanous, M. Maguire, S. Angelini, T. Salmassi, The first results from the ACOPO experiment, Nucl. Eng. Des. 169 (1997) 4957. [20] F. Mayinger, M. Jahn, H.H. Reineke, V. Steinbrenner, Examination of Thermohydraulic Processes and Heat Transfer in a Core Melt, Technical University of Hannover, Germany, 1976. [21] S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a vertical plate, Int. J. Heat Mass Transfer 18 (1975) 13231329. [22] S. Globe, D. Dropkin, Natural convection heat transfer in liquids confined by two horizontal plates and heated from below, J. Heat Transfer 81 (1959) 2428. [23] H. Esmaili, M. Khatib-Rahbar, Analysis of In-Vessel Retention and Ex-Vessel Fuel Coolant Interaction for AP1000, Energy Research Inc., Nuclear Regulatory Commission, Washington, DC, USA, 2004. [24] D. Magallon, Status and prospects of resolution of the vapour explosion issue in light water reactors, Nucl. Eng. Technol. 41 (2009) 603616. [25] M. Hirano, T. Yonomoto, M. Ishigaki, N. Watanabe, Y. Maruyama, Y. Sibamoto, et al., Insights from review and analysis of the Fukushima Daiichi accident, J. Nucl. Sci. Technol. 49 (2012) 117.

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[26] C.C. Chu, M.L. Corradini, One-dimensional transient fluid model for fuel coolant interaction analysis, Nucl. Sci. Eng. 101 (1989) 4871. [27] M.L. Corradini, B.J. Kim, M.D. Oh, Vapor explosions in light water-reactors  a review of theory and modeling, Prog. Nucl. Energy 22 (1988) 1117. [28] R.H. Chen, J. Wang, G.H. Su, S.Z. Qiu, M.L. Corradini, Analysis of KROTOS KS-2 and KS-4 steam explosion experiments with TEXAS-VI, Nucl. Eng. Des. 309 (2016) 104112. [29] I. Huhtiniemi, D. Magallon, H. Hohmann, Results of recent KROTOS FCI tests: alumina versus corium melts, Nucl. Eng. Des. 189 (1999) 379389. [30] B. Spindler, B. Tourniaire, J.M. Seiler, Simulation of MCCI with the TOLBIAC-ICB code based on the phase segregation model, Nucl. Eng. Des. 236 (2006) 22642270. [31] M. Reimann, Verification of the WECHSL code on melt concrete interaction and application to the core melt accident, Nucl. Eng. Des. 103 (1987) 127137. [32] B. Lin, S.Z. Qiu, G.H. Su, W.X. Tian, Y.P. Zhang, Development and verification of molten corium-concrete interaction code, Prog. Nucl. Energy 85 (2015) 701706. [33] M.T. Farmer, D.J. Kilsdonk, R.W. Aeschlimann, Corium coolability under ex-vessel accident conditions for LWRs, Nucl. Eng. Technol. 41 (2009) 575602. [34] M.P. Sherman, Hydrogen combustion in nuclear-plant accidents and associated containment loads, Nucl. Eng. Des. 82 (1984) 1324. [35] D. Baraldi, M. Heitsch, H. Wilkening, CFD simulations of hydrogen combustion in a simplified EPR containment with CFX and REACFLOW, Nucl. Eng. Des. 237 (2007) 16681678. [36] T. Huang, W.X. Tian, Y.P. Zhang, G.H. Su, S.Z. Qiu, X.T. Yang, et al., Development of DETAC and its application to the hydrogen detonation analysis, Prog. Nucl. Energy 85 (2015) 228238. [37] M. Manninen, A. Silde, I. Lindholm, R. Huhtanen, H. Sjovall, Simulation of hydrogen deflagration and detonation in a BWR reactor building, Nucl. Eng. Des. 211 (2002) 2750. [38] K. Hsu, A. Jemcov, Numerical investigations of detonation in premixed hydrogen-air mixture—assessment of simplified chemical mechanisms, in: Fluids 2000 Conference and Exhibit, 2000, pp. 2478. [39] H. Kim, Y.F.K. Lu, D.A. Anderson, D.R. Wilson, Numerical simulation of detonation process in a tube, CFD J. 12 (2003).

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C H A P T E R

15 Severe accident analysis with AC2 Andreas Wielenberg, Sara Beck, Thorsten Hollands, Liviusz Lovasz, Holger Nowack, Claus Spengler, Martin Sonnenkalb and Andreas Schaffrath Gesellschaft fu¨r Anlagen- und Reaktorsicherheit (GRS) gGmbH, Schwertnergasse, Cologne, Germany

The AC2 code suite integrates the thermal hydraulics system codes ATHLET, ATHLET-CD, and COCOSYS (COntainment COde SYStem) for the analysis of nuclear reactors at normal operation, for anticipated operational occurrences, design basis accidents, and design extension conditions up to severe accident (SA) conditions with radionuclide releases from the containment into the environment. GRS started the integration of its system codes into AC2 in 2016, recognizing first the increasing need for integral state-of-the-art simulations of scenarios with interaction between the cooling circuit and the containment. Second, against the background of advanced Gen-III/III 1 light-water reactors (LWRs) as well as several popular small modular reactor concepts, GRS saw the need for the realistic simulation of passive safety features with small driving forces and their interactions, both between different systems and between trains of one system [1,2]. Fig. 15.1 gives an overview of the current code architecture for the AC2 package and the role each system code plays. In this chapter, we present ATHLET-CD for SA in the cooling circuit in Section 15.2 and the SA modules of COCOSYS in Section 15.3. The THY module of COCOSYS and the ATHLET code are described in Chapter 12 in the thermal hydraulics code part of this book.

15.1 The severe accident code ATHLET-CD for in-vessel phenomena 15.1.1 Introduction ATHLET-CD extends the underlying ATHLET models and inputs with additional modules for the simulation of SA phenomena and processes. Consequently, nuclear

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00015-2

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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FIGURE 15.1

Architecture of the AC2 code package.

FIGURE 15.2

ATHLET-CD code structure and interfaces [3].

thermal hydraulics are provided by ATHLET. ATHLET-CD has a modular structure; the most important modules of the recent ATHLET-CD 3.2 are the following (see also Fig. 15.2): • ECORE calculates core heat-up, core degradation phenomena, and oxidation effects.

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• FIPREM simulates the fission product (FP) release from fuel rods after cladding failure. • SAFT computes transport and deposition of FP outside of the core region in the cooling circuit through multiple release paths. • FIPISO calculates the activities of the core material and released FP and the resulting decay as well as decay power on a nuclide basis. • AIDA and LHEAD are two modules for simulation of lower plenum (LP) processes and ex-vessel cooling. • MEWA describes debris bed behavior (still under major development). As a plug-in of ATHLET, ATHLET-CD uses the same numerical approaches as ATHLET. Moreover, ATHLET-CD is fully compatible with the NuT library. All modules use the timesteps defined by ATHLET except for the module SAFT that uses the ATHLET timestep as input and subdivides this timestep in its own time integration procedure. After a brief summary of the development history of ATHLET-CD, we describe the main ATHLET-CD modules in more detail in the following sections.

15.1.2 History of ATHLET-CD development The work of extending ATHLET with SA modules was started by GRS at the end of the 1980s in collaboration with IKE Stuttgart. The first step was integrating the KESS-III code developed by IKE Stuttgart [4,5] as the module ECORE for simulation of fuel and core degradation and the module EFIPRE for FP release (now: FIPREM) into ATHLET. This code was released as ATHLET-SA HEAT 0.1N in 1991 [6,7]. The further development made use of thermal hydraulics improvements in ATHLET and integrated additional codes coming from IKE Stuttgart and also IRSN into the code system. We show an overview of the history in Fig. 15.3. By 1997 the code had been renamed ATHLET-CD, and the FP transport module TRAPMELT had been replaced by SOPHAEROS V1.1 [8] developed by IRSN and available through the common ASTEC development. Also, at this time, the first version of the code manual was issued. With ATHLET-CD 1.1G in 2001 [9], some modules of the MESOCO code by IKE [10] for the simulation of severely degraded cores, such as particle beds, had been integrated and a core quench model had been added. The next steps were adding improved blockage models, oxidation models for melt and crust as well as boiling water reactor (BWR)-specific models such as B4C oxidation (ATHLET-CD 1.1K in 2003), integration of SOPHAEROS 1.2 [11], and pressuredependent release of Ag, In, and Cd in ATHLET-CD 2.0 [12]. ATHLET 2.1A in 2006 provided improved rod ballooning from the GRS code TESPA-ROD [13] and models for air oxidation as well as an initial coupling to the COCOSYS code. ATHLET-CD was now released in conjunction with ATHLET. The next release ATHLET-CD 2.2A in 2009 saw further major revisions [14]. With the FIPISO module a GRS code for transient nuclide inventory, power, and decay simulation [15] was added, and the IKE’s MEWA [16], a combination of MESOCO and IKE’s WABE (for water in debris beds), became the debris bed module. ATHLET-CD 2.2C saw melt relocation to the LP and the introduction of the

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FIGURE 15.3

15. Severe accident analysis with AC2

Time line of ATHLET-CD development.

dedicated zero-dimensional (0D) LP module AIDA as well as zirconium nitride formation models [17]. In ATHLET-CD 3.1A from 2016 the 2D LHEAD module for the LP utilized the ATHLET nodalization by extending the ECORE models downward, and a model for melt discharge to the containment (COCOSYS) was created. The current version ATHLET-CD 3.2 [3] is realized as a predefined plug-in for ATHLET. A model for radial melt spreading was implemented, the AIDA module was considerably upgraded, and the new SAFT module has continued the integration of the previous SOPHAEROS, allowing for multiple release paths for the first time.

15.1.3 ATHLET-CD modules and models Like other SA codes such as MELCOR [18] or ASTEC [19], ATHLET-CD also divides the core region horizontally into concentric rings and axially into different nodes (Fig. 15.4). It is assumed that in a radially and axially defined node all fuel rods, control rods, and structure materials behave identically. They are simulated with a so-called representative fuel rod that summarizes the extensive and intensive properties of all fuel rods/control rods and structure materials within a node. Grouping many fuel rods into a ring is a valid assumption as long as there are no significant changes in the boundary conditions in azimuthal direction along a ring.

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FIGURE 15.4 Side and top view of the core nodalization in AC2.

15.1.3.1 ECORE ECORE replaces the ATHLET rod models. It calculates the phenomena occurring during the early phase of an SA. A system of equations describing the energy balance of fuel, cladding, control rod materials, and melt/crust is solved separately using the implicit Euler method [20]. Coupling to ATHLET occurs at the boundary of the ATHLET-CD structures (cladding and/or melt/crust surfaces), where the heat transfer coefficient is calculated by ATHLET. The following equations describe the energy balances of the structures in ATHLET-CD: mFj cFpj dTjC mCj cCpj dt

dTjF dt


 F 5 2 kFCj AFCj TjF 2 TjC 1 Q_ j






 5 kFCj AFCj TjF 2 TjC 2 kCFlj Arodj TjC 2 TjFl 2 αCRelj ARelj TjC 2 TjRel

 i;i C C C CR 2αi;i11 Radj Ai;i11;j Ti;j 2 Ti11;j 2 αRadj Ai Ti;j 2 Ti;j 4
 X C n 2 αnCanj AnCanj TjC 2 TCan 1 Q_ j n51

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The description of the variables is listed in Section 15.6. This system of equations is C i;i11 solved by the implicit Euler method, but using the values of kFCj , kCFlj , αRad , TjFl , Q_ j , and j F C _ _ Q j from the previous timestep. The heat flux Q j incorporates heat flows in axial direction via heat conduction and radiation as well as heat losses to the core surroundings. Decay power is calculated either with a user-defined table or by using the FIPISO module (Section 15.2.3.3). For mechanical rod behavior, ECORE calculates the phenomena inside a rod until rod failure, taking the following processes into account: • change of internal pressure, considering fission gas release, fuel swelling, and porosity, and assuming ideal gas behavior for simplicity;
 • change of pellet radius, where fuel diameter is DF ðtÞ 5 DF;0 β~ F TF ðtÞ 2 TF;0 ; • ballooning, with different correlations available based on the works of Rosinger and Northwood [21] or Erbacher et al. [22]; and • rupture of cladding due to pressure and thermal load with the Henky stress parameter εH ϕ $ 0:38 or burst temperature via Chapmans correlation [23] or using the Hagrman model [24]. Ballooning changes the geometry of the cooling channel, which is captured in ATHLET by narrowing (eventually blocking) the flow paths and changing the adequate form factors. After failure of the fuel rods, FP release calculation starts, which is simulated by FIPREM (Section 15.2.3.2). After the cladding temperature reaches B1000 K, oxidation processes become relevant, contributing significantly to core heat-up. The oxidation models calculate the energy generation from the chemical reaction between metallic zirconium and steam/ air. The energy generated during oxidation is added to the cladding in the energy balance equations while also taking the changes in material properties (ZrZrO2) into account. In case of oxidation in steam atmosphere, the release of hydrogen and the consumption of steam are simulated within the related ATHLET thermofluid object. Oxidation is limited or even stopped in case of steam starvation. Oxidation is calculated on the outer side of the cladding until cladding failure, then also on the inner side. The oxidation rate follows the parabolic law dW 2 5 xp dt, with W as oxide layer thickness and xp as diffusion rate [25]. The temperature dependency of xp follows an Arrhenius formulation:   xp 5 Ae2B=ðRTÞ g ps ; where R is the gas constant (R 5 8.3143 J/mol K) and T is the reaction temperature in K. The rate constant A and activation energy B are derived from measured data, and g ps models a reduction factor to consider steam starvation. Currently, three correlation sets are implemented for different temperature regimes: Cathcart & Prater/Courtright, Cathcart & Urbanic/Heidrick, and Leistikow & Prater/ Courtright [14]. ECORE chooses the appropriate oxidation model depending on the temperature. The transition of the oxidation rate from parabolic kinetics to linear kinetics is triggered by user input regarding an oxidized layer thickness from where this transition is to be simulated. Simulation of oxidation continues after the formation of melt with the surface area reduced to that of the melt rivulets.

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Air oxidation and nitride formation are simulated likewise but with the adequate material properties. Different correlations are available; for air oxidation the Steinbru¨ck correlation [26] is recommended, whereas for nitride formation, Holland’s correlation [27] is applied. In case of a mixture flow (where steam and air are both present) a multiplicator rvap;Ox is used to activate/deactivate steam oxidation. This multiplicator is determined based on the mass fraction of oxygen xO2 5 pO2 =p: • no oxygen available, that is, unlimited steam oxidation xO2 # Xlow 5 1024 .rvap;Ox 5 1; • oxygen available, steam oxidation is suppressed xO2 $ Xhigh 5 1023 .rvap;Ox 5 0; and • Xlow # xO2 # Xhigh .linear interpolation for rvap;Ox between 1 and 0. In the early phase of core degradation, particularly the melting of the metallic zircaloy of the cladding and the dissolution of the UO2 pellets caused by liquid zircaloy are relevant. Zircaloy melting begins with reaching the melting point of β-Zry or α-Zr(O) at the inner side of the cladding. UO2 dissolution by molten zirconium can be considered with a modified correlation based on Hofmann et al. [28] or a combined diffusionconvection model according to Kim and Olander [29]. Metallic melt relocation starts if the melt reaches a user-defined temperature criterion or if the oxide layer thickness of the cladding is breached. In ATHLET-CD the relocation within the core is realized via a candling model. That means that the melt is relocated as a pure film flowing downward along the rod. The model is based on the assumption of wetting low-viscosity melt rivulets connected with a simultaneous formation of crust [30]. During the relocation, only the mass and energy balance of the liquid film is solved. The momentum balance is considered by assuming a constant mass flow. During the candling process, heat transfers toward the coolant and toward the still intact structures are considered, as well as the decay power transported due to the dissolution of FP from the UO2 pellets. The power due to melt oxidation is also included. As the temperature reaches the melting point of the UO2 pellets, the ceramic melt relocates downward (relocating also its internal decay power) along the still intact structures and analogously for metallic melt. The melt during the candling process also influences the flow path of the coolant. This can result in a complete blockage of the flow channel. Due to increased cooling (e.g., reaching the water level in the core), crust formation can occur. In this case, coolant can only flow around the blocked zone, while the melt accumulating earlier the blocked node can relocate to the adjacent rings [31]. The solidified crust, either metallic or ceramic, can remelt if it reaches the melting temperature again, continuing its relocation downward until the next solidification occurs or until reaching the lower grid plate. Melting of control rods and BWR structures is simulated similarly. The core structures are coupled to the surrounding ATHLET structures via heat conduction and via heat radiation in axial and radial direction. If the grid plate reaches a user-defined temperature criterion and/or the user-defined total melt mass, then the plate fails and the accumulated melt mass relocates to the LP of the reactor vessel. 15.1.3.2 FIPREM FIPREM calculates the FP release from the fuel rods after cladding rupture. The module predicts FP release from the fuel rods based on the integral release rate approach, using temperature-dependent release rates for various groups of FP and core structure materials.

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No retention processes are taken into consideration, that is, released FPs are assumed to enter the gas volume of the core region instantaneously. The release rate is calculated by using the partial pressure of the materials [32]. The release flow of a particular component x (assuming the release rate of a component is independent of other components and melt composition, but proportional to the ratio between the partial pressure of the component and the system pressure) in a core mesh i; j amounts to [12]: 0:75 rx;ij 5 Kx Tx;ij

px;ij pg;ij

where Kx is a material constant, Tx;ij is the temperature, px;ij is the partial pressure, and pg;ij is the system pressure in the core mesh i; j. The correlation between the temperature T and the (saturation) partial pressure px of a pure material x can be described by the Antoine equation: px 5 eAx Bx =ðT1Cx Þ where A, B, and C are material properties, derived from experiments for the specific materials. For barium, molybdenum, and ruthenium, because these elements are sensitive to oxidizing and reducing conditions, these conditions of the surrounding atmosphere are taken into account via a factor based on the works of Kruse [33]. The released FP masses and their decay power are subtracted from the core; their transport in the cooling circuit is calculated by the SAFT module. FP decay in the fuel rods and after their release in the cooling circuit is calculated by the FIPISO module. 15.1.3.3 FIPISO The models included in the FIPISO module can determine the initial core inventory based on materials in the representative fuel rods and their power history. For this a onedimensional cell burn-up system is used. FIPISO then simulates the further decay of the core inventory, on isotope level, applying explicit integration with the ATHLET timestep. After FP release from a rod is initiated, FIPREM calculates the released masses on an elemental level. FIPISO attaches to these the isotope spectrum of the respective core location, reduces the rod inventory accordingly, thereby reducing its decay power. The FP in the cooling circuit continues their decay while they are transported by the module SAFT. The energy of alpha and beta decay of FP in a control volume (CV) is absorbed by the fluid. The energy of gamma decay is added to the appropriate ATHLET heat structure. 15.1.3.4 SAFT The SAFT module calculates the transport and deposition of FP in gas flows outside of the core region in the cooling circuit up to transfer to the containment, simulating the main vapor phase and aerosol phenomena using mechanistic and semiempirical models. The models of SAFT are based on SOPHAEROS from ASTEC version 2.0 [34], which has been originally developed by IRSN. SAFT takes the THY boundary conditions from ATHLET thermofluid objects and heat structures. It considers 12 different families of species (elements, compounds, gas, volatile, etc.) and 5 physical states (suspended vapor/

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TABLE 15.1

371

List of simulated phenomena in SAFT [35].

Aerosol

Vapor

Gravitational settling

Homogeneous nucleation

Laminar and turbulent diffusion

Heterogeneous nucleation

Mechanical resuspension

Wall condensation

Eddy and bend impaction

Wall evaporation

Impaction in contractions

Wall sorption

Thermophoresis and diffusiophoresis

Vapor-phase chemistry

Fallback Brownian, gravitational, and turbulent coagulation

aerosol, vapor condensed on structural surfaces, aerosol deposited on structural surfaces, and vapor adsorbed on structural surfaces). A list of the phenomena that can be taken into account is given in Table 15.1. The chemical modeling is based on the calculation of thermodynamic chemical equilibrium in each CV while its method utilizes a transient approach based on the deviation from the equilibrium. The energy involved in chemical reactions as well as the carrier gas mass changes is neglected. The chemical speciation can change with temperature, carrier gas composition, and concentration of the different gaseous species. SAFT uses its own time integration procedure at the end of the ATHLET timestep. The elemental transport rates are passed on to FIPISO, which calculates the respective nuclide transport. The SAFT version implemented in ATHLET-CD 3.2 extends the already existing material database with additional data and also enables branching in defined release paths, which achieves a more realistically prediction of FP and aerosol behavior in the cooling circuit, especially during plant simulations. SAFT usually receives the FP source term from the core via FIPREM and FIPISO. Alternatively, an external source term can be specified, which facilitates the recalculation of experiments dedicated to the transport of certain materials, without considering FP release phenomena. The current version of SAFT cannot be applied to the core region itself or reliably calculate FP transport in the liquid phase (water). 15.1.3.5 AIDA/LHEAD In ATHLET-CD, there are two modules available to model the relocated molten material behavior in the lower head: AIDA and LHEAD. AIDA is a separate module, coupled to ATHLET-CD only via GCSM signals of ATHLET. AIDA starts after the lower grid plate failure for pressurized water reactors (PWRs) or control rod guide tube failure boiling water reactor (BWRs), triggered by control signals. The relocation process is not modeled in detail, instead the molten material appears instantaneously in the AIDA domain. AIDA simulates the thermal behavior of the molten corium pool, including pool segregation, with crust formation between corium and

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wall, the heat transfer through the crust, and reactor pressure vessel (RPV) wall and includes models for the wall damage, wall failure, and external vessel cooling. The corium pool is calculated with simplified, 0D balance equations. Additional empirical correlations are used to determine the heat fluxes. Homogeneous or stratified (twolayer) pool configuration models are available. The distribution of decay heat between the layers is defined by user input. AIDA considers top cooling conditions, where the heat flux from the corium pool can be added to the fluid in ATHLET CVs for the LP. For dry conditions, only radiative heat transfer is assumed and can be assigned to a user-defined heat structure. Heat transfer from the metallic layer to the vessel wall is calculated directly, while heat transfer from the oxidic pool toward a wall is calculated through a dynamically evolving crust. The LP wall consists of a hemispherical and a cylindrical part, which are nodalized both horizontally and radially. Heat conduction through the wall is solved two-dimensionally with a finite difference method. The temperature of each wall node is calculated with the following equation [36]:         Hn =2Ln λi;j 1 λi;j21 Ti;j21 2 Ti;j 1 Hn =2Ln λi;j 1 λi;j11 Ti;j11 2 Ti;j         dTi;j 1 Ln =2Hn λi;j 1 λi21;j Ti21;j 2 Ti;j 1 Ln =2Hn λi;j 1 λi11;j Ti11;j 2 Ti;j 5 ðρLn Hn cp Þ dt where Hn and Ln are the height and length of the nodes. If a node reaches the structure melting temperature and it received more energy than the latent heat of fusion for all the material in that node, it is considered molten. Then, the metallic mass is added to the total metallic mass of the molten pool (changing the height of the metallic layer), and the node is filled with ceramic or metallic melt, depending on the location of the node failure, see Fig. 15.5. The modeling of transient external vessel cooling is possible with predefined or calculated heat transfer coefficients, considering also boiling conditions. The damage and the failure of the RPV wall can be simulated via four different failure models: ASTOR approximation, LarsonMiller approach, rupture model, and wall ablation. For the latter, wall failure is predicted with a simple failure criterion taking into account the pressure

FIGURE 15.5

Model for heat conductivity in wall and wall ablation.

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FIGURE 15.6 Typical AIDA configuration.

difference, temperature, remaining wall thickness, and mass of the corium as well as the mass of the vessel wall below the corium pool level. Fig. 15.6 shows a typical AIDA model. Alternatively, the LHEAD module can be used. LHEAD extends the ECORE modeling to the LP and thus allows to use a more detailed nodalization of that domain based on CV in ATHLET. Moreover, a simplified modeling of the LP structures is possible. This is of interest, for example, for the late phase in BWR in order to consider special structures such as penetrations through the vessel (such as control rod guide tubes).

15.1.4 Numerical approach ATHLET-CD as a plug-in of ATHLET uses its numerics. It is also fully compatible with the NuT library (see Chapter 12 of this book). Most ATHLET-CD modules have their own integration routines that are identified earlier.

15.1.5 Specific models for certain reactor designs Several BWR-specific models are available in ATHLET-CD, which simulate the behavior of the canister walls and absorber blades, including their oxidation and melting as well as their impact on the flow paths within the core. These have been validated against BWR-specific experiments. For waterwater energetic reactors (WWERs) the hexagonal geometry of the fuel assemblies can be taken into account. There is a first test version allowing a rectangular nodalization of spent fuel pools for more realistic simulations [37].

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TABLE 15.2 Excerpt of ATHLET-CD validation status. Experiment/accident

ATHLET-CD version

CODEX AIT3

3.2

CORA 15

3.1A

CORA 28

3.2

CORA W2 (ISP-36)

3.1A

Halden IFA 650 3

2.0B

LIVE L11

3.2

PARAMETER SF3

3.2

Phe´bus FPT-3

3.2

QUENCH-03

3.1A

QUENCH-17

2.2C

TMI-2

3.2

15.1.6 Validation of ATHLET-CD From the ATHLET-CD validation matrix, 42 test cases have been successfully calculated with at least one ATHLET-CD version so far [38]. Selected validation results are, for example, presented in Ref. [39]. A separate validation report for ATHLET-CD is under preparation and will appear in 2020. An excerpt of the validation matrix is shown in Table 15.2. For the current version ATHLET-CD 3.2, several tests have been calculated for the first time or have been recalculated to compare the results with experimental data and, if applicable, the results of previous code versions to evaluate code predictiveness and model improvements. In general, ATHLET-CD 3.2 shows good agreement to the experimental data and better results than previous code versions or at least the same quality of results. The validation demonstrated that improvements of several code and model weaknesses identified based on user feedbacks from prior versions are effective [38]. The results of the validation are illustrated with two examples in the following sections. 15.1.6.1 Simulation of Phe´bus FPT-3 In the Phe´bus FP (Fission Product) program, performed by CEA and IRSN between 1993 and 2004, the focus was on the investigation of the phenomena during an SA and to generate data for SA code validation. A 900 MWe PWR was the basis for the design of the Phe´bus facility at the scale of 1:5000. In the last test FPT-3, conducted in 2004, the impact of B4C on fuel degradation as well as FP release and transport to the containment was investigated. The test can be divided into six phases: calibration, preoxidation, oxidation, three power plateaus, heat-up, and finally cooldown [40,41]. For the validation of ATHLET-CD 3.2, particularly the new FP transport module SAFT, recalculations were performed with ATHLET-CD 3.1A Patch 4 and ATHLET-CD

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FIGURE 15.7 FPT-3 relative iodine release into the containment [41].

3.2, which were compared to experimental data. The results of the simulation show that nearly no differences are predicted by both code versions for the thermal behavior in the core. The measured fuel and cladding temperatures are well captured by both code versions. The mass of H2, which is mainly generated in the first oxidation phase, is calculated qualitatively correctly but underestimated by both code versions, that is, 60 g with ATHLET-CD 3.2 compared to 105 g in the experiment. For ATHLET-CD 3.2 the molten mass of 1.8 kg is slightly overestimated by 0.2 kg [38,41]. In general, the released masses of FP are comparable in both simulations, because the release is mainly triggered by core temperatures and are acceptable compared to the measured values. The new module SAFT within ATHLET-CD 3.2 (green) predicts a higher deposition in the circuit that leads to lower release into the containment compared to ATHLET 3.1A (red) and a better agreement with the experiment (see Fig. 15.7). As iodine and its chemical composition are of high importance for the chemistry in the containment, the ratio between aerosol and gaseous I2 is relevant. In the experiment FPT-3, about 87% of the iodine release to the containment was in gaseous form. With ATHLET-CD 3.1A, only 10% of iodine is predicted as gaseous, while the new module SAFT within ATHLETCD 3.2 calculates up to 90% gaseous I2, which shows a very good agreement to the measured value. The quantitative analysis of the deposition along the circuit shows that ATHLET-CD 3.1A predicts a better agreement with the experiment in the hot and cold legs, while at the locations where the highest deposition occurred along the steam generator, the values calculated with the new module SAFT in version ATHLET-CD 3.2 are in better agreement to the experiment [38,41]. 15.1.6.2 AC2 application for a generic PWR accident scenario The postulated accident sequence is a medium break LOCA in the cold leg with simultaneous station blackout in a generic PWR (4-loop concept). After 500 seconds of nominal

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TABLE 15.3 Main sequence of events.

FIGURE 15.8

Event

Time (s)

Break opening

500

Reactor SCRAM

502

1st LSC

1760

Beginning of oxidation

3670

1st clad failure

4341

1st fuel failure

6385

Melting progress throughout the accident scenario [42].

operation the break is initiated in Loop 1 (with the pressurizer), at the middle of the cold leg loop seal. The size of the break is 400 cm2 or about 9% of the cross section. Due to the postulated station blackout, no active safety systems are available, only the hydroaccumulators work as intended [35,42]. The main sequence of events is presented in Table 15.3. SCRAM occurs with the break and station blackout is assumed disabling high- and low-pressure injection, thus accelerating accident progression. Cladding oxidation starts at around 3670 seconds, and by the end of the simulation, it is responsible for the generation of about 675 kg of H2. Core heatup starts between 3600 and 4200 seconds depending on the position. First cladding failure occurs at 4341 seconds, when the central rod bursts. The overall melting process in the core over time is illustrated in Fig. 15.8. Melt formation starts at around 4400 seconds, but initially, its source is solely the absorber and guide tubes materials. Some oxidation of the cladding takes place already before

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FIGURE 15.9 Temperature distribution at 515 s and Hydrogen concentration at 5500 s in the containment [42].

4200 seconds, but the H2 produced is negligible. Strong oxidation starts around 4700 seconds, when most of the core reaches 1200  C1300  C. First fuel failure occurs at around 6385 seconds in the middle of the core driven by the accelerating Zr oxidation. At this point, most of the control rods are already molten and some metallic melt can also be seen originating from the melting of the cladding material. As time progresses, the middle section, being the hottest part of the core, melts. At the end of simulation, all sections of fuel rods are almost completely molten (Fig. 15.8, right) except for short stubs at the top and bottom of the core. The first ceramic melt (UO2) appears around 6400 seconds. Afterwards, the main molten mass consists of ceramic melt, while the mass of the metallic melt stays practically constant after 8000 seconds. Some crust formation can be observed, but most of the material stays molten throughout the simulation. By the end of the simulation, B675 kg H2 is produced, which corresponds to about 20% of Zr being oxidized. Regarding FP release, the simulation shows that the main release of volatile I and Cs from the core happens at the beginning of the SA (melting of the core material), and after 10,000 seconds no further release from the core can be observed. ATHLET-CD predicts that most release volatiles are retained in the primary circuit, and only about 16%18% of the released Cs and I reaches the containment. Fig. 15.9 (left) depicts the containment temperature distribution 15 seconds after the break opening, illustrating the flow patterns simulated by COCOSYS. Importantly, the calculated peak containment pressure of 2.7 bar remained (far) below the venting and containment failure thresholds. AC2 also simulates the transport of H2 from the core to the containment. Fig. 15.9 (right) shows the H2 distribution in the containment at 5050 seconds predicted by COCOSYS and indicates the active recombiners (red squares). As time progresses, H2 becomes more homogenously distributed in the containment and more recombiners become active. The H2 concentration stays outside of the region where deflagration/detonation could occur over the whole time. Thus no challenge to containment integrity due to H2 deflagration is predicted.

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15.1.7 Scope of application and limits While ATHLET has some initial validation for alternative working fluids, the main focus of ATHLET-CD development has been on core degradation scenarios for LWRs. Consequently, ATHLET-CD does not include specific core degradation models for nonLWR designs or indeed specific models for the degradation of fuel assemblies different to LWRs. While simulations models with alternative working fluids can be set up in principle, they will utilize models developed for water-cooled reactors and will likely be unable to capture all relevant physical and chemical phenomena. In addition, there are no specific models required for pressure tubetype reactors. In this respect, ATHLET-CD is restricted to LWR power reactors of PWR, WWER, or BWR type and gas-cooled reactors equipped with vertical pinshaped fuel rods. The elliptical bottom head of the WWERs has to be modeled as semihemispherical, a specific model is under development. With some simplifications in the model, ATHLET-CD can be used to simulate SAs in spent fuel pools.

15.2 Severe accident analysis for containment phenomena with Containment Code System 15.2.1 Introduction The computer code COCOSYS is being developed GRS for the analysis of containment behavior in LWRs up to SA conditions. COCOSYS consists of three main modules that cover a range of related phenomena that are relevant for the evaluation of the containment behavior (see Fig. 15.10): • THY for the thermal hydraulics models, • AFP (aerosol and FP behavior) for the FP transport and their behavior in the containment, and • CCI (core concrete interaction) for the behavior of corium relocated to the containment after RPV failure. Communication among these main modules (separately executable packages) is accomplished via MPI (Message Passing Interface).

15.2.2 History of Containment Code System development The development of a containment code at GRS is originated already in the 1970s with the work on the code RALOC (radiolysis and local gas distribution in containments). First descriptions of RALOC can be found in Refs. [43,44]. In the late 1990s RALOC together with a few GRS codes for other relevant containment phenomena, which had been developed separately, were integrated into a first version of the COCOSYS [45] (see Fig. 15.11). Among them were FIPLOC [46] for aerosol and iodine behavior, FIPHOST [47] for aerosol transport, DRASYS [48] for the simulation of pressure suppression systems, and FIPISO [15] for FP behavior. Since then, COCOSYS has been continuously validated, updated, and improved for the comprehensive simulation of all relevant containment processes and conditions in LWR.

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FIGURE 15.10

COCOSYS code structure and interfaces. COCOSYS, Containment Code System.

FIGURE 15.11

Time line of COCOSYS development. COCOSYS, Containment Code System.

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These updates comprise different model features, code coupling to various versions of ATHLET-CD, and others, as summarized in Fig. 15.11. COCOSYS version V2.4 was released in 2010 and, among others, included a new iodine module AIM-3 (Advanced Iodine Model, 3rd version) [49], a spray jet model [50] and a wet resuspension model [51] developed at Ruhr-University Bochum, models for simulation of direct containment heating (DCH) and simple hydrogen deflagration and flame front propagation models (COMB/FRONT). In addition, the new heat transfer model CO1 combined free and forced convection with condensation models and is recommended as default. The recent version COCOSYS V3.0 was released with AC2 2019 and allows the complete flooding of nonequilibrium-type zones with water using the new junction type ATM_FULL for simultaneous transport of gaseous components and water, and the simulation of multiple corium pools in CCI (in parallel or as sequence in case of melt relocations after penetrating of confining structures like cavity sidewall or bottom). In addition, the coupling to ATHLET/ATHLET-CD 3.2 was improved, including the melt release from ATHLET-CD (AIDA) to COCOSYS (CCI) upon RPV failure, and there is a coupling interface to the coarse grid, single-phase CFD code CoPool by the Fraunhofer Institute for Industrial Mathematics ITWM for 3D simulation of thermal behavior inside nonboiling water pools (e.g., containment sump, pressure suppression pools).

15.2.3 The Containment Code System main modules 15.2.3.1 Thermal hydraulic module COCOSYS’ THY module is briefly described in Chapter 12 of this book. Importantly, THY includes several models that are mostly relevant for the simulation of SA sequences, including accident management. Therefore THY includes models for the simulation of pump and spray systems, different types of coolers, ventilation systems, and condensers. For simulation of design-specific details, some optional models are incorporated, for example, specific safety flaps, weight-dependent valves, or U-shape hydrolocks for Russian WWER- and RBMK-type containments. H2 and CO recombination can be simulated by thermal recombiners as well as by passive autocatalytic recombiners for several different types. Finally, the simplified combustion and flame propagation model FRONT allows to predict pressure pulses from H2 and CO combustion in the containment. It was validated against several H2 combustion experiments covering a broad spectrum of possible scenarios. 15.2.3.2 Aerosol and fission product module The AFP main module is used for best estimate simulations of the FP behavior in the containment. Interactions between the thermal hydraulics and the aerosol and FP behavior are considered. Within the course of SAs in nuclear power plants, FP can occur in different species within the containment. Gaseous FPs that are transported dissolved in the atmosphere must be distinguished from solid species that are bound to aerosol particles. While gaseous species are transported to water pools across the sump surface via diffusion, aerosol

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FIGURE 15.12

381 Hosts and forms

of fission products.

particles can deposit on water pool surfaces with subsequent settling within the water volume. Certain species that are bound to aerosols can disintegrate into species solved within the liquid phase. For the simulation of the transport of the FP within the containment, the FPs are treated as the radioactive part of the aerosol particles and of the radioactive NC gases, whereas their masses themselves do not affect the calculation of mass fluxes within the containment. An overview of possible hosts and forms of FP in the containment is given in Fig. 15.12. The numbers show FP in different conditions as calculated in AFP: 1. Dissolved gaseous species in the atmosphere, for example, Xe, Kr, I2, and RI. 2. Airborne species bound to aerosol particles, for example, CsI and AgI. 3. Deposited aerosol particles on wall structures in the atmosphere. In addition, adsorption and chemical reactions of gaseous species can occur on atmospheric wall structures. 4. Aerosol particles transported in the water phase. 5. Deposited aerosol particles on submerged wall structures. In addition, adsorption and chemical reactions of dissolved species can occur on submerged wall structures. 6. Dissolved species in the water phase, for example, I2 and RI. 7. Transport between adjacent zones via atmospheric junctions. In addition, transport through drainages is considered. 8. Trapped species in filter systems. All relevant processes related to FP and different carriers are considered: deposition of aerosol particles by natural processes or aided by technical systems such as retention in filters and washout by spray systems, washing-off from walls, and carrier change due to radioactive decay. AFP calculates the aerosol behavior of up to eight different aerosol components (e.g., CsI and CsOH), covering relevant aerosol physics and transport in water and gas phases. Chemical interactions of the three aerosol components CsI, IO3, and Ag are considered. Additional aerosol components (including water) may be specified, with the maximum of eight components. This limit was set upon computational efficiency considerations for such polydisperse aerosol calculations. Relevant processes and phenomena for transport, deposition, and remobilization of species are comprehensively considered. The module differentiates between soluble and insoluble as well as hygroscopic and nonhygroscopic aerosols. The four deposition processes

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sedimentation, diffusive deposition, thermophoresis, and diffusiophoresis are covered. The aerosol model contains models for four different aerosol processes: Brown’s agglomeration, gravitation agglomeration, turbulent shear agglomeration, and turbulent inertial agglomeration. The deviation of particles from spherical form is considered. For the calculation of condensation on aerosols, the moving-grid method reduces numeric diffusion between aerosol size classes considerably. In the case of hygroscopic aerosols, condensation may already occur under superheated conditions and can change the level of humidity in the atmosphere. This feedback is taken into account in the THY calculation as aerosol behavior close to saturation depends highly on humidity. Specific models for deposition on containment surfaces and water films running down such surfaces are available. Iodine chemistry is captured with the semimechanistic model AIM-3 [49], which is and has been improved according to the outcome of various THAI iodine [52] and other experiments, including OECD-BIP, PHEBUS-RTF, CAIMAN, and EPICUR tests. AIM-3 simulates in detail the transport and behavior of iodine species in a multicompartment geometry. It considers B70 different reactions in the gas and water phases of a zone. The transport of I between the compartments by gas and water flows as well as between atmosphere and sump is considered. There are special models for the simulation of HEPA fiber and granulate filters as well as an empirical model of a venturi scrubbertype filter. Retention of aerosols during gas flows through water pools is calculated with a modified SPARC-B model [53]. This allows, among others, simulation of pool scrubbing in the suppression pool of a BWR. The behavior of radioactive nuclides can be simulated with the help of the FIPISO model that calculates the decay of the FP inventory (up to 1296 isotopes) provided to COCOSYS, for example, from ATHLET-CD, see Section 15.2.3.3. 15.2.3.3 Core concrete interaction module and other ex-vessel corium issues In the case of RPV failure, the corium will relocate into the reactor cavity. The COCOSYS CCI module describes the following effects arising from the interactions of the corium with the atmosphere and structures in the containment: • local sources of thermal energy, FP, and NC gases; • melting of structural material and incorporation of molten material into the corium melt; • effect of deepwater layers in containment rooms on the coolability of the corium under top flooding conditions; • loss of containment integrity; and • melt relocations into other compartments within the containment after failures of structures. In COCOSYS the same model basis as of ASTEC/MEDICIS [54] is used for the solution of mass and energy balances of a single corium pool under molten coriumconcrete interaction (MCCI) conditions. The 2D shape of the corium pool (i.e., interface between corium and concrete) is in principle axisymmetric and is determined as a function of time using local energy conservation at each node in the boundary contour and with a common melting approach (Stefan’s equation). Both, homogeneous pools (with well-mixed metal and

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oxide melt fractions) and stratified configuration of two layers (oxide at the bottom and metal on top or vice versa) can be considered. Also, the pool may evolve with time from an initially homogenous pool to a stratified configuration. In the stratified configuration the sequence of layers (i.e., oxide, metal) from bottom to top is governed by layer densities so that prediction of layer inversion due to enrichment of the heavy oxide layer with light concrete decomposition products is possible. FP release from the MCCI pool is approximated assuming thermodynamic equilibrium between gas bubbles released from concrete decomposition and the melt. Heat transfer between melt and concrete is calculated based on a distribution of effective heat transfer coefficients along the pool interface in combination with a specified concrete decomposition temperature. The upward heat transfer from the upper interface of the pool (including a potential top crust) to the surrounding is calculated considering radiation and convection processes. In the case of top flooding condition, boiling heat transfer in a free convection configuration is considered. Multiple melt pools with interactions between molten corium and containment structures (sidewall, floor) may be defined in COCOSYS. This allows to consider a relocation pathway of the corium within containment rooms in case of structural failure of, for example, a sidewall or a floor due to concrete erosion. The MCCI model in COCOSYS has been successfully validated against a broad range of experiments, including the ACE, BETA, COMET, MACE, OECD-CCI, VULCANO, and MOCKA experiments [55]. Corium ejection from the RPV at elevated pressure can lead to a breakup of the corium jet with small corium particles quickly dispersed in the containment and leading to DCH. In COCOSYS, dedicated models are available for the following processes during DCH: • • • • •

entrainment of the deposited corium by gas flow, transportation of the gascorium mixture inside the containment, deposition of corium in the containment under the force of gravity, chemical reaction between entrained corium droplets and atmosphere, and heat transfer between atmosphere-borne or deposited corium and the containment atmosphere and structures.

The DCH model in COCOSYS was applied to several integral DCH experiments in the DISCO test facility in Karlsruhe. In the experiments the reactor cavities of KONVOI, EPR, and the French P’4 reactor types were modeled. Overall, compared with the measured data, satisfactory agreement of the integrally dispersed parts of the melt and the maximum pressures was achieved. Even blind calculations showed good predictive capability, provided that empirical model parameters were adapted to other experiments using the same geometrical design [56]. For the simulation of corium spreading on a containment floor, COCOSYS features a dedicated corium spreading model called LAVA [57].

15.2.4 Numerical approach The individual main modules (see Fig. 15.10) are by default coupled at macro-timestep level so that the frequency of parameter data exchange is relatively low. Additional

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coupling variants (calculation of the width of the synchronization intervals, data exchange) can be selected by the user. To manage the complexity of the data flow, data exchange is only allowed between the modules and the main driver. Since the main modules are independent, undesired side effects are avoided and maintenance of the overall system is facilitated. The overall timestep used in the COCOSYS system is based on the THY main module (ΔtTHY). However, this timestep may be further reduced according to requirements of other modules or dependent on user inputs for timestep management. 15.2.4.1 Thermal hydraulic module The main integration package inside the THY main module is FEBE, see the description in Chapter 12 in the thermal hydraulics code part. 15.2.4.2 Aerosol and fission product module The AFP main module simulates several different issues related to aerosols and FP: their physical behavior (aerosol physics), their transport and decay, their chemical behavior, and their retention during transport through water pools (pool scrubbing). The coupling between these four topics of the AFP module is realized using an internal management based on subordinate timesteps for different models within AFP. The AFP module receives the overall timestep ΔtTHY from the COCOSYS driver. First, the stationary pool scrubbing model is executed, resulting in decontamination factors for the corresponding junctions. Then, the subsequent polydisperse aerosol calculation is executed using the subordinate timestep level Δtae. The aerosol part consists of two parts: the condensation part using Δtcond and the aerosol depletion part using Δtdepl. FEBE is used as solver for the aerosol physical behavior. For condensation the system of ordinary differential equations is solved by an adaptive characteristic method to minimize numerical diffusion. After solving the aerosol problem over the complete timestep ΔtTHY, the FP and chemical equations are integrated using a subordinate timestep level Δttransp and Δtchemical, respectively. The FP equations are solved for each element separately with an explicit method of the FEBE package for all zones and junctions. The iodine equations are solved explicitly for each iodine compartment (one or several zones) separately. 15.2.4.3 Core concrete interaction module Similar to the ASTEC/MEDICIS code [54], the system of ODE for the mass, enthalpy, and the swelling (volume increase due to gas content) of the up to two layers forming the corium pool is solved partly implicitly with regard to the swellings and element masses and almost totally implicitly with regard to the layer temperatures. The implicit solution is obtained by an iterative NewtonRaphson method.

15.2.5 Models for specific reactor designs COCOSYS is developed with the objective to provide a tool kit to the user for building an adequate model of a typical LWR containment according to the specifics of the actual design. All models for containment phenomena relevant to reactor safety issues are on board, and the user interface provides enough versatility to select and combine the models

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via editing of the input deck so that the model simulates sufficiently the actual design of the plant. In the following a few examples are given in which specific design features of plant types can be simulated with specific COCOSYS models: • A bubble condenser is a complex passive pressure suppression system used in WWER-440 plants to limit the pressure rise in the containment during accidents. Its modeling requires simulating the reverse flow of water from the pressure suppression system (i.e., bubble condenser). In COCOSYS, this is achieved by a pump system without an active pump. The actual water volume flow rate is calculated based on the junction (piping) cross section, the given pressure loss coefficients, and the water density. The driving force results from the actual water levels and the pressure difference between the connected zones. In addition, the process can be controlled by valves. A spray system may be assigned to the pump outlet. The water-level characteristic for each zone can be described using a water volume-level table. The validation of the pressure suppression system model DRASYS in COCOSYS for WWER440/213 with bubble condenser is based on experiments in the EREC BC V213 facility. • A special vortex zone model is used for dynamic processes in a jet vortex condenser (JVC) installed in NPP of type WWER-440/230. A vortex zone in COCOSYS is subdivided into four zone parts: a downcomer or gas volume above the water (DC), a vortex chamber (VC), or gas volume behind the water, including the gas volume of the recirculation tank (RT), the water pool (POOL), and the water in the RT, if water exists there. The thermodynamic state of the zone parts is calculated using the equations of the equilibrium zone model. In case of an accident with large steam mass (and energy) release into the confinement, the pressure in the confinement rapidly increases. As a result of this, the JVC water is pushed from the DC through the jet nozzles into the VC. Passing the nozzles arranged under an attack angle of 45 degrees, the water starts to swirl inside the VC. A vortex funnel appears, that is, the water level in the DC simultaneously decreases whereas the level in the VC increases. When the water level at the periphery of the VC reaches its upper edge, the water starts to flood the RT and flows through recirculation pipes back into the POOL inside the VC. The water swirling in the VC ensures an efficient condensation of the steam from the steamgas mixture passing through the condenser. NC gases are directed via the outlet corridor to the environment. COCOSYS validation of the JVC model is based on experimental data from the JVC test facility RU-4 in Kashira (Russia). • The U-shaped hydrolock model is implemented in COCOSYS to be able to simulate the reactor cavity venting system of NPPs with RBMK. The hydrolock is an isolation device in the reactor cavity venting system and is initially filled with water. In case of pressure increase, the hydrolock is cleared, and the cavity gas mixture is vented. In COCOSYS the special U-LOCK junction consists of a normal atmospheric junction with a special equation set for the hydrolock. • For reducing the pressure increase during accidents in NPPs, a so-called ice condenser is installed in some plants as, for example, WWER-440 in Finland. The ice condenser containment system incorporates a large amount of water ice that acts as heat sink. In the COCOSYS model the ice beds are simulated as a cylinder structure.

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When the gas mixture flows along the ice surface, the steam will condense. The model considers forced convection as well as condensation according to Stefan’s law. The heat transferred to the ice leads to melting. The default surface temperature of the ice is assumed to be at constant temperature of 3  C. Condensate and molten water are transported to the sump of the zone in case of a nonequilibrium zone model. • A core catcher is an SA mitigation system for stabilization and long-term cooling of ex-vessel corium. A crucible-type core catcher concept is applied in NPPs with WWER-1000 reactor types built in China (Tianwan) and India (Kudankulam). A different concept with a large horizontal corium spreading area was realized for the core melt stabilization system of the EPR. A simplified, generic core catcher model is available in COCOSYS, which combines the existing CCI model in COCOSYS for the simulation of the corium/sacrificial material interaction (MCCI phase) in the core catcher with a transition to a retention phase, in which the status of the corium is simulated with the help of empirical heat transfer coefficients between corium and water-cooled horizontal or vertical core catcher walls. During the MCCI phase the model tracks the melting of the sacrificial material, corium oxidation, and a layer flip of stratified oxide and remaining metal layers in the core catcher. During the retention phase the model tracks the heat transfer from the corium to its water-cooled interfaces and the physical state of the corium. • A few junction models specific to certain NPP design are implemented, for example, safety flaps as used in WWER-440/230 or pressure difference controlled valves as used in RBMK-1000 reactors. • In the AP1000 reactor the passive containment cooling system (PCCS) is designed to reduce the containment pressure during accidents. When water flows down the external containment from a tank to enhance its effectiveness, heat from the containment dome is transferred to the external water film and finally to the countercurrent gas flow that develops by natural circulation in the annular space around the containment. Inside the containment, heat is transported via convection and condensation of steam to the internal containment wall. The performance of PCCS in AP1000 PWR can be studied using simplified geometrical models of the AP1000 geometry in the form of COCOSYS zone nodalization schemes and available liquid film models in COCOSYS [58].

15.2.6 Validation of Containment Code System The COCOSYS validation matrix covers all modules and is described in the accompanying user manual [59]. Furthermore, prior to each release a suite of regression tests is performed, and results are presented as part of the program documentation [59]. COCOSYS is validated on a wide spectrum of separate and integral experiments performed at German or international test facilities. The experiments performed in the former Battelle Model Containment and the former Heiß-Dampf-Reaktor as well as the ongoing tests in the THAI facility represent a strong pillar of the COCOSYS validation. Furthermore, GRS participates in several international experimental research programs (OECD THAI/BIP/STEM/ CCI), which are used for the validation of the AFP and the CCI modules. An excerpt of the considered validation cases is shown in Table 15.4.

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15.2 Severe accident analysis for containment phenomena with Containment Code System

TABLE 15.4 Summary of experiments used for validation of the severe accident models in Containment Code System [59]. Phenomenon

Facility

Experiment

Hydrogen combustion

BMC

Ix2, Ix9, Hx26, VANAM M4

HDR

E12.3.2

NUPEC

B26, B8-3

ENACEFF

RUN765

THAI

HD-2R, HD-15, HD-22, HD-24

BMC

Gx4

HDR

E11.8.1

THAI

HR-2, HR-35, HR-40, HR-41, HR-42

BMC

VANAM M2*, M3 (ISP-37), M4

KAEVER

B11 tests, ISP-44

THAI

Aer-1, Aer-3, Aer-4, AW-1, AW-2, AW-3 (part 1), AW-3 (LAB), AW-4, TH-14  TH-17

RTF

EPICUR

3B, P9T1, P10T1, P10T3, RTF1, RTF3, RTF5 OECD BIP: G-1, G-13 OECD BIP: G-4 . . . G-12 OECD BIP: A-7, A-9 S13, S14, S15, S111, AER1, AER2

THAI

AW-3 (part 2)

Passive autocatalytic recombiner

Aerosol behavior

Iodine chemistry

RTF

ACE3B, PHEBUS RTF 3, PHEBUS-5, P9T1, P10T1, P10T3

RTF-ISP41

PT02, P1T1, PHEBUS-1

CAIMAN

ISP-41 tests: 97/02, 01/01, 01/03

THAI

Iod-6 . . . Iod-30

PHEBUS

FPT1, FPT2, FPT3

Venting filter

ACE

EPRI-II series POSEIDON PA test series Aerosols: AA-19, AA-20

Molten coriumconcrete interaction (mostly performed in stand-alone mode)

BETA

V1.8, V3.3, V5.1, V5.2

ANL

COMET

ACE: L1, L6, L8 MACE: M3B, M4 OECD-MCCI: CCI-2, CCI-3, CCI-4, CCI-5 L1, L2, L3

MOCKA

3.1, 5.7, 6.3, 7.1

VULCANO

VB-U5, VB-U6, VBES-U5

KATS/ECOKATS

KATS tests no. 7, 14, 15, 17 and ECOKATS V1 and 1

Iodine transport behavior

Integral fission product tests Pool scrubbing

Melt spreading

(Continued)

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TABLE 15.4 (Continued) Phenomenon

DCH

Facility

Experiment

COMAS

Tests no. 5a, EU2b, EU3a, EU4

VULCANO

VE-U7

FARO

L32S

DISCO

D06 FH01 . . . FH03 H1 . . . H6 KH1 . . . KH7 L04 . . . L05

BMC, Battelle Model Containment; DCH, direct containment heating; HDR, Heiß-Dampf-Reaktor.

An example of the validation of the iodine model in the AFP module is presented in the following. In the THAI test facility operated by Becker Technologies, several multicompartment tests have been performed to study the iodine behavior and distribution under SA typical conditions in a multicompartment configuration like in a PWR containment. It is expected that iodine is not distributed homogeneously over the whole containment, but that there will be different iodine concentrations in different compartments, caused by local interactions of iodine with surfaces and different flow conditions [60,61]. The objective of the test THAI Iod-28 was to demonstrate the multicompartment behavior of gaseous, molecular I2 at high humidity, and the effect of painted surfaces (representative for decontamination paints in reactor containment) on I deposition, in contrast to steel surfaces. Reliable and consistent I data were measured in the THAI vessel subdivided into five compartments by six different gas scrubbers (see Fig. 15.13). The test procedure consisted of four test phases: preconditioning (phase 1), thermal stratification (phase 2), active mixing (phase 3), and the well-mixed (phase 4). In each of the test phases, different THY conditions have been set up in the multicompartments. The test duration lasted more than one day. Results are presented only for the time frame starting with the I2 injection into the upper part of the THAI facility. The I2 deposition on painted surfaces and on vessel steel surfaces was unexpectedly small so that the multicompartment effect was only limited. The small influence of paint on multicompartment I2 behavior could only be worked out via thorough posttest COCOSYS analyses and using strongly revised I2/paint and I2/steel interaction models. As an example, Fig. 15.14 shows the comparison of the I2 atmospheric concentration measurements from six gas scrubbers (dots) with COCOSYS results for its representative zone (solid lines). The results indicate an inhomogeneous I2 atmospheric concentration particularly in the earlier phase of the experiment with obvious differences between the upper and lower compartments. The weak I2/paint interaction in test Iod-28, despite significant relative humidity in the vessel, represented another motivation to revise the old model in COCOSYS, to allow for stronger chemisorption of I2, and to consider the influence of humidity. The improved model showed a satisfactory agreement with measurement data.

V. Severe accident codes

15.3 Quality assurance measures

FIGURE 15.13

389

THAI test Iod-28 experimental setup and location of GSs nos. 16 [60]. GSs, Gas scrubbers.

15.2.7 Scope of application and limits The focus of COCOSYS application is on the phenomena in containments of LWR (PWR, BWR) of Gen-II and Gen-III/III 1 plants. COCOSYS provides a tool kit for modeling a broad range of containment phenomena related to atmosphere THYs, aerosols and FP, and ex-vessel corium behavior. The applicability of numerous detailed models is documented in the code’s user manual. Importantly for codes such as COCOSYS that allow such a degree of flexibility to the user, there is also well-known strong usereffect on any results obtained. Hence, COCOSYS users should receive adequate training before they start building their own models or perform independent safety analyses.

15.3 Quality assurance measures The quality assurance process for ATHLET-CD and COCOSYS is the same as the one described in Chapter 12 in the thermal hydraulics codes part of this book.

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15. Severe accident analysis with AC2

FIGURE 15.14 THAI Iod-28: I2 atmospheric concentration—comparison of GS samplings versus COCOSYS posttest results [62]. GS, Gas scrubber.

15.4 Outlook and summary We have briefly presented the main features of the code ATHLET-CD, an extension of ATHLET for SA progression in the cooling circuit and the spent fuel pool. In addition, we described the relevant modules of the COCOSYS code for accident progression in the containment, including the prediction of FP releases to the environment. Both codes have been extensively validated against available experiments, standard problems, and test cases. They have generally performed well in several benchmarks, demonstrating that they meet or set the state-of-the-art in SA simulation. They are generally applicable to LWR designs, including WWERs. For other reactors, capabilities are more limited. Both codes have been coupled within AC2 for integral analysis of SAs, which we have illustrated with a brief example. As part of the state-of-the-art code system AC2, the models of ATHLET-CD/ COCOSYS are under continuing development and subject to further validation by GRS and its partners. Current development lines for ATHLET-CD focus on the following: Flexibilization of core nodalization in ECORE for locally asymmetric core degradation and spent fuel pool modeling, transferring LP phenomena models from AIDA to LHEAD and further improving code capabilities, enabling FP transport through the core and within liquid water in SAFT, and replacing semiempirical models for oxidation and FP release with improved mechanistic models. The integration of the debris bed module MEWA into the code will be completed.

V. Severe accident codes

Nomenclature

391

For COCOSYS the main development lines include the release of redesigned and extended AFP module with better capabilities for aerosol, chemical, and FP behavior, for example, allowing to consider changes in deposition area with sump water level or dissolution and wash-down of aerosols. The models for corium pool behavior in CCI will be extended to consider corium spreading underwater, particle bed formation, and coolability for better simulation of deepwater pools in contact with corium. For detailed modeling of conditions in large water pools, a coupling interface to CFD tools such as CoPool will be maintained and opened, for example, to OpenFOAM. Finally, one main activity will be in further integrating the codes into the AC2 package by enhancing coupling stability and performance, for example, allowing in more detail the transfer of mass and heat between ATHLET-CD and COCOSYS domains and simplifying the user interface. All these activities will require further validation of AC2 overall and its constituent codes. For this, and also for further improvements to some models, availability of new experimental data and new insights will be essential. For the latter, we expect the continuation of the investigation of the Fukushima Daiichi nuclear power plant to provide essential input to better understand SA phenomena and improve the model basis.

Nomenclature 1 Symbols AFCj AnCanj ARelj Arodj cp D H kFCj kCFlj L m p C Q_

area of between fuel and cladding (m2) area of canister wall (m2) area of the relocating material (m2) area of between fluid and cladding (m2) isobaric-specific heat capacity [J/(kg K)] diameter (m) height (m) heat transmission coefficient from fuel to cladding (W/m2 K) heat transmission coefficient from cladding to coolant (W/m2 K) length (m) mass (kg) pressure (Pa) additional heat from axial heat radiation and conduction, heat loss to environment (W)

F Q_ j R T TjC

power source (W)

TjF TjFl CR Ti;j n TCan TjRel rx;ij u; v; w x

temperature of fuel in node j (K)

j

gas constant (8.3143 J/mol K) temperature (K) temperature of cladding in node j (K) temperature of fluid in node j (K) temperature of absorber material (control rod) in node j (K) temperature of canister wall in node j (K) temperature of the relocating material in node j (K) release rate (kg/s) velocity (m/s) vapor mass fraction ()

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15. Severe accident analysis with AC2

xp αCRelj αnCanj

diffusion rate for oxidation (m2 /s) heat transfer coefficient between cladding and relocating material (W/m2 K) effective heat transfer coefficient between cladding and canister wall (W/m2 K)

αi;i11 Radj β~ F

effective heat transfer coefficient between claddings in different rings (W/m2 K) (average) radial thermal expansion coefficient of fuel (1/K) Henky stress parameter () specific heat conductivity [W/(m K)] density (kg/m3 ) specific mass transfer (kg/m3 ) mass transfer (kg)

εH ϕ λ ρ ψ Ψ

Subscripts, superscripts k l; L v; V

phase index liquid vapor

Abbreviations BWR CV DCH FP LWR MCCI NC PWR RI RPV SA WWER

boiling water reactor control volume direct containment heating fission product light water reactor molten coriumconcrete interaction non-condensable pressurized water reactor organic iodine compound reactor pressure vessel severe accident waterwater energetic reactor

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V. Severe accident codes

C H A P T E R

16 Integral severe accident codes: IMPACT/SAMPSON Marco Pellegrini Department of Nuclear Engineering and Management, The University of Tokyo, Tokyo, Japan

16.1 Introduction SAMPSON (Severe Accident analysis code with Mechanistic, Parallelized Simulations Oriented toward Nuclear Fields) is a code included in the IMPACT (Integrated Modular Plant Analysis and Computing Technology) code system, which was developed under the sponsorship from the Japanese Ministry of Economy, Trade and Industry. It is owned and developed by the Institute of Applied Energy (IAE), Japan and it has restarted substantial development after the occurrence of the accident at the Fukushima Daiichi Nuclear Power Station (NPS). The SAMPSON code contains lumped parameter and 3D modules that can analyze the severe accident (SA) phenomena occurring in a nuclear power plant from the fuel heat up and melt to the fission product (FP) transport to the reactor building and environment [1]. SAMPSON was developed as a combination of various solid experiences in computer codes for nuclear plant safety analysis. Regarding thermal hydraulics of the reactor coolant systems, the thermal-hydraulics analysis module is designed based on the RELAP code [2], for the core degradation, it takes advantage of the mechanistic concepts contained in the SIMMER code [3] for multiphase and multicomponent analysis. Finally, containment vessel pressure analysis traces back to the solid formulation of the CONTAIN code [4] for the containment analysis. In addition, it features several three-dimensional codes developed at IAE for the analysis of the lower head and penetration failure, debris spreading and MCCI in pedestal [5,6], and a module for the analysis of the suppression pool temperature distribution [7]. Totally the code comprises seven modules and one submodule. All the modules are managed by a central module named accident control module that has the task to activate/deactivate depending on the accident-selected scenario and transfer information between modules. As the accident progresses and new phenomena come into play, a new module dedicated to the analysis of those phenomena is automatically activated and interfaced with the others. Details of each module are presented in Table 16.1. The SAMPSON code is parallelized and computes

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00016-4

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TABLE 16.1 SAMPSON module description. Module name Study

Features

FRHA

Studies the temperature distribution and increase of fuel and control rods until melt

2D axial-symmetric domain of the fuel rod

FPRA

Evaluates the release of FP from the fuel matrix

2D axial-symmetric domain of the fuel pellet

THA

Evaluates the thermal hydraulics in the RCS

1D direction domain solving momentum equation for two phases

CVPA

Evaluates the thermal hydraulics in the PCV

Lumped parameter code solving mass and energy balance for two-phase steam water. Contains a submodule for the 3D model of the water pool

MCRA

Evaluates the molten material relocation and heat transfer in the core region

2D axial-symmetric domain 13 vertical nodes (10 rods and 3 lower structures) and 8 channels

DCA

Evaluates the debris quenching in the lower head

3D domain solving debris spreading and quenching, coupled with vessel temperature analysis

DSA

Evaluates spreading and concrete interaction in pedestal and D/W floor

3D domain, including sumps and pedestal discretization

FPTA

Evaluates transport of FPs in the pressure vessel and containment

Lumped parameter code solving mass and energy balance for the main FPs including chemical reactions, deposition and remobilization.

CVPA, Containment vessel pressure analysis; DCA, debris cooling analysis; DSA, debris spreading analysis; FP, fission product; FPRA, fission product release analysis; FPTA, fission product transport analysis in line; FRHA, fuel rod heat up analysis; MCRA, molten core relocation analysis; RCS, reactor coolant systems; THA, thermal hydraulics analysis.

each module on a different processor to gain computational speed. SAMPSON has the capability to employ a single module or a combination of modules, feature which is extremely useful for validation and thus often employed for research purpose into universities. The SAMPSON code has been validated against main SA experiments such as CORA and QUENCH experiments for core relocation [8 10], the OLHF tests for the lower head [11], CCI experiments for ex-vessel [5], and Phebus for FP transport [12].

16.2 SAMPSON main modules 16.2.1 Fuel rod heat up and molten core relocation Various phenomena can affect SA progression. Among them the most critical are: the oxidation of the metals, in particular zirconium, the methods of debris relocation, candling and solidification on the lower structures, and accumulation under the form of a particulate bed or molten pool. In general, the components do not relocate as they reach the melting point but due to lower temperature eutectics [13] as well as failure due to mechanism similar to creep [14]. The molten core relocation analysis (MCRA) module has been developed to reproduce the previous phenomena on the basis of mechanistic models. The MCRA is a multiphase, multicomponent, and multivelocity field code. In detail, the MCRA code has the following characteristics: V. Severe accident codes

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16.2 SAMPSON main modules

• Consideration of solid, gas, and liquid phases. MCRA models six gas components and nine liquid components and the phase change between solid and liquid components and between gas and liquid components. • Consideration of multivelocity fields. MCRA handles up to three velocity fields, including momentum exchange between components of different velocity fields. • Consideration of flow regimes and corresponding interfacial areas between components. • Consideration of structures in the core on which corium crust accumulates or melts. MCRA has two kinds of heat interactive structures (HIS), that is, annulus for rod structures and slab HIS on any six surfaces of a calculation cell. The MCRA module has nine liquid components, four structure components, and six gas components as presented in Table 16.2. Particle components are treated as liquid components because they act as a fluid and are assigned to a liquid velocity field. When any liquid component freezes into a crust on a structure, the crust is assigned to the structure component S9 that has the average material properties of the mixture composed of fuel, cladding, structures, and their oxides. When the structure melts, materials of the crust are reassigned back to their original liquid components, that is, droplets or solid particles, by the bulk phase change model. Liquid components, except for water, are treated as mixtures of the metal and its oxide. Thus the material composition should be stored in every computational cell and is convected by its velocity field. Currently, six gas components are considered. MCRA does not treat FP transfer but provides the velocity field to the module that evaluates the transport of the FPs and fission product transport analysis. (refer to Table 16.1). TABLE 16.2

Liquid, structure and gas components.

Liquid components L1

Water

L2

Liquid fuel material

L3

Liquid steel

L4

Liquid zirconium

L5

Liquid control material

L7

Fuel particle

L8

Steel particle

L9

Zirconium particle

L10

Control material particle

S1

Rod structure

S2

Zircaloy structure

S3

Steel structure

S4

Crust

g1

Steam

g2

N2

g3

O2

g4

H2

g5

Ar

g6

He

Structure components

Gas components

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MCRA solves the following equations: • nine mass conservation equations for liquid and six equations for gas components, respectively; • nine energy conservation equations for liquid and one for mixed gas components, respectively; and • three momentum conservation equations for two groups of liquid, that is to say, water and other materials and form (liquid and particles), and for a mixture of gas components. Mass and energy conservation equations of structure components are solved by the melting/freezing model, within the phase change model. The mass, momentum, and energy transfer between components in the MCRA depend on the interfacial area between them that needs to be evaluated depending on the flow regimes. MCRA is able to model two types of flow regimes: a pool flow regime, which is independent of the structures, and a channel flow regime model that is dependent on structures [15]. The pool flow regime model is formulated with two parameters: void fraction and entrainment rate [16], and Fig. 16.1 shows a sketch of the pool flow regime applied in the MCRA module. The software evaluated whether the condition in the cell is bubbly flow, in which the liquid component is predominant, or dispersed flow in case the gas component is predominant and liquid is assumed to be present as droplets. For intermediate ranges the code will assume a linear interpolation between the two conditions. Details of the interfacial area and method of evaluation and convection of number density are provided in Ref. [16].

16.2.2 Validation of the fuel rod heat up analysis and molten core relocation analysis modules The fundamental phenomena constituting the MCRA have been verified and validated against multiple experiments in the initial phase of development [16]. Hereafter, some of them will be briefly described and results are presented in Fig. 16.2. The validation of the interfacial area model and the momentum exchange model of the multivelocity field has been validated against the experiment by Leung et al. [17] of a bubble column of nitrogen FIGURE 16.1

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Sketch of the pool flow regime.

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FIGURE 16.2 MCRA validation against: (A) Leung et al. [18] experiment, (B) KROTOS-37 [19] pressure, and (C) melt penetration. MCRA, Molten core relocation analysis.

gas in water. Results are presented in Fig. 16.2A showing the superficial velocity against the average void fraction. The distribution of the calculated void fraction is in good agreement with the experiment throughout the range of void fraction showing that the interfacial area and its source terms as well as the momentum exchange functions are appropriately modeled for these kinds of flow. The validation of the vaporization and condensation models has been performed against the KROTOS-37 experiment [18] that deals with corium and water. The pressure transient curves of the experiment and calculation are shown in Fig. 16.2B. The calculated pressure increases more rapidly than the pressure of the experiment until 1.0 second. This difference is caused by the limitation of the one-dimensional calculation, that is, the melt penetrates into a larger volume of water than the actual volume and interacts thermally with a larger interfacial area of water. Consequently, the generated steam is larger and the pressure increases faster. The pressure decreases gradually after 1.6 seconds in the experiment, due to the gradual condensation of steam on the pressure vessel wall above the water level. In the calculation the pressure of 1.6 3 105 Pa is maintained because the thermal interaction of the gas space with the atmosphere is not considered. The melt is almost cooled down to the water temperature after 1.0 seconds in the calculation. Fig. 16.2C shows that the penetration rate in the calculation is relatively slower than in the experiment which is in agreement with the relatively larger interfacial area evaluated in the code due to limitations of the mesh. SA codes are sensitive to the employed mesh and geometry, hence once the geometry is expanded to plant scale, the model will lose accuracy. For this reason, during the first phase of development, the trend of the results has been considered more important than the exact agreement with the experimental data. Analysis has been performed also about the phase change of the fuel [16] but as experiments do not provide such detailed information, only verification calculations have been performed. An additional crucial phenomenon driving the accident progression is represented by the exothermal chemical reactions during Zircaloy oxidation through steam interaction, resulting in hydrogen generation and heat. At temperature above the α/β allotropic transformation temperature of zirconium, steam reacts with β-Zr to form a superficial layer of ZrO2 and an intermediate layer of oxygen-stabilized α-Zr(O). As the reaction proceeds,

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both the ZrO2 and the α-Zr(O) layers grow and the β-Zr matrix will eventually disappear. The generation of hydrogen in the core is particularly critical because it introduces a positive feedback where the temperature escalates and this process becomes impossible to be halted even in the case of very large water injection. Consequently, the clad and fuel will melt releasing FPs and relocating vertically in the core region. The analytical approach of the Zircaloy/steam oxidation is based on the use of a parabolic law of the form




w2 5 kp t where w represents the mass of oxygen absorbed by zirconium per unit area, kp is the parabolic reaction rate, and t is the reaction time. The reaction rate can be rewritten as   B kp 5 A exp 2 T




where A and B are two factors that need to be evaluated experimentally. Over the years, several scientists/groups of scientists have performed experiments on the high-temperature oxidation of zirconium in steam, attempting to extract the coefficients A and B of the previous equation from experimental data, which are reported in Table 16.3. The SAMPSON code has been assessed against the CORA-18 experiment [24] to confirm the model of zirconium water reaction. The CORA-18 experiment [24] was performed at TABLE 16.3 A and B coefficients of previous equation according to the literature. Urbanic Heidrick [21]

Prater [24]

Baker Just [20]

T , 1853K

T . 1853K

Cathcart [22]

Leistikow [23]

T , 1783K

T . 1783K

A

3330

29.6

87.9

36.22

52.418

110

3300

B

22,898

16,820

16,610

20,100

20,962

22,480

26,440

FIGURE 16.3 CORA-18 bundle [25].

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16.2 SAMPSON main modules

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Forschungszentrum Karlsruhe in Karlsruhe, Germany, in 1998 as part of the severe fuel damage program. The goal was to investigate the relevant fuel rod bundle damage mechanisms that occur in an uncovered core of a boiling water reactor (BWR), after an increase of temperature. In CORA-18 the central part of the facility represents the fuel rod bundle, which was enclosed in a Zircaloy shroud. The bundle is presented in Fig. 16.3. The bundle and shroud assembly was surrounded by an insulator composed of ZrO2 fiber and by a high-temperature radiation shield (HTS), the latter consisting mainly of ZrO2 and Al2O3 fiber plates. An annular space was left between the shroud insulator and the HTS for the movement of quench cylinder. The bundle was connected to the power supply system at both upper and lower ends. Results of the SAMPSON temperature excursion and hydrogen generation against the CORA-18 measurements are reported hereafter in Fig. 16.4. In general, all the correlations tend to overestimate the generation of hydrogen and consequently the heat and temperature increase of the structures. However, among them the correlations of Baker Just and Urbanic Heidrick

FIGURE 16.4 (A) Fuel rods cladding temperature at 350 mm, (B) channel box temperature at 750 mm, and (C) total hydrogen generation.

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are largely overestimated as these works are the earliest and pioneering works to develop Zircaloy steam correlations. For example, Urbanic Heidrick employ induction heating that results in lower accuracy compared to other experiments using furnace heating [13,25]. The simulation of the CORA-18 experiment gave also the possibility to validate control blade melting by eutectic reaction model. Bertrand et al. [26] qualitatively introduced that during a hypothetical SA transient, once the temperature of the control rod has reached approximately 1073K, a solid/solid B4C/SS interaction occurs. As it has been defined by Hofmann et al. [27], the chemical interaction between B4C and stainless steel results in the formation of two reaction layers. The first, adjacent to the B4C absorber material is very thin and has a rather homogeneous appearance; the second reaction layer is much thicker and is characterized by the presence of a great amount of second-phase precipitation in the SS-matrix, mainly along the grain boundaries. In order to define the B4C/SS reaction kinetics, the total reaction zone thickness of both reaction layers has been determined as a function of temperature and time. Over the years, various scientists have proposed different equations for the growth rate of the reaction zone, the most popular is the one proposed by Hofmann et al. [27], Nagase et al. [28], and Belovsky et al. [29]. Additional eutectic can be created by B4C and Zr, and hydrogen generation is relatively large for B4C. The effect of eutectic generation is clearly visible in the final status of the bundle in Fig. 16.5. The remaining rods are presented in gray, while the remaining

FIGURE 16.5 Comparison of bundle failure against the experiment. Left side SAMPSON/MCRA results and right side CORA-18 bundle sections [25]. MCRA, Molten core relocation analysis.

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16.3 3D containment modules

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structures (shroud, channel box, and control blade) are reported in black. The colored part represents existing rods and structures that melted and relocated. Each color represents the time when the melt occurs. It is clear how the rods themselves are quite intact but the central part is highly degraded, which is also in good agreement with the experiment (right side of the figure).

16.3 3D containment modules The modeling and numerical aspects of SAMPSON are in line with the state of the art of similar software such as MELCOR and MAAP. In addition, one of the unique characteristics of the SAMPSON code is the employment of modules that contain a full threedimensional geometry that can take into account of phenomena such as stratification or complex structures such as the pedestal (including sumps) of nuclear reactors.

16.3.1 POOL3D module In the classic lumped parameter approach, the wet well (W/W) is modeled as a single node volume, where gas and water phase coexist in a single point; therefore it is not possible to compute a temperature distribution inside the suppression pool. However, during the Fukushima Daiichi accident the hot water on the surface of the S/C played a vital role in the pressure buildup in the containment and it could be considered the triggering point of the Unit 3 failure of the reactor core isolation cooling system (RCIC) and subsequent core meltdown. The submodule POOL3D discretizes the water pool into a number of cells and it allows one to evaluate its temperature, velocity, and pressure distribution in all the three dimensions. The W/W is split into two different domains, the upper domain (gas space) is still considered as a single node volume and it simulates the atmosphere above the pool inside the lumped parameter module. The second volume is the suppression pool that is simulated by POOL3D. The two modules are interfaced in order to evaluate the mass and energy exchange between the suppression pool (S/P) and the containment, including, for example, phenomena of evaporation. POOL3D can recreate complex geometries with Cartesian and cylindrical meshes. POOL3D has been validated against various experiments, with water injection [30], steam, and steam with noncondensable gases [31] in order to confirm the capability of the code to reproduce the thermal stratification. Hereafter, some of the validation results are presented in Fig. 16.6. The previous results show the capability of the code to predict the temperature distribution in the case of relatively low steam injection. The main model for a correct prediction of the temperature distribution is the mixing term. The mixing term depends on various factors such as the regime of injection. That is to say, whether the steam is injected as a jet, bubbling, or chugging conditions. In addition, mixing is enhanced greatly in the case of injection of noncondensable gases together with steam. Details of the modeling are reported in Ref. [7].

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FIGURE 16.6 POOL3D comparison against experiments: (A) temperature history of the Shin experiment [31], (B) visualization of the stratification by SAMPSON/POOL3D, (C) LINX test-2 temperature history [32], and (D) comparison of temperature distribution.

In Fig. 16.7A an outline of POOL3D grid is presented, with an example of the pool of the Mark I containment. The three-dimensional torus is divided by an orthogonal Cartesian grid. The code is capable of computing hot steam/water injection in the pool and the associated momentum to predict mixing and stratification creation. Fig. 16.7B and C presents the application of the model to the accident of Fukushima Daiichi Unit 2 where the RCIC worked for almost 70 hours and steam/water was injected in the pool continuously. The generation of a hot layer on the top of the surface enhances the evaporation of the water that leads to a linear pressure increase in the containment (bottom figure of Fig. 16.7B).

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FIGURE 16.7 (A) POOL3D geometry for Mark I S/C, (B) RPV and PCV pressure computed by SAMPSON with POOL3D module, and (C) temperature distribution in the S/C water.

16.3.2 Debris spreading analysis module During the ex-vessel phase the corium relocating from the lower head spreads and accumulates on the containment floor creating a high-temperature molten pool. The molten pool attacks the concrete that loses water and structural integrity and a cavern expands until the molten pool reduces its temperature. The debris spreading analysis (DSA) module is a CFD module with moving boundaries. The code solves Navier Stokes equations using the simplified marker and cell [32]. The pressure distribution is calculated by the solver using the incomplete Cholesky conjugate gradient matrix method [33]. For convection analysis boundaries at which the debris melt cells face either the crust, the structure, or the free surface cells, matrix rearrangement in the calculation solver of the pressure distribution is processed automatically assigning a fluid flow condition during liquefaction and a wall condition in the case of solidification.

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The code is capable of evaluating the spreading modeling the free surface cells through a height function. Two assumptions that characterize the spreading and relational motion between the debris melt and the crust are described next. 1. Debris is a continuum body and restricted to the floor surface by gravity. Debris melt cannot scatter into the air and gas entrainment does not occur. 2. Crust can only be transported in a vertical direction. The first assumption means that debris melt transporting vacant air cells is collected into the lowest free surface cells on the floor or on the continuum debris top surface in the vertical direction. The second assumption represents a basic approach to solve the interaction between the debris melt and the crust. It results in the crust waves being proportional to the vertical motion of the debris melt upper surface under the crust. Three types of flow stop conditions are applied to characterize the debris spreading. The first is stop of the flow using the function of the free surface cell that has zero velocity until the cell volume reaches the full cell volume, and the cell attribution is changed to a debris melt cell. These stop criteria reproduced the effect of the minimum flow thickness. The second is stop of the debris melt cell by considering the flow yield strength. The third criterion is the solidification of each full cell volume by the judgment between the fluidity limit solidification fraction and the solidification fraction of the cell. It is calculated based on the cell-specific enthalpy, the liquidus, and solidus. The DSA module has been validated against main experiments on core concrete interaction [34]. The tests simulated debris for the core melt composition of a pressurized water reactor (PWR) mixed with concrete, and the decay heat in the early stage of the debris relocation onto the containment cavity floor was used (Fig. 16.8). More recently, the DSA module has been applied to the study of the Fukushima Daiichi accident. In the DSA module the concrete domain representing the primary containment vessel (PCV) consists of pedestal, drywell cavities or sumps, and the underlying floor Fig. 16.9A. The open space is also part of the domain and it contains the molten debris pool after the release from the vessel. The domain is reproduced by means of a discrete three-dimensional nodalization, in which each mesh cell holds a precise attribution depending on its composition and thermodynamics state. The cells are classified into two different types depending on their volume fraction and function [5]: a full volume cell is

FIGURE 16.8 Validation of the DSA code against the CCI-2 test [5]. DSA, Debris spreading analysis. (A) Contours of erosion at different time intervals, (B) lateral erosion depth plot, (C) axial erosion depth plot.

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FIGURE 16.9

(A) Top view of the pedestal and PCV with different sump configuration, (B) results of Unit 1 concrete erosion until the liner in the case of no water injection, and (C) horizontal section at the level of the bottom of the sumps.

assigned to a node representing melt, crust, or structural concrete, while fragmentary volume (free surface) cells are used at the fluid corium boundaries. Specifically, the set of cells representing the molten debris continuum is enclosed by the convection analysis boundary inside which the single-phase Navier Stokes equations are solved in order to calculate the mass transport and energy transfer. The heat and mass fluxes across the convection boundary are calculated by means of the free surface cells. They are partially filled volume nodes that serve as a buffer to handle the debris spreading and the heat transfer over the molten pool convection boundaries with the solid cells (crust and concrete) and the rest of the environment. The cold concrete cells across the debris interface progressively receive heat from the hot source, and the erosion of a concrete element is triggered when its temperature exceeds the ablation limit (even if the concrete degradation and gaseous decomposition eventually take place at lower temperatures). In Fig. 16.9B and C the results of the application of the DSA module to Unit 1 are presented on two main sections [35]. The software allows one to reproduce the details of the pedestal walls, opening slit, and sumps. The software reproduces the erosion of concrete which is aligned with the sumps, providing meaningful information for the decommissioning phase.

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16.4 Application of the SAMPSON code to the Fukushima Daiichi nuclear power plant accident The SAMPSON code was developed primarily to address SAs in PWR geometries. After the accident at Fukushima Daiichi, the IAE restarted the development introducing specific models for the BWR fleet and in particular for the findings at the Fukushima Daiichi NPS. Among the activities where SAMPSON development is pioneering in supporting the understanding of the accident at Fukushima Daiichi, the following can be mentioned: two-phase flow self-controlling behavior of the RCIC turbine in Unit 2 [36], clarification of the three pressure peaks period in Unit 2 and explanation of the complex PCV pressure behavior in Unit 3 following core meltdown [37].

16.4.1 Self-controlling behavior of the RCIC turbine in Unit 2 Fukushima Daiichi Unit 2 RCIC was restarted 2 minutes before the loss of DC power. In this condition the RCIC equipment would be assumed to work until the water level reached the main steam line (MSL) and then trip by overspeed. However, in reality the RCIC worked for almost 70 hours. Fig. 16.10A shows the first calculation results by TEPCO [38] conducted just 2 months after the accidents. In this calculation the RCIC was controlled by automatic start and stop operation (even though no DC was available). This means that if reactor pressure vessel (RPV) water level reached the high level, RCIC would be stopped automatically and if the RPV water level reached low level, RCIC would be restarted automatically. The prediction of the RPV pressure in Fig. 16.10A does not reproduce the calculation measurements. This is because the RCIC system requires little steam to inject an amount of water larger than the equivalent steam generated by the decay heat. Therefore the water level continuously increases up to the point when the RCIC stops functioning and the RPV pressurizes discharging steam into the S/C. This result helped confirming a possible operation of the RCIC equipment above design conditions or in a completely unexpected state.

FIGURE 16.10

(A) RPV pressure behavior in Unit 2 accident [39] and (B) RPV pressure and RCIC flow-rate

behavior.

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16.4 Application of the SAMPSON code to the Fukushima Daiichi nuclear power plant accident

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The real RPV pressure behavior indeed shows that the RPV pressure did not reach the safety relief valve (SRV) activation pressure set point for most of the transients. It is evaluated that RCIC operation during the accident was as follows [38]: 1. Due to the loss of DC power, the operators lost control of the RCIC that operated at full steam injection. 2. Due to the large RCIC water flow rate, the water level increased. 3. RPV water level reached the MSL. 4. Water started overflowing into the MSL, in other words, fluid in MSL became two-phase flow with low quality. 5. RCIC turbine system was driven by using two-phase flow from MSL branch line. 6. Two-phase flow brought the whole decay heat from RPV to S/C. 7. RPV pressure remained below the SRV set point. Fig. 16.10B shows the results employing the previous boundary condition with the SAMPSON code. The calculated mass of steam in the two-phase flow is about 1%, while 99% of water. The calculated RPV pressure with black line is in good agreement with measured RPV pressure presented with orange squares [36].

16.4.2 Three pressure peaks period in Unit 2 In Unit 2 the period from 76 to 83 hours after the scram is commonly referred to as the “three pressure peaks time period,” since the RPV pressure is characterized by three pressure peaks. During this period a large amount of H2 is released inside the PCV as a consequence of the core degradation and the zirconium/B4C/SS oxidation. During this period the SRV was closed and partially opened several times; therefore a mixture of steam and hydrogen was injected inside the S/C. The hydrogen injected into the S/C pressurizes the PCV up to 0.8 MPa as reported in Fig. 16.11. Looking at the measurements and SAMPSON prediction, the first pressure peak is caused by a small relocation of B4C and stainless steel into the lower plenum generating steam and increasing the RPV pressure. In the analysis 3.5 tons of debris (SS and B4C) are assumed to relocate in the lower plenum. With this assumption the calculation provides the same trend as the measurements but underestimated. The period of the second peak is characterized by the simultaneous RPV and PCV pressurization. RPV pressure grows up to 3.3 MPa, given by a huge release of steam from the lower plenum following a large debris slumping, and PCV pressure increases of 2.4 bars, due to hydrogen release in the PCV. The hydrogen is generated inside the RPV by oxidation of remaining fuel rods and debris sitting on the core plate. In order to be able to reproduce the second peak a fast slumping, around 200 seconds of 49 tons of debris were simulated to fall from the core plate to the lower plenum in order to generate enough steam to pressurize the RPV and to produce the amount of hydrogen needed to pressurize the PCV. The third peak is characterized by RPV pressurization due to the steam generated in the lower plenum by the quenching debris. Hydrogen is not generated due to the minimal amount of debris on the core plate which is highly oxidized.

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FIGURE 16.11

16. Integral severe accident codes: IMPACT/SAMPSON

PRV and PCV pressures during the three peaks period.

During the third peak the PCV pressure remains constant, because of the large mass of hydrogen in the containment. In the presented case the calculation follows the trend but the predicted level of oxidation appears smaller than in reality as the PCV pressure gradually decreases due to steam condensation in the D/W.

16.4.3 PCV pressure behavior in Unit 3 In Unit 3 the phenomena until the core degradation are relatively well understood and presented in early publications after the accident [39]. Nonetheless, the complex phenomena that occur after the depressurization by the automatic depressurization system (ADS) on March 13th at around 9:00 a.m. are still subject of debate. Activities with the SAMPSON code have helped one to suggest a possible scenario to interpret the convoluted pressure data. After the ADS activation the RPV pressure reduces quickly under the steam discharged by six SRVs. RPV and PCV pressure equalize and the pressure decrease is driven by the S/C vent. The TEPCO investigation indicates the possibility that eventually a single SRV was kept open due to DC power loss. In the SAMPSON analysis presented in Fig. 16.12, it is assumed that a single SRV remains open at 10:00 a.m. on March 13th (43.23 h) and that a portion of the debris starts slumping at this time. Subsequently a direct leak is assumed from the RPV to the D/W and around 7 tons of debris are assumed to slump from the central channel to the lower plenum. Thereafter, the pressure continues decreasing driven by the vent operation at the S/C. At 12 o’clock (45.23 h) the vent is assumed to close and the debris starts relocating completely from all the channels to simulate a loss of integrity of the core plate.

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16.4 Application of the SAMPSON code to the Fukushima Daiichi nuclear power plant accident

FIGURE 16.12

413

PCV pressure prediction by the SAMPSON code in Fukushima Daiichi Unit 3 [38].

After the debris relocates in the lower plenum, the plant is in a configuration of stable pressure value because water is being continuously injected through the recirculation loop, and the generated steam is evacuated from the S/C vent. This condition is presented in Fig. 16.12 from 45 to 48 hours. When the S/C vent is closed at 48 hours, the PCV pressure rises until it stabilizes at around 0.4 MPa under the effect of the PCV head flange leak (Fig. 16.12 from 50 to 54 hours). In addition, at this time a containment leak is assumed to occur at the penetration to the main steam isolation valve room, given the evidence provided by TEPCO. At this point the water injection is assumed to be not efficient due to large RPV pressure, and consequently the water in the lower plenum gradually dries out and the pressure is kept high by the water draining through the manhole at the RPV downcomer. After the last drop of water is dripped from the downcomer, the pressure reduces, at around 54 hours, driven by the D/W leak at the penetration as the head flange leak seals below 0.4 MPa. It takes some time for the external water injection to refill the recirculation pipe, and the particulate debris in the lower plenum eventually remelts and forms a molten pool that sits on the lower plenum. The lower plenum gradually melts and the debris is relocated externally in the pedestal at around 56 hours. Because of the PCV leakage, the pressure continues decreasing until some water is transferred from the S/C through the vacuum breaker to the D/W. Once the water reaches the D/W and comes into contact with the debris, steam starts to be generated and the pressure rises again (Fig. 16.12 from 60 hours). The same behavior keeps repeating until around 100 hours when the water injection is substantial and the pressure reduces because the D/W gets subcooled. The results of the previous assumptions are presented in Fig. 16.12 with a relatively correct agreement with the measurements, where the SAMPSON code is employed in a forensic approach and the code is “encouraged” to follow the defined scenario.

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16. Integral severe accident codes: IMPACT/SAMPSON

16.5 Advantages and disadvantages in the use of SAMPSON The SAMPSON code has been validated against main experiments and it has been successfully applied to the analysis of the Fukushima Daiichi accident [36,37,39 41]. The advantage of the SAMPSON code is that it evaluates the main phenomena involved in a SA with larger detail. This gives the opportunity to the analyst to consider more complex phenomena involved in the accident. The SAMPSON code is designed as a research tool so the interested organizations have access to the source code and can consider the implementation of sophisticated modeling. This was done as explained earlier for the RCIC two-phase flow behavior [10] and other studies such as the failure of the lower head by pipe ejection [11] or the study of MCCI in Unit 1 [35]. On the other hand, the SAMPSON code requires a relatively long computational time in particular during the analysis of the core relocation that can reach at least one order of magnitude slower than the real time. As a consequence, the probabilistic employment of SAMPSON for PRA or other usages might find limited application.

References [1] H. Ujita, et al., Development of severe accident analysis code SAMPSON in IMPACT project, J. Nucl. Sci. Technol. 36 (1999) 1076. Available from: https://doi.org/10.1080/18811248.1999.9726300. [2] C.D Fletcher, R.R. Schultz, RELAP5/MOD3 Code Manual, NUREG/CR-5535, 1992. [3] H. Yamano, et al., SIMMER-III: A Computer Program for LMFR Core Disruptive Accident Analysis Version 3.A Model Summary and Program Description, JNC TN9400 2003-071, 2003. [4] K.K. Murata, et al., Code Manual for CONTAIN 2.0: A Computer Code for Nuclear Reactor Containment Analysis, NUREG/CR-653, 1997. [5] M. Hidaka, T. Fujii, T. Sakai, Improvement of molten core concrete interaction model in debris spreading analysis module with consideration of concrete degradation by heat, J. Nucl. Sci. Technol. 53 (9) (2016) 1260 1275. [6] M. Hidaka, T. Fujii, T. Sakai, Development of the models for advection-diffusion of eroded concrete into debris and concrete volume reduction in molten core-concrete interactions, J. Nucl. Sci. Technol. (2017). [7] A. Buccio, M. Pellegrini, M. Naitoh, Suppression pool thermal-hydraulic analysis of Fukushima Daiichi Unit2 using pool-3D module of SAMPSON severe accident code, in: 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), Xi’an, 2017. [8] T. Ikeda, K. Katsuragi, N. Shirakawa, Analysis of international standard problem no. 45, QUENCH06 test at FZK by detailed severe accidents analysis code, IMPACT/ SAMPSON, J. Nucl. Sci. Technol. 40 (4) (2003) 246 255. [9] A. Prestigiacomo, A. Costa, H. Ninokata, M. Pellegrini, M. Naitoh, Molten core relocation analysis of CORA-17 and CORA-18 for the SAMPSON/MCRA validation, in: 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-16), Chicago, IL, 2015. [10] H. Lopez, M. Pellegrini, M. Naitoh, Validation and application of a new reflooding model for the SAMPSON code, in: 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), Xi’an, 2017. [11] F. Scarpa, M. Pellegrini, M. Naitoh, Validation of severe accident code SAMPSON debris cooling analysis module (DCA) against OLHF experiments and development of creep models, in: NUTHOS-11: The 11th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, Operation and Safety, October 9 13, 2016, Gyeongju, 2016. [12] T. Ikeda, M. Terada, H. Karasawa, K. Nakahara, M. Yamagishi, Analysis of core degradation and fission products release in Phebus FPT1 test at IRSN by detailed severe accidents analysis code, IMPACT/SAMPSON, J. Nucl. Sci. Technol. 40 (8) (2003) 591 603.

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[13] G. Schanz, et al., Advanced treatment of zircaloy cladding high-temperature oxidation in severe accident code calculations. Part I. Experimental database and basic modeling, Nucl. Eng. and Des. 232 (2004) 75 84. [14] Y. Pontillon, P.P. Malgouyres, G. Ducros, G. Nicaise, R. Dubourg, M. Kissane, et al., Lessons learnt from VERCORS tests. Study of the active role played by UO2 ZrO2 FP interactions on irradiated fuel collapse temperature, J. Nucl. Mater. 344 (2005) 265 273. [15] Y. Tobita, et al., Interfacial area modeling for a multi-phase, multi-component fluid-dynamics code, in: Int. Conf. on Multiphase Flows ’91 Tsukuba, Sept. 24 27, 1991, Tsukuba, 1991. [16] N. Satoh, H. Ujita, K. Miyagi, N. Shirakawa, H. Horie, K. Nakahara, et al., Development of molten core relocation analysis module MCRA in the severe accident analysis code SAMPSON, J. Nucl. Sci. Technol. 37 (3) (2000) 225 236. [17] J. Leung, G. Lambert, L. Stachyra, Transition to dispersed flow in a stagnant pool with gas injection, Trans. Am. Nucl. Soc. 38 (1981) 397. [18] I. Huhtiniemi, et al., OECD/CSNI Specialist Meeting of FCI, JAERI, Tokai, May 19 21, 1997 . [19] Baker L., et al. Studies of Metal Water-Reactions Between Zirconium and Water at High Temperatures. III. Experimental and Theoretical Studies of the Zirconium Water Reaction. ANL p. 6548, 1962. [20] V.F. Urbanic, T.R. Heidrick, High-temperature oxidation of Zircaloy-2 and Zircaloy-4 in steam, J. Nucl. Mater. 75 (1978) 251 261. [21] J.V. Cathcart, et al. Zirconium Metal-Water Oxidation Kinetics. IV. Reaction Rate Studies, ORNL/NUREG-17, 197, 1997. [22] S. Leistikow, et al., Oxidation kinetics and related phenomena of zircaloy-4 fuel cladding exposed to high temperature steam and hydrogen-steam mixtures under PWR accident conditions, Nucl. Eng. Des. 103 (1987) 65 84. [23] J.T Prater, E.L. Courtright, Zircaloy-4 Oxidation at 1300 to 2400 C, NUREG/CR-4889, PNL 6166, 1987. [24] S. Hagen, et al., Large Bundle BWR Test CORA-18: Test Results. FZKA 6031, Forschungszentrum Karlsruhe, Karlsruhe, 1998. [25] G. Schanz, Recommendations and Supporting Information on the Choice of Zirconium Oxidation Models in Severe Accident Codes, FZKA 6827, Forschungszentrum Karlsruhe, Karlsruhe, 2003. [26] F. Bertrand, et al., B4C control rod oxidation during a severe accident in a PWR reactor, separate effect and integral tests analysis for modeling purpose with the ICARE/CATHARE code, in: The 10th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-10), Seoul (CD- ROM, no. G00004), 2003. [27] P. Hofmann, et al., Reaction Behavior of B4C Absorber Material With Stainless Steel and Zircaloy in Severe LWR Accidents, KfK 4598, Kernforschungszentrum Karlsruhe GmbH, Karlsruhe, 1989. [28] F. Nagase, et al., Chemical interactions between B4C and stainless steel at high temperatures, J. Nucl. Mater. 245 (1997) 52 59. [29] L. Belovsky, et al., Chemical interactions in B4C-filled control rod segments above 1000 C under transient conditions, in: 5th International Conference on Nuclear Engineering (ICONE5), Nice (CD-ROM, No. 2184), 1997. [30] M.-S. Shin, H.-S. Kim, D.-S. Jang, S.-N. Lee, Y.-S. Lee, A numerical and experimental study on the mixing characteristics of a stratified thermal storage system, Korean Soc. Environ. Eng. (2003). [31] C. Walsche, F. de Cachard, Experimental Investigation of Condensation and Mixing During Venting of a Steam/Non-Condensable Gas Mixture Into a Pressure Suppression Pool, No. INIS-CH-022, 2000. [32] A.A. Amsden, F.H. Harlow, The SMAC Method: A Numerical Technique for Calculating Incompressible Fluid Flow, LA-4370, 1970. [33] J. Meijerink, H.A. Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput. 31 (1977) 148 162. [34] M.T. Farmer, S. Lomperski, D.J. Kilsdonk, et al. OECD MCCI Project 2-D Core Concrete Interaction (CCI) Tests: Final Report (OECD/MCCI-2005-TR05), 2006. [35] M. Di Giuli, A. Buccio, M. Pellegrini, M. Naitoh, Preliminary ex-vessel sensitivity study of Fukushima DaiIchi unit 1 using DSA1 and CVPA coupling modules of the Sampson Code, in: International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), Xi’an, 2017. [36] M. Pellegrini, M. Naitoh, Y. Kudo, S. Mizokami, Confirmation of severe accident code modeling in light of the findings at Fukushima Daiichi NPPS, Nucl. Eng. Des., 354 (2019). [37] M. Pellegrini, M. Naitoh, Three weeks analysis of the Fukushima Daiichi Unit 3 NPP by the SAMPSON code: contribution to the BSAF-2 project, Nucl. Eng. Des., 366 (2020).

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[38] S. Mizokami, D. Yamada, T. Honda, D. Yamauchi, Y. Yamanaka, Unsolved issues related to thermal-hydraulics in the suppression chamber during Fukushima Daiichi accident progressions, J. Nucl. Sci. Technol. 53 (2016). [39] M. Pellegrini, H. Suzuki, H. Mizouchi, M. Naitoh, Early Phase Accident Progression Analysis of Fukushima Daiichi Unit 3 by the SAMPSON Code, Nuc. Engi. Des. 186 (2014) 241 254. [40] M. Pellegrini, K. Dolganov, L.E. Herranz Puebla, H. Bonneville, D. Luxat, M. Sonnenkalb, J. Ishikawa, et al., Benchmark study of the accident at the Fukushima Daiichi NPS: best-estimate case comparison, Nuc. Tech. (2016). Available from: http://dx.doi.org/10.13182/NT16-63. [41] M. Pellegrini, L. Herranz, M. Sonnenkalb, T. Lind, Y. Maruyama, R. Gauntt, et al. , Main findings, remaining uncertainties and lessons learned from the OECD/NEA BSAF project, Nuc. Tech. (2020). Available from: https://doi.org/10.1080/00295450.2020.1724731.

V. Severe accident codes

C H A P T E R

17 Engineering-level system code for severe accident analysis: MELCOR Tangtao Feng1, Jun Wang2, Xin Li3, Ryan Dailey2 and George Vayssier4 1

Wuhan Second Ship Design and Research Institute, Wuhan, China 2Department of Engineering Physics, University of Wisconsin–Madison, Madison, WI, United States 3 Faculty of Science and Engineering, Waseda University, Shinjuku City, Tokyo, Japan 4 Eindhoven University of Technology, Eindhoven, Netherlands

17.1 Introduction MELCOR is a fully modular, engineering-level reactor simulation program that calculates the progression of serious accidents in light-water reactors (LWRs) [1]. It was initiated by the US Nuclear Regulatory Commission developed by Sandia National Laboratories for the purpose of risk assessment for second-generation nuclear power plants. A broad spectrum of severe accident phenomena in both boiling- and pressurized-water reactors (BWR and PWR, respectively) can be handled in MELCOR within a unified framework [2]. This includes the thermal-hydraulic response of the reactor’s primary coolant system, the reactor cavity, the containment, and the confinement buildings. In addition, accident scenarios are fully simulated, including loss of coolant (core uncovering), core heat up, fuel degradation, and core material melting and relocation. Later portions of accident simulation are possible as well, including core concrete attack and hydrogen production, transport, and combustion, as well as fission product release and transport behavior. MELCOR can handle severe accident management actions, such as flooding a damaged core, hydrogen ignition recombination, and IVMR. MELCOR can also be applied to analyze beyond-design-basis accident, which contains the estimation of severe accident source terms and their sensitivities, and uncertainty analysis [3]. MELCOR contains a series of integrated source packages. The mathematical and physical models in the packages are designed to be as lightweight as possible while ensuring accuracy [4]. Users are free to choose which source packages they wish to simulate for the

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00017-6

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concerned severe accident phenomena. This means that the user has substantial flexibility with MELCOR. MELCOR is now viewed as a state-of-the-art tool for accident source term calculations. Most models are mechanistic, and it has evolved as a repository for knowledge of severe accident phenomenology. The application of MELCOR is not limited to reactor accidents. A reactor’s thermalhydraulic response of the reactor cooling system (RCS), reactor cavity, containment, and confinement buildings can be simulated easily, which enables calculations regarding severe accident management actions [5]. Many complex systems are modeled well by MELCOR. Second, MELCOR could be used to the study of combustible gas generation, transport, and detonation. It can competently perform on gas behavior calculations for gasses such as hydrogen from zircaloy and steel as well as carbon monoxide from B4C and carbonaceous concrete. Third, radionuclide (RN) releases in the form of aerosols, and vapors are tracked with a degree of precision. The fission products in fuel and gap, aerosols from concrete attack, hygroscopic effects will also be considered during the simulation. Finally, MELCOR can analyze core heat up and degradation of LWRs and other designs such as hightemperature gas reactors. Relocation of decay heat sources, high-pressure melt ejection, direct containment heating (DCH), performance and impact of sprays, and engineered safety systems are also considered in MELCOR [6]. Therefore MELCOR is a fully integrated, engineering-level computer code that simulates the progression of severe accidents in a nuclear reactor. It is not a CFD code—it uses volumes (lumped parameter code). Hence, local effects cannot be well simulated. Further, it is 1D code, and the neutron kinetics is coupled as a 1D level. It is worth noting that MELCOR is a lumped parameter code and it still exist limitations. Hence, local effects cannot be well simulated compared with CFD codes. Further, MELCOR assumes that the energy release is independent of time and depends upon the energy spectrum of the neutron flux in the operating reactor and the composition of the reactor core. The neutron kinetics in MELCOR is not coupled yet. Fig. 17.1 displays the file relations used in MELCOR. For a standard MELCOR case, user inputs are mainly executed in two executable programs that are called MELGEN and

FIGURE 17.1

File relations in MELCOR code.

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MELCOR. Most of the input parameters are specified, processed, and checked in MELGEN, which produces the output file MEGOUT and the diagnostic file MEGDIA. Users can revise the error in MELCOR and MELGEN input files according to MEGOUT and MEGDIA. After an input check is satisfied, a restart file will be generated for the initial conditions of the simulation case. Then, the MELCOR program advances the case calculation through time based on the input files of MELGEN and MELCOR. Finally, the graphics metafiles are written under request by the HISPLT user input. It is important to note that the ability to manipulate sensitivity coefficients is an excellent feature for sensitivity and uncertainty analyses with MELCOR. Many empirical parameters in correlations are implemented as sensitivity coefficients in MELCOR. Users can easily change the sensitivity coefficients through input files for each package. In this manner the sensitivity of empirical correlations to describe fluid thermal hydraulics and heat transfer behavior can be easily studied. The MELCOR uncertainty engine implements two processes that are illustrated in Fig. 17.2. The engine creates a series of “N” MELCOR input file sets with all the common. gen files. The files are created in different “N” number of uncertainty file folders. It also creates uncertainty inputs specific to each MELCOR run. Based on some of those inputspecific times at cycle, the RN distribution is created in the RN parsing uncertainty deck

FIGURE 17.2 Diagram of the uncertainty information flow.

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generator. This data is then fed into the “N” uncertainty file folders, where each of the file folders is unique. Then, “N” number input files are run in MELGEN/MELCOR, and the results finally are submitted to the postprocessor.

17.2 Quality control MELCOR attaches great importance to quality control using the verification and validation (V&V) methodology to achieve and ensure the quality control process [7]. It presents a series of quality control work on sample tests and benchmark problems, consisting of both numerical analyses of full reactor plant problems and internationally renowned experiments. Moreover, these analyses will be repeated with every release of MELCOR to improve the quality control of new versions of the code. Comparison between the updated version and former versions is a good metric on the updated code assessment as updates are released. Assessment analysis work has been conducted historically among every code version, and it is one of the most important parts of the MELCOR development and improvement. Table 17.1 shows the historical review of MELCOR assessment studies, containing the validation test work for each new model added to the various versions of MELCOR. For example, fuel behavior mechanics for core heat up and degradation is simulated using a candling model, where verification of hydrogen generation was demonstrated in earlier versions of MELCOR based on the CORA-13, DF4, and LOFT tests [8]. MELCOR version 1.8.3 introduced extensions to treat aerosol agglomeration effects, and the validations were performed against the ACE as well as the DEMONA experiments. The hygroscopic aerosol effect was added in MELCOR version 1.8.5, and the validations were conducted using experimental data from VANAM, RTF, and AHMED [9 11]. The CONTAIN-MELCOR study assessed the containment spray scrubbing effects against measurements of the Containment Systems Experiment A9 test (Containment Spray CSE-A9). In addition, the Nevada Test Site hydrogen burn tests, as well as the integral effects test DCH containment heating experiments were integrated into the assessment work for numerous other containment behaviors in MELCOR version 1.8.5. Fuel release of fission products together with models for high burn-up MOX fuels was based on ORNL HI/VI and VERCORS experiments in this version. The fission product release models in version 1.8.5 were formalized as default options for code version 1.8.6. MELCOR version 1.8.6 also featured expanded modeling details for core melt progression processes, with newly included molten pool convection treatments. These extensions provided improved predictions of the TMI-2 accident. Some of these extensions are still currently under assessment. The Phebus FPT-1 test stands as the most comprehensive integrated assessment of core damage progression, hydrogen generation, fission product release, RCS deposition, and containment natural depletion processes. The Phebus FPT-1 test provides an excellent assessment database for key deposition behavior in the RCS and containment depletion. Besides the aforementioned experimental validation tests, MELCOR has conducted numerical analysis on the following phenomena with a series of simple test cases for V&V of the mathematical and physical models of the code. The analytical solutions were available in the MELCOR computer code manuals.

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TABLE 17.1

Historical review of MELCOR assessment studies.

Assessment

Validated object

Version 2.1

Version 1.8.5 Version 1.8.4 Version 1.8.3 Version 1.8.2 Version 1.8.1

ABCOVE: AB5 and AB6

Aerosols and vapors

O

3

3

3

3

3

ACE pool scrubbing

Aerosols and vapors

O

3

3

3

O

3

AHMED: RH 5 22,28,96,98

Aerosols and vapors

O

O

3

3

3

3

BCL pool scrubbing

Aerosols and vapors

O

3

3

3

3

3

BETHSY-6.9C (ISP-38)

RCS thermal hydraulics and integral tests

O

3

3

3

3

3

CCI:1, 2, and 3

Ex-vessel MCCI

O

3

3

3

3

3

Containment spray CSE-A9

Aerosols and vapors

O

O

3

O

3

3

CORA-13

Core heat up and degradation

O

3

3

3

3

O

CVTR: test 3, 4, and 5

Containment TH

O

3

3

3

3

3

DEMONA:B3

Aerosols and vapors

O

3

3

3

O

3

DF: DF4

Core heat up and degradation

O

3

3

3

O

3

FALCON: 1 and 2 Aerosols and vapors

O

3

3

3

3

3

Fan cooler tests

O

3

3

3

3

3

FLECHT_SEASET RCS thermal hydraulics and integral

O

3

3

3

3

O

GE level swell

RCS thermal hydraulics and integral

O

3

3

O

3

3

GE Mark I suppression pool

Containment TH

O

3

3

3

3

3

HDR-T31.5

/

O

3

3

3

3

3

HDR-V44

Containment TH

O

O

3

3

3

3

JAERI spray tests: Containment TH PHS 1,6

O

3

3

3

3

3

LACE LA4

Aerosols and vapors

O

3

3

3

3

3

LACE Turbulent Dep (LA1 and LA3)

Aerosols and vapors

O

3

3

3

3

3

Containment TH

(Continued)

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TABLE 17.1 (Continued) Assessment

Validated object

Version 2.1

Version 1.8.5 Version 1.8.4 Version 1.8.3 Version 1.8.2 Version 1.8.1

LHF/OLHF (OLHF-1)

Core heat up and degradation

O

3

3

3

3

3

LOFT:LP-FP-2

Core heat up and degradation

O

3

3

3

3

O

Marviken ATT-4

Aerosols and vapors

O

3

3

3

3

3

Marviken: CFT-21 Containment TH and JIT-11

O

3

3

3

3

3

MeltSpread model tests

Ex-vessel MCCI

O

3

3

3

3

3

NEPTUN: 5006 and 5007

RCS thermal hydraulics and integral

O

3

3

3

3

3

NTS burn: P01, P12, P15, P20

Containment TH

O

O

3

3

3

3

NUPEC: M-8-1, M-8-2

Containment TH

O

O

3

3

3

3

PBF SFD:1 4

Core heat up and degradation

O

3

3

3

3

3

PHEBUS B9 (ISP 28)

Core heat up and degradation

O

O

3

3

3

3

PHEBUS: FPT1 and FPT3

Core heat up and degradation

O

O

3

3

3

3

PNL ICE Condenser:11-6 and 16-11

Containment TH

O

O

3

3

3

O

POSEIDON: PA16,17,20

Core heat up and degradation

O

3

3

3

3

3

QUENCH (ISP45 or Quench-6)

Core heat up and degradation

O

3

3

3

3

3

RAS MEI

/

O

3

3

3

3

3

RTF: ISP41

Aerosols and vapors

O

O

3

3

3

3

SNL Melt Progression: MP1 and MP2

Core heat up and degradation

O

3

3

3

3

O

SNL/IET (DCH Tests): IET-1,3,6

Containment TH

O

O

3

3

3

3

STORM: SR-11 (ISP 40)

Aerosols and vapors

O

3

3

3

3

3

SURC: 1 and 2

Ex-vessel MCCI

O

3

3

3

3

3

(Continued)

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TABLE 17.1

(Continued)

Assessment

Validated object

Version 2.1

Version 1.8.5 Version 1.8.4 Version 1.8.3 Version 1.8.2 Version 1.8.1

TMI-2 accident

RCS thermal hydraulics and integral

O

O

3

3

3

3

VANAM: M3 (ISP37)

Aerosols and vapors

O

O

3

3

3

3

VERCORS

Aerosols and vapors

O

O

3

3

3

3

VI

Aerosols and vapors

O

O

3

3

3

3

VULCANO (VEU7)

Ex-vessel MCCI

O

3

3

3

3

3

MCCI, Molten corium-concrete interaction; RCS, Reactor cooling system; TH, thermal hydraulics.

1. 2. 3. 4. 5. 6.

saturated liquid depressurization; the adiabatic flow of hydrogen transient heat flow in a semiinfinite solid with convective boundary conditions; cooling of rectangular and annular heat structures in a fluid; self-initialization of steady-state radial temperature distributions in annular structures; and establishment of flow in a pipe.

These very simple, fast-running test cases can provide an excellent test of nodalization and time-step dependence. This table represents the V&V methodologies and quality assurance guidelines to develop models and simulation tools. This table reflects the development of the capability of the code of handling physical phenomena and the experiments used for this development. In MELCOR the validated objects of models mainly include five aspects, which are aerosols and vapor, containment TH, core heat up and degradation, RCS thermal hydraulics and integral tests, and exvessel MCCI models. The models earlier have been assessed against many different experimental data sets. As core heat up and degradation models are of crucial importance in addressing the importance of severe accident phenomena and severe accident code development, the validation study of the core heat up and degradation model will be introduced in the following section.

17.2.1 Verification and validation study of core heat up and degradation The CORA facility [12] was used to conduct ISP-31. The ISP-31 test bundle consisted of 16 heater rods, 7 unheated rods representing typical PWR fuel elements, and 2 absorber rods. The heater rods were 1.96-m long and made of tungsten. They were clad in Zircaloy-4. The test bundle was cooled with an argon/steam mixture that entered at the bottom of the bundle. Fig. 17.3 presents a simplified schematic of the CORA test facility. The test bundle was in the central region of this facility. Twenty-five fuel rods in the test bundle were surrounded by a Zircaloy-4 shroud with ZrO2 shroud insulation. The insulation enclosed these fuel rods to keep the heat loss at a minimum. The electric power system was connected to

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17. Engineering-level system code for severe accident analysis: MELCOR

FIGURE 17.3 Simplified schematic of the CORA test facility [13].

both the upper and lower ends of test bundle. This meant that the fuel rods were heated with a controllable power during the experiment. A steam generator produced steam from water, and then the argon and steam were superheated before flowing into the test bundle region. The mixed argon and steam were guided to the lower end of fuel rods. This entrance level for the mixed gases was set as the elevation of zero. In this experiment, argon was a protective gas for heated rods and it also assisted in guiding the steam out of the steam generator. The steam would react with the zirconium when exposed to the hot fuel rod. The unreacted steam was condensed in the surge condenser. Finally, the generated hydrogen was diluted in the dilution chamber with air. The diluted hydrogen was sent to the off-gas system at an acceptable concentration. As shown in Fig. 17.3, a quench tube filled with water was located in the region which was just below the test bundle. Water can be fed into the bundle region at a controllable speed. The initial elevation level of water was 2220 mm. In CORA-13 the quench water level was raised to an elevation of zero at 4875.0 seconds.

17.2.2 Bundle design The simplified schematic of bundle rod arrangement is displayed in Fig. 17.4. The fuel rods in the bundle consisted of 7 unheated and 16 heated rods. The electrically heated

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17.2 Quality control

FIGURE 17.4 Simplified schematic of bundle rod arrangement [14].

TABLE 17.2 Main parameters of bundle [14]. Parameters

Value (mm)

Pitch

14.3

Outside diameter of fuel rod

10.75

Cladding thickness

0.725

Diameter of tungsten rod (heater)

6.0

Length of heated rod

1960

Elevation of heated rod

2489 to 1471

Length of unheated rod

1672

Elevation of unheated rod

2201 to 1471

Heated length

1000

Elevation of lower grid spacer

25

Elevation of center grid spacer

496

Elevation of top grid spacer

880

rods were heated by the internal tungsten rod. Three spacers were employed to fix the positions of rods. The lower and upper grid spacers were made of Zircaloy-4 and the central grid spacer was made of Inconel-718. All materials used in real reactor fuel bundles were contained in the test bundle. Besides, Table 17.2 lists the main parameters used in the MELCOR simulation.

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The location of cross-sectional A A is displayed in Fig. 17.4, and the spatial variation of core temperature is displayed on the cross section. This cross section is symmetrical, and the vertical axis of symmetry is set as the position of zero.

17.2.3 Results of analysis CORA-13 was a completely blind exercise where only boundary and initial conditions were available [15]. All available parameters are input into the simulation, and all MELCOR input parameters are in good agreement with experiment conditions. Thus the variation of the MELCOR input parameters was not displayed. However, the main calculated results are presented for verification. Fig. 17.5 shows the comparison of water level in the quench cylinder. In CORA-13 the quenching process was initiated from the rise of the water in the quench cylinder at 4870 seconds. This indicates that the quench time of simulation is in accord with the experimental data. Thus the results show that the water level keeps constant at 200.0 mm before 4870 seconds, and this difference with measurement is acceptable. After 4870 seconds the behavior of fuel elements in the quenching process is strongly affected by water levels in the test bundle. Simulation results are reasonably close to the measured values. In other words, the MELCOR simulation reasonably reflected the elevation of the water level measured in the experiment. The MELCOR results are compared with experimental measurements and standard SCDAP/ RELAP5 assessment results, with the SCDAP/RELAP5 models developed by the SCDAP/ RELAP5 Development Team [16]. Comparisons of cladding temperature variations are displayed in Fig. 17.6 for the elevations of 0.35 m. No measurements were acquired after reflood occurred. As shown in Fig. 17.6, the MELCOR calculations predict slightly higher values than measurements in the period of 3600 4500 seconds. As a guess, the higher prediction in cladding FIGURE 17.5 Comparison of water level in the quench cylinder.

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17.3 Capabilities and limitations

427 FIGURE 17.6 Comparison of cladding temperatures at 0.35 m elevation.

temperature was due to more drops of hot fuel elements from the upper part that were predicted to collapse in MELCOR simulations. In summary, results show that MELCOR can predict the behavior of fuel elements for the reflood phase. The oxidation model can obtain correct cumulative hydrogen production as well. Due to the complex nature of fuel element interactions during reflood, the analysis program cannot completely reflect the complicated physical and chemical processes in detail. However, some important parameters can be correctly predicted and the development tendency can be obtained in this MELCOR simulation. The numerical simulation contributes to a better understanding of these complicated processes and helps one to find measures to mitigate the development of a severe accident. Specifically, when the core is already heavily damaged, the massive generation of hydrogen helped one to melt the core, so that a small quantity of flooding did not stop the core heat up, but it even contributed to melting the core through the vessel wall.

17.3 Capabilities and limitations Overall, MELCOR is an excellent severe accident code that can serve research purposes from SA analysis to SA management. However, there are still limitations in its current modeling capabilities. In this part, we take the important model (COR) to show the advantages of current MELCOR models. The model limitations of MELCOR are also described in this section.

17.3.1 Advantages MELCOR obtains powerful modeling capabilities using many newly enhanced models. These models include hemispherical lower head geometry, the formation of molten pools

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both in the lower plenum and the upper core. Furthermore, crust formation, convection in molten pools, stratification of molten pools into metallic (light and heavy) and oxide layers, partitioning of RNs between stratified molten pools complete an exhaustive list of newly enhanced models. Oxidation of zircaloy and steel can be modeled as being limited by both solid-state diffusions of oxygen through the oxide layer and gaseous diffusion of steam or oxygen through the mixture. The reaction of B4C with steam is also modeled. This translates to very effective modeling of the core region for various types of reactor configurations in MELCOR. All the important heat transfer processes are modeled in each COR cell. COR models can offer predictions of the complicated phenomena that occur during severe accidents. Fig. 17.7 presents the diagram of core/lower plenum nodalization using the MELCOR COR model. As shown in the figure, the core and lower plenum regions of the reactor vessel are divided into concentric radial rings and separate axial levels. Each cell may contain one or more components, as shown in Fig. 17.7. The primary difference between the FIGURE 17.7 Diagram of core/lower plenum nodalization using MELCOR COR model [17].

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429

supporting and nonsupporting structure components is whether they can support other core components (core support structures) or not (control rods or blades). COR packages can treat various processes of heat transfer and oxidation within the lower plenum and core. Radiation, conduction, and convection are added in the COR package to simulate the heat transfer and oxidation process. The local temperature calculation model (dT/dZ model, explained in the user’s manual) is used by the COR package to provide approximate local (core cell) fluid temperatures and gas compositions within the possibly larger CVH-package control volume. Fission power generation in anticipated transient without scram accident sequences (and in some experiments) is adopted. The mass relocation process is simulated using a candling model. In the candling model the behaviors of candling of molten core materials, the transport of additional nonmolten materials with the molten material, the radial relocation of molten pools, and the formation of flow blockages and molten pools are predicted. The further development of the radial relocation of molten pools and particulate debris can also be captured. Adopted in the COR package are the formation of particulate debris by various means from intact components, radial spreading of debris, and its axial relocation by gravitational settling and/or collapse of supporting component models.

17.3.2 Limitation of MELCOR There are several model limitations within MELCOR and the long list of uncertainties in severe accident phenomena. The limitation on the level of realism possible in the vaporization rate is not being able to change the composition of the molten alloy. Another limitation is that a pressure difference is not calculated for use in the computation of the break velocity—only the gravitational head is used. This is because of the lack of geometry information in MELCOR—the internal control rod pressure and the rate at which it decreases following a break depends on the internal free volume of the control rod. The internal volume does not input to MELCOR, only the alloy mass, node heights, and total cross-sectional area of rods per ring are available. It was, therefore, decided not to include the effect of internal rod pressure in the release model. Another limitation is that only the total cross-sectional area of rods per ring is input, which is the cross-sectional area, including the guide tubes. The internal cross-sectional area of the control rod and the number of rods per ring are not available. Looking back at the release equations, only the area ratio is necessary for calculating the release velocity; this ratio is input to the model. The break area per ring, which appeared in the equation for mass release rate, can be obtained from the cross-sectional area if this ratio is used. Due to the fact that the cross-sectional area in the code includes the guide tubes, the release rate will be incorrect unless the input area ratio accounts for the difference between the inside flow area of the control rods and the total area.

17.4 MELCOR version update history From 1982 to 1984, Sandia National Laboratories accomplished the definition of the code architecture, developed the fundamental models, and released the first functional versions of MELCOR.

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The updated MELCOR version 1.8.3 was released to users in September 1994. MELCOR modeling is general and flexible. Specific nodalization of a system is not forced on the user, which allows one to choose an appropriate level of complexity for the task at hand. Reactorspecific geometry is imposed only within the reactor core. Even with this restriction, one basic model suffices for the representation of either a BWR or a PWR core, and a wide range of modeling detail is possible. Thus with a relatively simple nodalization, MELCOR can function as a probabilistic risk assessment tool for light ware reactor nuclear power plants. MELCOR version 1.8.5 was released to users in October 2000. The version 1.8.5 developed many new modeling features and enhancements to previously existing models. New model features include an iodine chemistry model, a passive autocatalytic recombiner model, many improvements to the core degradation models, improvements to the hygroscopic aerosol model, enhancements to both the user control function feature and plotting features, and an update to several of the code’s default values. MELCOR version 1.8.6 was released to users in September 2005. Many new modeling improvements were added to the COR package so that it could better represent the late phase behavior of severe accidents. As part of this development, the bottom head (BH) package was eliminated and features formerly offered by the BH package were integrated into the COR package. New models in the COR package include hemispherical lower head geometry, models for simulation of the formation of molten pools in the lower plenum and the upper core, crust formation, convection in molten pools, stratification of molten pools into metallic (light and heavy) and oxidic layers, and partitioning of RNs between stratified molten pools, reflood quench model, control rod silver release mode, new B4C control rod oxidation model, and capability to model the PWR core outer periphery. Improvements to other MELCOR packages included models for the flashing of superheated vapor flows and the extension of CORSOR—booth release model to a second fuel type. MELCOR version 2.1 was released to users in August 2015. Many new modeling improvements were added. The most significant of these improvements was the modeling capabilities of CONTAIN, and the mechanistic fan cooler model like the CONTAIN model that was implemented into this version. Additional enhancements were the newly developed CORQUENCH model that was added to the CAV package. The air oxidation model developed by Paul Scherrer Institute was also implemented into MELCOR 2.1. Enhancements to radiation exchange models and implementation of Parallel Virtual Machine coupling were also included. Models for liquid metal reactors were included in this version and the sodium properties were added to MELCOR as a new liquid metal coolant in this version [3]. Other CONTAIN/LMR models were added for sodium fires as well.

17.5 Demonstration problems: Experiments for validation Accident tolerant fuel and cladding materials are under development to provide greater resistance to fuel degradation, oxidation, and melting if long-term cooling is lost in an LWR following an accident such as a station blackout (SBO) or loss of coolant accident. The MELCOR demonstration problems are research work for the analysis of SBO sequences and the examination of the effect of a loss of auxiliary feed-water (AFW). This research work considers accident tolerant cladding materials (e.g., FeCrAl alloy) and their effect on accident

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17.5 Demonstration problems: Experiments for validation

behavior. The MELCOR code models all related plant systems, plant phenomena, and transients in a wide range of systems, such as thermal-hydraulic performance, thermomechanical interactions, and chemical interactions. The rest of the relevant parts of the code comprise the PLOT program and the MACCS program, which is designed to analyze the off-site radiological consequences. There are a variety of code packages (COR, CVH, and FL) which model different portions of the reactor. A short-term station black out (STSBO) is a particular scenario within the general accident category of an SBO. The main difference between an STSBO and a long-term SBO is that there is no AFW or RCIC operation (BWR) in the former. For the STSBO severe accident scenario, the assumptions are as in Table 17.3. The nodalization scheme is shown in Fig. 17.8. As seen in this figure, the core of the SURRY plant is separated into 5 rings in the radial direction, and 10 nodes in an axial direction. The lower plenum and dome are also divided into several nodes. In the top dome, some nodes are coincident. This situation will influence the results of the reactor pressure vessel (RPV) water level. There are three steam generator loops in this plant: even though only one loop is shown. Benefits from the US Department of Energy’s efforts to promote the goal of enhancement of the accident tolerance of LWRs, relevant research becomes a hot topic in the United States. Several experimental and simulation-based research projects were conducted in the United States as a result. Through a vast literature review [19 22], ORNL’s research of FeCrAl (and FeCrAl oxide) was found from many thermal physical properties: enthalpy, specific heat, thermal conductivity, density, melting temperature, and latent heat of fusion. Enthalpy of FeCrAl (and FeCrAl oxide) constantly increases with the increase of temperature, and results show that the relationship between enthalpy and temperature is almost linear except between 1500K and 2000K. In the simulation the threshold value chosen to indicate notable hydrogen generation is 0.5 kg, which corresponds to a hydrogen mass of less than 0.1% of core-wide oxidation values. To verify the sensitivity of this threshold, 1% (6.6 kg) of the core-wide oxidation is used as the criterion to determine

TABLE 17.3 Accidents associated with short-term station black out [18]. Component

Status

RCS

Intact

CTMT (containment)

Intact

AC power

Failed

DC power

Failed

HHSI

Failed

LHSI

Failed

CCW

Failed

CTMT spray

Failed

Fan cooler

Failed

CCW, Component cooling water; CTMT, containment makeup tank; HHSI, high head safety injection; LHSI, low head safety injection; RCS, reactor cooling system.

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FIGURE 17.8

17. Engineering-level system code for severe accident analysis: MELCOR

Nodalization scheme of the SURRY plant core.

the time delay between the time of AFW failure and the time of rapid hydrogen generation for either zircaloy or FeCrAl as cladding materials. Fig. 17.9 presents the comparison of the time delay for ,0.1% and 1% core-wide oxidation. The detailed results can be found in the literature [22,23]. In the FeCrAl coating case, some material was predicted to have fallen below the support plate and thus the peak temperature above that location temporarily decreased. To help visualize the location of the materials for this case with no RCIC operations for a BWR case, one can look to the material distribution map for the core materials as shown in Figs. 17.10 and 17.11. Results show that FeCrAl can further delay core heat up and fuel degradation and reduce the total mass of hydrogen generated during the accident scenario, which can result in additional coping time for emergency procedures and operator actions. Similar trends were observed in the STSBO scenario just as in the case of immediate RCIC failure. Use of FeCrAl materials produces a modest delay in the onset of hydrogen generation (more than an hour) but can lead to the creation of more hydrogen within the RPV than zircaloy-based materials. As noted previously, this is related to the different oxidation kinetics of FeCrAl and zircaloy. While zircaloy has a higher reaction rate at lower temperatures, it

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17.5 Demonstration problems: Experiments for validation

433

FIGURE 17.9 Comparison of the time delay for ,0.1% and 1% core-wide oxidation [18].

FIGURE 17.10 RPV material distribution map for STSBO with zircaloy just following SRV opening failure. CL, Clad; FU, fuel; MP, MB, molten core debris; NS, nonsupport structure; OS, other steel structure; PD, PB, solid core debris; RPV, reactor pressure vessel; SS, supporting structure; SRV, surge relief valve. [24,25].

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FIGURE 17.11 RPV material distribution map for STSBO with FeCrAl clad just following SRV failure.

does not increase as much when higher temperatures are reached. In contrast, FeCrAl has a smaller reaction rate at lower temperatures but increases dramatically once the phase-change threshold temperature is reached. By using a zircaloy component that is coated with a material like FeCrAl, it appears to be possible to utilize some of the beneficial properties of both materials. In addition, the core temperature increases very fast, say around 0.5 C 1 C/s, and AM measures (repair flooding, hook on portable pumps) take quite some time, it is not contributing much.

Reference [1] D.L. Luxat, D.A. Kalanich, J.T. Hanophy, R.O. Gauntt, R.M. Wachowiak, MAAP-MELCOR crosswalk phase 1 study, Nucl. Technol. 196 (3) (2016) 684 697. [2] T. Sevo´n, A MELCOR model of the Fukushima Daiichi unit 1 accident, Ann. Nucl. Energy 85 (2015) 1 11. [3] L. Fernandez-Moguel, A. Rydl, T. Lind, Updated analysis of Fukushima unit 3 with MELCOR 2.1. Part 1: Thermal-hydraulic analysis, Ann. Nucl. Energy 123 (2019) 59 77. [4] R.O. Gauntt, R.K. Cole, C.M. Erickson, et al., MELCOR computer code manuals, Sandia Natl. Lab. Vol. 1 and Vol. 2 (2000) 6119. NUREG/CR.

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Reference

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[5] L. Fernandez-Moguel, A. Rydl, T. Lind, Updated analysis of Fukushima unit 3 with MELCOR 2.1. Part 2: Fission product release and transport analysis, Ann. Nucl. Energy 130 (2019) 93 106. [6] T. Noju, A. Yamaji, K. Matsumoto, X. Li, Sensitivity study of accident scenarios on MCCI for Fukushima Daiichi Unit-1 by MELCOR, in: International Congress on Advances in Nuclear Power Plants, ICAPP 2017, Fukui and Kyoto, Japan, 2017. [7] L. Humphries, B. Beeny, D. Louie, H. Esmaili, M. Salay, Non-LWR model development for the MELCOR code, in: 2018 26th International Conference on Nuclear Engineering, London, England, October 2018. [8] F.J. Souto, et al., MELCOR 1.8.2. Assessment: Aerosol Experiments ABCOVE AB5, AB6, AB7, and LACE LA2, SAND94-2166, Sandia National Laboratories, Albuquerque, NM, October 1994. [9] M. Firnhaber, T.F. Kanzleiter, S. Schwarz, et al., International Standard Problem ISP37: VANAM M3—A Multi Compartment Aerosol Depletion Test With Hygroscopic Aerosol Material: Comparison Report, Organization for Economic Co-Operation and Development-Nuclear Energy Agency, 1996. [10] J. Ball, G. Glowa, J. Wren, et al., ISP 41 Containment Iodine Computer Code Exercise Based on a Radioiodine Test Facility (RTF) Experiment, NEA/CSNI Rep., 2000. [11] J.M. Ma¨kynen, J.K. Jokiniemi, P.P. Ahonen, et al., AHMED experiments on hygroscopic and inert aerosol behavior in LWR containment conditions: experimental results, Nucl. Eng. Des. 178 (1) (1997) 45 59. [12] M. Firnhaber, et al., OECD/NEA-SCNI International Standard Problem No. 31 Cora-13 Experiment on Severe Fuel Damage: Comparison Report, Nuclear Energy Agency, OECD, Paris, France, 1993. [13] R.J. Gross, S.L. Thompson, G.M. Martinez, MELCOR 1.8.1 Calculations of ISP31: The CORA-13 Experiment, Sandia National Labs., Albuquerque, NM, 1993. [14] T. Feng, W. Tian, P. Song, et al., Spatial temperature distribution of fuel assembly pre-simulation for a new simple core degradation experiment, Prog. Nucl. Energy 111 (2019) 174 182. [15] S. Hagen, P. Hofmann, V. Noack, et al., Results of SFD Experiment CORA-13 (OECD International Standard Problem 31), Kernforschungszentrum Karlsruhe GmbH, Germany, 1993. [16] The SCDAP/RELAP5 Development Team, 1997 SCDAP/RELAP5/MOD3.2 Code Manual Volume V: Developmental Assessment. Appendix A SCDAP/RELAP5/MOD3.2 Assessment. NUREG/CR-6150 INEL-96/0422 Revision 1, vol. V, 1997. [17] L.L. Humphries, B.A. Beeny, F. Gelbard, D.L. Louie, J. Phillips, MELCOR Computer Code Manuals, vol. 2: Reference Manual Version 2.2.9541, SAND2017-0876, 2017. [18] N.E. Bixler, J.D. Brewer, R.O. Gauntt, State-of-the-Art Reactor Consequence Analysis (SOARCA) Project Best Modeling Practices vol. IV. NUREG-1935, SAND2008P, 2008. [19] L.J. Ott, K.R. Robb, D. Wang, Preliminary assessment of accident-tolerant fuels on LWR performance during normal operation and under DB and BDB accident conditions, J. Nucl. Mater. 448 (2014) 520 533. [20] B.J. Merrill, S.M. Bragg-Sitton, Status Report on Advanced Cladding Modeling Work to Assess Cladding Performance under Accident Conditions, INL/EXT-13-30206, Idaho Falls, ID, 2015. [21] C.P. Massey, K.A. Terrani, S.N. Dryepondt, B.A. Pint, Cladding burst behaviour of Fe-based alloys under LOCA, J. Nucl. Mater. 470 (2016) 128 138. [22] J. Wang, M. Mccabe, L. Wu, et al., Accident tolerant clad material modeling by MELCOR: benchmark for Surry short term station black out, Nucl. Eng. Des. 313 (2017) 458 469. [23] J. Wang, C. Troy, L. Michael, et al., Severe accident progression and effects of accident tolerant cladding, in: 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH-17, Xi’an, China, 2017. [24] R. Dailey, J. Wang, M.L. Corradini, Light Water Reactor Sustainability Program, Generic Boiling Water Reactor MELCOR Plant Model, U.S. Department of Energy, Office of Nuclear Energy, Washington, DC, 2018. [25] R. Dailey, J. Wang, M.L. Corradini, Development of a MELCOR BWR Model Progress Report, U.S. Department of Energy, Office of Nuclear Energy, Washington, DC, 2018.

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C H A P T E R

18 Moving Particle Semi-implicit method Zidi Wang1, Guangtao Duan2, Seiichi Koshizuka2 and Akifumi Yamaji3 1

Nuclear Safety Research Center, Japan Atomic Energy Agency, Ibaraki, Japan 2 Department of Systems Innovation, The University of Tokyo, Tokyo, Japan 3 Cooperative Major in Nuclear Energy, Waseda University, Tokyo, Japan

18.1 Introduction Complex thermal-hydraulic problems, in particular, multiphase flow with heat transfer and phase change as well as complex motion of interfaces, are widely involved in nuclear engineering. These problems used to be studied by experiments. Numerical analysis was possible for simplified systems based on model assumptions and experimental correlations. A typical example is the two-fluid model for water
steam two-phase flow. A flow regime map is necessary to be assumed firstly, then a transport equation is solved for each phase while the interactions between the phases are calculated based on the correlations. In recent years, with the development of numerical simulation techniques and computational power, various numerical methods have been applied to deal with such multiphase problems. In the field of computational fluid dynamic, several approaches based on the mesh-based methods are developed, including the front-tracking method [1], level-set method [2,3] and volumeof-fluid method [4]. Large deformation of the interfaces can be analyzed. However, a main issue of these mesh-based Eulerian approach is that the numerical diffusion might become severe when the deformation of the interface is very large. This makes the capture of sharp surfaces a little complicated. The Moving Particle Semi-implicit (MPS) method, proposed by Koshizuka and Oka [5], is a meshless Lagrangian particle method, which has great potential in tracking various free surfaces and interfaces for incompressible flow. Different from the conventional mesh-based method, the physical quantities are calculated as a set of arbitrarily distributed particles. The particles are distributed only in the area where the fluid exists and they move in a Lagrangian

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00018-8

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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18. Moving Particle Semi-implicit method

manner in the whole computational domain. Governing equations are discretized into particle interaction models that determine the motion of particles. It should be noted that the treatment of convection in this Lagrangian method is straightforward, whereas it is a complex problem when adopting Eulerian methods. Since the fluid is represented by the particles, large deformation of free surfaces can be easily and accurately tracked by the Lagrangian motion of particles [6]. In addition, the process of mesh generation, which usually takes time and expert knowledge in the mesh-based method, is not necessary. Since its development, it has been applied to a wide range of fluid mechanics, including nuclear engineering [7
9], ocean engineering [10], and civil engineering [11]. In nuclear engineering, the MPS method is an effective and robust approach for mechanism study and safety analysis, such as bubble dynamic, vapor explosion, jet and droplet behaviors, multiphase flow, molten core (corium) spreading, molten core concrete interaction (MCCI), and flooding. In this chapter, the basic theory of the MPS method is explained. Various applications to nuclear engineering are described in detail.

18.2 Moving Particle Semi-implicit method 18.2.1 Governing equations In the Lagrangian description of the Navier
Stokes equations, that is, mass conservation equation and momentum conservation equation, for an incompressible Newtonian fluid, can be written as follows:



Dρ 5 2 ρr u 5 0 Dt Du 1 F 5 2 rP 1 vr2 u 1 g 1 Dt ρ ρ

(18.1) (18.2)

where ρ is the density of the fluid, u is the flow velocity, P is the pressure, v is the kinematic viscosity, g is the gravitational acceleration, and F represents other forces, such as the surface tension.

18.2.2 Discretization scheme The basic concept of spatial discretization in MPS is the difference between two particles. Since mesh is no longer used, the difference between two particles can be calculated as shown in Fig. 18.1. In MPS, a particle would interact with other neighboring particles. Thus another basic concept is the effective radius re. As depicted in Fig. 18.2, the interaction between an arbitrary pair of particles is limited within the effective radius, otherwise the calculation cost would be very large and is not acceptable in large-scale problems. A weighted average of the differences with its neighboring particles is considered by introducing a weight function. The widely used one is given as:

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441

FIGURE 18.1 Difference between two particles.

FIGURE 18.2

Particle interaction within effective radius.

8r e 

 < 2 1; 0 , r , re

r w r ij 5 : 0; r $ re

(18.3)





where r 5
r ij
5
r j 2 r i
is the distance between particles i and j. In general, the effective radius re can be set from 2.0 to 5.0 times the particle size l0. In particular, re 5 2.1 l0 or 3.1 l0 is widely adopted. As the summation of the weight function values at neighboring particles, the particle number density ni of particle i is calculated as: X 

 (18.4) w
r ij
ni 5 j6¼i

The particle number density is considered to be proportional to fluid density, thus incompressibility is guaranteed by maintaining as a constant value n0 , which is the initial value calculated from the initial particle configuration. As shown in Fig. 18.3, the gradient operator, which is represented by the weighted average of gradient vectors between two neighboring particles, is given as:     d X φj 2 φi r j 2 r i 







w r ij (18.5) rφ i 5 0
r j 2 r i

r j 2 r i
n j6¼i

where φ is a scalar variable and d is dimensional number.

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18. Moving Particle Semi-implicit method

FIGURE 18.3 Gradient model.

FIGURE 18.4

Laplacian model.

In order to keep stability of the calculation, the following pressure gradient model (18.6), which can guarantee repulsive forces among particles, is usually adopted: hrPii 5

 

 d X Pj 2Pi;min 

2 r j 2 r i w
r ij
0 n j6¼i
r j 2r i


(18.6)

where Pi;min is the minimum pressure among the neighboring particles of particle i. Another important operator in MPS is the Laplacian operator. As shown in Fig. 18.4, the discretized formulation of Laplacian operator is modeled as distribution of the quantity from particle i to the neighboring particle j. The Laplacian operator in the MPS method is given as: 

 

  2d X  r2 φ i 5 0 φj 2 φi w
r ij
λn j6¼i

(18.7)

where d is dimensional number, λ is the Laplacian model coefficient. It is known that the Laplacian operator represents diffusion in physics and this Laplacian operator has been developed by referring to the analytical solution of the transient diffusion problem (Gaussian function) [12]. The central limit theorem guarantees that the repeated superposition of any function converges to the Gaussian function if the variance increase is the same as that of the Gaussian function. Thus the introduced Laplacian model coefficient

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443

λ is used to keep the same variance increase. Like n0 , λ is calculated from the initial particle arrangement and is defined as: P λ5


2 


w
r ij

r j 2r i


 P

j6¼i w r ij

j6¼i

(18.8)

It should be noted that the above operators are derived in a way like the finite difference method under the assumption that particle distribution is basically regular. The errors in these operators would increase for an irregular particle distribution due to the motion of particles. In order to improve the accuracy for the anisotropy of particle arrangements, higher order schemes have been formulated by using the Taylor expansion [13,14] and the method of least squares [15]. For instance, a widely used first-order gradient operator can be expressed as follows: 

  

 1 X φj 2 φi  rφ i 5 0

Ci r j 2 r i w
r ij
n j6¼i
r j 2r i
2

(18.9)

where 2

321 ! X

  r 2r r 2r 1
j i

j i
w
r ij
5 Ci 5 4 0 n j6¼i
r j 2r i

r j 2r i


(18.10)

is called a corrective matrix [14]. The verification test concerning different order discretization operators have been performed by Duan et al. [13]. Fig. 18.5 shows the convergence result for different discretization models. The observed convergence order is consistent with the analytical analysis: (1) the original, first order, and second corrective matrix gradient model exhibit zero, first, and second order of convergence, respectively; (2) the original, first order, and second corrective matrix Laplacian models exhibit minus first, zero, and first order of convergence, respectively.

FIGURE 18.5 Mean errors of different discretization operators [13]: (A) gradient models and (B) Laplacian models.

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18. Moving Particle Semi-implicit method

18.2.3 Detection of free surface particles The free surface boundary condition is detected from the decreasing of particle number density. A Dirichlet boundary condition is given to the free surface particles when solving the pressure field. The pressure is set to be the background pressure when the particle number density satisfies the following equation: ni , βn0

(18.11)

where n0 is the initial value of the particle number density given by Eq. (18.4), β is a parameter for surface detection and β 5 0:97 is usually adopted [16]. However, some internal particles may be misjudged as free surface particles. An additional detection condition proposed by Tanaka and Masunaga [17] is often utilized: 0

Ni , β N 0

(18.12)

where Ni is the number of neighboring particles, N 0 is the value in the initial particle 0 arrangement, and β is another parameter. Some more accurate detection methods based on geometrical information can be found in Refs. [15,18,19]. Recently, some so-called conceptual particle or virtual particle methods have been proposed to enhance the accuracy of the free-surface boundary [18
21].

18.2.4 Semi-implicit algorithm and pressure calculation As presented in Fig. 18.6, a prediction
correction two-step algorithm has been developed in the MPS method [5]. In the first (prediction) step, the viscosity and external force terms are calculated explicitly to obtain the temporary velocity ui and temporary position r i : FIGURE 18.6 Calculation algorithm of MPS. MPS, Moving particle semi-implicit method.

VI. Noval CFD methods

18.2 Moving Particle Semi-implicit method

445



k ui 2 uki 5 ðv r2 u i 1 F k ÞΔt

(18.13)

r i 5 r ki 1 ui Δt

(18.14)

In the second (correction) step, the mass conservation equation is calculated with the pressure gradient terms in the momentum conservation equation:



0

r ui 5 2 0

ui 5 2

ρ

1 Δt

2 ρ ρ0

k11

Δt  k11  rPi ρ

(18.15) (18.16)

where 0

ui 5 uk11 2 ui i

(18.17)

Assuming the fluid density is in proportion to the particle number density, and combining Eqs. (18.16) and (18.17), the pressure Poisson equation (PPE) is derived: 1 2 k11 1 ni 2 n0 r Pi 5 2 ρ Δt2 n0

(18.18)

where ni and n0 are the temporary and initial particle number densities, as defined in Eq. (18.4). Since the variables involved in each equation are multiple, the simultaneous linear equations can be expressed using a matrix. This can be easily solved using a linear solver, such as the conjugate gradient method. The pressure solving process is an implicit calculation and this is the reason why this algorithm is called semi-implicit algorithm. Finally, the temporary velocity is corrected by evaluating the pressure gradient term. 0

uk11 5 ui 1 ui i 0

5 r i 1 ui Δt r k11 i

(18.19) (18.20)

Pressure oscillation is a common problem in particle methods, the following PPE is usually adopted to achieve a more smooth pressure profile [22,23]:



1 2 k11 r u γ n 2 n0 α k11 r Pi 5 ð 1 2 γ Þ 2 1 P ρ Δt2 n0 Δt2 i Δt

(18.21)

where γ is a relaxation coefficient (0:01 , γ , 0:05) and α is an artificial compressible coefficient (1029 , α , 1026 ). Both γ and α are utilized to smooth and stabilize the pressure field. The main part of the source term is the divergence of temporary velocity, while the rightmost part introduces an artificial compressibility.

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18. Moving Particle Semi-implicit method

18.3 Application to nuclear engineering 18.3.1 Bubble dynamics Bubble dynamics is an important and complicated issue in the thermal-hydraulic field since it determines the heat transfer in the boiling or condensation process. This behavior has been studied by the MPS-MAFL method [24,25]. MAFL, which is short for meshless advection using flow-direction local grid, is a meshless scheme for advection terms. By combing this scheme with MPS method as an arbitrary Lagrangian
Eulerian description, it is effective to control the spatial resolution without losing the advantages of particle methods. Single bubble generation and departure in nucleate boiling on a heated wall was calculated by Yoon et al. [25]. A set of moving particles was used to represent the liquid phase while the vapor phase was evaluated by ideal gas law. The bubble
liquid interface was traced through the Lagrangian motion of interfacial particles. The particle size was set small enough near the heated wall and interface, so that the bubble deformation is well captured by the fine resolution. The interfacial heat transfer was determined by the energy variety of interfacial particles in each time step. The calculation results from Ref. [25] are depicted in Fig. 18.7. The subcooled liquid surrounding a small bubble was at 96 C with atmospheric pressure, while the heated wall temperature was set 110 C as the initial boundary condition. The size of initial vapor bubble was 0.3 mm in radius. The bubble radii grew fast in the initial 5 ms following the homogeneous theory. After that, the bubble departure behavior, which was affected by both the detaching force due to buoyancy and the force against the detaching force due to

FIGURE 18.7 Bubble growth in nucleate pool boiling (Twall 5 110 C, Tsat 5 100 C, and TN 5 96 C) [25].

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447

surface tension, was quite well simulated. The calculation results of bubble radius and heat transfer were compared with the experimental data [26] and good agreements were found. In the case of a Neumann boundary condition, a high heat flux is supplied from the wall, corresponding to a reactivity initiated accident of a light water reactor (LWR). In such accident, a large reactivity will be inserted and a high heat flux would be supplied from the fuel rods to subcooled water. This transient boiling phenomenon with high heat flux and high subcooling was studied by Heo et al. [27]. Good agreement was achieved with respect to the void fraction by comparing with an experiment carried out by Yamada et al. [28]. Some additional bubble dynamics were further investigated by several researchers. The bubble collapse due to condensation was studied by Tian et al. [29,30]. The calculated collapse time agreed well with that of the analytical theory. The hydrodynamic characteristics of single Taylor bubble rising in slug flow were analyzed by Li et al. [31]. The simulation results agreed well with both theoretical analysis and experimental results. Furthermore, the bubble dynamic during flow boiling was investigated by Chen et al. [7]. The dynamics of a single bubble under different levels of bulk liquid velocity, liquid subcooling, wall superheat, and surface orientation were studied and compared with experimental results.

18.3.2 Vapor explosion Vapor explosion, which might happen when the molten core comes into contact with the coolant, is one of the important issues in nuclear severe accidents. However, the mechanisms have not yet been clarified in experimental studies since this process is so rapid. One key process is the fragmentation of the melt, which is caused by the increase of the interfacial area between the melt and water. In order to investigate the mechanisms in vapor explosions, a study concerning the fragmentation of molten metal was carried out using MPS [16]. Two boiling models, namely, Ciccarelli
Frost’s model [32] and Kim
Corradini’s model [33], were adopted to simulate the physical process through particle generation. The processes of water jet impingement on a molten tin pool were calculated as collapse of a vapor film around a melt drop. A filament of the molten metal was predicted between two water jets as assumed in Ciccarelli
Frost’s model. The penetration of the water jet, which was assumed in Kim
Corradini’s model, was predicted only when the jet fluid density was assumed to be hypothetically larger than the actual density. The effects of density ratio between jet fluid and molten pool, jet velocity, jet length, and rapid boiling based on spontaneous nucleation were discussed in detail. Another application with regard to vapor explosions was single droplet fragmentation studied by Koshizuka and Oka [34]. In their study, a molten tin droplet of a diameter of 5 mm was impinged by 12 water jets with a velocity of 70 m/s. The water jets with such high speed in the simulation represented the nonuniform but strong forces, which are derived from spontaneous nucleation on the direct contact between water and melt. The simulation results showed that the melt droplet was strongly distorted and sharp filaments were extruded. This melt fragmentation process agreed well with the single drop steam explosion experiment carried out by Ciccarelli and Frost [32]. Based on the

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18. Moving Particle Semi-implicit method

simulation results, the mechanism of thermal fragmentation process in vapor explosions can be concluded that it is the nonuniform but strong forces around the melt droplets that cause the extrusion of the filaments [35].

18.3.3 Jet and droplet Jet and droplet play important roles in nuclear reactor safety. In case of a severe accident of LWRs, molten core jets would be dispersed in a water pool, boiling of water and solidification of the molten core materials (corium) would occur. In addition, in a hypothetical core disruptive accident of sodium-cooled fast breeder reactor, there is possibility that a large amount of molten fuel would break up in sodium coolant. A basic numerical analysis of jet break using MPS was carried out by Shibata et al. [36]. Fluid was discharged from the nozzle. Dependencies on the Weber number (We) and the Froude number (Fr) were investigated by varying the surface tension coefficient and the fluid velocity. The simulation results are shown in Fig. 18.8. The jet breakup lengths based on Fr and We showed good agreements with the experimental results [37]. It should

FIGURE 18.8 Simulation results of jet breakup [36]: (A) We 5 10, Fr 5 1.40; (B) We 5 100, Fr 5 1.40; and (C) We 5 100, Fr 5 3.36.

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449

be noted that the size distribution of droplets after the breakup was consistent with the Nukiyama
Tanasawa distribution [38], which is widely used as an experimental correlation. The behavior of jet injection into a pool was investigated by Ikeda et al. [39]. Their calculation was carried out to understand the behavior of jet penetration for the fuel
coolant interaction (FCI) process. Results showed that the penetration behavior was affected by the density ratio of the jet and pool fluids. The penetration depth in three-dimensional (3D) calculation showed good agreement with the experiment conducted by Park [40]. Impingement caused by melt jet is another important phenomenon concerning the progression of severe accident. It could happen in many circumstances. In case of core melting, the corium would impinge onto the lower core plate and the reactor pressure vessel (RPV) wall. Moreover, when the RPV fails, the corium would directly impinge onto the dry concrete. The erosion and heat-transfer characters of these molten jet impinging have been investigated using MPS [41
43]. Besides the melt jet, the liquid droplet could also cause impingements. The liquid droplet impingement is known as one of the reasons for pipe wall thinning in nuclear power plants. Single-droplet impingement was analyzed by Xiong et al. [44]. The simulation results agreed well with the existing correlations.

18.3.4 Multiphase flow instability The multiphase flow instability is of great importance for nuclear safety. It happens at both normal and abnormal conditions in boiling water reactors. For pressurized water reactors (PWRs), it could happen during some accident conditions, such as the loss-ofcoolant accident (LOCA). One of the most challenging aspects of dealing with two-phase flow is the fact that it could become many different flow patterns (e.g., bubbly, slug and annular) according to the spatial distributions and velocities of the liquid and vapor phases. The flow patterns will consequently affect the pressure drops and heat-transfer coefficients. From the viewpoint of numerical simulations, conventional method might be a little difficult to deal with such violate interfaces with coalescence and breakup of gas bubbles since multiple phases are involved. A simple and fundamental calculation of liquid
gas flow was simulated using the continuous acceleration multiphase MPS (MMPS) method developed by Duan et al. [45]. In this method, the multiphase fluids are modeled as a multiviscosity and multidensity fluid. As shown in Fig. 18.9, the liquid and gas phases flow into the rightangle tube from the left inlet and flow out from the top outlet. The liquid-to-gas density ratio was set to be 1000, heat transfer was not considered. A contour continuum surface tension model [46] was adopted. Initially, the gas phase was placed in the lower part of the horizontal tube. Due to the velocity difference between liquid and gas, gas phase broke up into two parts in the beginning. Following was the bubble rising, deforming, and breaking up in the vertical tube. Finally, a Taylor bubble was formed near the outlet, leaving a heavily deformed tail. The bubble coalescence and breakup in multiphase flows were proved to be easily handled by the MMPS method.

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18. Moving Particle Semi-implicit method

FIGURE 18.9 Snapshots of bubble rising in a right-angle tube [45]: (A) t 5 0.05, (B) t 5 0.1, (C) t 5 0.2, (D) t 5 0.5, (E) t 5 0.75, (F) t 5 1.0, (G) t 5 1.2, (H) t 5 2.0, and (I) t 5 5.0.

Another important phenomenon in multiphase flow instability is the Rayleigh
Taylor instability (RTI), which occurs at the interface between two fluids of different densities. For example, explosion may be triggered when corium leaks into a cooling water tank. The characteristics of heat transfer process and the finally vapor explosion strongly depend on the interface instability between corium and the coolant. In addition, the interface instability plays an important role in the FCI process and would raise the uncertainty of the consequence. Fig. 18.10 presents snapshots of RTI simulated by MMPS [45]. A sinusoidal function with an amplitude of 0.06 m at the interface was used for the initial fluctuation to induce RTI. The density ratio between the heavy fluid in the upper half and the light fluid in the lower half of the tank was 3.0. The characteristic mushroom caps caused by the vortices were predicted, which showed the potential of MPS for FCI or other flow instability involved studies.

VI. Noval CFD methods

18.3 Application to nuclear engineering

FIGURE 18.10

(D) t 5 1.5 s.

451

Snapshots of R
T instability with streamlines [45]: (A) t 5 0.4 s, (B) t 5 0.8 s, (C) t 5 1.2 s, and

18.3.5 In-vessel phenomena during severe accident Given the severe accident of a LWR, the fuel may melt and the corium would be retained in the RPV. Various phenomena involving heat transfer and phase change would happen during this in-vessel stage. In order to deal with the heat transfer process with melting and solidification, a phase transition process is modeled based on the energy conservation equation [Eq. (18.22)]. The temperature T and solid fraction γ are calculated as functions of enthalpy h, as defined in Eqs. (18.23) and (18.24).

T5

8 > > > > > > > > < > > > > > > > > :

Dh 5 kr2 T 1 Q Dt Ts 1 Ts 1

h , hs

h 2 hs ðTl 2Ts Þ hs # h # hl hl 2 hs Tl 1

γ5

h 2 hs ρCps

(18.22)

h 2 hl ρCpl

8 1 > > < h 2 hs

(18.23)

hl , h

h , hs

hs # h # hl h l 2 hs > > : 0 hl , h

(18.24)

Under the circumstance of high temperature, the melting point would drop significantly owing to the eutectic reaction. Some basic study concerning the mechanism of eutectic

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452

18. Moving Particle Semi-implicit method

melting were carried out by Mustari et al. [47,48]. Moreover, the fuel melting behavior due to eutectic reaction was studied by Li et al. [49]. The MPS method was adopted to model the dissolution of uranium dioxide by molten zircaloy at high temperatures, which is an important chemical process during severe accident. As a consequence of fuel melting, core debris would relocate and accumulate on lower core support structures and in the lower plenum of RPV. During this relocating process, an unneglectable phenomenon is that the core debris may interact with the lower head structures, such as the instrument tubes. Under the thermal attack of the high-temperature molten debris, the instrument tube inside the RPV may melt and open a path, through which the core melt could drain out of the RPV. The melt freezing behavior in an instrument tube is considered as a key factor. To address this problem, the penetration and solidification behavior of the molten core debris in simulated instrument tubes was studied by MPS [50,51]. Another important phenomenon that should be considered is the molten pool in the lower plenum of RPV, formed with the quenched debris as well as the intact fuel pellets melts. The pool may separate into several immiscible layers. These layers would influence the distribution of decay heat and heat transfer in the lower plenum and consequently determines the failure mode of vessel wall and penetrations of the lower head. Mechanism study of melting, stratification, and solidification behaviors were performed by MPS without relying on empirical correlations [52,53].

18.3.6 Corium spreading and molten core concrete interaction Once the RPV fails, the corium may be released onto the reactor containment floor. The subsequent corium behavior is known as corium spreading, which has been extensively studied for evaluating the long-term corium management (coolability, which depends on the corium thickness) and in some cases, potential failure of the reactor containment boundary. The corium spreading is also the key in designing core catchers of some advanced LWRs. For example, in European pressurized reactor, the corium is premixed with sacrificial concrete firstly to reduce its viscosity, before being discharged to a large area, where the mixture is spread to ensure sufficient cooling [54]. However, the corium spreading is quite complicated since it involves the interactions of thermal hydraulics, property change (e.g. viscosity), and phase change (crust formation and remelting). Due to the convenience of tracking interfaces by the moving particles, the MPS method has been employed to investigate this phenomenon by several researchers. The FARO-L26S core melt solidification experiment was analyzed by Kawahara and Oka [55]. The thermal equation, solid
liquid phase transition, and temperature dependent viscosity model are incorporated into the MPS method. In order to further investigate the crust-formation process, the corium spreading experiment VULCANO VE-U7 was studied by Yasumura et al. [56] and Duan et al. [57]. The crust formation process was modeled by viscosity escalation. In their study, it was found that the original MPS algorithm was not suitable for predicting termination of spreading by escalation of viscosity, because of numerical creeping that occurred in the correction step of the algorithm, when particle velocities were recalculated based on the pressure term. To address this problem, a novel algorithm, in which the viscosity term is calculated after pressure term, was proposed by Duan et al. [57].

VI. Noval CFD methods

18.3 Application to nuclear engineering

FIGURE 18.11

453 Sketch for the VULCANO VE-U7

experiment [57].

FIGURE 18.12 Spreading front positions between MPS calculation and experiment [57]. MPS, Moving particle semi-implicit method.

The configuration of VULCANO VE-U7 experiment is shown in Fig. 18.11 [57]. Hightemperature melt was introduced into the stabilization pool firstly. Then the melt began to spread into the concrete and ceramic channels. Solidification took place gradually, due to the heat loss at free surface and the substrates. Finally, crust formation near the front terminated the spreading. As illustrated in Fig. 18.12, the MPS with modified algorithm successfully predicted termination of the spreading. The qualitative distribution comparisons of solid fraction and temperature can be found in Fig. 18.13. A blunt spreading front and the adhesion of solidified melt to sidewall, as observed in the experiment, were quite well reproduced. Sharp increase of viscosity based on the MPS framework can effectively represent the crust formation (phase change) and terminate the spreading. As a long-term interaction of corium with the structural concrete, the so-called MCCI would potentially result in containment failure by melt through of the concrete basemat. MCCI may also contribute to overpressurization of the containment, as steam and other gases are released by the concrete decomposition. Extensive researches have been conducted to explore this phenomenon since it would have large impact on the release of fission production to the environment [58
62]. Similar to the corium spreading, this phenomenology involves various complex physical and chemical phenomena, which couple with multiphase heat transfer among corium, concrete or decomposition gases; phase change due to crust formation; chemical reactions; and so on. The MPS method has been applied to study these phenomena by taking its advantage in easily and accurately capturing interfaces [63
67]. Li and Yamaji [64,66] studied

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18. Moving Particle Semi-implicit method

FIGURE 18.13 Distributions of simulated solid fraction and temperature in VULCANO VE-U7 experiment [57].

FIGURE 18.14 Final cavity shapes of MPS result and VULCANO VB-U7 experiment [66]. MPS, Moving particle semi-implicit method.

potential mechanisms, which led to anisotropic and isotropic ablation of the different concretes in the CCI-2, CCI-3, and VULCANO VB-U7 experiments by focusing on melt/crust interactions. The effect of gas generation and the silica aggregates were also investigated. Fig. 18.14 presents the final cavity shape of calculation result for VULCANO VB-U7 experiment [66]. A half-cylindrical cavity full of corium was placed in a rectangular concrete block. The initial size of the cavity was 300 mm in diameter and 250 mm high while the

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18.3 Application to nuclear engineering

455 FIGURE 18.15 Final cavity shape of MPS result of CCI-3 experiment [67]. MPS, Moving particle semi-implicit method.

concrete block measured 600 mm 3 300 mm 3 400 mm. The cavity ablation profile and the overall axial and lateral ablation rates agreed well with the experimental measures. Silica aggregates were separately modeled in Case 1 while aggregates were neglected in Case 2. Results showed that thermally stable aggregates, which have a higher thermal conductivity, may be responsible for more stable basemat crust formation and lead to anisotropic ablation with more pronounced lateral ablation. Chai et al. [65,67] also investigated the CCI-2 and CCI-3 experiments based on the MPS method. In their study, the anisotropic ablation mechanism was discussed with chemical reaction model, mass diffusion model, buoyancy model and gas generation model. The effects of gas generation can be found clearly in Fig. 18.15. The simulated final cavity shape with gas generation model agreed with the CCI-3 experiment [68]. The results suggested that one possible reason for the anisotropic ablation profile observed is the gas release near the sidewall. The superficial gas would enhance the interface heat transfer. The lateral ablation may have been accelerated by the gas and heat generation induced by the superficial gas along the sidewall.

18.3.7 Flooding accident The Fukushima nuclear accident raises the importance of flooding study in nuclear reactor buildings. The flooding could cause the failure of the safety-related electrical equipment. What is worse, some floatable bodies, such as broken doors, emergency powers, or even parked vehicles, would worsen the effects of flooding by blocking the flow pass or increasing the water level. It is reported that some emergency powers, which were designed for the core cooling systems, were washed away by the flooding in the Fukushima accident. Losing the power for core cooling, the consequence was that several of the reactors underwent fuel melting, hydrogen explosions, and radioactive releases. Currently, the flooding analyses in the nuclear power plant are mainly based on 1-D approach, which is computationally very efficient. However, the accuracy is seriously limited due to the assumptions made on both fluid dynamics and geometries. For example, a key parameter concerned is the accurate estimation of the time until water reaches the critical components, such as electrical equipment. This is the available time for identifying and isolating the flooding source, which directly impacts the calculation in probabilistic risk assessments (PRAs). Hence, to achieve a more reliable assessment with less uncertainty, accurate and reliable 3D simulation of flood propagation is necessary. This is helpful for reducing conservatism and better decision-making.

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18. Moving Particle Semi-implicit method

The explicit moving particle simulation (EMPS) method has been adopted to study the flooding accident in nuclear plant buildings [69,70]. Different from the semi-implicit one, the pressure field is calculated explicitly by assuming weak compressibility in EMPS method. This is because, in a compressible fluid, the pressure wave propagates along with the speed of sound c, which satisfies the following equation: c2 5

dP dρ

(18.25)

Assuming that the background pressure is zero and the particle number density is proportional to the density, Eq. (18.24) can be rewritten as:  ρ  Pi 5 c2 00 ni 2 n0 (18.26) n Since the pressure in each time step is calculated explicitly, computational cost could be remarkably reduced [71]. Dam break flow over an isolated block based on EMPS was simulated by Wang et al. [69]. A tank with 3.22 m long and 1.0 m wide was used. Right part of the tank is 0.55 m depth water with a rectangular block of 0.40 m 3 0.16 m 3 0.16 m placed in the left part. Snapshots of water behavior, depicted in Fig. 18.16, agreed well with the experimental results [72]. Large deformation and propagation of water waves were quite well simulated. In an advanced nuclear power plant, the passive cooling systems are widely adopted to enhance plant safety. However, the failure of storage tanks, which provides the injection sources

FIGURE 18.16

Dam break over an isolated obstacle [69].

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18.3 Application to nuclear engineering

FIGURE 18.17

457 Floating bodies trans-

port in AP1000 [70].

for passive core cooling system, might also result in internal flooding. Fig. 18.17 shows a simulated internal flooding accident in AP1000 by hypothetically assuming a rupture of IRWST (in-containment refueling water storage tank). Three large bodies, which could be broken doors or other debris, were hypothetically assumed to be located in the reactor coolant system compartment. The water leaked from the IRWST firstly splashed onto the steam generator and the pumps, which were located in the steam generator subcompartment. With the increasing of water level, water overflowed to the reactor vessel cavity through the space around the hot leg and cold leg pipes. Subsequently, water reached the floating bodies and pushed them dropping to the steam generator subcompartment. After that, these three bodies were transported by the

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18. Moving Particle Semi-implicit method

water wave. During this flooding process, the bodies would strike the pumps, which may cause some safety problems. Such kind of problems could be analyzed by the EMPS method [70]. Another realistic flooding accident in PWRs could be caused by LOCA. During this accident, one concern is that thermal insulation would be stripped off and some broken and fragmented debris would be washed down by the discharged coolant. This would cause sump clogging when the scattered debris transported with the coolant on the containment floor. To study this strainer clogging accident, detailed analysis of the debris transport after large-break LOCA in a full-scale PWR containment vessel was carried out by Ui et al. using MPS [73].

18.4 Conclusion In this chapter, the fundamental of the MPS method is explained and its applications to nuclear engineering are presented. Three child methods of MPS, namely, MPS-MAFL, MMPS, and EMPS, are introduced as well. It has been demonstrated that the MPS method has robust and stable capability to deal with complex thermal-hydraulic problems and perform safety analyses in nuclear engineering. Although the applications mentioned above are mainly about the LWRs, some safety problems in sodium-cooled fast reactors have been studied by MPS as well [74
77]. In addition, the application of MPS is now spreading to other fields, including engine engineering [78] and biomechanics [79]. Detailed description can be found in the references [80,81]. Considering the current status, further enhancements of the MPS method are expected in the future, particularly in the following aspects: high order spatial and temporal discretization schemes which guarantee the convergence of simulations, stable and accurate discretization method for free surface, advanced treatment for solid wall boundary with complex geometry, improved solidification model to deal with crust fracture and complicated fluid
solid interaction, novel models for liquid
gas phase change, validated turbulence models for flow and heat transfer, new methods to reduce the computational cost, and improved interface treatment method for general multiphase flow.

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VI. Noval CFD methods

C H A P T E R

19 Lattice Boltzmann method code Shimpei Saito1 and Hui Cheng2 1

Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan 2Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai, P.R. China

19.1 Introduction In the nuclear engineering field, it is important to fully understand the molten fuel
coolant interaction (FCI) during a severe accident when designing nuclear reactor safety. As a result, the dispersion and cooling of liquid metal in water has been extensively investigated in the literature [1
5], going all the way back to Taylor’s classic experiment with mercury and water [6]. In these experiments, high-temperature melt and water are often used to simulate the core melt materials and coolant. Matsuo et al. [4,7] injected molten alloy with a melting point of 78 C (U-Alloy78) into a water pool, using high-speed visualization to help understand the mechanism behind melt jet breakup in water. The complexity of the FCI phenomena due to the strong thermodynamic and hydrodynamic coupling means that it is difficult to understand all the mechanisms simultaneously. Investigating the hydrodynamic interactions separately will thus help us to better understand the fundamental melt jet breakup processes. In addition, the heat transfer coefficient (HTC) between a high-temperature melt fragment and liquid plays a key role in modeling high-temperature melt
coolant interactions [8
13]. After the melt jets have dispersed, the melt fragments would settle in the coolant with phase change. In that case, accurate estimation of phase-change heat transfer between dispersed fragments and surrounding coolant is of great importance. Since a pioneering work of Nukiyama [14], boiling phenomena have been investigated via theoretical, experimental, and numerical works [15]. Due to the important role in investigating the heat transfer characteristics and mechanism of boiling, numerical simulations of boiling phenomena have been carried out since the late 1990s. In these Navier
Stokes
based simulations, level-set [16], front-tracking [17], and volume-of-fluid methods [18] are often used to

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00019-X

463

Copyright © 2021 Elsevier Ltd. All rights reserved.

464

19. Lattice Boltzmann method code

FIGURE 19.1 Fluid flow properties revealed at different scales by different simulation methods.

track the liquid
vapor interfaces. Since then, a lot of numerical studies have been conducted to investigate boiling phenomena (see review papers [19
22] for detail). However, most of them assume an initial vapor phase, that is, those methods cannot simulate nucleation in boiling. In this chapter, we focus on applications of lattice Boltzmann (LB) method (LBM) to two important severe accident phenomena during FCI: melt jet breakup and boiling twophase flow. The relations of the scale properties in fluid flow simulations are schematically illustrated in Fig. 19.1. Compared with other macroscopic CFD methods based on the Navier
Stokes equations, the LBM, which is constructed using mesoscopic kinetic equations, has several advantages. For instance, it is easy to incorporate mesoscale physics, such as interfacial breakup or coalescence, and easy to program and parallelize. Moreover, the computational cost for simulating realistic fluid flows is reasonable when compared with microscopic particle
based methods (e.g., molecular dynamics). For more details of this chapter, see Refs. [23
25].

19.2 Lattice Boltzmann multiphase models The LB models for two-phase or multiphase systems can be classified into four categories: • • • •

color-gradient model [26,27] pseudopotential model [28,29] free-energy model [30,31] mean-field model [32]

This classification may not be exhaustive, for instance, the latter two models are sometimes identified as phase-field models [33] since the Cahn
Hilliard or similar interface tracking equations can be derived from them. The abovementioned LB models can be identified as single-component (e.g., water/steam two-phase flow system) and twocomponent (e.g., air/water or oil/water two-phase flow systems) models. For details about the multiphase LB models, interested readers can refer to the comprehensive review papers [33
38] and references therein.

19.2.1 Color-gradient model and its application to jet breakup The color-gradient model possesses many strengths in simulations of multiphase/multicomponent flows, including strict mass conservation for each fluid and flexibility in

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19.2 Lattice Boltzmann multiphase models

465

adjusting the interfacial tension [39]. A static drop test is no longer needed to determine the interfacial tension; it can be directly obtained without any analysis or assumption. Moreover, the color-gradient model shows a very small dissolution property for tiny droplets or bubbles [36]. Color-gradient models, which are often referred to as R-K models, were first developed by Gunstensen et al. [27] who extended the two-component lattice gas automata model of Rothman and Keller [40]. Later, Grunau et al. [26] enabled the introduction of density and viscosity ratios by modifying the forms of the distribution functions. Latva-Kokko and Rothman [41] replaced Gunstensen’s maximization-recoloring step with a formulaic segregation algorithm. Instead of widening the interface width, Latva-Kokko and Rothman’s recoloring algorithm solves some issues with the previous color gradient
type model, namely, the lattice-pinning problem and the spurious velocities. Reis and Phillips [42] extended the model to a two-dimensional nine-velocity (D2Q9) lattice. They modified the perturbation operator to recover the Navier
Stokes equations correctly. The so-called Bhatnagar-Gross-Krook (BGK) [43] approximation refers to this simplest form of the collision operator, which forces all populations to relax toward an equilibrium state at the same rate. Despite its simplicity and phenomenal popularity, the BGK LB method is known to suffer from numerical instability under high-Re (low-viscosity) conditions. One way to overcome this issue is to modify the collision operator [44]. For example, multiple relaxation time (MRT) collision operators [45
47] have been widely used, even for multiphase flows, to enhance numerical stability and accuracy and reduce spurious currents near the interface. Later, Geier et al. [48] proposed a new collision operator based on the relaxation of central moments (CMs), which can be obtained by shifting the lattice directions according to the local fluid velocities. Many researchers have developed this approach to fully exploit the properties of CM-based schemes (see, e.g., De Rosis [49] and references therein). We introduce the CMs into color-gradient LBM to enhance numerical stability at extremely high Reynolds numbers. Now, let us present a three-dimensional color-gradient LB model and apply it to hydrodynamic simulations of melt jet breakup. The distribution functions move on a three-dimensional 27-velocity (D3Q27) lattice [50]. We adopt a lattice speed c 5 δx =δt 5 1, where
 δx and  δt are the lattice spacing and time step, respectively. The lattice velocities ci 5 jcix i;
ciy ; jciz i are defined as follows: ?
jcix i 5 ½0; 1; 21; 0; 0; 0; 0; 1; 21; 1; 21; 0; 0; 0; 0; 1; 21; 1; 21; 1; 21; 1; 21; 1; 21; 21; 1 ?;
ciy 5 ½0; 0; 0; 1; 21; 0; 0; 1; 21; 21; 1; 1; 21; 1; 21; 0; 0; 0; 0; 1; 21; 1; 21; 21; 1; 1; 21 ; jciz i 5 ½0; 0; 0; 0; 0; 1; 21; 0; 0; 0; 0; 1; 21; 21; 1; 1; 21; 21; 1; 1; 21; 21; 1; 1; 21; 1; 21? ; (19.1)

where ið 5 0; 1; . . . ; 26Þ represents the lattice-velocity directions and the superscript “?” is the transpose operator. Here, we employ Dirac’s bracket notation, where the “bra” operator h j denotes a row vector along one of the lattice-velocity directions and the “ket” operator j i denotes a column vector. The model represents two immiscible fluids as red and blue. Distribution functions fik represent the fluids k, where k 5 r and b denote “red” and “blue,” respectively, and i is the lattice-velocity direction. The total distribution function is defined as fi 5 fir 1 fib , and the evolution is expressed by the following LB equation: (19.2) fik ðx 1 ci ; t 1 1Þ 2 fik ðx; tÞ 5 Ωki ðx; tÞ;

 

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19. Lattice Boltzmann method code





where x 5 x; y; z and t are the position and time, respectively. The collision operator Ωki is made up of three suboperators [51]:  ð3Þ  ð1Þ  ð2Þ Ωki 1 Ωki Ωki 5 Ωki ; (19.3) where ðΩki Þð1Þ , ðΩki Þð2Þ , and ðΩki Þð3Þ are the single-phase collision, perturbation, and recoloring operators, respectively. We employ the general MRT (GMRT) framework [52,53] to describe the single-phase collision operator with nonorthogonal CMs, due to the simplicity of its relationship to the MRT and SRT collision operators. It should be noted that Fei et al. [53] propose a simplified version of De Rosis’ nonorthogonal CMs [49,54], showing a significantly reduced computational cost. In the GMRT framework the single-phase collision operator can be written as follows:
ð1 Þ 




ðΩÞ 5 2 M21 N21 KNM
f 2
f e 1 jFi;

(19.4)

where M, N, and K are the transformation, shift [52,53,55], and relaxation matrices, respectively. P k The P density of the fluid k is given by ρk 5 i fi . The P total fluid density is given by ρ 5 k ρk , and the total momentum is defined as ρu 5 i fi ci 1 F=2, where F is the body force. Note that the local velocity has been modified to incorporate the spatially varying body force [56]. To model the single-phase collision operator (Eq. 19.4), we use the nonorthogonal CMs proposed by De Rosis [49]. The transformation matrix M, the components of which are constant, transforms the distribution functions into raw moments. The shift matrix N, a lower triangular matrix with components given by the macroscopic velocity u, transforms the raw moments into CMs. The practical forms of M, M21 , N, and N21 are given in Ref. [24]. The relaxation matrix K is a diagonal matrix given by the following equation: 

s0 ; s1 ; s1 ; s1 ; s2ν ; s2ν ; s2ν ; s2ν ; s2ν ; s2b ; s3 ; s3 ; s3 ; s3 ; s3 ; s3 ; s3 ; K 5 diag ; s4 ; s4 ; s4 ; s4 ; s4 ; s4 ; s5 ; s5 ; s5 ; s5



(19.5)



5 si 5 5 s6 , the where the elements are the moments’ relaxation frequencies. If s0 5 model reduces to the BGK (single-relaxation-time) model. The subscripts represent the orders (e.g., 2 means second order). The parameters s2ν and s2b satisfy the following relations:

1 1 1 2 ; 3 s2ν 2

2 1 1 ζ5 2 ; 9 s2b 2

ν5

(19.6) (19.7)

where ν and ζ are the kinematic and bulk viscosities, respectively. Here, we use s0 5 s1 5 0 and s2b 5 s3 5 s4 5 s5 5 s6 5 1.

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19.2 Lattice Boltzmann multiphase models

For the single-phase collision operator, we use the following enhanced equilibrium distribution function [57] in three dimensions [23]:    9 3 9 9 (19.8) fie ðρ; uÞ 5 ρ ϕi 1 wi 3ðci uÞ 1 ðci uÞ2 2 u2 1 ðci uÞ3 2 ðci uÞu2 1 Φi ; 2 2 2 2









If Φi 5 0, Eq. (19.8) reduces to the standard form of an equilibrium distribution function up to third order. Using Eq. (19.8) improves the Galilean invariance of the variable density and viscosity ratios under the assumption of a small pressure gradient [57]. The weights, wi , are those of a standard D3Q27 lattice [58]. In addition, for a D3Q27 lattice, we can derive the following equations: 8
α; jci j2 5 0; > > <
2ð1 2 αÞ=19; jci j2 5 1; (19.9) ϕi 5
ð1 2 α Þ=38; jci j2 5 2; > > :
2 ð1 2 αÞ=152; jci j 5 3; and

8 2 3 ν
ðu rρÞ; > > < 1 16
νðG:ci  ci Þ; Φi 5 > 1 4
νðG:ci  ci Þ; > : 1 1
νðG:ci  ci Þ;



jci j2 5 0; jci j2 5 1; jci j2 5 2; jci j2 5 3;

(19.10)

where  is the tensor product, “:” represents tensor contraction, and
ν is the kinematic viscosity, which interpolates between the red and blue viscosities ν r and ν b via the following harmonic mean [59
61]: 1
ν

5

11φ 1 12φ 1 1 ; 2 νr 2 νb

(19.11)

where φ is the order parameter that distinguishes the two components in the multicomponent flow, defined as follows [39]:

 ðρr =ρ0r Þ 2 ðρb =ρ0b Þ

; φ5 (19.12) ðρr =ρ0r Þ 1 ðρb =ρ0b Þ where the superscript “0” indicates the initial density value at the beginning of the simulation. The order parameter value φ 5 1, 21, and 0 correspond to a purely red fluid, a purely blue fluid, and the interface between the two, respectively [51]. In the D3Q27 lattice framework the tensor G in Eq. (19.10) is defined as follows: G5

 1  u  rρ 1 ðu  rρÞ? ; 48

(19.13)

As established in Ref. [26], in order to obtain a stable interface, we must take the fluid density ratio γ into account, which is defined as follows: γ5

ρ0r 1 2 αb 5 ; 0 1 2 αr ρb

VI. Noval CFD methods

(19.14)

468

19. Lattice Boltzmann method code

The fluid pressures are given by an isothermal equation of state for the D3Q27 lattice: p 5 ρðcs Þ2 5 ρ


9ð1 2 α Þ ; 19

(19.15)


where α interpolates between αr and αb as follows [61]:


α5

11φ 12φ αr 1 αb ; 2 2

(19.16)

pffiffiffi We set αb 5 8=27, for which cbs 5 1= 3 [62,63]. The term jFi in Eq. (19.4) is a discrete forcing term that accounts for the body force F. In the GMRT framework [52], it is as follows:


0 1 21 21 jFi 5 M N I 2 K NM
F ; (19.17) 2
0 0 0 0  where I is the unit matrix, jFi 5 ðF0 ; F1 ; . . . ; F26 Þ? , and
F 5 F0 ; F1 ; . . . ; F26 ? is given by the following equation:
0
F 5 wi ½3ðci 2 uÞ 1 9ðci uÞci  F; (19.18)





Eqs. (19.16) and (19.17) reduce to the MRT forcing scheme [64] when we use N 5 I, and to Guo et al.’s original forcing scheme [56] when we use a single-relaxation time (not necessarily required that N 5 M 5 I). To model the interfacial tension, we use the generalized perturbation operator derived in Ref. [65] based on the idea of continuum surface force (CSF) [66] and follow [42] to obtain the interfacial tension as follows: " # 2

ð c rφ Þ i ð2Þ ðΩi Þ 5 A
rφ
wi

2 2 Bi ; (19.19)
rφ




Eq. (19.19) takes the correct form for an interfacial tension force in the Navier
Stokes equations when the lattice-specific variables Bi are chosen correctly. We have derived the following Bi values for the D3Q27 lattice framework: 8 2 10=27; jci j2 5 0; > > < 1 2=27; jci j2 5 1; (19.20) Bi 5 1 1=54; jci j2 5 2; > > : 2 1 1=216; jci j 5 3; In this model the interfacial tension can be given directly by the following equation: 4 σ 5 Aτ; 9

(19.21)

where τ is the relaxation time, and we have assumed that A 5 Ar 5 Ab . The parameter A controls the interfacial tension strength σ: Although the perturbation operator ðΩki Þð2Þ

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469

19.2 Lattice Boltzmann multiphase models

generates the interfacial tension, it does not guarantee the two fluids are immiscible. To promote phase segregation and maintain the interface, we apply the following recoloring operators [41,67,68]:

r  ð3 Þ ρ r ρρ 5 fi 1 β r 2 b cosθi fie ðρ; 0Þ; (19.22) Ωi ρ ρ  ð3Þ ρ ρρ Ωbi 5 b fi 2 β r 2 b cosθi fie ðρ; 0Þ; (19.23) ρ ρ where θi is the is the angle between rφ and ci defined by the following equation: cosθi 5



ci rφ

; jci j
rφ


(19.24)

Here, we set the parameter β 5 0:7 to reproduce the correct interfacial behavior with as narrow an interface as possible [65,67,69]. For the current model, we can derive the following continuity and Navier
Stokes equations via Chapman
Enskog analysis [56,65,70]:



where



@t ρ 1 r ðρuÞ 5 0;



(19.25)



@t ρu 1 r ðρuuÞ 5 2 rp 1 r Π 1 r S 1 F;

(19.26)



  2ν ? ðr uÞ; Π 5 ρν ru 1 ðruÞ 1 ρ ζ 2 D

(19.27)



is the viscous stress tensor, with D 5 3 in the three dimensions; the shear viscosity ν is given by Eq. (19.6) and the bulk viscosity ζ is given by Eq. (19.7). In Eq. (19.26) the r S term arises from the perturbation operator given by Eq. (19.19) and, according to the CSF idea, is equivalent to the interfacial force [65]. The capillary stress tensor S is given by the following equation: X X   ð2 Þ S 5 2 τδt Ωki ci ci ; (19.28)



i

k

The solutions of the present model with CMs [71] are consistent with the Navier
Stokes equations to second order in diffusive scaling [72,73] with the body [56] and interfacial [65] forces. Using the model described earlier, we then show liquid jet simulations. Fig. 19.2 illustrates the computational setup for our hydrodynamic melt jet breakup simulations. Initially, the computational domain consists entirely of blue particle distribution functions fib with zero velocity. The boundaries consist of an inflow boundary, wall boundaries, and an outflow boundary. 2 is a circular inflow boundary at the top of the domain, within 2 There ðx2xc Þ2 1 y2yc , Dj0 =2 , where ðxc ; yc Þ represents the center of the x
y plane. Here, the velocity uj0 is uniform, with corresponding equilibrium functions, and there are no artificial disturbances at this boundary. Wall boundaries cover the rest of the top and sides of the domain, with free-slip [50] boundary conditions. At the outflow boundary, we imposed a convective boundary condition [74].

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19. Lattice Boltzmann method code

FIGURE 19.2 Boundary conditions for the melt jet breakup simulations: (A) the boundaries consist of an inflow boundary, wall boundaries, and an outflow boundary, and (B) there is a circular inflow boundary of diameter Dj0 at the top, where the velocity uj0 is uniform.

First application of this model is the experiments of Ref. [7]. An alloy called U-Alloy78 (Osaka Asahi Co., Ltd.), with a melting point of 78 C, was injected into a stagnant water pool under atmospheric pressure. In this case, we discretized the computational domain into an 8Dj0 3 8Dj0 3 40Dj0 lattice with Dj0 5 30, resulting in a total of 240 3 240 3 1200 5 69; 120; 000 grid points being used in the simulation. We set the inlet velocity uj0 to 0.05, the jet density ρj 5 ρ0r to 1, and the coolant density ρc 5 ρ0b to 1=γ, where γ equals 8.34. Fig. 19.3 shows comparisons of the experimental results with the simulation. The simulations were numerically stable, even for very low kinematic viscosities of Oð1025 Þ. The simulation results reproduce the qualitative interfacial behavior well, that is, many fragments are generated as the jets penetrate each other, both around the leading edge and the side regions. For this case the details of the generated fragments and the flow field are shown in Fig. 19.4. We can find that the liquid jet column has large velocity, while the generated fragments have small velocity. In the snapshot at upstream region (Fig. 19.4B), the fragments generate from the unstable jet-coolant interface. Most of the fragments in this region are stretched, which appear not to be spherical shapes. The velocity magnitude of stretched fragments is large, while that of spherical ones is small. In the snapshot at downstream region (Fig. 19.4C), most of the fragments are spherical shapes with low velocity magnitude.

19.2.2 Pseudopotential model and its application to boiling In recent years, several kinds of LB methods for multiphase flows have been applied to simulate liquid
vapor phase transitions. Among the LB models the pseudopotential model and the phase-field model are widely used [33]. In most of the phase-field LB models, an interface tracking equation is solved to capture the liquid
vapor interface and a source term is incorporated into the continuity equation or the Cahn
Hilliard equation to define the phase transition. This implies that the rate of the liquid
vapor phase transition is an artificial input. The pseudopotential LB method [38] becomes most widely used for simulating multiphase flows. The most distinct feature of the method is that the phase

VI. Noval CFD methods

19.2 Lattice Boltzmann multiphase models

471 FIGURE 19.3 Comparison of jet breakup behavior for Dj0 5 20 mm, for the (A) experiment and (B) simulation.

separation is achieved via an interparticle potential. In the case considering temperature change, the liquid
vapor phase transition is driven by the equation of state. Hence no artificial phase-change terms need to be added to the temperature equation [33]. Here, we apply the pseudopotential LBM
based numerical simulations of a series of boiling phenomena, including nucleation, growth, coalescence, and departure of vapor bubbles. The target density ratio is set to be 1000. To keep numerical stability under such severe condition, we use the cascaded pseudopotential LB model of Lycett-Brown and Luo [75] to simulate fluid flow. The temperature equation is solved by a finite-difference scheme, instead of a thermal LB equation, to avoid the numerical error expected to appear in high-density ratio [76]. The distribution functions move
 on a two-dimensional 9-velocity (D2Q9) lattice [50].  The lattice velocities ci 5 jcix i;
ciy are defined as follows. ?
jcixi 5 ½0; 1; 21; 0; 0; 1; 21; 21; 1 ?;
ciy 5 ½0; 0; 0; 1; 21; 21; 1; 1; 21 ;

VI. Noval CFD methods

(19.29)

472

19. Lattice Boltzmann method code

FIGURE 19.4 (A) Snapshot of detailed interface structure for Dj0 5 20 mm. The color bar indicates the velocity magnitude normalized by the inlet velocity. (B) Magnified snapshot for upstream region. (C) Magnified snapshot for downstream region.

The LB equation with a general forcing term Fi can be written as in the following equation: f i ðx 1 ci ; t 1 1Þ 5 f i ðx; t Þ 1 F i ;

(19.30)

where fi is the postcollision distribution function. For the cascaded collision operator, particle distribution functions are expressed in terms of velocity moments of the distribution functions, with different relaxation rates associated with different moments. As in Ref. [52], the cascaded collision operator can be written in general form as follows:   fi ðx; tÞ 5 fi ðx; t 2 M21 N21 KNMðjfi i 2 jfie i ; (19.31) where K is the relaxation matrix, M is the transformation matrix, N is the shift matrix, and fie is the equilibrium distribution function. The form of Fi depends on the forcing scheme, for example, the exact-difference method [77] and Guo et al.’s method [56]. Here, we use the forcing scheme for cascaded pseudopotential LB model developed by Lycett-Brown and Luo [75,78]:  



ci ci 2 c2s I :Θ ðci 2 uÞ F ðci uÞðci FÞ ðci FÞ2 F F 2 2 Fi 5 ωi 1 1γ ; (19.32) 1 2τc4s c2s c4s 2cs ρ 2c4s ρ









VI. Noval CFD methods



19.2 Lattice Boltzmann multiphase models

473

where F is the external force vector expressed by the following equation: F 5 Fm 1 Fg ;

(19.33)

where Fm is the interparticle interaction force, and Fg is the gravitational force. The pseudopotential LB model requires a nonideal equation of state pEOS as described in Ref. [76]. Here, the Carnahan
Starling equation of state is adopted, which is given by the following equation [79]:

2

3 1 1 bρ=4 1 bρ=4 2 bρ=4 pEOS 5 ρRT 2 aρ2 ; (19.34)

3 12bρ=4 where a 5 0:4963R2 Tc2 =pc and b 5 0:18727RTc =pc . In the simulations, we set a 5 1=4, b 5 1, and R 5 a. In this LB model the thermodynamic consistency can be well approximated; it is able to accurately reproduce the wide range of coexistence curves [75]. Our LB model describes the following macroscopic equations: @t ρ 1 r ðρuÞ 5 0; (19.35)









@t ðρuÞ 1 r ðρuuÞ 5 2 r P 1 r Π 1 F; where P is the pressure tensor, and Π is the viscous stress tensor. For a temperature field, we used the following macroscopic equation:  ρcv ð@t T 1 u rTÞ 5 r ðλrT 1 φ;





(19.36)

(19.37)

where cv is the specific heat at constant volume, T is the temperature, λ is the thermal conductivity, and φ is the source term to trigger phase change. This equation can be derived from the local entropy balance defined in the diffuse interface modeling [80]:  ρTð@t s 1 u rsÞ 5 r ðλrT ; (19.38)





and the thermodynamic relationship [81]



@pEOS Tds 5 cv dT 1 T dv; @T ρ

(19.39)

One can derive the source term φ in Eq. (19.37) through Eqs. (19.38) and (19.39), which is derived as the following equation:

@pEOS φ5T r u; (19.40) @T ρ



To solve Eq. (19.40), we use the finite-difference method. The fourth-order Runge
Kutta scheme is adopted here. The coupling between the pseudopotential LB model and the finitedifference scheme is established via a nonideal equation of state given by Eq. (19.34). For the spatial discretization the isotropic central schemes (e.g., Ref. [82]) are employed to evaluate first-order derivative and the Laplacian. The computational domain for the pool boiling system is shown in Fig. 19.5. We set the two-dimensional x
y plane with W 3 H 5 600 3 150. The domain is initially filled with

VI. Noval CFD methods

474

19. Lattice Boltzmann method code

FIGURE 19.5 computational boiling.

Schematic of the domain for pool

liquid phase with the two-phase coexistence temperature Tb 5 0:485Tc . At this temperature the corresponding densities for liquid and vapor are evaluated as ρl B0:4616 and ρv 5 0:0004616 through the Maxwell construction. By choosing such temperature the ratio of coexistence densities is evaluated as ρl =ρv B1000. Periodic boundary conditions are imposed on the left and right sides of the computational domain. Outflow boundary is specified as the top boundary, in which we employ the simple Neumann boundary conditions for density distribution function and macroscopic temperature. At the bottom boundary the nonslip condition is applied as the solid wall condition. The bottom wall is a heating surface with a constant wall temperature Tw . The wall superheat is defined as ΔT 5 Tw 2 Tb , which is changed by tuning the wall temperature Tw . Gravitational accelera tion g 5 0; 2 g is acting on the whole computational domain. As in Ref. [76,83], small temperature fluctuations are added to the equation of state in the first grid point layer near the bottom wall to enhance bubble formation. Fig. 19.6 shows the evolution of density distribution at ΔT 5 0:0439. In each figure the interface is defined as the location of ðρl 1 ρv Þ=2. As seen in Fig. 19.6B, the low-density fluid region is generated along with the high-temperature wall, although the domain is filled only with the liquid phase in the initial state (Fig. 19.6A). The low-density fluid corresponds to vapor. When neighboring vapor bubbles approach, they coalesce with each other as shown in Fig. 19.6B. Owing to the heating surface, the vapor bubbles continue to grow after coalescence (Fig. 19.6C). Finally, the vapor bubbles grown enough depart from the bottom wall by buoyancy. From a series of processes, we can identify that the present boiling regime corresponds to the nucleate boiling. It is considered to be the first time of successful simulation of a series of pool boiling process at the density ratio of 1000 by using the pseudopotential LB approach. In addition, from the simulation results, the local heat flux can be calculated, which is  defined as qloc 5 2 λ @T=@y y50 . The average heat flux q can also be calculated by averaging qloc over time. For four cases of wall superheat, the evaluated heat flux is plotted on Fig. 19.7 with the typical snapshots of the boiling regime. Between ΔT 5 0:0439 and 0:0675, the heat flux q increases and bubble behavior seems to be nucleate boiling. It can be seen that the maximum heat flux (critical heat flux) is around 8:0 3 1026 in lattice unit. At more than ΔT 5 0:0769, the heat flux decreases. From the snapshot, we can see that the area

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475

19.2 Lattice Boltzmann multiphase models

FIGURE 19.6 Boiling process, including nucleation, coalescence, growth, and departure of vapor bubbles.

FIGURE 19.7 Boiling curve with typical snapshots.

covered with the vapor phase increases. The behavior of heat flux and vapor bubbles implies that this regime corresponds to the transition boiling. As a result, we can successfully simulate a part of boiling curve. Although the film-boiling regime is an important regime that should be simulated, from the result in this paper, we consider to obtain a prospect that the boiling curve with the density ratio of 1000 can be reproduced using our numerical method.

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19. Lattice Boltzmann method code

19.3 Summary In this chapter, we described the outline of multiphase LBM and its application to two thermal-hydraulic phenomena: melt jet breakup and boiling. Our original color-gradient and pseudopotential models were employed for these simulations. We showed that central moment
based LBM greatly enhanced numerical stability for multiphase flows with the high Reynolds number or high-density ratio. In addition to central moment
based approach, there are several ways to model collision term in the LBM, for example, tworelaxation time, regularized, cumulant, and entropic ones. These collision models have been recently reviewed and analyzed by Corexias et al. [84]. The trade-off between numerical stability (and/or accuracy) and cost (and/or simplicity) should be considered when the reader adopts the LBM, depending on the target phenomena.

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C H A P T E R

20 Code for nuclear materials Jianqi Xi Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI, United States

Neutron irradiation can induce significant changes in the physical and mechanical properties of nuclear materials in reactors. These changes result from the interaction of energetic particles with atoms in the materials. For instance, neutron irradiation initiates collision cascades, which produce point defects in materials. These point defects migrate, react, nucleate, and grow, and eventually induce the microstructural and microchemical evolutions in irradiated materials, which change the material properties. To account for all the important material properties and reactor phenomena, it is necessary to develop and utilize multiscale models and simulations to address a wide range of space and timescales, starting with the nucleus, electronic, and atomic structure (angstrom) all the way to the reactor components (meters), and from defect formation (femtoseconds) to the operating characteristic times (months, years). Fig. 20.1 illustrates the hierarchical multiscale modeling methodology, which integrates quantum mechanical modeling, molecular dynamics (MD) simulations, kinetic Monte Carlo (KMC), mean field rate theory/cluster dynamics modeling, to model the fates of defects and predict the microstructural evolutions in materials under neutron irradiation. The detailed microstructural information obtained from abovementioned methods can be used as a basis to study the mechanical behavior through meso- and continuum-scale models. In this chapter, we will briefly introduce these methods and the corresponding codes in the study of radiation in materials.

20.1 Electronic structure calculations in nuclear materials Density functional theory (DFT) is a computational quantum mechanical modeling method to study the electronic structure of materials. It solves the Schrodinger-like equation, in the Kohn
Sham scheme, for the electron densities of noninteracting electrons and

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00020-6

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FIGURE 20.1 Multiscale theoretical and computational methods used in the field of nuclear materials.

the additional exchange
correlation functional for the correction for electron
electron interactions to get the eigenvalue of ground state energy, εi , as follows [1]: " # ð  0 n r 2 h¯ 2 2 δEXC ½n 0 2 dr 1 r 1 Vext ðrÞ 1 e (20.1) φi ðrÞ 5 εi φi ðrÞ δnðrÞ 2me jr 2 r0 j where the first term in the left-hand side is the kinetic energy of electrons. Vext ðrÞ is the nuclear
electron interaction, which is regarded as an external potential on the basis of Born
Oppenheimer approximation [2]. nðrÞ is the electron charge density, which can be simply described as a sum of the individual electronic densities of the Kohn
Sham eigen 2 Ð nð r 0 Þ 0 P  wave functions, φi ðrÞ, as nðrÞ 5 ni51 φi ðrÞ . e2 jr 2 r0 j dr is the electron
electron Coulomb repulsion. The last term, EXC ½n, is the exchange interaction and dynamic correlation functional. To solve previous equation, the variational principle is used, as shown in Fig. 20.2. Using this approach, the properties of materials can be determined as a functional of electron density. DFT models have been providing unique information about the structure of defects produced under irradiation and about the nature of defects without involving experimental input parameters [3
5]. DFT models show up to be as quantitatively accurate and informative as the most advanced experimental techniques developed for the observation of radiation damage phenomena. They have effectively created a new paradigm for the scientific investigation and assessment of radiation damage effects, offering new insight into the response of materials to irradiation. Although DFT is an electronic ground state method, thereby it cannot directly suitable for simulation of the nonequilibrium radiation effects, it has been widely used related to radiation effects in many ways. DFT calculations are the standard method for

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FIGURE 20.2 Illustration of iterative solution for solving the Kohn
Sham equations based on the variational principle.

studying the properties of point defects and small defect clusters, regardless of how defects are produced: form thermally through the migration of atoms to surfaces or grain boundaries, or form under irradiation, in which an atom is displaced from a lattice site. In either case of DFT calculation a vacancy defect is formed by removing an atom from a lattice site in a supercell and by relaxing the resulting atomic structure. The formation energy of a vacancy in a charge state of q is calculated by using the following equation [6]:       Ef vacancy; q 5 ET vacancy; q 2 ET perfect 1 μ 1 qðεF 1 EVBM Þ

(20.2)

where ET ðvacancy; qÞ is the total energy of a supercell with one vacancy in a charge state q, and ET ðperfectÞ is the total energy of a perfect supercell in the neutral state. μ is the atomic chemical potential. εF is the Fermi level measured from the valence band maximum (VBM), which changes within the band gap, Eg. For ceramic materials, like UO2 fuel and SiC cladding, radiation-induced defects can have different charge states, thereby, it is necessary to consider the defect behavior [6
8] quantitative multiscale treatment of radiation damage, for example, the defect structure, defect formation, and binding energies [3
5,9]. Besides that, ab initio MD (AIMD) simulations within the framework of DFT calculations have so far been demonstrated to be a preferable tool to study the low-energy recoil events in materials (see Fig. 20.3 in aluminum nitride), which can thoroughly describe the dynamic displacement processes, defect configurations at the end of the collision cascades, and the threshold displacement energy in materials [10
12]. The interatomic potential in AIMD is based on electronic structure calculations instead of empirical fitting and thus can predict atomic dynamics with ab initio accuracy, as well as the effect of partial charge transfer in the recoil processes. Most DFT calculations of defect structures performed so far were carried out by using well-documented DFT programs, namely CASTEP (see Ref. [13] and

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FIGURE 20.3 Charge-density contours in the plane containing both an interstitial and a vacancy during the N½1 1 ~ 2 0 recoil event at 44 eV [8]: (A) t 5 0 fs, (B) t 5 20 fs, (C) t 5 300 fs, and (D) t 5 600 fs.

http://www.castep.org/), VASP (see Ref. [14] and http://www.vasp.at/), SIESTA (see Ref. [15] and http://icma.cat/leem/siesta/), QUANTUM ESPRESSO (see Ref. [16] and https://www.quantum-espresso.org), and ABINIT (see Ref. [17] and http:// www.abinit.org/).

20.2 Molecular dynamics simulations in nuclear materials MD simulation is one approach to simulate the motion of atoms in molecules or solids [18
20]. Generally, MD simulations have atomistic length and timescales, which reveal material changes that happen too fast and too small for experimental observations. Therefore these simulations provide information that can not only complement experimental observations but also reveal important events for longer time- and length-scale modeling methods. The crucial physics input to the method is the forces acting between atoms. These can be obtained from an analytical interatomic potential. This is different from the AIMD simulations, in which the forces are obtained from the quantum mechanical calculation method. In the simulations the trajectory of every individual atom in the system is described on the basis of Newton’s second law of motion. For a system of N particles the Newton equations to solve for each particle i are as follows: mi a~i 5

N X j51;j6¼i

~5 2 F

N X @Vi u~ij @rij j51;j6¼i

(20.3)

~ is the forces that interact with particle i, ~ where a~i 5 @v~i =@t 5 @2 ~ ri ri =@t is the acceleration, F is the position vector, v~i is the velocity vector, mi is the mass of particle, Vi is the potential energy with respect to position for particle i, and u~ij is a unit vector in the direction of i-j. The basic MD algorithm can be described as in Fig. 20.4.

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20.2 Molecular dynamics simulations in nuclear materials

FIGURE 20.4

Molecular dynamics basic

algorithm.

For a given system the forces acting on each atom are obtained by deriving equations, the force fields, where potential energy is deduced from the atomic positions [19]. After obtaining the forces the Newton’s equations of motion mentioned previously can be solved through the time integration numerical algorithms [18
21]. Here we show the most commonly used time integration algorithm, the so-called velocity Verlet algorithm [18
21] as an example: aðtÞ 5 2

1 rV ðrðtÞÞ m

  1 1 aðtÞΔt2 1 rðtÞΔt3 1 O Δt4 2 3! 1  rðtÞ 1 vðtÞΔt 1 aðtÞΔt2 2

(20.4)

rðt 1 ΔtÞ 5 rðtÞ 1 vðtÞΔt 1

  1 1 v t 1 Δt 5 vðtÞ 1 aðtÞΔt 2 2 1 rV ðrðt 1 ΔtÞÞ m   1 1 vðt 1 ΔtÞ 5 v t 1 Δt 1 aðt 1 ΔtÞΔt 2 2 aðt 1 ΔtÞ 5 2

(20.5)

(20.6) (20.7) (20.8)

Given an initial configuration of the N-particle system with boundary conditions and integration method, the previous equations can be calculated, and the position and velocity of each particle can be updated. MD simulation was initially developed to simulate vibrations in diatomic molecules, and its widest usage area is in molecular and biophysics. In 1960 it was first time used to simulate collision sequences in copper and found the effect of “recoil collision sequences,” which demonstrated the production of interstitials and vacancies in the collision (see Ref. [22]). Since then, MD simulations have been widely employed in the study of nuclear materials to provide insights into the underlying physics for primary damage processes

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(within some tens of picoseconds) [23,24]. For example, de la Rubia et al. have performed the collision cascades via MD simulations to study the radiation effects in metallic materials and first time showed the thermal spike in atomic level, which comprises the underdense core and overdense shell [25]. In the thermal spike region the temperature is in the order of 10,000K, which causes a large number of atoms displace from their original lattice sites. However due to the large thermal conductivity of metallic system, the cooling down of the thermal spike can be considered a very rapid recrystallization process of the hot liquid, which lasts for a few picoseconds. Since a recrystallization process tends to produce perfect crystal, it is natural that most of the displaced atoms generated in the thermal spike will eventually go back to the lattice sites. After that, some defects (like interstitials and vacancies) could survive in materials and evolve by defect reaction and migration and finally will be in charge of the microstructural evolution of nuclear materials [23,24]. The timescale of the defect production and evolution has been schematically shown in Fig. 20.5. Besides metals, numerous studies have been performed on cascade damage in

FIGURE 20.5

(A
D) Schematic illustration of defect production and evolution [23].

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ceramics [26
29]. It is generally reported that compared with radiation behavior in metals, the radiation response in ceramics is more complicated: some ceramic materials even become partial or fully amorphous in the collision cascades, especially at low irradiation temperature conditions [26,27,29], which have been attributed to the open crystal structure and the much slower recrystallization [29]. In addition to the radiation effects in bulk materials, MD simulations have also been used to study the irradiation of nanostructured materials [30
32]. Extensive reviews of radiation effects in nanostructured materials are available in Refs. [33
35], and we refer the reader interested in more details on irradiation of nanostructured materials to these. For a long time the radiation effects MD simulations were carried out with a wide range of different codes that were developed with different groups, and currently, the dominant MD simulation code is LAMMPS (https://lammps.sandia.gov), which is originally developed at Sandia National Laboratories [36].

20.3 Mesoscale modeling in nuclear materials field Although the DFT and MD approaches as already discussed have provided a wealth of information about energetic recoil cascades, point defect formation, migration, and even reactions, these methods are mainly focused on the study of radiation-induced defect in the length of atomic scale and the time is no longer than nanosecond scale. In reality, materials subject to irradiation often undergo instantaneous microstructural changes, which over the longer timescales (years) and length scales (microns) can induce changes to physical and mechanical properties, potentially compromising reactor and component performance on an engineering scale, as shown in Fig. 20.5D. In this part, we will introduce the mesoscale methods, including the KMC, rate theory, and its extended cluster dynamics models, to study the microstructural and microchemical evolution as a consequence of the evolution of defects produced in energetic recoil events. Besides that, the mesoscale and macroscale models, such as phase-field model and finite element methods, have also been extensive used in the nuclear field and many reviews of are available in Refs. [24,37,38], and we refer the reader to these.

20.3.1 Kinetic Monte Carlo Conceptually, the KMC method is one Monte Carlo method to simulate the time evolution of some processes with known rates, provided the subsequent transitions are not correlated with each other and are Poisson processes [37,39]. As all possible transitions and rates are known in the processes, then the KMC algorithm will randomly select one transition to happen with the selection probability, which is proportional to the transition rate. The time is then advanced after each transition with the simple equation: t 5 t 2 lnu=R, where u is a random number between 0 and 1, and R is the sum over all rates. Therefore once the transition rates are correctly given and the transitions are independent Poisson processes, the KMC algorithm will exactly simulate the real stochastic time evolution.

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Currently, there are at least two categories of KMC method based on how the objects are moving or reactions occurring: one is called the lattice KMC (LKMC, also called atomistic KMC), which is carried out on an atomic lattice [40
42], and one typical example is the simulation of vacancy diffusion in materials, where a vacancy is allowed to jump around the lattice with rates that depend on the local elemental composition [40]. Another one is the “object” KMC (OKMC), which is used to simulate “objects” that are assumed to move in a “background” of perfect crystal, that is, only the positions of the jumping objects are included in the simulation, not those of the “background” lattice atoms [43
45]. Since developed, OKMC has being a common tool for studying materials subject to irradiation [43
46]. This is not only because OKMC method depends inversely on the event jump rates, which can be used to study the long-time evolution, but also because radiation-induced defect evolution typically fulfills the OKMC precondition of being uncorrelated Poisson processes [43]. For example, OKMC has been used in the study of migration and bubble formation of He in tungsten (W) [46], which provided insights into the mechanism of He bubble formation in W and discussed the time and temperature dependence of bubble formation under He irradiation. In recent years the application of LKMC in radiation damage evolution has been very important to study the ordering reactions in alloys under irradiation [41,47]. For example, Clouet and Soisson used LKMC to study the Cu precipitations in FeCu alloys under irradiation [47]. However, in both methods, the major weakness is that all possible jumps and reactions between defects have to be known in advance and coded or parameterized into the KMC. For each specific system the possible jump events would be unique, this is one of the reasons that there are no commonly used KMC codes (like VASP for DFT and LAMMPS for MD).

20.3.2 Mean field rate theory and cluster dynamics Mean field rate theory has been developed in 1970s; since then, this method has becoming one of the most important computational tools to study the radiation damage evolution in materials [48
53]. Unlike the KMC model, mean field rate theory is a continuum model and therefore does not consider the motion of individual species in the materials as done by KMC model. Instead, the evolution of the concentration of each species is computed as a function of time and position. In mean field rate theory the defect evolution, such as selfinterstitial (SIA), I, and vacancy, V, is described through the evolution of defect concentrations, which is predicted by using the point defect balance equations as follows: dCI 5 gI 2 kI;V CI CV 2 DI k2I CI dt

(20.9)

dCV 5 gV 2 kI;V CI CV 2 DV k2V CV dt

(20.10)

where CI and CV are the concentration of SIA and vacancy, respectively. gI and gV are the rates of in-cascade generation of interstitial and vacancy, respectively. kI;V is a recombination rate constant. k2I and k2V are the strength of defect sinks, such as grain boundaries, cavities, dislocations, and precipitates, for the removal of SIA and vacancy, respectively. It is

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noted that mean field rate theory model only takes into account the evolution of radiationinduced point defect by defect recombination and absorption at defect sinks [38,48]. However, defects produced under neutron irradiation are normally complex, as shown in Fig. 20.6, including defect clusters, dislocation loops, and voids, which cannot be described by the mean field rate theory model. In order to more accurately describe the defect production, mobility, and clustering under irradiation, the cluster dynamics method has been developed on the basis of the mean field rate theory. Unlike the mean field rate theory model, the cluster dynamics framework is a set of mean fields coupled reaction
diffusion equations for defect production, migration, annihilation, and aggregation into defect clusters, dislocations, voids, and bubbles. Since developed, such model has been successfully applied to describe the radiation damage evolution in nuclear materials [54
57], such as the noble gas bubble evolution in tungsten [54,55], black spot formation in silicon carbide [56], and radiation-enhanced precipitation in steels [57]. Here we should note that, similar to the KMC model, up to now, we still do not have widely used cluster dynamics code. But in order to understand the concept of this model, we will briefly introduce the fundamental knowledge of cluster dynamics model. Alike to the point defect balance equations, the equation to describe the evolution of a cluster n can be written as follows:   dCn ~ 2 Dn k2 Cn 5 gn 2 r Jn 1 Rn C n dt



(20.11)

FIGURE 20.6 Schematic representation of radiation-induced defects in materials. Atoms displaced from their lattice sites form an interstitial
vacancy pair, that is, a Frenkel pair. These point defects migrate to form interstitial clusters, dislocation loops, and voids. They can also segregate to grain boundaries. Fission products, helium, can be attracted to vacancy clusters and form helium bubbles.

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FIGURE 20.7 Schematic illustration of defect cluster reactions during the recoil events.



where gn is the production of cluster n during the recoil events, and 2r Jn is the diffusion of cluster n, which depends on the concentration of gradient of the cluster n itself. k2n is the strength of defect sinks to absorb cluster n. Unlike the point defect balance equations in the mean field rate theory, the defect recombination is replaced with a more complex ~ which in principle can include interactions with any other cluster in reaction term, Rn ðCÞ, the system (see in Fig. 20.7). For a given cluster n,   ~ 5 k1 Cn21 1 k2 Cn11 2 k1 Cn 2 k2 Cn (20.12) Rn C n21 n11 n n where k is the reaction rate constant for the adsorption or emission reactions.

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21 Nuclear power plant cybersecurity Fan Zhang Department of Nuclear Engineering, The University of Tennessee, Knoxville, TN, United States

21.1 Introduction Instrumentation and control (I&C) systems serve as the “nervous system” of the nuclear power plants (NPPs) in the following aspects: provides operators with critical information of plant operation; enables operators to control the plant systems; protects the reactor core automatically during potential accidents [1]. I&C systems in most current fleets are analog while most NPPs under construction or in the design stages deploy the digital I&C systems. United States Nuclear Regulatory Commission (US NRC) has listed several advantages of the digital I&C system: (1) it can improve control and increase the operational efficiency; (2) it can improve the diagnostics of automatic plant protection systems; (3) it is expected to improve the safety. Therefore, as NPPs age, existing utilities are looking toward replacing the analog I&C systems with digital I&C systems as well. However, with all the benefits the digitalization brings, it also introduces new security challenges that are not part of the consideration of old analog systems as the increasing number of cyberattacks toward industry. Several cyber incidences have happened in the nuclear sector even before full digitalization. Due to the potentially very serious consequences of an accident, nuclear power is different from other industries. Safety objectives include controlling reactivity, maintaining core cooling, and protecting the integrity of the pressure barrier. A cyberattack that compromises any one of these three objectives could lead to severe consequences. Even in the absence of core damage or a radiological release, cyberattacks on NPPs could lead to economic consequences and loss of public trust, either of which would challenge continued operation. The cyber-threats include both insider threats and outsider threats. The insider threats are intentional or unintentional misuse or attack from current or former employees, contractors, vendors, or other business partners with a given access to the assets such as network, system, or data. Outsider threats include an individual or a group of individuals external to the organization who are not authorized with access to its assets but seeks to

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gain the assess and may cause misuse, for example, a disgruntled employee who wants to revenge the company. The outsiders could range from an individual hacker with idle curiosity to advanced persistent attackers and sophisticated nation states. Generally, almost all the cyberattacks contain two stages: reconnaissance and man-in-the-middle (MITM) [2]. Reconnaissance is the first phase of all the attacks in which the attackers find out the necessary information to access the network, such as the types of traffic that firewall lets through, hosts’ information in the network. MITM is the attack where the attacker secretly relays the communication, while eavesdropping between two parties without their awareness, that is, two parties believe that they are communicating with each other directly. In MITM the attacker is able to obtain the traffic between these two parties and to alter the packets in communication. Intrusion prevention systems (IPSs) prevent unauthorized access to the system, while intrusion detection systems (IDSs) detect unauthorized access to the system. Therefore IPSs are deployed as the first layer to prevent the reconnaissance and IDSs as the second layer to detect intrusion and cyberattack. There are different research conducted for intrusion prevention and detection to enhance the cybersecurity. Usually, IDSs are categorized into three types according to the detection mechanism: signature-based IDSs, anomaly-based IDSs, and hybrid IDSs. Signature-based IDSs detect known attacks by matching the predefined patterns. Therefore they are effective in detecting known attacks with low false alarm rates (FARs) since the similar patterns have been modeled but are unable to detect unknown attacks with patterns not in the database. In contrast, anomaly-based IDSs detect anomaly or potential attacks by modeling the system’s normal behavior and detecting deviations from normal behavior. They are customized to each system by modeling the normal behavior and are able to detect both known and unknown attacks, including zero-day attacks, since these behaviors are deviated from normal behavior. However, anomaly-based IDSs have a high false-positive (FP) rate due to their nature [3]. Hybrid IDSs combine the signature-based and the anomaly-based detection with high accuracy of signature-based methods for known attacks and the generalization capabilities of anomaly-based methods. This chapter is organized as follows: Section 21.2 states the differences of cybersecurity between I&C system and information technology (IT) system; Section 21.3 looks back the cyber-incidents in the history of the nuclear industry to demonstrate the needs of enhancing of cybersecurity; Section 21.4 summarizes cybersecurity regulations related to the nuclear industry, with an emphasis on International Atomic Energy Agency (IAEA) guidance, to introduce the cybersecurity perspectives from regulators’ standpoint; Section 21.5 summarizes some cybersecurity research using machine-learning algorithms that could be applied to NPPs; and Section 21.6 gives the conclusion.

21.2 Cybersecurity differences of instrumentation and control system and information technology system I&C systems are one type of industrial control systems (ICSs). Although the cybersecurity research in the IT domain is a mature one, adopting these cybersecurity approaches directly is not feasible for ICSs due to the large differences between ICSs and IT systems. First of all, IT systems prioritize confidentiality as the first security objectives and then followed by

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TABLE 21.1 Major characteristic difference between information technology (IT) and industrial control system (ICS) cybersecurity consideration. Characteristic

IT

ICS

Primary priority

Confidentiality

Availability [4]

Communication time

Delays tolerated

Time critical

Bandwidth

High

Limited

Patching and software update

Frequent and in time

Rare and slow or impossible [5]

Communication protocols

TCP/IP, UDP

DNP3, Modbus, Fieldbus, PROFINET, S7, OPC UA

Security standards

ISO-17799, NIST SP800-53

ISA99, NIST SP800, and specific standards for different industries

Cyber forensics

Available

Not deployed or limited

Penetration testing

Yes

No for field devices, may be for HMI

System life cycle

3 5 years

Usually more than 15 years

Physical components

COTS mostly

Small portion of COTS, more custom built or industry-qualified [5]

Data types

Cyber data

Cyber data and process data

Compromise consequence

Business impacts: finance and reputation

Business impacts, equipment damage, environmental destruction, and personnel safety

COTS, Commercially available off-the-shelf; HMI, human machine interface; DNP3, distributed network protocol 3; UDP, user datagram protocol.

integrity and availability, while ICSs prioritize availability first, followed by integrity and confidentiality [4]. The difference in objectives priority results in different strategies for cybersecurity in IT and ICSs. For example, to ensure the availability in ICSs, port scanning tools, and encryption techniques, which are commonly used in IT domain, may not be appropriate. This is because most ICSs have low bandwidth which IT techniques tend to occupy, so that they may impact system the availability and could lead to unintended component denial-of-service (DoS) [5]. Other major differences between IT and operational technology are summarized in Table 21.1; interested readers can find details with examples in Refs. [5,6]. With these differences between ICSs and IT systems, dedicated research is necessary to meet the unique requirements of ICS cybersecurity. This dissertation facilitates this issue from both overall and local cybersecurity strategy development.

21.3 Cyber-incidents in the history of the nuclear industry As digital systems are being considered as a replacement or enhancement of existing infrastructure in NPPs, there will likely be an increasing number of opportunities for

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attackers to directly or indirectly affecting these systems, which will have to be found and dealt with quickly in order to maintain public confidence in the nuclear industry. It is interesting to note that, although nuclear is likely one of the most security-conscious fields in existence, there have already been several cyber-incidents that have affected even analog I&C systems. The following is a brief overview of some documented cybersecurity events that have occurred at NPPs; it is not meant to be a complete overview and of course does not detail events that are yet to be documented or reported. In 2003 the Slammer work infected the Davis Besse NPP; this worm caused the safety parameter display system (SPDS) to be inaccessible to operators for 4 hours and 50 minutes [7]. In this cyber-incident the worm first traveled onto the corporate network via a tunnel behind the corporate firewall which had been created between a consultant’s office network and the corporate network. Ideally, the corporate firewall would have prevented infection from programs such as the Slammer worm; however, this tunnel bypassed that firewall and allowed the worm to enter into the network unobstructed. At this time, there was no firewall between the corporate network and the process control network, so the worm was then able to move onto the process control network and subsequently infect the SPDS. While the plant had been offline since 2002 and so suffered no direct physical consequences, this incident shows that even with established firewalls in an NPP which protect from the outside world, the NPP may still establish a connection to the Internet without knowledge of the appropriate personnel. In 2006 the Browns Ferry NPP Unit 3 was shut down manually after the DoS of the variable frequency drives (VFDs) and programable logic controllers (PLCs) [8]. The VFDs in this case drove circulation pumps, while the PLC served as a condensate demineralized controller, both of which have embedded microprocessors that enable the use of a mechanism known as Ethernet broadcasting to communicate data over Ethernet. This mechanism allows devices to communicate in an all-to-all manner, where a broadcasting device will send packets to all devices on a network and a receiving device will scan all packets received and determine which packets are meant for itself. In this specific incident the VFDs and PLCs were flooded with packets from the connected network and so were not able to perform the functions necessary to cool the reactor. While this incident was not directly caused by a cyberattack, it shows a possible scenario by which an entity could attack an NPP. In such a scenario the attacker might deploy a Slammer worm similar to that used in the Davis Besse incident to initiate a DoS attack on critical components such as the VFDs controlling recirculation pumps, while simultaneously using the worm to interfere with the SPDS in order to mask the attack. In 2008 Hatch NPP Unit 2 experienced an automatic reactor trip due to seven PLCcontrolled condensate demineralizer outlet valves closing at almost the same time, resulting in a temporary loss of feedwater [9]. The root cause was an engineer testing a software update for the plant’s chemistry data acquisition system server, which was on the corporate network and was utilized to collect data from process control network. However, unknown to the engineer, the synchronization program in the update automatically synchronized data on both process control network and corporate network. When the engineer rebooted the computer, the value zero was synchronized and sent to the PLCs controlling the demineralizer outlet valves. The PLC interpreted this as a command to switch to manual control with input of zero flow demand, which resulted in a temporary

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499

loss of feedwater. The safety system acted appropriately and, upon receiving a low water level signal, automatically scrammed the reactor. Although this was also not an intended cyber-event, it could potentially have been done maliciously by attackers, with the entry point being a computer update in the corporate network. In 2010 the Stuxnet attacked Iranian nuclear enrichment centrifuges and destroyed 984 of them [10]. This malware was brought into the facility on a USB flash drive initially and then exploited several zero-day vulnerabilities. It was specifically tailored to find hosts with Siemens software and injects its malicious code, then the code manipulates the Siemens PLCs, causing them to speed up and then slow down the centrifuges that incurred significant wear on the devices. Meanwhile, the malware masked the attack from operators by sending normal behavior data to sensor outputs. Stuxnet proved that a sophisticated cyberattack both does not require an Internet connection and that abnormal behavior indicative of an ongoing cyberattack can be hidden through the use of false data injection techniques. These indicate, ultimately, that the so-called air gap commonly employed in NPP and other secure facilities may not be enough for a determined and resourceful attacker. In 2014 one computer in the control room at Monju NPP was discovered to have been compromised and was shown to have been accessed over 30 times in the previous 5 days due to a malware attack [11]. It was believed that the malware introduced by a free application update was initiated by an employee on one of the computers in the corporate network. Then this compromised computer sent some data to a foreign command and control server. A similar incident occurred in 2016, when two malware programs—Conficker and W.32Ramnit— were discovered on several computers at Gundremmingen NPP in Germany [12]. The “air gap” is a network segregation measure used to secure vulnerable networks (such as a control network) by isolating them physically from unsecure networks (such as the Internet). All the nuclear facilities mentioned previously had implemented firewalls between the Internet and their corporate networks, and an “air gap” between their corporate network and their control network. These cyber-incidents indicate that firewalls and network segregation measures are not sufficient for defending critical facilities from cyberattacks for several reasons. First, firewalls alone may not be sufficient to ensure absolute network segregation, as was the case with the Davis Besse incident. Second, even for cases where the network architecture is such that a network is completely isolated from the outside world, systems that support removable media within the network may still provide an accessible entry point. Lastly, standard intrusion prevention techniques are not resilient to insider attacks and may actively misinform operators if tampered with. Therefore a secure network architecture is one with sufficient network segregation measures which is also coupled with an efficient cyberattack detection system; such a system is crucial for fast detection and response to cyber-threats and is essential for maintaining public confidence in nuclear power in the coming decades.

21.4 Regulations Industry uses cybersecurity standards and guidance to deploy the cybersecurity activities. There are some general industrial standards series such as ISA 99 [13] and NIST SP800 [14] for the overall industrial cybersecurity. This section overviews the standards and guidance

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specific for cybersecurity in the nuclear industry. They are provided by the IAEA and International Electrotechnical Commission (IEC) internationally, and the US NRC and Nuclear Energy Institute (NEI) within the United States. This section first presents a detailed overview of guidance published by IAEA, then summarizes other standards and guidance at a high level since most provided guidance has similar basic instructions for deployment in different levels of detail.

21.4.1 International Atomic Energy Agency guidance IAEA is an international organization that promotes the peaceful use of nuclear energy. In regards to cybersecurity the IAEA assists member states in improving cybersecurity capabilities at state organizations and licensees through guidance development, training courses, information exchange, and coordinated research projects. The cybersecurity guidance of the IAEA is published in the IAEA Nuclear Security Series (NSS). NSS provides international consensus guidance on nuclear security to support member states. There are four sets of publications in NSS: Nuclear Security Fundamentals, Nuclear Security Recommendations, Implementing Guides, and Technical Guidance. Nuclear Security Fundamentals give objectives and principles and are the basis for Nuclear Security Recommendations, which are the applications of fundamentals and provide the general approaches, concepts, and strategies. Implementing Guides state how the recommendations should be applied, and Technical Guidance is the detailed guidance that explains specific implementation and technical subjects. The documents related to cybersecurity are NSS No. 20 (Objective and Essential Elements of a States Nuclear Security Regime) in Nuclear Security Fundamentals [15], NSS No. 13 (Nuclear Security Recommendations on Physical Protection of Nuclear Material and Nuclear Facilities) in Nuclear Security Recommendations [16], NSS No. 23-G (Security of Nuclear Information) in Implementing Guides [17], NSS No. 17 (Computer Security at Nuclear Facilities) [18], and NSS No. 33T (Computer Security of Instrumentation and Control Systems at Nuclear Facilities) [19] in Technical Guidance. IAEA also released three draft guidance, including draft technical guidance NST036 (Computer Security of Instrumentation and Control Systems at Nuclear Facilities) and draft implementing guidance NST045 (Computer Security for Nuclear Security) [20]. Major concepts and requirements from these NSSs are summarized here. NSS No. 20 is the primary publication in the IAEA NSS as a Nuclear Security Fundamental, which applies to nuclear material as well as other radioactive material and their associated facilities and activities. It defines, “the objective of a States nuclear security regime is to protect persons, property, society, and the environment from harmful consequences of a nuclear security event.” It stresses that the cybersecurity is a part of the nuclear security and defines 12 security regimes, including identification and assessment of nuclear security threats, use of risk-informed approaches, and detection of nuclear security events. NSS No. 13, as the recommendation document, gives general strategies to fulfill the requirement in NSS No. 20. For example, risk management, graded approach, and defensein-depth are three strategies that could be applied as risk-based protection systems and measures. In terms of cybersecurity, NSS No. 13 suggests that “computer based systems that are used for physical protection, nuclear safety and nuclear material accountancy and control should be protected from compromise, which includes but is not limited to cyberattack,

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501

manipulation and falsification”; configuration management, access control, and record of access should be deployed for the computer systems and software to ensure the security. “Information” is defined as knowledge regardless of its existence and expression form in NSS No. 23-G. Information security is the security strategies implemented to ensure the confidentiality, integrity, and availability of information. Sensitive digital assets are defined as digital assets that store, control, process, or transmit sensitive information, or that otherwise serve a significant function for the NPP. No. 23-G defines four levels of security, which are unclassified, restricted, confidential, and secret from low security to high. The consequences of each level being compromised are increasing accordingly. If unclassified information is compromised, the facility is not required to deploy additional security measures. Compromise of restricted information would likely affect diplomatic relations adversely, cause distress, and make operation difficult. Compromise of confidential information would likely cause damage to areas including diplomatic relations, operational effectiveness, and security; when this happens, the facility should shut down or otherwise substantially disrupt significant national operations. If secret information is compromised, it would likely cause serious damage, threaten to life directly, and raise international tension. NSS No. 23-G also gives security categorization examples to guide facilities on how to classify different items to the corresponding levels. NSS No. 17 proposed a graded approach to computer security with details about requirements, deploy strategies, and an example of how to apply the graded approach. One implementation is categorizing system into zones and assigning different security levels. Zones are a logical and physical concept for grouping systems with similar protection demands together to make administration easy and effective. Each zone has a security level assigned. Security levels define the security protection degree required, that is, each level requires different sets of protection measures. A security level can have multiple zones assigned to it. An example is given where the generic level measures are applied to all the zones and security levels range from level 5 (level of least protection needed) to level 1 (level of most protection needed). It also points out that the risk assessment process should be fed back into and influence the graded approach. Generic levels contain basic security measures such as security gateways, IPSs, IDSs, and anomaly detection systems in place. Level 1 performs accident prevention functions, where all network data flows from systems in lower security levels are forbidden to enter level 1. Physical access to level 1 systems is strictly controlled and remote maintenance access is forbidden. NSS No. 33T focuses on the protection of I&C system cybersecurity with detailed implementation suggestions. It recommends a risk-informed approach, in which a facility computer security risk management (CSRM) process should be implemented to identify the system I&C vulnerabilities to cyberattack and the consequence of a successful compromise. The results are utilized to assign different security measures to different security levels. Cybersecurity policies should be applied throughout the I&C life cycle activities, including both common elements of all life cycle phases and specific life cycle activities. Common elements include management systems, cybersecurity reviews and audits, configuration management, verification and validation, security assessments, documentation, design basis, access control, protection of the confidentiality of information, security monitoring, overall defensive computer security architecture, and defense-in-depth against compromise. Specific life cycle activities contain predeveloped item selection, design and implementation of I&C systems, integration of I&C systems, system validation, overall installation and commissioning, operations and maintenance, and modification. Detailed requirements and suggestions are given in each

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activity, for example, configuration management requires that the configuration documents for I&C systems computer security measures should be protected from unauthorized access or compromise and should be classified as sensitive information. Only authorized personnel can gain access to this information on a need-to-know basis. NST036 pointed out that cybersecurity considerations should be included in every phase of the digital I&C system life cycle [21]. It provides competent authorities and facilities with guidance on cybersecurity measures for digital I&C systems, including graded approach, security levels, and security zones. It also covers the relationship between cybersecurity and safety. NST045 provides policy makers, competent authorities, operators, and nuclear security professionals with guidance on developing, implementing, and integrating cybersecurity into all aspects of nuclear security. This includes identification of sensitive digital assets, assessment of threats, vulnerabilities and impact arising, graded approach deployment with security levels and zones, risk assessment for defining the cybersecurity requirement, and security qualification of devices and services [20]. It defines the roles and responsibilities of different entities, including vendors, competent authorities, the State, and other relevant entities.

21.4.2 International Electrotechnical Commission standard IEC is an international organization that promotes international cooperation on standards and is a conformity assessment body for all fields of electrotechnology. Developed by Subcommittee 45A (SC45A) of the IEC, the IEC 62645 standard titled Nuclear Power Plants— Instrumentation and Control Systems—Requirements for Security Programmes for Computer-Based Systems published in August 2014 addresses I&C systems in nuclear facilities and is the first IEC document targeting cybersecurity [22]. IEC 62859, titled Nuclear Power Plants— Instrumentation and Control Systems—Requirements for Coordinating Safety and Cybersecurity, published in the end of 2016, is the second document addressing safety and cybersecurity [23]. It aims to provide an actionable framework to coordinate safety and cybersecurity for the design, implementation, and operation of I&C systems, which integrates cybersecurity into safety architecture and system. Comparing between the IEC and IAEA suite, the content contained in IEC 62645 and IEC 65859 is also included in IAEA guidance; the new IEC 63096 focusing specifically on cybersecurity controls’ selection and application from the included security controls catalog, in order to prevent, detect, and react to cyberattacks targeting I&C systems, is under preparation and targeting to be issued in 2019 [24]; cybersecurity controls are not fully covered by IAEA standards currently.

21.4.3 Nuclear Regulatory Commission guidance The US NRC is an independent agency of the US government that develops policies and federal regulations for commercial nuclear power reactors and other uses of nuclear material through licensing, inspection, and enforcement of its requirements, protecting public and environment health and safety. Therefore the NRC actively provides regulations to protect licensed NPPs against cyberattacks. In March 2009 the NRC released Title 10 of the Code of Federal Regulations (10 CFR) 73.54, Protection of Digital Computer and Communication Systems and Networks, which requires NPPs to ensure that digital computer and communication

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FIGURE 21.1 Simplified cybersecurity level architecture in NRC RG 5.71 [26]. NRC, Nuclear Regulatory Commission.

systems and networks related to safety, security, and emergency preparedness (SSEP) functions are protected against cyberattacks, up to and including design basis threats [25]. Regulatory Guide 5.71 (RG 5.71) [26] released in 2010 provides guidance on how to comply with 10 CFR 73.54. It provides a cybersecurity plan template and set of security controls. It requires a site to deploy defense-in-depth strategies to protect critical digital assets (CDAs) and recommends a leveled defensive architecture as shown in Fig. 21.1 [26]. Level 4 is the highest secured level which contains CDAs that are important to safety and security functions, so it must be protected from other lower levels. Data diodes should be deployed to allow one-way data communication from Level 4 to Level 3, from Level 3 to Level 2 as shown in the arrows in Fig. 21.1. In November 2015 NRC released 10 CFR 73.77, “Cybersecurity Event Notifications” [27]. It requires NPPs to record and report cybersecurity events happening at NPPs, including notifying the NRC within 1 hour after discovery of a cyberattack that impacts emergency preparedness (SSEP) functions and related support systems and equipment.

21.4.4 Nuclear Energy Institute guidance The nuclear industry works with the NRC to enhance cybersecurity of NPP. The NPPs in the United States follow NEI guidance to comply their cybersecurity plan with NRC cybersecurity requirements. NEI guidance includes NEI 08 09, “Cybersecurity Plan for Nuclear Power Reactors” [28], NEI 10-09, “Addressing Cybersecurity Controls for Nuclear Power Reactors” [29], NEI 13-10, “Cybersecurity Control Assessments” [30], and NEI 15-09, “Cybersecurity Event Notifications” [31]. NEI 08 09, similar to part of RG 5.71, gives a cybersecurity plan template, including a defensive strategy with a defensive architecture and a catalog of security controls based on NIST SP 800-82 “Guide to Industrial Control System Security” and SP 800-53 “Recommended Security Controls for Federal Information Systems.”

21.5 Cyberattack detection research using machine-learning algorithms Most commercially available off-the-shelf cybersecurity software are usually signaturebased intrusion prevention and detection platforms, which use predetermined rules to perform prevention and detection. Recently, with the development of the artificial intelligence, more and more research adopt machine-learning algorithms to perform cyberattack detection.

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21.5.1 General procedure of building a machine-learning model Before introducing any detailed machine-learning algorithms, the general procedure of building a model is given in the following: 1. Data preprocessing: This may include the removal of features with a large percentage of not-a-number values and near-constant values; these features typically do not convey useful information. 2. Features selection: This usually contains three steps: a. Remove some data features based on the understanding of the context of a certain data set. b. Divide the data into training and testing data and sometimes divide into training, testing, and validation. c. Identify a subset of useful features based on training data, for example, reducing the dimension of the data set based on correlation analysis. 3. Model training: Train a model using the training data. 4. Model testing: Feed the test data into the trained model and get the predicted values. 5. Obtain residuals: Compare the predicted values with the real values of the test data and get the model performance. 6. Model selection: Select the best model for the application based on model performance and the application needs such as accuracy, interpretability, and computing cost. Root mean square error and mean absolute error are commonly utilized to assess the accuracy [32]. 7. Model performance characteristic: Characterize the model performance for validation data. There are four types of detection results: true-positive (TP), FP, true-negative (TN), and false-negative (FN) as shown in Table 21.2. Different researchers use different model performance assessment metrics, which are explained here first before go into the detailed research. 1. Accuracy 5 (TP 1 TN)/(TP 1 TN 1 FP 1 FN). This assesses the classification rates, which measures the proportions of the correct results. The drawback of this assessment is significant when the classes are unbalanced. For example, in a cyberattack detection data set, 98% of the data points are not attacked and only 2% are. When all the data points are classified to be not an attack, this assessment still shows the model has 98% accuracy. Therefore this assessment is not suitable for unbalanced data sets. 2. Precision 5 TP/(TP 1 FP). This assesses the correct, which is the ratio of data points correctly classified as an attack to all the data points classified as attacks. TABLE 21.2 Confusion matrix. Actual class is an attack

Actual class is not an attack.

Predicted class is an attack

TP, correct detection

FP, incorrect detection

Predicted class is not an attack

FN, missed detection

TN, correct normal

FN, False-negative; FP, false-positive; TN, true-negative; TP, true-positive.

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3. Correct detection rate 5 TP/(TP 1 FN). This assesses the detection rate, which is the ratio of data points correctly classified as an attack to all the data points that represent as attacks. 4. Negative predictive value 5 TN/(TN 1 FN). This assesses the ratio of data points that are correctly classified as not an attack to all the data points that represent not attacks. 5. TN rate 5 TN/(TN 1 FP). This assesses the ratio of data points that are correctly classified as not an attack to all the data points that represent not attacks. 6. FAR 5 FP/(TN 1 FP). This assesses the ratio of data points that are incorrectly classified as an attack to all the data points classified as attacks.

21.5.2 Cyberattack detection using cyber data This section briefly explains several machine-learning algorithms for intrusion detection using cyber data, including host system and network traffic data, followed by one or two example research. 21.5.2.1 Artificial neural networks Artificial neural networks (ANNs) are composed of interconnected artificial neurons which give different weight to different inputs. The output of each layer will be the input of the next layer and the layers between the input and output layer of the model are hidden layers. ANNs were first proposed in 1958 and were further developed during the 1970s before becoming popular again in recent years with increasing commercial adoption. Cannady proposed a signature-based IDS using ANNs as a multicategory classifier [33]. The data set used was generated by a RealSecure network monitor, in which 3000 out of 10,000 events were simulated cyberattacks by the Internet Scanner and Satan programs. Nine features were selected after analysis: protocol identifier, source and destination port and address, ICMP type and code, raw data, and its length. An ANN model was trained using the data label of normal and different attack category. The training and testing root mean square error was 0.058 and 0.070, respectively. This supervised classification model using network data was an early milestone when the majority of the IDSs were rule-based. Hodo, et al. trained a supervised multilevel ANN model using internet packet traces to thwart distributed-denial-of-service (DDoS) attacks against a simulated Internet of Things (IoT) network [34]. The data set used in this experiment was traffic captured via a network tap based on a simulated five-node (four nodes as clients and one node as a server) IoT network avoiding modification of the live traffic. The attacker launched a DDoS attack against the server node by sending over 10 million packets. The model gives a result of 99.4% accuracy in classification and shows the effectiveness in detecting various DDoS/ DoS attacks. Chawla et al. proposed an IDS based on recurrent neural networks (RNNs) using sequences of system calls in host data [35]. The data set used to examine the effectiveness of the model is the Australian Defence Force Academy Linux Dataset (ADFA-LD), which consists of 833 normal training sequences, 746 attack sequences, and 4372 validation sequences. The results show a 100% true detection rate and a FAR of 60%.

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21.5.2.2 Bayesian network A Bayesian network is a type of probabilistic graphical model that represents the variables and their conditional dependence using Bayesian inference [36]. Variables are presented as nodes in the network to show their relationships, which requires expert knowledge. Kruegel et al. proposed an event classification based on Bayesian networks to model the intermodel dependencies and aggregate additional data such as model confidence [37]. With the ability of adding additional information, this model has fewer false alarms. The MIT Lincoln Labs 1999 Defense Advanced Research Projects Agency (DARPA) data set [38] was used to evaluate the model. The results show that the approach achieved a TP rate of 100% and a 0.2% FP rate, while the traditional threshold method yields a FP rate of about 0.4% with the same TP rate. 21.5.2.3 Decision trees A decision tree is a tree-like structure that represents classifiers and branches. The internal node represents a test for an attribute; the branch represents the test result; the leaf node represents a classification decision [39]. The decision tree method will be detailed in Chapter 3, Nuclear Engineering Software Quality Assurance. Kruegel et al. replaced the signature detection engine of a well-known open-source tool Snort [40], with decision trees to provide faster detection [41]. Snort uses a single line description of each rule so that it detects misuse by comparing the behavior of its rules. The decision tree chose the most discriminating variable in the rule base to improve the speed. The data set used to evaluate the proposed approach in a data set with 10-day TCP dump files in one 1999 DARPA data set. The results showed an average 40% performance gain over Snort. 21.5.2.4 K-Nearest neighbor KNN (K-nearest neighbor) classification is a simple technique that classifies an object by a majority vote of its neighbors. The object is assigned to the most common class among its k-nearest neighbors. The detail of the KNN method will be given in Chapter 3, Nuclear Engineering Software Quality Assurance. Liao and Vemuri applied a KNN-based model to classify program behavior based on the frequencies of system calls for intrusion detection [42]. Twenty-four attacks within the two-week 1998 DARPA BSM audit data were utilized to examine the effectiveness of the model. The results show a 100% detection rate for the 16 known attacks and a 75% detection rate for 8 novel attacks (6 detected out of 8). 21.5.2.5 Ensemble learning For a given problem, KNN and decision trees search the hypothesis space to determine a hypothesis that makes good predictions. However, identifying a good hypothesis may be nontrivial. In contrast, an ensemble method is able to combine the predictions from multiple machine-learning algorithms together to determine a better hypothesis than the best one alone. Bagging and random forest are two ensemble methods that combine several decision trees which have been applied to intrusion detection in some research [3]. A

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brief introduction of Bagging and random forest method is given here and will be detailed in Chapter 3, Nuclear Engineering Software Quality Assurance. 21.5.2.6 Bagging Bagging reduces the variance of a decision tree by averaging votes when predicting a class. It creates m subsets with n samples per subset from the original data set. These n individual samples are generated from the original data set by uniformly sampling with replacement [43]. Gaikwad and Thool investigated the Bagging method with a partial decision tree (PART) as a base classifier for intrusion detection [44]. The preprocessing used genetic algorithm to choose 15 features out of 41 features from NSL-KDD data set to build the model. Compared to Naive Bayes, PART, C4.5, Bagging with Naive Bayes, Bagging with C4.5, the model based on bagging and PART obtained the highest accuracy of 99.7166% with TP rate of 0.784 and FP rate of 0.172 through cross validation. 21.5.2.7 Random forest Random forest consists of many decision trees based on randomly picked subsets. Random forest yields predictions from all the subtrees, which have less correlation than bagging by constraining only one predictor out of a subset to be used in the split of a tree [45]. The prediction result is determined by majority voting or weighted voting. A single decision tree splits by selecting a single variable, while a random forest splits by selecting multiple variables at each split point. A major advantage of random forest is that if the number of trees increases, the variance of the model decreases with the same bias. However, compared to the decision tree, the disadvantage of the random forest is that it is hard to interpret. Resende and Drummond published a literature survey of the research conducted using random forest-based IDS since 2000 [46]. Zhang et al. [47] proposed a random forest based network IDS for misuse detection. The model was evaluated by the KDD 99 data set and the result shows that the model outperforms most reported unsupervised anomaly detection approach when evaluating by the same data set, which reaches a 65% detection rate with 1% FP rate. The IDS research using machine-learning algorithms mentioned previously based on three relevant public data sets, DARPA, KDD 99 [48], and NSL-KDD, are summarized in Table 21.3. These three public data sets were widely utilized in network-based IDSs development. DARPA TABLE 21.3

Intrusion detection systems using machine-learning algorithms based on public data sets.

Research

Algorithm

Data set

Results

Kruegel et al. [37]

Bayesian network

DARPA

100% true-positive and 0.2% false-positive

Kruegel and Toth [41]

Decision trees

DARPA

40% performance gain over snort

Liao and Vemuri [42]

KNN

DARPA

100% detection rate

Gaikwad and Thool [44]

Bagging

NSL-KDD

78.4% true-positive and 17.2% false-positive

Zhang et al. [47]

Random forest

KDD99

65% detection rate with 1% false-positive rate.

DARPA, Defense Advanced Research Projects Agency.

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is the base data with raw TCP/IP Dump files with 6.2 Gb training data and 3.67 Gb testing data; KDD99 is the set that extracted and processed 41 features from DARPA for machinelearning research with 4,898,431 kb training data and 125,973 kb testing data; and NSL-KDD is a size reduced data set with duplicates removed and has 311,029 kb training data and 22,544 kb testing data. More details of these three data sets can be found in [49].

21.5.3 Cyberattack detection using process data Process data includes sensor data and commands, which is unique in industrial cybersecurity since IT network does not provide this type of data. Process data could reflect the status of the industrial process, which is a feasible and promising approach for cyberattack detection in control system. Goh et al. proposed an unsupervised learning approach based on long short term memory RNN (LSTM-RNN) to detect cyberattack based on process data [50]. RNNs were widely used in temporal sequence prediction. However, it has limitations when training on longterm temporal sequences due to the vanishing gradient problem. LSTM-RNN overcomes this shortcoming by adding memory to the network. In order to detect the small deviation of predicted values from the actual sensor data, the cumulative sum method is then applied to the residuals obtained by LSTM-RNN. The upper and lower control limits are defined by the validation data. The data set used to investigate the effectiveness of this method was collected from a large scale Secure Water Treatment Testbed (SWaT), which is built by the Singapore University of Technology and Design [51]. This testbed consists of six stages to process raw water disputes for cybersecurity research. The SWaT data set was generated from the testbed under 7 days of normal operation and 4 days with cyberattack scenarios. The data related to the first stage process was used in Ref. [50], which contains 10 cyberattacks scenarios. These cyberattacks were simulated by altering the sensor data input to the sub-control systems, including altering single points and multipoints together. The results show that 9 out of 10 attacks can be detected by the proposed approach and can also identify a false sensor. There were three FP alarms that were assumed to be results from previous attacks by the authors; however, these could also be a drawback of the approach. In addition, the approach is not applied to all of the process stages due to a large amount of data. Therefore an algorithm with lower computational cost is needed for faster cyberattack detection. Gawand et al. developed a monitoring approach for detecting cyberattacks based on process data using least square approximation and convex hull approach [52]. A simple fourtank system control model was developed using state equations to serve as a virtual testbed to verify and validate the proposed model. This system contains the two pumps speed as inputs and two water tank levels as output. Two attacks were implemented numerically in this system, and the detection results showed that these two models were effective. Kiss et al. proposed a clustering-based approach using Gaussian mixture model [53]. The Tennessee-Eastman chemical process data was used and three different cyberattacks—replay, Austin time junction, and DoS attack—were simulated by modifying the data to examine the effectiveness of the model. The results showed that the model could detect the simulated attack effectively. Nader et al. investigated two one-class classification algorithms, support vector data description (SVDD) and kernel principal component analysis (KPCA), for cyberattack

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detection [54]. Real data from a SCADA gas pipeline tested and the water treatment plant was used as the training and testing data, in which the abnormal transient was regarded as the cyberattack. The results showed that the KPCA has better detection performance than SVDD for those data. Eggers proposed two intrusion detection models based on PCA and independent component analysis (ICA) with static and moving window to detect simultaneous cyber and physical attacks in NPPs [55]. Eggers acquired real-time normal process data from a data historian of an NPP and modified it to simulate a hypothetical simultaneous attack scenario. In this simulated attack the attacker created a small break loss of coolant accident physically with a simultaneous false data injection attack in which the attacker sent normal data to fool the safety system in order to prevent the reactor shut down. After the data analysis, 29 signals collected under 7 days of 100% power operation were selected to test attack detection, including the reactor coolant system temperature, pressure, flow rate, pressurizer level, reactor building (RB) pressure, RB sump level, makeup tank water level, makeup flow, letdown flow, and radiation monitors [55]. Six hypothetical false data injection attack scenarios were simulated. In each scenario the author modified a 15 minute interval of data of each signal to generate the hypothetical attack. The results show that the PCA and ICA with a moving window approach can detect the attacks successfully. Zhang et al. proposed a multiple-layer cyberattack detection system combining cyber data and process data [56]. The system contains three attack-detection modules by applying machine-learning algorithms. The first defense layer consists of commercial intrusion prevention methods, including firewalls, data diodes, and data gateways, which had been deployed in NPPs already. The second defense layer contains cyberattack detection models using network traffic and host system data, including the supervised classification module 1 and unsupervised module 2. Module 1 detects known cyberattacks with historic patterns. Module 2 detects unknown attacks that are not included in the attack database in module 1 by applying unsupervised data analytics to the network and host system data. However, module 1 and 2 are not effective for cyberattacks without a detectable cyber trace, such as an insider attack. Module 3 monitors process data to detect the effects of cyberattacks by applying unsupervised models to detect small deviations from normal operation. A realtime testbed was built combining a physical flow-loop facility and a control system. Several cyberattacks, including DoS, MITM, and false data injection, were conducted to generate the data set to evaluate this system. The results show that the system is able to detect these cyberattacks effectively. State prediction based cyberattack detection using process model has been researched as well. These techniques predefine a system’s secure states and critical states based on system knowledge and analysis. When a current state matches the critical state database, a cyberattack is detected. Svendsen and Wolthusen built a model to predict future states to detect physical anomalies by using physical process models together with techniques from feedback control theory [57]. Such methods require a detailed analysis and a detailed model of the process which make such methods hard to implement in real application for several reasons: 1. It may be hard to obtain a detailed model, or the model could be complex which requires high computational cost and system engineers.

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2. An industrial process is a dynamic and sophisticated process. Therefore the detailed model of the process usually varies with time. It is difficult to obtain all the transient models. When a new operation state is introduced, the overall model needs to be updated accordingly. 3. This type of model lacks generality since it is based on a specific process model. Therefore the model has low portability. 4. It may fail to detect unknown critical states, such as zero-day attack.

21.5.4 Discussion The lack of available data is a significant issue for both model development and evaluation. Machine-learning models can only learn as much information as the data contains, and it is therefore hard to develop a good model when the data is not sufficient. Moreover, most research related to cyberattacks is not evaluated independently of the research itself and is usually taken in the context of the research being conducted, as there is not a single standard data set that researchers can utilize. The DARPA data set was published in 1999 and was utilized for lots of cybersecurity research at the time; however, it may be outdated due to rapid progress in the IT world, for example, some features shown in the DARPA dataset are no longer available in current networks. There is a need for a universal data set for cyberattacks on industrial systems; it would be beneficial if there was such a data set made universally available for model development and evaluation.

21.6 Conclusion The number of industry-targeted cyberattacks is increasing, together with complexity. Understanding the start-of-the-art for cybersecurity in NPPs is essential for improving the cybersecurity of these facilities. With this in mind, this chapter first identifies the differences existing between IT and ICS cybersecurity concerns; the chapter then looks back the history of cyber-incidents that have occurred in the nuclear industry to illustrate that current cybersecurity strategies may not be sufficient to keep up with progress made in digitalizaiton, as well as the growth of current cyberattacks. By going over relevant government regulations with emphasis on IAEA guidance, this chapter also gives a unique view of cybersecurity from the perspective of regulators. Other than applying the required or recommended measures by regulators, adopting new machine-learning techniques is promising to enhance cybersecurity for industrial concerns. Therefore cyberattack detection research using machine-learning algorithms is reviewed in the end to provide some insights in the cybersecurity research. Industry-targeted cyberattacks are growing in both number and complexity with each passing year. It is intuitive that understanding the current state-of-the-art in the cybersecurity of NPPs is essential for improving the cybersecurity of these facilities. However, a survey of the history of past cyber-incidents reveals that current strategies may not be enough to keep up with both the progress made in digitalization as well as the increasing sophistication and growing attack surfaces that come from this progress. In addition, the

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conscientious cybersecurity expert must take into account not just the direct technical perspective but also those perspectives held by both government bodies and regulators. Machine-learning techniques can be applied as a promising enhancement to cybersecurity efforts for industrial concerns; as a result, an overview of the entire field as it specifically relates to ICSs is necessary in order to do this effectively.

Acknowledgment The author would like to acknowledge the Lloyd’s Register Foundation and the International Joint Research Center for the Safety of Nuclear Energy for partial funding of this research. Lloyd’s Register Foundation helps to protect life and property by supporting engineering-related education, public engagement, and the application of research. The author would like to acknowledge. Oracle Corporation for partial funding of this research.

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[20] IAEA, Computer security for nuclear security-draft Implementing Guide. ,https://www-ns.iaea.org/downloads/security/security-series-drafts/implem-guides/nst045.pdf., 2016. [21] IAEA, Computer Security of Instrumentation and Control Systems at Nuclear Facilities—draft technical guide. ,http://www-ns.iaea.org/downloads/security/security-series-drafts/tech-guidance/nst036.pdf., 2014. [22] IEC, IEC 62645:2014: nuclear power plants—instrumentation and control systems—requirements for security programmes for computer-based systems. ,https://webstore.iec.ch/publication/7311., 2014. [23] IEC, IEC 62859:2016: nuclear power plants—instrumentation and control systems—requirements for coordinating safety and cybersecurity. ,https://webstore.iec.ch/publication/26131., 2016. [24] J. Bochtler, E. Quinn, E. Bajramovic, Development of a New IEC Standard on Cybersecurity Controls for I&C in Nuclear Power Plants—IEC 63096, NPIC & HMIT, 2017. [25] US Nuclear Regulatory Commission, NRC: 10 CFR 73.54: protection of digital computer and communication systems and networks. ,https://www.nrc.gov/reading-rm/doc-collections/cfr/part0/7/3/part0/7/3-0/0/ 54.html., 2009. [26] US Nuclear Regulatory Commission, Regulatory Guide 5.71, Cyber Security Programs for Nuclear Facilities, 2010. [27] US Nuclear Regulatory Commission, NRC: 10 CFR 73.77 cyber security event notifications. ,https://www. nrc.gov/reading-rm/doc-collections/cfr/part073/part073-0077.html., 2015. [28] Nuclear Energy Institute, NEI 08-09 Rev 6 compliance for nuclear facilities. ,https://www.nrc.gov/docs/ ML1011/ML101180437.pdf., 2010. [29] Nuclear Energy Institute, Addressing Cyber Security Controls for Nuclear Power Reactors, 2011. [30] Nuclear Energy Institute, Cyber Security Control Assessments, 2015. [31] Nuclear Energy Institute, Cyber Security Event Notifications, 2016. [32] T. Chai, R.R. Draxler, Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature. Geoscientific Model Development 7 (3) (2014) 1247 1250. [33] J. Cannady, Artificial neural networks for misuse detection, in: Proceedings of the National Information Systems Security Conference, vol. 26, Baltimore, MD, 1998. [34] E. Hodo et al., Threat analysis of IoT networks using artificial neural network intrusion detection system, in: Proceedings of the 2016 International Symposium on Networks, Computers and Communications (ISNCC), IEEE, 2016, pp. 1 6. [35] A. Chawla, B. Lee, S. Fallon, P. Jacob, Host based intrusion detection system with combined CNN/RNN model, in: Proceedings of Second International Workshop on AI in Security, 2018. [36] F.V. Jensen, et al., An Introduction to Bayesian Networks, vol. 210, UCL Press, London, 1996. [37] C. Kruegel, D. Mutz, W. Robertson, F. Valeur, Bayesian event classification for intrusion detection, in: Proceedings OFACSAC 2003, Las Vegas, NV, 2003, p. 14. [38] J. Mchugh, Testing intrusion detection systems: a critique of the 1998 and 1999 DARPA intrusion detection system evaluations as performed by Lincoln laboratory, ACM Trans. Inf. Syst. Secur. (TISSEC) 3 (4) (2000) 262. [39] J.R. Quinlan, Induction of decision trees, Mach. Learn. 1 (1) (1986) 81. [40] B. Caswell, J. Beale, Snort 2.1 Intrusion Detection, Elsevier, 2004. [41] C. Kruegel, T. Toth, Using decision trees to improve signature-based intrusion detection, Proceedings of the International Workshop on Recent Advances in Intrusion Detection, Springer, 2003, pp. 173 191. [42] Y. Liao, V.R. Vemuri, Use of k-nearest neighbor classifier for intrusion detection, Comput. Secur. 21 (5) (2002) 439. [43] L. Breiman, Bagging predictors, Mach. Learn. 24 (2) (1996) 123. [44] D. Gaikwad, R.C. Thool, Intrusion detection system using bagging with partial decision treebase classifier, Procedia Comput. Sci. 49 (2015) 92. [45] L. Breiman, Random forests, Mach. Learn. 45 (1) (2001) 5. [46] P.A.A. Resende, A.C. Drummond, A survey of random forest based methods for intrusion detection systems, ACM Comput. Surv. (CSUR) 51 (3) (2018) 48. [47] J. Zhang, M. Zulkernine, A. Haque, Random-forests-based network intrusion detection systems, IEEE Trans. Syst. Man Cybern. C Appl. Rev. 38 (5) (2008) 649. [48] KDD, KDD Cup 1999 data. ,http://kdd.ics.uci.edu/databases/kddcup99/kddcup99.html., 1999.

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References

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[49] S.V. Manharlal, Enhancing Performance of Intrusion Detection Systems Using Data Fusion Techniques (Ph.D. thesis), Gujarat Technological University, 2018. [50] J. Goh, S. Adepu, M. Tan, Z.S. Lee, Anomaly detection in cyber physical systems using recurrent neural networks, in: Proceedings of the 2017 IEEE 18th International Symposium on High Assurance Systems Engineering (HASE), IEEE, 2017, pp. 140 145. [51] J. Goh, S. Adepu, K.N. Junejo, A. Mathur, A dataset to support research in the design of secure water treatment systems, Proceedings of the International Conference on Critical Information Infrastructures Security, Springer, 2016, pp. 88 99. [52] H.L. Gawand, A. Bhattacharjee, K. Roy, Securing a cyber physical system in nuclear power plants using least square approximation and computational geometric approach, Nucl. Eng. Technol. 49 (3) (2017) 484. [53] I. Kiss, B. Genge, P. Haller, A clustering-based approach to detect cyber attacks in process control systems, in: Proceedings of the 2015 IEEE 13th International Conference on Industrial Informatics (INDIN), IEEE, 2015, pp. 142 148. [54] P. Nader, P. Honeine, P. Beauseroy, 1p-norms in one-class classification for intrusion detection in SCADA systems, IEEE Trans. Ind. Inform. 10 (4) (2014) 2308. [55] S.L. Eggers, Adapting Anomaly Detection Techniques for Online Intrusion Detection in Nuclear Facilities (Ph.D. thesis), University of Florida, 2018. [56] F. Zhang, H.A.D.E. Kodituwakku, W. Hines, J.B. Coble, Multi-layer data-driven cyber-attack detection system for industrial control systems based on network, system and process data, IEEE Trans. Ind. Inform. 5 (7) (2019) 4362. [57] N. Svendsen, S. Wolthusen, Using physical models for anomaly detection in control systems, Proceedings of the International Conference on Critical Infrastructure Protection, Springer, 2009, pp. 139 149.

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C H A P T E R

22 Artificial neural network introductions Jing Zhang and Guanghui Su Shaanxi Key Lab of Advanced Nuclear Energy and Technology, School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an, P.R. China

22.1 What is artificial neural network The artificial intelligence has attracted broad attention and has been widely applied in the field of nuclear engineering. This work focuses on the existing application of artificial neural network (ANN) in the thermal-hydraulic phenomenon, especially the heat transfer characteristics. This section mainly introduces the basic neural network and back propagation (BP) network. In addition, the extension such as genetic neural network (GNN) has been stated. ANN abstracts the neural network of human brain on information processing, thus different networks forms in according to different connection modes [1]. ANN works as an operational model including numerous nodes (or neurons) connected to each other. There are extension neural network such as BP network (BPN), wavelet neural network (WNN), and GNN. BP network (BPN) is in essence a feedback network. Similar to other typed of neural network, there are at least one hidden layer and a linear output layer in the BPN. The hidden layer could use functions such as sigmoid function as the transfer function, and the output layer uses transfer function such as linear function. The BPN learning process composes of the signal forward propagation and the error backward propagation. The signal forward propagation process means that the inputs are transmitted from input layer to output layer, going through the hidden layer. With the output deviation from desired value, the error is transferred back. The neurons are transferred backward layer by layer, which is sharing the output error. Thus all the weights are adjusted corresponding to the error signal variation. These two processes are periodic until the error meets the accuracy requirements or reaching learning number limit [2].

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00022-X

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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22. Artificial neural network introductions

Balcilar et al. [3] considered that the BPN has a higher precision than original neural networks. BPN does well in predicting thermal-hydraulic phenomena. However, BPN has the following shortcomings [4]. There are difficulties in choosing training parameters, including the activation function, the neurons in hidden layers, the momentum term, and the learning speed; the slow convergence speed and the poor computational efficiency decrease the feasibility, hence time-consuming impedes in training the BPN with an acceptable accuracy; in addition, it may fall into a local minima error, when the training process terminates before reaching an universal minima error. Therefore the BPN is needed to be optimized by new algorithm such as genetic algorithm (GA) and wavelet analysis (WA), to overcome the aforementioned shortcomings. GA is a metaheuristic inspired by the natural selection process. GA has the advantages of self-organization, self-programming, essential parallelism, and robustness. The global search optimization technique of GA replaces the individual search to avoid the minima error and optimize weights and thresholds. The WNN introduces the advantages of wavelet transform, that is, the local characteristics of time-frequency space. In the WNN the two key parameters of scaling factor and translation factor are introduced into the ANN. The sigmoid function of ANN is replaced with the nonlinear wavelet basis function to establish the similar neural network structure of BPN. Therefore the WNN features better abilities of function approximation, high convergence speed, pattern recognition, and fault-tolerant ability.

22.2 Theory of artificial neural network 22.2.1 Mathematical models and structures of artificial neural network 22.2.1.1 Basic artificial neural network model The ANN consists of numerous interconnected neutrons, which is the basic managing units of ANN. The framework of ANN with one hidden layer is illustrated in Fig. 22.1.

FIGURE 22.1 network.

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Construction of neural

22.2 Theory of artificial neural network

For single neutron the mathematical model is written as follows: (" ) # n X   wij xi t 2 τ ij 2 Tj oj ðtÞ 5 f

517

(22.1)

i51

where xi is the input at the time of t, oj ðtÞ is the output at the time of t, τ ij is the time delay between the input and output, Tj is the threshold of the j neuron, wij is the connection coefficient from neuron i to neuron j, namely, the weight, and f is the transfer function. The training process of ANN is to minimize the system error E by adjusting weights. The system error is E5

n  X 2 dj ðtÞ2oj ðtÞ

(22.2)

j51

where dj ðtÞ demonstrates the desired output at the time of t. 22.2.1.2 BPN model The typical BP neural network (BPN) is shown in Fig. 22.2. The BPN features one or more hidden layers composing of sigmoid neurons and an output layer composing of linear neurons. Fig. 22.2 is a typical single hidden layer BPN with hidden layer transfer function of tansig, and the output layer transfer function is the purine function. The learning rules are thus derived. The number of input neurons is set as k, and any one of them is denoted by k. The number of neurons in the hidden layer is i, and any neuron is denoted by i. The number of neurons in the output layer is j, and any of them is denoted by j. Then the weight between the input layer and the hidden layer is denoting as wki, the weight between the hidden layer and the output layer is denoting as wij, the hidden layer output is denoting as a1 , the output is denoting as a3 5 y, the hidden layer transfer function is denoting as f1 , the output layer transfer function is denoting as f2 , and the input training parameter is denoting as

FIGURE 22.2 BP network structure composed of two layers of neurons. BP, Back propagation.

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xk (k 5 1,2,. . .,K). Set m be the number of iterations, then the weight and the actual output are both functions of m. P The input of the ith neuron in the hidden layer is Kk51 wki ðmÞxkm ðmÞ, the input of the jth P K 1 neuron in the hidden PIlayer is a1i ðmÞ 5 f1 ð k51 wki ðmÞxkm Þ, the output of the ith neuron in the output layer P is layer is i51 wij ðmÞai ðmÞ, the output of the jth neuron 2 PJ  in the output yj ðmÞ 5 a2i ðmÞ 5 f2 ð Ii51 wij ðmÞa1i ðmÞÞ, the total error is EðmÞ 5 12 j51 dj 2yj ðmÞ . 22.2.1.2.1 Weight adjustment between the hidden layer and output layer

Since BP network takes mean square error (MSE) as the default network performance parameter, the process of network learning is actually the process of minimizing MSE. Hence the learning rule of gradient descent is usually used in learning process. In this learning rule the weight adjustment is proportional to the partial value of the error to weight, and the sign is opposite. The difference of the error between the actual output and the expected output to the weight between the hidden layer and the output layer is: @EðmÞ @EðmÞ @yj ðmÞ 5 @wij ðmÞ @yj ðmÞ @wij ðmÞ

! I  0 X 1 wij ðmÞai ðmÞ a1i ðmÞ 52 dj 2 yj ðmÞ f 2

(22.3)

i51

The learning rules is according to gradient descent, the adjustment of wij ðmÞ is Δwij ðmÞ 52η

@EðmÞ @wij ðmÞ



5 η dj 2 yj ðmÞ



f 02

I X

! wij ðmÞa1i ðmÞ

(22.4) a1i ðmÞ

i51

The adjusted weights are obtained: wij ðm 1 1Þ 5 wij ðmÞ 1 Δwij ðmÞ

(22.5)

22.2.1.2.2 Weight adjustment between the input layer and hidden layer

The difference of the error between the actual output and the expected output and the weight between the input layer and the hidden layer is: @EðmÞ @EðmÞ @yj ðmÞ @a1i ðmÞ 5 @wki ðmÞ @yj ðmÞ @a1i ðmÞ @wki ðmÞ

! ! I I K X X  0 X 1 0 52 dj 2 yj ðmÞ f 2 wij ðmÞai ðmÞ wij ðmÞf 1 wki ðmÞxk xk i51

i51

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k51

(22.6)

519

22.2 Theory of artificial neural network

The adjustment of wki is: Δwki ðmÞ 52η 

@EðmÞ @wki ðmÞ

5 η dj 2 yj ðmÞ



f 02

! ! I I K X X X wij ðmÞa1i ðmÞ wij ðmÞf 01 wki ðmÞxk xk i51

i51

(22.7)

k51

Therefore the adjusted weight is: wki ðm 1 1Þ 5 wki ðmÞ 1 Δwki ðmÞ

(22.8)

BP network continuously adjusts the weight of network according to Eqs. (22.5) and (22.8), until meeting the expected error value or reaching the predetermined adjustment step number. Afterward the trained neural network could be obtained. 22.2.1.2.3 The implement of BPN by MATLAB

MATLAB neural network toolkit provides newff functions to create a forward BPN. The format of the call is net 5 newffðPR; ½S1; S2; . . .; SN; fTF1 TF2 . . . TFNg; BTF; BLF; PFÞ:

(22.9)

where PR is the R 3 2 maximum and minimum value matrix of input elements in R dimension; Si is the number of network neurons in layer i; TFi is the transfer function of layer i, and the default is tansig function. BTF is training function of neural network, and the default is trainlm function. BLF is the learning function of weight/deviation of neural network and PF is a performance evaluation function with default function of MSE. 22.2.1.3 Genetic neural network model The GA includes the operations of encoding and decoding, initial population generation, fitness evaluation, selection, crossover, and mutation [5]. The GNN employs the simple GA (SGA). SGA adopts only the basic genetic operators of mutation, crossover, and selection. SGA is shown as follows: SGA 5 ðC; E; P0 ; M; Φ; Γ; Ψ; Þ

(22.10)

where C means the individual coding; E stands for the individual fitness evaluation function, P0 and M demonstrates the initial population size and population size, respectively; Φ; Γ; Ψ are the selection, crossover, and mutation operations; in addition, T is the termination conditions. The steps of GA is as follows: Step 1. The solutions are in the form of chromosomes. The chromosome adopts binary coding method to deal with the weight and threshold of neural network. Step 2. The initial population generates randomly, where initial population work as a start point of the iterative search. The function of initiation operation is     pop 5 initializega populationsize; bouds; evalFN; eval-ops; options (22.11)

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22. Artificial neural network introductions

Step 3. The chromosome encode was numerically conducted by fitness function, which is of great importance in evaluating individual. The fitness function is        Fitness function 5 Σ qexp 2 qcal =qcal 2=n 1 Σ abs qexp 2 qcap =qcal =n: (22.12) Step 4. Selection operation chooses the best performing chromosomes in the population, guaranteeing a greater chance of surviving from one generation to the next and a larger population proportion over time. The selection probability of chromosome is based on the fitness function. The function of selection operation is:     newpop 5 selectFunction oldPop; options (22.13) Step 5. Crossover operator is performed on new population afterward to ensure that new chromosomes would improve population. For this operation, two chromosomes are split and then combined with the remaining part of each other. The function of crossover operation is   ½C1 ; C2  5 crossover P1 ; P2 ; pounds; params (22.14) Step 6. Mutation operation is used to avoid local extremes by randomly introduce extra information of a bit value to the chromosome. The mutation is a GA mechanism where we change a bit value. This operation prevents losing diversity during the genetic search. The function of mutation operation is   ½child 5 mution parent; bound; params (22.15) Based on the advantages of GA, the weights and thresholds of neural network are optimized by GA. Input signals should be converted into genetic gene in chromosome form. Then chromosome generates randomly to initiate the population. The key parameters of individual number, crossover rate, selection rate, and mutation rate is thus determined. Fitness function is the reciprocal of quadratic sum of the deviation between predicted values and desired values. Using roulette wheel selection, new individual is selected. Crossover operation enables the exchange between two chromosomes and production of new individual. Mutation algorithm effectively avoids premature convergence. By applying the SGA, appropriate weight and threshold are obtained. The GA based on GNN reduces training time and improve accuracy. GNN optimizes the weights and thresholds by genetic operation such as coding, selection, crossover, and mutation. The flowchart of GNN is illustrated in Fig. 22.3. 22.2.1.4 Wavelet neural network model As to the WNN, the input signal is transmitted through the input layer of WNN. The activation function of wavelet neurons in hidden layer of WNN is the wavelet basis function of the parent wavelet function ψðxÞ. Morlet wavelet function is often used as the parent wavelet function of hidden layer neurons, which is a Gaussian function with finite support, symmetry, and cosine modulation. Therefore Morlet wavelet function (Eq. 22.16) is used to replace S function as the activation function of hidden layer to construct a compact WNN, which has the ability to approach the nearest target function. Moreover, since the wavelet basis functions have the scaling and translation factor, the size, position, and shape of

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22.2 Theory of artificial neural network

521

FIGURE 22.3 Flowchart of GNN. GNN, Genetic neural network.

wavelet window could be changed, which is suitable to the training process of WNN. WA features more accurate, flexible, and effective function approximation ability than ANN. yðxÞ 5 cosð1:75xÞe2ð1=2Þx

2

(22.16)

22.2.2 Training process of neural network At first, the input parameters need to be normalized before training, which can improve the training speed and precision. As to the transfer function, the Sigmoid Function is regarded as transfer function of the hidden layer and linear function works as the transfer function of the output layer, since a sigmoid function is monotonic and changes within the range of horizontal asymptotes. Hence the input parameters can take any value and the outputs, always converge ability and a linear function enable the output of any value. The neural network is established and training work is started after setting training times and convergence error. What is more, the number of neurons in hidden layer has a significant influence on the neural network quality. The average error changes over the number of neurons in hidden layer, the example of which illustrated in Fig. 22.4. The neural network should be trained several times to avoid overfitting and the errors are averaged after removing the maximum and

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22. Artificial neural network introductions

0.38 0.36

Relative error Root mean square error

0.34 0.32 0.30

Error

0.28 0.26 0.24 0.22 0.20 0.18 0.16 0.14 0.12 0.10 5

10

15

20

25

30

Number of neurons in hidden layer FIGURE 22.4

Errors for various hidden layer neuron numbers.

minimum with varying neutron number. The start number usually sets as the number of inputs in input layer. The number of initial neurons can be determined by the following empirical formula (Eq. 22.17). Generally, the averaged error decreases with increasing hidden layer neurons and this trend slow down with more neutrons. In this figure, this trend is negligible with certain number of neurons in hidden layer. Too many neurons in hidden layer may lead to overfitting as well as longer training time; hence, one hidden layer with certain number of neurons should be an appropriate structure for the neural network. pffiffiffiffiffiffiffiffiffiffiffiffi nl 5 n 1 m 1 a (22.17) where nl means the neutrons in the hidden layer, n means the neutrons in the input layer, and the m means the neutrons in the output layer; in addition, the a is a constant ranging from 1 to 10. The database employed for neural network could be classified into three groups: most data are employed for neural network training; to avoid overfitting the remaining data were applied for validation and precision evaluation during training, respectively.

22.3 Artificial neural network applications in T/H problem The existing correlations were derived within a certain experiment range, which can only be developed to the specific conditions. Therefore new methods should been employed to expand

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22.3 Artificial neural network applications in T/H problem

523

the application. The ANN has been used to correlate flow regimes [68], pressure drop [9,10], onset of nucleate boiling (ONB) [11], critical heat flux (CHF) [1215], onset of nucleation boiling [11], boiling curve [16], and heat transfer coefficients (HTCs) [1720]. These studies shows that neural network works as an effective way to describe the complicated phenomenon and obtain better results due to its abilities of associative memory, nonlinear mapping, and knowledge processing. However, the existing investigations of thermal-hydraulic phenomenon with ANN aim at the special problems on the foundation of their own measured data, thus the limitation of application range is the main problem. Therefore more studies are necessary to find out the thermal-hydraulic mechanisms in the field of nuclear application. In recent years, GA [2124] and WA have been adopted to optimize the ANN. The extension of neural network (GNN) has a shorter search time and higher convergence speed by the utilization of parallelism and global searching. Furthermore, the aforementioned neural network has a higher accuracy than ANN according to existing literature [24]. To make clear the flow and thermal mechanisms and improve the accuracy of thermal-hydraulic parameter prediction, GNN and WNN could provide a promising method to obtain the measured data.

22.3.1 Prediction of critical heat flux The heat-transfer characteristics such as the CHF have been widely investigated all over the word. The CHF phenomenon may be happy in the reactor core, which may seriously affect the fuel safety due to the heat transfer deterioration. According to the occurrence mechanisms, the CHF could be divided into two categories: the DNB (departure from nuclear boiling) and the dryout CHF. There has been several researches that utilize the neural network for critical flow prediction. Moon and Chang [25] related ANN to fuzzy clustering for CHF prediction. Mazzola [26] coupled the neural network with an analytical correlation. Zhao et al. [27] applied ANNs approach to predict Nusselt number of transition boiling on the downward-facing heated surface under different gap sizes conditions. Peng and Ling [28] used a neural network analysis of thermal characteristics on plate-fin heat exchangers with limited experimental data. Hakeem et al. [29] developed an ANN method to predict the temperature profiles in a vertical thermosiphon reboiler. Su et al. [30] applied ANNs to the prediction of CHF under low pressure and flow oscillation conditions for both natural and forced circulation, the BP neural network (BPN), as a simple type of ANN, is proved to be an effective approach for predicting and analyzing the influences of parameters on CHF. Here we give the examples of ANN to the CHF analysis in concentric-tube open thermosiphon. An ANN (ANN) is adopted for predicting CHF of concentric-tube open thermosiphon, which is successfully based on the experimental data from the literature (Chen). There is no relevant work dedicating to the CHF characteristics analysis in concentric-tube open thermosiphon. Using the experimental data, predicting the CHF for concentric-tube open thermosiphon of R113, water, and R22 was performed under various operating conditions and geometrical parameters. According to the key parameters affecting CHF, the input parameters of the ANN are proposed in the dimensionless form, including density ratio, the ratio of the heated tube length to the inner diameter of the

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outer tube, the ratio of frictional area, and the ratio of equivalent heated diameter to characteristic bubble size. The output is Kutateladze number, Ku. The input layer consists of four neurons and the output layer has one neuron. In addition, the number of hidden neurons is seven, which is enough to describe the thermal-hydraulic phenomena. The ANN predictions show reasonable agreement with the test data. The mean relative error (MRE) of the ANN prediction is 8.46%. The results show that the ANN provides a better accuracy than the existing empirical correlations in the CHF prediction, which has been illustrated in Fig. 22.5. The effects of various parameters on CHF prediction were analyzed based on the ANN prediction, including the tube size, L/Di, and pressure. Another example is the BP algorithm optimized ANN with three layers. This BPN is employed to predict CHF in saturated forced convective boiling on a heated surface with impinging jets. Impinging jet means that fluid impinging directly upon the heated surface. This phenomenon features a thin impingement boundary layer at the impacted area and a short flow path. This characteristic features higher heat transfer abilities than other heat transfer method. The superiority enlarges the application area in energy and other fields with high heat flux. Due to the feasibility of impinging jets, heat transfer abilities and CHF have been studied by experimental and theoretical methods. So far, correlations predicting CHF in forced convective boiling on a heated surface with single or multiple impinging jets have been generalized based on experiment. Sharan and Lienlard [31] proposed a correlation. And the correlation of Monde [32] is based on the CHF data in the V-regime. Monde and Okuma [33] suggested the equation for L-regime CHF based on the fluids of water and R113, the atmosphere pressure was investigated. Monde [34] experimentally studied the CHF of R12 at with higher pressures range (0.62.8 MPa). Xu and Hangan [35] investigated the effects of stagnation conditions from the view of Reynolds number and boundary conditions, and the distance between the jet and the heated surface is found to have tiny impact on the CHF with the distance larger than the characteristic length of ringvortex formation. FIGURE 22.5 Prediction of CHF with ANN. ANN, Artificial neural network; CHF, critical heat flux.

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22.3 Artificial neural network applications in T/H problem

Experimental data was employed as the input of ANN, 70% of which act as the training data of ANN, 15% data were employed for the validation of the neural network and the complete independent test, respectively. The input parameters of the ANN are liquid-to-vapor density ratio, the ratio of characteristic dimension of the heated surface to the diameter of impinging jet, reciprocal of the Weber number, and the number of impinging jets, Nj. The output is dimensionless heat flux. The root mean square (RMS) error of ANN is 17.39%, with most errors staying between 6 20%. The results are shown in Fig. 22.6. Based on the trained ANN, the influences of the main parameters on CHF have been analyzed, including jet velocity, L/D, pressure, and the number of impinging jets. CHF increases with jet velocity and decreases with L/D and Nj. The increase trend of CHF with pressure inverses to decrease. In addition to the ANN, the application of GNN is shown as well, which predicts dryout-type CHF for the upward flow in vertical narrow annuli with heating on both side. Taking the GNN advantages of global optimal searching, quick convergence speed and solving nonlinear problem, the GNN model is established and trained, aiming at offering a CHF prediction with higher precision. The GNN model is established with a wide range of test data. The pressure (P) varies from 1 to 15 MPa, mass flow rate (G) changes from 50 to 400 kg/m2 s, critical quality (Xc) is within 0.390.98, and heat flux (q) comes from 10 to 400 kW/m2. The ANN with a hidden layer is applied. The transfer function is the hyperbolic tangent function, and the linear function of purelin is used in output layer. The training function, a gradient descending function, is based on adaptive learning rate. The weighted sum of the previous layer outputs is summed up, which is mapped by a nonlinear activation function. The results agree well with practical behavior as they are generally understood. At last, the predictions of GNN on the CHF for narrow annular channel with gaps of 0.95 and 1.5 mm are validated by the test data (Fig. 22.7). Thus it proved the GNN is useful and valuable, which could effectively predict CHF. The effects of main parameters are analyzed, covering pressure, mass flow rate, and qualitybased on the validated GNN. This GNN method helps figuring out the profound thermalhydraulic mechanisms in annular channel. The local conditions hypothesis remains unaffected by other variable in addition to system pressure, mass flow rate, and critical quality.



FIGURE 22.6 A comparison between experimental and predicted CHF data. CHF, Critical heat flux.

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FIGURE 22.7 Comparison between prediction results and experimental data.

22.3.2 Prediction of nucleate boiling heat transfer coefficient Surface boiling is widely used due to a low superheat requirement, which could be divided into two categories according to the flow behaviors, namely, pool boiling and flow boiling. Flow boiling has been the research focus of nuclear engineering. Flow boiling is a crucial phenomenon both in the boiling-water reactor (BWR) and the pressurizedwater reactor (PWR). Moreover, it appears under natural circulation condition as well. Flow boiling features two priorities: [36] first, flow boiling usually provides higher HTCs than other types of boiling, thus effective heat transfer characteristics can be achieved to smoothly deliver the heat from the core; second, the allowance higher coolant outlet temperature before boiling enhances the system efficiency. Thus it is essential to obtain an accurate prediction of the HTC. However, the local evaporation mechanism is complex since the bubble growth on the heating surface is under an additive influence along flow direction. Besides, convective boiling and nucleate boiling have similar intensity under certain conditions in flow boiling. Both the above two situations increase the difficulty of HTC study. Consequently further research on HTC of flow boiling is necessary. Numerous studies on HTC of flow boiling have been performed by both experimental and theoretical methods. Correlations based on conventional channels have been proposed for HTC. Both the two main mechanisms (nucleate boiling and convective boiling) are mentioned in Chen’s correlation, which is applicable to the entire saturation boiling before DNB [37]. Shah [38] employed the Froude number to give reasonable predictions of the HTC in horizontal tubes based on the two mechanisms proposed by Chen. Gungor and Winter [39] suggested a correlation based on Chen’s correlation, predicting the flow boiling heat transfer shows precise prediction of vertical and horizontal flow, tubes, and annuli under saturated and subcooled conditions. There are other correlations based on the two mechanisms as well,

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covering Kandlikar’s correlation [40], Jung’s correlation [41] and Wattelet correlation [42]. New correlations are developed on the foundation of existing correlations, and reasonable agreement is obtained under certain conditions. In addition to the theoretical investigations, the experimental studies were carried out on the HTC for various fluids. And the measured data were used as the validation of the aforementioned correlations. The GungorWinterton correlation shows good agreement with Kuo and Wang’s [43] experimental data for the fluids of HCFC-22. However, Shah’s correlation embodies an underestimation of these data. Kandlikar’s correlation fits well with Kim and Shin’s [44] test data for R22 and R410A, while for the experimental data of R22 by Seo and Kim [45], overestimations are obtained. These correlation’s predictions agree with the experimental results for R22 and R507 only at low or medium pressures, according to Greco and Vanoli [46]. Besides, more experiments have been conducted for various fluids [4749]. The above investigations show the situation that the previously mentioned correlations could not provide satisfying prediction under all conditions. These correlations were obtained from a narrow range of test conditions, and the feasibility of these correlations is restricted to a special condition. In this section, we would like to give an example of predicting the HTC from small to conventional scale by applying ANN. Comparing to conventional channels, the flow boiling heat transfer ability in small-diameter channels embodies a better performance. Thus substantial studies have been carried out on the HTC. Since the flow and thermal mechanisms differ among the channels with large and small size. The correlations for conventional channels may not provide a promising accuracy in predicting the boiling HTC for small-diameter channels. Several researchers [5054] presented that the dominant phenomenon of nucleation in small-diameter channels becomes weaker in conventional channels. As to the flow characteristics, laminar flow was also observed in small channels [55,56]. Several correlations were suggested especially for the flow boiling HTC in small-diameter channels. Kandlikar and Steinke [57] modified correlation for small channels. Zhang et al. [56] revised Chen’s correlation to predict the HTC in mini channels. Jacobi and Thome [58] established a new model by considering the situation that thin liquid film evaporation surrounding elongated bubbles dominates. The systematic flow boiling heat transfer characteristics were summarized in review literatures to focus on small channels [5961]. However, these correlations are only applicable to a narrow scale of conditions and even contrary trends are obtained between investigations. The profound understanding of flow boiling is necessary. Both the BPN and GNN are employed here to predict the HTC of flow boiling. The training data for neural network comes from the literatures [43,46,48,55,6274], covering both small-diameter and conventional channels. According to the above-discussed theory, ANN with one hidden layer is enough to deal with the problem according to Zhang [75]. The input parameters are as follows: the vapor quality x, mass flux G, heat flux q, internal diameter D, and physical parameter ϕ (φ5ðCpf =μf Þ0:4 kf 0:6 ). In addition, the output is the predicted HTC by ANN. The results shown in Figs. 22.8 and 22.9 demonstrate that both BPN and GNN could provide reasonable predictions. The predicted errors of ANN’s are constrained between the lines of plus and minus 30%, and the errors of the GNN predictions are within plus or minus 25%. The MRE (11.34%) and RMS error (17.16%) of GNN are smaller than those of BPN (14% and 20.5%, respectively). Consequently, GNN shows a higher accuracy than BPN in the HTC estimation. This makes sense because of the optimization of neural

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FIGURE 22.8 Comparison BPN predictions with test data.

Predicted value by ANN[kW/(m2K)]

25

x=y

Data point 20

of

+30%

15

–30% 10

5

0 0

5

10

Experimental

15

20

25

value[kW/(m2K)]

FIGURE 22.9 Comparison of GNN predictions with test data. GNN, Genetic neural network.

Predicted value by GNN[kW/(m2K)]

25 Data point

+25% x=y

20

15

–25% 10

5

0 0

5

10

Experimental

15

20

25

value[kW/(m2K)]

network with GA could improve ANN precision. The error comparison of GNN with previous correlations are conducted as well, for R410A, R22, and R134A (Table 22.1), where GNN shows a higher precision. It has been proved that GNN fits the test data best. Based on the validated BPN and GNN application, the influences of various parameters on flow boiling HTC could be analyzed, covering pressure P, the vapor quality x, the mass flux G, the heat flux q, and the inner diameter D.

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TABLE 22.1

Precision comparison of genetic neural network (GNN) with existing correlations.

Models

Relative error (%) for R410A

Relative error (%) for R22

Relative error (%) for R134A

GNN

11.80

9.33

13.97

GungorWinterton

31.07

33.20

24.10

Shah

33.39

37.20

24.00

Kandikar

38.59

25.50

26.20

22.3.3 Prediction of onset of nucleate boiling in vertical narrow annuli For fluid with the bulk liquid temperature below the saturated state, there still exists bubble generating near to the heating wall due to a certain superheat degree, though bubbles could not form and enter the bulk flow. This phenomenon is defined as the subcooled flow boiling, the location at which the bubbles appear is the ONB. Under this circumstance the small bubbles may largely affect the subcooled boiling characteristics. Since the ONB means that the flow regime transmits from single-phase to two-phase flow, it is of great significant in the study of boiling mechanisms, accurate prediction of the ONB could provide an effective access to recognize the boiling process. The appearance of bubbles would increase the heat-transfer ability and the pressure resistance. In the practical application of reactor, there are key points in the thermal-hydraulic analysis, namely, the ONB and the DNB. These two factors may largely affect the reactor safety. During the bubble condense and movement toward bulk fluid, the heat transfer between the wall and the fluid is influenced. The example of ONB prediction by ANN has been adopted in this section [76], taking the ONB in vertical upward flow through narrow annuli as example. The GNN is used to predict ONB point and the effect of parameters on ONB for bilaterally heated narrow annuli tubes within the experimental range. The GNN model has advantages of its globe optimal searching, quick convergence speed, and solving nonlinear problem. The results agree well with practical behavior as it is generally understood. Studies [7781] have focused on subcooled flow boiling and particularly ONB, most of the models depend on the heat flux and wall superheat at boiling incipience. Hsu [82] proposed the bubble growth criterion, which related the nucleation bubble growth to the saturation temperature of the liquid at the bubble tip. Li and Cheng [83] developed the ONB model of micro-channels based on wall superheat, considering the effects of dissolved gas, contact angle, microcavities, and corners. Ghiaansiaan [84] found that the ONB models and correlations for conventional channel tent to underestimate the heat flux. Situ et al. [85,86] done experimental work on the bubble behaviors in forced convective flow during the ONB phenomenon, where several new phenomena were observed. Liu et al. [87] adopted the rectangular channels to study the ONB. On the foundation of GA and ANN a GNN model could be established for the estimation of ONB with bilateral heating, which provides a promising access to better understand the ONB phenomenon. The GNN model has advantages of its globe optimal searching, quick convergence speed, and solving nonlinear problem. The test data for narrow annuli with 0.95, 1.5 and 2.0 mm gaps are collected as the input. During the training process the above data have been divided into two parts,

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FIGURE 22.10 Comparison between GNN prediction results and experimental data. GNN, Genetic neural network.

the training data and the testing data. A percentage of 75 and 25 of the total data were adopted for training and testing, respectively. The GNN prediction results have a good agreement with test data, proving the prediction ability of GNN on the ONB, as shown in Fig. 22.10. Most errors lay between the error lines of 6 15%. Thus it could be concluded that the GNN is an effective method in predicting the ONB in vertical upward flow through narrow annuli. The dependence of qONB on system pressure, mass flux, wall superheat, and geometrical structure are discussed based on the validated GNN. In addition to the GNN application in the ONB estimation, the WNN has been employed [88]. The cubic B-spline wavelet transform are applied as the local modulus maxima. The function of wavelet transformation demonstrates the local properties in the joint region of the time-frequency space. WNN model combines the advantages of ANN and the WA, showing perfect ability in solving nonlinear problem. Therefore the ONB was predicted as well for upward flow in vertical narrow annuli with bilateral heating. Similar to the GNN application, the test data for narrow annuli with 0.95, 1.5, and 2.0 mm gaps are collected as the input. The WNN predictions show reasonable accuracy in predicting the experimental data, proving the feasibility of WNN (Fig. 22.11). The relationship of the ONB and relevant parameters are analyzed by the validated WNN, including the system pressure, wall superheat, and mass flow velocity.

22.3.4 Characteristic points of boiling curve The wavelet has the priority of reasonable localization characteristic. It has been applied widely in theory and practice. The Fourier transform are vulnerable to fall into the weak localization in the time and frequency regions. Wavelet transform could be used to overcome these shortages. Therefore the wavelet is applied to study the singularity of boiling curves. It is well known that the boiling curve describes the relation between the heat flux superheat at wall. The typical boiling curve is shown in Fig. 22.12. Three typical regions are illustrated, including nucleate boiling, transition boiling, and film boiling regions,

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FIGURE 22.11

531

Comparison between GNN prediction results and experimental data. GNN, Genetic neural

network.

FIGURE 22.12

Schematic diagram for flow

boiling curves.

though the real situation usually only embodies one or two parts of them. Complicated heat and flow mechanisms are covered in the boiling curve, which contain a series of phenomena. Hence, accurately predicting the boiling curve may encounter many problems. Numerous working conditions especially complicate this situation. The CHF, which has increasing limit, is a crucial parameter in the nuclear engineering, which even decides the safety margins of reactor core and steam generators (SG). In the SG the continuously occurring vapor in the second side may form a gas film on the surface, which introduces the heat transfer deterioration; hence, the sudden increase of

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surface temperature would lead to the heater destruction. In the design of all kinds of reactor like the pressurized-water nuclear reactors, enough sufficient thermal (power) margin must be guaranteed to ensure the reactor units operates under the safety condition and has the ability to keep the radioactivity inside the reactor. This is especially of great significant to fuels, where abundant energy generates and the heat transfer deterioration are more easily to happen. The limitation of which is determined by the CHF. Therefore those characteristic points of boiling curve are of great importance. Here we seek an efficient approach to predict the boiling curve by utilizing the advantages of wavelet based on the existing numerous test database [89]. The CHF and minimum film boiling starting point are described by the multiresolution WA. The good localization characteristic of WA enables its predicting the boiling curves. As to the characteristic points such as the ONB and CHF, the GNN mode is applied. It has been mentioned that the GNN model features quick convergence speed and global optimal searching in solving nonlinear problem. A wide variety of test data have been collected as the database. By adopting the basic theories models of the wavelet modulus maxima detection and GNN, the local modulus maxima detection of cubic B-spline wavelet transform determines the characteristic points such as ONB and CHF in the boiling curve. Afterward the characteristic points of boiling curves are predicted by GNN, which has been validated by comparisons with the test data. The BP network is used here with the structure of two hidden layers in the evaluation of characteristic points. The data of pressure, mass flux, and inlet subcooling are employed as the input of input layer, namely, the input is in three dimensions. The output is in one dimension with the only output of CHF, qmin or wall superheat corresponding to qmin. The units in first and second hidden layer are 35 and 25, respectively. A large range of experimental data was used here for the training and testing database of neural network. Sixty percent of the test data are employed as the training database, 10% are used for validation, and the remaining 30% are for testing. The MSEs of the training, validation and testing are 0.06319, 0.07912, and 0.08475, respectively. The prediction results of CHF, qmin and wall superheat corresponding to qmin, are shown in Figs. 22.1322.15, which show the comparison between predictions and test data. These figures illustrate that GNN shows a good ability in estimating the CHF, qmin or wall superheat corresponding to qmin, with the RMS errors of 7.18%, 6.24%, and 12.5%, respectively. Most of the errors are within the range of 6 10%, reasonable agreement is obtained between the predictions and the experimental data for these characteristic points of boiling curves. Similar to the previous work, the influences of pressure, mass flux, and inlet subcooling degree on CHF are investigated using the GNN. The results agree with practical behavior as they are generally understood.

22.3.4 Prediction of leak before break leak rate As the typical design basis accidents, the loss of coolant accident (LOCA) steam and the SG tube rupture (SGTR) accident greatly endanger the reactor safety. The small leakage from the pipe crack can be detected before break or rupture. The location and size of crack

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FIGURE 22.13 Comparisons between the experimental data and GNN predicted results of CHF. CHF, Critical heat flux; GNN, genetic neural network.

FIGURE 22.14 Comparisons between the experimental data and GNN predicted results of qmin. GNN, Genetic neural network.

is identified by the leakage, and timely measures would be taken to avoid break and the subsequent accident such as LOCA and SGTR. Thus the leak before break (LBB) concept is proposed, which has been widely applied to enhance the defense-in-depth barrier of reactor and simplify equipment redundancy, showing advantages in reactor safety and economy. The LBB phenomenon may appear in different types of reactors, including PWR [9093], heavy-water reactor [94], BWR [95], super critical water-cooled reactor [96], high

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FIGURE 22.15 Comparisons between the experimental data and GNN predicted results of wall superheat corresponding to qmin. GNN, Genetic neural network.

temperature gas-cooled reactor [97], and sodium-cooled fast reactor [98]. Various crack locations were considered well, such as SG tubes [99,100] and steam pipelines [101]. The leak through crack, which determines the sensitivity of leak-detection system and the estimation of the crack size, is definitely of great importance in LBB concept. Accurate leak prediction ensures that the leak is detectable before the unstable crack propagation. The critical flow models has been the research focus of LBB study due to the complicated phenomenon. The feasibility of existing critical models [102107] is limited since these models are developed based on conventional pipes and orifices. Experimental and theoretical research on the leak through crack has been performed both for artificial [9496,100,108110] and natural crack [95,99,101], respectively. Critical flow for conventional channel have been modified for leakage through crack. However, most of the revised models, developed according to particular experiment conditions, show poor precision with narrow applicable range. There’s lack of a systematically and comprehensively method to accurately estimate the LBB leak for single-phase and multiphase, subcritical and supercritical, chocked or unchocked, and multiple fluids. Further investigation on LBB leak rate is necessary. To understand the flow mechanism through crack and improve prediction accuracy, the GNN, trained by testing data, is first adopted to predict leak rate of LBB under various conditions. The influence of thermodynamic properties and crack morphologies on leak rate are conducted on the foundation of the GNN predictions. Furthermore, a leak rate correlation is proposed by GA according to the flow mechanism through crack, providing a simple and efficient way for leakage prediction. Since the GNN shows an excellent interpolation prediction, more training data with a wider scale could improve the feasibility and precision of GNN. This study tries to employ as much data as possible, covering the common conditions and crack morphologies. The training data for neural network, a total of 398 groups, are collected from the literatures

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[9497,99101,108112]. The range of the adopted experimental data has been collected, including the scale of pressure P, temperature T, crack opening displacement (COD) σ, crack depth Ld, crack length CL, the local roughness μl , the area ratio of inlet to outlet AR, kind of fluids, and type of cracks. The artificial and natural cracks with various shapes (rectangle, ellipse, and rhombus) and area ratios of inlet to outlet are considered. The thick of the primary pipe and SG tubes are taken into account, as well as the crack length and local roughness. In addition, the subcooled, saturated, superheat, and supercritical states are included. Except for water, the fluids of helium and carbon dioxide are also adopted as well. From the leakage models for critical flow and pressure drop, we figure out the parameters that determine the leak rate, which can be divided into two categories: the thermodynamic properties and the crack morphologies. For the convenience of discussion and analysis, all the parameters are expressed in the form of dimensionless quantities according to the physical mechanism. The thermodynamics properties contain the stagnation pressure Po, temperature To, and back pressure Pb. The critical flow depends on the stagnation pressure and temperature. The dimensionless number ω 5 ðCPo To Psat ðTo ÞÞ=ν lo , is a unique function of the stagnation state for subcooled water. Thus it can be used to demonstrate the stagnation condition. Nevertheless, it fails to describe the stagnation state of saturated and supercritical fluids. To better describe the stagnation state the dimensionless number ω is modified as: ω5

  Psat ðTo Þ ν lg 2 ho ν lo hlg

(22.18)

ω is the function of stagnation pressure, temperature, and enthalpy. For the supercritical pressure the corresponding saturated pressure and temperature under the isentropic assumption is applied in Eq. (22.18), since the pressure drop from the supercritical to subcritical can be regard as an isentropic process and the flow resistance is negligible. The pressure difference between the inlet and outlet is quantified as ðPo 2 Pb Þ=ðPcri 2 Pb Þ. The crack morphologies, which have significant influence on the pressure drop, consist of the crack depth Ld, COD σ, crack length CL, the crack shape, the area ratio of inlet to outlet AR, local roughness μl , global roughness μg , the number of turns nl , and the percentages of 45 degree angles NR. According to the pressure drop model, the hydraulic diameter D is adopted to present the crack shape, COD σ and crack length CL; the crack depth Ld is transformed into dimensionless number Ld/D; the local roughness μl is quantified as μl /D; the ratio of particulate diameter to the hydraulic diameter D (5:0E26 =D) is used for plugging phenomenon; and the area ratio of inlet to outlet AR is considered as well. In addition, the entrance resistance coefficients Cd and the expansion exponent γ in models are empirical coefficients instead of test parameters, and some geometry properties (global roughness μg , the number of turns nl , and the percentages of 45 degrees angles NR) could not be measured. To avoid the uncertainties, these parameters are not selected as input by neural network, taking advantages of associative memory, nonlinear mapping, and knowledge processing. With respect to the neural network output the experimental results employed for training GNN are in the form of flow rate or mass flux, which are transformed into the dimensionless Reynolds at entrance by GD=u, u is the dynamic viscosity.

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The LBB leakage is estimated by BPN and GNN. One hidden layer is enough to deal with the  problem according to Zhang [75]. The inputs include six dimensionless variables, Psat ðTo Þ=ν lo ðν lg =hlg Þ2 ho , ðPo 2 Pb Þ=ðPcri 2 Pb Þ, Ld/D, μl /D, AR, and 5:0E26 =D, and Reynolds number is set as the output. The number of neurons in hidden layer determines the neural network quality. The averaged error changes over the number of neurons in hidden layer. Too many neurons in hidden layer may lead to overfitting as well as longer training time, hence one hidden layer with 30 neurons may be suitable for the neural network in this prediction. The results shown in Fig. 22.16 indicate that both ANN and GNN can accurately predict the LBB leakage. The ANN’s predictions stand between the lines with the error of plus and minus 30%, and the error of the GNN predictions lay between plus 30% and minus 25%. The MRE and RMS error of GNN (22.7% and 37.1%, respectively) are smaller than those of ANN (26.1% and 56.9%, respectively). Consequently, GNN provides a higher accuracy than ANN on the estimation of LBB leakage, because the optimization of neural network with GA can improve the precision of ANN. The comparison of GNN estimations with the existing model predictions (Moody, Fauske, HEM, and isentropic model), as well as the results of commercial software (PICEP and SQUIRT) in literatures [9092]. Overall, GNN is superior in LBB leakage estimation, compared to the existing models and commercial software. Unlike PICEP and SQUIRT, which adopt the HNEM, the models used here seriously overestimate the testing data due to the isentropic assumption. Moreover, the GNN is more extensively applicable, which could be used to evaluate the leak rate of supercritical and multiple fluids (carbon dioxide and helium). The influences of parameters, both thermodynamic properties (stagnation pressure, temperature, and back pressure) and crack morphologies (COD σ, crack length CL, crack shape, crack depth Ld , local roughness μl , and the area ratio of inlet to outlet AR), on LBB leakage were analyzed based on the validated GNN. In addition, the sensitivity investigations of other fluids such as helium and carbon dioxide are conducted by GNN as well. The change of LBB leakage over one parameter was studied by fixing the others.

FIGURE 22.16 Comparison of ANN/GNN predictions with experimental data: (A) ANN predictions and (B) GNN predictions. ANN, Artificial neural network; GNN, Genetic neural network.

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References

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C H A P T E R

23 New direction of nuclear code development: artificial intelligence Lianshan Lin1 and Xing Wang2 1

Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, United States 2Department of Nuclear Engineering, Pennsylvania State University, State College, PA, United States

23.1 Introduction Applying artificial intelligence (AI) or automatic methods to the design, operation, and maintenance of nuclear power plants (NPPs) has been a long-lasting goal of nuclear engineers and scientists. There are three fundamental motivations that fuel this aspiration: (1) efficiency; (2) reliability, and; (3) continuity [1 3]. A nuclear reactor is a complex system that requires systematic planning and controlling to achieve the desired performance and safety. Intelligent methods, such as expert systems, fuzzy logic, and neutral networks, can substantially reduce the working load for human cognition and reasoning and thus improve the NPP efficiency. For reactor operation the larger number of parameters and system interactions can pose stress on operators, especially during emergency conditions. Automatic systems that can provide real-time diagnostics have the potential to take some uncertainties out of the operators’ decision and increase the NPP reliability. Continuous investment for more efficient and reliable nuclear reactors will inevitably lead to more sophisticated systems that have to be managed automatically. In addition, the development of intelligent and automatic methods is an effective approach to preserve human knowledge on current reactors that would benefit the optimization of future NPPs. It is interesting to notice that nuclear power technology and AI were born almost at the same time. While the Dartmouth workshop in 1956 declared the birth of AI as an independent research field, the world’s first nuclear-powered submarine, USS Nautilus, was launched in 1954 at Groton, Connecticut, and in the same year the Obninsk nuclear power station generated electricity industrially for the first time. Despite two distinct areas, AI has been influencing the development of nuclear power from the outset. This relationship can be clearly observed in the early implementation of instrumentation and control system in 1960s [4] and

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00023-1

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the extensive research on various expert systems for the diagnostics, maintenance, and management of NPPs in 1980s [5,6]. During the recent rise of AI since 2010 that features deep learning, we also see an ever-increasing interest in applying data-orientated AI techniques to every aspect of nuclear power, including the code development for neutronics [7], thermohydraulics [8 10], and reactor safety [1,11]. Encouraging results have been obtained by some pioneering works. However, past research and development (R&D) has also shown that many AI-related NPP projects couldn’t survive in a long term. For example, quite a few expert systems in the 1980s stopped as prototypes, reflecting the inherent complexity of the reactor design, operation, and maintenance [2]. Therefore it is meaningful to review these previous efforts and summarize guidance for the future AI applications to nuclear power. There are three parts in this section. First, a short introduction to the spring and winter of AI in the past 60 years is presented. Second, we summarize the R&D of NPP expert systems, which was one of the research hot spots in the nuclear community during 1980s. Although the focus of these expert systems is mostly on reactor diagnostic, maintenance, and decision support, beneficial experience can still be learned from these efforts for current nuclear AI research. Third, we briefly highlight some recent works that utilize machine learning techniques for nuclear code development.

23.2 A brief history of artificial intelligence The great Three Laws written in Isaac Asimov’s popular Robot series in 1940s have built the general principles of human-created AI that “a robot may not injure a human being or, through inaction, allow a human being to come to harm; a robot must obey orders given it by human beings except when such orders would conflict with the First Law; a robot must protect its own existence as long as such protection does not conflict with the First or Second Law.” Expectation of AI in these fictions synchronized with the invention of the programmable digital computer, a machine based mathematical reasoning system in the 1940s. The computing machine and the ideas behind it at that age inspired a handful of scientists to begin seriously discussing the possibility of building an electronic brain. Grounding us back in the applications of AI technology nowadays, though its development is right in another rising hype, it should still stay at the very beginning of a long history when compared to Asimov’s final destination. The initiation of AI research, or the definition of AI itself, was coined at a workshop held on the campus of Dartmouth College during the summer of 1956 [12], which was organized by the computer scientist John McCarthy who later became a professor at Stanford. Those who attended that workshop, such as Dr. Marvin Minsky, Dr. Claude Shannon, and Professor Herbert A. Simon, became the leaders of AI research for decades. Many of them predicted that a machine as intelligent as a human being, like the robot in Asimov’s fictions, would exist in no more than a generation and they were funded with millions of dollars to realize it. The years after the Dartmouth conference were an era of discovery, of sprinting across new ground. Many AI-related theories and basic computing frameworks were developed from 1956 to 1974, which are known as the golden years. Direct evidence of first popularity of AI research can be illustrated by the histogram in Fig. 23.1, which shows the number of publications on the topic of AI from 1952 to 1981.

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23.2 A brief history of artificial intelligence

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Year FIGURE 23.1 Golden years and AI winter reflected in publication number, from 1952 to 1981. AI, Artificial intelligence.

Between 1966 and 1968, the number of publications reached the first peak followed by a significant drop in 1969 before reaching another peak in 1976. Most of the AI research focused on “reasoning as search” algorithms to find a resolution of a problem, and natural language processing to mimic human being’s communication. The importance of natural language processing was that if a machine could carry out conversations so realistic that human being were fooled into thinking they were communicating with a human being rather than a program, it then passed the famous Turing’s Test brought by Alan Turing in 1950 and would be claimed as a real AI or “thinking machine.” Unfortunately, none of the algorithms or machines had passed this test yet. Eventually, real progress of AI technology proved that the difficulty of such reasoning machine and natural language processing projects, if not mission impossible, had obviously been underestimated by these pioneers. In 1973 the United States and British Governments stopped funding aimless research into AI, and the difficult years that followed would later be known as “AI winter.” Therefore the sudden drop of publication number in the topic of AI after the year 1976 it (Fig. 23.1) is not surprising. Seven years later, a visionary initiative by the Japanese Government inspired governments and industry to provide AI research with billions of dollars, but by the late 1980s the growth of computing power, particularly on computer hardware, did not expand as fast as needed by the contemporary AI algorithms. A typical computer configuration for performing AI software at that time included a 16-bit microprocessor running at 8 MHz with 1 MB of RAM, and a 30-MB hard disk, or an IBM PC that had 3-MB extended memory, 2.5-MB expanded memory, 650-KB low memory, 30-MB hard disk, and 1.2-MB and 360-KB floppy drives [5]. Without promising applications in industry, disappointed investors became disillusioned and withdrew funding again.

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23. New direction of nuclear code development: artificial intelligence

After the AI winter, the development of AI technology did not stop but grew at a slower speed. In the 1970s the logic programming language Prolog was created [13]. Prolog uses a subset of logic, or “rules,” that permits tractable computation. Rule-based AI technology provided a foundation for the expert systems developed later on, substantially influencing major AI research during 1970s and 1980s. In the meantime, the computer hardware kept evolving according to Moore’s Law, that is, doubling the number of transistors on the same microchip with only half price every 2 years. Enhanced by faster computing hardware, AI technology reached another peak in 1996 97 when the first computer chess-playing system Deep Blue won a chess game against the then reigning world champion Garry Kasparov under regular time controls [14]. Deep Blue employed custom very-large-scale integration chips to execute the alpha beta search algorithm in parallel [15], an example of Good OldFashioned Artificial Intelligence that can be classified as a brute-force approach. However, neither the victory of Deep Blue nor the prosperity of expert systems was able to keep boosting the AI rise into the new millennium. The Deep Blue itself brought few effects on industry at that time. Early successful expert systems were also found expensive to maintain, difficult to update, and only useful for a few special contexts [16]. An obvious drop in publication can be observed in Fig. 23.2 during the late 1990s and early 2000s. The most recent rise of AI featured with deep learning was largely driven by the availability of big data. Thanks to advances in hardware such as graphics processing unit, algorithms, mobile network, cloud computing, high performance computing, and open source technologies, acquiring, processing, and sharing big data has never been so accessible. Investment and interest in AI boomed in the second decade of the 21st century, when machine learning was successfully applied to many problems in both academia and industry, such as face

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1952 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015 2017 2019

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Rises of AI reflected in publication number, from 1952 to 2019. AI, Artificial intelligence.

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recognition and self-driving automobiles. The Association for Computing Machinery named Yoshua Bengio, Geoffrey Hinton, and Yann LeCun recipients of the 2018 ACM A.M. Turing Award for their conceptual and engineering breakthroughs that have made deep neural networks a critical component of current AI research. As shown in Fig. 23.2, there is a nearly exponential increase in publication after 2010, which was mostly fueled by deep learning and there is no sign for this rise to stop. Note that in Fig. 23.2, the overall number of publications in 2019 was incomplete by the time of preparation of this manuscript, and more publications than the 2018s outcome are expected.

23.3 Artificial intelligence research in nuclear power industry in the 1980s As mentioned in the introduction, nuclear engineers have always welcomed the potential applications of AI in NPPs. One good example is the extensive R&D of expert systems in the nuclear community in the 1980s. A good collection of these efforts can be found in the proceedings of the American Nuclear Society topical meeting on AI and other innovative computer applications, which was held in 1987 at Snowbird, UT [5]. The conference attracted experts from 15 countries or regions and a wide spectrum of groups, including universities, national laboratories, federal agencies, equipment vendors, utility industry, and small businesses. As written in the preface of the proceedings, “there was a strong impression that application of this (AI) technology to nuclear power plants is inevitable. The benefits to improved operation, design, and safety are simply too significant to be ignored” [5]. There were eight major application areas of expert systems in NPPs [2], which included (1) diagnostics and surveillance, for example, monitoring plant behavior and diagnosing equipment malfunctions. (2) Outage planning, for example, optimizing the refueling activities. (3) Compliance with specification, for example, classifying emergency conditions and resolving ambiguous situations. (4) Operational advisor, for example, guiding the removal of residual heat and plant maneuvers. (5) Mitigation of accident consequences, for example, managing evacuation in real time and predicting plume travel. (6) Reactor safety assessment, for example, monitoring and predicting the conditions of reactor core and containment. (7) Reviewer aid, for example, providing a consistent framework and interactive process for the reviewing licensing applications. (8) Nuclear training, for example, instructing operators using the intelligent expert systems. A few examples of these expert systems are provided next. Argonne National Laboratory and EI International Inc. developed a System State Analyzer (SSA), which can extract knowledge from a real NPP system by making single new observations of the system and then apply the learned example to estimate the true system state [17]. One key step for developing this analyzer is using the learned state vectors to update the rules for quantitatively determining a state. SSA offered the capability of identifying failed sensors and of detecting the abnormal reactor conditions. Application of SSA to a real nuclear reactor, EBR-II, showed that SSA can only identify what it has learned. Further research also found that the real plant problems are not simply a matter of abnormal signals but rather more subtle and require a fairly high-resolution analysis tool. The authors claimed that SSA could be such a tool with further optimization. Stony Brook University worked on an expert system to assist the refueling process at the Fast

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Flux Test Facility in Richland, WA [18]. Researchers discovered that such a developing process is like developing a two-way compiler that requires the domain knowledge from specialists to be translated accurately to the semantic contents, as well as the semantic content to be decompiled as action routines for future refueling work. This two-way nature complicates the expert system development, which usually needs several rounds of iteration to completely document the specialists’ knowledge. An expert system for improving nuclear emergency response, Emergency Planner (EP), was proposed by Rensselaer Polytechnic Institute [19]. The EP system is based on the GEN-X expert system shell and the decision tree framework. It determines the emergency event level classification by asking a series of questions on plant parameters. The EP system is also expected to be a useful tool for training NPP personals by playing the “what-if” games. Introduction to more expert systems can be found in the previous literature [5]. However, as reviewed by Dr. Robert Uhrig and other experts in 1989, the pace at which these AI technologies were being applied to the real operation of nuclear facilities remained quite slow, and most proposed expert systems ended as prototypes [2,6]. In addition to the inherent drawbacks of expert systems such as difficulties in maintenance and updating, three issues impeded the implementation of these expert systems in power utility [2]. The primary concern is compatibility. Can the failure of the new system generate a challenge to the existing safety system in NPPs? Will the operator get confused by the multiple sources of information? Utilities appeared to be reluctant to introduce these expert systems until these concerns can be addressed properly. The second issue is validation and verification. For software project management, verification checks whether the designed specifications are correctly realized, and validation checks whether the software fulfills the user’s needs. NPP is a complex system with many control parameters and operation conditions. The expert systems for NPPs, especially those working on incomplete data or fuzzy logic, can have so many possible states that make it unfeasible to conduct an exhaustive test. The third issue is the human AI interaction. Specifically, two fundamental questions are worth further exploring. One is that whether users, that is, plant operators and personnel, can fully trust the evaluation and decision made by expert systems. The other one is whether users can become so dependent on the expert systems that ignore other indicators from the NPP real operating conditions. These questions become especially important when the judgment from AI does not agree with human’s judgment during emergency conditions. Although these three issues were proposed for expert systems in 1980s, current applications of machine learning to nuclear power may face very similar challenges as well.

23.4 Recent application of artificial intelligence in nuclear power plant code For the most recent rise, AI research is dominated by machine learning and big data. Machine learning algorithms use statistics to recognize correlations between data in the massive dataset in order to make predictions without being explicitly programmed to do so [20]. Popular machine learning algorithms include neural networks, decision trees, support vector machines, genetic algorithms, etc. A machine learning model is usually developed by training the model using a training dataset, that is, iteratively optimizing the model parameters to minimize the prediction errors, and evaluating the model using a test

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dataset. Among these algorithms, deep learning, literally neural networks with multiple layers, draws most attention because of its capability of automatically extracting effective classification features in high-dimensional data through its multiple processing layers [21]. Deep learning has been successfully applied to many different domains such as image recognition and is regarded as a “universal approximator” [22]. Conventionally, simulations for NPPs rely on mechanistic or semianalytical equations that often involve multiple coupled physical processes. When doing these simulations, a frequently encountered situation is that the datasets, either from experiments or simulations on prototype systems, are available but the underling equations are missing due to the complex physics. Machine learning seems to be an effective approach to develop predictive models to surrogate these mechanistic or semianalytical models. Some pioneering researches have applied this strategy to thermohydraulic and neutronic simulations. Dr. Nam Dinh and coauthors developed the data-driven thermal fluid (DTF) models [9,22,23], in which machine learning is applied to extract subgrid-scale physics models for thermal fluid simulations using data from either experimental measurements or high-fidelity simulations on a finer scale. Depending on the requirement levels for preknowledge (i.e., physical mechanisms) and training data, DTF models can be classified into five frameworks (type I V), with type I having the highest requirement for utilizing physical mechanisms and the lowest requirement for training datasets, and vice versa for type V DTF models [9]. Specifically, type I and II models were used to predict Reynolds stress for solving Reynolds-averaged Navier Stoke equations [22]. The results suggest that a substantial amount of training data is required to ensure the predictive capability of these DTF models. Type V models have also been developed to improve the accuracy of coarse-grid computational fluid dynamics (CFD) calculations. Fine-mesh CFD simulations with millions of cells can offer accurate description for an NPP component but is computationally intensive and unfeasible to scale up. Meanwhile, affordable coarse-grid CFD simulations usually contain intrinsic errors. The machine learning techniques are used to recognize the correlation between the fine-mesh and coarse-grid CFD simulation data on the same question. With such a DTF model, we will be able to get simulation results with the fine-mesh quality but at the cost of coarse-grid calculation. In other words, machine learning is applied here to construct the governing equations for calculating the errors of coarse-grid simulations using the simulation conditions as input parameters. Promising results have been obtained showing that this machine learning framework can correct the error of new coarse-grid calculations. A similar idea has also been tried for neutronics simulation [7]. Both decision trees and neutral networks are used to link the sensitivity vectors in Monte Carlo N-Particle code version 6 (MCNP6) to the calculation bias, that is, the difference between MCNP6 simulation and experimental measurement. These machine learning algorithms are able to accurately predict the bias using the sensitive vectors. In addition, the parameters in the developed decision tree model can reveal which isotopes and reactions in the MCNP6 are the leading reasons for the divergence from experimental measurements. Like expert systems for NPPs, the applications of machine learning techniques for nuclear code development also face some unique challenges. First is the data availability. Typically, a machine learning algorithm performs best when there is a large quantity of high-quality data available. The training datasets should be both relevant and comprehensive in terms of

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the physical processes we plan to learn [10,22]. Massive labeled data exits for some commercial deep learning applications such as face recognition, but it is usually not the case for NPP applications. As discussed in Ref [9]. high-fidelity simulations and high-throughput experiments can be the effective approaches to get abundant data for future machine learning research. Similar to expert systems, the second issue is code validation and verification, and the third issue is compatibility. How can we demonstrate the developed model is not overfitting? How to prove that the model successfully captures all the necessary physics? Can the failure or instability of the machine learning models affect the existing codes for the simulation, monitoring, and operation of NPPs? Machine learning models in other application fields are likely facing similar issues, and we can definitely learn from them on how to address these issues. However, the intrinsic complex nature and the high safety standard of NPPs require us to pay even more attention to these issues. Recently, the Department of Energy in United States launched the Generating Electricity Managed by Intelligent Nuclear Assets (GEMINA) program, which aims at developing real-time digital replicas of nuclear reactors based on advanced sensors and simulations tools [24]. The digital replica of a physical system is also named as the digital twin, which could provide a large amount of highquality data and also act as a reliable platform for validating machine learning algorithms. For example, the research team in University of Michigan will design a scalable digital twin of a molten salt loop to model the maintenance need of the loop. Using GE Hitachi’s BWRX300 boiling water reactor as a prototype, GB will develop operational and health digital twins to enable continuous monitoring and predictive maintenance. These ongoing researches are likely to provide more substantial examples showing how to address the challenges AI faces for NPP applications.

References [1] M. Gomez-Fernandez, K. Higley, A. Tokuhiro, K. Welter, W.K. Wong, H. Yang, Status of research and development of learning-based approaches in nuclear science and engineering: a review, Nucl. Eng. Des. 359 (2020). Available from: https://doi.org/10.1016/j.nucengdes.2019.110479. [2] R.E. Uhrig, Use of expert systems in nuclear power plant, Seoul, Korea. ,https://www.osti.gov/servlets/ purl/5853089., 1989. [3] H. Basher, Autonomous control of nuclear power plants. Oak Ridge, TN. ,https://doi.org/10.2172/885601., 2003. [4] International Atomic Energy Agency, Modern Instrumentation and Control for Nuclear Power Plants, International Atomic Energy Agency, Vienna. ,https://www.iaea.org/publications/5721/modern-instrumentation-and-control-for-nuclear-power-plants., 1999. [5] M.C. Majumdar, D. Majumdar, J.I. Sackett, International Overview. In: Artificial intelligence and other innovative computer applications in the nuclear industry, Am. Nucl. Soc. Top. Meet. Artif. Intell. Other Innov. Comput. Appl. Nucl. Ind, Plenum Press, New York, Snowbird, UT, 1988. Available from: https://doi.org/ 10.1007/978-1-4613-1009-9. [6] J.A. Bernard, Applications of artificial intelligence to reactor and plant control, Nucl. Eng. Des. 113 (1989) 219 227. Available from: https://doi.org/10.1016/0029-5493(89)90073-3. [7] P.A. Grechanuk, Using Machine Learning to Predict MCNP Bias, Los Alamos National Lab. (LANL), Los Alamos, NM, 2018. https://doi.org/10.2172/1416276. [8] B.N. Hanna, N.T. Dinh, R.W. Youngblood, I.A. Bolotnov, Machine-learning based error prediction approach for coarse-grid Computational Fluid Dynamics (CG-CFD), Prog. Nucl. Energy. 118 (2020) 103140. Available from: https://doi.org/10.1016/j.pnucene.2019.103140.

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[9] C.W. Chang, N.T. Dinh, Classification of machine learning frameworks for data-driven thermal fluid models, Int. J. Therm. Sci. 135 (2019) 559 579. Available from: https://doi.org/10.1016/j.ijthermalsci.2018.09.002. [10] H. Bao, N.T. Dinh, J.W. Lane, R.W. Youngblood, A data-driven framework for error estimation and meshmodel optimization in system-level thermal-hydraulic simulation, Nucl. Eng. Des. 349 (2019) 27 45. Available from: https://doi.org/10.1016/j.nucengdes.2019.04.023. [11] M. Gomez Fernandez, A. Tokuhiro, K. Welter, Q. Wu, Nuclear energy system’s behavior and decision making using machine learning, Nucl. Eng. Des. 324 (2017) 27 34. Available from: https://doi.org/10.1016/j. nucengdes.2017.08.020. [12] A. Kaplan, M. Haenlein, Siri, Siri, in my hand: who’s the fairest in the land? On the interpretations, illustrations, and implications of artificial intelligence, Bus. Horiz 62 (2019) 15 25. Available from: https://doi.org/ 10.1016/j.bushor.2018.08.004. [13] D. Crevier, AI: The Tumultuous History of the Search for Artificial Intelligence, Basic Books, Inc, New York, 1993. [14] M. Mcphee, K. Baker, C. Siemaszko, Deep Blue, IBM’s supercomputer, defeats chess champion Garry Kasparov in 1997, New York Daily News. ,https://www.nydailynews.com/news/world/kasparov-deepblues-losingchess-champ-rooke-article-1.762264., 2015 (accessed 13.04.20). [15] F.H. Hsu, M.S. Campbell, A.J. Hoane, Deep blue system overview, Proc. Int. Conf. Supercomput, Association for Computing Machinery, New York, 1995, pp. 240 244. Available from: https://doi.org/10.1145/ 224538.224567. [16] S.H. Liao, Expert system methodologies and applications-a decade review from 1995 to 2004, Expert. Syst. Appl 28 (2005) 93 103. Available from: https://doi.org/10.1016/j.eswa.2004.08.003. [17] J. Mott, R. King, W. Radtke, Process Diagnostics and Transient Advisor. In: A generalized system state analyzer for plant surveillance, Artif. Intell. Other Innov. Comput. Appl. Nucl. Ind, Springer, Boston, MA, 1988, pp. 241 249. Available from: https://doi.org/10.1007/978-1-4613-1009-9_30. [18] D.E. Smith, Operation Analysis AIDS. In: Documentation of knowledge in the development of Cleo, a refueling assistant for FFTF, Artif. Intell. Other Innov. Comput. Appl. Nucl. Ind, Springer, Boston, MA, 1988, pp. 607 609. Available from: https://doi.org/10.1007/978-1-4613-1009-9_73. [19] A. Salame-Alfie, G.C. Goldbogen, R.M. Ryan, W.A. Wallace, M.L. Yeater, Emergency Response. In: An expert system for improving nuclear emergency response, Artif. Intell. Other Innov. Comput. Appl. Nucl. Ind, Springer, Boston, MA, 1988, pp. 205 212. Available from: https://doi.org/10.1007/978-1-4613-1009-9_26. [20] J.R. Koza, F.H. Bennett, D. Andre, M.A. Keane, Genetic Algorithms/Genetic Programming in Design. In: Automated design of both the topology and sizing of analog electrical circuits using genetic programming, Artif. Intell. Des, 96, Springer, Dordrecht, 1996, pp. 151 170. Available from: https://doi.org/10.1007/97894-009-0279-4_9. [21] Y. Lecun, Y. Bengio, G. Hinton, Deep learning, Nature 521 (2015) 436 444. Available from: https://doi.org/ 10.1038/nature14539. [22] C.-W. Chang, J. Fang, N.T. Dinh, Reynolds-averaged turbulence modeling using deep learning with local flow features: an empirical approach, Nucl. Sci. Eng (2020) 1 15. Available from: https://doi.org/10.1080/ 00295639.2020.1712928. [23] Y. Liu, X. Sun, N.T. Dinh, Validation and uncertainty quantification of multiphase-CFD solvers: a datadriven Bayesian framework supported by high-resolution experiments, Nucl. Eng. Des. 354 (2019) 110200. Available from: https://doi.org/10.1016/j.nucengdes.2019.110200. [24] ,https://arpa-e.energy.gov/sites/default/files/documents/files/GEMINA_Project_Descriptions_FINAL.pdf.

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C H A P T E R

24 Temporal data mining in nuclear site monitoring and in situ decommissioning Z.J. Sun1 and A. Duncan2 1

Department of Health Physics and Diagnostic Science, University of Nevada Las Vegas, Las Vegas, NV, United States 2Material Sciences and Technology, Savannah River National Laboratory, Aiken, SC, United States

24.1 Introduction Big Data, a concept widely popular nowadays, is defined as extremely large and complex data sets that need to be analyzed computationally to reveal patterns, trends, and associations and is difficult to process using noncomputational methods [1]. Temporal data mining (TDM) is an active and rapidly evolving area in big data science. In 2006 Laxman and Unnikrishnan first gave a complete survey on TDM theories and developed new algorithms to discover frequency episodes in the event stream [2,3]. The proposed new algorithms are, both space-wise and time-wise, significantly more efficient than the earlier algorithms [4]. These novel TDM techniques soon found their applications in neuronal network studies and the automobile industry [5
7]. A few years ago, Savannah River National Laboratory (SRNL) established an in situ decommissioning (ISD) Sensor Network Test Bed, a unique, small-scale, and configurable environment, for the assessment of prospective sensors on the actual ISD system [8
10]. The ISD sensor network, just like an automobile assembly line, generates a large amount of data with sequential time stamps [2]. During the years of 2010
14 a large data set was collected with the effort of obtaining baseline data [11]. Is it possible to borrow the concepts and algorithms of TDM and apply them to nuclear site monitoring and ISD research? Since all the data collected from the ISD Test Bed are time-specific, age-specific, and development stage-specific, they are ideal for TDM analysis to validate system performance and reveal unknown patterns of material failure, liquid leaking, and radiation field changing.

Nuclear Power Plant Design and Analysis Codes DOI: https://doi.org/10.1016/B978-0-12-818190-4.00024-3

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Copyright © 2021 Elsevier Ltd. All rights reserved.

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In this chapter, we first discuss the concept of frequent episodes and the algorithms used to discover them, as well as the experimental setup in the ISD Sensor Network Test Bed. Then, the TDM algorithms were applied to the baseline data collected by the test bed from 2011 to 2014, for the purpose of finding the frequent episodes patterns and any abnormalities prior to any sudden physical changes in the system. The results have demonstrated the feasibility of using TDM to validate ISD system performance. Some abnormal patterns may have the potential for prediction of system failures.

24.2 Theoretical: Frequent episode and discovery algorithms For the ISD Sensor Network Test Bed, all collected data can be viewed as a long single sequence of ordered pairs ðEi ; ti Þ, which are called “events.” In each event ðEi ; ti Þ, Ei is referred to as an event type and ti is the time of occurrence. The data can be referred to as an event sequence (or event stream). The temporal patterns referred to as episodes are ordered collections of event types. For example, (A-B-C) denotes a temporal pattern where an event type A is followed (sometime later) by a B and a C in order. When events of appropriate types appear in the data sequence in the same order, these events are said to constitute an occurrence of the episode. Fig. 24.1 shows the most common types of episodes encountered in practice. Frequent episodes are the episodes that occur sufficiently often along the event sequence. The frequent episode framework aims to discover all episodes that occur often in the data [12]. Initially, sliding windows (or some fixed-width) over the data sequence were considered as the method to discover episodes. The frequency of an episode is defined as the number of such windows in which the episode is found to occur at least once (multiple occurrences of an episode in a window have no effect on the frequency). The importance of this frequency definition is that whenever a window contains an episode [say (A-B-C)], it also contains all of its subepisodes [like (A-B), (A-C)]. Thus all subepisodes are at least as frequent as the corresponding episodes. For an episode to be frequent (i.e., for its frequency to exceed the user-defined threshold), all its subepisodes must be frequent as well. This allows us to set up a level-wise search for all frequent episodes in the data, starting from the smallest episodes and then combining them to obtain the frequent FIGURE 24.1 Types of episodes: (A) serial episode, chained events; (B) parallel episode, synchronized events; (C) neither serial nor parallel episode, synfire-chain events.

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episodes of progressively larger sizes. Such procedure is an essentially temporal equivalent of the Apriori algorithms for obtaining frequent sets of items in unordered databases [13,14].
 Consider an N-node episode α 5 Vα ; , α ; gα where Vα 5 fv1 ; . . . ; vN g. Two occurrences, h1
 ’v and h2 , of the episode α are said to be nonoverlapped if, either (1) h ð v Þ . h v ; v AV 2 i 1 j i j α
 or (2) h1 ðvi Þ . h2 vj ’vi ; vj AVα . A collection of occurrences of α is said to be nonoverlapped if every pair of occurrences in it is nonoverlapped. The corresponding frequency F for episode α is defined as the cardinality of the largest set of nonoverlapped occurrences of α in the given event sequence. The algorithms to count F of the nonoverlapped episodes in serial/parallel episodes are described in Table 24.1. Details of other algorithms can be found in Ref. [2]. A set of significant frequent episodes associated with each target event type is obtained based on formal connections between frequent episodes and hidden Markov models TABLE 24.1

Algorithms for typical nonoverlapped episodes in serial/parallel episodes.

1. Algorithm for nonoverlapped count for serial episodes  Input: Set C of candidate N-node serial episodes, event stream s 5 , ðE1 ; t1 Þ; . . . ðEn ; tn . , frequency threshold λmin A½0; 1 Output: The set F of frequent serial episodes in C 1 for all event types A do 2 Initialize waitðAÞ 5 φ 3 for all αAC do 4 Add (α, 1) to waitðα½1Þ 5 Initialize α:freq 5 0 6 Initialize bag 5 φ 7 for i 5 1 to n do / * n is length of data stream */ 8 for all (α; j) A waitðEi Þ do 9 Remove (α; j) from waitðEi Þ 10 Set j0 5 j 1 1 11 if j0 5 ðN 1 1Þ then 12 Set j0 5  1 13 if α j0
5 Ei then 14 Add α; j0 to bag 15 else
 16 Add α; j0 to waitsðα½j0 Þ 17 if j 5 N then 18 Update α:freq 5 α:freq 11 19 Empty bag into waitsðEi Þ 20 Output F 5 fαAC such that α:freq $ nλmin } 2. Algorithm for nonoverlapped count for serial episodes  Input: Set C of candidate N-node serial episodes, event stream s 5 , ðE1 ; t1 Þ; . . . ðEn ; tn . , frequency threshold λmin A½0; 1 Output: The set F of frequent serial episodes in C 1 2 3 4 5

for all event types A do Initialize waitðAÞ 5 φ for all αAC do for each event type A in α do Set a 5 number of events of type A in α (Continued)

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TABLE 24.1 (Continued) 6 Add (α, a) to waitðAÞ 7 Initialize α:freq 5 0 8 Initialize α:counter 5 0 9 Initialize bag 5 φ 10 for i 5 1 to n do 11 for all (α; j) A waitðEi Þ do 12 Update α:counter 5 α:counter 11 13 Remove (α; j) from waitðEi Þ 14 if j .
1 then  15 Add α; j0 to bag 16 if α:counter 5 N then 17 Update α:freq 5 α:freq 11 18 Reset α:counter 5 0 19 For each event type A in α do 20 Set a 5 number of events of type A in α 21 If A 5 Ei then 22 Add ðα; aÞ to bag 23 else 24 Add ðα; aÞ to waitsðAÞ 25 Empty bag into waitsðEi Þ 26 Output F 5 fαAC such that α:freq $ nλmin } 3. Nonoverlapped count with expiry times (serial episodes)  Input: Set C of candidate N-node serial episodes, event stream s 5 , ðE1 ; t1 Þ; . . . ðEn ; tn . , frequency threshold λmin , expiry time TX Output: The set F of frequent serial episodes in C 1 for all event types A do 2 Initialize waitðAÞ 5 φ 3 for all αAC do 4 Add (α, 1) to waitðα½1Þ 5 Initialize α:freq 5 0 6 Initialize bag 5 φ 7 for i 5 1 to n do 8 for all (α; j) A waitðEi Þ do 9 if j 5 1 then   10 update α:init j 5 ti 11 else    12 Update α:init j 5 α:init j 2 1 13 Remove (α; j) from waitðEi Þ 14 if j ,  N then  15 if α j
1 1 5 Ei then 16 Add α; j 1 1 to bag 17 else 18 Add ðα; 1 1Þ
to waitsðα½j  1  1Þ 19 if j 5 N and ti 2 α:init j # TX then 20 Update α:freq 5 α:freq 11 21 For all 1 # k , jαj do 22 Empty bag into waitsðα½k 1 1Þ 23 Remove ðα; k 1 1Þ from bag 24 Empty bag into waitsðEi Þ 25 For all αAC such that α:freq $ λmin do 26 Add α to the output F (Continued) VII. Special or new direction

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TABLE 24.1

557

(Continued) 4. Noninterleaved count for serial episodes

 Input: Set C of candidate N-node serial episodes, event stream s 5 , ðE1 ; t1 Þ; . . . ðEn ; tn . , frequency threshold λmin A½0; 1 Output: The set F of frequent serial episodes in C 1 for all event types A do 2 Initialize waitðAÞ 5 φ 3 for all αAC do 4 Add (α, 1) to waitðα½1Þ 5 Initialize α:freq 5 0 6 Initialize bag 5 φ 7 for i 5 1 to n do / * n is length of data stream */ 8 for all (α; j) A waitðEi Þ do 9 if j , 
N then  10 if α; j 1 1
2 = waitsðα½j 1 1 then  11 Remove   α; j from waitsðEi Þ 12 if α j
1 1 5 Ei then 13 Add α; j 1 1 to bag 14 else
  15 Add α; j 1 1 to waitsðα½j 1 1 16 If j 5 1 then 17 Add ðα; 1Þ to bag 18 if j 5 N then 19 Remove (α; j) from waitðEi Þ 20 Update α:freq 5 α:freq 11 21 Empty bag into waitsðEi Þ 22 Output F 5 fαAC such that α:freq $ nλ min }

(HMMs), and a mixture of such HMMs is used to estimate the likelihood for every target event type. The posterior probability P½DY jΛY  follows the equation: 0 1 J h i K K X P½DY jΛY  5 L P½Xi jΛY  5 L @ θj P Xi jΛαj A i51

i51

j51

where DY 5 fX1 ; X2 ; . . . ; XY g is a set of Y event sequences that constitute our data set. P θj , j 5 1; ::; J are the mixture coefficients of ΛY (with θj A½0; 1’j and Jj51 θj 5 1) [2]. The abovementioned algorithms of frequent episode discovery framework and HMM models are implemented along with temporal constraints by a computer program called TDMiner (see Fig. 24.2). TDMiner is a TDM tool that mines frequent episodes from a long sequence of events. The program has two versions (Java and C11) and provides a suite of mining techniques for different types of frequent episodes. It also has tools for visualizing the results obtained from mining. The current version of TDMiner is inherited from the Gminer program of General Motor, which was used to search the frequency episodes in automobile assembling lines in Michigan and an online catalog of Amazon.com [15]. The original code of the program can be obtained at the Github website [16]. To adapt the TDM analysis in ISD Sensor Network Test

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Bed, some original codes were modified. The code was recompiled in Eclipse 4.6 (Neon) for Java version 8.151 environment. These modifications significantly reduced the frequent episode searching time and improved the performance of the TDMiner program.

24.3 Computational: Application of TDMiner TDMiner is a frequent episode mining tool useful to find interesting patterns or trends in large sequential data sets (Fig. 24.2). This tool can be used to find frequent episodes in large sequential data sets. It offers a choice of different frequency measures and the associated candidate generation strategies. It can be used to mine both serial and parallel episodes. Further, mining can be carried out with a variety of time constraints on the episodes. For example, constraints can be placed on the time span of the episode, or time interval between two consecutive events in an episode, etc. This tool can also be used for visualization of the data sequence and the episodes embedded in it. There are four simulator models to generate data sequences with embedded frequent episodes in it. Three of them are modeled to simulate multineural spike data and the fourth one is a generic data generator. The user interface of this tool has four main tabs: Event Sequence Loader, Frequent Episode Miner, Visualization, and Simulators. The working of this tool is explained by explaining the functionalities under each of these tabs.

FIGURE 24.2 TDMiner 2.0 was recompiled and running on the server (tdminer.scsu.edu) with the capability of multicore parallel computing.

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24.3.1 User interfaces of TDMiner The event file that is to be loaded should be in CSV (comma-separated value) format. Each event is represented by the name of the event type followed by the time of occurrence in a new line. For generalized event streams, each line would have the event type, start time, and end time separated by commas. Example: Normal event sequence

Generalized event sequence

A, 2

A, 2, 6

B, 3

B, 4, 7

F, 7

G, 7, 11

To load the event stream specify the path in the text box provided for “Event sequence file name.” (The screenshot of the interface is given next), or click the button to browse and select the file. As soon as the file is loaded, the number of occurrences for each event type is presented automatically in the table at the left-hand side along with the histogram plot in the graph at the right-hand side of the window. Click the “Suggest Threshold” button to automatically obtain a frequency threshold. The frequency threshold is calculated from the histogram such that events that occur frequently are separated from events that occur sparsely. The “Reset” button restores the original magnification of the histogram plot (Fig. 24.3). The tab “Frequent Episode Miner” allows for the mining of different types of episodes with or without temporal constraints. Here, one has to choose the algorithm and various parameters needed by the algorithm. The drop-down menu gives the list of frequency counting algorithms is shown in Fig. 24.4. The frequency counting algorithms we applied most are • Serial Episode Discovery • Fast Non-overlapped count(Serial) • Non-overlapped count with episode expiry constraint(Serial) • Non-overlapped count with interevent expiry constraint(Serial) • Non-overlapped count with interevent interval constraint(Serial) • Discovery of episodes & interevent intervals(Serial) • Parallel Episode Discovery • Non-overlapped count(Parallel) • Non-overlapped count with episode expiry constraint(Parallel) 1. Fast Non-overlapped count(Serial): This allows for fast mining of serial episodes. However, this algorithm will not allow any temporal constraints to be imposed. The following steps are to be followed to mine episodes using this algorithm: a. Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.”

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FIGURE 24.3

The Event Sequence Loader tab of the TDMiner.

FIGURE 24.4

Dropdown menu of Frequent Episode Miner tab.

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b. Choose the “Fast Non-overlapped count(Serial)” algorithm and the corresponding candidate generation algorithm “Apriori candidate generation(Serial)” gets automatically selected. c. Uncheck the “Allow repeated event types” option to avoid mining of episodes that have repeated events. d. Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for onenode episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set by clicking the “Suggest Threshold” button in “Event Sequence Loader”). e. Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from two-node episode onward. (The default value is 1.) f. Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.) g. Click the “Start mining” button to get the list of frequent episodes of different sizes. h. Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. Uncheck the “Show all cyclic permutations” option to avoid listing of episodes which are cyclic permutation of another frequent episode (Fig. 24.5).

FIGURE 24.5 Fast Non-overlapped count(serial) in TDMiner.

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2. Non-overlapped count with episode expiry constraint(Serial): This algorithm mines only those episodes that satisfy the episode expiry constraint specified. In any occurrence of an episode the difference between the times of the last and first events constituting this occurrence is called the span of the occurrence. Under the episode expiry constraint, only those occurrences, the span of which is less than or equal to the expiry time specified by the user, would be counted. The following steps are to be followed to mine episodes using this algorithm: • Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.” • Choose the “Non-overlapped count with episode expiry constraint(Serial)” algorithm and the corresponding candidate generation algorithm “Apriori candidate generation (Serial)” gets automatically selected (Fig. 24.6). • Uncheck the “Allow repeated event types” option to avoid mining of episodes that have repeated events. • Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for one-node episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set using “Suggest Threshold” button in “Event Sequence Loader.”)

FIGURE 24.6

Non-overlapped count with episode expiry constraint(Serial) in TDMiner.

VII. Special or new direction

24.3 Computational: Application of TDMiner

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• Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from two-node episode onward. (The default value is 1.) • Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.) • Enter the value of “Episode expiry.” This specifies the maximum span of an episode. • Click the “Start mining” button to get the list of frequent episodes of different sizes. • Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. Uncheck the “Show all cyclic permutations” option to avoid listing of episodes which are cyclic permutation of another frequent episode. 3. Non-overlapped count with interevent expiry constraint(Serial): This algorithm mines episodes with interevent expiry constraint. The constraint here specifies the maximum allowable time between the successive events of the episode. Suppose (A, t1), (B, t2), and (C, t3) constitute an occurrence of the serial episode (Aa`Ba`C), then (t2 2 t1) and (t3 2 t2) are the interevent times for this occurrence. Under interevent expiry constraint an occurrence is counted only if the interevent times are less than or equal to the Interval Expiry time specified by the user. The following steps are to be followed to mine episodes using this algorithm: • Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.” • Choose the “Non-overlapped count with interevent expiry constraint(Serial)” algorithm and the corresponding candidate generation algorithm “Prefix-suffix candidate generation” gets automatically selected. • Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for one-node episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set using “Suggest Threshold” button in “Event Sequence Loader.”) (Fig. 24.7) • Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from two-node episode onward. (The default value is 1.) • Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.) • Enter the value of “Interval Expiry.” The interevent times in all occurrences of the episode that are counted would be less than or equal to this value. • Click the “Start mining” button to get the list of frequent episodes of different sizes. • Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. Uncheck the “Show all cyclic permutations” option to avoid listing of episodes which are cyclic permutation of another frequent episode. 4. Non-overlapped count with interevent interval constraint(Serial): This algorithm mines serial episodes with an interval constraint for interevent times. The constraint is specifies an interval for interevent times. In all occurrences counted by the algorithm the interevent times would be in this interval. Unlike the interevent expiry constraint where we have only an upper bound on the interevent times, here we have

VII. Special or new direction

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FIGURE 24.7

24. Temporal data mining in nuclear site monitoring and in situ decommissioning

Non-overlapped count with interevent expiry constraint(Serial) in TDMiner.

both an upper bound and a lower bound for interevent times. The following steps are to be followed to mine episodes using this algorithm: • Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.” • Choose the “Non-overlapped count with interevent interval constraint(Serial)” algorithm and the corresponding candidate generation algorithm “Prefix-suffix candidate generation” gets automatically selected. • Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for one-node episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set using “Suggest Threshold” button in “Event Sequence Loader.”) • Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from two-node episode onward. (The default value is 1.) • Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.) • Enter the lower and higher value of “Interval Expiry.” In every occurrence of the episode counted by the algorithm, the interevent times would be in this interval.

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24.3 Computational: Application of TDMiner

565

FIGURE 24.8 Non-overlapped count with interevent interval constraint(Serial) in TDMiner.

• Click the “Start mining” button to get the list of frequent episodes of different sizes. • Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. Uncheck the “Show all cyclic permutations” option to avoid listing of episodes, which are cyclic permutation of another frequent episode (Fig. 24.8). 5. Discovery of episodes & interevent intervals(Serial): This algorithm not only discovers frequent episodes but also discovers the interevent intervals with which consecutive events in the episode occur frequently. Suppose Aa`Ca`D is a frequent episode, which means that, often, A is followed sometime later by C, which is followed by D. The interevent times in these occurrences might also be following a pattern depending upon the nature of the process generating the data. If the timing information between consecutive events is also of interest, then this algorithm is to be used. A list of intervals has to be entered, which denote all the possible interevent interval constraints. (These may be guessed with some knowledge of the data or the process generating the data.) The output will be a list of frequent episodes along with an interval for every interevent time. Each such interval would be one of the intervals specified by the user. Suppose the set of intervals specified are (0
5), (5
10), and (10
20), then, one of the output frequent episodes could be A (0
5)- B (10
20)-C. This means that there are a sufficiently

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FIGURE 24.9

24. Temporal data mining in nuclear site monitoring and in situ decommissioning

Discovery of episodes & interevent intervals(Serial) in TDMiner.

large number (depending on the frequency threshold) of occurrences of A-B-C with the interevent times between A and B being in the interval (0,5) and the interevent times between B and C being in the interval (10,20). The algorithms searching for the interval possibilities only work among the intervals specified as part of input by the user. The following steps are to be followed to mine episodes using this algorithm (Fig. 24.9). • Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.” • Choose the “Discovery of episodes & interevent intervals(Serial)” algorithm and the corresponding candidate generation algorithm “Candidate generation for interval discovery” gets automatically selected. • Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for one-node episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set using “Suggest Threshold” button in “Event Sequence Loader.”) • Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from two-node episode onward. (The default value is 1.) • Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.)

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24.3 Computational: Application of TDMiner

567

• Click the “Enter Intervals” button to enter the intervals in a new window. Enter the “T_low” and “T_high” value of the interval and click “Add” button to enter the interval. To remove an already added interval uncheck, the checkbox corresponding to that interval. Finally click “Ok” button after all the intervals have been entered. • Click the “Start mining” button to get the list of frequent episodes of different sizes along with the discovered interevent times. • Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. 6. Non-overlapped count(Parallel): All the algorithms considered so far are for serial episodes. This algorithm discovers frequent parallel episodes. The frequency measure is the number of nonoverlapped occurrences. Recall that in a parallel episode the events constituting an occurrence can be in any temporal order. The following steps are to be followed to mine parallel episodes using this algorithm (Fig. 24.10). • Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.”

FIGURE 24.10

Non-overlapped count(Parallel) in TDMiner.

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24. Temporal data mining in nuclear site monitoring and in situ decommissioning

• Choose the “Non-overlapped count(Parallel)” algorithm and the corresponding candidate generation algorithm “Apriori candidate generation(Parallel)” gets automatically selected. • Uncheck the “Allow repeated event types” option to avoid mining of episodes, which have repeated events. • Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for one-node episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set by clicking the “Suggest Threshold” button in “Event Sequence Loader”.) • Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from two-node episode onward. (The default value is 1.) • Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.) • Click the “Start mining” button to get the list of frequent episodes of different sizes. • Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. Uncheck the “Show all cyclic permutations” option to avoid listing of episodes, which are cyclic permutation of another frequent episode. 7. Non-overlapped count with episode expiry constraint(Parallel): This algorithm mines parallel episodes with an episode expiry constraint specified. The constraint specifies the maximum allowable time between the first and last events constituting an occurrence of the episode. The following steps are to be followed to mine parallel episodes using this algorithm: • Load the data sequence using “Event Sequence Loader” or generate a data sequence using an appropriate model in “Simulators.” • Choose the “Non-overlapped count with episode expiry constraint(Parallel)” algorithm and the corresponding candidate generation algorithm “Apriori candidate generation (Parallel)” gets automatically selected. • Uncheck the “Allow repeated event types” option to avoid mining of episodes that have repeated events. • Enter the values of “Freq. Th. (1 node),” which is the frequency threshold used for one-node episodes, and “Freq. Th.,” which is the frequency threshold used for episodes with more than one node. (These values can be automatically set by clicking the “Suggest Threshold” button in “Event Sequence Loader”.) • Enter the value of “Th. decay factor.” The frequency threshold gets decayed by this factor after every iteration from a two-node episode onward. (The default value is 1.) • Enter the value of “Max. Episode size.” It is the maximum size of the episode that will be mined. (The default value is 10.) • Enter the value of “Episode expiry.” This specifies the maximum span of an episode. • Click the “Start mining” button to get the list of frequent episodes of different sizes. • Click the “Save episodes” button to save the list of frequent episodes onto a file. Click the “Clear Episodes” button to clear the list of frequent episodes. Uncheck the “Show all cyclic permutations” option to avoid listing of episodes, which are a cyclic permutation of another frequent episode (Fig. 24.11).

VII. Special or new direction

24.3 Computational: Application of TDMiner

FIGURE 24.11

569

Non-overlapped count with episode expiry constraint(Parallel) in TDMiner.

24.3.2 Verification and validation of TDMiner The verification and validation of TDminer were conducted by two methods: internal validation and external or experimental validation. 1. The data generator and simulators of the program realized internal validation. Synthetic data streams with embedded frequent episodes in it can be generated using these simulators. The three models available for data generation are Simulator Model 1, Simulator Model 11, and Poisson Model. The data generator is a generic data synthesizer, which generates data having frequent episodes (with temporal constraints) embedded in randomly generated data. This is meant for generic synthetic data generation (i.e., not specific to model multineural spike data) synthetic. A pattern to be embedded is specified by a set of event types and the interevent times. The following steps are to be followed to generate data to validate the program (Fig. 24.12). • Enter the list of labels given to the neurons in the space given beside “Event Types (space separated).” • Enter the episodes that have to be embedded have in the space given beside “Episode” in the following format A(T1, ΔT1)-B(T2, ΔT2)-C(T3, ΔT3). Here B occurs in the interval [T2, T2 1 ΔT2] after A has occurred. Similarly, C occurs after B and A after C within the respective specified intervals.

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570

FIGURE 24.12

24. Temporal data mining in nuclear site monitoring and in situ decommissioning

Internal validation with data generator of TDMiner.

• Instead of entering the episode directly in the abovementioned format, the episode can be constructed by entering the “Event Type,” “Delay”(T), and “Variability”(ΔT) and adding the event by clicking the “Add” button. • Click the “Add” button beside “Episode” to add the episode to the episode list. • Enter the value of “Noise Prob.”. This the probability with which a random event occurs in data stream if no event of an episode is scheduled at the present clock. • Enter the value of “Data Length,” which specifies the length of the data sequence. • Click the “Generate Sample” button to generate a sample sequence. The episodes will be highlighted in the event sequence that is shown in the text box. • Click the “Generate Sequence” button to load the generated data stream. With data generators and simulators the program can automatically create data streams to verify and validate the frequency episode discover framework described before. 2. External or experimental validation. The current version of TDMiner is inherited from the Gminer program of General Motor, which was used to search the frequency episodes in automobile assembling lines in Michigan and an online catalog of Amazon.com [15]. In the study of General Motors the stamping plant data consist of a sequence of event codes that describe the dynamical status of a stamping line that makes automotive body parts. The faults logged are first partitioned based on the physical layout

VII. Special or new direction

24.4 Experimental: In situ decommissioning Sensor Network Test Bed and data collection

571

of machines in the plant, to obtain fault sequences that can be subjected to TDM analysis. The frequent episode discovery algorithms are run on these sequences and the significant frequent episodes (or fault correlations) reported to the plant engineers to assist them in fault diagnosis. The algorithms have been incorporated into a fault diagnosis toolbox in one of GM’s engine manufacturing plants. The data mining algorithms were able to unearth interesting and unexpected fault correlations that were deemed useful. The performance of these algorithms was assessed on historic data. Based on this, the method was considered useful by the plant engineers as an aid for routine troubleshooting on the work floor. It was reported one example of a pattern discovered during historic data analysis, which influenced the decision to use this technique as a fault diagnosis tool on a regular basis [15]. Another interesting aspect of our data mining framework is that there is no need for any detailed modeling of the underlying manufacturing process. Apart from some heuristics based on the plant engineers’ experience, there is no need to use any other detailed knowledge of the data generation process. This advantage is highlighted in another example result reported, where the root cause of a problem was in a new machine that was installed in the plant, the characteristics of which were not yet known to the plant engineers. A similar case of experimental validation was reported in the data analysis of the historical data of the ISD Sensor Network Test Bed (see the next section). The number of extrema events created by four thermocouples (T3, T2, T4, and T1) is 18,125; 8845; 5203; and 2040, which show the T3 thermocouple is the most sensitive sensor in temperature measurement. If limited by the 12-hour time constraint, in all events from four thermocouples (T1H, T1L, T2H, T2L, T3H, T3L, T4H, T4L), TDMiner shows that the most frequent episodes in the event stream are “T3H-T2H-T4H-T1H” and “T3L-T2L-T4L-T1L,” which had 618 and 629 cases, respectively, within 6 months. These two frequency episodes and their orders in the event chain verified the experimental setup of the ISD senor test bed: T3, the most sensitive to temperature change, is outside and located on the aluminum frame; T2 and T1 are reluctant and were cemented in about 2-in. block responding slower, while the last one T4 is buried about 4 in. inside and supposed to be the last one to respond in the time consequence. However, before we use the TDM technique, we do not know that T1 is the most delay response one. When these frequent episodes dig out, the technician went back to check the experimental setup and found that there was air gap existed in cement with thermocouple 1. Both cases at General Motors and ISD Sensor Network Test Bed indicated that TDM can be used to discover some temporal patterns of interest to the researchers and engineers. TDM can unearth useful (nontrivial) information that was previously unknown to the data owner.

24.4 Experimental: In situ decommissioning Sensor Network Test Bed and data collection During the last decade the Office of Environmental Management at the Department of Energy (DOE-EM) focused on reducing the footprint of over 60 years of nuclear research

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24. Temporal data mining in nuclear site monitoring and in situ decommissioning

and weapons testing/production. Although these nuclear facilities are no longer operational today, they are still carrying various degrees of radiation contamination resulting from years of operation. To completely close down these facilities, a cost-effective practice is to dispose of the facilities in place (i.e., in situ) and permanently entomb a portion of a structure, or the entire structure, with its contaminants. The contaminants would be bound to the structure via a grout material that used to fill voids in the entombed structure. This ISD can safely trap contaminants and significantly reduce the cost of demolition, removal of the structure, transportation, and disposal. In order to monitor whether the entombed structure maintains the proper “health” to trap contaminants, a complex sensor network must be deployed during the grout filling. This network is supposed to monitor the structure continuously and reliably for many years in the future. The P-Reactor at Savannah River Site started running on February 2, 1954, and played a significant role in the discovery of neutrinos [17]. This reactor was operated until 1988 when it was shut down (see Fig. 24.13). The facility was identified by DOE-EM as a place to implement ISD approaches. It needs to be partially demolished, and the remainder of the below grade structure will be filled with over 100,000 cubic yards of grout fill. To address the technical need for incorporating a monitoring system into this ISD facility identified in Technical Task Plan SR-09-17-01 [18], scientists at SRNL have established an ISD Sensor Network Test Bed based on two concrete blocks removed from the outer wall of the P-Reactor Building (see Fig. 24.14). The size of Block A was 880 (length) 3 360 (width) 3 410 (height), and the size of Block B was 36 0 (length) 3 360 (width) 3 43.50 (height). Three types of commercial off-the-shelf sensors from RocTest were tested on this Sensor Network Test Bed: temperature sensors, biaxial tiltmeters, and surface-mount vibrating wire strain gauges [19]. The specifications of these

FIGURE 24.13

P-Reactor in operation days at the Savannah River Site.

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24.4 Experimental: In situ decommissioning Sensor Network Test Bed and data collection

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FIGURE 24.14 Dashboard used to display user-specified data. The dashboard was based on a picture of the ISD Sensor Network Test Bed. In the middle is the structural frame holding multiplexer, data logger, and solar panel and controller units.

sensors are listed in Table 24.2. The blocks and sensors were placed in the field on a concrete pad along with an 8
20 aluminum frame that housed the multiplexers, data logger, and solar panel controller. Sensors’ power was provided by a Sun-Saver-6 Photovoltaic Controller attached to a 50 W Kyocera solar panel, which charged a 12 V battery. Sensor cables from the blocks were threaded back through the frame structure to the multiplexers, which were connected in parallel to the CR1000 logger. The sensors were wired to three multiplexer units, two of which allowed a maximum of 16 separate sensors and the third one allowed a maximum of 8 sensors to be connected. The three multiplexer units were connected in parallel to a CR1000 logger, which gave a total capacity of 40 sensor connections. The data logger used the NL115 Ethernet and CompactFlash module, which enabled the use of an Ethernet port for remote connectivity and allowed up to a 2 GB CompactFlash memory card to be connected for data storage. If all 40 sensors were activated and gathered data points each hour, the logger could hold a maximum of 35,900 days of data before reaching its capacity. Fig. 24.14 indicates the custom dashboard to display the data retrieved from the sensors in a format that can easily be read by users. Since the background is the picture of the test bed, users can easily attribute data values to the physical location of the sensors on the concrete blocks. The data logger was connected to a wired network via the NL115 module and existed

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24. Temporal data mining in nuclear site monitoring and in situ decommissioning

TABLE 24.2 Sensors and their specifications for sensor network test bed at Savannah River National Laboratory. Sensor type

Temperature sensors

Biaxial tiltmeter

Vibrating wire strain fauges

Model

TH-T

TUFF TILT 801s

SM-5A

Range



6 3 degrees

3000 με



250 C to 1150 C 

Resolution

0.1 C

0.0006 degrees (10.5 μradian)

1 με (min) with MB-3TL

Accuracy/ repeatability

6 0.5% F.S.

0.001 degree

1/ 2 0.5% F.S.

Thermistor

3 kΩ

N/A

Operation temperature

N/A



225 C to 170 C

220 C to 180 C

Numbers installed

5

2

5

Function

Temperature monitoring and moisture migration

Expansion of cracks, monitoring structural movement

Strain change detection

Remarks

PVC cylindrical housing, anchored with Quickret Bonding Adhesive

Epoxyed to the surface of the concrete blocks

Surface mount, attached across a preexisting crack

3 kΩ 

on an extended VLAN (Virtual Local Area Network) of SRSNet, which allowed remote access to data retrieval and administration. The data acquisition server was running a Red Hat Linux 5 system. An Enterprise DB system in the server retrieved the data from the logger on an hourly basis. Custom scripts written by Python were employed to read, parse, and insert the data into a PostgreSQL database on the server. The raw data were available via a desktop program, which allowed the user to specify a range of dates and sensor types. All the historical/baseline data of the test bed in this paper were retrieved from the server in CSV format.

24.5 Data analysis and discussions The baseline raw data from ISD Sensor Network Test Bed were collected continuously from June 2011 to January 2014. It has 273,078 records of battery information (voltage and local temperature), strain information (strains of two blocks and the corresponding local temperatures at the locations of strain gauges), temperature information of four thermocouples epoxied inside the two concrete blocks, and tiltmeter data (tilt degrees and local temperatures of tiltmeters). The units are Volt, Celsius, angle degrees, μstrains, respectively. All of the records are time stamped in the format of “mm:dd:yyyy hh:mm.” Data points were collected in 5 min interval. Most of the data points were continuous except the days when the system was turned off for troubleshooting. The column structure of the data table is shown in Table 24.3.

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24.5 Data analysis and discussions

TABLE 24.3

The columns in the in situ decommissioning data table.

Column

Unit

Function

Sensor origin

Time stamp

Mm/dd/yyyy hh:mm

1

Voltage of battery

Volts

2

Battery

Temperature of battery

Celsius

3

Battery

SM5A_LU(1)

μstrain

4

Strain gauge

SM5A_LU(2)

μstrain

5

Strain gauge

SM5A_LU(3)

μstrain

6

Strain gauge

SM5A_LU(4)

μstrain

7

Strain gauge

SM5A_LU(5)

μstrain

8

Strain gauge

SM5A_T(1)

Celsius

9

Strain gauge temperature

SM5A_T(2)

Celsius

10

Strain gauge temperature

SM5A_T(3)

Celsius

11

Strain gauge temperature

SM5A_T(4)

Celsius

12

Strain gauge temperature

SM5A_T(5)

Celsius

13

Strain gauge temperature

THT1

Celsius

14

Temperature sensor 1

THT2

Celsius

15

Temperature sensor 2

THT3

Celsius

16

Temperature sensor 3

THT4

Celsius

17

Temperature sensor 4

Tilt_Xd(1)

Angle deg

18

Tiltmeter X

Tilt_Xd(2)

Angle deg

19

Tiltmeter X

Tilt_Xd(3)

Angle deg

20

Tiltmeter X

Tilt_Xd(4)

Angle deg

21

Tiltmeter X

Tilt_Yd(1)

Angle deg

22

Tiltmeter Y

Tilt_Yd(2)

Angle deg

23

Tiltmeter Y

Tilt_Yd(3)

Angle deg

24

Tiltmeter Y

Tilt_Yd(4)

Angle deg

25

Tiltmeter Y

Tilt_T(1)

Celsius

26

Tiltmeter temperature

Tilt_T(2)

Celsius

27

Tiltmeter temperature

Tilt_T(3)

Celsius

28

Tiltmeter temperature

Tilt_T(4)

Celsius

29

Tiltmeter temperature

Tilt_X(1)

Degrees

30

Tiltmeter X

Tilt_X(2)

Degrees

31

Tiltmeter X (Continued)

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TABLE 24.3 (Continued) Column

Unit

Function

Sensor origin

Tilt_X(3)

Degrees

32

Tiltmeter X

Tilt_X(4)

Degrees

33

Tiltmeter X

Tilt_Y(1)

Degrees

34

Tiltmeter Y

Tilt_Y(2)

Degrees

35

Tiltmeter Y

Tilt_Y(3)

Degrees

36

Tiltmeter Y

Tilt_Y(4)

Degrees

37

Tiltmeter Y

FIGURE 24.15

Temperature data collected by four thermocouples in consecutive 7 days.

From the baseline data from sensors, it is evident that all readings have a clearly daily (24 h) cycle. This trending is highly related to the temperature cycle on a daily basis. Fig. 24.15 shows the temperature data collected by four thermocouple sensors within 1 week. THT1 and THT2, corresponding to the sensors on the front side of Block A, trend each other as expected sunrise and sunset schedule. THT3 is the control sensor attached to the aluminum frame and directly exposed to daily weather conditions. This sensor appears noisy because it responds to temperature fluctuations faster compared with the other sensors insulated by the cement and epoxy. One can notice that during 6/28/2011
6/30/2011, temperature curves have two peaks, which exactly matches the thunderstorm events recorded in historical weather data of Aiken County between the two dates. Fig. 24.16 shows the battery voltage (V) and the temperature of battery ( C) in the same consecutive 7 days as shown in Fig. 24.15. Besides the daily charge cycle matching the temperature fluctuation, one can notice the thunderstorms on 6/28 and 6/30 caused the dips in temperature

VII. Special or new direction

24.5 Data analysis and discussions

FIGURE 24.16

Battery voltage (V) versus the temperature of battery ( C) in consecutive 7 days.

FIGURE 24.17

Reading collected from strain gauges in consecutive 7 days.

577

and voltages too. Similarly, the readings from strain gauges and tiltmeters in Figs. 24.17 and 24.18 have daily cycles with some fluctuations from thunderstorms as well. However, the fluctuations from tiltmeter are relatively small and there is no clear evidence to indicate that noticeable difference of the tiltmeter readings exists in between the x and y directions.

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24. Temporal data mining in nuclear site monitoring and in situ decommissioning

FIGURE 24.18

Typical tiltmeter graph showing angle (degrees) versus time in consecutive 7 days.

FIGURE 24.19

High (peak) and low (valley) events in thermocouple (T1) data stream.

To search frequent episodes in data stream of four thermocouples, an event stream was constructed based on the peak and trough turning points on temperature plots of each thermocouple. Any peak point on the temperature curve of thermocouple 1 is defined as “T1H” event if and only if the value of this point is “higher” than the adjacent data points in both directions. Any trough point will be defined as “T1L” event if and only if the value of this point is “lower” than the nearby data points (see Fig. 24.19). The combination of all these extrema points creates

VII. Special or new direction

24.5 Data analysis and discussions

FIGURE 24.20

579

Relationships of different types of events.

a bunch of serial episodes in the event stream. Similar events were constructed into other thermocouples. During a 6-month period in 2011 when thermocouples were working continuously, the number of extrema events created by T3, T2, T4, and T1 are 18,125; 8845; 5203; and 2040, which show the T3 thermocouple is the most sensitive sensor in temperature measurement. In all events from four thermocouples (T1H, T1L, T2H, T2L, T3H, T3L, T4H, T4L), TDMiner generated totally 8 3 4 5 32 types four-node episodes. If limited by the 12-h time constraint, one can notice that the most frequent episodes in the event stream are “T3H
T2H
T4H
T1H” and “T3L
T2L
T4L
T1L”, which had 618 and 629 cases, respectively, within 6 months (see Fig. 24.20). These two frequency episodes and their orders in the event chain verified the experimental setup of the ISD senor test bed: T3, the most sensitive to temperature change, is outside and located on the aluminum frame; T2 and T1 are reluctant and were cemented in about 2-in. block responding slower, while the last one T4 is buried about 4 in. inside and supposed to be the last one to respond in the time consequence. However, it looks like T1 is the most delay response one, which suggested there exists some insulation mechanism around T1. The technician disassembled the thermocouple and found there was air gap in cement around thermocouple 1. Also, one can notice that the direction of change is the exact same: peak points of T3 will lead to the following peak points of the other three thermocouples, while low points of T3 also lead following low points of other thermocouples. To seek the frequent episodes in the continuous data stream of thermocouple (T), strain gauge (S), biaxial tiltmeter (B), and voltage charged (V), we defined high and low events in 24-h period to construct eight events (TH, TL, SH, SL, BH, BL, VH, VL) to create a consecutive event stream, which with time stamp in minutes can be regarded as a sequel events stream. If we approximate time stamps to date without hour and minutes, the event stream is a mixture of serial and parallel episodes (or synfire-chain events). TDMiner results have indicated that the most frequent parallel episodes in the event stream are “VH
TH
SL
BH” and “VL
TL
SH
BL.” These two frequent episodes confirmed the time sequences of responses of sensors: battery charge is the most sensitive, then the thermocouple changes, the strain gouge reading changes, and finally the biaxial tiltmeter reading changes, the most reluctant to respond. TDMiner also found some abnormal frequent episodes in frequent episode generation, such as 8- and 12-node episodes in 1-day time constraint, which might be caused by rain or cloudy conditions on the same day. However, lacking multiple node episodes does not mean that there is no rain on that day: rain might occur in the night but did not create multiple node episodes. The multiple node episodes may be brought out by various factors, including the occasional movement of equipment by technicians. It is not certain how often an abnormal frequent episode leads to a certain significant/sudden change in the ISD Sensor Network Test Bed.

VII. Special or new direction

580

24. Temporal data mining in nuclear site monitoring and in situ decommissioning

The relationship of events is shown in Fig. 24.20. One can notice that all of the relations are highly correlated to thermocouple (TH or TL), which suggests that the temperature might be the cause of changes of events. Another important thing is that battery voltage, tiltmeter angle, and temperature are in the same trend. They increase or decrease together. On the contrary, the transformation of the strain gauge is in the opposite direction. When the temperature goes up, the tension dips down, which has confirmed a typical mechanical response of strain sensors.

24.6 Conclusion and future work We applied TDM frequent episode discovery framework and algorithms to the baseline data of the ISD Sensor Network Test Bed. The tentative results have proved that TDM techniques are effective tools for validating ISD performance. Frequent episodes in the data stream have confirmed the daily cycle of the sensor responses and established time sequences of different types of sensors, which was verified by the actual experimental setup of the ISD Sensor Network Test Bed. Although the discovery of frequent episodes has demonstrated the correlations of events among these sensors, it does not “dig out” enough abnormal frequency episodes, which may contain information of early indication of system failure. Furthermore, it is not clear how often an abnormal frequent episode leads to a certain significant “incidents” in the ISD system, which may be due to the following: (1) the abnormal frequent episodes are very rare under normal conditions. Baseline recorded data are regular routine of sensor data and did not record too many points in sudden changes in the system. But it may be possible to find more episodes if some “incidents” data points in the event stream can be generated manually; (2) these abnormal frequent episodes are very small signals in the baseline data of ISD test bed and may be buried in the background noise of voltage and current changes. Both causes can be eliminated if we can successfully install a well-controlled data acquisition system and manually produce some incident events. With more data points available, more abnormal episodes may become visible in the event stream, and then it will be practical to estimate the likelihood of target episodes with material degrading so that to predict possible system failures.

References [1] S.J. Dhoble, N. Shelke, Investigative research on big data: an analysis, Int. J. Innovative Res. Sci. Eng. Technol. 4 (6) (2015) 4476
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1059. [8] P.L. Lee, et al., Technology Requirements for In-Situ Decommissioning (ISD), Savannah River National Laboratory, Savannah River Site, Aiken, SC, 2009. SRNL-RP-2009-00269. [9] G. Song, et al., Development of a Remote Monitoring Sensor Network for In Situ Decommissioned Structures, Savannah River National Laboratory, Savannah River Site, Aiken, SC, 2010. SRNL Panel Report. SRNL-RP-2010-01666. [10] K.E. Zeigler, et al., Development of a Sensor Network Test Bed for ISD Materials and Structural Condition Monitoring, Savannah River National Laboratory, Savannah River Site, Aiken, SC, 2011. SRNL-STI-2011-00193. [11] K.E. Zeigler, B.A. Ferguson, Development of an in-situ decommissioning sensor network test bed for structural condition monitoring, in: WM2012 Conference, Phoenix, Arizona, AZ, 2012. [12] H. Mannila, H. Toivonen, A. Inkeri Verkamo, Discovery of frequent episodes in event sequences, Data Min. Knowl. Discov. 1 (3) (1997) 259
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499. [14] R. Srikant, E. Agrawal, Mining sequential patterns: generalization and performance improvements, in: Fifth International Conference on Extending Database Technology (EDBT ’96), 1996, pp. 3
17. ,https://doi.org/ 10.1109/ICDE.1995.380415.. [15] D. Patnaik, et.al., Efficient episode mining of dynamic event streams, data mining (ICDM), in: 2012 IEEE 12th International Conference on, 2012, pp. 605
614. [16] Github, ,https://github.com/patnaikd/tdminer. (published in 02/18/2018, accessed 02.01.2020). [17] C.L. Cowan Jr, F. Reines, F.B. Harrison, H.W. Kruse, et al., Detection of the free neutrino: a confirmation, Science 124 (3212) (1956) 103
104. Available from: https://doi.org/10.1126/science.124.3212.103. [18] U.S. Department of Energy, Office of Engineering and Technology, In-situ decommissioning: a strategy for environmental management. ,https://energy.gov/sites/prod/files/02-17-09ISDFact-Sheet-V9.pdf., 2009. [19] Roctest Ltd., ,http://www.roctest-group.com. (accessed 22.01.20.)

VII. Special or new direction

Index Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively.

A Ab initio MD simulations (AIMD simulations), 485 AC2 application for generic PWR accident scenario, 375 377 temperature distribution at 515 s and hydrogen concentration, 377f code package, 363, 364f Acceleration algorithms, 208 Accelerator-driven systems (ADSs), 186 187 Acceptance testing plan (ATP), 59 61, 70 Accident tolerant cladding materials, 430 431 Accuracy, 504 ACER code, 98 Advanced reactor, 313 314 AEGIS code, 104 105 Aerosol and fission product module (AFP module), 380 382, 384 Agile development methodology (ADM), 58, 64 Agile-lean development methodology (ALDM), 64 AI winter, 545 546 AIDA/LHEAD module, 371 373, 373f “Air gap”, 499 Air oxidation, 369 ALCYONE, 207 208 fuel performance code for GEN II and III, 210 223 3D simulation results and integral validation of ALCYONE code, 218 223 general presentation, 210 212 international benchmarks, 223 physical models, 212 218 ALFRED reactor, application to safety assessment of, 193 198 American Nuclear Society (ANS), 145 Analysis of thermal hydraulics of leaks and transients (ATHLET), 7, 277 ATHLET-CD AIDA/LHEAD, 371 373 development, 365 366, 366f ECORE, 367 369 FIPISO, 370 FIPREM, 369 370 modules and models, 366 373, 367f

numerical approach, 373 SAFT, 370 371 scope of application and limits, 378 specific models for certain reactor designs, 373 validation of ATHLET-CD, 374 377 COCOSYS thermal-hydraulic module THY, 298 305 system thermal-hydraulic code ATHLET, 277 297 Analytic nodal method (ANM), 110 ANC9 code, 109 110 Anomaly-based IDSs, 496 Anticipated operational occurrences (AOOs), 277 APOLLO2 code, 102 Application programmer interface (API), 87 88 Approximate block Newton methods (ABN methods), 80 82 Argonne National Laboratory (ANL), 313 314 Ariane 5 launch vehicle, 56 Artificial intelligence (AI), 18, 543 547 application in nuclear power plant code, 548 550 research in nuclear power industry, 547 548 Artificial neural network (ANN), 16, 18, 505, 515 516 applications in T/H problem, 522 536 characteristic points of boiling curve, 530 532 CHF prediction, 523 525 leak before break leak rate prediction, 532 536 nucleate boiling heat transfer coefficient prediction, 526 528 ONB in vertical narrow annuli prediction, 526 528 prediction of onset of nucleate boiling in vertical narrow annuli, 529 530 theory of, 516 522 basic ANN model, 516 517 BPN model, 517 519 GNN model, 519 520 wavelet neural network model, 520 521 training process of neural network, 521 522 Association for Computing Machinery (ACM), 546 547 ASTOR approximation, 372 373 ASTRID project, fuel design for, 230 Atomistic KMC. See Lattice KMC (LKMC) Atucha-II Nuclear Power Plant, 168

583

584

Index

Atucha-II Nuclear Power Plant (Continued) application to safety analysis, 175 179 Atucha-II large break loss-of-coolant accident transient, 175 179 AURORA code, 101 Automatic depressurization system (ADS), 412 Auxiliary feed-water (AFW), 430 431 Average channel (AC), 193

B Back propagation network (BPN), 515, 517 519, 523 implementation by MATLAB, 519 weight adjustment between hidden layer and output layer, 518 weight adjustment between input layer and hidden layer, 518 519 Bagging, 507 Bamboo-Core code, 112 113 Bamboo-Lattice, 106 107 Base irradiation, 218 219 Beginning of life (BoL), 184 185 Benchmark and in-vessel retention analysis, 347 349 Bhatnagar-Gross-Krook (BGK) LB method, 465 Big data, 553 Black-box coupling process, 80 81 solvers, 80 Boehm model, 64 65, 66f Boeing 737 Max-8 series, 57 Boiling characteristic points of boiling curve, 530 532 phenomena, 463 464 process, 463 464, 475f pseudopotential model and application to, 470 475 two-phase flow, 464 Boiling-water reactor (BWR), 7, 84, 100, 168, 237, 277 278, 365 366, 417, 526 full-size fine-mesh bundle tests pressure drop benchmark, 243 245 single-phase flow benchmark, 244 245 two-phase flow benchmark, 245 full-size fine-mesh bundle tests void benchmark, 249 251 Born Oppenheimer approximation, 483 484 Boron tracking model, 293 294 Bottom head package (BH package), 430 Boundary-layer stripping, 349 BROADR code, 97 Bubble condenser, 385 Bubble dynamics, 446 447 Bulk condensation, 38 39 Bulk evaporation, 38 39

Bundle design, 424 426 Burn-up (BU), 162 163 BWR full-size fine-mesh bundle tests (BFBT), 237

C Cahn Hilliard equation, 470 471 Capillary stress tensor, 469 CARACAS approach, 212 213 CASMO-4, 100 101 CASMO-4E, 101 CATHARE code, 3, 8 CCCCR code, 98 CCCP method, 101 Central moments (CMs), 465 CFX code, 3, 12 13 Chapman Enskog analysis, 469 Chebyshev Rational Approximation Method, 106 107 Chemical reaction model, 352 353 Chen correlation, 268, 527 Chorin’s projection method, 16 Ciccarelli Frost’s model, 447 Cladding effective stress, 148 149 oxidation, 272 temperature, 145 Classic lumped parameter approach, 405 Closure equations, 265 271, 317 interface to gas heat transfer, 265 266 interface to liquid heat transfer, 266 interfacial mass-transfer rate, 265 shear at phase interface, 269 270 wall shear force to gas, 270 271 wall shear force to liquid, 271 wall-to-gas heat transfer, 266 267 wall-to-liquid heat transfer, 268 269 Cluster dynamics, 490 492 Coarse mesh finite difference scheme (CMFD scheme), 106 107 Coarse-grid CFD simulations, 549 COBRA code, 3, 10 COBRA-I, 10 COBRA-II, 10 COBRA-III, 10 COBRA-IIIC, 10 Code coupling, 85 86, 296 297 Code development process of nuclear power plant, 25 26, 26f Code for nuclear materials electronic structure calculations in nuclear materials, 483 486 MD simulations in nuclear materials, 483 486, 487f mesoscale modeling in nuclear materials field, 489 492

Index

Code validation COPRA code, 339 344 crust thickness distribution along polar angle, 343f crust-wall gap size on crust thickness distribution, 344f diffusive boundary-layer thickness, 344f heat flux distribution along polar angle, 342f temperature distribution along pool height, 341f temperature field from corium pool simulation, 340f transient local heat flux at polar angle, 341f transient variation of crust growth rate at polar angle, 342f transient variation of liquidus temperature at crust interface, 343f velocity distribution from corium pool simulation, 340f DETAC code, 357 358 distribution of monitoring points, 358f pressure between code results and experimental data, 357f pressure history at two sides of internal wall, 358f MOCO code, 355 356 ablation depth with CCI-2 experiment, 355f melt temperature with CCI-2 experiment, 356f thermal explosion analysis simulation code, 350 351 Cole Rohsenow correlation, 39 Collision probability method (CPM), 102 Color-gradient model, 464 470 Comma-separated value format (CSV format), 559 Commissariat a` l’Energie Atomique et aux Energies Alternatives (CEA), 102 CEA-JAEA collaboration, 230 Compact integral effects test (CIET), 325 326, 327f experiments, 325 326 fluid temperature at heater outlet of SAM results, 329f SAM and RELAP5 3D simulation results, 328f SAM results and power step-change experimental data, 328f CompactFlash module, 572 573 Compatibility, 68 Component assembly model, 63 64 Components coding (CC), 58 Components integration (CI), 58 Computational geometry, 126 127 Computational reactor physics, 4 Computational fluid dynamics (CFD), 3, 75 76, 235, 549 CFX code, 12 13 code, 12 14 Fluent code, 13 STAR-CD code, 14

585

TransAT code, 13 14 Computed tomography (CT), 249 250 Computer security risk management (CSRM), 501 502 Concrete ablation model, 354 Condensation on spray, 40 Conduction model, 338 339, 338f Conductive heat flux, 338 Conficker program, 499 Confusion matrix, 504, 504t Conservation equations, 263 264 Consortium for the Advanced Simulation of Light Water Reactors (CASL), 4, 88 93, 235 237 Constant TM (cTM), 242 Constitutive equations interfacial heat and mass transfer, 287 288 interfacial shear, 286 of TRACE, 263 274 closure equations, 265 271 conservation equations, 263 264 heat conduction equations, 271 272 wall friction and form losses, 286 287 working fluid properties, 285 286 Constructive solid geometry (CSG), 124 CONTAIN code, 397 Containment Code System (COCOSYS), 277 containment phenomena with COCOSYS, 378 389 history of, 378 380, 379f main modules AFP module, 380 382 core concrete interaction module and ex-vessel corium issues, 382 383 models for specific reactor designs, 384 386 numerical approach, 383 384 scope of application and limits, 389 THY module, 380 validation of COCOSYS, 386 388 SA analysis for containment phenomena with, 378 389 thermal-hydraulic module THY, 298 305 COCOSYS THY modeling basis, 299 302 COCOSYS validation, 302 304 history of THY development, 298 scope of application and limits, 305 THY modeling basis, 299 302 additional models, 302 fluid properties, 301 heat conduction, heat transfer, and interfacial heat transfer, 301 302 junction models, 300 301 numerical approach, 302 thermal-hydraulic equations, 299 300 validation, 302 304, 303t THAI TH-27 pressure history, 304f

586 Containment Systems Experiment A9 test (CSE-A9 test), 420 Containment thermal-hydraulic analysis code, 25 Continuous-Energy Transport Module (CENTRM), 105 Continuum surface force (CSF), 468 Control network, 499 Control rods (CRs), 4 Control volumes (CVs), 281, 370 Conventional mesh-based method, 439 440 Coolant Boiling in Rod Arrays Two Fluids (COBRA-TF), 83, 235 237 assessment, 237 code, 12, 235 237 Coolant conditions, 145 COPRA code, 333 344, 334f code validation, 339 344 conduction model, 338 339 crust model, 336 338 governing equations, 334 335 radiation model, 339 turbulence model, 335 336 COR packages, 429 CORA test, 423 424, 424f CORA-13, 426 Core concrete interaction module, 382 384 Core degradation, 397 Core simulator (CS), 90 Corium cooling model, 354 355 spreading, 452 455 CORQUENCH model, 430 Correct detection rate, 505 Corrosive fission products release, 213 214 Countercurrent flow, 273 Countercurrent flow limitation (CCFL), 273 Coupled multiscale thermal-hydraulics codes, 14 16 consortium for advanced simulation of light water reactors, 14 15 MOOSE, 14 Coupling coupling-derivatives, 81 procedure of ABN-J method, 80 Crack extension modeling in fuel, 215 macroscopic scale, 215 microscopic scale, 215 Crack morphologies, 535 Critical digital assets (CDAs), 502 503 Critical discharge models, 293 Critical flow, 272 273 Critical heat flux (CHF), 281, 522 523, 531 532 prediction, 523 525 ratios, 348 349

Index

Cross section generation codes, 99 109. See also Whole-core computational codes AEGIS code, 104 105 APOLLO2, 102 Bamboo-Lattice, 106 107 CASMO-4, 100 101 DRAGON4, 103 104 ECCO code, 108 109 HELIOS, 101 MC2 3 code, 107 108 PARAGON code, 106 SCALE code system, 105 106 SRAC, 102 103 WIMS, 99 100 Crust model, 336 338 Custom TimeStepper object, 87 88 Cyber-incidents in nuclear industry history, 497 499 Cyberattack detection using process data, 508 510 research, 503 510 Cybersecurity system, 17, 501 502

D Dancoff factors, 100, 102 Darcy Weisbach friction factor, 287 Data Transfer Kit (DTK), 92 Data-driven thermal fluid models (DTF models), 549 Davis Besse NPP, 498 Debris spreading analysis module (DSA module), 407 409 Decision trees, 506, 548 549 Deep Blue, 546 Defense Advanced Research Projects Agency (DARPA), 506, 510 Denial-of-service (DoS), 496 497 Density functional theory (DFT), 483 484 Departure from nucleate boiling (DNB), 237, 523 Design basis accidents (DBA), 168, 179 180, 277 Design extension conditions (DECs), 277 DETAC code, 356 358 code validation, 357 358 mathematical model, 356 357 Detached eddy simulation (DES), 12 13 Detailed design (DD), 58 Deterministic method, 123 Diagonal matrix, 466 DIF3D/VARIANT/REBUS code, 114 Differential momentum conservation equation, 283 Diffusion process, 337 Diffusiophoresis, 381 382 Diffusive deposition, 381 382 Digital systems, 497 498 Dirac’s bracket notation, 465 466

Index

Direct containment heating (DCH), 380, 418 Discretization scheme, 440 443 Distributed-denial-of-service attacks (DDoS attacks), 505 “Divide-and-conquer” strategy, 76 77 DOE. See US Department of Energy (DOE) DONJON4 code, 111 112 DRAGON4 code, 103 104 DYN3D codes, 4, 83 84, 112 “Dynamic memory allocation” method, 15 Dynamic-link library (DLL), 15 16

E EBR-II benchmark, 324, 324f, 326f ECCO code, 108 109 ECORE model, 367 369 Eigenvalue calculation, 129 130 Electric Power Research Institute (EPRI), 12, 238 Electronic structure calculations in nuclear materials, 483 486 Emergency Planner (EP), 547 548 Energy conservation equation, 30 Energy equation for liquid and gas phases, 264 Energy storage model, 147 Enhancement factor, 268 269 Ensemble learning, 506 507 Entry-level guidance, 27 Environmental Management at Department of Energy (DOE-EM), 571 572 ERRORR code, 98 ESFR-SMART European project code-to-code comparisons, 230 Essential unified process, 64 Ethernet broadcasting, 498 European Reactor Analysis Optimized calculation System (ERANOS), 115 European Reference Simulation Platform for Nuclear Reactors (NURESIM), 4 European supply of safe nuclear fuel project (ESSANUF project), 168 Evaluated nuclear data file (ENDF), 97, 98f Event sequence loader, 567 Evolutionary prototyping, 62 63 Ex-vessel corium issues, 382 383 Ex-vessel reactor cavity, 349 EXCELL option, 103 104 Exothermal reaction equations, 353 Experimental prototyping, 62 63 Experimental research, 23 Expert Group on Innovative Fuels (EGIF), 186 187 Expert systems, 543 Explicit moving particle simulation method (EMPS method), 456

587

Exploratory prototyping, 62 63 Extended cladding oxidation model, 180 181

F False alarm rates (FARs), 496 False-positive (FP), 496 Fast breeder reactor (FBR), 165 Fast reactor (FR), 107 applications, 162 conditions preliminary assessment against, 186 198 TRANSURANUS for, 187 189 Figure-of-merit (FOM), 129 Film-boiling regime, 474 475 Fine-mesh CFD simulations, 549 Finite element method (FEM), 9, 314 FIPISO module, 370 FIPREM module, 369 370 Fission gas behavior modeling, 165 167, 212 213 Fission gas release (FGR), 151 152, 165 166, 208 209 Fission products (FP), 213 215, 365, 397 Five-equation model, 284 Fixed-source calculation, 130 FLICA code, 11 Flooding accident, 455 458 Flow mixing, 238 242 General Electric 3X3 benchmark, 239 242 two-channel single-phase flow split problem, 238 239 Flow regime map, 439 Fluent code, 3, 13 Fluid dynamics, 315 316 Fluid properties, 301 Fluid density ratio, 467 468 Fluoride salt cooled high-temperature reactor (FHR), 313 314 Flux tally, 129 Form loss, 273 Fountain model, 63 Fourth-order explicit Runge Kutta method, 42 44 Fourth-order Runge Kutta scheme, 473 “FRACAS-I” model, 148 FRAPCON code, 6, 141 assessments, 152 154 FRAPCON-3 v1. 1, 141 FRAPCON-3 v1. 2, 141 FRAPCON-3 v1. 3, 141 FRAPCON-3. 2, 141 FRAPCON-3. 3, 141 FRAPCON-3. 4, 141 FRAPCON-3. 5, 141 FRAPCON-4. 0, 141 model order, 144f

588

Index

FRAPCON code (Continued) relations, 142f FRAPTRAN code, 6, 142, 154 158 model order, 144f relations, 142f RIA condition, 155 158 Free surface particles detection, 444 Frequent episodes algorithms for nonoverlapped episodes, 555t and discovery algorithms, 554 558, 554f Froude number (Fr), 448 449 Fuel element analysis code, 24 formation and closure of fuel central void, 188 189 restructuring, 225 226 Fuel assemblies (FAs), 3, 175, 320 321 Fuel codes, 5 6. See also System codes FRAPCON/FRAPTRAN, 6 GERMINAL, 6 TRANSURANUS, 6 Fuel modeling under accident conditions (FUMAC), 168, 180 181 Fuel performance codes (FPC), 162 architecture and generic tools for, 207 208 Fuel rod heat up, 398 400 validation of, 400 405 performance analysis codes assessments, 152 158 code structures and physical models, 143 152 limitations, 143 objectives, 141 142 relations, 142 Fuel Rod Analysis Program-Transient code (FRAP-T code), 142 Fuel-cladding mechanical interaction (FCMI), 197 Fuel coolant interaction (FCI), 349, 449, 463 Fukushima Daiichi accident, 408 409 SAMPSON code application to, 410 413 PCV pressure behavior in Unit 3, 412 413 self-controlling behavior of RCIC turbine, 410 411 three pressure peaks period in Unit 2, 411 412 Fukushima nuclear accident, 455 Functional suitability, 67 Fuzzy logic networks, 543

G Gadolinia (Gd2O3), 167 168 Gap closure and relocation model, 226 227 Gap heat conductance, 146 Gas-cooled reactor models, 294 Gauss elimination method, 81 Gaussian function, 442 443

Gaussian mixture model, 508 Gauss Jordan elimination with partial pivoting, 45 52 General Control Simulation Module (GCSM), 278, 291 General design (GD), 58 General Electric (GE), 237 General Electric 3X3 benchmark, 239 242 single-phase flow benchmark, 239 240 two-phase flow benchmark, 240 242 General MRT (GMRT), 466 Generalized coarse mesh rebalance method (GCMR method), 105 Generalized cross section parameterization module, 112 Generic data generator, 558 Generic plug-in interfaces, 297 Generic PWR accident scenario, 375 377, 376f Genetic algorithm (GA), 516, 548 549 Genetic neural network (GNN), 515, 519 520, 521f, 525 GERMINAL, 207 208 code, 6 fuel performance code for GEN IV, 224 231 general presentation, 224 225 international benchmarks, 230 231 physical models, 225 228 validation and application for fuel design, 228 230 Gminer program of General Motor, 570 571 Good Old-Fashioned Artificial Intelligence (GOFAI), 546 Governing equations, 334 335 Gradient model, 442, 442f Graphical user interfaces (GUIs), 161 162 GROUPR code, 98 “Groupwise-ENDF” file (GENDF file), 99 GUIs. See Graphical user interfaces (GUIs) Gungor Winterton correlation, 526 527 Gunther Kreith correlation, 38 39

H Halden Boiling Water Reactor (HBWR), 168 Halden Reactor Project (HRP), 168 HAMBO code, 11 Hanford Engineering Division Laboratory (HEDL), 186 187 HDFView, 92 Heat balance equation, 336 conduction, 301 302 equations, 271 272 generation, 145 pipe modeling, 326 327 temperature distributions of single-and seven-cell models, 329f

Index

transfer, 301 302, 315 316, 318f model, 345 347 relationships, 347 Heat conduction and heat transfer package (HECU package), 278, 288 290, 289f Heat conduction objects (HCOs), 280 281 Heat transfer coefficients (HTCs), 285, 463 464, 522 523 HEDL P-19 irradiation experiment, assessment against, 189 193 HELIOS tool, 101 Helium, 167 release, 212 213 Henstock and Hanratty model, 248 Heterogeneous mechanical behavior, 215 Hidden Markov models (HMMs), 555 557 High burn-up structure (HBS structure), 162 163 High-temperature cladding oxidation model, 180 High-temperature gas reactor primary loop modeling, 328 330 Homogeneous-fluid model, 39 40 Horizontal stratified flow regime, 264 Hot channel (HC), 193 Human AI interaction, 548 Hybrid IDSs, 496

I Ice condenser, 385 386 Idaho National Laboratory (INL), 7, 85 86 In situ decommissioning (ISD), 18 and data collection, 571 574 dashboard, 573f P-reactor in operation days, 572f sensors and specifications, 574t sensor network test bed, 553 In-vessel phenomena, 363 378 during severe accident, 451 452 In-vessel retention analysis (IVR analysis), 333, 347 349 Incremental model, 63 Independent component analysis (ICA), 509 Indonesian Lion Air Boeing 737 Max-8 passenger plane, 57 Industrial control systems (ICSs), 496 497 INEEL data, 347, 348f Information, 501 security, 501 Information technology (IT), 496 cybersecurity differences of I&C systems and IT system, 496 497 INSPYRE European project, 231 Institute for Transuranium Elements (ITU), 161 162 Institute of Applied Energy (IAE), 397

589

Instrumentation and control systems (I&C systems), 495, 501 502 cybersecurity differences of I&C systems and IT system, 496 497 Integral effects tests, 275 Integral nonregression tests, 210 Integral severe accident codes 3D containment modules, 405 409 SAMPSON advantages and disadvantages in use of SAMPSON, 414 code application to Fukushima Daiichi nuclear power plant accident, 410 413 main modules, 398 405 module description, 398t Integrated Modular Plant Analysis and Computing Technology (IMPACT), 397 Integration testing plan (ITP), 59 61, 70 Intelligent methods, 543 Interface to gas heat transfer, 265 266 to liquid heat transfer, 266 Interface current techniques (ICT), 102 Interfacial heat and mass transfer, 265, 287 288, 301 302 Interfacial shear, 286 Intergranular fission gas behavior, 166 167 Intermediate heat exchanger (IHX) primary inlet temperature, 324, 325f Internal gas response, 151 152 International Atomic Energy Agency (IAEA), 162, 496, 500 502 International Electrotechnical Commission (IEC), 499 500, 502 International Fuel Performance Experimental database (IFPE database), 168, 170 Interpellet plane (IP plane), 218 219 Intrusion detection systems (IDSs), 495 496 Intrusion prevention systems (IPSs), 495 496 Inverted annular film boiling, 267 Iodine stress corrosion cracking (I-SCC), 213 215 Iraqi Scud missile, 56 ISO/IEC 25010, 67 ISO/IEC 9126, 65 66 Isotopic vector evolution, 212 Iterative methodology, 58, 63 IVRASA code, 345 349 benchmark and in-vessel retention analysis, 347 349 heat transfer model, 345 347 relationships, 347 melt pool configuration, 345f

590

Index

J Jacobian matrix, 78 80 Jacobian-free Newton Krylov method (JFNK method), 9, 78 80, 314 Jakob number, 39 Jet and droplet, 448 449 Jet vortex condenser (JVC), 385 Joint Oxyde Gaine formation (JOG formation), 224 225 and interaction with thermomechanical behavior, 227 228 Joint Research Centre (JRC), 161 162 Junction models, 300 301

K K-nearest neighbor (KNN), 506 Kelvin Helmholtz instabilities (KH instabilities), 349 Kernel principal component analysis (KPCA), 508 509 Kim Corradini’s model, 447 Kinetic Monte Carlo method (KMC method), 483, 489 490 Kirchhoff law, 339 Kohn Sham scheme, 483 484, 485f Krylov vector, 81 Krypton, 151

L Lagrangian method, 439 440 Lahey Moody model, 240 241 LAMMPS code, 489 Laplacian model, 442 443, 442f Laplacian operator, 442 443 Large break-LOCA (LB-LOCA), 168 Large eddy simulation (LES), 12 13 Large-scale test facility (LSTF), 294, 295f, 296f Larson Miller approach, 372 373 Lattice Boltzmann method (LBM), 16 17, 464 multiphase models, 464 475 color-gradient model, 464 470 pseudopotential model and application to boiling, 470 475 Lattice KMC (LKMC), 490 Lattice velocities, 471 472 Lead bismuth eutectic (LBE), 164 Leak before break (LBB), 532 534 leak rate prediction, 532 536 Leakage effects, 100 101 Lean development methodology (LDM), 58, 64 Light-water reactor (LWR), 4, 75 76, 107, 141, 166, 235, 279, 363, 417, 447 Lightweight Integrating Multiphysics Environment (LIME), 91 92 Linear heat rates (LHRs), 162 Long short term memory RNN (LSTM-RNN), 508

Los Alamos National Laboratory (LANL), 8 Loss-of-coolant accidents (LOCAs), 83, 161 162, 279, 449, 532 534 analysis, 237 condition, 158 Low-Reynolds-number k ε turbulence model, 335 Lower plenum processes (LP processes), 365 Lumped parameter, 397 heat transfer equations, 29

M Machine-learning, 548 549 algorithms, 503 510 cyberattack detection using cyber data, 505 508 ANNs, 505 bagging, 507 Bayesian network, 506 decision trees, 506 ensemble learning, 506 507 KNN, 506 random forest, 507 508 cyberattack detection using process data, 508 510 general procedure of building machine-learning model, 504 505 models, 510, 549 550 Macro-group calculation, 100 101 Main steam line (MSL), 410 Main steam line break (MSLB), 4 Maintainability, 68 Man-in-the-middle (MITM), 495 496 Maneuvering Characteristics Augmentation System (MCAS), 57 MARGARET model, 210 213 Mars Climate Orbiter, 56 MARS code, 3 Mass equation for liquid and gas phases, 263 Mass relocation process, 429 Mass transport and reactor kinetics, 317 Massachusetts Institute of Technology (MIT), 235 237 Material conservation equations, 168 Mathematical model, 356 357 MATLAB, BPN implementation by, 519 MATPRO fuel rod model, 10 MATXSR code, 98 MC21 code, 124 MC2 3 code, 107 108 McCall model, 64 65, 65f MCCG option, 103 104 Mean field rate theory, 490 492 Mean square error (MSE), 518 Mechanical models, 147 150, 163, 165, 217. See also Thermohydraulic models Mechanism-based codes for SA analysis

Index

COPRA code, 333 344 DETAC code, 356 358 IVRASA code, 345 349 MOCO code, 352 356 thermal explosion analysis simulation code, 349 351 MELCOR, 8 9, 417 capabilities and limitations, 427 429 advantages, 427 429 limitation of MELCOR, 429 experiments for validation, 430 434 file relations in MELCOR code, 418f MELCOR version 1. 8. 3, 430 MELCOR version 1. 8. 5, 430 MELCOR version 1. 8. 6, 430 MELCOR version 2. 1, 430 quality control, 420 427 bundle design, 424 426 results of analysis, 426 427 V&V study of core heat up and degradation, 423 424 uncertainty information flow, 419f version update history, 429 430 Melt jet breakup, 463 464 Mesh-based Eulerian approach, 439 Meshing and finite element library (libMesh), 313 314 Meshless Lagrangian particle method, 439 440 Mesoscale modeling in nuclear materials field, 489 492 KMC method, 489 490 mean field rate theory and cluster dynamics, 490 492 Message Passing Interface (MPI), 114 Metallic melt relocation, 369 Method of characteristics (MOCs), 99 100, 105 Microgroup calculations, 100 101 Mid-pellet (MP), 210 212 Minimum film boiling (MFB), 288 289 temperature models, 266 267 Mixed oxide (MOX), 161 162 MOCO code, 352 356 chemical reaction model, 352 353 code validation, 355 356 concrete ablation model, 354 corium cooling model, 354 355 Modeling and simulation (M&S), 14 15, 88 Modified Pauling relationship, 11 Modular Accident Analysis Program (MAAP), 9 Modular high-temperature gas reactor (MHTGR), 328 330, 330f Molecular dynamics (MD), 483 simulations in nuclear materials, 483 486, 487f Moller relationship, 11 Molten core relocation analysis (MCRA), 398 400

591

validation of, 400 405 Molten corium/core concrete interaction (MCCI), 352, 382 383, 439 440, 452 455 Momentum conservation equation, 445 Momentum equation for liquid and gas phases, 264 Monte Carlo (MC), 161 162 codes, 124 125, 124t method, 123 Monte Carlo N-Particle code (MCNP code), 124 MCNP6, 124, 549 Moving particle semi-implicit method (MPS method), 439 445 application to nuclear engineering, 446 458 bubble dynamics, 446 447 corium spreading and molten core concrete interaction, 452 455 flooding accident, 455 458 in-vessel phenomena during severe accident, 451 452 jet and droplet, 448 449 multiphase flow instability, 449 450 vapor explosion, 447 448 discretization scheme, 440 443 free surface particles detection, 444 governing equations, 440 semi-implicit algorithm and pressure calculation, 444 445 MultiApp system, 87, 87f Multidimensional analysis, 215 218 Multiphase flow, 439 instability, 449 450 Multiphase MPS method (MMPS method), 449 Multiphysics, 75 76 computational scheme for fuel rod type geometries, 208 209 algorithm, 208 global scale, 208 209 local scale, 209 software implementation, 209 coupling, 76 current status of research, 82 93 methods, 76 82 Multiphysics Object-Oriented Simulation Environment (MOOSE), 9, 14, 85 88, 313 314 MOOSE-wrapped apps, 87 88 Multiple-layer cyberattack detection system, 509 Multiscale analysis, 215 218 modeling methodology, 483

N Narrow resonance approximation (NR approximation), 103

592

Index

Natural Circulation Experiment loop (NACIE loop), 15 Navier Stokes equations, 331, 407, 409, 440, 463 464, 549 Negative predictive value, 505 NEPTUNE multiscale coupled simulation platform, 15 16 Neumann boundary conditions, 188 Neural networks, 548 549 Neutral networks, 543 Neutron irradiation, 483 Neutron kinetics (NEUKIN), 112, 278, 290 Neutronic(s) modeling of nuclear reactors, 99 and thermal-hydraulic code-to-code coupling, 82 84 Newton’s second law of motion, 486 Newtonian fluid, 440 Nitride formation, 369 Nitrogen, 151 NJOY code, 97 99 NL115 Ethernet, 572 573 Nodal expansion method (NEM), 110 111 Noncondensable gases (NC gases), 279, 285 Nonequilibrium model, 300 “Nonregression” principle, 162 North American Air Defense Command, 56 NRC. See US Nuclear Regulatory Commission (NRC) Nuclear data processing codes, 97 99 NJOY, 97 99 Nuclear Energy Agency (NEA), 252 253 expert group on innovative fuels, 230 Nuclear Energy Institute (NEI), 499 500, 503 Nuclear engineering, 446 458 field, 463 SQA for, 68 71 implementation framework, 69 71 V&V, 71 Nuclear physics deterministic code cross section generation codes, 99 109 nuclear data processing codes, 97 99 whole-core computational codes, 109 115 Nuclear Power Engineering Corporation (NUPEC), 243 Nuclear power plants (NPP), 23, 168, 495, 543 544 AI application in nuclear power plant code, 548 550 code, 23 27 classification, 24 25 development examples, 27 42 development process, 25 26, 26f development skills, 26 27 cybersecurity cyber-incidents in history of nuclear industry, 497 499 cyberattack detection research using machinelearning algorithms, 503 510

differences of I&C systems and IT system, 496 497, 497t IAEA guidance, 500 502 IEC, 502 NEI, 503 NRC, 502 503 regulations, 499 503 emerging methods for, 16 18 artificial intelligence and ANN, 18 cybersecurity system, 17 LBM, 17 PPM, 16 17 TDM, 18 firewall system, 16 source code, 42 52 system analysis code, 24 Nuclear Power Station (NPS), 397 Nuclear power technology, 543 544 Nuclear reactions products, 212 Nuclear reactors, 3, 543 Nuclear safety, 55, 449 Nuclear Security Series (NSS), 500 Nuclear thermal-hydraulic analyses, 3 Nucleate boiling, 268 heat transfer coefficient prediction, 526 528 Numerical analysis, 24 Numerical multiphysics project (NUMPS project), 83 Numerical schemes, 317 318 Numerical simulation method, 75 76 Numerical Toolkit (NuT), 281, 291 293 NURESAFE European project, 84 85, 86f Nusselt numbers (Nu numbers), 301

O “Object” KMC (OKMC), 490 Off-the-shelf cybersecurity software, 503 One-dimensional system codes (1D system codes), 3 Onion burning of Gd isotopes, 184 185 Onset of nucleate boiling (ONB), 252 253, 522 523 in vertical narrow annuli prediction, 526 528 Open gap, 148 149 OpenCalphad thermochemical solver (OC thermochemical solver), 213 215 OpenMC, 125 methodologies in, 125 130 Monte Carlo codes, 124 125, 124t Monte Carlo method, 123 usage, 130 135 data library, 131 geometry definition, 131 material definition, 131 output description, 135 plots definition, 132

Index

preparation, 130 Python API, 135 settings definition, 131 simulation in serial and parallel, 132 134 tally definition, 131 verification and validation, 135 137 Operator splitting methods (OS methods), 76 78, 77f Ordinary differential equation (ODE), 209 Organization for Economic Co-operation and Development Nuclear Energy Agency (OECD NEA), 162, 252 253 Oxide pool, 345 346 Oxide-cladding joint, 6

P Pacific Northwest National Laboratory (PNNL), 141 PANTHER code, 110 Parabolic law, 402 PARAGON code, 106 Parallel virtual machine interface (PVM interface), 15 Partial decision tree (PART), 507 Partial differential equations (PDEs), 14, 76 Particle sorting, 17 Passive containment cooling system (PCCS), 386 Peak power node (PPN), 189 Peak-cladding temperature (PCT), 176 177 Pellet-cladding interaction (PCI), 170, 210 212 Pellet-cladding mechanical interaction (PCMI), 162 163 Pellet-to-cladding gap model, 218 Pellets temperature distributions, 146 Performance efficiency, 67 Phebus FPT-1 test, 420 Phe´bus FPT-3 simulation, 374 375, 375f Phenomena Identification and Ranking Tables (PIRT), 274 Physical models, 163 Physics integration kernels (PIKE), 91 92 PICEP software, 536 PLEIADES fuel software environment ALCYONE fuel performance code for GEN II and III, 210 223 architecture and generic tools for fuel performance codes, 207 208 GERMINAL fuel performance code for GEN IV, 224 231 multiphysics computational scheme for fuel rod type geometries, 208 209 verification process and quality control, 209 210 Plenum gas temperature model, 147 Plutonium redistribution model, 188 Point defect balance equations, 490 491 Point models, 209

593

“Point-ENDF” file (PENDF file), 99 Pointwise Multigroup Converter (PMC), 105 Poisson processes, 489 POOL3D module, 405 406 Porous medium theory, 334 Portability, 68 Portable, Extensible Toolkit for Scientific Computation (PETSc), 313 314 Positive void reactivity coefficient, 175 Post-CHF flow regime, 264 Postirradiation examinations (PIEs), 182 Power plants, 3 Power ramp test, 219 223 Prandtl Reuss rule, 149 151 Pre-CHF flow regime, 264 Precision, 504 Preconditioning, 78 79 Predictor corrector approach, 100 Pressure calculation, 444 445 drop, 243 249 boiling-water reactor full-size fine-mesh bundle tests pressure drop benchmark, 243 245 Risø round tube benchmark, 245 249 oscillation, 445 Pressure Poisson equation (PPE), 445 Pressurized conduction cooldown transient (PCC transient), 328 330 Pressurized heavy water-cooled and moderated reactor (PHWR), 175 Pressurized-water reactor (PWR), 5, 27, 83, 100, 168, 237, 277 278, 417, 449, 526 subchannel and bundle tests void benchmark, 251 254 rod bundle benchmark, 254 single subchannel benchmark, 252 254 Pressurizer, 34 42. See also Reactor model development, 35 40, 274 empirical correlations, 38 40 governing equations, 36 38 numerical scheme, 40 41 verification, 41 42 Probabilistic risk assessment (PRA), 9, 455 PRODHEL model, 212 Programable logic controllers (PLCs), 498 Projection-based particle method (PPM), 16 17 Prolog, 546 PROTEUS code, 331 Prototyping methods, 62 63 Pseudo-3D full-core conjugate heat transfer, 321 323, 323f Pseudopotential model and application to boiling, 470 475

594 Pump models, 273 Purdue Advanced Reactor Core Simulator code (PARCS code), 83, 110 111, 272 PURR code, 98 PVMEXEC general coupling program, 15 PWR subchannel and bundle tests (PSBT), 237 Python API, 135, 136t

Q Quality assurance (QA), 277, 305. See also Software quality assurance (SQA) measures, 378 389 Quality control of MELCOR, 420 427

R R-K models. See Color-gradient model RACHEL model, 210 213 Radial power density distribution, 167 Radiation damage, 484 LKMC in, 490 in nuclear materials, 491 model, 339 Radioactive nuclides, 382 Radiological consequence analysis code, 25 Radionuclide (RN), 418 Ramp terminal level (RTL), 170 Random forest, 507 508 Random number generators (RNGs), 125 126 Random walk, 127 Rapid application development model (RAD model), 58, 63 Rapid prototype model, 63 Rational unified process (RUP), 64 Rayleigh Taylor instability (RTI), 349, 450 Reactivity-initiated accident (RIA), 161 162 Reactor, 27 34, 28f. See also Pressurizer core, 28 30 lower and upper chamber, 30 model development, 28 30 numerical scheme, 30 31 verification, 31 34 steady-state results, 31 32 transient results, 32 34 Reactor cooling system (RCS), 418 Reactor core analysis code, 24 Reactor physics, 23 24 analysis code, 24 25 Reactor pressure vessel (RPV), 175, 371 372, 430 431, 449 REBUS code, 114 Recirculation tank (RT), 385 Reconnaissance, 495 496

Index

RECONR code, 97 Recrystallization process, 487 489 Recurrent neural networks (RNNs), 505 Reich Moore (RM), 97 RELAP code, 397 RELAP5 code, 3, 7 RELAP5/N-K-coupled codes, 4 RELAP5 3D code, 3, 7 8 Relative root-mean-square error (rRMSE), 239 240 Relaxation matrix, 466 Reliability, 68 Requirements analysis (RA), 58 RETRAIN code, 3 Reynolds number related TM model (ReTM model), 242 Risø round tube benchmark, 245 249 Road map of nuclear codes computational fluid dynamics code, 12 14 coupled multiscale thermal-hydraulics codes, 14 16 emerging methods for NPPs, 16 18 fuel codes, 5 6 subchannel analysis code, 10 12 system codes, 6 9 Root mean square error (RMSE), 504 Rule-based AI technology, 546 Rupture model, 372 373

S Safety, security, and emergency preparedness (SSEP), 502 503 Safety parameter display system (SPDS), 498 SAFT module, 370 371, 371t SALOME software, 84 SAS4A/SASSYS-1 deterministic analysis tool, 330 331 Savannah River National Laboratory (SRNL), 553 SCALE code system, 105 106 Schrodinger-like equation, 483 484 SCOPE2 code, 113 114 Scrumban method, 64 Secure Water Treatment Testbed (SWaT), 508 Security, 68 Sedimentation, 381 382 Self-controlling behavior of RCIC turbine, 410 411 Semi-implicit algorithm, 444 445 Sensitivity analysis (SA), 71 Separate effect tests, 274 Sequential model, 58 Serpent code, 124 Serpent 2 code, 84 Severe accident (SA), 333, 363, 397 analysis for containment phenomena with COCOSYS, 378 389

Index

code ATHLET-CD for in-vessel phenomena, 363 378 ATHLET-CD modules and models, 366 373 history of ATHLET-CD development, 365 366 in-vessel phenomena during, 451 452 Severe accident analysis code with mechanistic, parallelized simulations oriented toward nuclear fields (SAMPSON), 397 advantages and disadvantages in use of, 414 code application to Fukushima Daiichi nuclear power plant accident, 410 413 main modules fuel rod heat up and molten core relocation, 398 400 module description, 398t SG tube rupture (SGTR), 532 534 Shear at phase interface, 269 270 Short-term station black out (STSBO), 430 431 Shutdown heat removal tests-17 (SHRT-17), 4 5 Sigmoid function, 521 Signature-based IDSs, 496 Simple four-tank system control model, 508 Simple GA (SGA), 519 SIMTRAN codes, 4 SIMULATE-3 code, 109 Six-equation model, 281 284 “SKEL” scheme, 210 Slammer worm, 498 Small modular reactors (SMRs), 277 278 Smoothed particle hydrodynamics (SPH), 16 SMRs. See Small modular reactors (SMRs) Sodium fast reactor (SFR), 6, 313 314 Software quality, 64 68, 66t, 67t, 68t control, 210 Software quality assurance (SQA), 55 elements, 71t events, 56t for nuclear engineering, 68 71 SDLC, 58 64 Software quality requirements and evaluation (SQuaRE), 66 67 Software requirements specifications (SRS), 57 58 Software testing model (STM), 59 61 Software/system development life cycle (SDLC), 58 64, 59t Source code, 42 52 Fourth-order explicit Runge Kutta method, 42 44 Gauss Jordan elimination with partial pivoting, 45 52 Space-Dependent Dancoff Method, 106 Spatial discretization, 319 321, 319f, 321f in MPS, 440 Spatial models, 209

595

Spiral model, 63 Spray droplets, 40 SQUIRT software, 536 Standard Reactor Analysis Code (SRAC), 102 103 Star-CCM code, 3 STAR-CCM 1 code, 331 STAR-CD code, 14 State prediction based cyberattack detection, 509 510 Station blackout (SBO), 430 431 Steady-state calculation (SSC), 291, 293 Steam generators (SGs), 531 532 Steam separators model, 274 Streamline-upwind/Petrov Galerkin and pressurestabilizing/Petrov Galerkin schemes, 321 STSBO scenario, 432 434 Subapp, 87 SUBCHANFLOW code, 84 Subchannel analysis code, 10 12. See also Coupled multiscale thermal-hydraulics codes COBRA code, 10 CTF code, 12 FLICA code, 11 HAMBO code, 11 MATRA code, 11 THINC code, 11 VIPRE code, 12 Subchannel codes CTF assessment, 237 CTF code, 235 237 flow mixing, 238 242 pressure drop, 243 249 VIPRE-01 code, 238 void fraction, 249 254 Subcommittee 45A (SC45A), 502 Subcooled nucleate boiling, 268 Super-Ramp irradiation experiment, assessment against pressurized water reactor, 170 174 Superhomogenization method (SPH method), 104 Support vector data description (SVDD), 508 509 Support vector machines, 548 549 Surface boiling, 526 Swelling, 165 166 SYBIL option, 103 104 System Analysis Module (SAM), 9, 313 314, 318f, 323f, 325f integration and coupling, 330 331 implementation in other codes, 331 implementation in STARCCM 1 code, 331 implementation in system code, 330 331, 331f software development, 314 319 current capabilities, 319 models, 315 318 structure, 314 315, 314f

596 System Analysis Module (SAM) (Continued) verification and demonstration CIET experiments, 325 326 EBR-II benchmark, 324 heat pipe modeling, 326 327 high-temperature gas reactor primary loop modeling, 328 330 pseudo-3D full-core conjugate heat transfer, 321 323 spatial and temporal discretization, 319 321 three-dimensional finite element flow model, 321 System codes, 6 9, 330 331, 331f ATHLET, 7 CATHARE, 8 MAAP, 9 MELCOR, 8 9 RELAP5, 7 RELAP5 3D, 7 8 SAM, 9 TRAC, 8 System error, 517 System State Analyzer (SSA), 547 548 System testing plan (STP), 59 61, 70 System thermal-hydraulic code ATHLET, 277 297, 278f code coupling, 296 297 history of ATHLET development, 279 281, 280f modeling basis constitutive equations, 285 288 GCSM, 291 HECU, 288 290 neutron kinetics, 290 numerical approach and new NuT, 291 293 SSC, 293 TFD equations, 281 285 scope of application and limits, 297 specific models for certain reactor designs boron tracking model, 293 294 critical discharge models, 293 gas-cooled reactor models, 294 validation, 294 296

T Tallies and statistics, 127 129 TDMiner, 557 558, 558f application of, 558 571 internal validation with data generator of TDMiner, 570f user interfaces of TDMiner, 559 568 verification and validation of TDMiner, 569 571 Temperature feedback, 29 30 Temperature-dependent thermal conductivities, 316 317

Index

Temporal data mining (TDM), 16, 18, 553 application of TDMiner, 558 571 data analysis and discussions, 574 580 columns in in situ decommissioning data table, 575t temperature data collected by thermocouples, 576f typical tiltmeter graph showing angle, 578f frequent episode and discovery algorithms, 554 558 in situ decommissioning sensor network test bed and data collection, 571 574 Temporal discretization, 319 321, 319f, 321f Tennessee-Eastman chemical process data, 508 Theory analysis, 23 24 Therac-25 medical accelerator incident, 57 Thermal analysis, 163 164 Thermal explosion analysis simulation code, 349 351 basic assumption, 349 350 code validation, 350 351 Thermal EXplosion Analysis Simulation model (TEXAS model), 349 350 Thermal hydraulic module (THY module), 363, 380, 384 codes quality assurance measures, 378 389 SA analysis for containment phenomena with COCOSYS, 378 389 SA code ATHLET-CD for in-vessel phenomena, 363 378 development, 298 Thermal model, 216 Thermal-hydraulic (T-H) analysis, 333, 397 code, 261 computer code ATHLET, 277 278 COCOSYS, 298 conditions, 75 76 equations, 299 300 field, 446 modeling capability, 100 models, 237 phenomenon, 522 523 problems, 23 24 Thermo-fluid-dynamics (TFD), 278 equations, 281 285 3D model, 284 285 five-equation model, 284 NC gases, 285 six-equation model, 281 284 Thermo-fluid-dynamics objects (TFO), 281 Thermochemical analysis, 213 214 Thermodynamic properties, 535

Index

Thermodynamics of Advanced Fuels International Database (TAF-ID), 214 Thermohydraulic models, 144 147 cladding temperature and heat generation, 145 coolant conditions, 145 gap heat conductance, 146 pellets temperature distributions, 146 plenum gas temperature model and energy storage model, 147 Thermophoresis, 381 382 THERMR code, 98 THINC code, 11 Three-dimensional (3D), 284 285 calculations, 99 containment modules, 405 409 debris spreading analysis module, 407 409 POOL3D module, 405 406 coolant mixing, 3 effects, 314 315 finite element flow model, 321 flow in channel of parallel plates, 322f flow problem in lid-driven cavity, 322f natural convection in square cavity, 322f neutron kinetics, 83 Three-dimensional 27-velocity lattice (D3Q27 lattice), 465 467 Title 10 of Code of Federal Regulations (10 CFR), 502 503 TRAC code, 8 TRAC-BF1, 8 TRAC-PF1, 8 TRAC/RELAP Advanced Computational Engine (TRACE), 248, 261 code, 83 constitutive equations of TRACE, 263 274 features, 261 263 validation, 274 275 Training process of neural network, 521 522 TransAT code, 13 14 Transient Reactor Analysis Code/Reactor Excursion and Leak Analysis Program (TRAC/RELAP), 261 Transport cross section (TRANSX), 98 TRANSURANUS burn-up model (TUBRNP), 167, 184 185 TRANSURANUS code, 6, 161 162 application to water reactor conditions, 168 186 application to water water energetic reactor conditions, 179 186 burn-up module, 167 168 for fast reactor conditions, 187 189 preliminary assessment against fast reactor conditions, 186 198

597

structure, 162 168 TRANSURANUS-FBR burn-up model, 167 168 TRANSURANUS-LWR burn-up model, 167 168 Tribal Build, Integrate, and Test System (TriBITS), 92 TRIVAC solver modules, 111 Tungsten (W), 490 Turbulence model, 335 336 Turbulent mixing (TM), 238 239 Turing’s test, 544 545 Two-channel single-phase flow split problem, 238 239 Two-dimensional 9-velocity lattice (D2Q9 lattice), 471 472 Two-phase forced convection, 268

U U-Alloy78, 463, 470 UCSB data, 347, 348f Uncertainty analysis (UA), 71 Unified process methodology, 58, 64 Unit nonregression tests, 210 Unit testing, 25 26 Unit testing plan (UTP), 59 61, 70 UNRESR code, 97 Unsupervised learning approach, 508 URFRIC model, 165 US Department of Energy (DOE), 7, 88, 235 237 US Nuclear Regulatory Commission (NRC), 5, 141, 237, 495, 502 503 Usability, 67 User interfaces of TDMiner, 559 568 discovery of episodes & interevent intervals(serial) in TDMiner, 566f dropdown menu of frequent episode miner tab, 560f event sequence loader tab of TDMiner, 560f fast non-overlapped count(serial) in TDMiner, 561f non-overlapped count with episode expiry constraint(parallel) in TDMiner, 569f non-overlapped count with episode expiry constraint(serial) in TDMiner, 562f with interevent expiry constraint(serial) in TDMiner, 564f non-overlapped count(parallel) in TDMiner, 567f User requirements (URs), 55 User-defined functions (UDFs), 5

V V-model, 59, 61, 61f Valence band maximum (VBM), 484 485 Validation, 26, 294 296, 295t of ATHLET-CD, 374 377, 374t AC2 application for generic PWR accident scenario, 375 377

598

Index

Validation (Continued) simulation of Phe´bus FPT-3, 374 375 of COCOSYS, 386 388, 387t of TDMiner, 569 571 Vapor explosion, 447 448 Variable frequency drives (VFDs), 498 Variational nodal method (VNM), 112 Velocity Verlet algorithm, 487 Verification and validation (V&V), 57 58, 71, 135 137 efforts, 321 methodology, 420 423 study of core heat up and degradation, 423 424 Very-large-scale integration chips, 546 VIPRE code, 3, 12 VIPRE-01 code, 238 Virtual Environment for Reactor Applications (VERA), 4, 89 90 Virtual Environment for Reactor Applications Core Simulator (VERA-CS), 235 237 Virtual junctions, 299 Virtual Local Area Network (VLAN), 573 574 Void drift mechanism (VD mechanism), 240 241 Void fraction, 249 254 boiling-water reactor full-size fine-mesh bundle tests void benchmark, 249 251 pressurized-water reactor subchannel and bundle tests void benchmark, 251 254 Void-based Wallis wall friction multiplier, 247 248 Vortex chamber (VC), 385 VULCANO VE-U7 experiment, 453, 453f, 454f

to gas, 270 271 to liquid, 271 wall-to-gas heat transfer, 266 267 wall-to-liquid heat transfer, 268 269 Water reactor conditions, application to, 168 186 Waterfall model, 58, 60f Water water energetic reactor (WWER), 168, 279, 373 application to, 179 186 Wavelet analysis (WA), 516 Wavelet neural network (WNN), 515, 520 521 Weak coupling, 77 78 Weakly compressible SPH (wcSPH), 16 Weber number (We number), 448 449 Whole-core computational codes, 109 115. See also Cross section generation codes ANC9 code, 109 110 Bamboo-Core, 112 113 DIF3D/VARIANT/REBUS code, 114 DONJON4, 111 112 DYN3D, 112 ERANOS, 115 PANTHER code, 110 PARCS, 110 111 SCOPE2 code, 113 114 SIMULATE-3 code, 109 WIMSR code, 98 Winfrith improved multigroup scheme (WIMS), 99 100

X Xenon, 151

W W-model, 61, 62f W.32Ramnit program, 499 Wall ablation, 372 373, 372f friction and form losses, 286 287 shear force

Z ZENITH code, 101 Zirconium, 272 Zirconium diboride (ZrB2), 167 168 Zirconium oxide, 272