Computational and Experimental Simulations in Engineering: Proceedings of ICCES 2020, Volume 1 3030646890, 9783030646899

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Mechanisms and Machine Science 97

Satya N. Atluri Igor Vušanović Editors

Computational and Experimental Simulations in Engineering Proceedings of ICCES 2020. Volume 1

Mechanisms and Machine Science Volume 97

Series Editor Marco Ceccarelli , Department of Industrial Engineering, University of Rome Tor Vergata, Roma, Italy Editorial Board Alfonso Hernandez, Mechanical Engineering, University of the Basque Country, Bilbao, Vizcaya, Spain Tian Huang, Department of Mechatronical Engineering, Tianjin University, Tianjin, China Yukio Takeda, Mechanical Engineering, Tokyo Institute of Technology, Tokyo, Japan Burkhard Corves, Institute of Mechanism Theory, Machine Dynamics and Robotics, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany Sunil Agrawal, Department of Mechanical Engineering, Columbia University, New York, NY, USA

This book series establishes a well-defined forum for monographs, edited Books, and proceedings on mechanical engineering with particular emphasis on MMS (Mechanism and Machine Science). The final goal is the publication of research that shows the development of mechanical engineering and particularly MMS in all technical aspects, even in very recent assessments. Published works share an approach by which technical details and formulation are discussed, and discuss modern formalisms with the aim to circulate research and technical achievements for use in professional, research, academic, and teaching activities. This technical approach is an essential characteristic of the series. By discussing technical details and formulations in terms of modern formalisms, the possibility is created not only to show technical developments but also to explain achievements for technical teaching and research activity today and for the future. The book series is intended to collect technical views on developments of the broad field of MMS in a unique frame that can be seen in its totality as an Encyclopaedia of MMS but with the additional purpose of archiving and teaching MMS achievements. Therefore, the book series will be of use not only for researchers and teachers in Mechanical Engineering but also for professionals and students for their formation and future work. The series is promoted under the auspices of International Federation for the Promotion of Mechanism and Machine Science (IFToMM). Prospective authors and editors can contact Mr. Pierpaolo Riva (publishing editor, Springer) at: [email protected] Indexed by SCOPUS and Google Scholar.

More information about this series at http://www.springer.com/series/8779

Satya N. Atluri Igor Vušanović •

Editors

Computational and Experimental Simulations in Engineering Proceedings of ICCES 2020. Volume 1

123

Editors Satya N. Atluri Mechanical Engineering Texas Tech University Lubbock, TX, USA

Igor Vušanović Faculty of Mechanical Engineering University of Montenegro Podgorica, Montenegro

ISSN 2211-0984 ISSN 2211-0992 (electronic) Mechanisms and Machine Science ISBN 978-3-030-64689-9 ISBN 978-3-030-64690-5 (eBook) https://doi.org/10.1007/978-3-030-64690-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, 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 publisher, 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 publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

This book gathers the latest advances, innovations, and applications in the field of computational engineering, as presented by leading international researchers and engineers at the 26th International Conference on Computational & Experimental Engineering and Sciences (ICCES). ICCES covers all aspects of applied sciences and engineering: theoretical, analytical, computational, and experimental studies and solutions of problems in the physical, chemical, biological, mechanical, electrical, and mathematical sciences. As such, the book discusses highly diverse topics, including data-driven computational modeling; biomedical engineering and biomechanics; sound and vibration; computational and experimental materials and design; engineering and experimental sciences; modern computational methods; modern developments in mechanics of materials and structures; multi-scale and multi-physics fluid engineering; structural integrity and longevity; and materials design and simulation. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations.

v

Contents

Influence of Ballast Track on Vertical Response of Multi-span Simply-Supported Bridges Under Railway Traffic . . . . . . . . . . . . . . . . . M. D. Martínez-Rodrigo, A. Romero, E. Moliner, J. Chordà, and P. Galvín Data-Driven Fluid Flow Simulations by Using Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kazuhiko Kakuda, Yuto Morimasa, Tomoyuki Enomoto, Wataru Okaniwa, and Shinichiro Miura Ultralight Metallic/Composite Materials with Architected Cellular Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Maryam Tabatabaei and Satya N. Atluri Spectroscopic Characterization and Molecular Dynamics Simulation of Tin Dioxide, Pristine and Functionalized Graphene Nanoplatelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Olasunbo Farinre, Hawazin Alghamdi, and Prabhakar Misra Determination of Strength and Fracture Toughness from Indentation Tests in the Framework of Finite Fracture Mechanics . . . . . . . . . . . . . . Jonathan Hahn and Wilfried Becker A Flow Study in the Cyclone with Particle Separations . . . . . . . . . . . . . Karel Fraňa, Christian Neubert, Sylvio Simon, Arastun Mammadov, and Fariz Amirov

1

14

20

29

44 52

Nonreflecting Outlet Boundary Conditions for Smoothed Particle Hydrodynamics Simulation of Small-Scale Open-Channel Flow . . . . . . . Thanh T. Bui and Susumu Nakata

60

Study on Material Point Method with Different Influence Factors of Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jingjing Zhang, Jinglin Luo, and Mian Jiang

72

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viii

Contents

Study on Dali-Baoshan Section of Anning-Baoshan Oil Product Pipeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wang Li, Liqiao Huang, Wenhua Ma, and Zhijian Zhang A New Locking-Free Thick/Thin Shell Element with Incompatible Approximation in a General Orthogonal Curvilinear Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jingxu Chen, Yongchang Cai, and Pengfei Yan

84

95

Homogenization and Frequency Analysis of Composite Sandwich Panel with Fiber Reinforced Polymer Matrix Laminated Faces . . . . . . . 117 Eva Kormanikova, Milan Zmindak, Kamila Kotrasova, and Pavol Novak Dynamic Simulation of Natural Gas Filter Separator Depressurization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Yue Song, Fanpeng Meng, Zhenpeng Hao, Lei Wang, Dan Li, and Shuangjie Yuan Design and Analysis of the Human Airbag . . . . . . . . . . . . . . . . . . . . . . 133 Lu Chen, Dong Mao, and Qiang Gao Study on the Separation Technology of HGS and Its Effect on the Temperature Field of the Wellbore During the Multi-gradient Drilling in Deep Water . . . . . . . . . . . . . . . . . . . . . . . 139 Ruiyao Zhang, Jun Li, Gonghui Liu, Ting Yue, Hongwei Yang, and Hailong Jiang ALOHA Anti-collision Algorithm for Frame Idle Slot Removal and Collision Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Hong-wei Deng, Wei Zeng, Ming Yao, and Jia-li Kong Experimental Investigation of the Evolution of Permeability and Porosity of Fushun Oil Shale After High Temperature . . . . . . . . . . 171 Mengtao Cao, Yide Geng, and Pengfei Wu Study on Commissioning Techniques for Oil Transportation Pipeline with Large Elevation Difference and Continuous U Shape . . . . . . . . . . . 182 Wang Li, Liang Feng, Qiqi Chen, Xiaohua Chen, and Wenlong Jia Application of Functional Safety Analysis in Refined Oil Station . . . . . . 191 Wang Li, Xiaohua Chen, Zhen Ma, and Jiawen Long CFD Modelling and Simulation of Drilled Cuttings Transport Efficiency in Horizontal Annulus During Gas Drilling Process: Effect of Gas Injection Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Kaiyu Zhang, Jirui Hou, and Zhuojing Li Research on Wellbore Temperature Field in Deep-Water CML Dual Gradient Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 Geng Zhang, Jun Li, Liu Gonghui, Yang Hongwei, and Wang Jiangshuai

Contents

ix

Full-Scale Forced Vibration Tests of a Railway Bridge . . . . . . . . . . . . . 224 Andreas Andersson Multi-period Infrared Image Generation Based on Multi-conditional Cycle Generative Adversarial Networks . . . . . . . . . . . . . . . . . . . . . . . . . 233 Xiaoxiang Qi, Min Li, Le Ma, Ying Zhu, and Yu Song Infrared Image Derivation Method for Generative Adversarial Network with Object Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Ying Zhu, Min Li, Le Ma, Xiao Xiang Qi, and Yu Song Research on Performance Optimization of Nuclear Power System Based on Improved Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 245 Bo Yang Research of University Education Intelligent Agent . . . . . . . . . . . . . . . . 252 Jun Xing, Chengbo Yin, and Linlin Dai Optimal Design of Natural Gas Gathering Systems with Production Capacity Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Yuan Xu, Wei Zhao, Bowen Ren, Bohong Wang, Yi Wang, and Yongtu Liang Operating Parameters Optimization of Natural Gas Purification Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276 Yuan Xu, Yang Zhang, Lianghui Guo, Yi Wang, and Yongtu Liang Preliminary Study on Integrated Simulation of Natural Gas Gathering Pipeline Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Yuan Xu, Bowen Ren, Wei Zhao, Feng Xu, Yi Wang, and Yongtu Liang Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

Influence of Ballast Track on Vertical Response of Multi-span Simply-Supported Bridges Under Railway Traffic M. D. Martínez-Rodrigo1(B) , A. Romero2 , E. Moliner1 , J. Chordà1 , and P. Galvín2 1 Mechanical Engineering and Construction Department, Universitat Jaume I,

12071 Castellón, Spain [email protected] 2 Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, 41092 Sevilla, Spain

Abstract. In this contribution the vertical response of multi-span single-track simply-supported railway bridges is addressed. The main objective is to assess the influence of the track components and its continuity on the bridge acceleration response under the passage of railway convoys. To this end, a preliminary bidimensional numerical model is presented including a discrete model for the track. The model is calibrated with the proof load test results performed on the structure in the past. A sensitivity analysis is performed showing the effect the track components stiffness and damping considered under resonant and non-resonant conditions. Finally, a recent experimental campaign performed by the authors on an existing bridge is presented and the structural response under two trains is compared with numerical predictions. Preliminary conclusions regarding the effect of the track components and the ballast coupling between adjacent decks are finally extracted. Keywords: Railway bridges · Ballast track · Experimental measurements · Vertical acceleration · Bridge dynamics · Resonance

1 Introduction Railway induced vibrations are a matter of concern for engineers and authorities in recent societies. In many countries, nowadays High-Speed services allow intense mobility between distant highly populated urban areas. The crescent density of traffic and the train operational speeds require, nonetheless, an outstanding response of railway infrastructures in order to ensure traffic safety, passenger comfort and adequate environmental conditions in the surrounding area. Comprising an important proportion of the railway infrastructure, railway bridges have received considerable attention in the last years and, to ensure traffic safety and passenger comfort, their design must accomplish strict requirements [1]. In particular, short-to-medium span simply-supported (SS) bridges with ballasted tracks are prone to experience high deck vertical accelerations which may lead to ballast deconsolidation, rail misalignment and derived problems [2–12]. In this context, a deep understanding © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 1–13, 2021. https://doi.org/10.1007/978-3-030-64690-5_1

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M. D. Martínez-Rodrigo et al.

of train-track-bridge interaction mechanisms is essential in order to be able to predict and assess the dynamic response of such structures. A state-of-the-art review on the evolution of numerical models and experimental tests focusing on validation, safety assessment and long-term performance investigation of train-track-bridge systems was recently presented by Zhai et al. [5]. Railway axle loads and bridges interact through the track infrastructure. The track distributes the axle loads and may exert a restraining effect on the bridges’ boundary conditions [6] and a coupling effect among different spans of the same viaduct [7], or between adjacent single-track decks [8]. Nevertheless, in many publications the effect of the track is disregarded and the influence of the super-structure composed by the rails, sleepers and ballast, in ballasted tracks, is still not well known. In this contribution, the dynamic behavior of multi-span single-track bridges is investigated with the aim of evaluating the effect of the continuity of the track on the bridge vertical response. In Sect. 2 an existing bridge object of study is described, along with the numerical model. In Sect. 3, the results of a preliminary sensitivity analysis on a few track parameters is presented. In Sect. 4, the results of an experimental campaign recently performed on the bridge are compared with numerical predictions. Finally, some conclusions are extracted regarding the effect of the track super-structure on the bridge acceleration response.

2 Bridge Description and Numerical Model 2.1 Bridge Description The bridge under study is a bridge crossing the Old Guadiana River in the conventional railway line Madrid-Alcázar de San Juan-Jaén in the Alcázar de San Juan-Manzanares section (see Fig. 1). It is a double track concrete bridge composed by two identical SS bays. The horizontal structure is formed by two structurally independent decks, one for each track. Each deck is composed by a concrete slab resting on five pre-stressed concrete rectangular girders with no transverse stiffening elements (see Fig. 2). The longitudinal girders rest on the two abutments and on a central support through neoprene bearings. Each deck accommodates a ballasted track with Iberian gauge UIC60 rails and mono-block concrete sleepers each 0.60 m.

Fig. 1. Bridge over Old Guadiana River photographs

Influence of Ballast Track on Vertical Response of Multi-span SS Bridges

3

2.2 Numerical Model In a first approach, the numerical model described in what follows is used. Only half of the deck is represented as two successive Bernoulli-Euler (B-E) beams resting on elastic supports, accounting for the neoprene bearings vertical stiffness. The two rails are simulated as an equivalent single B-E beam as well. A three layer discrete track model (see Fig. 3) as the one proposed by Zhai [9] is implemented, where the damping and stiffness of rail pads, ballast and subgrade are included at the sleepers positions.

Fig. 2. Old Guadiana Bridge cross-section

Fig. 3. Numerical track-bridge interaction model

In order to simulate the axle vertical forces, a constant moving load model is selected, therefore neglecting vehicle-structure interaction effects in a first approach. The model, as described above, is generated using Finite Elements in Ansys software. Then, the equations of motion of the complete system are integrated in the time domain applying Newmark-Betta constant acceleration algorithm programmed in Matlab.

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3 Sensitivity Analysis over Track Parameters First, a sensitivity analysis is performed on four track parameters: the stiffness and damping coefficients of the rail pads, K p and C p , and of the ballast, K b and C b . In the last years, different authors have proposed discrete track models for the analysis of railway induced vibrations. Figure 4 shows the evident dispersity in the values for these four parameters admitted in previous publications. First, a set of nominal or reference values for all the track parameters is defined on the basis of the literature review. Then, the bridge parameters, assumed identical in both bays, (Modulus of Elasticity E bi , moment of inertia I zbi and linear mass mbi ) are adjusted in order to reproduce static and dynamic tests performed on the structure right before its opening. In Table 1 the bridge and track reference parameters assumed are included. These will be the ones used in the experimental validation (Sect. 4). The fundamental frequency of the track-bridge system for these parameters equals 10.07 Hz. A damping ratio of 1.565% is assigned to any mode as per [23] for pre-stressed concrete bridges of the particular span length. K p (MN/m)

C p(MNs/m)

K b (MN/m)

C b (MNs/m)

Kouroussis (2015)

Kouroussis (2015)

Kouroussis (2015) Kouroussis (2015)

Kouroussis (2011)

Kouroussis (2011)

Kouroussis (2011) Kouroussis (2011)

Fig. 4. Rail pad and ballast layer stiffness and damping values admitted by different authors in the past for comparable ballast layers thicknesses and sleepers distances [6, 9–20]

As per the subgrade stiffness and damping coefficients inside the bridge, 100 K f and 0 Ns/m have been assigned as it is assumed that the ballast layer rests directly on the concrete slab inside the bridge. A track length of 20 m is included before and after the two-span bridge, equivalent to more than 30 times the sleeper distance, which is considered adequate attending to previous publications [21, 22]. A sensitivity analysis is performed on this length ensuring the convergence of results. For the sensitivity analysis the response of the bridge is obtained under the circulation of an artificial train of 20 equidistant loads of 210 kN separated 18 m, with the aim of inducing two clear resonances on the structure. The bridge time-history response in terms of displacements and accelerations is obtained for 60 velocities of circulation in

Influence of Ballast Track on Vertical Response of Multi-span SS Bridges

5

Table 1. Bridge-track reference parameters Rail and bridge parameters

Track parameters per rail seat

Ar (m2 )

76.86E−4

K p (N/m)

1E8

Er (Pa)

2.1E11

C p (Ns/m)

7.5E4

I zr (m4 )

3055E−8

M sl (kg)

300

ρr (m3 )

7850

K b (N/m)

1.933E8

Dsl (m)

0.60

C b (Ns/m)

5.88E4

L bi (m)

11.93

M b (kg)

317.91

7.09E9

K f (N/m)

7.3987E7

mbi (kg/m)

8727

C f (Ns/m)

3.115E4

ζbi (%)

1.565

K w (N/m)

7.84E7

K n,bi (N/m) st/dyn

11.165E8/22.33E8

C w (Ns/m)

8E4

(I z ·E)bi

(Nm2 )

the range [40, 100] m/s. A Chebyshev order 3 filter is applied to the acceleration response filtering contributions below 1 Hz and above 60 Hz. Maximum response envelopes are obtained for values of the track parameters: [0.5, 1, 2, 4] · Kp [0, 0.5, 1, 2] · Cp [0.5, 1, 2, 4] · Kb [0, 0.5, 1, 2] · Cb .

(1)

where the values of K p , C p , K b and C b are those in Table 1. Figure 5 shows the evolution of the maximum acceleration, which always takes place in the center of the second span, in absolute value in terms of the velocity for isolated variations of each track parameter. In all the plots shown in Fig. 5 three resonant peaks can be detected, corresponding to second, third and fourth resonances of the fundamental mode, which in the reference case presents a frequency f 1 = 10.07 Hz. r,j=2

V1

=

km df1 km km r,j=3 r,j=4 3.6 = 326.27 V1 V1 = 217.5 = 163.1 2 h h h

(2)

The individual variations considered in the track do not affect significantly the reference fundamental frequency. From the observation of Fig. 5(c)–(d) it may be concluded that the influence of the variations in the rail pads and ballast damping constants is negligible on the maximum acceleration response of the bridge for the reference values of the remaining parameters. The parameter that seems to affect the most the acceleration envelope at the most critical section is the rail pad stiffness K p , leading to a decrease in the maximum acceleration at resonance as K p reduces (for more flexible rail pads). This effect is more visible for higher resonance orders. The same tendencies, although in a less pronounced manner, are observed in terms of the variations considered in the ballast stiffness K b .

2

amax @ x=1.5L (m/s )

2

amax @ x=1.5L (m/s )

6

M. D. Martínez-Rodrigo et al. 4.0 K p 2.0 K p 1.0 K p 0.5 K p

(a)

4.0 K b 2.0 K b 1.0 K b 0.5 K b

(c)

V (km/h)

(b)

0.0 Cb 0.5 Cb 1.0 Cb 2.0 Cb

(d)

V (km/h)

Fig. 5. Results from sensitivity analysis over track parameters

4 Experimental Validation 4.1 Experimental Campaign Description In May 2019 the authors performed an experimental campaign on Old Guadiana Bridge with the purpose of characterizing the structure and soil dynamic properties along with the bridge dynamic response under railway traffic. As per the acquisition equipment, a portable acquisition system LAN-XI of Brüel & Kjaer was used. The acquisition system fed the sensors (accelerometers) and an instrumented impact hammer in the case of the soil tests. It also performed the Analog/Digital conversion (A/D). The A/D was carried out at a high sampling frequency that avoided aliasing effects using a low-pass filter with a constant cut-off frequency. The sampling frequency was fs = 4096 Hz. The acquisition equipment was connected to a laptop for data storage. Endevco model 86 piezoelectric accelerometers were used with a nominal sensitivity of 10 V/g and a lower frequency limit of approximately 0.1 Hz. The acquisition system was configured to avoid the sensors’ overload (Fig. 6). From the dynamic characterization of the soil, which was carried out by the by Spectral Analysis of Surface Waves test a rather stiff soil was identified with a shear wave velocity higher than 250 m/s in the upper soil layer. The bridge response depends on soil-structure interaction (SSI) and soil stratigraphy. However, due to the high soil stiffness identified, in a first approach this effect is disregarded.

Influence of Ballast Track on Vertical Response of Multi-span SS Bridges

7

Fig. 6. Experimental campaign photographs

As per the bridge structure, eighteen accelerometers are connected to the lower horizontal surface of the decks longitudinal girders in the locations indicated in Fig. 7. SPAN 1

SPAN 2

Track 1 DCK 2

DCK 2

DCK 1

DCK 1

Track 2

Fig. 7. Sensors placement in experimental campaign

4.2 Structure Response Under Railway Traffic During the 2019 campaign the response of the structure was recorded under the circulation of different trains. Two of these circulations are included in this section. Both correspond to the medium distance Renfe Altaria Talgo VI train travelling along tracks 2 and 1 (see Fig. 7) in the directions South-North (Manzanares-Alcázar de San Juan) and North-South, respectively. Figure 8 and Fig. 9 show photographs of the trains and a scheme of the axles distances. Also, Table 2 includes the train axles arrangement and loads. First, the speeds were identified from the frequency associated to the bogie distance leading to approximately 155 km/h in both cases. Then, the response of the bridge was calculated using the numerical model described in Sect. 2.2 with the properties included in Table 1, with the exception of structural damping which was assumed as 3.1% for the fundamental frequency, 10.065 Hz, and 1.56% for 90 Hz (Eurocode value). The first value was identified during the proof load test. The numerical response, integrated in the time domain using the full FE model, is also filtered between 1 and 30 Hz, applying the same procedure as with the experimental records. Given the bidimensional

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M. D. Martínez-Rodrigo et al.

nature of the numerical model, only the response at sensors installed underneath beams 3 and 8 is compared with the numerical predictions.

Fig. 8. Renfe Altaria Talgo VI trains crossing Old Guadiana Bridge

It is verified that the bridge maximum acceleration did not exceed the limit established by the Serviceability Limit State for traffic safety in the case of ballasted tracks [1] according to the measurements in all the sensors.

Fig. 9. Renfe medium distance Altaria Talgo VI train axle scheme Table 2. RENFE Altaria Talgo VI features Train

N

d(m)

d 1 (m)

l 1 (m)

l 2 (m)

P1 (kN)

P2 (kN)

P3 (kN)

Altaria

7

13.14

–

3.44

3.3

225

70

140

Figure 10 shows an experimental vs. numerical comparison of the vertical acceleration at sensors 5 and 6 under the circulation of the northbound train, in the time (a)–(b) and frequency (c)–(d) domains. The Talgo passenger coaches present a distance between shared axles of 13.14 m. The theoretical resonant speed associated to this length for the third resonance of the fundamental mode is approximately 159 km/h, which is quite close to the real speed. This can be detected in the time-history plots where two oscillations of decreasing amplitude take place in between the passage of consecutive axles. km km df1 3.6 = 158.7 ≈ 154.8 =V (3) 3 h h The accuracy of the numerical model is quite reasonable up to 30 Hz, both at L/2 and 3L/4 of the first span, although the numerical model overpredicts the acceleration r,j=3

V1

=

Influence of Ballast Track on Vertical Response of Multi-span SS Bridges (b)

2

a @ x=0.5 L (m/s )

a @ x=0.75L (m/s 2)

(a)

Numerical

Experimental A5

Numerical

Experimental A6

t (s)

2

(c) Numerical Experimental A5

f (Hz)

a @ x=0.75L (m/s 2/Hz)

t (s)

a @ x=0.5 L (m/s /Hz)

9

(d) Numerical Experimental A6

f (Hz)

Fig. 10. (a)–(b) Time history and (c)–(d) frequency content of the acceleration response at sensors 5 and 6 induced by Altaria Talgo VI train. Numerical prediction (black trace) vs. experimental measurements (red trace). Northbound train (track #2).

for contributions close to the bridge fundamental frequency. This can be associated to vehicle-structure interaction which is not taken into account and can be of importance, specially at resonance; or to other energy dissipation mechanisms amplitude dependent such as the interaction between the adjacent decks, etc. Figure 11 shows the same type of comparative for the southbound train. In this case the acceleration is compared at sensors 13 and 17, located at mid-span of the second and first spans, respectively. Again, the time-history response is well reproduced, specially after the passage of the locomotive. In the frequency domain again, a predominant peak is detected showing the important contribution of the fundamental mode with a certain overprediction of the acceleration in the numerical case. Finally, the coupling effect between the adjacent decks is evaluated in forced vibration. Figure 12(a)–(c) represent for the northbound train travelling along track #2 the experimental response measured at sensor 5 (at mid-span under the loaded track) and, simultaneously, at sensor 17 (at mid-span under the adjacent unloaded track). The transmission of vibrations between the two decks is evident, even though these are only connected by the continuous ballast layer. At the unloaded sensor the frequency peaks associated to the excitation (e.g. bogie distance) which are visible in the low frequency

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M. D. Martínez-Rodrigo et al. (b)

a @ x=1.5 L (m/s 2 )

2

a @ x=0.5 L (m/s )

(a)

Numerical

Numerical

Experimental A13

(c) Numerical Experimental A13

f (Hz)

a @ x=1.5L (m/s 2/Hz)

t (s)

2

a @ x=0.5 L (m/s /Hz)

t (s)

Experimental A17

(d) Numerical Experimental A17

f (Hz)

Fig. 11. (a)–(b) Time history and (c)–(d) frequency content of the acceleration response at sensors 13 and 17 induced by Altaria Talgo VI train. Numerical prediction (black trace) vs. experimental measurements (red trace). Southbound train (track #1).

range in the loaded sensor, almost not perceptible; but the acceleration at the fundamental frequency reaches 60.6% de value in the loaded sensor. The same effect may be observed under the circulation of the southbound train when one compares the response between sensors 13 (under loaded track) and 12 (adjacent deck at symmetrical position). In this case the maximum acceleration in the unloaded sensor at the fundamental frequency in the frequency domain attains 48.5% the same maximum measured at sensor 13. This vibration transmission can be caused both by the continuous ballast layer and by the common foundations shared by the decks. In the opinion of the authors this phenomenon deserves further investigation. Implementing a 3D model of the bridge-track system would permit to evaluate the vibration transmitted between the decks close to the shared border in the frequency range of interest.

Influence of Ballast Track on Vertical Response of Multi-span SS Bridges

11

Altaria Talgo VI @154.8 km/h (Track #1)

(a)

(b)

2

a @ x=0.5 L (m/s )

Altaria Talgo VI @154.8 km/h (Track #2)

Exp. A5

Exp. A17

Exp. A13

2

a @ x=0.5L (m/s /Hz)

t (s)

f (Hz)

Exp. A12

t (s) (c)

(d)

Exp. A5 Exp. A17

Exp. A13 Exp. A12

f (Hz)

Fig. 12. (a)–(b) Time history and (c)–(d) frequency content of the acceleration response at sensors 5 and 17 induced by the northbound train, and at sensors 13 and 12 induced by the southbound train.

5 Conclusions In the present study the effect of the track components on the vertical acceleration response of multi-span ballasted bridges is evaluated. To this end, a planar track-bridge interaction numerical model is implemented and the results are compared to experimental measurements. The track is represented using a three-layer discrete model. The main preliminary conclusions that can be extracted are the following: • There is a very high dispersion in the track parameters admitted by different authors for similar track infrastructures. The rail-pad stiffness seems to affect the most the bridge maximum acceleration specially at high-order resonances, leading to lower amplitudes for higher flexibilities of this parameter. The ballast stiffness affects in a similar way, although to a lower extent. • The experimental vs. numerical predictions in the case of Old Guadiana bridge are reasonable in the sensors located along the longitudinal axis of the decks, as there is

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no contribution of the torsion mode at those locations. The numerical model tends to overestimate the real response close to the bridge natural frequency. • The transmission of vibrations from the loaded deck to the unloaded deck is relevant. This may be caused by the continuous ballast layer but also by the shared foundations of the two decks. In the authors’ opinion this effect is not well known and should be investigated using a 3D model of the complete bridge.

Acknowledgements. The authors would like to acknowledge the financial support provided by the Spanish Ministries of Economy and Competitiveness and of Science and Innovation under research projects BIA2016-75042-C2 and PID2019-109622RB; US-126491 funded by the FEDER Andalucía 2014–2020 Operational Program; Generalitat Valenciana under research project [AICO2019/175] and the Andalusian Scientific Computing Centre (CICA).

References 1. CEN EN-1990, Eurocode: Basis of structural design. Annex 2: Application for bridges (2002) 2. ERRI D214: Rail bridges for speeds > 200 km/h. final report. Part a. Synthesis of the results of d 214 research. European Rail Research Institute (1999) 3. Hoorpah, W.: Dynamic Calculations of High-Speed Railway Bridges in France – Some Case Studies Dynamics of High-Speed Railway Bridges. Taylor & Francis, Boca Raton (2008) 4. Zacher, M., Baeßler, M.: Dynamic Behaviour of Ballast on Railway Bridges. Dynamics of High-Speed Railway Bridges. Taylor & Francis, Boca Raton (2008) 5. Zhai, W., Han, Z., Chen, Z., Ling, L., Zhu, S.: Train-track-bridge dynamic interaction: a state-of-the-art review. Veh. Syst. Dyn. 7, 984–1027 (2019) 6. Rigueiro, C., Rebelo, C., da Silva, L.S.: Influence of ballast models in the dynamic response of railway viaducts. J. Sound Vib. 329, 3030–3040 (2010) 7. Liu, K., Lombaert, G., De Roeck, G.: Dynamic analysis of multispan viaducts with weak coupling between adjacent spans. J. Bridge Eng. ASCE 19(1), 83–90 (2014) 8. Rebelo, C., da Silva, L.S., Rigueiro, C., Pircher, M.: Dynamic behaviour of twin single-span ballasted railway viaducts. Field measurements and modal identification. Eng. Struct. 30, 2460–2469 (2008) 9. Zhai, W., Wang, K., Lin, J.: Modelling and experiment of railway ballast vibrations. J. Sound Vib. 270, 673–683 (2004) 10. Kouroussis, G., Connolly, D.P., Alexandrou, G., Vogiatzis, K.: The effect of railway local irregularities on ground vibration. Transp. Res. Part D 39, 17–30 (2015) 11. Sun, Y.Q., Dhanasekar, M.: Influence of the railway track parameters to the vertical and lateral impact. In: Conference on Railway Engineering, Wollongong (2002) 12. Jesús, A.H., Dimitrovová, Z., Silva, M.A.G.: A statistical analysis of the dynamic response of a railway viaduct. Eng. Struct. 71, 244–259 (2014) 13. Naemi, M., Zakeri, J.A., Esmaeili, M., Mehrali, M.: Dynamic response of sleepers in a track with uneven rail irregularities using a 3D vehicle–track model with sleeper beams. Arch. Appl. Mech. 85, 1679–1699 (2015) 14. Lombaert, G., Degrande, G., Kogut, J., François, S.: The experimental validation of a numerical model for the prediction of railway induced vibrations. J. Sound Vib. 297, 512–535 (2006)

Influence of Ballast Track on Vertical Response of Multi-span SS Bridges

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15. Kouroussis, G., Gazetas, G., Anastasopoulos, I., Conti, C., Verlinden, O.: Discrete modelling of vertical track–soil coupling for vehicle–track dynamics. Soil Dyn. Earthq. Eng. 31, 1711– 1723 (2011) 16. Esveld, C.: Modern railway track. Delft University of Technology (2001) 17. Nguyen, K., Goicolea, J.M., Gabaldón, F.: Comparison of dynamic effects of high-speed traffic load on ballasted track using a simplified two-dimensional and full three-dimensional model. J. Rail Rapid Transit 228(2), 128–142 (2012) 18. Zhai, W.M.: Two simple fast integration methods for large-scale dynamic problems in engineering. Int. J. Numer. Meth. Eng. 39, 4199–4214 (1996) 19. Bongini, E., Poisson, F.: Ground vibrations simulation cases parameters. Technical report, SNCF, France (2009) 20. Chen, Z., Zhai, W., Wang, K.: A locomotive-track coupled vertical dynamics model with gear transmissions. Veh. Syst. Dyn. 55(2), 244–267 (2017) 21. Lou, P.: A vehicle-track-bridge interaction element considering vehicle’s pitching effect. Finite Elem. Anal. Des. 41, 397–427 (2005) 22. Clark, R.A., Dean, P.A., Elkins, J.A., Newton, S.G.: An investigation into the dynamic effects of railway vehicles running on corrugated rails. J. Mech. Eng. Sci. 24(2), 65–76 (1982) 23. CEN EN-1991–2, Eurocode 1. Actions on structures. Part 2: Traffic loads on bridges (2003)

Data-Driven Fluid Flow Simulations by Using Convolutional Neural Network Kazuhiko Kakuda(B) , Yuto Morimasa, Tomoyuki Enomoto, Wataru Okaniwa, and Shinichiro Miura Nihon University, Narashino, Chiba 275-8575, Japan [email protected]

Abstract. In this paper, we present the data-driven fluid flow simulations using the deep CNN (Convolutional Neural Network) with the parametric softsign activation functions. To simulate the fluid flow problems, the particle-method approach based on SPH (Smoothed Particle Hydrodynamics) is used herein. The GPUimplementation consists mainly of the search for neighboring particles in the locally uniform grid cell using hash function. We construct significantly the deep CNN architectures with novel activation functions, so-called parametric softsign. Numerical results demonstrate the workability and validity of the present approach through the dam-breaking fluid flow simulations with free surface. Keywords: Particle method · Fluid simulation · Data-driven · CNN · Activation functions · Parametric softsign

1 Introduction In the massive simulation-based fields of science and engineering, it is indispensable to demonstrate the fluid flow behavior in real-time. To simulate effectively the largescale fluid flow problems, there are significantly particle-based approaches, such as SPH (Smoothed Particle Hydrodynamics) [1, 7], MPS (Moving Particle Semi-implicit) [4], and so forth. Recently, the data-driven fluid flow approaches have increasingly become an important strategy for solving efficiently various problems, such as physics-based fluid simulation using the regression forests [5], the parameterized fluid simulations using the generative neural network [3], the RANS turbulence modelling using the tensor basis neural network [6], and so forth. In our previous work, we have proposed newly the parametric softsign activation functions [2] to avoid zero-values in negative part of ReLU used widely in CNN (Convolutional Neural Network). The purpose of this paper is to present the data-driven fluid flow approach by using the deep CNN with the parametric softsign activation functions. As the particle-based fluid simulation, we adopt the GPU-based SPH method with quantic-spline kernel functions [8]. The GPU-implementation consists mainly of the search for neighboring particles in the locally uniform grid cell using hash function. On the other hand, we construct the latent space network [3] based on the deep CNN using some datasets obtained from the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 14–19, 2021. https://doi.org/10.1007/978-3-030-64690-5_2

Data-Driven Fluid Flow Simulations by Using Convolutional

15

SPH simulations. The workability and validity of the present approach are demonstrated on the dam-breaking fluid flow simulation with free surface.

2 Statement of Problem Let  be a bounded domain in Euclidean space R with a piecewise smooth boundary . The unit outward normal vector to  is denoted by n. Also,  denotes a closed time interval. The motion of a viscous fluid flow is governed by the following Navier-Stokes equations for Lagrangian form: 1 Du = − ∇p + ν∇ 2 u + g + f surf Dt ρ Dρ = −ρ∇ · u Dt

in  × Ω in  × Ω

(1) (2)

where u is the velocity vector, p is the pressure, ρ is the density, ν = μ/ρ is the kinematic viscosity coefficient, μ is the viscosity coefficient, g is the external force vector, e.g., gravity, D/Dt stands for the Lagrangian differentiation, and f surf is the surface tension vector. In addition to Eqs. (1) and (2), we prescribe the Dirichlet and Neumann boundary conditions, and the initial condition, u(x, 0) = u0 , where u0 denotes the given initial velocity vector.

3 SPH Formulation In the SPH-framework, the integral representation of a function f (r) is given by     f (r) = ∫ f r W r − r , h d r Ω

(3)

  where W r − r , h is the smoothing kernel function, which satisfies the normalization condition with some properties, and h is the smoothing length defining the influence area of the kernel function (see, Fig. 1). The numerical form at particle a to Eq. (3) is obtained by approximating the integral representation: f (ra ) =

 mb b

ρb

f (rb )Wab

(4)

where mb and ρb is the mass and the density at particle b, respectively, and Wab = W (ra − rb , h). To evaluate accurately the free surface with surface tension, we use the following quantic-spline functions [8] as the kernel function: ⎧ ⎨ (3 − q)5 − 6(2 − q)5 + 15(1 − q)5 (0 ≤ q ≤ 1) W (r) = σ (3 − q)5 − 6(2 − q)5 (5) (1 ≤ q ≤ 2) ⎩ 5 (2 ≤ q ≤ 3) (3 − q)

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Fig. 1. Particle interaction models (3D).

and W (r) = 0 for q ≥ 3, where q = 3r/h, σ = 63/478π h2 and 9/40π h3 for 2D and 3D, respectively. The particle form at particle a for the pressure gradient term in Eq. (1) can be written as

   1 pb pa − ∇p = − mb 2 + 2 + Πab ∇a Wab (6) ρ ρa ρb a b where ∇a stands for the gradient taken with respect to the coordinates of particle a, and Πab denotes the numerical viscosity. On the other hand, the second term of right-hand side, namely, the viscous term in Eq. (1) is discretized as ν∇ 2 ua =

 mb rab · ∇a Wab (μa + μb )uab ρa ρb r2ab

(7)

b

4 CNN Architectures In this section, we construct the latent space network [3] based on the deep CNN using some datasets, namely velocities and the reciprocal sum of the distance between particles, obtained from the SPH simulations. Following to Reference [3], the learning procedure in this study is given as Step 1: As illustrated in Fig. 2(a), the input datasets such as velocity vectors and so on are compressed by the encoder and converted to latent codes in the autoencoder. The CNN architecture of the encoder consists of 17 convolutional layers with one fully-connected tanh layer (see Fig. 2(b)). Step 2: The latent codes as input are reconstructed by the decoder, and stored as output data. For the decoder, we adopt the CNN architecture consisting of 13 convolutional layers (see Fig. 2(c)). By repeating these two steps, the velocity fields etc. using the so-called autoencoder are obtained as shown in Fig. 2.

Data-Driven Fluid Flow Simulations by Using Convolutional

17

Step 3: By use of the decoder network with the initial latent code, the velocity vector fields at time step (t + s) are sequentially derived from those of time step t. As shown in Fig. 3, the network consists of three fully-connected layers using the parametric softsign activation functions [2] with batch normalization and dropout of 0.1. The parametric softsign activation functions which were derived on the steady advection-diffusion system in fluid dynamics framework, are given as follows: v (v ≥ 0) (8) g(v) = eα v eα +|v| (v < 0) Where α is the ad hoc parameter.

(a) Autoencoder

(b) Encoder network

(c) Decoder network

Fig. 2. CNN architectures

Fig. 3. Latent space network (n = 3)

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5 Numerical Example In this section, we present numerical results obtained from applications of the abovementioned approach to the dam-breaking fluid flow simulation. The initial velocities in this problem are assumed to be zero everywhere in the interior domain. We set also the gravity of 9.8 [m/s2 ]. The fluid simulations are carried out on a 12 GB NVIDIA® Titan V GPU and/or an Intel i9-7900X CPU with 64 GB memory, and the CNN & latent space network are evaluated on a 11 GB NVIDIA® GeForce RTX 2080Ti GPU. 5.1 Dam-Breaking Fluid Flow Simulation Table 1 gives the summary of the parameters for the dam-breaking fluid flow problem with free surface. The fluid flow problem of broken dam includes many interesting phenomena, namely large deformation of free-surfaces, very violent motions including splashing, and so forth. The dam-breaking fluid flow problem has been extensively used to verify the applicability and validity of the numerical methods. Figure 4 shows the velocity fields at time step of 350 by using the autoencoder network (see Fig. 2(a)), the reconstructed result with ELU and the present approach through comparison with ground truth image. The loss time-history for the reconstructed velocity fields is shown in Fig. 5. Our approach outperforms the latent space network with ELU activation function. In Table 2, we present the comparison of the SPH simulation time and our CNN approach time to get the velocities up to 12,500 time steps. We can see also from Table 2 that our CNN performance leads to approximately 139 times speed-up. Table 1. A summary of the parameters.

Tank area Number of total particles Number of fluid particles Initial distance of two particles Density Viscosity coefficient Surface tension coefficient Time increment

(a) Ground Truth

(b) Autoencoder

8L×4L [m2], L=0.146 [m] 11,171 8,756 0.00292 [m] 1000 [kg/m3] 0.001 [Pa・s] 0.002361 [N/m] 0.0001 [s]

(c) Result using ELU

(d) Present

Fig. 4. Comparisons with ground truth for velocity fields at time step of 350.

Data-Driven Fluid Flow Simulations by Using Convolutional

(a) Loss for the reconstructed results

19

(b) Loss for the results divided by autoencoder

Fig. 5. Loss time-history for the reconstructed velocity fields.

Table 2. Comparison of SPH simulation time and our approach time.

SPH simulation time [s] (12,500 time steps) Our CNN approach time [s] Speed up [×]

80.568 [s] 0.58 [s] 138.91

6 Conclusions We have presented the data-driven fluid flow approach by using the deep CNN with the parametric softsign activation functions. We have adopted the SPH approach as the fluid simulation, and constructed the latent space network based on the deep CNN with the parametric softsign activation functions. The qualitative agreement between the present result and the ground truth image appears also satisfactory.

References 1. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astr. Soc. 181, 375–389 (1977) 2. Kakuda, K., Enomoto, T., Miura, S.: Nonlinear activation functions in CNN based on fluid dynamics and its applications. CMES: Comput. Model. Eng. Sci. 118(1), 1–14 (2019) 3. Kim, B., Azevedo, V.C., Thuerey, N., Kim, T., Gross, M., Solenthaler, B.: Deep Fluids: A generative network for parameterized fluid simulations. Eurographics 38(2), 59–70 (2019) 4. Koshizuka, S., Oka, Y.: Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl. Sci. Eng. 123, 421–434 (1996) 5. Ladicky, L., Jeong, S., Solenthaler, B., Pollefeys, M., Gross, M.: Data-driven fluid simulations using regression forests. ACM Trans. Graph. 34(6), 1–9 (2015) 6. Ling, J., Kurzawski, A., Templeton, J.: Reynolds averaged turbulence modelling using deep neural networks with embedded invariance. J. Fluid Mech. 807, 155–166 (2016) 7. Lucy, L.B.: A numerical approach to the testing of the fission hypothesis. Astron. J. 82(12), 1013–1024 (1977) 8. Morris, J.P., Fox, P.J., Zhu, Y.: Modeling low reynolds number incompressible flows using SPH. J. Comput. Phys. 136, 214–226 (1997)

Ultralight Metallic/Composite Materials with Architected Cellular Structures Maryam Tabatabaei1(B) and Satya N. Atluri2 1 Department of Materials Science and Engineering, Pennsylvania State University, University

Park, Pennsylvania, PA 16802, USA [email protected] 2 Texas Tech University, Lubbock, TX, USA

Abstract. Due to the emergence of technologies enabling the fabrication of complex cellular materials, new materials with higher mechanical efficiency than the constituent material have been introduced. Combination of optimized cellular architectures with high-performance metals and composites can result in lightweight materials with mechanical properties previously unattainable at low densities. Consequently, new materials can be designed to maximally fit the target application. There is a wide range of important applications including energy absorption, metamaterial, thermal management, and bioscaffold for ultralight architected cellular metals as well as airframes and shape morphing for ultralight architected cellular composites. Therefore, it is of importance to propose a nearly exact and highly efficient methodology to study low-mass metal and composite systems with architected cellular structures. We present the simplest initial computational framework for the analysis, design, and topology optimization of such cellular materials. In the present methodology, the repetitive Representative Volume Element (RVE) approach is employed to model the actual cellular metallic/composite micro-lattices. Each member of the cellular material is modeled using only one finite beam element with 12 degrees of freedom (DOF), and the nonlinear coupling of axial, bidirectional-bending, and torsional deformations is studied for each spatial three-dimensional (3D) beam element. The large deformation analysis of the cellular strut members is performed utilizing mixed variational principle in the updated Lagrangian co-rotational reference frame. The explicit form of the stiffness matrix is calculated under the effect of plasticity for the case of the cellular metals and under the effect of nonlinear flexible connections for the case of the cellular composites. Then, we use newly proposed homotopy methods to solve the algebraic equations. Keywords: Architected cellular metals/composites · Plastic hinge mechanism · Nonlinear flexible connections · Homotopy methods

1 Introduction Nature benefits from high stiffness and strength low-weight materials by evolving architected cellular structures. For example, trabecular bone, beaks and bones of birds, plant © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 20–28, 2021. https://doi.org/10.1007/978-3-030-64690-5_3

Ultralight Metallic/Composite Materials

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parenchyma, and sponge optimize superior mechanical properties at low density by implementing a highly porous, complex architected cellular core [1]. The same engineering and architectural principles at the material scale have been used by humankind to develop materials with higher mechanical efficiency and lower mass in many weightcritical applications. The emergence of advanced manufacturing technologies such as additive manufacturing and three-dimensional (3D) laser lithography offer the opportunity to fabricate ultralight metallic and composite materials with intricate cellular architecture to location-specific requirements. For example, the world’s lightest metal [2, 3], Fig. 1(a), and reversibly assembled ultralight carbon-fiber-reinforced composite materials [4], Fig. 1(b), with micro-architected cellular structures have been recently fabricated at HRL Laboratories and MIT Media Lab-Center for Bits and Atoms, respectively.

(a)

(b)

Fig. 1. (a) Metallic cellular microarchitecture [2, 3] and (b) assembly of a cuboct carbon-fiberreinforced composite microlattice [4].

Architected cellular materials enable to include the effect of the structural hierarchy in the determination of the bulk material properties [5]. For example, fiber-reinforced cellular composites recently fabricated at MIT Media Lab-Center for Bits and Atoms exhibit structure on more than one length scale [4], and metallic microlattice materials recently fabricated at HRL Laboratories span three different length scales (nm, µm, mm) [2, 3]. Cheung and Gershenfeld [4] fabricated a cubic lattice of vertex-connected octahedrons, called cuboct, consisting of solid bars with square cross section t × t and length l. They examined only ultralight cellular composites with thickness-to-length ratio, = t/l smaller than 0.1 and obtained stretch-dominated lattice-based composites. To form volume-filling lattice structure, they [4] produced many small cross-shaped building blocks assembled by mechanical interlocking connections. Each building block constitutes four conjoined strut members to one locally central node where a shear clip is inserted after the assemblage of all blocks. Strut members are composed of unidirectional fiber composite beams and looped fiber load-bearing holes [4]. Schaedler et al. [2] and Torrents et al. [3] fabricated nickel-based micro-architected cellular materials composed of hollow tube members with L = 1 to 4 mm node-to-node spacing, D = 100

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M. Tabatabaei and S. N. Atluri ◦

to 500 µm strut diameter, t = 100 to 500 nm wall thickness, and θ = 60 inclination angle. The unit cell of micro-architecture was an octahedron without any basal members. Such architected cellular materials have offered specific mechanical properties (stiffness, strength, toughness and energy absorption) at low-density regions, which makes them appropriate for a variety of engineering applications. For example, efforts are under way to employ the functionality of the cellular metallic/composite materials in energy absorption [6], mechanical metamaterials [7], bioscaffolds [8], and in adaptive structures [9]. In the current work, the fiber-reinforced cellular composites recently fabricated at MIT Media Lab-Center [4] and nickel-based micro-architected cellular materials recently fabricated at HRL Laboratories [2, 3] are modeled using repetitive Representative Volume Element (RVE) approach consisting of nodes and strut members which mimic the topology of the cellular material. Each member of the ultralight cellular metallic/composite materials is considered as single finite three-dimensional (3D) beam element, and member generalized strains and stresses are calculated under the nonlinear coupling of axial, bidirectional-bending, and torsional deformations. The plastic hinge method [10, 11] is employed to study the effect of plasticity on the mechanical response of the micro-architected cellular metal. Using this method, plastic hinge can be formed along the cellular member everywhere the plasticity condition in terms of generalized stress resultants is satisfied. The effect of nonlinear flexible connections of the micro-architected cellular composite is studied using the standardized Ramberg-Osgood function [12] for the moment-rotation relation of flexible connections. The explicit form of the tangent stiffness matrix is derived utilizing the mixed variational principle [13] in the co-rotational updated Lagrangian reference frame. Then, we employ the Newton homotopy algorithm [14] to solve the algebraic equation F(X) = 0, in which X is the solution vector for the equilibrated nodal generalized coordinates. In contrast to the Newton-type algorithms which require to invert the Jacobian matrix, homotopy methods avoid inverting the Jacobian matrix, which makes them simpler to use when the Jacobian is nearly singular. The outline of the paper is as follows. The fundamental concepts of the present methodology are given in Sect. 2. Section 3 is devoted to model micro-architected cellular metallic materials fabricated at HRL Laboratories [2, 3] and ultralight cellular composites fabricated at MIT Media Lab-Center [4] using the current methodology and compare the calculated mechanical properties with the corresponding experimental measurements. Finally, a conclusion is presented in Sect. 4.

2 Computational Approach Due to the consideration of the nonlinear coupling of the axial, bidirectional-bending, and torsional deformations for the large-deformation analysis, the following displacement field is considered for each 3D spatial beam element in the co-rotational updated Lagrangian reference u1 (x1 , x2 , x3 ) = u1T (x2 , x3 ) + u10 (x1 ) − x2

∂u20 (x1 ) ∂u30 (x1 ) − x3 , ∂x1 ∂x1

Ultralight Metallic/Composite Materials

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u2 (x1 , x2 , x3 ) = u20 (x1 ) − θˆ x3 , u3 (x1 , x2 , x3 ) = u30 (x1 ) + θˆ x2 ,

(1)

where, u1T (x2 , x3 ) is the warping displacement due to the torsion T , u10 (x1 ) is the axial displacement at the centroid (x2 = x3 = 0), u20 (x1 ) and u30 (x1 ) are the transverse bending displacements at the centroid along x2 - and x3 -axes, respectively, and θˆ is the twist angle around x1 -axis. Using the Green-Lagrange strain components in the updated Lagrangian co-rotational frame, the member generalized strain, E is determined as below ⎡  2  2 ⎤ u10,1 + 21 u20,1 + 21 u30,1 ⎢ ⎥ −u20,11 ⎢ ⎥ (2) E=⎢ ⎥, ⎣ ⎦ −u30,11 θˆ,1 resulting in the following member generalized stresses, σ σ = DE.

(3)

The matrix D is determined upon the mechanical properties of the constituent material; for the cellular composite, it includes the anisotropic properties of the base material, and for the cellular metal, it includes the linear elastic properties of the parent material. The functional of the mixed variational principle, H for an RVE consisting of N members can be expressed in terms of the incremental components of the second PiolaKirchhoff stress tensor, Sij1 . and the displacement field, ui , as follows H=



N m=1



    1  1 0 1 ¯ −B Sij + τij uk,i uk,j + Sij ui,j + uj,i − ρbi ui dV − Ti ui dS , 2 2 Vm Sσm

(4)

where, Vm (m = 1, 2, · · · , N ) is the volume of the mth member, Sσm is the m member surface with the prescribed traction, and T¯ i and bi (i = 1, 2, 3) are, respectively, the components of the boundary tractions and the body forces per unit volume in the current configuration. Invoking the variation of H leads to the following relation  

N

N δβ T (−Hβ + Ga) + δaT GT β + K N a − F + F0 = 0. δH = m=1

m=1

(5) To study the effect of plasticity for the case of the micro-architected cellular metal, the plastic hinge mechanism is employed, which considers the formation of plastic hinge everywhere along the beam element when the plasticity condition is satisfied. The increment of the plastic work at the ith plastic hinge, dwiP is determined on the basis of the incremental plastic nodal displacement, d aPi as p

pT

dWi = d ai σ .

(6)

The incremental plastic  nodal displacement can be expressed using the potential  ∂fk (σ ,σY ) function φk = as ∂σ p

d ai = d λk φ k ,

(7)

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M. Tabatabaei and S. N. Atluri

here, d λk is a positive scalar, and f (σ , σY ) = 0 is the plastic potential explaining the plasticity condition in terms of the stress components at the location of the plastic hinge and the Yield stress, σY . To study the effect of nonlinear flexible connections for the case of the microarchitected cellular composite, nonlinear rotational springs are modeled at the ends of the adjacent members. The increment of the spring rotation can be expressed as

α φi = (−1)α

α Mi αSt i

i = 2, 3, α = 1, 2,

(8)

in which, α Mi is the incremental momentum along xi − axis at node α, and α Sit is the instantaneous rotational rigidity of the spring along xi − axis at node α. Employing the moment-rotation relation based on the standardized Ramberg-Osgood function, S t which is the slope of the moment-rotation curve, dM d φ is obtained as (9) Including the plastic works done by plastic hinges for the case of the cellular metal and including the incremental energy spent at nonlinear rotational springs for the case of the cellular composite into the mixed variational principle and then invoking its variation modifies Eq. (5) to the following equation   N  T 

N T ˆ βˆ + Ga ˆ + ˆ βˆ + K N a − F + F0 = 0. (10) δ βˆ −H δaT G m=1

m=1

ˆ for the large deformation analysis of ultralight Therefore, the stiffness matrix, K, cellular metal/composite is derived explicitly as ˆ TH ˆ −1 G ˆ + KN . Kˆ = G

(11)

Then, to solve the incremental tangent stiffness equations (F(X) = 0) using homotopy method, we consider the following scalar Newton homotopy function, hn (X, t) =

1 1 F(X)2 + F(X 0 )2 , 2 2Q(t)

t ≥ 0,

(12)

resulting in, 2 ˙ 1 QF T X˙ = −  T 2 B F, 2 QB F

t ≥ 0,

(13)

∂F , and Q(t) is where, B is the Jacobian (tangent stiffness) matrix evaluated with B = ∂X a positive and monotonically increasing function to enhance the convergence speed.

Ultralight Metallic/Composite Materials

25

3 Ultralight Architected Cellular Metallic/Composite Materials 3.1 Metallic Octahedral Micro-architecture Metallic cellular materials fabricated at HRL Laboratories [2, 3] are nickel-based materials with octahedral configuration without any basal members. Micro-architected metals consist of hollow tube strut members with the length of L = 1 − 4 mm, the strut diameter of D = 100 − 500 µm, the wall thickness of t = 100 − 500 nm, and the ◦ inclination angle of θ = 60 . Using the RVE approach in conjunction with plastic hinge method, we model a nickel-based cellular material with L = 1200 µm, D = 175 µm, and t = 26 µm and compare the calculated mechanical results with the corresponding experimental measurements. For this study, an RVE consisting of 36 nodes and 64 strut members is considered under compressive loading, Fig. 2(a). The structural geometry of the strut member is also shown in Fig. 2(b).

4a (b)

z

y a

x a

(a)

Fig. 2. (a) An RVE consisting of 36 nodes and 64 strut members and (b) the structural geometry of the strut member.

Using the present methodology, the engineering stress-engineering strain curve is calculated and plotted in Fig. 3. The Young’s modulus and the yield stress are calculated as 0.7841 GPa and 7.3704 MPa, respectively. The experimental measurements reported by Torrents et al. [3] for the tested micro-lattice with the strut diameter D = 175 ± 26 µm, strut length L = 1200 ± 36 µm, and wall thickness t = 26.00 ± 2.6 µm exhibit

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M. Tabatabaei and S. N. Atluri

the Young’s modulus of 0.58 ± 0.003 GPa and the yield stress of 8.510 ± 0.025 MPa. As it is found, there is a good agreement between our calculated mechanical properties and those measured experimentally by Torrents et al. [3].

Fig. 3. Stress-strain curve of the cellular metallic micro-lattice subjected to compression.

3.2 Flexible Cuboct Carbon Fiber-Reinforced Polymer Composite The cuboct cellular lattice of carbon fiber-reinforced polymer composite at MIT Media Lab-Center [4] is fabricated by vertex-connected octahedrons, Fig. 4(a). The lattice is composed of slender members with φ = t/l < 0.1 in which t is the width of the square cross section and l is the length of the strut member, Fig. 4(b). Since the cellular structure is formed by assembling identical building blocks, we consider that connections are flexible and introduce nonlinear rotational springs at flexible connections. Using the repetitive RVE approach and the standardized Ramberg-Osgood functions for the moment-rotation relation of the nonlinear rotational springs at flexible connections, we model a cuboct sample with l = 0.9 cm including 21 nodes and 48 elements. By changing the width of the cross section, t, various samples with different values of φ are modeled and, then, loaded under compression. The Young’s moduli for the ultralight cellular composite materials with t/l < 0.1 are calculated and compared with the corresponding experimental results given by Cheung and Gershenfeld [4] in Table 1. As it is seen from Table 1, there is an excellent agreement between computational and experimental results.

Ultralight Metallic/Composite Materials

27

(b)

(a) Fig. 4. (a) An RVEs including 21 nodes and 48 elements and (b) strut member geometry. Table 1. Comparison between results calculated from the current methodology and corresponding experimental results reported by Cheung and Gershenfeld [4]. t/l

Young’s Modulus (GPa) Present Study

Experiment (Ref. [4])

Flexible Connections

Rigid Connections

4.6995 × 10−2

1.8729 × 10−2

1.8731 × 10−2

1.4190 × 10−2

4.7127 × 10−2

1.8839 × 10−2

1.8842 × 10−2

1.4080 × 10−2

4.7226 × 10−2

1.8919 × 10−2

1.8921 × 10−2

1.4760 × 10−2

4.7456 × 10−2

1.9116 × 10−2

1.9118 × 10−2

1.4430 × 10−2

4.7522 × 10−2

1.9171 × 10−2

1.9173 × 10−2

1.4300 × 10−2

4 Conclusion Throughout this study, we present a computational methodology for the analysis, design, and topology optimization of ultralight metals or composites with architected cellular structures. The repetitive RVE approach is employed to mimic the fabricated cellular material. Each member of the architecture is modeled using only one finite 3D beam

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element with 12 DOF, and the nonlinear coupling of axial, bidirectional-bending, and torsional deformations is studied for each spatial beam element. For the large elasticplastic deformation analysis of micro-architected cellular metallic materials, the plastic hinge method is utilized in such a way that plastic hinges can be formed everywhere along the beam when the plasticity condition is satisfied. For the large deformation analysis of the cuboct cellular composite with flexible connections, the standardized Ramberg-Osgood function is employed to introduce the moment-rotation relation at flexible nodes. One of the fabricated nickel-based cellular microstructures is modeled using an RVE with 36 nodes and 64 elements, and its mechanical properties under compression are calculated and compared with the corresponding experimental results. Moreover, a series of fabricated cuboct cellular composites with different thickness-tolength ratio are simulated using an RVE with 21 nodes and 48 elements, and the calculated Young’s moduli are compared with the corresponding experimental measurements. We find a very good agreement between our computational results and experimental reports available in the literature.

References 1. Schaedler, T.A., Carter, W.B.: Architected cellular materials. Annu. Rev. Mater. Res. 46, 187–210 (2016) 2. Schaedler, T.A., Jacobsen, A.J., Torrents, A., Sorensen, A.E., Lian, J., Greer, J.R., Valdevit, L., Carter, W.B.: Ultralight Metallic Microlattices. Science 334, 962–965 (2011) 3. Torrents, A., Schaedler, T.A., Jacobsen, A.J., Carter, W.B., Valdevit, L.: Characterization of nickel-based microlattice materials with structural hierarchy from the nanometer to the millimeter scale. Acta Mater. 60, 3511–3523 (2012) 4. Cheung, K.C., Gershenfeld, N.: Reversibly assembled cellular composite Materials. Science 13, 1219–1221 (2013) 5. Lakes, R.: Materials with structural hierarchy. Nature 361, 511–515 (1993) 6. Evans, A.G., He, M.Y., Deshpande, V.S., Hutchinson, J.W., Jacobsen, A.J., Carter, W.B.: Concepts for enhanced energy absorption using hollow micro-lattices. Int. J Imp Eng. 37, 947–959 (2010) 7. Christensen, J., Kadic, M., Wegener, M., Kraft, O., Wegener, M.: Vibrant times for mechanical metamaterials. MRS Commun. 5(3), 453–462 (2015) 8. Hutmacher, D.W.: Scaffolds in tissue engineering bone and cartilage. Biomaterials 21, 2529– 2543 (2000) 9. Hutchinson, R.G., Wicks, N., Evans, A.G., Fleck, N.A., Hutchinson, J.W.: Kagome plate structures for actuation. Int. J. Solids Struct. 40, 6969–6980 (2002) 10. Hodge, P.G.: Plastic Analysis of Structures, Series in Engineering Sciences, McGraw-Hill, New York (1959) 11. Ueda, Y., Yao, T.: The plastic node method: a new method of plastic analysis. Comp. Meth. Appl. Mech. Eng. 34, 1089–1104 (1982) 12. Ramberg, W., Osgood, W.R.: Description of stress-strain curves by three parameters. National Advisory Committee for Aeronautics, Technical Note 902. Washington DC. (1943) 13. Reissner, E.: On a variational theorem for finite elastic deformations. J. Math. Phys. 32, 129–135 (1953) 14. Liu, C.S., Yeih, W., Kuo, C.L., Atluri, S.N.: A scalar homotopy method for solving an over/under determined system of non-linear algebraic equations. CMES: Comput. Model. Eng. Sci. 53, 47–71 (2009)

Spectroscopic Characterization and Molecular Dynamics Simulation of Tin Dioxide, Pristine and Functionalized Graphene Nanoplatelets Olasunbo Farinre, Hawazin Alghamdi, and Prabhakar Misra(B) Howard University, Washington, DC 20059, USA [email protected]

Abstract. Tin dioxide (SnO2 ) is a semiconductor used in lithium batteries, solar cells, as a photocatalyst, and for optronic device applications, due to its large direct band gap, high electron mobility, thermal stability, large absorbance and storage of light features, and cost-effectiveness. The present study concentrates on SnO2 as a gas sensing material because of its enhanced selectivity for combustible and toxic gases. Our spectroscopic investigation focuses on tetragonal rutile SnO2 , aimed at studying its physical and chemical properties for gas sensors. We have characterized SnO2 using X-Ray diffraction (XRD) to confirm its tetragonal rutile structure and calculate its crystallite size. Additionally, Raman spectroscopy with a heated cell has been used to obtain the Raman active vibrational modes in the temperature range 303.15–443.15 °K in order to study the anharmonic effects. We have indeed observed a red shift in the Raman spectra for the A1g and B2g vibrational bands, while the Eg band exhibited no measurable change due to the temperature increase. Furthermore, Scanning Electron Microscopy (SEM) has been used to determine the surface morphology of SnO2 and the 3-dimensional view of an individual spherical grain. Graphene nanoplatelets (GnPs) have also been investigated for toxic gas sensing applications due to their lightweight, large surface area and low cost of fabrication. The presence of functional groups (e.g. ammonia, fluorocarbon and carboxyl) in the nanoplatelets enhances the surface interactions between the molecules being sensed (e.g. NOx and SO2 ) and the nanoplatelets themselves, thereby improving the sensing abilities of the GnPbased sensors. We have utilized SEM, Raman and XRD techniques for surface and structural characterization of the pristine and functionalized GnPs. Our results show that the major vibrational modes of graphene, namely the D, G and 2D peaks, are observed in the Raman spectra of both pristine and functionalized GnPs. The increase in the ID /IG values for functionalized GnPs reflects a smaller crystallite size upon functionalization of the pristine GnPs, which is also supported by our XRD results. A red shift in the frequency of the 2D peak is observed upon an increase in carboxyl functionalization from 7 wt% to 35 wt% because the carboxyl group behaves as an electron donor (n-type dopant) when attached to the edges of the graphene lattice. In addition, we have utilized MD simulation using the LAMMPS software code to study the vibrational properties of GnPs for better understanding of its Raman properties suitable for the development of gas sensors. O. Farinre and H. Alghamdi---These authors contributed equally to this work © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 29–43, 2021. https://doi.org/10.1007/978-3-030-64690-5_4

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O. Farinre et al. Keywords: Tin (IV) oxide · Tin dioxide (SnO2 ) · Graphene nanoplatelets (GnPs) · Functionalized GnPs · Scanning electron microscopy (SEM) · Raman spectroscopy · X-ray diffraction (XRD) · Molecular dynamics (MD) simulation

1 Introduction 1.1 Tin Dioxide (SnO2 ) Cassiterite or tin (IV) oxide, also known as stannic oxide (SnO2 ), is an n-type metal oxide semiconductor material with a large direct band gap of 3.6 eV at room temperature and elevated electron mobility [1]. It has been used as a photocatalyst, a heat reflector for solar cells, in lithium ion batteries and optronic devices as electrodes, and most commonly in gas sensing devices [2]. Gas sensor materials have been increasingly explored to monitor air quality indoors and in factories and the automotive industry. Much effort has also been exerted in developing miniature sensors for diagnosing diseases through exhaled breath analysis [3]. Metal oxide gas sensors in general have high sensitivity and excellent stability at elevated temperatures in comparison to polymers and metals. However, metal oxides sensors have low selectivity toward reducing gases and have been customized in the form of composites and thin films to enhance their selectivity characteristics. Based on previous studies, pure SnO2 can detect hydrogen (H2 ), carbon monoxide (CO), and methane (CH4 ) [4]. The tetragonal rutile structure of SnO2 is the base for technology due to its stable crystal structure [5]. This crystalline structure of SnO2 has space-group 14 and lattice constants a = b = symmetry of P42 /mnm with point group symmetry D4h 4.82 Å and c = 3.23 Å [1]. Not too many studies have been conducted regarding the anharmonic effects of SnO2 occurring at elevated temperatures, which are crucial to a better understanding of the thermodynamic stability of SnO2 and its properties for thermal transport [6]. In this present study we have characterized SnO2 by using X-ray diffraction (XRD) spectroscopy to confirm its tetragonal rutile structure and determine the associated crystallite size and interplanar distance. We have also recorded the Raman vibrations at elevated temperatures and observed a red shift with increasing temperatures for certain Raman active modes. Moreover, Scanning Electron Microscopy (SEM) provided the surface morphology of SnO2 and helped determine its grain size. Apart from the experimental work, we have utilized Molecular Dynamics (MD) simulation within the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) interface to obtain the lattice constants of SnO2 and the vibrational properties within the Brillouin zone.

Fig. 1. Unit cell of SnO2 containing Sn cations and O anions.

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1.2 Graphene Nanoplatelets (GnPs) Environmental pollution caused by burning fossil fuels, motor vehicles powered by gasoline, emissions released from manufacturing industries, are a growing global concern because of the associated negative impact on human and animal health, and on the Earth’s climate system. Graphene and its derivatives, such as graphene oxide (GrO), are suitable candidates for gas sensing applications due to their high surface area, excellent thermal conductivity and stability, and high mechanical rigidity [7]. In addition, functionalization of graphene further improves the adsorption of gas molecules on its surface, which in turn improves the sensing capabilities, such as quick response to adsorbed gas molecules even at low concentrations (~ parts per million level) and shorter recovery time [8]. These unique characteristics can overcome the major shortcomings of the metal oxide semiconductor-based sensors, which have low selectivity for target gas molecules, high operating temperatures and high-power consumption [9]. Graphene nanoplatelets (GnPs) are a new type of nanoparticle that can be regarded as derivatives of graphene and graphite, since they are manufactured by exfoliating graphite and composed of a few layers of graphene. In addition, GnPs can be produced on a large scale gives it an edge over graphene [10] for numerous applications (e.g. gas sensing, flexible electronics and energy storage). The chemical reactivity of the carbon atoms localized at the edges of GnPs makes it feasible to functionalize GnPs at the edges, as shown in Fig. 2. GnPs have the same honeycomb structure as two-dimensional (2D) graphene. The carbon atoms are arranged in a hexagonal shape with an atomic distance of 1.42 Å. Each carbon atom is connected to three other neighboring carbon atoms via three (σ ) sigma bonds and one π -bond. The three σ covalent bonds are formed by the hybridization of 2 s and 2p atomic orbitals of neighboring carbon atoms to form sp2 orbitals, while the pz orbital forms the π -bond. GnPs are like graphite in terms of their interlayer distance of approximately 3.35 Å, which has been obtained using the XRD technique. Each of these nanoplatelets consists of small stacks of platelet-shaped graphene sheets that typically have a thickness in the range ~ 0.34–100 nm [11].

Fig. 2. Diagram showing functional groups (ammonia, carboxyl, hydroxyl and fluorocarbon) attached to the edges of four graphene layers with an interlayer distance of 3.35 Å.

In this section, we report the characterization of pristine and functionalized GnPs (incorporating individually carboxyl, fluorocarbon, nitrogen, oxygen, ammonia and argon) by utilizing Raman spectroscopy, SEM and XRD characterization techniques.

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MD simulations were also carried out using the LAMMPS software code to provide additional insight into the vibrational properties of the GnPs and to facilitate comparison with experiment.

2 Materials and Methods 2.1 Experimental Tin Dioxide (SnO2 ): Tin dioxide powder with 325 mesh, 99.9% purity, was commercially purchased from US Research NanomaterialsTM . The Raman instrument used was a SmartDXR™ spectrometer from Thermo Electron with an excitation wavelength of 780 nm. A Ventacon™H4-200 heated cell was employed to control the temperature of the SnO2 powder sample during the Raman measurements. A Thermo Scientific ARLTM EQUINOX 100 X-Ray diffractometer was used to record the XRD spectra of SnO2 . The XRD instrument had a Cu-K α monochromatic radiation source at a wavelength of λ = 1.5406 Å. The beam size was approximately 5 mm × 300 μ m, along with a spinning stage. A Thermo Scientific Phenom PureTM Desktop SEM with an electron optical magnification in the range 80–65,000x was used to study the surface morphology of both SnO2 and GnPs. Graphene Nanoplatelets (GnPs): The pristine GnPs supplied by US Research NanomaterialsTM , Inc. had a planar size of 4–12 and planar thickness of 2–8 nm. Each nanoplatelet is composed of ~ 3–6 layers of graphene sheets. The functionalized GnPs supplied by Graphene SupermarketTM had a planar size of 0.3–5 and planar thickness < 50 nm. The carboxyl (COOH) functionalized GnPs with 35 wt% functionality purchased from Cheap Tubes Inc.TM had a planar size of 1–2 and planar thickness of 3–10 , with each nanoplatelet composed of approximately 4 layers.

2.2 Computational and Simulation Method Tin Dioxide (SnO2 ): The Buckingham interatomic potential was used to demonstrate the interactions between the Sn and O atoms. This potential can be applied by using the shell model available in the CORESHELL package in LAMMPS. Each SnO2 molecule is split into a core of charge X and a satellite (shell) of charge Y connected by a harmonic spring, where the total charge is X + Y. The USER-PHONON package in LAMMPS is added to develop the phonon dispersion curves for SnO2 and utilized the Verlet algorithm, an (NPT) ensemble [13], and compiled the core/shell model to compare the lattice constants SnO2 with other studies. Graphene Nanoplatelets (GnPs): The optimized Tersoff and Brenner empirical interatomic potential [12] was used to describe the interactions between the carbon atoms in GnPs. The Tersoff potential is commonly employed to calculate the phonon properties of graphene and its derivatives in MD simulations because the optimized parameter sets yield vibrational frequencies that are in better agreement with experimental data. Trilayer graphene was used initially for our GnP model because the individual platelets in

Spectroscopic Characterization and Molecular Dynamics Simulation

33

the GnP samples consist of short stacks of 3–6 layers of graphene. A supercell consisting of 10 Å × 10 Å unit cells was created for each layer with a total of 600 atoms to model trilayer graphene. The length of the simulation box used in the x and y directions were: LX = 24.85 Å, LY = 21.52 Å, with a vacuum region of 35 Å applied in the z direction, in order to avoid interaction between the periodic images. A time step of 0.002 ps (metal units) was used during the NVE simulation - with a total run time of 16 ns - for proper equilibration of the system.

3 Results and Discussion 3.1 Tin Dioxide (SnO2 ) XRD data of SnO2 were collected from 2θ = 20◦ to 2θ = 80◦ . We have observed the diffraction angle values that are correlated with Miller Indices (hkl) at 26.78° (1 1 0), 34.04° (1 0 1), 38.25° (2 0 0), 51.98° (2 1 1), 55.01° (2 2 0), 62.13° (3 1 0), 64.97° (1 1 2), and 66.15° (3 0 1). Each index set represents different faces of the SnO2 crystalline structure, which confirms the rutile tetragonal structure (with reference cardJCPDS#411445), as shown in Fig. 3. The (1 1 0) plane symbolizes the face with the lowest energy in a single crystal of SnO2 [14, 15]. We have calculated the crystallite size (D) of SnO2 by utilizing the Debye-Scherrer formula given by Eq. (1): D=

Kλ β cos θ

(1)

where K = 0.89 is the shape factor for a cubic unit cell for spherical crystalline solids, β represents the full width at half maximum (FWHM) of the spectral line, λ is the wavelength of the X-ray beam, and θ is the Bragg angle. In order to obtain the value of β we have fitted the most pronounced peak (1 1 0) by using the Cauchy-Lorentz distribution in the Fityk software. Also, using Bragg’s law we have calculated the interplanar distance (d) given by Eq. (2): d=

λ 2 sin θ

Fig. 3. XRD pattern of SnO2 in powder form.

(2)

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The crystallite size (D) of SnO2 powder was determined to be 19.044 nm and the interplanar distance (d) ~ 3.335 Å, as displayed in Table 1. Table 1. Calculated crystallite size (D) and interplanar distance (d) of SnO2 powder. Sample

2˚ (110)

FWHM (2˚)

Crystallite size (D) (nm)

Interplanar Distance (Å)

SnO2 powder

34.04

0.424

19.044

3.335

The tetragonal rutile structure of SnO2 contains 15 optical phonons in the Brillouin zone at the  point, as given by Eq. (3):  = 1A1g + 1A2g + 1B1g + 1B2g + 1Eg + 1A2u + 2B1u + 3Eu

(3)

The Raman-active modes are A1g , B1g , B2g , along with the doubly degenerate Eg mode. The main three Raman-active modes are: A1g (634 cm−1 ), B2g (775 cm−1 ), and Eg (475 cm−1 ), as shown in Fig. 4. In these Raman vibrations, the O2− ions are vibrating, whereas the Sn4+ ions are stationary. In the A1g , B1g , and B2g vibrational modes, the oxygen vibrates perpendicular to the c-axis, and in the Eg mode the oxygen vibrates along the c-axis. In both Raman-active vibrational modes, A1g and B2g , a shift toward lower wavenumbers (i.e. a red-shift) is observed as the temperature increases, whereas the Eg (475 cm−1 ) mode exhibited little or no change with temperature. These shifts toward lower frequencies confirms the anharmonicity effect in SnO2 [6] (see Fig. 5).

Fig. 4. Raman Spectra of SnO2 powder at increasing temperatures from 303°K to 443°K.

SEM images were captured for SnO2 powder at 2 μ m magnification (see Fig. 6), following which we chose four different images of the SnO2 powder sample to obtain 3D views of individual grains. The average dimensions of a single grain are summarized in Table 2.

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Fig. 5. Wavenumber shift plotted as a function of temperature in the range 303-443°K for (a) Eg , (b) A1g , and (c) B2g vibration bands of SnO2 . Table 2. Averaged X, Y, and Z dimensions of four different spots of SnO2 powder. Sample

XAverage (μm) YAverage (μm) ZAverage (μm)

SnO2 powder 0.49

0.51

0.75

Fig. 6. SEM image of SnO2 powder at 2 μm magnification, showing an individual grain of SnO2 .

MD simulations were performed to study the vibrational properties of tin dioxide (SnO2 ) at elevated temperatures. A precondition for successfully using MD simulation is the availability of dependable interatomic potentials describing the interactions between the atoms in the crystalline lattice [13]. We have used the Buckingham potential for the Core/Shell model that is consistent with a core connected to a 0.1 mass ratio shell by a harmonic spring to illustrate dipole effects [16]. We are using the polarizable model in the LAMMPS software within CORESHELL package to enable the core/shell pair style potentials and the USER-PHONON package for map-file to calculate the phonon dispersion curves [8]. This potential is suitable for semiconductors and lattice vibrations and is shown in Eq. (4): Buckingham 

Uij

r  Cij − ij rij = Aij e ρij − 6 rij

(4)

Eq. (4) describes the short-range interaction between the i and j ions, where the first term represents the repulsion with parameters Aij and ρij , and the second term represents

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Sn

O

One-unit cell structure of SnO 2

Top view

Overall view of (110) plane

Fig. 7. Tetragonal rutile structure of SnO2 showing the super cell of size (2 × 2 × 10) Å.

the van der Waals interaction, where Cij is the van der Waals constant and rij is the interatomic distance between i and j [13]. The coefficients of the Buckingham potential are derived from Lewis and Catlow 1985 [16]. The rutile-like phase SnO2 system is developed as a 2 Å × 2 Å × 10 Å supercell, with a total of 480 particles (240 Sn and 240 O) and two types of bonds between Sn-O (i.e. 2.09, 2.08 Å), as shown in Fig. 8 [1]. The tin dioxide system is equilibrated by keeping the number of atoms, pressure, and temperature constant by performing the NPT ensemble to obtain the lattice parameters (i.e. a = b = 4.774690730 Å and c = 3.212953059 Å). The time of the run is 10 ns, with time steps of 0.005 ps. The first principle calculation done by Lan et al. is in good agreement with our results [6]. 3.2 Graphene Nanoplatelets (GnPs) The SEM images of pristine and functionalized GnPs are shown in Fig. 8 and they depict how the platelet shaped GnPs are stacked randomly on each other forming aggregates. For 35 wt% concentration of carboxyl in the GnPs, as compared to the 7 wt%, the SEM images show that the platelets are tightly grouped to form conglomerates due to the high number of oxygen-containing functional groups in the sample. Aggregates of GnP samples are composed of platelets with diameters in the range 2.8–11.8 μ m, depending on the number of platelets stacked in the aggregates, as shown in Table 3. The main idea is to provide an approximate estimate of the lateral dimensions and thickness of the aggregate particle size of pristine and functionalized GnPs. The Raman spectra of pristine and functionalized GnPs are shown in Fig. 9, where the D, G and 2D bands are observed, which confirms the Raman signature of graphene. The G band is attributed to the in-plane vibration of the sp2 bonded carbon atoms [17]. It also corresponds to the E2g irreducible representation of longitudinal optical (LO) and transverse optical (TO) phonon modes at the gamma () point of the Brillouin zone. The D band indicates the degree of disorder in the sp2 carbon lattice and corresponds to the A1g irreducible representation of the transverse optical (TO) phonon modes at the K

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37

Fig. 8. SEM images: (left) pristine GnPs; (middle) functionalized GnPs with 7wt% concentration of carboxyl; and (right) functionalized GnPs with 35 wt% concentration of carboxyl.

Table 3. Average measurements along the x, y, z axes of aggregates of pristine and functionalized graphene nanoplatelets (GnPs).

point of the Brillouin zone [18]. The 2D band on the other hand is the second order of the D band and activated by two-phonon double resonance Raman scattering. In Fig. 9, the D band intensities of the functionalized GnPs are observed to be higher than the D band intensity of the pristine GnPs. In addition, the presence of a weak D’ peak is observed in the Raman spectra of functionalized GnPs, which is activated by two-phonon double resonance Raman scattering involving one LO phonon near the  point [19]. We note that the D’ peak disappears when the percentage of carboxyl in the GnPs is increased from 7 wt% to 35 wt% but reappears as a combination (D + D’) peak, as shown in Fig. 10. Table 4 shows the calculated averages over five measurements of the frequencies of the D, G, 2D peaks, and the relative intensities (ID /IG ) of the D and G bands of pristine and functionalized GnPs. The values of ID /IG are used to verify the successful functionalization of graphitic nanomaterials, as shown in Table 4. Earlier research studies have shown that there is an indirect linear relationship between the inplane crystallite size (Da ) and ID /IG [20]. Thus, an increase in ID /IG of functionalized

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Fig. 9. Raman spectra of pristine and functionalized graphene nanoplatelets: (a) Carboxyl-GnPs, (b) Fluorocarbon-GnPs, (c) Nitrogen-GnPs, (d) Ammonia-GnPs, (e) Oxygen-GnPs, (f) ArgonGnPs, and (g) Pristine-GnPs.

GnPs reflects a smaller crystallite size and our XRD experimental data support this result. Table 4 shows that the 2D peak of GnPs functionalized with 35 wt% carboxyl shifts to a lower frequency when compared to the 2D peak of pristine GnPs, because the carboxyl (-COOH) group behaves as an electron donor (n-type dopant). The wavenumber of the 2D band is expected to shift to lower values upon n-type doping in graphene, as reported in earlier studies [21].

Fig. 10. (Left) Raman spectra of GnPs functionalized with 7 wt% of carboxyl, with inset clearly showing the D’ peak near the G peak; (Right) Raman spectra of GnPs functionalized with 35 wt% of carboxyl showing the D + D’ feature.

The XRD spectra of pristine and functionalized GnPs are shown in Fig. 11, where the diffraction peaks (002), (100) and (110) are clearly observed in the spectra. The interlayer spacings (d002 ) of pristine and functionalized GnPs have been calculated using Bragg’s formula shown in Eq. (5), while the crystallite sizes (out-of-plane (Dc ) and in-plane (Da )) are calculated using the Scherrer Eq. (6). The constants 0.89 and 1.84 are the Scherrer constants, FWHM (002) and FWHM (100) are the full width half maximum of the diffraction peaks (002) and (100), respectively, and θ is the Bragg angle corresponding to

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Table 4. Average intensity ratio (ID /IG ) of the D and G bands, along with experimental uncertainties, for pristine and functionalized graphene nanoplatelets.

the diffraction peaks: (002) and (100). The diffraction peak (002) found at approximately 260 for the pristine and functionalized GnPs corresponds to an interlayer distance in the range 0.335–0.338 nm, which agrees well with the interlayer

Fig. 11. XRD spectra of pristine and functionalized GnPs.

Distance of graphite [22]. The (002) and (100) peaks yield important information about the crystallite dimensions (Da and Dc ). Table 5 shows the calculated values of the interlayer spacing and average crystallite sizes of pristine and functionalized GnPs. The smaller in-plane crystallite size (Da ) of the functionalized GnPs, as compared to their pristine form, can be attributed to the splitting of the GnP sheets into fragments during the plasma functionalization process, especially over long durations. For instance, during graphene oxide (GrO) synthesis, research has shown that acids and oxidizing agents can break the graphene oxide sheets into ones of smaller lateral size when exposed for long oxidation times [23]. 2d002 sin θ =λ

(5)

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Table 5. Out-of-plane crystallite size (Dc ), interlayer distance (d), and the in-plane crystallite size (Da ) of pristine and functionalized graphene nanoplatelets.

Dc =

0.89λ 1.84λ , Da = FWHM (002)(2θ )xCOSθ FWHM (100)(2θ )xCOSθ

(6)

Classical MD simulations were performed to study the vibrational properties of pristine GnPs. Trilayer graphene has 6 atoms in its primitive unit cell and therefore resulting in a total number of 18 vibrational modes. Each of the irreducible representations in monolayer graphene gives rise to three irreducible representations in trilayer graphene. The number of optical modes is calculated using 3 N – 3, where N = 6, giving a total of 15 optical modes (longitudinal optical (LO), transverse optical (TO), out-of-plane optical (ZO)), while the rest are acoustic phonon vibrational modes: longitudinal acoustic (LA), transverse acoustic (TA) and out-of-plane acoustic (ZA). We are more interested in the in-plane optical vibrational modes at the gamma (Γ ) and K points (LO and TO), as shown in Fig. 12, because they play a crucial role in the Raman and infrared (IR) spectra of GnPs. At the Γ point, the optical modes are decomposed into B2g , E2g , A2u and E1u vibrational modes, while the acoustic modes are decomposed into E1u + A2u modes. The E2g and E1u doubly degenerate modes are Raman and infrared active modes, respectively, while the A2u mode is infrared active and the B2g mode is optically inactive. The E 2g mode at the Γ point (TO + LO modes) and the A1g mode at the K point (TO mode) are the Raman G and D peaks, respectively. The E 2g mode at the Γ point of trilayer graphene evolves into: E 2g = 2E2g +E1u , while the A1g mode at the K point evolves into: A1g = 2E + A1g [24]. Our calculated results show the wavenumber of the evolved E2g mode are as follows: 1574 cm−1 (Raman G band), 1581 cm−1 (Raman G band) and 1590 cm−1 (IR active band). The calculated value of the G band agrees well with our experimental result (Gexp = 1581 cm−1 ). The frequency of the evolved A1g mode are calculated to be: 1421 cm−1 (D band), 1451 cm−1 (E mode) and 1464 cm−1 (E mode). These results are promising and show that MD simulations can be used in analyzing the Raman spectra of pristine GnPs.

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Fig. 12. (left) Trilayer graphene in simulation box; (right) Longitudinal Optical (LO) and Transverse Optical (TO) modes plotted at Γ - and K-points.

4 Summary In summary, we have confirmed the tetragonal rutile structure of powdered SnO2 and determined the crystallite size (D) and interplanar distance (d) from XRD measurements. Also, the surface morphology of SnO2 grain was obtained using SEM. SnO2 powder was tested at different temperatures in the range 303.15–443.15°K to confirm the red shift of the Raman peaks for A1g and B1g , whereas Eg exhibited little or no change. In addition, we have utilized Raman spectroscopy, SEM and XRD) techniques to study the structural and vibrational properties of pristine and functionalized GnPs. Our results show that the major vibrational modes of graphene, the D, G and 2D peaks, are observed in the Raman spectra of pristine and functionalized GnPs. Also, a red shift in the frequency of the 2D peak is observed upon an increase in carboxyl functionalization from 7 wt% to 35 wt% because the carboxyl group behaves as an electron donor (n-type dopant) when attached to the edges. In addition, an increase in the relative intensities (ID /IG ) of the D and G peaks for functionalized GnPs is observed with carboxyl functionalization. The increase in the ID /IG ratio for functionalized GnPs reflects a smaller crystallite size upon functionalization, which is supported by our XRD results. Overall, our results are promising and show that GnPs are promising candidates for manipulating and enhancing the sensitivity of gas sensors and promoting selective gas sensing through doping for a wide range of environmental applications. Acknowledgement. We acknowledge the Extreme Science and Engineering Discovery Environment (XSEDE) allocation support (Grant No. TG-DMR190126) for providing the computational resources utilized for conducting our research relating to the Molecular Dynamics (MD) simulations of the vibrations associated with tin dioxide and graphene nanoplatelets.

References 1. Zakaryan, H.A., Aroutiounian, V.M.: Investigation of cobalt doped tin dioxide structure and defects: Density functional theory and empirical force fields. J.Contemp. Phys. (Armenian Academy of Sciences) 52(3), 227–233 (2017)

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2. Camacho-López, M.A., Galeana-Camacho, J.R., Esparza-García, A., et al.: Characterization of nanostructured SnO2 films deposited by reactive DC-magnetron sputtering. Superf y Vacio 26, 95–99 (2013) 3. Liu, H., Zhang, L., Li, K.H.H., Tan, O.K.: Microhotplates for Metal oxide semiconductor gas sensor applications-towards the CMOS-MEMS monolithic approach. Micromachines 9, (2018). https://doi.org/10.3390/mi9110557 4. Korotcenkov, G., Brinzari, V., Ham, M.H.: Materials acceptable for gas sensor design: Advantages and limitations. In: Key Engineering Materials, Vol. 780, pp. 80–89 (2018) Trans Tech Publications Ltd 5. Lan, T., Tang, X., Fultz, B.: Phonon anharmonicity of rutile TiO 2 studied by Raman spectrometry and molecular dynamics simulations. Phys. Rev. B – Condens. Matter. Mater. Phys. 85, 1–11 (2012). https://doi.org/10.1103/PhysRevB.85.094305 6. Lan, T., Li, C.W., Fultz, B.: Phonon anharmonicity of rutile SnO 2 studied by Raman spectrometry and first principles calculations of the kinematics of phonon-phonon interactions. Phys. Rev. B 86(13), 134302 (2012) 7. Tian, W., Liu, X., Wenbo, Yu.: Research progress of gas sensor based on graphene and its derivatives: A review. Appl. Sci. 8(7), 1118 (2018) 8. Raval, B., Banerjee, I.: Functionalized graphene nanocomposite in gas sensing. In: Functionalized Graphene Nanocomposites and their Derivatives, pp. 295–322. Elsevier (2019) 9. Sarf, F.: Metal oxide gas sensors by nanostructures. In: Gas Sensors. IntechOpen (2019) 10. Cataldi, P., Athanassiou, A., Bayer, I.S.: Graphene nanoplatelets-based advanced materials and recent progress in sustainable applications. Appl. Sci. 8(9), 1438 (2018) 11. Jang, B.Z., Zhamu, A.: Processing of nanographene platelets (ngps) and ngp nanocomposites: a review. J. Mater. Sci. 43(15), 5092–5101 (2008) 12. Lindsay, L., Broido, D.A.: Optimized tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene. Phys. Rev. B 81(20), 205441 (2010) 13. Sun, X., Chen, Q., Wang, C., Li, Y., Wang, J.: Melting and isothermal bulk modulus of the rocksalt phase of ZnO with molecular dynamics simulation. Phys. B: Condens. Matter 355(1–4), 126–133 (2005) 14. Batzill, M., Diebold, U.: The surface and materials science of tin oxide. Prog. Surf. Sci. 79(2–4), 47–154 (2005) 15. Henry, J., Mohanraj, K., Sivakumar, G., Umamaheswari, S.: Electrochemical and fluorescence properties of SnO2 thin films and its antibacterial activity. Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 143, 172–178 (2015) 16. Armstrong, P., Knieke, C., Mackovic, M., Frank, G., Hartmaier, A., Göken, M., Peukert, W.: Microstructural evolution during deformation of tin dioxide nanoparticles in a comminution process. Acta Mater. 57(10), 3060–3071 (2009) 17. Dai, J., Peng, C., Wang, F., Zhang, G., Huang, Z.: Effects of functionalized graphene nanoplatelets on the morphology and properties of phenolic resins. J. Nanomater. 2016, 1–7 (2016). https://doi.org/10.1155/2016/3485167. Article ID 3485167 18. D Sfyris, GI Sfyris, and C Galiotis. Stress intrepretation of graphene e-2 g and a-1 g vibrational modes: theoretical analysis. arXiv preprint arXiv:1706.04465 (2017) 19. Wu, J.B., Lin, M.L., Cong, X., Liu, H.N., Tan, P.H.: Raman spectroscopy of graphene-based materials and its applications in related devices. Chem. Soc. Rev. 47(5), 1822–1873 (2018) 20. Casimir, D., Alghamdi, H., Ahmed, I.Y., Garcia-Sanchez, R., Misra, P.: Raman spectroscopy of graphene, graphite and graphene nanoplatelets. In: 2D Materials. IntechOpen (2019) 21. Rius, G., Godignon, P.: Epitaxial Graphene on Silicon Carbide: Modeling, Characterization, and Applications. CRC Press, New York (2018)

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22. Mohr, M., Maultzsch, J., Dobardzic, E., Reich, S., Milosevic, I., Damnjanovic, M., Bosak, A., Krisch, M., Thomsen, C.: Phonon dispersion of graphite by inelastic x-ray scattering. Phys. Rev. B 76(3), 035439 (2007) 23. Shojaeenezhad, S.S., Farbod, M., Kazeminezhad, I.: Effects of initial graphite particle size and shape on oxidation time in graphene oxide prepared by hummers’ method. J. Sci. Adv. Mater. Devices 2(4), 470–475 (2017) 24. Yan, J.A., Ruan, W.Y., Chou, M.Y.: Phonon dispersions and vibrational properties of monolayer, bilayer, and trilayer graphene: Density-functional perturbation theory. Phys. Rev. B 77(12), 125401 (2008)

Determination of Strength and Fracture Toughness from Indentation Tests in the Framework of Finite Fracture Mechanics Jonathan Hahn and Wilfried Becker(B) TU Darmstadt, 64287 Darmstadt, Germany [email protected]

Abstract. Many technically relevant materials show brittle failure behaviour. For a safe and reliable use often a fracture mechanical assessment is important for which the knowledge of the fracture mechanical characteristics is essential. The classical identification of these characteristics often requires much effort so that indentation tests seem to be an advantageous alternative. The common use of sharp indenters, however, is connected with some uncertainty how to describe the fracture process properly and the results cannot be reproduced in a reliable manner. On this background we suggest the use of blunt spherical indenters and a physically motivated modelling of the crack initiation in the framework of finite fracture mechanics. This allows a qualitatively good explanation of experimental findings. Keywords: Indentation cracks · Finite fracture mechanics · Parameter identification

1 Introduction As brittle materials are often prone to fracture failure the knowledge of their fracture mechanical properties is essential. The identification of these properties often requires a big experimental effort, in particular when well-defined fracture specimens have to be manufactured with defined initial cracks. The effort can be reduced by the identification of the fracture toughness through indentation tests as suggested for instance by Evans [1]. In most cases a sharp indenter (Vickers, Berkovich) is used to generate cracks at the indentation location. The generated cracks can be detected reasonably well and their dimensions are identified microscopically. Then simple relations give the fracture toughness, see e.g. Lawn et al. [2]. The relations, however, contain an empirical correction factor that has to be identified experimentally and that depends on the underlying material. This gives raise to several points of criticism as it is summarized by Quinn/Bradt [3]. A proper fracture mechanical derivation is difficult due to the complex stress state, the complex crack patterns and localized plastic yielding at the indenter tip and round-robin studies reveal serious problems with the reproducibility of results. On this background we suggest the use of blunt axisymmetric indenters in the framework of finite fracture mechanics. This is to enable a physically motivated modelling © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 44–51, 2021. https://doi.org/10.1007/978-3-030-64690-5_5

Determination of Strength and Fracture Toughness from Indentation Tests

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of the crack initiation without the need of empirical correction factors. In addition to the fracture toughness also the strength of the material can be identified at the same time. A similar approach has been suggested recently by Strobl [4]. We extend the approach to spherical indenters where an analytical modelling is possible. In combination with a robust parameter identification the approach should allow to identify strength and toughness at the same time from simple tests.

2 Modelling Approach For the case of spherical indenters the crack generation process has already been investigated experimentally by a larger number of authors, for instance by Langitan et al. [5], Warren [6] and Mouginot/Maugis [7]. Typically the spherical indenter is pushed normally onto the material specimen. The initiation of cracks is recorded acoustically, optically or by means of the identified force-displacement behavior. Langitan/Lawn did not observe a simple circular crack but the growth of a conically propagating crack. Beyond this Warren and Mouginot/Maugis observed a two-phase process, starting with a flat cylindrical or slightly conical crack outside the contact radius, with a transition to a conically growing crack when the contact force is continuously increased, see Fig. 1.

Fig. 1. Phases of crack generation and growth: Indenter is pressed on surface (a), initiation of an initially cylindrical crack (b), subsequent conical crack growth (c).

In the following we model the first step of this process and assume an instantaneous crack formation. This process can be described by means of finite fracture mechanics.

3 Coupled Stress and Energy Criterion It was Hashin [8] who for the first time formulated the setting of finite fracture mechanics (FFM) by the hypothesis of an instantaneous sudden crack initiation step with a finite crack length. As a necessary and sufficient condition for this crack generation step we assume the fulfillment of the coupled criterion suggested originally by Leguillon [9]. This means a combination of the classical strength-of-materials approach with linearelastic fracture mechanics. According to that along the newly generated crack surface c a stress and an energy criterion have to be fulfilled at the same time. For the unique characterization of the crack its radius r0 and its length a are sufficient. These quantities together with the failure load Ff are unknown in the beginning and have to be determined (Fig. 2).The strength or stress criterion can be written in the form

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Fig. 2. Relevant quantities and parameters for modelling crack initiation: Indenter radius R, contact radius c, crack radius r0 , crack length a, Young’s modulus E and Poisson’s ratio ν of the material specimen, Young’s modulus Eind and Poisson’s ratio νind of the indenter.

F(σ ) ≥ σc ∀x ∈ Ωc

(1)

where a stress function F(σ ) is compared with a critical stress quantity σ c The energetical criterion is based on the classical Griffith criterion formulated in an averaged manner: a ¯ = 1 ∫ G da ≥ Gc G a 0

(2)

Herein the quantity G means the differential energy release rate, whereas averaging over the crack length a leads to the so-called incremental energy release rate. For crack initiation this incremental energy release rate has to be equal to or larger than the fracture toughness Gc . The really initiated crack surface fulfills both subcriteria for a minimal force F. This failure load is denoted as Ff . The crack surface is characterized in a unique manner by the crack radius r0 and the crack length a so that the following optimization problem is given:  ¯ Ff = min { F|F(σ (F, x, r0 )) ≥ σc ∀x ∈ Ωc ∧ G(F, a, r0 ) ≥ Gc . (3) a,r0 ,F

The involved subcriteria are addressed in more detail in the following.

4 Stress Criterion For the considered contact between a spherical indenter and an infinite half space in the case of linear elasticity there are stress solutions. They can be derived from Boussinesq’s solution for an elastic half space under a normal single force and can be found e.g. in the teaching books of Johnson [10] and Fischer-Cripps [11]. They are the basis for the stress criterion formulated here. We restrict ourselves to the radial tensile stress in the cylindrical coordinates (Fig. 2), which are dominating the stress field in the experimentally observed region of crack generation. The stress criterion means σr (F, x) ≥ σc ∀x ∈ c

(4)

According to Fischer-Cripps [11] the radial stress can be represented as follows:

Determination of Strength and Fracture Toughness from Indentation Tests

σr =

3F 2π c2



      1 − 2ν c2 c2 u z 3 z 3 + √ 1− √ 2 2 2 2 3 r u u u +c z

√   

u z c 1−ν +√ u 2 tan−1 √ + (1 + ν) −2 c u c +u u

Herein the quantity u is given by the geometrical entities r, z and c as   2 1  2 r + z 2 − c2 + r 2 + z 2 − c2 + 4c2 z 2 u= 2

47

(5)

(6)

While r and z denote the cylindrical coordinates in radial and depth direction the quantity c is the contact radius. According to Johnson [10] it can be calculated through     2  3FR 1 − ν 2 1 − ν 3 ind + c= (7) 4 E Eind Herein E and ν are the elastic properties of the specimen and Eind and νind characterize the elastic properties of the indenter. In this way the stress criterion is completely specified.

5 Energy Criterion For the calculation of the energy release rate we can follow the same approach as it has already been used by Strobl [4] and Mouginot/Maugis [7]. In doing so, we assume that the stress field in the uncracked half space (that means in the material specimen) in essence remains the same during crack generation. Then the stress intensity factor for a crack with the length z under mode I loading in good approximation can be calculated with the method of weighting functions according to  z z σr (˜z ) ∫√ k(˜z )d˜z (8) KI (z) = 2 π 0 z 2 − z˜ 2 (compare Tada [12]). Herein the function k can be approximated as k(˜z ) ≈ 1 + 0.3(1 − z˜ /z). This way it is taken into account that the crack starts from a free surface. For linear elastic material behavior there is a simple relationship between the stress intensity factor K I and the energy release rate G: G=

1 − ν2 KI . E

As a consequence the energy criterion can be formulated as:  a 1 − ν2 1 G= KI2 (z)dz ≥ Gc . E a 0

(9)

(10)

The two integrations for the use of the energy criterion can be performed numerically. Furtheron, by means of dimension analysis it can be shown that   r0 a F ,ν . (11) G = φ ξ = ,η = R c c

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Correspondingly it is sufficient to determine the dimensionless function φ in order to determine the energy release rate for any arbitrary load F and any indenter radius R. In this connection also the normalized crack radius ξ and the normalized crack length η are introduced. Both quantities are normalized with respect to the contact radius c.

6 Numerical Determination of the Energy Release Rate For the verification of the analytically determined energy release rate a finite element model is implemented for the material specimen. The effect of the indenter is taken into account by prescribed displacements uz in depth direction over the contact surface. For a spherical indenter according to Fischer-Cripps [11] the displacements are of the following form: uz uz,max

=1−

r2 ∀r ≤ c 2a2

(12)

Herein uz,max denotes the maximal indentation displacement. The simulation is performed for the uncracked configuration and for a series of cracked configurations. The energy release rate then results from the difference of the elastic total potential. As the indenter displacements are prescribed the crack initiation does not cause a change of the

Fig. 3. Results of finite fracture mechanics for an indenter radius R = 1 mm. In the upper half the failure load Ff in dependence of the normalized crack radius ξ = r0 /c. In the lower half the normalized crack length η0 = a/c again in dependence of the normalized crack radius.

Determination of Strength and Fracture Toughness from Indentation Tests

49

external potential. Thus, only the change of the internal potential i is to be taken into account: G

FE

=

Πiuncracked − Πicracked 2π r0 · a

(13)

The energy release rates obtained in this way can be approximated well by the analytical modelling.

7 Determination of the Failure Load With the stress and energy criterion the optimization problem (3) is defined completely and is to be solved. The solution can be obtained in the following step-wise and heuristic manner: First for a given crack radius we determine the minimal load for which both subcriteria are fulfilled. The subcriteria are employed in the following normalized form f =

G σr and g = σc Gc

(14)

The stress criterion reflects the monotonic decrease of the radial stress σ r with increasing depth. This gives an upper bound for the crack length. At the same time there is a monotonous increase of the incremental energy release rate and thus a lower bound for the crack length. The critical load Ff results from the requirement that the upper and lower bound are identical. This kind of optimization has to be performed for a series of potential crack radii. In this way for each considered radius value a corresponding failure load Ff and a normalized finite crack length η0 are obtained. In Fig. 3 these results are given in dependence of the crack radius. It is outside the contact radius where the load required for failure attains a minimum before it rises again for larger crack radii. The minimal failure load Ff is the force that generates a crack of length a = η0 c at the radius position r0 = ξ 0 c.

8 Validation by Experimental Data Mouginot/Maugis [7] have published a larger number of experimental findings for cracks initiated by indentation tests. Here we consider the experimental findings for boron silica glass specimens with a polished surface. For the boron silica glass a Young’s modulus of E = 80 GPa and a Poisson’s ratio of ν = 0.22 were identified by Mouginot/Maugis; for the steel indenter E = 210 GPa and ν = 0.33 were assumed. The employed indenters had the radius values 0.79, 2.37, 3.17, 5.15, 7.53, 12.7 and 15.87 mm. The indenters were driven against the material with a low displacement controlled speed. Crack initiation was recorded optically together with the corresponding force. The available data are used to determine the strength σ c and the fracture toughness Gc of the boron silica glass. As an error measure for the failure load we introduce the following quantity pred :  ⎛ ⎞  pred exp 2   n Ff − Ff 1 ⎝ ⎠ pred =  (15) exp n F f i−1

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exp

Herein Ff means the predicted failure load whereas Ff means the experimentally obtained failure load. We assume that those combinations of material strength and fracture toughness that minimize pred characterize the material in the best way. This leads to the material properties σ c = 722 MPa and Gc = 23.46 N/m. The corresponding comparison of calculated and experimentally obtained failure loads is given in Fig. 4. Obviously, the experimental data can be reproduced in a satisfying manner.

Fig. 4. Comparison of predicted and experimental failure loads (from Mouginot/Maugis [7]).

The comparison of these material parameters with the results of other authors, however, reveals some discrepancies. The fracture toughness K Ic for boron silica glass is given in the range between 0.7 and 0.9 MPa mm1/2 , see e.g. [13] or [14]. From Gc on the other hand we get a fracture toughness of 1.44 MPa mm1/2 . Also the strength value 790 MPa is comparatively large. Petzold [15] for instance specifies the range from 30 to 90 MPa. This, however, corresponds to an effective strength with some flaws in the material. For glass without any defect we can expect much higher theoretical strength values [15]. According to Leguillon [16] not the effective but an ideal strength value has to be employed within finite fracture mechanics. Beyond this potential reasons for the deviations of the fracture toughness values might be plastic effects or friction between indenter and the specimen. All these aspects require further investigations.

9 Conclusions A compact analytical model for the crack generation in indentation tests with spherical indenters has been presented. The model is based on the coupled criterion of finite fracture mechanics. The stress field required for the stress criterion results from a superposition of Boussinesq solutions. Under the assumption of a negligible effect of the crack on the

Determination of Strength and Fracture Toughness from Indentation Tests

51

stress field the incremental energy release rate has been determined in an approximate manner. This approach could be verified by means of the finite element method. The derived model is able to explain and predict the size effects in the failure load. Also it allows the simultaneous determination of strength and fracture toughness. There is, however, some deviation to available literature values. This should be investigated in further studies.

References 1. Evans, A.G., Charles, E.A.: Fracture toughness determinations by indentation. J. Am. Ceramic Soc. 59(7–8), 371–372 (1976) 2. Lawn, B.R., Evans, A.G., Marshall, D.B.: Elastic/plastic indentation damage in ceramics: the median/radial crack system. J. Am. Ceramic Soc. 63(9–10), 574–581 (1980) 3. Quinn, G.D., Bradt, R.C.: On the vickers indentation fracture toughness test. J. Am. Ceramic Soc. 90(3), 673–680 (2007) 4. Strobl, M., Dowgiałło, P., Seelig, T.: Analysis of Hertzian indentation fracture in the framework of finite fracture mechanics. Int. J. Fracture 206(1), 67–79 (2017). https://doi.org/10. 1007/s10704-017-0201-7 5. Langitan, F.B., Lawn, B.R.: Hertzian fracture experiments on abraded glass surfaces as definitive evidence for an energy balance explanation of auerbach’s law. J. Appl. Phys. 40(10), 4009–4017 (1969) 6. Warren, P.D.: Determining the fracture toughness of brittle materials by Hertzian indentation. J. Euro. Ceramic Soc. 15(3), 201–207 (1995) 7. Mouginot, R., Maugis, D.: Fracture indentation beneath flat and spherical punches. J. Materials Sci. 20(12), 4354–4376 (1985) 8. Hashin, Z.: Finite thermoelastic fracture criterion with application to laminate cracking analysis. J. Mech. Phys. Solids 44(7), 1120–1145 (1996) 9. Leguillon, D.: Strength or toughness? a criterion for crack onset at a notch. Euro. J. Mech. A Solids 21(1), 61–72 (2002) 10. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985) 11. Fischer-Cripps, A.C.: Introduction to Contact Mechanics. Springer, US (2007) 12. Tada, H., Paris, P.C., Irwin, G.R.: Stress Analysis of Cracks Handbook. ASME Press (2000) 13. Deriano, S., Jarry, A., Rouxel, T., Sangleboeuf, J.-C., Hampshire, S.: The indentation fracture toughness (Kc) and its parameters: the case of silica-rich glasses. J. Non-Cryst. Solids 344(1– 2), 44–50 (2004) 14. Boccaccini, A.R., Rawlings, R.D., Dlouhy, I.: Reliability of the chevron-notch technique for fracture toughness determination in glass. Mater. Sci. Eng. A347(1–2), 102–108 (2003) 15. Petzold, A., Marusch, H., Schramm, B.: Der Baustoff Glas. Verlag Bauwesen, Berlin (1995) 16. Leguillon, D., Martin, E., Sevecek, O., Bermejo, R.: What is the tensile strength of a ceramic to be used in numerical models for predicting crack initiation? Int. J. Frac. 212(1), 89–103 (2018)

A Flow Study in the Cyclone with Particle Separations Karel Fraˇna1(B)

, Christian Neubert2 , Sylvio Simon4 and Fariz Amirov3

, Arastun Mammadov3 ,

1 Technical University of Liberec, Studentska 2, 46117 Liberec, Czech Republic

[email protected] 2 Brandenburgische Technische Universität Cottbus –Senftenberg, Universitätsplatz 1,

01968 Senftenberg, Germany [email protected] 3 Faculty of Mechanical Engineering and Robotics, Azerbaijan Technical University, 25 H. Dschavid Ave., AZ1073 Baku, Azerbaijan [email protected], [email protected] 4 Mechanical Engineering Electrical and Energy System, Brandenburgische Technische Universität Cottbus – Senftenberg, Universitätsplatz 1, 01968 Senftenberg, Germany [email protected]

Abstract. Unsteady turbulent flows with solid particles of different sizes in the cyclone were studied numerically and experimentally. The grid studies and influence of the boundary condition prescription on the flow behavior in the cyclone and the effectiveness of the particle separation were studied firstly numerically. The turbulent flow was calculated by means of Large Eddy Simulations and this flow problem was calculated parallel using eight processors. It was found theoretically that pressure at the bottom outlet of the cyclone has a significant impact on the particle separation. This impact of the pressure at the cyclone function was examined also using experiments and pressure distributions for different flow rate intensities for several locations in the cyclone were determined. These experimental results can be used for a validation of numerical results. Furthermore, the larger losses were observed in the immersion tube due to higher flow velocity and impulse exchange in the vortex core. Keywords: Cyclone flows · Particle separations · Pressure distributions

1 Introduction A particle behavior in the gas is a typical flow problem that can be found in many situations. The flow particle simulation enables e.g. to estimate a propagation of the particle pollution in the environment or to solve the particle influence in the technical equipment. Particle simulation represents the complex problem in which the one phase (gas or liquid) is a continuous flow problem and particle behavior can be viewed as a discrete problem. The problem of the multiphase flow problem can be found in [1] or in [5]. The knowledge of the particle flow simulation in the environmental problem can be adopted for the simulations of the seed flow. In the work [2], the approach of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 52–59, 2021. https://doi.org/10.1007/978-3-030-64690-5_6

A Flow Study in the Cyclone with Particle Separations

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combining computational fluid dynamics (CFD) for continuum fluid and the discrete element method (DEM) for discrete particles has been used to study the fundamentals of coupled particle–fluid flows. Additionally different CFD–DEM models have been adopted for the numerical testing. The developed DEM-CFD model was applied to study the particles and air flow in a rotating drum and it can satisfactorily capture the flow patterns in the drum such as the particle flow in the radial direction and air flow in the horizontal direction, after particles falling show the tangential velocity and pressure drop decreased as was demonstrated in [3]. In the other study showed in [7], the model CFDDEM successfully captured the key flow features in a gas cyclone, such as the strands flow pattern of particles, and the decrease of pressure drop and tangential velocity after loading solids. The effect of solid loading ratio is studied and analyzed in terms of gas and solid flow structures, and the particle–gas, particle–particle and particle–wall interaction forces. The same numerical approach was successfully used for the simulation in the medium cyclones in [7] and [8]. Besides that there is an idea to express the influence of the particle in the flow by a change of the appropriate flow properties. In the work [9], the presence of particles is taken into account in terms of effective viscosity, which is defined by means of both Newtonian and non-Newtonian (Bingham plastic) models. In this case the dispersed phase equation closure is based on particle buoyancy as well as on shear-induced selfdiffusion effects. The proposed approach allows us to study sediment transport problems and the related evolution of bed forms, without requiring the generation of curvilinear coordinate systems and time-consuming step-by-step regridding. This paper is organized as follows: in Sect. 2 a mathematical model is introduced with details of the computational mesh. The experimental device and operation conditions are discussed. In Sect. 3 results of numerical simulation and experimental measurement of the pressure distribution is presented. In Sect. 4 main results are summarized and further research in the field of the particle separation the cyclone is illuminated.

2 Problem Formulation 2.1 Mathematical Model and Simulation The solver Discrete Phase Model – DPM (DMPFoam) was used for a simulation of particle behavior. The numerical approach is based on the idea to solver the continuous phase represented by the environment of the particles and discrete phase representing the particle itself. The continues phase is calculated by means of the equations from (1) to (4), ∂ ∂ ∂ ∂ (ρ) + (ρ · u) + (ρ · v) + (ρ · w) = 0 ∂t ∂x ∂x ∂x

  ∂  ∂ ∂ ∂  ρ · u · v − τyx + ρ · u2 + p − τxx + (ρ · u) + (ρ · u · w − τzx ) − ρ · gx = 0 ∂t ∂x ∂y ∂y    ∂  ∂ ∂  ∂  ρ · v · u − τxy + ρ · v 2 + p − τyy + ρ · v · w − τzy − ρ · gy = 0 (ρ · v) + ∂t ∂x ∂y ∂z   ∂ ∂  ∂ ∂  ρ · w · v − τyy + ρ · w2 · p − τzz − ρ · gz = 0 (ρ · w) + (ρ · w · u − τxz ) + ∂t ∂x ∂y ∂z

(1) (2) (3) (4)

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Where u,v and w are velocities in x,y,z coordinate system, ρ is density, p is pressure and g is a gravity. The action on the particles can be express as a balance of forces acting on the particle. In generally, drag force, lift force, gravity and so called a force generated by the pressure gradient are taken into account in calculations. The equation describes this balance force can be express as in (5). m

  mf d mf dup ∇p + = 6π rp μp (u − v) − (u − v) + mp − mf g dt ρf 2 dt  

+ 6rp p2 π μf ρf

t

. . . d τ,

(5)

t0

where index p or f express particle or fluid, rp is radius of particle, m is mass weight and u or v expresses velocities. Computational grid was generated by means of the snappyhexmesh tool and calculations were treated as an unsteady and as a three dimensional problem. To calculate a turbulent feature, the Large Eddy Simulation approach was adopted. 2.2 Experiments An experimental setup to measure pressure differences at the cyclone was designed to confirm the results of the initial analytical flow models (Fig. 1). The individual components of the test design were dimensioned in such a way that the experimental setup could be easily modified.

Fig. 1. Schematic representation of the experimental setup

The cyclone, which was manufactured using an additive production process, was connected via a polyvinyl chloride (PVC) pipe to a radial fan (Angelo-Po, Carpi, Italy,

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Art. Nr. 601599). A constant air flow generated by the radial fan was running through the PVC pipe with a length of 26.3 D (2000 mm) to the cyclone. The air flow was directed tangentially into the cyclone housing in which a central outflow pipe, the immersion pipe, was located. To measure pressure changes at the cyclone, pressure sensors (Panasonic, Tokyo, Japan, DP-111 A E P J) were placed at four different locations of the cyclone (Fig. 2). Measurements of the sensors were transmitted via a NI measuring module (NI-6008) to a computer where the values were recorded and displayed graphically with the software “NI LabVIEW 2015” (version 15.0, current revision 7.0).

Fig. 2. Diagrammatic representation of the measuring points at the cyclone. L-variable length of the dip tube.

3 Results Numerical simulations were carry out for different mesh resolutions starting from 442 t. cells up to 1.1 mil. cells. This grid study did not revealed any significant influence of the grid resolution on the particle behavior. Another study was focused on the influence of the boundary type conditions at the inlet/outlet on the flow character and particle distributions. The velocity prescription for inlet boundary conditions enabled to fully control flow character in the cyclone. Figure 3 illustrates instantaneous velocity vector field in the cyclone depicted by color indicating the intensity of the flow. The particles are entering into the cyclone with different sizes. The color of particles indicates velocity field of each particle. Turbulent flow features was calculated by Large Eddy Simulation approach and more about different turbulent techniques applied in the unsteady flow can be found, for instance, in [6]. However, from the practical point of view, the prescription of the pressure different at the boundary conditions is more useful in regards to the experimental settings. The main objective of the work was to identify a suitable ratio between pressure outlets. Figure 4 shows velocity vector field and dynamics of the particles. The color indication of the particle now represents its diameters or sizes respectively. If the pressure prescribed at the bottom is lower, particles of all size are falling down, however, if the pressure is a higher, that small particles visualized by blue color have a tendency to levitate.

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Fig. 3. Particles and flow vectors for velocity inlet boundary condition.

Fig. 4. Particles and flow vectors in the cyclone for different pressure intensities at the bottom outlet 3.7 Pa resp. 3.9 Pa.

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Figure 5 shows three diagrams, each with four colors (white, red, blue and green). The four colors represent where the pressure measurement was made on the cyclone. The white graph shows that this measurement was taken at the inlet of the cyclone. The red graph shows the measurement at the lower edge of the dip tube, while the blue graph shows the pressure measurement at the upper edge of the dip tube. At the lower outlet of the cyclone a fourth pressure measurement was made which is shown in a green graph. Figure 2 illustrates this once again. These pressure measurements were carried out with 3 3 three different flow velocities. In Fig. 3 A with 0.212 ms , in Fig. 3 B.) with 0.239 ms and in Fig. 3 C) with 0.247

m3 s .

Fig. 5. Representation of the pressure conditions in the cyclone

The pressure was measured at the cyclone at different flow velocities and a constant depth of the immersion tube of 130 mm. Figure 6 shows pressure differences in dependence on the flow rate intensity express by a flow velocity. At higher flow velocity, the pressure changes at the inlet also increased. Due to the geometrical properties and the inner surface of the cyclone, pressure losses were determined as displayed by the white graphs. At the upper edge of the immersion tube (blue graph) the pressure increased from 0.1 kPa to 0.16 kPa with increasing flow velocity; however, with further increase of the velocity, the pressure decreased to 0.14 kPa. At the lower edge of the immersion tube, represented by the red graph, the pressure drop was more prominent at higher flow velocity. The pressure changes at the lowest outlet of the cyclone (green graph) showed hardly any change in the pressure difference, since the outlet was closed. Pressure loss in the separation chamber was expected due to wall friction and was confirmed by the measured values. However, the larger losses were observed in the immersion tube due to overspeeds and impulse exchange with the vortex core. The highest circumferential speed is on a cylindrical surface defined by the immersion tube, which is only slightly narrower than the immersion tube.

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Fig. 6. Summary of pressure differences as a function of flow velocity.

4 Conclusion The numerical simulation of the particle separation in the cyclone was studied numerically. This study confirmed that this particle behavior in the cyclone varied based in the pressure outlet prescription. Furthermore, the flow behavior in the real cyclone was examined experimentally and the pressure distribution was found. However, these results were relatively higher because of the fact, that the cyclone was printed using 3D technology and the surface roughness was too coarse leading to the higher friction coefficient and higher total pressure drop. In the future it is planned that with the 3D printed prototype tests will be carried out under real conditions. In further steps, a further prototype made of stainless steel will follow to significantly improve the surface quality of the cyclone inside wall. This will have a positive effect on the wall friction, which will be reduced. The new stainless steel prototypes will be used for further suction tests with seeds, sand and soil under laboratory conditions. In this context, further considerations and tests are necessary to control and regulate the air flow in order to achieve a better separation and separation behavior in case of further foreign particle contamination. These new results will be used for extended validation of the numerical results. Acknowledgment. The work has been financially supported by Federal Ministry for Economic Affairs and Energy based on a decision of the German Bundestag, FKZ: 16KN072922 and the project “Hybrid materials for hierarchical structures”, reg. no. CZ.02.1./0.0/0.0/16_019/0000843 provided by the European Union and the Czech government.

References 1. Kai, H., Ari, J., Sirpa, K., Hannu, K., Markku, K., Antti, K., Mikko, M., Veikko T.: Multiphase flow dynamics theory and numerics. VTT Technical Research Centre of Finland, Vuorimiehentie 3, Finland (2009)

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2. Zhou, Z., Kuang, S., Chu, K., Yu, A.: Discrete particle simulation of particle-fluid flow. Model formulations and their applicability. J. Fluid Mech. 661, 482–510 (2010) 3. Wangchai, S., Hastie, D., Wypych, P.: DEM-CFD Modelling of particle flow mechanisms in dustiness testers. In: Proceedings (2016) 4. Chu, K.W., Wang, B., Xu, D.L., Chen, Z.X., Yu, A.B.: CFD–DEM simulation of the gas–solid flow in a cyclone separator. Chem. Eng. Sci. 66(5), 834–847 (2011) 5. Fraˇna, K., Attia, S., Stiller, J.: A bubble formation in the two-phase system. In: Rodrigues, J.M.F., Cardoso, P.J.S., Monteiro, J., Lam, R., Krzhizhanovskaya, V.V., Lees, M.H., Dongarra, J.J., Sloot, P.M.A. (eds.) ICCS 2019. LNCS, vol. 11539, pp. 580–586. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22747-0_43 6. Fraˇna, K., Stiller, J.: A hybrid urans/les approach used for simulations of turbulent flows. Springer Proc. Phys. 131, 139–142 (2010). https://doi.org/10.1007/978-3-642-02225-8_32 7. Chu, K.W., Wang, B., Yu, A.B., Vince, A.: CFD-DEM modelling of multiphase flow in dense medium cyclones. Powder Technology 193(3), 235–247 (2009) 8. Wang, S., Luo, K., Chenshu, H., Fan, J.: CFD-DEM study of the effect of cyclone arrangements on the gas-solid flow dynamics in the full-loop circulating fluidized bed. Chem. Eng. Sci. 172, 199–215 (2017) 9. Lalli, F., Esposito, P.G., Piscopia, R.: Fluid–particle flow simulation by averaged continuous model. Comput. Fluids 34 (2004)

Nonreflecting Outlet Boundary Conditions for Smoothed Particle Hydrodynamics Simulation of Small-Scale Open-Channel Flow Thanh T. Bui(B) and Susumu Nakata Ritsumeikan University, Shiga 525-8577, Japan [email protected]

Abstract. In this paper, we propose a nonreflecting outlet boundary condition (NROBC) for particle-based fluid simulation as a combination of inflow/outflow algorithm and periodic boundary condition. We assume to use δ-SPH scheme for weakly compressible flows. In the inflow/outflow algorithm, the domain is divided into four zones: fluid, wall, inflow and outflow zones. The NROBC proposed in this paper inherits the advantage of the periodic boundary condition in the sense that the number of particles is constant. This property contributes to conservation of total mass and insertion of inflow particles without rearranging process. The physical quantities such as density and velocity at the inflow zone are unknown depending on the situation. Our boundary condition supports both cases, prescribed and non-prescribed, and the loss of the accuracy is small even if the quantities are non-prescribed at the inflow zone. In addition, tensile instability is effectively reduced by particle shifting technique. Several simulations are presented to validate and demonstrate the applicability and versatility of the proposed technique. Comparisons between numerical results and analytical solutions are provided with very low Mean Square Error Percent (MSEP) in both test cases. Keywords: Fluid simulation · SPH · Open boundary · Periodic boundary condition

1 Introduction Open boundary conditions are difficult to implement in smoothed particle hydrodynamics (SPH) method. A number of investigation about this issue has been previously addressed by different authors. In many SPH simulations, periodic boundary conditions are employed [1, 2], where the particle distribution is continually recycled so that the particles pass through the outlet, it is vice versa at the inlet. The drawbacks of this technique are the violation by the outlet velocity field after re-inserted.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 60–71, 2021. https://doi.org/10.1007/978-3-030-64690-5_7

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For accurate open boundary conditions, Lastiwka et al. [3] proposed a model for the imposition of permeable boundary conditions for gas dynamics. Unfortunately, this method is difficult to apply to hydrodynamic problems with the free surface. AlvaradoRodrıguez et al. in [4], utilizing a different formulation based on an anisotropic wave equation for the velocity field at the outlet. Vacondio et al. [5] introduced open boundary conditions using Riemann invariants. Federico et al. [6], Tafuni et al. [7] presented an implementation of open boundary conditions for a weakly compressible SPH scheme suitable for the free surface flow. In their methods, inflow and outflow zones are respectively attached to the upstream and downstream of the computational domain. When inflow particles cross the fluid domain, new particles will be created in the inflow zone accordingly, while once a particle flows out the outflow zone, it will be eliminated from the simulation. Ferrand et al. [8] and Leroy et al. [13] introduced a different approach based on the generalization of the semianalytical boundary conditions method to impose unsteady open boundaries in a weakly compressible and incompressible SPH model. In the present work, we propose a fast and simple approach for nonreflecting outlet boundary condition (NROBC) treatment using SPH. This scheme is a hybrid of in/outflow algorithm and periodic boundary condition. Instead of eliminating outflow particles which cross outflow region, these outflow particles will be immediately transferred to the opposite end similarly to periodic boundary condition with new physical quantities such as densities and velocities appropriately interpolated at the inflow zone. Therefore, the mass conservation will be satisfied and removing a violation as periodic boundary condition. Several simulations are presented to validate the proposed technique.

2 The SPH Model 2.1 Governing Equations In the SPH method, the governing equations for weakly compressible SPH in its Lagrangian form are: (1) (2) where ρ, u, p, μ, and F are the density, velocity, pressure, dynamic coefficient of viscosity, and body force, respectively. 2.2 The δ-SPH Model The δ-SPH scheme was proposed by Antuono et al. [9]. This scheme adds a proper artificial diffusive term to the continuity equation to reduce the high-frequency oscillations

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in the pressure field, which is typical in the standard weakly compressible SPH model. The governing equations of the δ-SPH model are written as:

(3)

where ρi , pi , and ui are the density, pressure, and velocity associated with the i-th particle, respectively, F is the body force, Wij is the kernel function, which is a positive radial function with a compact support, h is the smoothing length, μ is the viscosity, ρ0 is a reference density, and c0 is the speed of sound. c0 is usually chosen according to the following as [10].    (4) c0 ≥ 10 max Umax , pmax /ρ0 where Umax and pmax are the maximum expected velocity and pressure, respectively. According to the weakly compressible approach, this ensures a less than 1% density variation; in addition, the Mach number of the flow should be 0.1 or less. The parameter δ is set equal to 0.2 in all the simulations, and n is the number of dimensions. The viscous term πij and diffusive term ψij are represented following [9].

3 Boundary Conditions 3.1 Solid Boundary In this work, several layers of wall particles were generated at the channel bottom by reflecting fluid particles onto solid boundary areas. The wall particles are fixed throughout the whole simulation. A no-slip boundary condition is implemented along the solid boundary and the information of solid particles is only interpolated from fluid particles every time step as follow in [11]: N g ρi

g ui

j∈fluid

= N

=

m

ρj ρjj Wij

mj j∈fluid ρj Wij

−

N

j∈fluid

N

(5)

m

uj ρjj Wij

mj j∈fluid ρj Wij

(6)

where ρ g and ug are the density and velocity associated with the i-th ghost particles, respectively. The information of ghost particles only come from fluid particles that belong to f as shown in Fig. 1. The pressure will be calculated by the state of equation as in Eq. (3).

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Fig. 1. Schematic of a wall particle (in black) and its associated support domain intersecting with the fluid domain (blue particles)

3.2 Nonreflecting Outlet Boundary Condition In this section, a non-reflecting outlet boundary condition (NROBC) which is a hybrid of in/outflow algorithm and periodic boundary condition is presented. The computing domain is divided into four sets of particles as follows: fluid, wall, inflow, outflow particles as Fig. 2. In a similar way to the in/out-flow algorithm, inflow zone is placed in front of the fluid zone so that the attached zone covers a region as wide as the kernel support. Inflow particles move according to their velocity until they cross the inflow zone and become fluid particles. In terms of fluid particles, their information evolves in accordance with the SPH governing equations. The fluid particles which cross the fluid zone will become outflow particles. Unlike most of inflow/outflow algorithms, outflow particles which cross outflow zone will be immediately transferred to the opposite end similarly to periodic boundary condition.

Fig. 2. Initial sketch of the computational domain: different colors are associated to different sets of particles.

Generally, most inflow/outflow algorithms eliminate outflow particles that cross the outflow region and create new inflow particles at the inflow region. In the case of the different velocity profiles at the outlet zone, the number of particles inserted to the computational domain is not as equal as eliminated particles. It leads to a loss of total mass where conservation of mass is violated. Besides, the array structure of particles

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is distributed sequential as described in [6]: inflow particles, fluid particles, outflow particles and boundary particles at every time step. For the simulation with the above inflow/outflow algorithm, a re-arranged process for the structure of total particles is required at every time step which leads to high computational cost. The advantage of our approach is to preserve the total number of particles throughout the simulation by inserting inflow particles immediately into the computational domain after passing the outlet zone. In addition, the management of total particles are based only on the type of particles. Hence, this avoids the re-arranged process for the structure of total particles at every time step. Due to the hybrid of in/out-flow boundaries and periodic boundary condition, this approach is flexible to solve various kinds of test cases whether prescribed boundary condition or non-prescribed boundary condition. + Boundaries with Prescribed Values Let us assume that velocity and pressure conditions at the inlet are prescribed. The velocity and pressure are enforced the desired values. The inflow particles that cross the inflow zone become fluid particles and they will be treated as fluid particles. The fluid particles pass through fluid zone become outflow particles and they will be treated as outflow particles. The outflow particles are either possible to impose specific outflow conditions as inflow particles or handling as fluid particles. Outflow particles that pass through outflow zone will be re-inserted at inlet zone with same y-coordinate positions and the values are same the desired values at the inflow zone. + Boundaries with Non-prescribed Values Let us assume that velocity and pressure conditions at the inlet are non-prescribed. The in/out-flow particles will be treated as fluid particles that evolve following the SPH governing equations. On the contrary, the values of new inflow particles are calculated as Eq. (7) and Eq. (8). N ρiinlet

j∈fluid

= N

m

ρj ρjj Wij

mj j∈fluid ρj Wij N mj j∈fluid uj ρj Wij

uiinlet = N

mj j∈fluid ρj Wij

(7)

(8)

4 Test Cases Two test cases of viscous open-channel flow in the laminar regime were simulated with prescribed value and non-prescribed value. The results obtained through simulation by I. Federico [6] have been used here as a reference solution. In this simulation, fluid flow moves with a distribution of velocity u(z) for 2D channel flow as equation:  ρgs0  2hz − z 2 (9) u(z) = 2μ

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where ρ is density, g is the gravity acceleration, s0 is the bottom slope, h is the surface depth, μ is the dynamic viscosity and z is the vertical abscissa which origin is located at the channel bottom The Reynolds number is calculated by equation: Re =

ρUh μ

(10)

where velocity U is evaluated be the average velocity profile U =

1h ∫ u(z)dz h0

(11)

The length of fluid domain is L = 2 h and the slope s0 = 0.001. For both cases, the fluid particles are initialized with analytical solution by Eq. (9). The sound speed is selected equal 10u (z = h). The model of simulation depicts as Fig. 3.

Fig. 3. Sketch of the elementary fluid domain.

The tensile instability in SPH is always challenging, especially for the simulation with high Reynolds numbers. In this simulation, we use a particle shifting technique in [12] to remove for this issue of simulation. 4.1 Viscous Open-Channel Flow with Prescribed Boundary Condition In this case, the initial boundary condition is imposed as follows: zf (t = 0) = zi (t) = h

 ρgs0  2hz − z 2 2μ pf (z, t = 0) = pi (z, t) = ρg(z − h)

uf (z, t = 0) = ui (z, t) =

(12)

Velocity and pressure at the inflow zone are enforced desired values throughout simulation. On the contrary, at the outflow zone, the outflow particles are treated as fluid particles where initial information the same as the inflow particles and then their information evolves in accordance with the SPH governing equations.

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At the channel bottom, we are enforced a no-slip condition through several layers of ghost particles. The objective of the simulation is to verify the velocity field of fluid particles throughout the simulation and compare with the analytical solution in Eq. (9). The simulation is carried out for a long enough time in order to check the stability of the fluid flow. The particles are initially distributed with a resolution 4x = 4h/125 with 2000 particles and applied for Re = 10,100 and 200, respectively. Figure 4 illustrates particles distribution and velocity field at t(g/h)1/2 = 100 for Re = 10, 100 and 200, respectively. It can be seen that the flow develops in almost parallel layers over the entire computational domain. The results obtained using the proposed technique are in good agreement with the inflow/outflow algorithm by Federico [6] throughout the flow domain.

(a)

(a)

(a)

(b)

(b)

(b)

Fig. 4. Particles distribution and velocity field at t(g/h)1/2 = 100 at Re = 10, 100 and 200. (a). the proposed technique, (b) I. Federico [6]

In order to verify the stability of proposed technique, we carry out a comparison between the analytical solution in Eq. (1) and the numerical results obtained by SPH at three different x-positions: x = 0 (inflow threshold), x = h (middle of fluid domain)

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and x = 2 h (outflow threshold). Figure 5 shows a good agreement between analytical and numerical profiles. The performance of the proposed technique is approximately the same analytical solution at all three different x-positions. Therefore, it demonstrates the stability of this technique throughout the computational domain.

Fig. 5. Comparisons between analytical solution and numerical results at t(g/h)1/2 = 100 for Re = 10, 100 and 200 at x = 0, x = h and x = 2 h.

Fig. 6. The Mean Square Error Percent (MSEP) for Re = 10 with the proposed technique and inflow/outflow by I. Federico [6]

To check the convergence of velocity field between the proposed technique and analytical solution, a mean square error is calculated by Eq. (5) at x = h (middle of the fluid domain) with a resolution 4x = 4h/125.  a  n 2 N 1  uj − uj RMSEP = × 100% (13) N uja j=1

Where, ua and un are the analytical and numerical velocity, respectively. N is the number of velocity values.

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Figure 6 illustrates the MSEP of the velocity field of the proposed technique and inflow/outflow by I. Federico [6]. As the figure, it can be seen that the MSEP of the proposed technique is low with the maximum error is about 0.1% at the resolution 4x. The performance of the MSEP is significantly lower to compare with inflow/outflow in I. Federico [6] at three different spatial resolutions even though the resolution x with 31000 particles. Figure 7 also depicts the MSEP of the velocity field of proposed technique at Re = 100 and 200 with a peak error about 0.2%.

Fig. 7. The Mean Square Error Percent (MSEP) for Re = 100 and Re = 200 with the proposed technique

4.2 Viscous Open-Channel Flow with Non-prescribed Boundary Condition In SPH, there are many simulations where the fluid flow has driven by a body force F in Eq. (3). Therefore, the fluid particles obtain the propagation and evolution of both velocity and pressure fields during the simulation. It leads to unpredictable values at the inflow/outflow region. In order to demonstrate the effectiveness and applicability of the proposed technique. In this case, we assume that the velocity and pressure of the inflow zone are non-prescribed. In/out-flow particles are treated the same as fluid particles. The initial state is imposed as follows: zf (t = 0) = zi (t = 0) = zo (t = 0) = h

 ρgs0  2hz − z 2 2μ pf (z, t = 0) = pi (z, t = 0) = po (z, t = 0) = ρg(z − h) uf (z, t = 0) = ui (z, t = 0) = uo (z, t = 0) =

(14)

The outflow particles pass through outflow zone will be vice versa inflow zone and their information is calculated as Eq. (7) and Eq. (8). The ghost particles are also enforced a non-slip condition. The simulation is carried out as same as an above test case with a resolution 4x = 4h/125 for Re = 10, 100 and 200, respectively.

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Figure 8 illustrates particles distribution and velocity field at t(g/h)1/2 = 100 for Re = 10, 100 and 200, respectively. As the figure, a fluctuation at the channel top appears due to its free surface state. Overall, the results obtained using the proposed technique are in agreement with inflow/outflow algorithm by Federico [6] throughout the flow domain.

(a)

(b)

(a)

(b)

(a)

(b)

Fig. 8. Particles distribution and velocity field at t(g/h)1/2 = 100 at Re = 10, 100 and 200. (a). the proposed technique, (b) I. Federico [6]

Figure 9 shows a comparison between analytical and numerical profiles. The performance at Re = 10 is approximately at three different x-positions with the highest error around 0.6% as shown in Fig. 10. The result of the MSEP obtained significantly lower to compare with inflow/outflow in I. Federico [6] at the same spatial resolution. At the higher Reynold number Re = 100 and Re = 200, the numerical results have a slightly different with a difference of about 1.2% and 2% as shown in Fig. 11, respectively.

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Fig. 9. Comparisons between analytical solution and numerical results at t(g/h)1/2 = 100 for Re = 10, 100 and 200 at x = 0, x = h and x = 2 h

Fig. 10. The Mean Square Error Percent (MSEP) for Re = 10 with the proposed technique and inflow/outflow by I. Federico [6]

Fig. 11. The Mean Square Error Percent (MSEP) for Re = 100 and Re = 200 with the proposed technique

5 Conclusions In this paper, an approach based on the hybrid of in/outflow algorithm and periodic boundary condition is presented. This approach is also discretized into four sets of particles as follows: fluid, wall, inflow, outflow particles like as most of the inflow/outflow algorithm. However, the outflow particles which cross the outflow zone will be immediately vice versa similarly the periodic boundary condition. The value of these particles

Nonreflecting Outlet Boundary Conditions for Smoothed Particle Hydrodynamics

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is imposed on a prescribed boundary condition or non-prescribed boundary condition, respectively. Hence, it removed a violation from the periodic boundary condition. Several numerical tests demonstrated that the proposed technique is obtained good results with a high agreement with the analytical solution.

References 1. Joseph, P.M., Patrick, J.F., Zhu, Y.: Modeling low reynolds number incompressible flows using SPH. J. Comput. Phys. 136(1), 214–226 (1997) 2. Lee, E.-S., Moulinec, C., Xu, R., Violeau, D., Laurence, D., Stansby, P.: Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method. J. Comput. Phys. 227(18), 8417–8436 (2008) 3. Lastiwka, M., Basa, M., Quinlan, N.J.: Permeable and non-reflecting boundary conditions in SPH. Int. J. Numer. Meth. Fluids 61(7), 709–724 (2009) 4. Carlos, E.A., Jaime, K., Leonardo, D.G.S., José, M.D., Eduardo de la, C.S.: Nonreflecting outlet boundary conditions for incompressible flows using SPH. Comput. Fluids, 159, 177– 188 (2017) 5. Vacondio, R., Rogers, B.D., Stansby, P.K., Mignosa, P.: Sph modeling of shallow flow with open boundaries for practical flood simulation. J. Hydraul. Eng. 138(6), 530–541 (2012) 6. Federico, I., Marrone, S., Colagrossi, A., Aristodemo, F., Antuono, M.: Simulating 2D openchannel flows through an SPH model. Euro. J. Mech. B/Fluids 34, 35–46 (2012) 7. Tafuni, A., Domínguez, J.M., Vacondio, R., Crespo, A.J.C.: A versatile algorithm for the treatment of open boundary conditions in smoothed particle hydrodynamics GPU models. Comput. Meth. Appl. Mech. Eng. 342, 604–624 (2018) 8. Ferrand, M., Joly, A., Kassiotis, C., Violeau, D., Leroy, A., Morel, F.X., Rogers, B.D.: Unsteady open boundaries for SPH using semi-analytical conditions and Riemann solver in 2D. Comput. Phys. Comm. 210, 29–44 (2017) 9. Antuono, M., Colagrossi, A., Marrone, S., Molteni, D.: Free-surface flows solved by means of SPH schemes with numerical diffusive terms. Comput. Phys. Commun. 181(3), 532–549 (2010) 10. Antuono, M., Marrone, S., Colagrossi, A., Bouscasse, B.: Energy balance in the δ-SPH scheme. Comput. Methods Appl. Mech. Eng. 289, 209–226 (2015) 11. Douillet-Grellier, T., De Vuyst, F., Calandra, H., Ricoux, P.: Simulations of intermittent twophase flows in pipes using smoothed particle hydrodynamics. Comput. Fluids 177, 101–122 (2018) 12. Sun, P.N., Colagrossi, A., Marrone, S., Antuono, M., Zhang, A.M.: Multi-resolution Deltaplus-SPH with tensile instability control: towards high reynolds number flows. 224, 63–80 (2018) 13. Leroy, A., Violeau, D., Ferrand, M., Fratter, L., Joly, A.: A new open boundary formulation for incompressible SPH. Comput. Math Appl. 72, 2417–2432 (2016)

Study on Material Point Method with Different Influence Factors of Temperature Jingjing Zhang1(B) , Jinglin Luo2 , and Mian Jiang1 1 The School of Mechatronics Engineering, Foshan University, #33 Guang-yun-lu, Shishan,

Nanhai, Foshan, Guangdong, People’s Republic of China [email protected] 2 School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, Guangdong, China

Abstract. An improved material point method (MPM) algorithm is proposed in this paper with considering shock temperature and melting point of the analyzed material with a high pressure. This algorithm is especially well suited for high-speed impacts cases which accompany with great deformations and high temperature environment. A Taylor impact test has been taken as an example to analyze the influence of the material softening caused by high temperature and the importance of shock temperature and melting point affected by high pressure in a high-speed impact simulation by MPM. Compared to the result simulated by classic MPM, the accuracy of the result simulated by the improved MPM which considers shock temperature and melting point affected by high pressure has been improved. Keywords: Material point method · Plastic deformation · Shock temperature · Melting point

1 Introduction In recent years, a large number of alternatives to standard finite element (FE) methods have been proposed for the solution of engineering problems in solid mechanics, particularly those involving very large deformations, which is a challenge to any Lagrangian mesh-based method due to mesh distortion and the computational expense of re-meshing during a simulation. Mesh-less methods, such as the element-free Galerkin method [1] and others remain computationally uncompetitive, while other options that are suggested have other disadvantages, e.g. the re-meshing and interpolation technique with small strain [2], which is itself still mesh-based, the discrete element method [3] (computationally expensive for real-world geometries), or smoothed particle hydrodynamics, [4] which has difficulties with solid material modeling. An exciting alternative to the options discussed above is the material point method (MPM) which is first described in 1994 by Sulsky [5, 6]. In MPM, discretization occurs via mesh-less material points within the problem domain, which are enclosed in a separate mesh of conventional FE methods. Information, such as the density and others, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 72–83, 2021. https://doi.org/10.1007/978-3-030-64690-5_8

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is stored at material points from step to step of analysis in MPM. The calculations are computed on the surrounding background grids with input data obtained by interpolation from the material points. The grid is restored to its original location at the end of each time step to avoid the mesh distortion problems of finite element methods. Therefore, MPM is suitable for simulating the process of impact, fracture and other phenomenon which accompanies with large deformations. Meanwhile, compared to other mesh-less methods, it is unnecessary to search a point’s neighborhood points in MPM as the governing equations are solved on a regular grid. Hence, MPM has a higher efficiency than other mesh-less methods. At present, MPM has been widely used in the engineering simulations. Many scholars have improved the algorithm according to their needs. Sulsky etc. [5, 6] simulated the process of Taylor impact test and spherical steel fragments penetrating aluminum target plates problem. Huang Peng [7], Ma Zhitao [8] simulated the problems of lowspeed impact penetration by MPM. Chen [9–11] simulated the dynamic failure of brittle materials under impact loading and the failure of materials under local heating by MPM either. Temperature is one of the most important factors that affect the characteristics of a material. During the simulation process mentioned above by MPM, most of the simulation process has only considered the effect of large deformations on the temperature rise. However, during the high-speed impact problems, such as a Taylor impact test, the adiabatic compression and shock wave dissipation effect caused by impact will cause a drastic temperature change of a structure. The changed temperature is called shock temperature, but the classic material point method does not take it into account. Meanwhile, a high pressure will increase the melting point of materials. Hence, the shock temperature and melting point affected by high pressure will be considered in MPM in this article.

2 The Material Point Method 2.1 Governing Equations The accuracy of a numerical model depends on its ability to obey the three governing equations: balance of mass, momentum and energy conservation. Conservation of mass is ensured by the equation Dρ + ρ∇ · v = 0 Dt

(1)

Where v = v(x, t) is the spatial velocity and ρ = ρ(x, t) is the current density. ∇ is the gradient operator and ∇· is the divergence of the vector field. Conservation of momentum is ensured by the equation ρ

Dv = ∇ · σ + ρ b Dt

(2)

Where σ = σ (x, t) is the Cauchy stress tensor and b = b(x, t) is the specific body force.

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J. Zhang et al.

Conservation of energy is ensured by the equation ρ

dε DE = σ · + ρs Dt dt

(3)

Where E is the internal energy per unit mass in the current configuration. ε = ε(x, t) is the strain and d ε/dt is the corresponding strain rate. s is the inner heat sources. 2.2 Discretization A series of material points are discretized in MPM to store information (shown in Fig. 1).

Fig. 1. Discrete material points

The density of a continuum can be expressed approximately by the equation ρ(xi ) =

np 

mp δ(xi − xip )

(4)

p=1

Where np is the number of the discrete material points. mp is the mass and xip is the position of the material point P. δ is the Dirichlet function. To formulate the governing equation of MPM, Eqs. (1) to (3) must be given in a discrete form either. 2.3 The Steps of MPM Algorithm The general algorithm of MPM can be given as follows. 1. A background mesh is generated. 2. The information is transferred from the material points to the grid nodes. 3. The forces of grid nodes are solved and the boundary conditions are imposed on the grid nodes.

Study on Material Point Method with Different Influence Factors

75

4. The equation of momentum is solved at the grid nodes. 5. According to the results attained from step 4, the information is transferred back to the material points and the state variables of material points, such as velocity, position, are updated. 6. The strain and vortex increments of material points are solved and the density and stress of material points are also updated. 7. The increases of temperatures caused by plastic deformations of material points are computed and the temperatures of material points are updated. 8. The deformed mesh is abandoned and a new background mesh is generated. As mentioned earlier, temperature is one of the most important factors that affect the characteristics of a material and the adiabatic compression and shock wave dissipation effect caused by impact will cause a drastic temperature change of a structure. But the classic MPM algorithm has only considered the effect of large deformation on the temperature rise. Therefore, we will consider the shock temperature in MPM as follows.

3 Improved MPM Johnson-cook constitutive model is a visco-plastic model and it is suited to a circumstance with high strain rate and high temperature. The model is ensured by the equation σy = (A + Bεpn )(1 + C ln ε˙ ∗ )(1 − T ∗m )

(5)

Where σy is the von-Mises yield stress. A, B, n, C, m are five material constants which are obtained from tests. εp is the effective plastic strain. ε˙ ∗ is the dimensionless equivalent plastic strain-rate and T ∗m is the homologous temperature. T ∗m =

T − Tr ∈ [0, 1] Tm − Tr

(6)

Where T is the current temperature of the structure. Tr is the room temperature and Tm is the melting temperature of the material. According to Eqs. (5) and (6), σy is approximately equal to A if the strain and the strain rates are small enough and T = Tr . σy increases with the increase of the strain or the strain rates. However, σy is approximately equal to zero which lead a structure to deform easily if T is approximately equal to Tm . The phenomenon is called material softening. A Taylor impact test [12] is taken as an example to verify the material softening and the importance of shock temperature in a high-speed impact simulation by MPM. The material of the cylinder in the impact test is copper and it impact on a rigid boundary with 190 m/s. The parameters of the cylinder are shown in Table 1.

76

J. Zhang et al. Table 1. Parameters of the cylinder Parameters

Values

Length/mm

25.4

Diameter/mm 7.6 ρ/(g/cm3 )

8.93

E/GPa

117

υ

0.35

A/MPa

157

B/MPa

425

n

1.0

C

0.0

m

1.0

Tmelt /K

300.0

Troom /K

1400

c0 /(m/s)

3940

s

1.49

γ0

2.0

The final length L of the Taylor impact test is 16.2 mm and the final diameter D is 13.5 mm. The diameter W of the position from the bottom 0.2L0 is 10.1 mm. During the simulated process of the Taylor impact test, the distance between two material points is 0.38 mm and there are 21772 points are discretized. The calculation model of the Taylor impact test by MPM is shown in Fig. 2. The simulation time is set as 80 µs and the kinetic energy of the cylinder is close to zero at 80 µs. 3.1 Material Softening Effect The material softening effect will be verified in this section. Figure 3 shows the results of XZ plane when Y is equal to zero of the Taylor impact test with an initial temperature of 30 K, 300 K, 1000 K and 1500 k. These four results are simulated by classic MPM algorithm without considering any temperature factors. Table 2 shows the geometric parameters of the simulated cylinder at 80 µs. The relative error is established by L, D and W and it is ensured by the equation   1 |L| |D| |W | × 100% (7) + +  = 3 L D W Figure 3 and Table 2 show that the cylinder has a greater deformation with the increase of material temperature under the same condition. The results mentioned above are caused by the reason of the yield stress decreases with the increase of material

Study on Material Point Method with Different Influence Factors

77

Fig. 2. The calculation model of the Taylor impact test by MPM 30K

300K

15

15

10

10

5

5

0

-10

-5

0

5

10

0

-10

-5

1000K 15

10

10

5

5 -10

-5

0

5

10

5

10

1500K

15

0

0

5

10

0

-10

-5

0

Fig. 3. The results of XZ plane when Y is equal to zero of the Taylor impact test with different initial temperature

temperature. Therefore, it is important to consider the influence of temperature in MPM algorithm when the algorithm is applied for simulation. We will consider the factors of plastic deformations and shock temperature in MPM algorithm in the following sections. 3.2 Work of Plastic Deformations The deformation processes of low strain-rate and high strain-rate are different in their simulated processes. The low strain-rate phenomenon is usually treated as an isothermal process while the high strain-rate phenomenon is usually treated as an adiabatic process. During an adiabatic process, the work of plastic deformations is converted to heat and causes an increase of temperature.

78

J. Zhang et al. Table 2. The geometric parameters of the simulated cylinder at 80 µs Initial temperature/K

L/mm

D/mm

W/mm

Relative error/%

Test results

16.20

13.50

10.1

30

16.18

12.68

9.28

4.73

300

15.41

13.31

9.43

4.41

1000

12.37

16.84

9.91

16.74

1500

10.10

22.69

7.78

42.90

The work of plastic deformations is related to the strain-rate. W = sεP

(8)

Where S is the equivalent effective stress and εP is the plastic strain increment. The increase temperature caused by plastic deformations is ensured by the equation T1 =

β W ρcp

(9)

Where cp is the material’s specific heat at a constant pressure and β = 0.9 is the coefficient of plastic work converted to heat. The Taylor impact test mentioned above is taken as the example to analyze the influence of plastic deformations in MPM algorithm with an initial temperature of 30 K. Figure 4 shows the simulated result of the case in this section at 80 µs. The final length of the cylinder is 17.16 mm. The final diameter is 12.17 mm and the final diameter of the position from the bottom 0.2L0 is 9.00 mm. Compared to the test, the relative error is 8.89%.

Fig. 4. The results of XZ plane when Y is equal to zero of the Taylor impact test with considering plastic deformations

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79

3.3 Shock Temperature Shock temperature is an important parameter during the process of impact compression analysis [13]. It can be obtained by thermodynamic function, conservation equation and Hugoniot curve. There are three methods to obtain the shock temperature [14–18]: 1. Obtained from Gruneisen state equation and Hugoniot curve; 2. Obtained from three-term equation of state; 3. Obtained from Gruneisen state equation which is taken the isentropic line as the reference line. According to the conclusions analyzed by Tang [19], the first method has the least parameters to compute the shock temperature but it does not consider the influence of phase change. The second method has the most comprehensive considerations and it has the most parameters to compute the shock temperature. The last method is related to the isentropic line which means that the accuracy of the computed shock temperature depends on the choice of the isentropic equation. Compared the computed shock temperature to the test, the results show that the second method has a good result in both solid phase and liquid phase while the first method has a good result in solid phase only. We do not consider liquid phase in this paper and the first method has the least considered parameters. Hence, the first method is taken as the method to obtain the shock temperature in MPM algorithm. According to the thermodynamic functions,   (10) de + pdv = cv dT + (δe/δv)T + p dv p + (δe/δv)T = T (δS/δv)T = Tcv γ /v

(11)

Equation (12) can be derived, de + pdv = cv dT + Tcv (γ /v)dv

(12)

Where cv is the material’s specific heat at a constant volume. γ is the parameter of Gruneisen. v is the specific volume and e is the specific internal energy. Combination of the Eq. (12) with the parameters of the Hugoniot curve,  dTH γ 1  + TH = pH + (v0 − v)(dpH /dv) dv dv v 2cv

(13)

Where the subscript H stands for the parameters which are under the state of Hugoniot curve. The subscript 0 stands for the parameters which are under the state of zeropressure. γ is ensured by the equation γ0 γ = v v0 μ η= 1+μ Equation (11) and (12) are taken into Eq. (10) and Eq. (16) can be obtained.  η c02 λx2 T2 = T0 exp(γ0 η) + exp(γ0 η) exp(−γ0 x)dx 3 cv 0 (1 − λx)

(14) (15)

(16)

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J. Zhang et al.

Where c0 and λ are parameters of Gruneisen. Equation (17) can be obtained by using the Taylor expansion of Eq. (16) at η = 0 and retaining the first three items. T2 = T0 exp(γ0 η) +

c02 1 3 1 exp(γ0 η)[ λη3 + ( λ2 − γ0 λ)η4 ] cv 3 4 4

(17)

According to the theory of the shock temperature caused by impact compression, the seventh step of MPM algorithm mentioned in Sect. 2.3 should be changed as follows. The shock temperature of material points are computed and the temperatures of material points are updated. Figure 5 shows the simulated result when the plastic deformations and shock temperature are comprehensively considered at 80 µs. The final length of the cylinder is 16.75 mm. The final diameter is 13.46 mm and the final diameter of the position from the bottom 0.2L0 is 9.00 mm. Compared to the test, the relative error is 4.86%.

Fig. 5. The results of XZ plane when Y is equal to zero of the Taylor impact test with considering plastic deformations and shock temperature

3.4 Melting Point Affected by High Pressure The melting points of materials can affect the von-Mises yield stress in Johnson-Cook constitutive model shown in Eq. (5). The material will melt and the flow stress will be 0 when the temperature generated by impact compression reaches or exceeds the melting point of material. Therefore, it is necessary to calculate the melting point in the simulation method. In general, high pressure will increase the melting points of materials and the melting points of materials with high pressure can be calculated by Simon formula. 6γ +1

p/α = (Tm /Tm0 ) 6γ −2 − 1

(18)

Where Tm0 is the melting point with zero pressure. Tm is the melting point with p pressure. α and γ are parameters of the material. Hence, the melting point of a material

Study on Material Point Method with Different Influence Factors

81

with high pressure can be calculated by Eq. (19). Tm =Tm0

p α

6γ −2 6γ +1 +1

(19)

Figure 6 shows the simulated result when the plastic deformations, shock temperature and melting point affected by high pressure are comprehensively considered at 80 µs. The final length of the cylinder is 16.10 mm. The final diameter is 13.21 mm and the final diameter of the position from the bottom 0.2L0 is 9.40 mm. Compared to the test result, the relative error is 3.23%.

Fig. 6. The results of XZ plane when Y is equal to zero of the Taylor impact test with considering plastic deformations, shock temperature and high pressure

The results of three cases have been integrated into Table 3. Table 3. The geometric parameters of the simulated cylinder at 80 µs with different cases Case

L/mm

D/mm

W/mm

Relative error/%

Test results

16.20

13.50

10.1

–

Considering plastic deformations only

17.16

12.17

9

8.89

Considering plastic deformations and shock temperature

16.75

13.46

9

4.86

Considering plastic deformations, shock temperature and melting point affected by high pressure

16.10

13.21

9.4

3.23

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J. Zhang et al.

4 Conclusions The MPM algorithm has been improved with considering shock temperature and melting point affected by high pressure in this paper. A Taylor impact test has been taken as an example to analyze the influence of the material softening and the importance of shock temperature and melting point caused by high pressure in a high-speed impact simulation by MPM. The results show that yield stress decreases and the cylinder deforms more easily with the increase of material temperature. Compared the relative errors of the case which considers plastic deformations only, the results of the case which considers plastic deformations and shock temperature together and the results of the case which considers plastic deformations, shock temperature and melting point caused by high pressure, we find that shock temperature and melting point caused by high pressure play much more important roles in a high-speed impact simulation. Therefore, it is necessary to consider the influence of shock temperature and melting point caused by high pressure in MPM algorithm to simulate the process of an impact test. Acknowledgement. This paper is funded by Project of Education Bureau of Guangdong Province (grant numbers: 2018KQNCX276).

References 1. Belytschko, T., Lu, Y.Y., Gu, L.: Element-free Galerkin methods. Int. J. Numer. Method Eng. 37(2), 229–256 (1994) 2. Tian, Y., Cassidy, M.J., Randolph, M.F., Wang, D., Gaudin, C.: A simple implementation of RITSS and its application in large deformation analysis. Comput. Geotech. 56(1), 160–167 (2014) 3. O’Sullivan, C.: Particulate Discrete Element Modelling: A Geomechanics Perspective. CRC Press, London (2011) 4. Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, Singapore (2003) 5. Sulsky, D., Chen, Z., Schreyer, H.L.: A particle method for history-dependent materials. Comput. Methods Appl. Mech. Eng. 118(1–2), 179–196 (1994) 6. Sulsky, D., Zhou, S.J., Schreyer, H.L.: Application of a particle-in-cell method to solid mechanics. Comput. Phys. Commun. 87(1–2), 236–252 (1995) 7. Huang, P., Zhang, X., Ma, S., et al.: Contact algorithms for the material point method in impact and penetration simulation. Int. J. Numer. Meth. Eng. 85(4), 498–517 (2001) 8. Ma, Z., Zhang, X., Huang, P.: An object-oriented MPM framework for simulation of large deformation and contact of numerous grains. Comput. Model. Eng. Sci. (CMES) 55(1), 61–87 (2010) 9. Chen, Z., Hu, W., Shen, L., et al.: An evaluation of the MPM for simulating dynamic failure with damage diffusion. Eng. Fract. Mech. 69(17), 1873–1890 (2002) 10. Chen, Z., Feng, R., Xin, X., et al.: A computational model for impact failure with shear-induced dilatancy. Int. J. Numer. Meth. Eng. 56(14), 1979–1997 (2003) 11. Chen, Z., Gan, Y., Chen, J.: A coupled thermo-mechanical model for simulating the material failure evolution due to localized heating. Comput. Model. Eng. Sci. 26(2), 123–137 (2008) 12. Johnson, G.R., Holmquist, T.J.: Evaluation of cylinder-impact test data for constitutive model constants. J. Appl. Phys. 64(8), 3901–3910 (1988)

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13. Williams, Q., Jeanloz, R., Bass, J., et al.: The melting curve of iron to 250 gigapascals: a constraint on the temperature at Earth’s center. Science 236, 181–183 (1987) 14. Brown, J.M., McQueen, R.G.: Phase transitions, Grüneisen parameter, and elasticity for shocked iron between 77 GPa and 400 GPa. J. Geophys. Res.: Solid Earth 91(B7), 7485–7494 (1986) 15. Rice, M., McQueen, R.G., Walsh, J.: Compression of solids by strong shock waves. Solid State Phys. 6, 1–63 (1958) 16. McQueen, R.G., Marsh, S.P.: The equation of state of solids from shock wave studies. In: High Velocity Impact Phenomena, pp. 293–417 (1970) 17. Lyzenga, G., Ahrens, T.J.: Multiwavelength optical pyrometer for shock compression experiments. Rev. Sci. Instrum. 50(11), 1421–1424 (1979) 18. Miller, G.H., Ahrens, T.J., Stolper, E.M.: The equation of state of molybdenum at 1400 °C. J. Appl. Phys. 63(9), 4469–4475 (1988) 19. Tang, W., Zhang, R., Hu, J., Jing, F.: Approximation calculation methods of shock temperature. Adv. Mech. 28(4), 479–487 (1998)

Study on Dali-Baoshan Section of Anning-Baoshan Oil Product Pipeline Wang Li1(B) , Liqiao Huang2 , Wenhua Ma3 , and Zhijian Zhang1 1 PipeChina Southwest Pipeline Company, Chengdu 610041, China

[email protected] 2 China University of Petroleum, Beijing 102249, China 3 PetroChina Pipeline Company, Langfang 065000, China

Abstract. With the injection of drag reducer produced by Baker Hughes to DaliBaoshan section of Anning-Baoshan Oil Pipeline, the flow rate can be increased from the designed 95 m3 /h to 115 m3 /h. For each monitoring point along the pipeline, obvious pressure drop can be observed, thus the purpose of increasing the throughput has been achieved effectively. Since the increase of throughput, Anning-Baoshan Oil Product Pipeline can increase earnings of pipe transmission by about 6.5 million yuan per year. In this paper, relative experimental researches on the increase of the Dali-Baoshan section of the Anning-Baoshan Pipeline Product Oil have been carried out. Keyword: Anning-Baoshan oil product pipeline · Increase pipe throughput · Drag reducer

1 Review of Anning-Baoshan Oil Product Pipeline Anning-Baoshan Oil Product Pipeline, located in Yunnan Province, owns a trunk line of 385.3 km. The first station of the pipeline is Anning Initial Station where the pipe starts. Then the pipeline passes through Chuxiong Pump Station and Dali Delivery Station with pump along the way, and is transported to Baoshan Terminal Station. Parameters of each section are as follow: Anning-Chuxiong section is 132.8 km long, with pipe diameter of 406.4 mm and transmission capacity of 173 × 104 t/a; Chuxiong-Dali section is 91.2 km long, with pipe diameter of 323.9 mm and pipeline transmission capacity of 173 × 104 t/a; Baoshan-Dali section is 161.3 km long, with pipe diameter of 219.1 mm and transmission capacity of 57 × 104 t/a. There are 4 stations and 18 valve rooms in total, including 7 monitoring valve rooms. Elevation along the pipeline is shown in Fig. 1 as well as the settings of each station and valve room (Table 1).

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 84–94, 2021. https://doi.org/10.1007/978-3-030-64690-5_9

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85

Fig. 1. Elevation diagram of Anning-Baoshan Oil Product Pipeline

Table 1. Overall arrangements of stations in Anning-Baoshan Oil Product Pipeline Station

Type of valve chamber

Length (km)

Station distance (km)

Elevation (m)

Anning Station

Origin station

0

/

1938.8

Chuxiong Station

Pump station

132.8

21.52

1894.6

Dali Station

lateral pump station

224

22.56

2016.2

Baoshan Station

Terminal station 385.3

7.66

1691

2 Parameters of Relevant Equipment in Dali Station There are 4 pumps in Dali Delivery Station with pump whose parameters are shown in Table 2 and motor power shown in Table 3. The performance curves of the two types of pumps are shown in Fig. 2 and Fig. 3. Table 2. Parameters of pumps in Dali Station Designations of pumps P0401 P0402 P0403 P0404 Rated head (m)

150

300

300

300

Rated flow (m3 /h)

100

100

100

100

86

W. Li et al. Table 3. Parameters of motors in Dali Station Designations of motors

P0401 P0402 P0403 P0404

Voltage (V)

380

380

380

380

Frequency (Hz)

50

50

50

50

Power (kw)

75

132

132

132

Revolving speed (r/min) 2975

2980

2980

2980

Rated current (A)

135

237

237

237

Efficiency (%)

0.89

0.89

0.89

0.89

Duty

S1

S1

S1

S1

Fig. 2. Performance curve of pump P0401

3 Analysis of the Demand to Increase the Transmission and Related Content Mains power supply of Dali Delivery Station with pump adopts single-bus connection with voltage of 10 kV, rated current of 630 A, transformer rated capacity of 630 kVA and voltage of 400 V after transformation. Power supply of main pump motor in Dali Delivery Station with pump is 380 V, and rated current of motor P0401 is 135 A, rated current of P0402, P0403 and P0404 motor are 237 A.

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87

Fig. 3. Performance curve of pump P0402

According to market forecasting by downstream sales company in Yunnan province, to ensure the oil supply of Baoshan Oil Depot, the transportation volume of Dali-Baoshan section should reach 120 m3 /h. Calibration of relevant parameters and hydraulic analysis are carried out in detail in the rest of this paper. Table 4. Results of pumps in Dali Delivery Station with pump calculated at the flow rate of 100 m3 /h Test order

Pump number

Flow (m3 /h)

Corresponding head (m)

Corresponding efficiency (%)

Shaft power (Kw)

Real current (A)

Rated current (A)

1

P0401

100

155

74.1

45.5

101

135

2

P0402

100

300

75.5

86.5

196

237

3

P0403

100

300

75.5

86.5

196

237

4

P0404

100

300

75.5

86.5

196

237

It can be observed from Table 4 and Table 5 that under current pump and motor condition in Dali station, the flow rate of Dali-Baoshan section should be able to reach 120 m3 /h. (1) Maximum throughput that can be achieved without adding drag reducer (Fig. 4) (Table 6)

88

W. Li et al.

Table 5. Results of pumps in Dali Delivery Station with pump calculated at the flow rate of 120 m3 /h Test order

Pump number

Flow (m3 /h)

Corresponding head (m)

Corresponding efficiency (%)

Shaft power (Kw)

Real current (A)

Rated current (A)

1

P0401

120

150

72.2

54.3

/

135

2

P0402

120

276.8

74.2

97.4

190

237

3

P0403

120

276.8

74.2

97.4

191

237

4

P0404

120

276.8

74.2

97.4

191

237

Fig. 4. Hydraulic gradient diagram of Dali-Baoshan section at the flow of 104 m3 /h (diesel)

By reducing the distribution capacity of Dali Delivery Station with pump, the maximum transmission capacity of Dali-Baoshan section is 104 m3 /h based on the selection of fuel delivery pump in the existing Dali Delivery Station with pump. (2) Maximum diesel transportation in Dali-Baoshan section (added drag reducer) (Fig. 5) (Table 7)

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89

Table 6. Maximal diesel throughput of Dali-Baoshan section (no agent added) Designations of stations Anning Initial Station

Length

Elevation

Distance

Inlet pressure

Outlet pressure

Flow

km

m

km

MPa

MPa

m3/h

0.6

5.2

274

3.6

8.9

0.0

1887 —

Chuxiong Delivery Station with pump

138.0

Dali Delivery Station with pump

229.1

Baoshan Terminal Station

395.5

1899

43.0

274 2012

91.1

5.1

11.0 104

1706

166.4

7.0 —

Fig. 5. Hydraulic gradient diagram of Dali-Baoshan section at the flow of 125 m3 /h (diesel with drag reducer)

Based on the existing selection of pump type in Dali Delivery Station with pump, the maximum transmission capacity of Dali-Baoshan section is 125 m3 /h by setting up skid-mounted drag reducer on the outbound pipeline of Dali Delivery Station with pump, the increase rate of which is 20.2%.

90

W. Li et al.

Table 7. Maximal diesel throughput of Dali-Baoshan section (drag reducer added, spare pump turned on) Designations of stations

Length

Elevation

Distance

Inlet pressure

Outlet pressure

Flow

km

M

km

MPa

MPa

m3/h

Anning Initial Station

0.0

1887

0.6

5.3

245

Chuxiong Delivery Station with pump

138.0

4.0

9.6

Dali Delivery Station with pump

229.1

Baoshan Terminal Station

395.5

— 1899

43.0

245 2012

91.1

6.3

10.7 125

1706

166.4

7.0 —

(3) Maximum gasoline throughput in Dali-Baoshan section (no drag reducer) (Fig. 6) (Table 8)

Fig. 6. Hydraulic gradient diagram of Dali-Baoshan section at the flow of 134 m3 /h (gasoline with no agent added)

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91

Table 8. Maximal gasoline throughput of Dali-Baoshan section (no agent added, spare pump turned on) Designations of stations

Length

Elevation

Distance

Inlet pressure

Outlet pressure

Flow

km

M

km

MPa

MPa

m3 /h

Anning Initial Station

0.0

1887

0.6

4.6

254

Chuxiong Delivery Station with pump

138.0

3.8

8.5

Dali Delivery Station with pump

229.1

Baoshan Terminal Station

395.5

— 1899

43.0

254 2012

91.1

6.1

10.4 134

1706

166.4

6.1 —

Based on the existing selection of the oil pump in Dali Delivery Station with pump, maximum gasoline throughput in Dali-Baoshan section is 134 m3 /h, which is equivalent to the maximum diesel transmission with drag reducer added. Therefore, it is not necessary to consider utilizing drag reducer and increasing gasoline throughput. It can be seen from the above analysis that the flow between Dali Station and Baoshan Station can be increased to 125 m3 /h with the injection of drag reducer.

4 Field Test Drag reducer produced by Baker Hughes has been applied to conduct the drag reducing test during the transportation of diesel in Dali-Baoshan Section. The dosing rate applied in the test is 5 ppm. The hydraulic gradient diagram is shown in the figure below. It can be seen from Fig. 7 that after adding drag reducer at the concentration of 5 ppm, the flow rate in Dali-Baoshan section can be increased to 115 m3 /h, and there is still a large amount of pressure in the equipment and pipeline of Dali Station.

5 Economic Analysis Table 9 shows the comparison of economy before and after increasing throughput in Dali-Baoshan section. (1) Through inquiring about the price from manufacturers, a set of skid-mounted drag reducer about 500,000 yuan. (2) Through inquiring about the price from manufacturers, the price of drag reducer is 113,160 yuan per barrel (the volume of which is 984 L). Drag reducer adopted is from the same manufacturer as Lanzhou-Chengdu-Chongqing Oil Products Pipeline and bulk purchase is available.

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Fig. 7. Hydraulic gradient diagram of Dali-Baoshan section (diesel)

By the date of June 30, 2019, Baoshan Oil Depot had received 159,800 m3 of diesel in the first half of 2019 which is about 133,400 tons. Tsinghua Curve Oil Depot in Dali received 256,600 m3 of diesel which is about 214,200 tons. According to the requirements of Yunnan Sales Company, the output of Tsinghua Curve Oil Depot will decrease appropriately since the increase of throughput in the Dali-Baoshan section while the overall output of Tsinghua Curve Oil Depot and Baoshan Oil Depot will increase by 112,200 m3 which is about 93,600 tons per year. Therefore, it is estimated that in the second half of 2019, Baoshan Oil Depot will receive 235,500 m3 of il which is about 192,300 tons. Tsinghua Curve Oil Depot in Dali will receive 242,000 m3 oil, about 201,800 tons. It is estimated that Dali Station needs 1.15 m3 of drag reducer (5 ppm injection), about 132,250 yuan. (3) When Anning-Dali throughput increase 46500 tons/half a year (increase of throughput accounted for about 7%), electricity costs of Anning station to Anbao direction and Chuxiong Station will increase 6.2% (monthly electricity costs of Anning Initial Station to Anbao direction is about 150000 yuan, and monthly electricity costs of Chuxiong Station is about $250000), which increases 148800 yuan altogether. The total operating power of pumps in Dali Station will increase from 108.2 kW to 143 kW, and the electricity consumption in half a year will increase (1664 h) by 412 million yuan. According to the Dali electricity price at 0.532 yuan/(kW h), the electricity cost of Dali Station will increase by 22,100 yuan. (4) It has been estimated that in the second half of 2019, throughput in Anning-Dali section will increase additional 46,500 tons and throughput in Dali-Baoshan section will increase 58,900 tons. Pipe transportation revenue will increase 3,641,500 yuan according to Yunnan refined oil pipeline transportation price at 0.183 yuan/(ton km).

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Table 9. Economy comparison before and after throughput increase (10,000 yuan) Order

Item

Cost before increase

Cost before increase

D-value

1

Skid-mounted drag reducer

0.00

50.00

−50.00

2

Drag reducer

0.00

13.225 (half a year)

−13.225

3

Transformation of automatic system

0.00

10.00

−10.00

3

Electricity cost

0.00

17.09

−17.09

4

Pipe transportation earnings

0.00

364.15 (half a year)

364.15

5

Sum

/

/

273.835

From the above analysis and Table 9, it can be concluded that after adding drag reducer in Dali-Baoshan section, the pipeline transport income can be increased by about 2.74 million yuan in half a year regardless of the initial investment. For each year following, the annual revenue of pipeline transportation will increase by about 6.68 million yuan.

6 Conclusion In this study, hydraulic characteristics of oil product pipeline in Dali-Baoshan section are analyzed, and parameters of equipment in Dali Station were calibrated. Dali-Baoshan section is found to be qualified to the requirements of adding drag reducer to enhance throughput. Then through field tests, it has been proved that the throughput of DaliBaoshan section can be increased to 115 m3 /h, and there is still surplus ability for pressure-bearing of equipment and pipeline in Dali Station. Afterwards, by means of evaluating economic benefits of increasing throughput, we can find that pipeline income can be increased of about 6.68 million yuan each year with drag reducer added.

References 1. Jia-rong, A.N., Lin, J.I.A.: Studies of increasing the throughput technology of oil products pipeline. Pipeline Tech. Equip 2, 6–8 (2012) 2. Dai, X., Guo, X., Li, G., et al.: Preliminary preparation and performance testing of composite oil product DRA. Oil Gas Storage Transp. 35(10), 1078–1082 (2016) 3. Zhu, L.: Study on the Mechanism of Oil Mixing in Large Drop Sequence of Finished Oil. Southwest Petroleum University (2017) 4. Ren, Y.: Study and Application on Drag-Reduction Characteristic of Internal Coatings on Product Pipeline. East China University of Science and Technology (2010) 5. Liang, X.: Pipeline operation and management of refined oil products. Petroleum Industry Press (2011) 6. Dai, X., Wang, Y., Li, J., et al.: The comparison of operation technology for oil product pipeline between China and Russia. Nat. Gas Oil 36(02), 7–12 (2018)

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7. He, B., Shan, W., Yu, P.: Effect and economic evaluation of drag reducing agent in oil pipeline. China Sci. Technol. Inf. 15, 210–211 (2011) 8. Xia, Y.: Oil pipeline operation and technical management. China Science and Technology Press (2010)

A New Locking-Free Thick/Thin Shell Element with Incompatible Approximation in a General Orthogonal Curvilinear Coordinate System Jingxu Chen(B)

, Yongchang Cai, and Pengfei Yan

State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, People’s Republic of China [email protected]

Abstract. A new locking-free thick/thin shell element with incompatible approximation (SEIA) in a general orthogonal curvilinear coordinate system is proposed for the analysis of the thick/thin shell. The key points for the development of the present element include the definition of the incompatible polynomial displacement approximation in each independent element and the utilization of the fictitious thin layers to ensure the displacement conformity between adjacent elements. Superior to most available shell elements, the SEIA avoids the shear and membrane locking naturally without the adoption of numerical expediencies, has concise theoretical derivation and easy numerical implementation, is insensitive to element distortions and thus provides reliable solutions for the thick/thin shell. The present work also initiates a methodology to develop locking-free thick/thin shell elements. Numerical investigations and comparisons demonstrate the convergence and robustness of the present element. Keywords: Thick/thin shell · Locking-free · Incompatible approximation · Curvilinear coordinate

1 Introduction Given its high load bearing capacity compared with the plate and small volume compared with the solid, the curved thin-walled shell structure is widely used in the automotive, mechanical, aerospace, biomedical and civil engineering industries [1–4]. The middle surface of the shell is a curved surface where the in-plane displacement and the transverse displacement usually occur simultaneously [5]. Due to the membrane-bending coupling in the shell, the mechanical analysis of the shell is much more complicated than the analysis of the plate and thus has received widespread attention recently [6]. At present, the commonly used shell elements include the thin shell element based on the Kirchhoff/Love assumption and the thick/thin shell element based on the Reissner/Mindlin assumption [7]. The Kirchhoff/Love assumption neglects the shear effect and has the C1 continuity requirement [8]. In the finite element method, the satisfaction of C1 continuity is quite difficult, and special skills are needed to construct the thin shell element [9]. Therefore, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 95–116, 2021. https://doi.org/10.1007/978-3-030-64690-5_10

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the available thin shell element is either a nonconforming element or a conforming element with complicated theoretical derivation and difficult numerical implementation [10]. Based on the Reissner/Mindlin assumption, the construction of the thick/thin shell element considering the shear effect is relatively easy because only C0 continuity is required [11]. However, the thick/thin shell element often encounters the shear and membrane locking when applied to thin shells, for example, the three-node triangular flat shell element by Zhang et al. [12], the four-node quadrilateral element by Wang et al. [13], the EXG element by Kulikov et al. [14], the DKMQ24 element by Katili et al. [15], the three-dimensional superparameter shell element by Hahn et al. [16], and the three-dimensional relative DOFs shell element by Li et al. [17]. Numerical expediencies, such as the reduced/selected integration, the assumed shear strain/stress approach, the hybrid/mixed formulation and the refined nonconforming element method, have to be employed to eliminate the shear and membrane locking. The employment of these numerical expediencies will lead to new problems, such as spurious zero energy modes, complicated theoretical derivation, cumbersome numerical implementation and the numerical oscillation of the calculation results [18]. Great effort has been put into the research of thick/thin shell elements using isogeometric analysis for the past few years [19–22]. Within the theoretical framework of isogeometric analysis, the error introduced by the geometric approximation is eliminated at the source, and the accuracy of the structural response analysis is improved [23–25]. The isogeometric shell element can also avoid the shear and membrane locking by simply increasing the order of the displacement function with no need for numerical expediencies [26]. Although it has the above-mentioned advantages, the geometric modeling system of isogeometric analysis is mainly based on the nonuniform rational B-spline, and the complexity for simulating the discontinuities or multi-patches in shell structures hinders its application by researchers to a certain extent [27]. In summary, given the complexity of the mechanical property and the difficulty in the mathematical processing, the construction of a simple, efficient, robust and locking-free thick/thin shell element remains one of the hottest and most challenging research topics in the field of mechanical analysis and engineering computation [28]. Based on the Reissner/Mindlin theory, a new locking-free thick/thin shell element, the SEIA, is proposed in this paper. The third order polynomial is employed to define an incompatible displacement approximation in each independent element and fictitious thin layers are utilized to ensure the displacement conformity between adjacent elements, which makes the SEIA avoids the shear and membrane locking and maintain the displacement conformity, simple formulation and easy numerical implementation. is insensitive to element distortion, has a good convergence rate and high accuracy and provides reliable solutions for thick/thin shells. The paper is organized as follows. The geometric description of the shell in a general orthogonal curvilinear coordinate system is briefly introduced in Sect. 2. The theoretical formulation of the SEIA is deduced in detail in Sect. 3. Section 4 demonstrates the high performance of the present element with six typical numerical examples. Finally, in Sect. 5, the work in this paper is concluded, and the future steps are proposed.

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2 Curvilinear Coordinate System of the Shell As depicted in Fig. 1, a generic shell element is a three-dimensional body bounded by two close surfaces. The middle surface of the shell is equidistant from these two surfaces and can be taken as the reference surface for the governing equations [5, 6]. The position vector R(α1 , α2 , α3 ) of an arbitrary point P in the three-dimensional shell is defined as

Fig. 1. Description of the position of an arbitrary point

R(α1 , α2 , α3 ) = r(α1 , α2 ) + α3 n(α1 , α2 )

(1)

where r(α1 , α2 ) is the position vector describing the projective point P 0 on the middle surface; α1 and α2 are the principal curvature line directions of the middle surface; α3 is the normal direction specified by the following unit normal vector:     (2) n(α1 , α2 ) = r,1 × r,2 /r,1 × r,2 , where r,i = ∂r/∂αi for i = 1, 2 and the symbol × represents the vector product. By means of differential geometry (α1 , α2 ), the degenerate, single curved, double curved and other types of shells can be defined and studied in a unified manner. Differential geometry also provides the definition of the well-known Lame coefficients h1 , h2 and h3 = 1 as well as the main curvature radii of the reference surface r1 and r2 along axes α1 and α2 [5]. For instance, for the spherical coordinate system in Fig. 2 α1 = θ, α2 = ϕ, α3 = 0,

(3)

r1 = r, r2 = r,

(4)

h1 = r, h2 = r sin θ,

(5)

∂h1 /∂α2 = 0, ∂h2 /∂α1 = r cos θ.

(6)

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Fig. 2. Coordinate system and parameters of a point on the middle surface

Fig. 3. Coordinate system and parameters of an arbitrary point

Supposing that h1 , h2 , r1 and r2 are the curvilinear parameters of the middle surface of the shell, the curvilinear parameters at location α3 on the normal of the shell in Fig. 3 can be written as follows: hα1 3 = h1 (1 + α3 /r1 ), hα2 3 = h2 (1 + α3 /r2 ),

(7)

r1α3 = r1 (1 + α3 /r1 ), r2α3 = r2 (1 + α3 /r2 ).

(8)

3 Formulation of the SEIA 3.1 Incompatible Approximation in Each Element Consider a linear elastic shell undergoing infinitesimal deformation. Figure 4 shows a general orthogonal curvilinear coordinate system α1 α2 α3 for the middle surface of a shell, where α1 and α2 are the principal curvature line directions of the points on the middle surface. The middle surface of the shell is discretized into arbitrary polygonal elements in the curvilinear coordinate system α1 α2 α3 , as shown in Fig. 4. According to the well-known

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α2

α1

Fig. 4. Discretization with polygonal elements

Reissner/Mindlin theory, the displacement function for an arbitrary element ei can be defined as follows: ⎧ ⎨ u1 (α1 , α2 , α3 ) = u10 (α1 , α2 ) − α3 θ1 (9) u (α , α , α ) = u20 (α1 , α2 ) − α3 θ2 , ⎩ 2 1 2 3 u3 (α1 , α2 , α3 ) = u30 (α1 , α2 ) where u10 , u20 and u30 are the in-plane and transverse displacements at the middle  T surface; u = u1 u2 u3 is the displacement vector of an arbitrary point P(α1 , α2 , α3 ) in the shell; θ1 and θ2 are the rotations of the normal to the cross section; α3 is the coordinate in the transverse direction. We assume that ⎧ ⎪ u10 = Pau10 ⎪ ⎪ ⎪ ⎪ ⎨ u20 = Pau20 (10) θ1 = Paθ1 , ⎪ ⎪ θ2 ⎪ θ2 = Pa ⎪ ⎪ ⎩ u = Pau30 30 where au10 , au20 , aθ1 , aθ2 and au30 are the vector of generalized approximation DOFs of element ei ; P(α1 , α2 ) is the third order simple polynomial basis function. Substituting Eq. (10) into Eq. (9), the displacement approximation in element ei can be further expressed as u = Ne a e ,

(11)

T  where u = u1 u2 u3 is the displacement approach of element ei along axes α1 , α2 and α3 ; ae is the element DOFs where T  (12) ae = a1 a2 · · · a50 ;

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Ne is the shape function of element ei where ⎡

⎤ P 0 −α3 P 0 0 Ne = ⎣ 0 P 0 −α3 P 0 ⎦. 0 0 0 0 P

(13)

In this work, P is taken as  2 α α α2 α3 α2 α α α2 α3 , P(α1 , α2 ) = 1 α10 α20 α10 10 20 20 10 10 20 10 20 20

(14)

where α10 = α1 − α1i ; α20 = α2 − α2i ; (α1i , α2i ) is the curvilinear coordinate of the central point of element ei . As seen, the third order displacement approximation can be constructed without difficulty in the SEIA, which is more convenient than that in the finite element method, because a third-order finite shell element is usually constructed by including the highorder derivatives of displacement in the nodal DOFs, which often leads to the daunting complexity in the formulation and numerical implementation. Theoretically speaking, an element of arbitrary shape can be employed in the present work. However, taking into account the good adaptability of triangular element to the complex geometrical boundaries of the shell, only triangular elements, as shown in Fig. 5, have been used and investigated in the following derivation and numerical examples. α2

e

α1

Fig. 5. Discretization with triangular elements

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The strain-displacement relation of the linear elastic problem in the curvilinear coordinate system is expressed as ⎧ ⎪ ε11 = ∂u1 /(h1 ∂α1 ) + u2 ∂h1 /(h1 h2 ∂α2 ) + u3 ∂h1 /(h1 ∂α3 ) ⎪ ⎪ ⎪ ⎪ ε22 = u1 ∂h2 /(h1 h2 ∂α1 ) + ∂u2 /(h2 ∂α2 ) + u3 ∂h2 /(h2 ∂α3 ) ⎪ ⎪ ⎨ ε33 ≈ 0 , ⎪ γ12 = ∂u1 /(h2 ∂α2 ) − u1 ∂h1 /(h1 h2 ∂α2 ) + ∂u2 /(h1 ∂α1 ) − u2 ∂h2 /(h1 h2 ∂α1 ) ⎪ ⎪ ⎪ ⎪ γ23 = ∂u2 /∂α3 − ∂u2 h2 /(h2 ∂α3 ) + ∂u3 /(h2 ∂α2 ) ⎪ ⎪ ⎩ γ31 = ∂u1 /∂α3 − u1 ∂h1 /(h1 ∂α3 ) + ∂u3 /(h1 ∂α2 ) (15) where h1 , h2 and h3 = 1 are the Lame coefficients along axes α1 , α2 and α3 , respectively. The substitution of Eq. (11) into Eq. (15) results in ε = Bae ,

(16)

 T where ε = ε11 ε22 γ12 γ23 γ31 is the strain vector and B is the strain matrix. For an isotropic linear elastic material, the stress-strain relation in element ei is expressed as σ = DBae , where the elasticity matrix ⎡ ⎤ 1ν 0 0 0 ⎢ν 1 ⎥ 0 0 0 ⎢ ⎥ ⎢ ⎥ D = D0 ⎢ 0 0 (1 − ν)/2 0 0 ⎥, ⎢ ⎥ ⎣0 0 ⎦ 0 0 (1 − ν)/(2k) 00 0 0 (1 − ν)/(2k)

(17)

(18)

  where D0 = E/ 1 − ν 2 ; E is the elastic modulus; ν is the Poisson ratio. Because σ33 300, the CIFSA algorithm’s tag loss ratio curve increases sharply compared with CIRC-FSA, and when the number of tags N > 450, the TLR curve of the CIRC-FSA algorithm shows an upward trend. This is because the CIRC-FSA algorithm completely removes idle and collision slots, which remarkably improves the system’s recognition performance and significantly reduces the tag loss ratio. (4) When the number of tags or tag density in the signal area is very large, the increase in the TLR of all the algorithms is evident.

6 Conclusion In this paper, we proposed an ALOHA anti-collision algorithm for frame idle slot removal and collision reduction to address the collision problems of tags. In the proposed algorithm, the number of tags is initially grouped and the number of tags X in a group is determined. The frame length L is set to be much larger than the number of grouped tags X (L >> X), then a combined chaotic mapping pseudo-random generator is used to make the tag select more uniform time slots, remarkably reducing or avoiding the collision of the tags. Finally, according to the modified protocol of GAAS, the collision tags are concentrated toward the end of the last successful time slot and combined with the reservation model to remove idle and collision slots and achieve fast identification of tags. Simulation experiments demonstrated that, compared to conventional algorithms, the throughput of CIRC-FSA increases much more rapidly with the number of tags, especially when the number is more than 1000, facilitating a high throughput of ~1.00. Compared with the free slot algorithm based on the reservation model, the throughput rate of the algorithm is significantly improved. The total number of time slots required

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for the entire identification process increases linearly, which effectively improves the efficiency of the RFID system, increases the stability of the system throughput rate, and reduces the cost of the tags. For the identification of a large number of tags, the CIRCFSA algorithm exhibits immense potential for applications requiring fast and rapid tag identification. Acknowledgments. This research was supported by the Scientific Research Project of the Hunan Provincial Department of Education (18A332), the Science and Technology Plan Project of Hunan Province (2016TP1020), and the Application-Oriented Special Disciplines, Double First-Class University Project of Hunan Province (Xiangjiaotong [2018] 469).

References 1. Li, X.-W.: Research on tag identification technology of mobile RFID system. Dissertation, Southwest Jiaotong University, Chengdu (2014) 2. Zhang, X., Hu, Y.: Research on RFID anti-collision algorithm for adaptively assigning time slots in packets. Chin. J. Electron. 44(6), 1328–1335 (2016) 3. Hou, P., Wang, Z., Yan, C.: Improvement of the anti-collision algorithm based on RFID tag. Comput. Sci. 46(11A), 359–362 (2019) 4. Yang, L.: Research on anti-collision of mobile tag in dynamic RFID system. Dissertation, Southwest Petroleum University (2016) 5. Su, J., Xie, L., Yang, Y., Wen, G., Meng, Q.: UHF RFID anti-collision algorithm based on idle slot elimination. Chin. J. Electron. 45(2), 307–314 (2017) 6. Li, X.-W., Feng, Q.-Y., Chen, Y.-H.: System performance evaluation method of anti-collision protocol in mobile RFID system. J. China Railw. Soc. 36(4), 42–47 (2014) 7. Dong, H., Sheng, K., Ma, J., Yao, H.: Research on adaptive frame slot Aloha anti-collision algorithm based on first come first served based on tag grouping. J. Guangxi Univ. Sci. Technol. 29(1), 61–68 (2018) 8. Xiong, T.W., Tan, X., Yan, N., et al.: Modeling and simulation of RTLS based on UHF RFID. J. Syst. Simul. 23(1), 212–216 (2011) 9. Fu, Y., Qian, Z., Meng, J., Wang, X.: Aloha anti-collision algorithm for frame slot based on continuous slot prediction. Chin. J. Electron. 44(9), 2081–2086 (2016) 10. Yuan, L., Du, Y., He, Y., Lü, M., Cheng, Z.: Anti-collision algorithm of ALOHA tag with dynamic recognition of packet dynamic frame slots in parallel. J. Electron. Inf. Technol. 40(4), 944–950 (2018) 11. Chen, R.: Improved ALOHA anti-collision algorithm based on dynamic frame time slot. J. Qiqihar Univ. (Nat. Sci. Ed.) 32(1), 21–25 (2016) 12. Wang, D., Li, X.-W.: A dynamic frame slot ALOHA algorithm for accurate tag estimation in dynamic RFID systems. J. China Railw. Soc. 40(7), 88–92 (2018) 13. Li, L., Cui, X., Li, M.: Research on anti-collision algorithms in tag moving scenes. Res. Comput. Appl. https://doi.org/10.19734/j.issn.1001-3695.2018.12.0884 14. Yan, Y., Hao, R., Zhang, C., Wang, H.: Generation and analysis of pseudo chaotic sequences of tent maps. J. Taiyuan Univ. Technol. 39(5), 66–69 (2008) 15. Katz, O., Ramon, D.A., Wagner, I.A.: A robust random number generator based on a differential current-mode chaos. Masters Thesis, IEEE Educational Activities Department (2008) 16. Lei, X., Sanglu, L.: Radio Frequency Identification Technology—Principle, Protocol and System Design, 2nd edn., p. 303. Science Press, Beijing (2016)

Experimental Investigation of the Evolution of Permeability and Porosity of Fushun Oil Shale After High Temperature Mengtao Cao1,2 , Yide Geng1,2(B) , and Pengfei Wu1,2 1 College of Mining Engineering, Taiyuan University of Technology, No. 18 Xin Kuang-yuan

Road, Yingze West Street, Taiyuan 030024, People’s Republic of China [email protected] 2 Key Laboratory of In-Situ Modified Mining of Ministry of Education, Taiyuan University of Technology, No. 18 Xin Kuang-yuan Road, Yingze West Street, Taiyuan 030024, People’s Republic of China

Abstract. It is a key issue of how to improve the efficiency and security in the development of oil shale, which is associated with the evolutions of permeability, pore and fracture structures of oil shale under the condition of high temperature. To investigate the influences of temperature and tri-axial stresses on the permeability of oil shale, the WYF-1 high-temperature and high-pressure pyrolysis reaction device and Smart perm III impulse-type gas permeability measuring apparatus were used to test the oil shale samples after a temperature ranging from 20 °C to 600 °C. Moreover, the mercury intrusion porosimetry was also used to analyze the evolution of pore and fracture structure inside the specimen. The results show that the temperature has a significant effect on the permeability of oil shale that can be divided into three stages: low growth stage, rapid growth stage, and steady stage. At the low growth stage that the temperature is from 20 °C to 300 °C, the weight loss rate and porosity change of oil shale are rare and the permeability of oil shale gradually increases with raising the temperature, and the volumetric stress (13 MPa, 26 MPa, 39 MPa) has little effect on the permeability; However, for the rapid growth stage with the temperature from 300 to 400 °C, its weight loss and porosity increased rapidly, and the permeability increased sharply by 24.3 to 92.4 times of that at the temperature of 300 °C, the volume stress showed an obvious effect on the permeability; Lastly, for the temperature from 400 to 600 °C, the weight loss rate and porosity further increased but the growth rate slowed down, resulting in that the permeability nearly kept constant with temperature, and the volumetric stress has a larger influence on the permeability. Besides, the mercury intrusion porosimetry was used to investigate the distribution law and connectivity characteristics of pore and fractures. The porosity sharply increased with the temperature reaching 400 °C and further increased with the temperature until 600 °C, which corresponds to the evolution of permeability of oil shale. This research can provide some guidance for the selection of a reasonable pyrolysis temperature in the process of in situ pyrolysis of oil shale. Keywords: Oil shale · High temperature · Permeability

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 171–181, 2021. https://doi.org/10.1007/978-3-030-64690-5_16

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1 Introduction Oil shale, also known as kerogen shale, is mainly composed of a large number of inorganic minerals and solid organic kerogen contained in its skeleton, and kerogen is pyrolyzed at a certain temperature and converted into shale oil and gas products. Consequently, to some extent, oil shale can be regarded as alternative energy for petroleum [1–3]. It has been reported that there are almost 4.8 trillion barrels of oil shale reserves in the world, and the reserves in China (around 354 billion barrels) are occupying 7% of the world’s reserves [4]. As an unconventional energy source, oil shale has a broad development prospect. Generally, oil shale can be exploited by conventional ex-situ exploitation and in-situ exploitation. In terms of the conventional ex-situ exploitation, oil shale is extracted to the surface by the methods of opencast or underground, and then shale oil and hydrocarbon gas can be obtained by distillation method at low temperature. However, for in-situ exploitation, shale oil and gas products can be obtained through heating an oil shale formation with different heating methods [5–7]. Up to now, although in-situ underground exploitation technology is still in the research and development stage, it has a bright application prospect and value with the merit of no large-scale mining, less occupation of land, and high exploitation rate. In high-temperature conditions, the kerogen in the oil shale is converted into shale oil and gas after pyrolysis, resulting in a large number of pores and cracks and providing more penetration channels. Many researchers [7–12] have studied the pore and fracture structures of oil shale before and after using the method of MIP or micro-CT et al. The results demonstrated that the pyrolysis dramatically affected the pore structure, and a larger number of fractures emerged when the temperature was higher than 350 °C. Tiwari et al. [10] found that the distribution of kerogen was related to the value of porosity and the pyrolysis led the generation of a larger fracture channel; Using the µCT scan technology, Saif et al. [11] dynamically monitored the pyrolytic process of the oil shale and observed that the number of interconnected pores and porosity significantly increased. The permeability is a key physical parameter to recover shale oil and gas products from the oil shale seam. For a given rock, its permeability can be influenced by many factors, including pore pressure, volumetric stress, and temperature. For example, the permeability of natural rock decreases as the volumetric rises at room temperature, but it may be enhanced by heating the rock to a high temperature. So, it is significant to clearly understand the permeability sensitivity to temperature variation of the oil shale formation. Kang et al. [13] investigated the permeability of the cylindrical oil shale sample with the axial direction almost parallel to the original bedding at temperatures up to 500 °C and found that the permeability dramatically grew at around 350 °C. Yang et al. [14] reported that the oil shale permeability at 600 °C was 3.0 × 10−8 m2 , which is almost 600 times that at room temperature. Dong et al. [15] investigated the permeability evolution of oil shale under in-situ conditions and stated that the permeability of oil shale dramatically increased for the temperature larger than the initial threshold, and threshold temperature is related to the tri-axial stress state.

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The permeability test methods described by the scholars before are nearly all traditional steady-state methods, and the permeability of the tested oil shale specimens is all parallel to the bedding orientation. The results of the previous studies show that the temperature has a great influence on the permeability of the oil shale. But, this method is time-consuming and inaccurate because the internal structure of oil shale at room temperature is very dense. Besides, the effect of external in-situ stresses and the effect perpendicular to the bedding orientation under actual buried geological conditions were not considered during the test. In this paper, the gas permeability test device developed based on the pressure pulse attenuation method is used to test the permeability of oil shale perpendicular to the bedding orientation under different temperature and volume stress conditions. Besides, mercury intrusion porosimetry and weight loss tests were also conducted to investigate the variation of porosity and weight loss with the temperature, and it can provide a better explanation to the permeability variation with temperature and volumetric stress.

2 Testing Methods and Procedure 2.1 Specimen Preparation In this test, the large pieces of oil shale specimens removed from the open-pit mine in Fushun were immediately wrapped in plastic wrap and delivered to the Key Laboratory of In-Situ Modified Mining of Ministry of Education at the Taiyuan University of Technology. A rock drilling machine was used to drill three cylindrical specimens with a diameter of 50 mm along the direction perpendicular to the bedding of the oil shale. All the specimens were processed and polished to a height of 15 mm by a grinder and some sandpapers, and the parallelism of upper and lower ends was guaranteed to be within 0.05 mm. At the same time, six oil shale specimens with a size of 7 mm × 8 mm were drilled perpendicular to the bedding direction to conduct a mercury intrusion test. It should be noticed that all the specimens were drilled from the same oil shale rock. 2.2 Testing Apparatus 1. Pyrolysis device The WYFI high-temperature and high-pressure pyrolysis reactor (in Fig. 1) developed by the Taiyuan University of Technology was used in the pyrolysis experiment. The device is composed of pyrolysis reactor, constant pressure pump, temperature control system, gas-liquid product, collection device, gas cylinder, and data collection system. Through constant pressure pump and temperature control system, the device can achieve a constant temperature and constant pressure environment of 20 °C to 600 °C, 0.1 to 20.0 MPa. The internal size of the reactor is 65 mm × 135 mm, which can be used to simulate the in-situ stress environment pyrolysis test for rock specimens smaller than this specification.

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Fig. 1. WYF-I high-temperature and high-pressure pyrolysis reaction device

2. Permeability test device Smart perm III gas permeability measurement was adopted to conduct the permeability test, and the device utilizes the core pulse pressure attenuation test method proposed by BRACE in 1968[16], which can measure the permeability from 9.87 × 10−8 to 9.87 × 10−3 µm2 . Figure 2 showed a schematic diagram of the structure of a gas permeability measuring instrument. The main features of the device are that it has upstream and downstream gas chambers and can maintain constant pressure so that the entire rock specimen is in a relatively stable stress state. In the process of permeability measurement, open the micro-osmosis valve of the test piece, so that the upstream and downstream gas chambers produce a gas pressure difference of up to 0.25 MPa; set a reasonable collection pressure difference interval, and calculate by monitoring the relationship between the gas pressure difference and time rock mass [17].

Fig. 2. Smart III gas permeability measurement instrument

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−14696S1 μg Lfz   f1 Apm V11 + V12

(1)

k=

where k is the permeability of rock; s1 – attenuation coefficient, its value is the slope of the natural logarithmic function of the ratio of the product of the pressure difference between the upstream and downstream and the pore pressure at a certain moment to the product of the pressure difference between the upstream and downstream and the original pore pressure at the original moment. μg – gas dynamic viscosity, Pa · s; L – the length of the cylindrical specimen, mm; fz – gas compression correction factor; f1 – mass flow correction factor; A – the cross-sectional area of a cylindrical core, m2 ; Pm – pore pressure, Pa; V1 – the volume of the upstream air chamber, m3 ; V2 – the volume of the downstream air chamber, m3 ; 3. Porosity testing The POREMASTER-33 mercury intrusion meter produced by Quantachrome in the United States was used to test mercury intrusion of oil shale specimens after pyrolysis at different temperatures. 2.3 Testing Procedure This paper mainly focuses on the change of permeability of oil shale specimens after pyrolysis at different temperatures under different volume stress and pore pressure conditions. Because the burial depth of the Fushun oil shale deposit is from 291 m to 613 m and the average burial depth is 445 m, three different depths of 200 m, 400 m and 600 m were selected in the permeability test to simulate the actual in-situ stress state with in-situ stress gradient of 0.025 MPa/m. To ensure the tightness of specimens during the permeability test, the maximum pore pressure under each volume stress condition should not be more than 3 MPa less than the confining pressure, and the pore pressure interval should be set to 2 MPa. The settings of axial pressure, confining pressure, and pore pressure are shown in Table 1. The specific test steps are as follows: 1. Load the oil shale specimens into the pyrolysis reactor, heat the specimens to 100 °C, and keep the valve normally open to ensure the gas pressure in the kettle is at 0.1 MPa and maintain the temperature constant for 6 h; 2. After the testing specimens are cooled in the kettle, take them out and weigh them, and randomly take small test specimens with a diameter of 7 mm for the mercury intrusion test, and then three tested specimens with a diameter of 50 mm in the gas

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Depth/m

Axial pressure/MPa

Confining pressure/MPa

Volumetric stress/MPa

Pore pressure/MPa

200

5

4

13

1

400

10

8

26

1, 3, 5

600

15

12

39

1, 3, 5, 7, 9

permeability test device according to the settings of different volume stress and pore pressure conditions in Table 1; 3. After the test is completed, the three large tested specimens and the remaining small tested specimens are put into the pyrolysis reactor again, heated to 200 °C, and kept at a constant temperature for 6 h. Repeat step 2 until all permeability and mercury intrusion tests after pyrolysis with the temperature from 100 °C to 600 °C, are completed.

3 Results and Discussion The permeability of oil shale with the temperature Figure 3 given the variation of the pore volume and weight loss of oil shale after pyrolysis at different temperatures. As shown in Fig. 3, under normal temperature condition (20 °C), the oil shale structure is relatively dense with a pore volume of the only 0.0022 cm3 /g; When the pyrolysis temperature increased from 100 °C to 300 °C, the pore volume of the oil shale specimen increased from 0.0052 cm3 /g to 0.0162 cm3 /g, which was 210% of that at 20 °C; but when the temperature increased to 400 °C, the pore volume of oil shale rapidly increased to 0.0952 cm3 /g, which was about 4.9 times of that at 20 °C; From 400 °C to 600 °C, the pore volume continued to grow as the temperature rise, the pore volume of oil shale reached its maximum value at 600 °C, but the growth rate of pore volume at this stage was relatively slow.

Fig. 3. Lateral morphological changes of the samples after pyrolysis

Figure 4 also showed the variation of the weight loss rate of oil shale after pyrolysis at different temperatures (20 °C to 600 °C). From 20 °C to 300 °C, the weight loss of oil shale specimens gradually increased to 4.12%, but it sharply increased to 11.03%

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Fig. 4. Variations of the pore volume and weight loss of oil shale after pyrolysis at different temperatures

when the temperature reached 400 °C. With the increase of temperature, the weight loss continued to increase, whereas the weight loss rate was lower compared to that at 400 °C. It demonstrates that the change law of the oil shale weight loss rate with pyrolysis temperature is consistent with that of the pore volume. Figure 5 given the variation of oil shale permeability after pyrolysis at different temperatures under different volume stress and pore pressure conditions, and under certain volumetric stress and pore pressure conditions, the permeability of oil shale showed a significant stepwise change with the increase of pyrolysis temperature. Based on the variations of weight loss rate, the volume of the pore, and permeability with the temperature, the effect of pyrolysis temperature on oil shale can be divided into three stages as follows: (1) The first stage is from 20 °C to 300 °C, and the variation of permeability of oil shale is very weak during this stage. Under the condition of volumetric stress σv = 13 MPa, after pyrolysis reaction at 300 °C, the permeability of the specimens increased from 0.53 × 10−8 m2 to 1.65 × 10−8 m2 . For the three volumetric stress conditions, the permeability of the specimens increased by 1.54 to 2.11 times during this stage. During this stage, the influence of temperature on oil shale mainly includes the heat evaporation of interlayer water and adsorbed water, while, after heating, the weight loss of oil shale changes little and fewer new pores and cracks caused by water evaporation are created due to the low water content in the oil shale. During the heating process, a crack appeared on the side of the specimen along the bedding plane, but because the crack is perpendicular to the direction of gas penetration, and a single crack cannot form an obvious fracture network structure, the contribution of the crack to the gas permeability is very weak. (2) Second stage: 300–400 °C. The kerogen in the oil shale begins to pyrolyze, and the generated oil and gas products are discharged with the effect of pore pressure, and

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Fig. 5. Permeability variation with the temperature at different volume stress and pore pressure

the weight loss rate of the test piece increases rapidly. The pyrolysis kerogen forms a new pore crack structure in the test piece, the porosity of the test piece increases rapidly, the pore volume increases from 0.0162 cm3 /g to 0.0951 cm3 /g, and multiple openings can be observed on the side of the test piece Different cracks parallel to the direction of the bedding. The newly formed fissures intersect each other inside the specimen, forming a complex seam network structure, which rapidly increases the seepage channel, so the specimen permeability increases rapidly. Under the condition of volumetric stress σv = 13 MPa, the permeability of the oil shale specimen increased from 1.53 × 10−8 µm2 to 142.50 × 10−8 µm2 when the pyrolysis temperature increased from 300 °C to 400 °C. (3) Third stage: 400 to 600 °C. During this stage, the kerogen in the oil shale is further pyrolyzed with the increase of temperature; however, since most of the kerogen in the samples in the previous stage has been pyrolyzed, the rate of increase in the weight loss rate of the samples in this stage decreases. Besides, the original crack opening increased and accompanied by new cracks but the growth of pore cracks generated by pyrolysis turn to be slower compared to the previous stage, so the permeability of the specimen further increased, but the growth rate slowed

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down. Under the condition of volume stress σv = 39 MPa and pore pressure pm = 9 MPa, the permeability of the specimen increased from 104.07 × 10−8 µm2 to 180.62 × 10−8 µm2 when the pyrolysis temperature increased from 400 °C to 600 °C, the increase rate is only 73.56%. Under three different stress conditions, the permeability increased by only 1.69 to 2.49 times. The permeability of oil shale with the volumetric stress. Figure 6 illustrated permeability variation with the volumetric stress under different pyrolysis temperatures, and under the same pyrolysis temperature conditions, the permeability gradually decreased with the increase of volume stress; on the other hand, because the pyrolysis temperature has a staged effect on the oil shale pore cracks, the change of permeability with volume stress also has the obvious stage effect.

Fig. 6. Permeability variation with the volumetric stress under different pyrolysis temperature (Pm = 1 MPa)

The first stage refers to the temperature from 20 °C to 300 °C, and the porosity of oil shale is lower, and the compression of pores and cracks caused by the increase of volumetric stress is limited, which leading to that the permeability decreased slowly with the increase of volumetric stress, and the decrease increment of permeability ranged from 3.66% to 14.15%. The second stage is the temperature ranging from 300 °C to 400 °C, and the larger number of cracks generated in the specimen, and then was compressed by the volumetric stress, which leads to the decrease of the permeability. During this stage, the permeability of oil shale decreased to 117.83 × 10−8 µm2 under the volumetric stress of 39 MPa from 151.52 × 10−8 µm2 under the volumetric stress of 13 MPa. In the third stage, from 400 °C to 600 °C, as the pyrolysis temperature increases, the original fracture opening in oil shale further increases, new fractures are still being generated, and the effect of volumetric stress on fracture deformation is further enhanced.

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When the volumetric stress increased from 13 MPa to 39 MPa, the permeability of the specimen after pyrolysis at 600 °C decreased from 377.61 × 10−8 µm2 to 253.59 × 10−8 µm2 , and the degree of reduction in permeability at this stage increased to 32.84% to 41.79%.

4 Conclusions Oil shale is a source rock with low permeability but extremely sensitive to temperature, and heat injection is an effective method to modify the permeability of oil shale under in-situ conditions. In this paper, the permeability change of oil shale under different temperatures and In-situ stress conditions was investigated with the combination of the mercury injection experiment, weight loss experiment. (1) The temperature effect on the porosity and weight loss rate of oil shale can be divided into three stages. From 20 °C to 300 °C, the interlayer water and adsorbed water in the oil shale begins to evaporate, and the weight loss rate and porosity of the specimen show a slight increase; when the temperature increased from 300 °C to 400 °C, the kerogen in the rock body pyrolyzed and the weight loss rate and porosity increased rapidly; From 400 °C to 600 °C, the kerogen in the specimens was further pyrolyzed, and the weightlessness and porosity were further increased, but the growth rate slowed down. (2) The temperature effect on the permeability of oil shale can be divided into three stages. From 20 °C to 300 °C, the permeability of oil shale had a very weak increase, and it only increased by 1.54 to 3.13 times of that at 20 °C; while the temperature increased from 300 °C to 400 °C, the permeability of oil shale increased rapidly, and it increased by 24.3 to 92.4 times of that at 30 °C; For the temperature ranging from 400 °C to 600 °C, the growth rate of the permeability slowed down, and it only increased to 1.69 to 2.49 times of that at 400 °C. (3) Under different temperatures, the effect of the volumetric stress on permeability can be divided into three stages. For the temperature ranging from 20 °C to 300 °C, the effect of volumetric stress on the permeability of oil shale is small; When the temperature increased from 300 °C to 400 °C, the effect of volume stress on the permeability increased significantly, and the permeability decreased by 22.23% with the increase of volume stress; From 400 °C to 600 °C, the effect of volumetric stress on permeability is further enhanced, the degree of reduction of permeability increased to 32.84% to 41.79%.

References 1. Fletcher, T.H., Gillis, R., Adams, J., Hall, T., Mayne, C.L., Solum, M.S., Pugmire, R.J.: Characterization of macromolecular structure elements from a green river oil shale, II. characterization of pyrolysis products by13C NMR, GC/MS, and FTIR. Energy Fuels 28(5), 2959–2970 (2014)

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2. Solum, M.S., Mayne, C.L., Orendt, A.M., Pugmire, R.J., Adams, J., Fletcher, T.H.: Characterization of macromolecular structure elements from a green river oil shale, I. Extracts. Energy Fuels 28(1), 453–465 (2014) 3. Hillier, J.L., Fletcher, T.H., Solum, M.S., Pugmire, R.J.: Characterization of macromolecular structure of pyrolysis products from a Colorado green river oil shale. Ind. Eng. Chem. Res. 52(44), 15522–15532 (2013) 4. World Energy Council. World Energy Resources: 2013 Survey. http://www.worldenergy.org/ publications/2013/world-energyresources-2013-survey/. Accessed 13 Apr 2017 5. Symington, W.A., Olgaard, D.L., Otten, G.A., Phillips, T.C., Thomas, M.M., Yeakel, J.D.: ExxonMobil’s Electrofrac Process for in situ oil shale conversion. In: 26th Oil Shale Symposium, Colorado School of Mines, 16–18 October. Colorado Energy Research Institute, Colorado (2006) 6. Looney, M.D., Polzer, R., Yoshioka, K., Minnery, G.: Chevron’s plans for rubblization of Green River Formation oil shale (GROS) for chemical conversion. In: 31st Oil Shale Symposium, Colorado School of Mines, 17–19 October. Oil Shale Technology and Research, Colorado (2011) 7. Zhao, J., Yang, D., Kang, Z., Feng, Z.: A Micro-CT study of changes in the internal structure of Daqing and Yan’an oil shale at high temperatures. Oil Shale 29(4), 357–367 (2012) 8. Kang, Z.Q., Yang, D., Zhao, Y.S., Hu, Y.Q.: Thermal cracking and corresponding permeability of Fushun oil shale. Oil Shale 28(2), 273–283 (2011) 9. Coshell, L., Mclver, R.G., Chang, R.: X-ray computed tomography of Australian oil shales: non-destructive visualization and density determination. Fuel 73(8), 1317–1321 (1994) 10. Tiwari, P., Deo, M., Lin, C.L., Miller, J.D.: Characterization of oil shale pore structure before and after pyrolysis by using X-ray micro CT. Fuel 107, 547–554 (2013) 11. Saif, T., Lin, Q., Bijeljic, B., Blunt, M.J.: Microstructural imaging and characterization of oil shale before and after pyrolysis. Fuel 197, 562–574 (2017) 12. Geng, Y., Liang, W., Liu, J., Cao, M., Kang, Z.: Evolution of pore and fracture of oil shale under high temperature and high pressure. Energies Fuels 31, 10404–10413 (2017) 13. Kang, Z.Q., Yang, D., Zhao, Y.S., Hu, Y.Q.: Thermal cracking and corresponding permeability of Fushun oil shale. Oil Shale 28, 273–283 (2011) 14. Yang, L., Yang, D., Zhao, J., et al.: changes of oil shale pore structure and permeability at different temperatures. Oil Shale 33(2), 101–110 (2016) 15. Dong, F., Feng, Z., Yang, D., Zhao, Y., Derek, E.: Permeability evolution of pyrolyticallyfractured oil shale under in situ conditions. Energies 11, 3033 (2018) 16. Brace, W.F., Walsh, J.B., Fragos, W.T.: Permeability of granite under high pressure. J. Geophys. Res. 73, 2225–2236 (1968) 17. Jones, S.C.: A technique for faster pulse-decay permeability measurement in tight rocks. SPE Form. Eval. 12(1), 19–26 (1997)

Study on Commissioning Techniques for Oil Transportation Pipeline with Large Elevation Difference and Continuous U Shape Wang Li1(B) , Liang Feng1 , Qiqi Chen1 , Xiaohua Chen1 , and Wenlong Jia2 1 PipeChina Southwest Pipeline Company, Chengdu, China

[email protected] 2 Southwest Petroleum University, Chengdu, China

1 Preface China-Myanmar Crude Oil Pipeline and Yunnan Product Oil Pipeline encounter large elevation difference along the route. Within 50 km range, there are four locations that elevation difference is larger than 1000 m, making a few U shapes. Being categorized as continuous U shape large elevation difference pipeline, partial water filling and onwards oil displacement scheme was selected for commissioning. The complexity of the commissioning process is heavily increased by implicit hydraulic characteristics, partially filled flow and air block caused by large elevation difference. Therefore, this study has analyzed the venting location selection, partial water filling quantity, hydraulic characteristics during displacement and disposition of emulsified diesel. Solutions are presented for the challenges that might be experienced during the commissioning of continuous U shape large elevation difference pipeline, which might be a good reference for future design, commissioning and operation of similar pipelines (Fig. 1).

Fig. 1. Elevation chart of China-Myanmar crude oil pipeline

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 182–190, 2021. https://doi.org/10.1007/978-3-030-64690-5_17

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2 Impact Analysis of Gas Accumulation During Commissioning During the production commissioning, the terrain factors have great influence on the gas accumulation of the pipeline. Under relatively flat terrain, the drop of the pipeline is small, so the gas accumulation of the pipeline will be less when put into production, and the gas-bearing section is basically absent. And in the continuous undulating pipeline, due to the larger drop, the head after the high point (exhaust point) to form a dissatisfied flow continues to flow downstream, to the lowest point to form a liquid seal, this will cause the pipeline to accumulate gas, the formation of many gas-bearing section [1]. As the commissioning, in addition to the phenomenon of liquid sealing in the downhill section, gas fragmentation, migration and re-accumulation will also occur in the pipeline [2]. In the case of small volume of transportation and slow velocity, the gas trapped in the downhill section gathers at the high point to form a gas mass. Under the action of buoyancy and inter-phase friction, the gas can remain stationary [3]. When the flow velocity reaches a certain value, the surface tension of the air mass cannot remain intact under the interphase friction force and the turbulent impact force of the liquid phase. When flowrate is high, the gas may not stay at a relatively high point, but is carried downstream by the liquid. In this way, the gas forms a bubble flow or tiny slug flow in the downstream tube [4]. These gases may not be very obvious in the flat section of the terrain, but when they pass through the downstream uphill section with a steep slope, the gas moves faster in the uphill section due to the influence of buoyancy, gradually coalescing into large bubbles or slugs and reforming air mass. At the same time, since the buoyancy action direction of the air mass in the uphill section is the same as that of the liquid flow direction, the air mass will migrate to the downstream. When it comes to the downhill section with large slope, the buoyancy action direction of the air mass is opposite to that of the liquid flow direction, and then stays in the downhill section [5].

BS

MD

LF

AN

Fig. 2. Variation diagram of theoretical and actual pressure difference between stations

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Figure 2 shows the change of theoretical and actual head difference with time during the actual production process, and the difference is proportional to the gas content, so it can represent the gas content and gas resistance of the pipeline. It can be seen from the figure that the head difference of each station changes periodically with time, indicating that the gas migrates by the way of accumulation, discharge, re-accumulation and redischarge. In the continuous undulating pipeline, due to the influence of topography, gas is likely to exist in both the up-slope and down-slope sections of the pipeline, and the presence of gas also greatly affects the flow of liquid. According to the momentum equation, when the section V present (or ), liquid flow will change, at the same time because of the existence of gas inside the liquid energy loss cannot be recycled, lead to the section of the pressure loss is bigger.

3 Impact Analysis of Oil Mixing During Commissioning The mixing process of oil replacement water in large drop pipeline is similar to that of sequential conveying process. Due to the difference in density and viscosity between water and oil, as well as the influence of unstable operation and height difference, the actual oil mixing amount will be more than the theoretical calculation amount. At the same time, the mixture of oil and water is likely to increase due to multiple shutdowns during the production process [6]. For large drop pipelines, the mixing of oil in the height difference, the stopping of oil transmission and the oil-water emulsification phenomenon after the shearing of the pressure reducing valve in the large drop pipelines should be fully considered. According to the emulsification theory, after the oil/water is vigorously stirred, a part of the work done by the external force is converted into the interface energy of the system, which increases the contact interface area, and the emulsion is formed by the dispersion of one kind of liquid in another kind of liquid with very small particles. According to the second law of thermodynamics, under constant temperature and pressure, the system of matter has the tendency to reduce free energy automatically. When oil/water emulsion is formed, its contact interface and interface energy are both large. From the perspective of thermodynamics, the emulsion is an unstable system. After the agitation stops, the internal phase particles collide and merge due to Brownian motion, and soon the oil and water are layered. Emulsifiers (surfactants) are needed to form a stable oil/water emulsion. Under normal circumstances, the oil-water displacement process of pipeline, won’t appear strong oil-water emulsion phenomenon [7]. But the big gap between the pipe may be after a vigorous stirring, ups and downs along the section of shear diffusion, pressure reducing valve, and may have some dirt in pipeline (natural emulsifier), make the oil and water form a stable emulsion, and by gravity settling difficult demulsification, must be used under the conditions of demulsifier dehydration. During Commissioning, the pipe with a part of the gas can’t discharge, with oil head moves downstream, the emulsion will replace the water and the gas contact, friction increases rapidly, so the alternate with bubble breakage rate, liquid and gas capacity increase, gas rate increases, along which resulted in increased section of additional pressure loss [8] (Fig. 3).

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Fig. 3. Elevation chart of China-Myanmar crude oil pipeline (NuJiang Section)

4 Commissioning of Large Drop Pipeline (Nu Jiang) At 14:00 on May 26, the oil head arrived at MS station and began to cross the Nujiang river. At 22:28 on May 27, after the oil head crossed the high point of F2, the outbound pressure of MS was too high, and there was a risk of overpressure, so the pipeline were shut down urgently. Between May 28 to June 1, several attempts were made to start up, but none was successful. Table 1 shows some pressure data from MS to F2 high point. Table 1. Some pressure data from MS to F2 high point L (km) H (m) P1 (MPa) P2 (MPa) P3 (MPa) MS 106.8 6#

115.7

883

14.26

13.58

14.68

873

14.04

13.41

14.47

LL 153.3

1854

4.05

3.28

4.51

8#

161.1

1800

4.11

3.37

4.61

F2

174.4

2183

0.09

0.00

1.60

Note: 1. P1 is the measured data on May 31; 2. P2 and P3 are measured data on June 1

5 Abnormal Pressure Analysis According to the principle of energy conservation [1], the pressure at the two measuring points should satisfy the following relationship, P1 + ρgZ1 = P2 + ρgZ2 + Pf + Pa

(1)

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Where, P1 -the hydrodynamic pressure at point 1, Pa; Z1 -the elevation of point 1, m; P2 -the hydrodynamic pressure at point 2, Pa; Z2 -the elevation of point 2, m; Pf -the friction losses from 1 to 2; Pa-additional pressure loss due to gas accumulation in pipeline from 1 to 2. By deforming formula (1), formula (2) is obtained. P2 = P1 − ρg(Z2 − Z1 ) − Pf − Pa

(2)

In the commissioning of continuous undulating section, there are three flow forms in the pipeline according to the different terrain. (1) Air mass segment Although many exhaust measures are taken during the commissioning, a certain amount of gas is often accumulated in the pipeline (as shown in Fig. 4). These gases are partly due to the unreasonable location of the exhaust point, resulting in incomplete discharge of the gas accumulation section. The other part is the gas section broken and dispersed in the pipeline. In the up-slope section of the pipeline, these gases reassemble and migrate, and finally stay in the down-slope section of the pipeline as air mass. Take the air mass in the downhill section of Fig. 4 as an example, its force can be expressed by the following formula, ρg Ag gsinθ1 − ρl Ag gsinθ1 + τi Si = 0

Fig. 4. Schematic diagram of bubble breaking process

(3)

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Where, ρg - the density of the gas in the air mass, kg/m3 ; L - density of liquid, kg/m3 ; Ag - cross sectional area of air mass, m2 ; τi - air mass by fluid shear stress, Pa. Si perimeter length between liquid and air mass, m; The first term in Eq. (3) represents the component force of air mass gravity along the pipeline direction. The second term represents the component of air mass buoyancy along the pipeline direction. The third term is the force between the air mass and the liquid. Since the length of the air mass is very small, its internal pressure can be considered to be consistent, and there is no pressure gradient. (2) Air bubble section

Fig. 5. Schematic diagram of bubble aggregation process

Under the inter-phase friction force and the liquid phase turbulence impact force, the air mass will break up and disperse into the liquid in the form of small bubbles (downslope section in Fig. 4), which will be carried by the liquid to flow downstream (upslope section in Fig. 5) until it reaggregates in the upslope section. During commissioning, due to the repeated occurrence of air mass fragmentation and aggregation, the flow in most pipelines is not the single-phase flow of pure liquid, but the bubble flow in the multi-phase flow. According to the relation proposed by Gregory [2], after the air mass is broken into bubbles, the calculation formula of liquid holdup in the pipe segment is, Hl =

1+



1

vs 1.39 8.66

Where, vs —The velocity of the gas-liquid mixture, m/s;

(4)

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The frictional resistance loss of the bubble flow can be calculated by the Shaw - Sean – Brill [3] method,   2 2fm ρm vm dp = (5) − dx D Where, ρm —The average density of a gas-liquid mixture, kg/m3; fm—Fanning friction coefficient of gas-liquid mixture; (3) The corner in the pipe Due to the presence of air, liquid have not freely between gravitational potential energy and kinetic energy transformation, according to the principle of conservation of momentum, after a V-shaped (or ) bent under additional pressure loss can be obtained from, P0 = ρa[v2 − v1 cos(θ1 + θ2 )]

(6)

Where, v1 —The velocity of the liquid in the first half, m/s; v2 —The velocity of the liquid in the second half, m/s; a—Wave velocity in liquid, m/s; θ1 —The Angle between the first half of the pipe and the horizontal line, rad; θ2 —The Angle between the second half of the pipe and the horizontal line, rad; The Eq. (6) is considered in the most serious case. In fact, the accumulated gas in the pipeline may not be enough to generate such a large pressure loss. Therefore, the actual additional pressure loss is, Pa = kP0

(7)

The actual commissioning is a cycle of the above three conditions, in which the pressure loss includes two aspects: frictional resistance loss and additional pressure loss at the corner. As for the frictional resistance loss, according to the analysis in (2) Air bubble section, we believe that the whole pipe segment is in the bubble flow state, which can be calculated. It must be pointed out that the liquid phase in the bubble flow should be the emulsion formed by the mixture of oil and water. It is the presence of the emulsion that intensifies the process of air mass breaking and carrying. However, in the analysis and calculation, there is a lack of relevant data of on-site oil and water emulsion. For the additional pressure loss at the turning point, the momentum equation (Eq. 6) can be used first to calculate the maximum momentum loss, and then the appropriate gas accumulation coefficient can be selected to obtain the final pressure loss in combination with the gas-holding condition of the pipe section. When there is only liquid in the pipe, According to the Dancy formula, the pressure difference of the pipe before inflation can be obtained, and the pressure difference after inflation in the pipe is the pressure difference measured on the spot. The value of can refer to the detection value of the day, while the value of a is about 1100 m/s. V = v ×

L a

(9)

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Where, V—gas volume, m3 ; v—the velocity difference, m/s; L—the length of pipeline, m; a—water hammer wave speed, m/s. According to the above calculation method, the gas content of each section can be obtained. The calculated results are shown in Table 2. Table 2. The gas content of each section Section

D (mm)

E (mm)

L (km)

V (m3 )

Vtotal

Gas content

Nujiang Section

813

12.7

64.38

31

32385

0.09%

Lancangjiang Section

813

12.7

156.20

18

78573

0.02%

MD to LF

813

12.7

202.82

110

102025

0.11%

LF to AN

610

9.5

44.93

8

12724

0.06%

It can be seen from Table 2 that the maximum gas content in the pipeline is about 0.1%, and it is believed that the energy loss of the pipeline has reached the maximum under this gas content, and the gas product coefficient is taken to be 1. If the pipeline is a pure liquid phase pipeline, the gas accumulation coefficient is set as 0. According to this rule, the gas accumulation coefficient of the four sections of pipeline is set as 1, 0.2, 1 and 0.6 respectively. After obtaining the product gas coefficient, the theoretical pressure values at each point can be calculated. The results of each section are shown below (Table 3). Table 3. Calculated values of pressure at each point in working condition 1 ρg(Z2 − Z1 ) (MPa)

Pf (MPa)

Pa (MPa)

theoretical value (MPa)

Actual pressure (MPa)

0

0

14.26

14.26

0.14

1.93

4.20

4.05

3.30

0.05

0.09

L (km)

H (m)

MS

106.8

883

0

LL

153.3

1854

7.99

F2

174.4

2183

10.70

0.21

Note: 1. The value of viscosity is 7 mm2 /s, density is 840 kg/m3 ; 2. The value of flowrate is 1015 m3 /h; 3. The gas accumulation coefficient is 1.0

During the commissioning, the gas in the pipeline will be repeatedly broken, migrated and reassembled, and finally all the gas will be discharged from the pipeline. Therefore, the pressure difference varies with the change of the gas accumulation at different moments, which is the main reason for the difference in the measured values at different moments.

6 Conclusions This paper analyzes the causes of abnormal pressure in some sections of China-Myanmar crude oil pipeline during the commissioning. Based on the instantaneous momentum

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balance and the gas content of each section, the pressure values of the monitoring points along the line are calculated theoretically. The calculated results are in good agreement with the measured values. This shows that gas in pipeline is the main cause of abnormal pressure. The dynamic process of gas fragmentation, migration and accumulation leads to the difference of the pressure difference at different times. It is worth noting that the oil-water emulsion formed by mixing oil greatly enhances the capacity of liquid to carry gas, so the length of mixing oil section should be minimized during the commissioning of liquid pipeline.

References 1. Spurk, J.H.: Fluid Mechanics (2001) 2. Chen, X.J.: Advances in the study of multiphase flow. Prog. Nat. Sci. 2, 113–118 (1991) 3. Flory, J.H., Small, D.S., Cassano, P.A., et al.: Comparative effectiveness of oral diabetes drug combinations in reducing glycosylated hemoglobin. J. Comp. Eff. Res. 3(1), 29–39 (2014) 4. Xu,Y., Song, X.: Study on the gas diffusing rule for the “gas-to-gas process” of gas transmission pipeline during commissioning. Oil Gas Storage Transp. (2008). 5. Guangli, X., Guozhong, Z.: An experiment on dewatering for lower location of pipeline. Oil Gas Storage Transp. 30, 369–372 (2011) 6. Gerfen, K.: CTA Morgan street station. Architect 102, 114–119 (2013) 7. Sears, J., Glitman, K., et al.: Measure for Measure: Energy Utility Model for Standardized Evaluation of Transportation Efficiency Measures. Transp. Res. Rec. 2375, 1–7 (2018) 8. Sargent, L.H., Taylor, D.G.: IEEE 2017 IEEE Transportation Electrification Conference and Expo (ITEC) - Chicago, IL, USA (2017.6.22–2017.6.24)] 2017 IEEE Transportation Electrification Conference and Expo (ITEC) - Commissioning of a Motor-Generator Unit, vol. 2017, pp. 516–521 (2017)

Application of Functional Safety Analysis in Refined Oil Station Wang Li1(B) , Xiaohua Chen1 , Zhen Ma1 , and Jiawen Long2 1 PipeChina Southwest Pipeline Company, Chengdu, China

[email protected] 2 Southwest Petroleum University, Chengdu, China

Abstract. In recent years, the HAZOP analysis method has been widely used in the process safety analysis and evaluation of long-distance oil and gas pipeline stations. However because it cannot give quantitative assessment, whether the risk can be controlled within acceptable range by safety measures can hardly be judged. To compensate for these deficiencies, LOPA analysis was introduced on the basis of HAZOP analysis. By studying the characteristics of HAZOP and LOPA analysis methods and the relationship between them, it is found that the two can be complementary and combine to enhance the safety analysis effect. Taking a pipeline station of refined oil for example, the assessment effect of the proposed HAZOP-LOPA risk assessment method is discussed. The results show that the HAZOP-LOPA method can not only quantify the risk, but also determine whether the existing safety measures are sufficient or not. The HAZOP-LOPA method can effectively overcome the shortcoming of HAZOP analysis method and improve the accuracy of risk assessment. Keywords: HAZOP · LOPA · Refined oil · Station

1 Introduction As a key part to ensure the normal operation of the entire oil transportation system, the station plays a role of regulation and control in the oil transportation process. The station is composed of numerous facilities, operating in a complex mode which is controlled by a complicated controlling system. Once there is any accident in the station, serious consequences such as fire, explosion and environmental pollution may be caused. Therefore, it is of great significance to carry out functional safety assessment for station to find out and control the possible risks in its production and operation.

2 Overview of Analysis Methods 2.1 HAZOP HAZOP (Hazard and Operability) analysis is a method of security analysis proposed by Imperial Chemical Industries (ICI) in the 1960s. After more than 50 years of improvement, it has been widely applied in engineering projects in China and abroad, becoming a common hazard and risk analysis method [1]. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 S. N. Atluri and I. Vušanovi´c (Eds.): ICCES 2020, MMS 97, pp. 191–198, 2021. https://doi.org/10.1007/978-3-030-64690-5_18

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Hazard and Operability analysis is a structured and systematic analysis method [2]. In HAZOP analysis, a well-trained and experienced team leader leads members from all fields. The “deviations” of the operating status from the normal status is analyzed using “guide words”, identifying the potential risks to people and equipment and thus ensuring the safety of the system. HAZOP analysis includes four basic steps, as shown in Fig. 1 [3]. Hazard and Operability analysis is widely used in oil and gas pipeline process safety analysis due to its comprehensiveness, systematization and structural characteristics [4]. But as a qualitative analysis method, HAZOP has its limitations, summarized as: (1) The success of HAZOP depends largely on the ability and experience of the team leader and team members as well as their cooperation; (2) HAZOP analysis considers each node separately and only analyzes the effects of each deviation on the node, without considering the interaction between nodes; (3) HAZOP analysis can neither quantify the risk nor judge whether the existing protection measures are effective or not [5].

Fig. 1. Diagram of HAZOP analysis procedure

2.2 LOPA Layer of Protection Analysis (LOPA) is a semi-quantitative risk assessment method proposed by the American chemical council in the late 1980s [6]. On the basis of the

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qualitative risk analysis, LOPA aims to further make quantitative description of the risks, including the accurate description of the accident scene and the recognition of existing independent protection layer, thus estimating whether the risk level of the system is within the acceptable risk standard when this scenario occurs. If the risk is larger than the allowable level, additional appropriate protection layer should be added to lower the risk below the acceptable level. The detailed process of LOPA analysis is shown in Fig. 2 [7]. LOPA analysis is a kind of simplified semi-quantitative assessment method. It has the following advantages: (1) Compared with qualitative risk analysis, LOPA analysis is more quantitative and can avoid the influence of subjective factors on risk control decision; (2) Although it is not as accurate as quantitative risk analysis, LOPA analysis is simple and convenient, which can improve the efficiency of risk analysis and save the analysis cost; (3) LOPA analysis is an important assessment tool for the security integrity level (SIL), and can provide more accurate and visualized results compared with graphology method; (4) The contributions of different independent protection layers in reducing the risk can be known, based on which more economic and reasonable protection measures can be proposed. Though so many advantages, LOPA still has its limitation. That is, most of its parameters were derived from empirical values which were obtained according to large number of engineering practices and experiments, thus the result using LOPA analysis is not accurate enough [8].

Fig. 2. Flow chart of LOPA

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2.3 HAZOP-LOPA HAZOP and LOPA are related with each other in many aspects: (1) the serious accident scenario screened by HAZOP analysis is the basis for LOPA analysis [9, 10]; (2) the consequences and corresponding severity caused by deviation in the analysis of HAZOP provide important reference for LOPA analysis; (3) the causes of deviation and their occurrence frequencies in the analysis of HAZOP offer direct information for the initial events and their occurrence frequencies in LOPA analysis; (4) the safety measures determined by HAZOP analysis offer basis for the identification of independent protective layers (IPLs) and their protective effects [11–13]. The relationship between HAZOP and LOPA analysis is shown in Fig. 3. It can be seen that LOPA analysis is the inheritance and development of HAZOP analysis, which further quantifies HAZOP’ results [14]. The combination of HAZOP and LOPA can overcome the deficiencies of HAZOP analysis and determine the SIL level of safety instrumented system. Moreover, the deviation from HAZOP can be agreed upon through the LOPA analysis, deepening the understanding of the evaluators and making the suggestions more scientific and targeted [15].

Fig. 3. Diagram of relation between HAZOP and LOPA

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3 Steps of HAZOP-LOPA (1) Preparation Determining the analysis scope; collection data; preparing implementation plan; determining team members; making meeting record form, etc. (2) Performing HAZOP analysis Dividing the analysis scope into nodes; describing design intent of target node; calculating the deviation; analyzing the consequences caused by deviation; finding the reasons for the deviation; making a list of the existing safety protection measures; risk level assessment; proposal of suggestions and measures; analyzing and recording; repeating the whole procedures of performing HAZOP analysis for other nodes respectively. (3) Perform LOPA analysis Picking up the accident scenes exposed to high risk according to the results of HAZOP analysis, determining the occurrence probability of initial event, conditional event and consequential event; calculating the frequency of remaining events; identifying the existing independent protective layers and safety protection measures, and meanwhile determining their failure probabilities; calculating the frequencies of events relieved; determining the risk after being relieved and evaluating whether it can be accepted or not; based on the evaluation, judging whether additional measures are needed, if yes, proposing relevant suggestions [16]. (4) Writing the HAZOP-LOPA analysis report accordingly.

4 Case Study HAZOP-LOPA analysis method is applied to evaluating the initial station of a longdistance products oil pipeline. The normal operation of this station is divided into 8 nodes for analysis, such as transferring the oil transported to the station into the oil tanks at the tank farm (OIT); transporting the oil in oil tanks outside; transferring the oil between tanks; launching chamber; discharging pollution, etc. Through HAZOP analysis, 191 existing or potential problems are found, and 278 suggestions are proposed. While through LOPA analysis, 15 detailed suggestions are given. Taking the high oil level deviation in the process of OIT for example, the application of HAZOP-LOPA analysis method in the products oil station is illustrated. As with the large deviation of the oil level in the tank, the reasons and the occurrence probability are analyzed. The consequences the deviation may cause and the seriousness of the consequences are listed in a table. Then the existing protection measures are found out. After that the residual risk level is determined and corresponding suggestions are proposed. The matrix describing the risk level is shown by Table 1, while part of the HAZOP analysis results are shown in Table 2.

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Probability Consequence

1

2

3

4

5

1

Low

Low

Low

Low

Low

2

Low

Low

Low

Medium

Medium

3

Low

Low

Medium

Medium

High

4

Low

Medium

Medium

High

High

5

Medium

Medium

High

High

High

Table 2. Part of HAZOP analysis results Deviation

Possible cause

Consequence

Protection measures

Risk matrix

High oil level

Content gauge failure

Tank boil-overs, economic losses, environment pollution, fire, casualties

1. High liquid (5:4) level High interlocking, closing the valve front tank; 2. Regular checking of content gauge; 3. Monitoring; 4. Combustible gas detector; 5. Flame detector; 6. Ignition source management; 7. Lightning rod and grounding grid; 8. Calculating liquid level variation regularly

Suggestions 1. Transferring the signals of content gauge failure to the station and making alarms; 2. Recording the oil level showing by the content gauge during the process of storing the oil into the tank; 3. Mounting equipment to make alarm or take interlock action when the content gauge value remains unchanged for a certain time period in the process of storing the oil into the tank

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Based on the results of HAZOP analysis, LOPA analysis is conducted for the above scenario to quantitatively assess the risk level. The corresponding LOPA analysis results are shown in Table 3. Table 3. Part of LOPA analysis results Scenarios

Acceptable

Initial event

Conditional

Consequences

Unrelieved

Independent

Relieved event

risk level

and frequency

event

modification

event

protection

frequency

and frequency

and frequency

frequency

layer and

Content gauge

Content gauge

Ignition

1 × 10−3

failure; 0.1

regular

probability; 0.1

Suggestion

frequency Content gauge