Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core [1st ed.] 9789811595646, 9789811595653

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Shengyao Jiang · Jiyuan Tu · Xingtuan Yang · Nan Gui

Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core

Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core

Shengyao Jiang Jiyuan Tu Xingtuan Yang Nan Gui •

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Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core

123

Shengyao Jiang Tsinghua University Beijing, China

Jiyuan Tu RMIT University Melbourne, VIC, Australia

Xingtuan Yang Tsinghua University Beijing, China

Nan Gui Tsinghua University Beijing, China

ISBN 978-981-15-9564-6 ISBN 978-981-15-9565-3 https://doi.org/10.1007/978-981-15-9565-3

(eBook)

Jointly published with Tsinghua University Press The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: Tsinghua University Press. © Tsinghua University Press 2021 This work is subject to copyright. All rights are reserved by the Publishers, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Foreword by Goodarz Ahmadi and Takashi Hibiki

Since the Three Mile Island accident in 1979 and the Chernobyl accident in 1986, designing an inherently safe nuclear reactor has attracted worldwide attention. In this context, “the generation IV advanced nuclear power system”, was proposed. In an effort to optimize the High-Temperature Gas-cooled Reactor (HTGR), considered as a safe and efficient reactor, Institute of Nuclear and New Energy Technology (INET) at Tsinghua University has developed a demonstration reactor and conducted extensive research in the past decades. This book provides a comprehensive collection of the research methods and achievements of the authors’ team on HTGR over the years. This book starts with an introduction to HTGR and the critical issues such as pebble flows, gas-phase hydrodynamics, and inter-phase heat transfer (thermal-hydraulics) inside the reactor core. It provides a detailed understating of the granular flow, which is quite interesting and meaningful. Granular flow is common, but its dynamics is quite complicated, especially for the quasi-static flow regime inside the HTGR core. To provide a deep understanding of the flow mechanisms, the authors have carried out both experimental, phenomenological analysis, and numerical studies using the discrete element method and the continuum approach. Flow characteristics such as velocity, mixing, intermittency, as well as the subdivision of flow regimes are explained thoroughly in this book. The inherent safety of HTGR at high power requires a thorough knowledge of the two-phase heat-transfer processes. In this regard, a full-radius-scale heat-transfer testing facility has been built, and an overview of the experimental process for measuring the thermal properties of a pebble bed under different conditions is presented. The authors have also developed several numerical models, including thermal radiation and conduction, which have been shown to be appropriate for the heat-transfer study of the pebble bed. Each model and its application are explained in detail. These innovative research works are of great significance to ensure the balance between safety and economic competitiveness.

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Foreword by Goodarz Ahmadi and Takashi Hibiki

Last but not least, the discussions relating to the optimization of the pebble bed, including the two-region pebble bed, wall structure, and friction optimization, are all promising techniques, which can promote future impactful ideas in the design of pebble beds. This book is full of profound, innovative, and instructive insights. It introduces state-of-the-art research progresses on pebble flow and heat transfer, with interesting underlying physics revealing the complicated interactions and mechanisms in the HTGR core. We recommend this book to those who are interested in multiphase flows and heat transfer. The research methods introduced in this book can also be applied to many other fields such as chemical industries, mineral processing, geophysical applications, agricultural industries, pharmaceutical industries, energy production, powder technology, and so on. For professionals, researchers, and engineering designers working with pebble beds, this book is an excellent reference and source of inspiration, especially for the future development of HTGR.

July 2020

Goodarz Ahmadi Distiguished Professor Clarkson University Potsdam, USA

Takashi Hibiki Professor Emeritus Purdue University West Lafayette, USA

Foreword by Hongguang Jin

High-Temperature Gas-cooled Reactor (HTGR) is considered one of the most promising solutions for Generation IV advanced reactors by researchers in the nuclear energy field. Extensive studies have been carried out in China, the USA, Germany, and South Africa, which have promoted the development of pebble-type HTGR significantly. Among such efforts, Prof. Jiang and his team from Institution of Nuclear and New Energy Technology (INET) of Tsinghua University in China have had extraordinary contribution. Approved as one of the “Major Project”s of National Science and Technology and based on the forward studies of 10MW high-temperature reactor (HTR-10), the pebble flow and the heat transfer in the pebble-type HTGR are investigated profoundly. The high-temperature reactor-pebble-bed module (HTR-PM) is under construction in Shandong Province in China. A great number of findings from prior studies have been validated in this project, which provided instructive knowledge to scientists and personnel in the nuclear power industry. High uniformity and the minimum stagnation of the pebble flow are highly desired with graphite-coated fuel pebbles in the fuel cycle to prevent overheating at specific areas when the reactor is in operation. By conducting experimental comparisons of different bed configurations, Prof. Jiang and his group have investigated the state of the art of the scheme of pebble-bed configuration and identified the bulk dynamics and phenomena of pebble flows. Based on the work, they have proposed relevant parameters to analyze the flow pattern and uniformity, and optimized the Particle Tracking Velocimetry (PTV) method, which has proven to be very effective. According to the experiments and velocity characteristics of the pebble bed, a correlation time and a new intermittency index are proposed from both macroscopic and microscopic perspectives to analyze the flow pattern, which has significant value to future optimization of the pebble flow. To optimize the efficiency of the pebble flow with substantially more cases, numerical models and schemes must be established and adopted. In this work, the Discrete Element Method (DEM), a widely utilized approach, is employed. The DEM successfully simulates a real-scale three-dimensional pebble-bed reactor HTR-PM, and it is reasonable to consider that the pebble flow is a mass flow vii

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problem within the main body of the bed while a funnel flow problem within the conical base. Further optimization of the established model is carried out. In addition to the investigation of the preferable wall structure, Prof. Jiang’s team has performed an optimization study on flow-corrective insert, conical base, and discharging silo from the reactor’s geometric perspective. The authors also contributed to the optimization of friction and flow dynamics from the mechanical perspective. The optimizations are very helpful for practical implementations and further developments of HTGR in the nuclear industry, particularly the 600MW-HTR-PM project. Quasi-static pebble flow in HTGR has provided numerous ideas to the solution of non-uniformity and stagnation in the fuel cycle. In addition, heat transfer in a pebble bed is of vital importance for the safety of the reactor. Therefore, experiments in the full-radius-scale heat test facility measure the effective thermal diffusivity and conductivity in four independent tests. Compared with SANA (Secure Decay Heat Removal in German) and HTTU (High-Temperature Test Unit in South Africa), this work expands the temperature range of the effective thermal conductivity in the reactor and the methodology can be applied to the measurement for temperatures up to 1600 °C, significantly contributing to the improvement of the inherent safety for HTGRs. Numerical models of heat transfer in pebble beds of HTGRs present a comprehensive view on obtaining effective thermal conductivity. Continuum and discrete methods are adopted, and varying scales of radiation are discussed. Among convective, conductive, and radiative heat transfers, radiation is particularly important as the operating temperature in the reactor is about 800 °C and can reach 1600 °C in transient or severe accidents. In addition, radiation accounts for most of the transferred heat. The Short-range Radiation Model (SRM), the improved Short-Range Model (SRM+), the Long-range Radiation Model (LRM), the Microscopic Scale Model (MSM), the Semi-Empirical Model (SEM), and the Sub-Cell radiation Model (SCM) perform well under specific circumstances and inspire the subsequent researches. Based on SRM, further improvement in coupled CFD-DEM simulations by taking the coolant into consideration is pioneering in the new smoothed void fraction method, which provides a brand-new view and challenge to investigate it profoundly. I highly recommend this technical book to those who are interested in the nuclear power industry, and also to professionals in the development of nuclear energy, multiphase flow and heat transfer. Although Prof. Jiang’s team focused on the complex system of helium and pebbles coupled with neutron-physics which exists in the nuclear reactor core, the common solutions and schemes provided in this book are indeed also applicable for the gas–particle multiphase flow and high-temperature heat transfer systems in other research fields, e.g., the packed beds or the spouted/fluidized beds in Engineering Thermophysics. This work not only

Foreword by Hongguang Jin

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demonstrates the latest developments in HTGRs technology, but also proposed numerous ideas about pebble flow and heat transfer in pebble beds. The radiative heat transfer particularly deserves close and careful reading if you are carrying out projects in a similar field.

July 2020

Prof. Hongguang Jin Academician of CAS, President of the Chinese Society of Engineering Thermophysics, Institute of Engineering Thermophysics, Chinese Academy of Sciences Beijing, Peoples’ Republic of China University of Chinese Academy of Sciences Beijing, Peoples’ Republic of China

Acknowledgments

Firstly, I would like to thank my research group (Collaborative Innovation Center of Advanced Nuclear Energy Technology, Institute of Nuclear and New Energy Technology (INET) at Tsinghua University), Prof. Zuoyi Zhang (Dean of INET), Prof. Yujie Dong (Deputy Dean of INET), and all colleagues of Key Laboratory of Advanced Reactor Engineering and Safety, who have participated in the compilation of this book. It is because of your unremitting support that this book is completed. It is of great pleasure to work with such an excellent research team, with regular discussion and exchange of ideas, sharing of the project progress, and helping each other unsparingly. This book is the result of our team effort. Thanks for your contribution in revising the first draft, sharing your opinions, and putting forward so many valuable suggestions. Secondly, I would like to thank all the people and organizations who have supported this book and our research, in particular, the support from the national major science and technology project (2011ZX06901-003), National High Technology Research and Development Program of China (863) (2014AA052701), as well as Tsinghua University Press and Springer Nature. The publication of this book is inseparable from your contribution. Thanks to all prior works cited in this book, from which we obtained countless inspiration. These inspirational works have laid the foundation and are of great value to our research. Finally, I would like to thank all the researchers, designers, and regulators involved in the research project of the high-temperature gas-cooled reactors. We are looking forward to the continued joint efforts to contribute to the future development of HTGR.

July 2020

Shengyao Jiang Tsinghua University Beijing, Peoples’ Republic of China

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Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 High-Temperature Gas-Cooled Reactor (HTGR) . . . . . . 1.1.1 Classification and Brief History . . . . . . . . . . . 1.1.2 Main Features and Advantages . . . . . . . . . . . . 1.2 Pebble Bed Type HTGR in Tsinghua University . . . . . 1.2.1 Competative Technical Routes . . . . . . . . . . . . 1.2.2 Heat Transfer Investigations . . . . . . . . . . . . . . 1.3 Pebble Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Discharging/recirculating Granular Flow . . . . . 1.3.2 Very Slow Pebble Flow in HTGR . . . . . . . . . 1.3.3 Pebble Flow Intermittency . . . . . . . . . . . . . . . 1.3.4 Importance of Flow Uniformity . . . . . . . . . . . 1.3.5 Optimization of Pebble Flow Design . . . . . . . . 1.3.6 Review of State-of-the-Art Work . . . . . . . . . . 1.4 Pebble Bed Heat Transfer . . . . . . . . . . . . . . . . . . . . . . 1.4.1 Gas-Pebble Heat Transfer . . . . . . . . . . . . . . . . 1.4.2 Pebble Thermal Radiation . . . . . . . . . . . . . . . . 1.4.3 Effective Thermal Diffusivity and Conductivity 1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Experiments in Pebble Flows . . . . . . . . . 2.1 Experimental Test Facility . . . . . . . . . 2.2 Phenomenological Methods . . . . . . . . 2.2.1 Drainage Pebble Experiment . 2.2.2 Central Area Method . . . . . . 2.2.3 Side Area Method . . . . . . . . 2.2.4 Pre-filled Stripes Method . . . 2.2.5 Pre-filled Core Method . . . . .

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2.3 Pebble Flow in Two-Region Beds . . . . . . . . . . . . . . . . . . 2.3.1 Formation of Two-Region Arrangements . . . . . . . 2.3.2 Mixing Zone and Stagnant Zone . . . . . . . . . . . . . 2.3.3 Motion of Pebbles . . . . . . . . . . . . . . . . . . . . . . . 2.3.4 Equilibrium Conditions and Flow Characteristics . 2.4 Pebble Flow Mechanism Analysis . . . . . . . . . . . . . . . . . . 2.4.1 Quasi-Static Pebble Flow . . . . . . . . . . . . . . . . . . 2.4.2 Distribution of Contact Force . . . . . . . . . . . . . . . 2.4.3 Basic Physics of Quasi-Static Flow . . . . . . . . . . . 2.4.4 Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Particle Velocimetry Measurements . . . . . . . . . . . . . . . . . 2.5.1 Measurement Techniques . . . . . . . . . . . . . . . . . . 2.5.2 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . 2.5.3 Flow Correlation and Intermittency . . . . . . . . . . . 2.5.4 Pebble Arch Formation . . . . . . . . . . . . . . . . . . . . 2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Numerical Methods and Simulation for Pebble Flows 4.1 Discrete Element Methods . . . . . . . . . . . . . . . . . . . 4.2 Gravity-Driven Flow Regime Characterization . . . . 4.2.1 Flow Behavior Characteristics . . . . . . . . . . 4.2.2 Kinetic Versus Kinematic . . . . . . . . . . . . . 4.2.3 Energy Span Versus Standard Deviation . . 4.2.4 Recirculation Rates and Times . . . . . . . . .

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3 Experiments in Pebble Bed Heat Transfer . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Experimental Facility and Methodology . . . . . . 3.2.1 Configuration of Heat Test Facility . . . 3.2.2 Data Processing Algorithm . . . . . . . . . 3.2.3 Preliminary Tests in Vacuum . . . . . . . 3.2.4 Short Summary . . . . . . . . . . . . . . . . . 3.3 Effective Thermal Diffusivity and Conductivity 3.3.1 Experimental Processes . . . . . . . . . . . 3.3.2 Methodology Description . . . . . . . . . . 3.3.3 Quadratic Polynomial Function Results 3.3.4 Improved Method to Reduce Errors . . 3.3.5 Uncertainty Analysis . . . . . . . . . . . . . 3.3.6 Short Summary . . . . . . . . . . . . . . . . . 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.3 Three-Dimensional Pebble Flow . . . . . . . 4.3.1 Voidage Distributions in HTR-10 4.3.2 3D Pebble Flow in HTR-PM . . . 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Numerical Models for Pebble-Bed Heat Transfer . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Continuum Modeling of Pebble Radiation . . . . . . . . . . . . . 5.2.1 Uniform Effective Thermal Conductivity (uETC) . . 5.2.2 Approximation Function Method . . . . . . . . . . . . . 5.2.3 Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Discrete Modeling of Pebble Radiation . . . . . . . . . . . . . . . 5.3.1 Voronoï Cells and Cutoff Scales . . . . . . . . . . . . . . 5.3.2 Short-Range Radiation Model (SRM) . . . . . . . . . . 5.3.3 Short-Range Radiation Model Plus (SRM+) . . . . . 5.3.4 Long-Range Radiation Model (LRM) . . . . . . . . . . 5.3.5 Microscopic Scale Model (MSM) . . . . . . . . . . . . . 5.3.6 Overall Effective Thermal Conductivity at ks  kr . 5.3.7 Semi-Empirical Radiation Model (SEM) . . . . . . . . 5.3.8 Sub-Cell Radiation Model (SCM) . . . . . . . . . . . . . 5.3.9 Application of SCM for Pebble Beds . . . . . . . . . . 5.3.10 Application of SCM for Clumped-Pebbles . . . . . . . 5.3.11 Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 CFD-DEM Coupled Simulation and Development . . . . . . . 5.4.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Heat Transfer Modeling . . . . . . . . . . . . . . . . . . . . 5.4.3 Smoothed Void Fraction Method . . . . . . . . . . . . . 5.4.4 Benchmark Problem of HTR-10 Reactor . . . . . . . . 5.4.5 Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Further Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Evaluation of Emissivity Effects in Four Radiation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.2 Mechanism of Contact Thermal Resistance . . . . . . 5.5.3 Efficient Computing of View Factor . . . . . . . . . . . 5.5.4 Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Applications: Two-Region Pebble Beds . . 6.1 Experimental Measurements . . . . . . . 6.1.1 The Size of the Two Regions 6.1.2 Equilibrium Conditions . . . . 6.1.3 Flow Field in the Vessel . . . .

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6.2 Size Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Numerical Setup . . . . . . . . . . . . . . . . . . . 6.2.2 Transient Phenomenological Analysis . . . . 6.2.3 Shape and Size of Mixing Region . . . . . . . 6.2.4 Mixing Index . . . . . . . . . . . . . . . . . . . . . . 6.2.5 Effect of Particle Size on Stagnant Region . 6.2.6 Short Summary . . . . . . . . . . . . . . . . . . . . 6.3 Density Difference and Loading Ratio Effects . . . . 6.3.1 Simulation Setup . . . . . . . . . . . . . . . . . . . 6.3.2 Results and Discussion . . . . . . . . . . . . . . . 6.3.3 The Size of Central Region . . . . . . . . . . . 6.3.4 Stagnant Condition . . . . . . . . . . . . . . . . . . 6.3.5 Retention of Initial Loading Pebbles . . . . . 6.3.6 Axial Velocity . . . . . . . . . . . . . . . . . . . . . 6.3.7 Short Summary . . . . . . . . . . . . . . . . . . . . 6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Applications: Pebble Flow Optimizations . . . . . . . . . . . . . 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Wall Structure Optimization . . . . . . . . . . . . . . . . . . . . 7.2.1 Numerical Methods and Setup . . . . . . . . . . . . 7.2.2 Wall Structure Effect . . . . . . . . . . . . . . . . . . . 7.2.3 Stagnant Rate . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4 Mean Kinematic Energy and Eulerian Velocity 7.2.5 Extra Dispersion Effect . . . . . . . . . . . . . . . . . . 7.3 Flow-Corrective Insert Optimization . . . . . . . . . . . . . . 7.3.1 Numerical Setup . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Pebble Bed Without Insert . . . . . . . . . . . . . . . 7.3.3 Insert Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.4 Some Discussions . . . . . . . . . . . . . . . . . . . . . 7.3.5 Insert Design . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Conical Base Optimization . . . . . . . . . . . . . . . . . . . . . 7.4.1 Simulation Setup and Bed Configuration . . . . . 7.4.2 Simulation Results and Discussions . . . . . . . . . 7.5 Friction Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 7.5.1 Numerical Setup . . . . . . . . . . . . . . . . . . . . . . 7.5.2 Particle–Wall Friction . . . . . . . . . . . . . . . . . . . 7.5.3 Particle–Particle Friction . . . . . . . . . . . . . . . . . 7.5.4 Criteria for Flow Pattern Evaluation . . . . . . . . 7.5.5 Friction Control in Practical Pebble Bed . . . . . 7.5.6 Application in Full-Scale Pebble-Bed Reactor . 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

Introduction

1.1 High-Temperature Gas-Cooled Reactor (HTGR) A worldwide effort is underway to develop more economical, efficient, environmentally acceptable, and safer nuclear energy for electricity generation and industrial process heat applications. A High-Temperature Gas-cooled Reactor (HTGR) is considered as a safe, efficient, environmentally acceptable, and economical hightemperature energy source for electricity generation and industrial process heat applications such as the production of hydrogen. High-temperature gas-cooled reactor [1], is one of the most probable solutions among the generation IV advanced reactors [2, 3].

1.1.1 Classification and Brief History High-temperature gas-cooled reactor has been developed for decades due to its attractive inherent safety and ability to provide a high-temperature for the industry. There are two existing schemes of the nuclear reactor core in HTGRs. One is formed by graphite prismatic blocks with embedded fuel pellets and the other is a pebble bed filled with fuel elements. The prismatic core high-temperature gas-cooled reactor includes the Gas TurbineModular Helium Reactor (GT-MHR) [4, 5], in the USA and Russia, and the HighTemperature Thorium Reactor (HTTR) [6, 7], in Japan. The pebble-bed hightemperature gas-cooled reactor is the current mainstream technical solution for the HTGR. It has been chosen by many test and demonstration facilities, including the prototype reactor known as Arbeitsgemeinschaft Versuchs Reaktor (AVR) in Germany [8–10], the Modular Pebble Bed Reactor (MPBR) in the USA [11, 12], the Pebble Bed Modular Reactor (PBMR) in South Africa [13, 14]. As a demonstration reactor, i.e., the 10MW High-Temperature Gas-cooled Reactor Test Module, named HTR-10, was developed by the Institute of Nuclear and new Energy Technology © Tsinghua University Press 2021 S. Jiang et al., Multiphase Flow and Heat Transfer in Pebble Bed Reactor Core, https://doi.org/10.1007/978-981-15-9565-3_1

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1 Introduction

(INET) at Tsinghua University in China. The HTR-10 is among the few test reactors of high-temperature reactor over the world [15–18]. HTGRs are being deployed very rapidly and are intended to be commercialized for large-scale applications in the near future. The High-Temperature Reactor-Pebble bed Modules (HTR-PM) was approved as one of the national major science-technology projects of China [19]. The HTR-PM is under construction in Shandong Province of China.

1.1.2 Main Features and Advantages Helium-cooled pebble bed in the high-temperature gas-cooled reactor (HTGR) has the structure of packed sphere fuel balls in the reactor core. In contrast to conventional reactors, there are no structured fuel assemblies in a pebble-bed HTGR. The HTGR configures the core with a packed pebble bed composed of randomly and densely packed mono-sized spherical pebbles. The HTGR core is cooled by helium gas under high pressure, e.g., about 7 MPa for the HTR-PM nuclear reactor [20, 21]. The fuel element of high-temperature gas-cooled reactor is made by dispersing allceramic coated particles in a graphite sphere matrix, which can maintain integrity up to 1600 ◦ C [18]. Pebbles traverse the core under gravity and their positions are determined by the flow of the pebble bed. Pebble-bed HTGR runs in a recirculating mode. Pebble elements are drained out from the discharge hole at the base of the core, whereas new elements are reinserted into the core at the top. When the pebble bed achieves an equilibrium state, the total number of pebbles in the core is approximately constant. The pebble-bed high-temperature gas-cooled reactor meets all kinds of requirements of the generation IV advanced reactor system. One of the most outstanding advantages of the pebble-bed high-temperature gas-cooled reactor is its inherent safety. Other advantages, such as modularity, short construction period, non-stop reloading [8, 9], market flexibility, and broad applications such as high-temperature process heat, are also significant compared with current operating Generation II and Generation III reactors. Hence, the pebble-bed HTGR has drawn great public attention and it is generally recognized as the most promising reactor type in the USA, and even in the world in this century. The pebble-bed reactor is becoming the mainstream technical solution for HTGRs. In 2006, China included the high-temperature gas-cooled reactor project in the Outline of the National Medium- and Long-term Science and Technology Development Plan (2006–2020).

1.2 Pebble Bed Type HTGR in Tsinghua University The HTGR has been studied for decades at the INET of Tsinghua University in China, for exploring and developing modular HTGR technology. For pebble-bed HTGR reactor, the core is filled with large quantities of mono-sized large pebbles

1.2 Pebble Bed Type HTGR in Tsinghua University

3

in a recirculating mode. Each pebble contains many small tristructural-isotropic (TRISO) fuel particles (Fig. 1.1). To study such reactors, the HTR-10 was built in 2000, at the INET of Tsinghua university (Fig. 1.2) [22]. It reached the criticality in 2000, and its full-power operation started in 2003. The excellent characteristics

Fig. 1.1 The pebble model Fig. 1.2 The HTR-10 reactor

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1 Introduction

Fig. 1.3 The HTR-PM reactor

of pebble-bed HTGR had been demonstrated by a series of experiments using the HTR-10 reactor from April 2003 to September 2006 [23]. In views of the excellent performance of HTR-10, the High-Temperature ReactorPebble-bed Module (HTR-PM) is regarded as a promising candidate for the generation IV advanced reactor. The HTR-PM developed by the INET at Tsinghua University has two units of 250MWth at Shidao Bay in China. As a demonstration plant, the HTR-PM (Fig. 1.3), with two units of 250MWth at Shidao Bay in China, is planned to be connected to the grid at the end of 2021.

1.2 Pebble Bed Type HTGR in Tsinghua University

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1.2.1 Competative Technical Routes The main technical goals of the HTR-PM project are as follows: demonstration of inherent safety; demonstration of economic competitiveness; confirmation of proven technologies; standardization and modularization [23]. In severe accidents, e.g., a loss-of-coolant and depressurized accident under full-power operation, the core temperature will increase above its normal operation core temperature transiently. The inherent safety requires that the maximum fuel element temperatures should always be lower than the limiting temperature of 1600 ◦ C. If this criterion is met, no core melting occurs, and no dedicated emergency systems are necessary when all conceivable accidents occur [19, 23]. There are two critical measures to improve the economy of HTR-PM by increasing the outlet temperature to 1000 ◦ C and configuring a 458 MWth reactor with a two-zone annular core as an optimization design [19, 24]. The inherent safety depends on the robust thermal-hydraulic design of reactor at normal operation and extreme emergencies. The robust design validates the desirable characteristics of the generation IV nuclear power system such as inherent safety features and capability to provide a high-temperature. In the present design, the helium temperatures at reactor core inlet/outlet are 250 ◦ C/750 ◦ C, and the produced steam state in the steam generator outlet is 13.25 MPa/567 ◦ C. The most crucial issue from a commercial perspective is the economic competitiveness, compared with the light water reactors (LWRs), which are the primary reactors in the world. According to the cost comparison, the present HTR-PM is 10–20% more expensive than PWR at the same electric power if the current HTRPM parameters are employed [25]. The current HTR-PM reactor and fuel element technologies have the potential of achieving 950 ◦ C to even 1000 ◦ C in helium outlet temperature. This a typical temperature produced by Very High-Temperature gascooled Reactor (VHTR). The improved temperature will enhance the efficiency and power of electricity generating and make HTR-PM more competitive in economy cost. Moreover, a single reactor with a significant thermal power can also be designed to enhance its economic competitiveness while the inherent safety can be reserved.

1.2.2 Heat Transfer Investigations As stated above, the inherent safety of HTGR at a higher power level, meaning better economic competitiveness compared with other reactors, requires a distinct knowledge on effective thermal diffusivity and conductivity of pebble bed at hightemperature range. Especially, the effectivity thermal diffusivity will determine the maximum transient temperature after the accident, and the effectivity thermal conductivity will determine the maximum steady-state temperature inside the reactor core during the decay heat removal period. The pebble bed is represented as a porous structure, and its heat transfer is a combination of solid heat conduction inside or

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between solid fuel elements, thermal radiation between the surfaces of adjacent spheres, and the gas heat convection. According to existing heat transfer researches for a porous media, the radiation effect will account for more than 50% of total heat transfer at moderate temperatures in some porous media [26–28], and radiation heat transfer will be apparently affected by different packing structure and density. Moreover, in the loss-of-coolant and depressurized accident, the gas heat convection isn’t essential. Two previous experiments on the effective conductivity of a graphite pebble bed were conducted by the SANA facility in Germany, in 1996 [29] and the HTTU in South Africa [30, 31] in 2012. Since it was difficult to maintain the steady temperature distribution in the test facilities at very high-temperatures, the effective thermal conductivities obtained by the steady-state method could achieve as high as 1000 ◦ C in the SANA and 1200 ◦ C in the HTTU, which were inappropriate to present the drastic growth of effective thermal conductivity (above 1200 ◦ C) caused by the radiation heat transfer at higher temperature. The distinct knowledge of effective thermal diffusivity and conductivity of pebble bed contributes to realizing the heat transfer at higher thermal power and outlet helium temperature, which means a better balance between safety and economic competitiveness. A full-radius-scaled heat test facility has been developed by the INET of Tsinghua University in China to measure these two parameters up to 1600 ◦ C under vacuum condition (20 Pa) and atmospheric pressure (105 Pa). It’s consistent with the test facilities of the SANA in Germany, and the HTTU in South Africa, that the geometry of the bed core is an annulus with a cylindrical graphite heater in the center [32]. The primary purpose of this test is to obtain the effective thermal diffusivity from environmental temperature to 1600 ◦ C via an inverse method using the transient temperature of a whole heating process. The effective thermal diffusivity and conductivity can be calculated through experimental transient temperatures in the pebble bed, and the relevant data processing algorithm of the inverse method has been studied theoretically [33]. The secondary purpose is to provide an overview of the heating process and temperature distribution inside randomly accumulated fuel balls in the pebble bed. The overview can afford a validation of numerical simulation of Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD) for the thermal-fluid systems.

1.3 Pebble Flows 1.3.1 Discharging/recirculating Granular Flow The detailed understanding of slow flow in dense granular systems has remained one of the central challenges within the field of granular materials. Granular flow is an attractively simple and yet surprisingly complex subject. Slow and dense flows pose a considerable challenge to theorists due to many-body interactions and nonthermal fluctuations [34]. Beyond their fundamental scientific interest, such flows

1.3 Pebble Flows

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have essential engineering applications. For example, the efficiency and safety of the pebble-bed nuclear reactor depend on the degree of mixing [35–37]. The process of silo discharge can be considered an example of the complexity of granular flows. Lots of experimental and simulation studies have been carried out over the past decades. Usually, the orifice is opened at the bottom of the silo filled with grains. The effects of the orifice size on the flow characteristics have been widely studied. In general, bigger orifices may result in more homogeneous pebble flow, while smaller orifices can develop pebble flow intermittencies [38]. The flowrate oscillations caused by different sizes of orifice seem not to be dominated by any particular frequency. Moreover, the flow of granular materials inside a quasi-twodimensional silo was measured and compared with some existing models, including the kinematic model, void model, and the spot model [39]. The basic mechanism of granule flow has not been fully understood yet, especially this specific pebble flow in a reactor core. However, the flow field characteristic is vital to the efficiency and safety of HTGR. The behavior of the pebbles should be ensured to fulfill thermal-hydraulic rules and radiation safety requirements. Experimental and numerical studies have shown features of variously shaped particles flowing through silos with different geometries. Still, those cases all belong to free outflow and more focus on the prediction of outflow rate [40–42]. The law governing the pebble flow is an important topic and crucial for the design of the pebble-bed reactor. It is an attractively simple and yet surprisingly complex subject. Fast, dilute flows are known to obey classical hydrodynamics, but slow and dense flows pose a considerable challenge to theorists [43], due to many-body interactions and non-thermal fluctuations. The underlying physical mechanism of dense granular flow is far from fully understood, although it is very familiar to us, e.g., sand in an hourglass [43].

1.3.2 Very Slow Pebble Flow in HTGR The pebble flow characteristics are the basis of geometrical design, neutronic design and nuclear fuel cycle of the pebble bed reactor core. The reactor physics, thermal engineering, and nuclear fuel cycle designs all depend on the pebble flow. Therefore, the pebble flow plays a fundamental role in the design improvement and thermal safety analysis of the pebble-bed high-temperature gas-cooled reactor [44]. The pebble flow in pebble-bed reactors is a unique particle flow or granular flow. In contrast to conventional reactors, there are no structured fuel and reflector assemblies in the pebble-bed HTGR. Discrete baseball-size graphite-coated fuel pebbles instead of the structured fuel rods are used to form the pebble-bed HTGR core. The stochastically and densely accumulated hundreds of thousands of fuel pebbles flow downward very slowly through the core of the pebble-bed reactor driven by gravity. This a very slow particle flow is called a pebble flow. The pebbles are loaded from the top of the reactor core and discharged from the bottom. The pebble-bed HTGRs run in a circulating mode with fresh fuel pebbles loaded from bed top and used fuel

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pebbles discharged from the bed bottom. The loading rate is precisely equal to the discharging rate, so the total number of the fuel pebbles in the core remains constant during the operation. Different from other types of granular flow, the flow rate of the pebbles in the reactor is slow that the equivalent flow velocity in HTGR is lower than most granular flows in several orders. In most applications, it can be viewed as a pebble system composed of the equivalent stagnant pebbles. This is a new flow regime of extremely slow pebble flow. Granular flow is an attractively simple and yet surprisingly complex subject [45]. To date, the detailed understanding of the slow and dense granular flows has not been obtained and remains one of the critical challenges in the fields of the granular science and technology. In general, the fast and dilute flows can be analyzed by the classical hydrodynamics. In contrast, the slow and dense flows pose a considerable challenge to theorists in terms of the complex many-body interactions and non-thermal fluctuations. Moreover, the slow granular flows have many important engineering applications [46], e.g., the new pebble-bed nuclear reactors [47], whose efficiency and safety depend on the degree of the mixing in prolonged granular drainage (