Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors 9780081019801, 9780081019818, 0081019807

Table of contents :
Front Cover......Page 1
Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors......Page 4
Copyright......Page 5
Contents......Page 6
Contributors......Page 12
Foreword......Page 16
Preface......Page 18
Nomenclature......Page 20
1.1. Nuclear energy and fast reactors......Page 26
1.3. Short history of liquid metal reactors......Page 27
1.4. Benefits and drawbacks of liquid metals as coolants......Page 29
1.5. European liquid metal reactor designs......Page 30
1.5.1. ASTRID (Fig. 1.2)......Page 31
1.5.1.3. Description of the safety concept......Page 32
1.5.2. ALFRED......Page 33
1.5.2.2. Description of the primary cooling system......Page 34
1.5.3. MYRRHA......Page 35
1.5.3.2. Description of the primary cooling system......Page 36
1.5.4. SEALER......Page 37
1.5.4.1. Introduction......Page 38
1.6. Guidance......Page 39
References......Page 40
2.2. Identification......Page 42
2.4.1. Basic phenomena......Page 44
2.4.2. Core thermal hydraulics......Page 47
2.4.3. Pool thermal hydraulics......Page 51
2.4.4. System thermal hydraulics......Page 57
2.4.5. Guidelines......Page 62
References......Page 64
Further reading......Page 68
Chapter 3: Thermal-hydraulic experiments with liquid metals-Introduction......Page 70
References......Page 72
3.1.1. Introduction......Page 74
3.1.2. Scaling and theory......Page 75
3.1.2.1. Forced convection for pool-type investigation......Page 76
3.1.2.2. Natural convection for pool-type investigation......Page 77
3.1.2.4.1. Laser Doppler anemometry......Page 78
Irregular sampling......Page 80
3.1.2.4.2. Particle image velocimetry......Page 81
Illumination requirements......Page 82
Image requirements......Page 83
3.1.2.4.3. Laser-induced fluorescence......Page 84
3.1.2.4.4. Refractive index matching techniques......Page 85
Matching fluid with solid (F2S)......Page 86
Matching solid with fluid (S2F)......Page 87
Absorption coefficient......Page 88
Thin walls......Page 89
3.1.3. Fuel bundle experiments......Page 90
3.1.3.1. Mean flow and turbulence characteristics......Page 91
3.1.3.3. Periodic flow pulsations......Page 92
3.1.3.4. Fluid-structure interaction......Page 94
3.1.3.5. Effect of wire wraps......Page 95
3.1.4. Pool-type experiments......Page 96
3.1.4.1. Scaling for pool-type experiments......Page 99
3.1.4.2. MYRRHABELLE water model......Page 100
3.1.4.3. PIV measurements in MYRRHABELLE......Page 101
3.1.4.3.2. Natural convection......Page 102
References......Page 104
Further reading......Page 107
3.2.1. Introduction......Page 108
3.2.1.2. Fuel assembly thermal-fluid-dynamic......Page 110
3.2.2. HLM large pool design......Page 111
3.2.4. Core simulator design......Page 113
3.2.4.2. Numerical set-up......Page 115
3.2.4.3. CFD results......Page 116
3.2.5. Steam generator design......Page 119
3.2.5.1. RELAP5 modeling......Page 122
3.2.5.2. Results......Page 124
3.2.6. Test section pressure drop......Page 126
3.2.7. Final remarks......Page 128
References......Page 129
3.3.1. Introduction......Page 132
3.3.1.2. Special features of liquid metals and their impact on the facilities......Page 133
3.3.1.2.2. Chemical interactions......Page 134
3.3.1.2.3. Corrosion (compatibility with solid materials)......Page 135
3.3.2.1.1. Pumping devices......Page 136
3.3.2.1.2. Heat exchangers......Page 137
3.3.2.2. Instrumentation......Page 138
3.3.2.2.1. Flow rate......Page 139
3.3.2.2.2. Differential pressure......Page 140
3.3.2.3. Some examples at KIT: The THEADES (LBE) and KASOLA (Na) loops......Page 141
3.3.3.1. Reproducible operating conditions......Page 143
3.3.3.2. In-situ calibration of instruments and data acquisition chain......Page 144
3.3.3.3. Some examples at KIT: Rod bundles (LBE), backward-facing step (Na)......Page 145
3.3.4. Conclusions......Page 148
References......Page 149
Chapter 3.4: Operational aspects of experimental liquid metal facilities......Page 152
3.4.1. Preoxidation......Page 154
3.4.2. LBE melting and first time filling......Page 155
3.4.3. Gas conditioning sequence (inerting)......Page 156
3.4.5. LBE filling......Page 157
3.4.6. Pump startup and shutdown......Page 159
3.4.8. Draining......Page 160
3.4.9.1. LBE solidification: Valve operation/actuation......Page 162
3.4.9.2. Pressure surge......Page 163
3.4.9.3. Instrumentation......Page 164
3.4.9.4. System performance monitoring......Page 165
3.4.10. Cleaning of the facility/test section......Page 167
3.4.11. Summary......Page 169
References......Page 170
3.5.1. Introduction......Page 172
3.5.2. Ultrasound-based methods......Page 173
3.5.3. Inductive measurement techniques......Page 176
References......Page 179
4.1. Convective heat transfer with liquid metals......Page 182
4.1.2. Convective heat transfer correlations......Page 184
4.2. Hydrodynamic model for STH codes......Page 187
4.3. Thermodynamic properties for the liquid metals to be implemented in a STH code......Page 190
4.3.1. Liquid phase......Page 191
4.3.2. Vapor phase......Page 192
4.4.1. RELAP5/Mod3.3 modified code......Page 193
4.4.2.1. Facility description......Page 194
4.4.2.2. NACIE RELAP5 model and application: Isothermal and ULOF transient......Page 199
4.5.1. CATHARE code......Page 205
4.5.3. SPECTRA code......Page 206
4.5.4. SAS4A/SASSYS-1 code......Page 207
References......Page 208
Further reading......Page 209
Chapter 5: Subchannel analysis for LMR......Page 210
5.1.1. Structure of LMR fuel assemblies......Page 211
5.1.3. Tasks of reactor core thermal hydraulic analysis......Page 214
5.2. SCTH analysis......Page 216
5.2.1. Basic equations......Page 217
5.2.1.2. Momentum conservation......Page 218
5.2.1.3. Energy conservation......Page 219
5.2.2.1. Pressure drop......Page 220
5.2.2.2. Heat transfer......Page 221
5.2.2.3. Transversal exchange......Page 223
Flow sweeping......Page 224
Turbulent mixing......Page 226
Large scale oscillation......Page 229
5.2.2.4. Local wall temperature distribution......Page 230
5.2.3. Examples......Page 233
References......Page 235
Further reading......Page 236
6.1. Direct numerical simulation......Page 238
6.2. Large-eddy simulation......Page 239
6.3. Reynolds-averaged Navier Stokes equations......Page 240
References......Page 242
6.1.1.1.1. The Navier-Stokes equations......Page 244
6.1.1.1.2. The scalar transport equation......Page 245
6.1.1.1.3. Length and time scales in turbulent flows......Page 247
6.1.1.2. Direct numerical simulation techniques......Page 249
6.1.1.3.3. Outflow open boundary conditions......Page 252
6.1.1.3.4. Boundary conditions for the thermal field......Page 253
6.1.1.3.6. Statistical treatment of numerical solutions......Page 254
6.1.1.4. Results: Channel flow......Page 255
6.1.1.5. Results: Nonplanar geometries......Page 261
6.1.1.6. Conclusions......Page 265
References......Page 266
6.1.2.1. Introduction......Page 270
6.1.2.2. LES equations......Page 273
6.1.2.2.1. Governing equations......Page 274
6.1.2.2.3.1. Practical LES equation set......Page 275
6.1.2.2.4. Heat transfer in LES......Page 277
6.1.2.3.1. Eddy-viscosity models......Page 278
6.1.2.3.1.2. The WALE model......Page 279
6.1.2.3.2.1. The approach......Page 280
6.1.2.3.2.2. The dynamic Smagorinsky model......Page 282
6.1.2.3.3.1. The approach......Page 283
6.1.2.3.4.1. The Reynolds analogy and the eddy heat diffusivity approach......Page 284
6.1.2.3.4.2. The case of liquid metals......Page 285
6.1.2.4.1. The turbulent channel flow......Page 287
6.1.2.4.2. Validation of the V-LES/T-DNS approach......Page 289
6.1.2.4.3. V-LES/T-DNS at higher Reynolds......Page 290
6.1.2.5. Concluding remarks......Page 294
References......Page 295
Chapter 6.2.1: Turbulent heat transport......Page 298
6.2.1.1. Understanding the peculiarities of heat transfer modeling in turbulent liquid metal flows......Page 300
6.2.1.1.1. Incomplete modeling of turbulent heat flux......Page 301
6.2.1.1.3. Time scale ratio......Page 302
6.2.1.2. Modeling of turbulent heat transfer......Page 303
6.2.1.2.1. Second-moment closures......Page 304
6.2.1.2.2.1. Explicit AHFM......Page 305
AHFM-2000 ()......Page 306
AHFM-2005 ()......Page 307
AHFM-NRG ()......Page 308
6.2.1.2.3. Generalized gradient diffusion hypothesis......Page 310
6.2.1.2.4. Simple gradient diffusion hypothesis......Page 311
6.2.1.3. Summary......Page 313
References......Page 314
Further reading......Page 317
6.2.2.1. Introduction......Page 318
6.2.2.2.2. Methodology......Page 319
6.2.2.2.3. Fluid dynamics in rod bundles......Page 320
6.2.2.2.4. Flow-induced vibration by large-scale periodic vortices......Page 324
6.2.2.3.1. Description of the experiment......Page 326
6.2.2.3.2. Methodology......Page 327
6.2.2.3.3. Dynamics in stable regime......Page 328
6.2.2.3.4. The prediction of divergence......Page 329
6.2.2.3.5. The post-divergence regime......Page 332
Acknowledgment......Page 333
References......Page 334
6.2.3.1. Introduction......Page 336
6.2.3.2. Experiments and correlations......Page 338
6.2.3.3.1. CFD benchmarking......Page 340
6.2.3.3.2. Reduced resolution modeling......Page 346
6.2.3.3.3. Deformations......Page 350
6.2.3.4. Simulation of accidental conditions......Page 351
6.2.3.4.1. Blockages due to particles......Page 352
6.2.3.4.2. Blockages due to lost objects or migrating parts......Page 355
6.2.3.4.3. Inter-wrapper flow......Page 356
6.2.3.5. CFD and chemical reactions simulation......Page 357
6.2.3.6. Summary......Page 358
References......Page 360
Further reading......Page 365
Chapter 6.2.4: (U)RANS pool thermal hydraulics......Page 366
6.2.4.1. Identification of the relevant physics......Page 367
6.2.4.2.1. Diversification and redundancy strategy......Page 368
6.2.4.2.2. Gross numbers-order of magnitude analysis......Page 369
6.2.4.2.3.1. Meshing in STAR-CCM+......Page 370
6.2.4.2.3.2. Meshing in OpenFOAM......Page 371
6.2.4.2.4. Physical modeling considerations......Page 372
6.2.4.2.6. Global control......Page 373
6.2.4.2.7. Geometrical macroscopic simplifications......Page 374
6.2.4.2.9. Porous media approach in the core......Page 375
6.2.4.2.10. Porous media approach in the primary heat exchangers......Page 377
6.2.4.3.1. General flow field......Page 378
6.2.4.4. Closing thoughts......Page 382
References......Page 383
7.1.1. Modeling scales in reactor thermal-hydraulics......Page 386
7.1.2. Interactions between scales......Page 387
7.1.3. Simulating multi-scale phenomena......Page 389
7.2.1. Domain decomposition versus domain overlapping......Page 391
7.2.2. Coupling at hydraulic boundaries......Page 393
7.2.3. Coupling at thermal boundaries......Page 396
7.2.4. Time schemes and internal iterations......Page 398
7.2.5. Implementation considerations......Page 399
7.3. Development and validation of multi-scale approaches......Page 400
7.3.2. Small and intermediate-scale validation......Page 401
7.3.3. Large-scale and integral validation......Page 403
References......Page 406
8.1. Introduction......Page 408
8.2. Safety authorities requirements......Page 409
8.3.1. Functional tests......Page 412
8.4. Validation......Page 413
8.4.1. PIRT (list of cases)......Page 415
8.4.2. Choice of an appropriate computational scheme......Page 416
8.4.4. Experimental database for validation......Page 417
8.4.5. The validation process......Page 418
8.4.6. Coverage matrix......Page 421
8.5.1. Uncertainty analysis......Page 422
8.5.2. Sensitivity analysis......Page 424
8.5.3. Segregated treatment of aleatory and epistemic variables......Page 425
8.5.5. Tools for uncertainty and sensitivity analysis......Page 426
8.7. Conclusion......Page 428
References......Page 429
9.1. Introduction......Page 432
9.2. Preprocessing......Page 435
9.3. Simulation......Page 438
9.4. Turbulence......Page 439
9.5. Postprocessing......Page 441
References......Page 442
10.1. Conclusions......Page 446
10.2. Outlook......Page 448
Index......Page 450
Back Cover......Page 464

Citation preview

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

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Woodhead Publishing Series in Energy

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors Edited by

Ferry Roelofs NRG, Research and Innovation EU H2020 SESAME Project Proposal Manager and Vice Chair of the Project Management Board

An imprint of Elsevier

Woodhead Publishing is an imprint of Elsevier The Officers’ Mess Business Centre, Royston Road, Duxford, CB22 4QH, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom Copyright © 2019 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein).

Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-08-101980-1 (print) ISBN: 978-0-08-101981-8 (online) For information on all Woodhead publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Joe Hayton Acquisition Editor: Maria Convey Editorial Project Manager: John Leonard Production Project Manager: Swapna Srinivasan Cover Designer: Christian J. Bilbow Typeset by SPi Global, India This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 654935 The information provided by the authors reflects the authors’ view. The European Commission is not responsible for any use that may be made of the information it contains

Contents

Contributors Foreword Preface Nomenclature 1

2

3

Introduction to liquid metal cooled reactors F. Roelofs 1.1 Nuclear energy and fast reactors 1.2 Liquid metal reactor design 1.3 Short history of liquid metal reactors 1.4 Benefits and drawbacks of liquid metals as coolants 1.5 European liquid metal reactor designs 1.6 Guidance References

xi xv xvii xix 1 1 2 2 4 5 14 15

Thermal-hydraulic challenges in liquid-metal-cooled reactors F. Roelofs, A. Gerschenfeld, M. Tarantino, K. Van Tichelen, W. D. Pointer 2.1 Introduction 2.2 Identification 2.3 Categorization 2.4 Thermal hydraulic challenges References Further reading

17

Thermal-hydraulic experiments with liquid metals—Introduction J. Pacio

45

3.1

Rod bundle and pool-type experiments in water serving liquid metal reactors M. Rohde, P. Planquart, C. Spaccapaniccia, F. Bertocchi 3.1.1 Introduction 3.1.2 Scaling and theory 3.1.3 Fuel bundle experiments 3.1.4 Pool-type experiments 3.1.5 Conclusions

17 17 19 19 39 43

49 49 50 65 71 79

vi

Contents

3.2

3.3

3.4

3.5

References Further reading

79 82

Design of experimental liquid-metal facilities M. Tarantino, I. Di Piazza, D. Martelli, D. Rozzia, R. Marinari, A. Pesetti, P. Lorusso 3.2.1 Introduction 3.2.2 HLM large pool design 3.2.3 Gas enhanced circulation 3.2.4 Core simulator design 3.2.5 Steam generator design 3.2.6 Test section pressure drop 3.2.7 Final remarks References

83

83 86 88 88 94 101 103 104

Construction of experimental liquid-metal facilities J. Pacio, M. Daubner, F. Fellmoser, W. Hering, € W. Jager, R. Stieglitz, T. Wetzel 3.3.1 Introduction 3.3.2 Thermo-hydraulic loop facilities 3.3.3 Thermo-hydraulic test sections 3.3.4 Conclusions References

107

Operational aspects of experimental liquid metal facilities G. Kennedy, I. Di Piazza, S. Bassini 3.4.1 Preoxidation 3.4.2 LBE melting and first time filling 3.4.3 Gas conditioning sequence (inerting) 3.4.4 Preheating 3.4.5 LBE filling 3.4.6 Pump startup and shutdown 3.4.7 Cooling 3.4.8 Draining 3.4.9 General notes and precautions during operation 3.4.10 Cleaning of the facility/test section 3.4.11 Summary References

127

Measurement techniques for liquid metal based nuclear coolants T. Wondrak, S. Franke, N. Krauter, S. Eckert 3.5.1 Introduction 3.5.2 Ultrasound-based methods 3.5.3 Inductive measurement techniques 3.5.4 Conclusions References

107 111 118 123 124

129 130 131 132 132 134 135 135 137 142 144 145 147 147 148 151 154 154

Contents

4

5

6

vii

System thermal hydraulics for liquid metals N. Forgione, D. Castelliti, A. Gerschenfeld, M. Polidori, A. Del Nevo, R. Hu 4.1 Convective heat transfer with liquid metals 4.2 Hydrodynamic model for STH codes 4.3 Thermodynamic properties for the liquid metals to be implemented in a STH code 4.4 RELAP5/Mod3.3 modified code and application 4.5 Other STH codes used in the SESAME project References Further reading

157

Subchannel analysis for LMR X. Cheng 5.1 Introduction 5.2 SCTH analysis References Further reading

185

CFD—Introduction F. Roelofs, A. Shams 6.1 Direct numerical simulation 6.2 Large-eddy simulation 6.3 Reynolds-averaged Navier Stokes equations 6.4 Reduced resolution RANS 6.5 Low-resolution CFD References

213 213 214 215 217 217 217

6.1.1

219

6.1.2

Direct numerical simulations for liquid metal applications I. Tiselj, E. Stalio, D. Angeli, J. Oder 6.1.1.1 Introduction 6.1.1.2 Direct numerical simulation techniques 6.1.1.3 Boundary and initial conditions 6.1.1.4 Results: Channel flow 6.1.1.5 Results: Nonplanar geometries 6.1.1.6 Conclusions References

157 162 165 168 180 183 184

186 191 210 211

219 224 227 230 236 240 241

Large-eddy simulation: Application to liquid metal fluid flow and heat transfer 245 Y. Bartosiewicz, M. Duponcheel 6.1.2.1 Introduction 245 6.1.2.2 LES equations 248 6.1.2.3 Subgrid-scale models 253 6.1.2.4 Application 262 6.1.2.5 Concluding remarks 269 References 270

viii

Contents

6.2.1

6.2.2

6.2.3

6.2.4

7

Turbulent heat transport A. Shams 6.2.1.1 Understanding the peculiarities of heat transfer modeling in turbulent liquid metal flows 6.2.1.2 Modeling of turbulent heat transfer 6.2.1.3 Summary References Further reading Simulation of flow-induced vibrations in tube bundles using URANS J. De Ridder, L. De Moerloose, K. Van Tichelen, J. Vierendeels, J. Degroote 6.2.2.1 Introduction 6.2.2.2 Instability-induced vibration: Vortex-induced vibrations by axial flow in a bundle of tubes 6.2.2.3 Movement-induced vibration 6.2.2.4 Conclusions Acknowledgment References

273 275 278 288 289 292 293

293 294 301 308 308 309

Core thermal hydraulics F. Roelofs, I. Di Piazza, E. Merzari 6.2.3.1 Introduction 6.2.3.2 Experiments and correlations 6.2.3.3 Simulation of operational behavior 6.2.3.4 Simulation of accidental conditions 6.2.3.5 CFD and chemical reactions simulation 6.2.3.6 Summary References Further reading

311

(U)RANS pool thermal hydraulics L. Koloszar, V. Moreau 6.2.4.1 Identification of the relevant physics 6.2.4.2 MYRRHA operating condition case as the quintessence of the pool modeling application 6.2.4.3 A look behind the curtains 6.2.4.4 Closing thoughts References

341

Multi-scale simulations of liquid metal systems A. Gerschenfeld, N. Forgione, J. Thomas 7.1 Introduction and motivation 7.2 Multi-scale coupling algorithms 7.3 Development and validation of multi-scale approaches 7.4 Conclusion References

311 313 315 326 332 333 335 340

342 343 353 357 358 361 361 366 375 381 381

Contents

8

9

10

ix

Verification and validation and uncertainty quantification C. Geffray, A. Gerschenfeld, P. Kudinov, I. Mickus, € D. Grishchenko, D. Pointer M. Jeltsov, K. Ko€op, 8.1 Introduction 8.2 Safety authorities requirements 8.3 Verification 8.4 Validation 8.5 Techniques for uncertainty and sensitivity analysis 8.6 Extension to coupled codes 8.7 Conclusion References

383

Best practice guidelines for nuclear liquid metal CFD F. Roelofs, P. Planquart, L. Koloszar 9.1 Introduction 9.2 Preprocessing 9.3 Simulation 9.4 Turbulence 9.5 Postprocessing 9.6 Summary References

407

Conclusions and outlook F. Roelofs, P. Planquart 10.1 Conclusions 10.2 Outlook

421

Index

383 384 387 388 397 403 403 404

407 410 413 414 416 417 417

421 423 425

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Contributors

D. Angeli Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, Reggio Emilia, Italy Y. Bartosiewicz Institute of Mechanics, Materials and Civil Engineering, UCLouvain, Louvain-la-Neuve, Belgium S. Bassini SCK CEN, Mol, Belgium F. Bertocchi Department of Radiation Science and Technology, Delft University of Technology, Delft, The Netherlands

D. Castelliti Commissariat a` l’Energie Atomique et aux Energies Alternatives (CEA), Saclay, France X. Cheng KIT, Karlsruhe, Germany W. D. Pointer Oak Ridge National Laboratory, Oak Ridge, TN, United States M. Daubner Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany L. De Moerloose Department of Flow, Heat and Combustion Mechanics, Ghent University, Ghent, Belgium J. De Ridder Department of Flow, Heat and Combustion Mechanics, Ghent University, Ghent, Belgium J. Degroote Department of Flow, Heat and Combustion Mechanics, Ghent University, Ghent, Belgium A. Del Nevo Agenzia nazionale per le nuove tecnologie, l’energia e lo sviluppo economico (ENEA), FSN-ING-PAN, Camugnano, Italy I. Di Piazza Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy; ENEA, Kista, Stockholm, Sweden; SCK CEN, Mol, Belgium M. Duponcheel Institute of Mechanics, Materials and Civil Engineering, UCLouvain, Louvain-la-Neuve, Belgium

xii

Contributors

S. Eckert Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany F. Fellmoser Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany N. Forgione Dipartimento di Ingegneria Civile e Industriale, Universita` di Pisa, Pisa, Italy; DEN-Service de Thermohydraulique et de M
ecanique des Fluides (STMF), CEA, Universit
e Paris-Saclay, Gif-sur-Yvette, France S. Franke Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany C. Geffray DEN-Service de Thermohydraulique et de M
ecanique des Fluides (STMF), CEA, Universit
e Paris-Saclay, F-91191, Gif-sur-Yvette, France A. Gerschenfeld CEA, Gif-sur-Yvette, France; Advanced Nuclear Systems (ANS) Institute, Nuclear System Physics Expertise Group SCK.CEN, Mol, Belgium; DENService de Thermohydraulique et de M
ecanique des Fluides (STMF), CEA, Universit
e Paris-Saclay, Gif-sur-Yvette, France D. Grishchenko Division of Nuclear Engineering, Royal Institute of Technology, Stockholm, Sweden W. Hering Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany R. Hu Nuclear Science and Engineering Division, Argonne National Laboratory, Lemont, IL, United States W. J€ ager Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany M. Jeltsov Division of Nuclear Engineering, Royal Institute of Technology, Stockholm, Sweden G. Kennedy SCK CEN, Mol, Belgium L. Koloszar von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium; Department of Energy and Environment, Center for Advanced Studies, Research and Development in Sardinia (CRS4), Pula, CA, Italy K. K€ o€ op Division of Nuclear Engineering, Royal Institute of Technology, Stockholm, Sweden N. Krauter Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany

Contributors

xiii

P. Kudinov Division of Nuclear Engineering, Royal Institute of Technology, Stockholm, Sweden P. Lorusso Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy R. Marinari Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy D. Martelli Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy E. Merzari Argonne National Laboratory, Lemont, IL, United States I. Mickus Division of Nuclear Engineering, Royal Institute of Technology, Stockholm, Sweden V. Moreau Von Karman Institute for Fluid Dynamic (VKI), Sint-Genesius-Rode, Belgium; Department of Energy and Environment, Center for Advanced Studies, Research and Development in Sardinia (CRS4), Pula, CA, Italy J. Oder Reactor Engineering Division, “Jozˇef Stefan” Institute, Ljubljana, Slovenia J. Pacio Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany A. Pesetti Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy P. Planquart Environmental and Applied Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium D. Pointer Oak Ridge National Laboratory, Oak Ridge, TN, United States M. Polidori Agenzia nazionale per le nuove tecnologie, l’energia e lo sviluppo economico (ENEA), FPN-SICNUC-SIN, Bologna, Italy F. Roelofs Nuclear Research & Consultancy Group (NRG), Petten, The Netherlands M. Rohde Department of Radiation Science and Technology, Delft University of Technology, Delft, The Netherlands D. Rozzia Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy A. Shams Nuclear Research & consultancy Group (NRG), Petten, The Netherlands

xiv

Contributors

C. Spaccapaniccia Environmental and Applied Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium E. Stalio Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Modena, Italy R. Stieglitz Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany M. Tarantino ENEA, Kista, Stockholm, Sweden; Experimental Engineering Division, Department for Fusion and Technologies for Nuclear Safety and Security, ENEA, Brasimone (Bo), Italy J. Thomas DEN-Service de Thermohydraulique et de M
ecanique des Fluides (STMF), CEA, Universit
e Paris-Saclay, Gif-sur-Yvette, France I. Tiselj Reactor Engineering Division, “Jozˇef Stefan” Institute, Ljubljana, Slovenia K. Van Tichelen SCK CEN; Belgian Nuclear Research Centre, Mol, Belgium l

J. Vierendeels Department of Flow, Heat and Combustion Mechanics, Ghent University, Ghent, Belgium T. Wetzel Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany T. Wondrak Department of Magnetohydrodynamics, Institute of Fluid Dynamics, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany

Foreword

The European Atomic Energy Community (EU/Euratom) Research and Training framework programs are benefitting from a consistent success in pursuing excellence in research and facilitating pan-European collaborative efforts in nuclear fission and across a broad range of nuclear science and technologies. For the long-term sustainable development of nuclear energy, innovative nuclear systems such as Gen-IV reactors and transmutation systems need to be developed for meeting future energy and climate challenges on earth. Thermal hydraulics is recognized as a key scientific challenge, and it is an opportunity for the development of innovative reactor systems. From 2015, EU/Euratom cofounded the project H2020-SESAME (thermal hydraulic Simulations and Experiments for the Safety Assessment of Metal-cooled reactors) following a successful open call for proposals. SESAME not only gathers 23 partners from 9 European countries (The Netherlands, Belgium, France, Germany, Italy, Slovenia, Czech Republic, Sweden, and Switzerland) but also benefits from international cooperation with US DoE laboratories (Argonne National Laboratory (ANL) and Oak Ridge National Laboratory (ORNL)) under a EU/Euratom-DoE framework agreement supporting the development of nuclear energy research including innovative reactor concepts (I-NERI). The consortium has a long-standing experience in the field of nuclear technology and nuclear thermal hydraulics; most of them have successfully cooperated in related EU/Euratom projects; pan-European experience and knowledge is being further capitalized together with modeling, simulation, validation, and infrastructure capabilities from (a) previous or on-going projects including H2020-ESNII +, FP7-ADRIANA, CP-ESFR, LEADER, MAXSIMA, SEARCH, THINS, CDT and HeLiMNet, FP6EUROTRANS, EISOFAR, and ELSY and (b) GIF 2009 R&D Outlook and GIF 2013 Technology Roadmap of the Generation IV international Forum, IAEA 2012 status updates on fast reactors, IAEA 2014 summary workshop report on priorities in Modeling and Simulation for Fast Neutron Systems, OECD/NEA 2011 TAREF report on infrastructures and R&D needs for sodium fast reactor safety, SNETP 2013 Strategic Research and Innovation agenda, 2010 European Sustainable Nuclear Industrial Initiative (ESNII), and 2015 Deployment strategy. SESAME supports mainly the development of liquid-metal reactor technologies identified within ESNII (SFR-ASTRID, LFR-ALFRED, and ADS MYRRHA) by addressing their prenormative, fundamental, and safety-related challenges being (a) the development and validation of advanced numerical approaches for the design and safety evaluation of advanced reactors; (b) the achievement of a new or extended validation base by creating new reference data;

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Foreword

(c) the establishment of best practice guidelines, verification and validation methodologies, and uncertainty quantification methods for liquid-metal fast reactor thermal hydraulics.

The fundamental and generic nature of the SESAME project also provides results of relevance for the safety assessment of contemporary light-water reactors. By extending its knowledge base, it will contribute to the development of robust safety policies in European Member States and further. SESAME allows enhancing and further developing European experimental facilities and numerical tools. Finally, SESAME also closely interacts with the European liquid-metal-cooled reactor design teams, who actively advised on the content of the project. As the prime end-users, the results stemming from the project should ensure that their innovative reactor designs reach the highest safety standards using frontier scientific developments. Gen-IV innovative nuclear reactors are also very attractive to young students, scientists, and engineers engaging in a nuclear career thanks to the related scientific challenges characterized by higher operating temperatures and studies on hightemperature materials, corrosion effects, heavy liquid-metal thermodynamics, innovative heat exchangers, fast neutron fluxes for both breeding, and enhanced burning of long-lived wastes. Development, fabrication, and testing of entirely new nuclear fuels, advanced fuel cycles, and fuel recycling concepts including partitioning and transmutation are required, all promoting excellent topical opportunities for internships or PhD studies within R&D laboratories. Beyond the obvious educational merit for young engineers investing on average into additional 2 years’ fast reactor studies, scientists and engineers would also have a broader expertise when working on enhanced LWR technology and crosscutting safety, core physics, engineering, and material areas. Also, a successful Gen-IV design team would highly benefit from “systemic” and “interdisciplinary” specialists in the various scientific disciplines involved such as neutronics, thermal hydraulics, materials science, and coolant technologies together with “assembling” engineers capable to perform optimized integrations of all topical results into “realistic” reactor components and “most efficient” balance of plants. EU/Euratom Education, Training, Skills and Competences sustainable objectives are fulfilled as national and European “technological schools” are today evolving successfully toward “international training platforms” (or centers of excellence), for example, in France, Belgium, Germany, Italy, Sweden, the Netherlands, or the United Kingdom. All reviewed papers published and this textbook are the result of a common effort of all partners involved, and it is very appreciated from the entire scientific community. I would like to express my gratitude on behalf of EU/Euratom to all of them. Roger Garbil, Scientific/Technical Project/Policy Officer European Commission, Euratom—Nuclear Fission Energy

Preface

It has always been in the back of my mind Dreaming about going to the corners of time I always wanted to fly in strange machines “Strange Machines” (the Gathering)

In 2012, we embarked on a trip that finally led to the compilation of this textbook. We took the initiative to set up a new European collaborative project in the frame of liquid-metal-cooled nuclear reactors. This project is called “thermal-hydraulic Simulations and Experiments for the Safety Assessment of MEtal-cooled reactors” (SESAME). One of the main outcomes of this project should be a textbook to support students, young professionals, and other people interested in the topic of nuclear liquid-metal thermal hydraulics. This textbook is the resulting team effort of a collection of experts in the field explaining the state of the art. In addition, the challenges we are still facing in our field are described. We hope that this textbook will be helpful to you, as a reader, and we hope that you will pass our and your knowledge along to colleagues and other international experts. Before you start reading the book, let me take the opportunity to acknowledge the people who played an essential role in the compilation of this book. First of all, many thanks to the European Commission who funded the SESAME collaborative project in 2015. Special thanks to Roger Garbil of the European Commission who always supported us in our endeavors. Of course, I should thank all the participants in the SESAME project; these are too numerous to mention here, but you know who you are. You made this all happen. You joined our “strange machine” and made this project a very special one. You joined on special events like the memorable concert of the Italian heavy (liquid) metal band Blue Hour Ghosts in the reactor hall in Brasimone. There is also a sad note. Unfortunately, just before finishing the first draft of this book, we received the message that our SESAME colleague and great scientist, Prof. Jan Vierendeels, suddenly passed away. He will always be in our memories as the unique person he was. Many thanks to the SESAME project coordination team existing of Afaque Shams, Abdalla Batta, Vincent Moreau, Ivan Di Piazza, Antoine Gerschenfeld, and Philippe Planquart under the excellent lead of Mariano Tarantino. Finally, many thanks also to our transatlantic collaborators who enrich our work by adding their own expertise and contributions. Special thanks to Elia Merzari and Dave Pointer being the main representatives of our US colleagues. Personal thanks go out to a very special colleague. She not only typically shares my ideas but also constructively expresses her own opinion and vision. Katrien Van

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Preface

Tichelen, I like to thank you for all the years of being in this field together, working out our ambitious plans, flying in “strange machines,” living our dreams, drinking “one more” beer, and just being friends. Finally, it would not have been possible to realize this textbook without the people supporting me at home. Thanks a lot to my parents who have always encouraged me to take my own decisions, to follow my own path, and supported me in all my endeavors. Last but certainly not least, thanks to my wife Susanna and my two boys Casper and Jorim, who have to cope with me at home, whether I am jolly, stressed, busy, or tired. They are always there to support me. You know I will always love you. And like no other, you know it has always been in the back of my mind, dreaming about going to the corners of time and wanting to fly in strange machines. Ferry Roelofs

Nomenclature

ACB ADRIANA ADS Ag AHFM AHP Al ALFRED ALINA ALIP AP ASCHLIM ASTRID ATHLET BC BFS BN BOL BOR BPG BR BREST BWR CAD CATHARE CCD CDA CDF CDT CEFR CFD CFL CGCFD CHEOPE CIFT CIRCE CLEAR

above core barrel ADvanced Reactor Initiative and Network Arrangement accelerator-driven system silver algebraic heat flux model analytic hierarchy process aluminum Advanced Lead Fast Reactor European Demonstrator Karlsruhe experiments with Li and Na free jet annular linear induction pump anisotropic porosity assessment of computational fluid dynamics codes for heavy liquid metals Advanced Sodium Technological Reactor for Industrial Demonstration Analysis of THermal hydraulics of LEaks and Transients boundary condition backward-facing step Bystrie Neytrony (Russian for fast neutron) beginning of life Bystrij Opytnyj Reaktor (Russian) best practice guidelines Bystrie Reaktor (Russian) Russian lead-cooled fast reactor design boiling water reactor computer-aided design code for analysis of thermal-hydraulics during an accident of reactor and safety evaluation charged-coupled device core disruptive accident cumulative density function central design team Chinese experimental fast reactor computational fluid dynamics Courant-Friedrichs-Lewy coarse-grid-CFD CHEmistry and OPErations contactless inductive flow tomography CIRColazione Eutettico (Italian) China LEAd-based research reactor

xx

CMOS CO2 COCO COLCHIX COMPLOT CORRIDA CPU Cr CRAFT CRBRP CS CSM Cu DEM DES DFR DHR DITEFA DNS DOE EBR EDM EFR EIE EISOFAR ELFR ELSY EM EOS ESCAPE ESFR ESFR-SMART ESNII ESNII + Eu EUROTRANS F2S FALCON FBG FBTR FEA FEP FIV FLIP FFT FFTF FPS

Nomenclature

complementary metal oxide semiconductor carbon dioxide water model of EFR cold pool water model of EFR hot pool COMponent LOop Testing corrosion in dynamic alloys central processing unit chromium Corrosion Research for Advanced Fast reactor Technologies Clinch River breeder reactor project core simulator computational structural mechanics copper discrete element method detached eddy simulation Dounreay Fast Reactor decay heat removal DIvertor TEst FAcility direct numerical simulation Department of Energy experimental breeder reactor eddy diffusivity model European fast reactor extraneously induced excitations Roadmap for a European Innovative SOdium-cooled FAst Reactor European Lead Fast Reactor European Lead-cooled SYstem electromagnetic equation of state European SCAled Pool Experiment European Sodium Fast Reactor European Sodium Fast Reactor Safety Measures Assessment and Research Tools European Sustainable Nuclear Industrial Initiative preparing ESNII for HORIZON 2020 Euler number European research program for transmutation of high level nuclear waste in an ADS fluid to solid Fostering ALfred CONstruction fiber Bragg gratings fast breeder test reactor finite element analysis fluorinated poly(ethylene-propylene) flow-induced vibration flat linear induction pump fast Fourier transform fast flux test facility fuel pin simulator/functional performance specification

Nomenclature

FSI Gen GGDH GIF Gr H2O HeLiMNet Hg HLM HPC HTR HX IAEA IET IIE IQN-ILS IT IVMR IVR JESSICA JSFR KALLA KASOLA KNK LAMPRE LBE LDA LDV LEADER LECOR LES LFR LFV LIF LIMMCAST LM LMR LMFR LOCA LWR MAXSIMA MCP MEKKA MICAS Mo MOX MSR MYRRHA

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fluid-structure interaction generation generalized gradient diffusion hypothesis Generation IV International Forum Grash of number water heavy liquid metal network mercury heavy liquid metal high-performance computing high-temperature reactor heat exchanger International Atomic Energy Agency integral effect test instability-induced excitations interface quasi-Newton with inverse Jacobian from a least squares model integral test in-vessel melt retention in-vessel retention water model of EFR hot pool Japanese sodium fast reactor KArlsruhe Liquid metal LAboratory Karlsruhe Sodium Laboratory Kompakte Natriumgek€uhlte Kernreaktoranlage Karlsruhe (German) Los Alamos Molten Plutonium Reactor Experiment lead-bismuth eutectic laser Doppler anemometry laser Doppler velocimetry Lead-cooled European Advanced DEmonstration Reactor LEad CORrosion large eddy simulation lead-cooled fast reactor Lorentz force velocimetry laser-induced fluorescence Liquid Metal Model for Continuous CASTing liquid metal liquid-metal reactor liquid-metal fast reactor loss-of-coolant accident light-water reactor Methodology, Analysis, and eXperiments for the Safety In MYRRHA Assessment mechanical pump Magnetohydrodynamic Experiments in NaK Karlsruhe water model of ASTRID hot pool molybdenum mixed oxide molten salt reactor Multi-purpose hYbrid Research Reactor for High-tech Applications

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MYRRHABelle MYRTE Na NaK NACIE NCL NDN NEA NEPTUN Nd Ni NPSH Nu OECD PARCS Pb PbBi PbO PCCM PDF Pe PEC PFBR PFR PID PIRT PIV PLACE PLANDTL PLC PMMA Pr Prt PSD PTV PWR QDNS R&D RAMONA RANS RBC Re RELAP Ri RIM RSM RVACS RVMS S2F

Nomenclature

MYRRHA Basic sEt-up for Liquid Flow Experiments MYRRHA Research and Transmutation Endeavour sodium sodium potassium NAtural CIrculation Experiment natural convection loop nondimensional number Nuclear Energy Agency water model of EFR neodymium nickel net positive suction head Nusselt number Organization for Economic Cooperation and Development Purdue Advanced Reactor Core Simulator lead lead bismuth lead oxide predictive capability maturity model probability density function Peclet number Prova Elementi Combustibile (Italian) Prototype Fast Breeder Reactor prototype fast reactor proportional integral derivative process identification and ranking table particle image velocimetry PLAnt for Cleaning of large Equipment plant dynamics test loop programmable logic controller poly(methyl methacrylate) Prandtl number turbulent Prandtl number power spectral density particle tracking velocimetry pressurized water reactor quasi-DNS research and development water model of EFR Reynold-averaged Navier-Stokes Rayleigh-Benard convection Reynolds number Reactor Excursion and Leak Analysis Program Richardson number refractive index matching Reynolds stress model reactor vessel auxiliary cooling system regularized variational multiscale solid to fluid

Nomenclature

SAMRAT SCTH SEALER SEARCH SEFOR SESAME SET SFR SGDH SGS SGTR SNE-TP SNR SOLTEC SPECTRA SRQ SST St STH SVBR Ta TC TEC-FM TELEMAT THEADES THESYS THINS TMBF UDV ULOF UPS UQ URANS US UTTT VELLA VOF VMS V&V VVUQ W WALE Xe YAG YLF

xxiii

ScAled Model of Reactor Assembly for Thermal hydraulic studies subchannel thermal hydraulics Swedish Advanced Lead-cooled Reactor Safe ExploitAtion Related CHemistry for HLM reactors Southwest Experimental Fast Oxide Reactor thermal hydraulic simulations and experiments for the safety assessment of metal-cooled reactors separate effect test sodium-cooled fast reactor simple gradient diffusion hypothesis sub-grid scale steam generator tube rupture Sustainable Nuclear Energy Technology Platform Schneller Natriumgek€uhlter Reaktor (German) SOdium Loop for TEst materials and Corrosion facilities Sophisticated Plant Evaluation Code for Thermal-hydraulic Response Assessment system response quantity shear stress transport Strouhal number system thermal hydraulics Svintsovo-Vismutovyi Bystryi Reaktor (Russian) tantalum thermocouple transient eddy-current flow meter Test Loop for Lead Material testing Thermal-hydraulics and ADS Design Technology for Heavy Liquid Metals Systems Thermal Hydraulics of Innovative Nuclear Systems turbulence model for buoyant flows ultrasound Doppler velocimetry unprotected loss of flow uninterruptible power supply uncertainty quantification unsteady RANS The United States ultrasound transit-time technique Virtual European Lead LAboratory volume of fluid variational multiScale verification and validation verification, validation and uncertainty quantification tungsten wall-adapting local eddy viscosity xenon yttrium aluminum garnet yttrium lithium fluoride

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Introduction to liquid metal cooled reactors

1

F. Roelofs Nuclear Research & Consultancy Group, Petten, The Netherlands

1.1

Nuclear energy and fast reactors

Nuclear energy today is one of the most important sources of electricity worldwide with a small ecological footprint and low carbon emissions. Nuclear reactors use uranium (or alternatively thorium) as natural resource to produce energy. The identified resources and additional exploitable resources of uranium are sufficient to support continued use and significant growth of nuclear energy production for well over 300 years. On top of that, there is proof that uranium can be “mined” from seawater. Today, this is economically not viable, but if natural resources get scarce and more research is put into the economic efficiency of uranium extraction from seawater, in time, this will become economically viable. However, the amount of uranium effectively used in the widely spread watercooled nuclear reactors can be improved a lot: in these thermal reactors, only a very small amount of the uranium is actually split into fission products and producing energy. By switching to fast reactors, uranium can be used much more efficiently. This requires switching to different, less common, types of coolant. Already since the dawn of nuclear energy production, this was recognized and investigated. The first reactor to produce electricity, the Experimental Breeder Reactor I (EBR-I), was in fact such a fast reactor. It was not cooled by water but by a mixture of sodium and potassium. At the time, the known reserves of uranium were limited, which gave a strong incentive to search for reactors that could use the uranium in an efficient way. These reactors are often referred to as “breeding” reactors, since in the reactor not only uranium is split and energy is produced but also plutonium is formed from nonfissile uranium isotopes, which as such again can be split and produce energy. By changing the design of the reactor core, the same reactor can be used to transmute long-lived radioactive elements into fission products that are much less long-lived and less radiotoxic. In this way, the amount and radiotoxicity of nuclear waste can be significantly reduced. History taught us that the water-cooled reactors matured earlier and succeeded in conquering the nuclear energy production market. Other types of reactors, among which the fast reactors, did not get a chance to mature that rapidly, even though quite a few fast reactors were constructed and operated as will be explained later in this chapter. As fast reactors operate with fast neutrons inducing fission reactions, they cannot be cooled by water that would slow down (or moderate) the neutrons. Alternatively, another coolant has to be used. Liquid metals form a category of promising Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors. https://doi.org/10.1016/B978-0-08-101980-1.00001-6 Copyright © 2019 Elsevier Ltd. All rights reserved.

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Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

coolants for such fast reactors. Mostly, liquid sodium has been applied, for its great heat transport and neutronic characteristics. However, sodium also has its drawbacks, especially stemming from its chemical reactivity with air and water. Other liquid metals, such as lead or lead-bismuth eutectic, do not react violently with air and water and are also considered for that reason.

1.2

Liquid metal reactor design

Nuclear reactor design is highly multidisciplinary. In each reactor, disciplines like fuel and material science, reactor physics, thermal hydraulics, and structural mechanics interact. This makes nuclear engineering one of the most demanding professions. There may be only a few people who have a thorough understanding covering all these disciplines. Most engineers specialize in one or two of the disciplines allowing them to obtain a deep understanding. Designing a reactor and performing safety assessments of reactors therefore remain a team effort and strongly depend on the interaction between people and the integration by the few engineers having a basic understanding of all involved disciplines. This book puts the focus on the specialized topic of liquidmetal thermal hydraulics for advanced (fast) nuclear reactors, a discipline that is essential for liquid-metal fast reactor design and the subsequent safety assessment of the design and the reactor as built.

1.3

Short history of liquid metal reactors

For an elaborate overview on the liquid-metal fast reactor designs constructed and operated all over the world, excellent textbooks are available. In IAEA (2012, 2013), such overviews can be found. More recently, Pioro (2016) provided an overview of the most recent developments not only focusing on liquid-metal fast reactors but also covering a wider range of advanced nuclear reactor designs. Fig. 1.1 sketches the history of liquid-metal fast reactors worldwide. Even before the EBR-I, which was the sodium-potassium-cooled first nuclear reactor to produce electricity, there was the experimental mercury-cooled Clementine reactor in the United States. As can be seen in the figure, after EBR-I, the United States and the rest of the world mostly switched to the use of pure sodium. The United States operated sodium-cooled experimental and prototype reactors until the early 1990s. Today, the United States still has a limited active program on liquid-metal-cooled reactors but has no such reactor in operation. In Europe, the development of liquid-metal-cooled reactors started in the early 1960s resulting in experimental reactors being constructed in France, the United Kingdom, Italy, and Germany. In France, after successfully operating the experimental Rapsodie reactor, the prototype reactor Phenix was constructed and operated, followed by the construction and operation of the commercial Superphenix power plant. The Phenix reactor successfully provided electricity to the grid. The reactor was taken from the grid in 2009, after which for 1 year several important safety tests were performed providing unique data to future liquid-metal fast reactor designers and

Introduction to liquid metal cooled reactors

3

Fig. 1.1 History of liquid-metal fast reactors worldwide.

safety engineers. In parallel, the United Kingdom operated the experimental DFR and prototype PFR sodium-cooled reactors. Germany operated the experimental KNK-II reactor and constructed in collaboration with neighboring countries Belgium and the Netherlands the prototype SNR-300 sodium-cooled reactor that was eventually never put into operation for political reasons. Similarly, the Italian experimental PEC reactor was constructed but never put into operation after Italy decided to phase out nuclear energy production after the events in Chernobyl in the mid-1980s. That was also the time when in Europe the forces joined and the design of the European fast reactor (EFR) began that was brought to a quite advanced design stage before the project was abandoned in the mid-1990s. Nowadays, several countries in Europe are involved in the design of future liquid-metal-cooled fast reactors. The most important ones will be highlighted later in this chapter. Just a few years after the United States, also Russia started the development of a fast reactor program. They constructed and operated the experimental BR5/10 reactor and later the experimental BOR60 reactor that is still operational today. In the 1970s, Russia constructed the prototype BN350 reactor followed by the somewhat larger prototype BN600 reactor. Recently, in 2015, Russia started operating the commercial BN800 power plant, and they are designing now the even larger BN1200 power plant. All these reactors are sodium cooled. Russia is the only country with operational experience concerning lead-bismuth-cooled reactors that they used in their military submarines from the 1970s to the 1990s.

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Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

In Asia, the development of nuclear power production started later. Japan started the operation of the experimental Joyo sodium-cooled reactor in the mid-1970s. Later, they constructed and operated in phases the prototype Monju reactor. However, due to some technical and societal issues, recently, it was decided to stop this reactor and also limit further developments. China only recently embarked on the operation of liquidmetal-cooled reactors with the experimental CEFR. They have ambitious plans to further develop their sodium and their lead and lead-bismuth experience with several designs for experimental and prototype reactors. Finally, India, which for a long time was more or less isolated from the rest of the world with respect to nuclear developments, started considering fast reactors for the efficient use of their scarce uranium resources. They constructed and operated the experimental sodium-cooled FBTR since the 1990s and are currently commissioning the PFBR sodium-cooled reactor.

1.4

Benefits and drawbacks of liquid metals as coolants

From a thermal hydraulic point of view, the use of liquid metals as coolants brings new challenges and the need for advanced tools compared with dealing with coolants like water and gas. The benefits and drawbacks of using liquid metals are listed and shortly described later. More elaborate explanations can be found, for example, in IAEA (2012) or in GIF (2002) or GIF (2014). The following benefits can be identified related to the application of liquid metal as a coolant in nuclear reactors: l

l

l

l

l

l

l

l

l

The neutronic characteristics of liquid metals are such that neutrons created by fission in the fuel are not moderated, and a sufficient amount of fast neutrons remains at disposal to keep the nuclear chain reaction going. Metals are liquid at the operating temperatures of the nuclear reactor with sufficient margin toward the evaporation point. Therefore, the system can be operated without pressurization in contrast to water-cooled reactors, and the reactors can be operated at low pressure. Liquid metals typically possess good heat transport characteristics and high heat capacity allowing efficient transport of heat generated in the core with relatively small systems and providing grace time in case of accident situations. The high density of liquid metals relaxes the conditions for establishing natural circulation cooling loops in accident situations. The high boiling point of liquid metals, at least above 850°C for sodium, mitigates issues with core voiding. For lead, the very high boiling point of about 1750°C practically prevents voiding in the core possibly leading to a clad failure, because the clad itself will have failed before the boiling point of lead is reached. A high efficiency for electricity production can be achieved by the application of liquid metal because of the relatively high operating temperatures that can be achieved. Compared with all other advanced nuclear reactor concepts, there is relatively large operating experience with liquid-metal-cooled reactors, especially with sodium-cooled reactors. The application of lead or lead-alloys as coolant allows integration of steam generators in the reactor vessel. For sodium alternative, secondary cooling options based on gas are being investigated. The heat transport characteristics of lead and lead-alloys allow large fuel rod pitches that result in low pressure drops and enable application of natural circulation.

Introduction to liquid metal cooled reactors l

l

5

The high density of lead may induce, depending on the type of fuel, that molten fuel floats and thus in the case of a fuel melt near the core outlet moves in the direction of lower or no power. A lead or lead-alloy reactor pool ensures a high self-shielding capacity.

As always, also in nuclear engineering, there is no free lunch. The following drawbacks can be identified related to the application of liquid metal as a coolant in nuclear reactors: l

l

l

l

l

l

l

The typical high mass of liquid-metal-cooled systems (especially lead- and lead-bismuthcooled systems) requires special measures for seismic events. Corrosion issues may be always present, but they increase especially at temperatures above 600°C. When operating temperatures above 600°C are envisaged, which should in principle be beneficial especially for lead and lead-alloys, new materials need to be developed to withstand the corrosion issues. In-service inspection in opaque coolant is significantly more difficult than in transparent coolants like water and gases as optical inspection methods cannot be applied. Apart from that, the high density and elevated operation temperature of liquid metals create higher forces on inspection tools that therefore need to be specially developed and tested. The high melting point of liquid metals requires preheaters and measures against solidification of the coolant in case of shutdown, both during normal operation and during accident situations. The high mass of lead and lead-alloys leads to erosion issues in the components of the primary cooling system. This limits the coolant speed in such systems below 2 m/s as a rule of thumb. The chemical reactivity of sodium with air and water requires a sealed coolant system and special measures to prevent (nuclear) consequences of such reactions. Typically, this involves multiple barriers between sodium and the environment. Also, it requires special care in the heat transfer from the primary sodium circuit toward the eventual energy conversion circuit. Mostly, an intermediate sodium loop is designed to prevent a chemical reaction between primary sodium and the water-steam loop of the energy conversion circuit. Obviously, this increases costs and at the same time leads to a loss of efficiency. Therefore, studies are ongoing to eliminate such an intermediate circuit. During irradiation of lead-bismuth, highly radiotoxic polonium is produced that should be confined at all times.

1.5

European liquid metal reactor designs

As illustrated before, worldwide, quite some effort has been put in the development of liquid-metal-cooled nuclear reactors. Ongoing developments are mostly related to design work of future liquid-metal-cooled reactors. The main projects that can be identified are the further development of the Russian sodium reactor line with the BN1200, a scaled-up version of the commercial BN800 reactor that was put into operation recently. Also in Russia, the lead technology is being pushed toward commercialization by the design of the lead-bismuth-cooled prototype SVBR small reactor and the lead-cooled larger prototype BREST reactor. In Japan, the design work on advanced reactors has been put to hold after the tsunami in 2011. However, in

6

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

China and India, design work progresses with follow-up prototypes in the line of the CEFR in China and the PFBR in India. China is also embracing the lead technology in the so-called CLEAR reactor line. The main design efforts in Europe are illustrated below.

1.5.1 ASTRID (Fig. 1.2) Fig. 1.2 ASTRID primary circuit internals (©CEA).

Full name: Designer: Reactor type: Electric capacity: Thermal capacity: Coolant: System pressure: System temperature: No. of safety trains: Emergency safety systems: Residual heat removal systems: Design status: New/distinguishing features:

Advanced Sodium Technology Reactor for Industrial Demonstration ASTRID Consortium (CEA, Framatome, JAEA, and MFBR) Sodium fast reactor 600 MW(e) 1500 MW(th) Sodium

> > > 0:01Pe > > ðCheng and TakÞ < 1000 < Pe  2000  

0:8  1:6 + 9  104 Pe 1:25 0:018Pe Prt ¼ > > > > 0:01Pe > > 2000 < Pe  6000 >

1:25 : 0:018Pe0:8  3:4

The influence of the Peclet number on the turbulent Prandtl number can be visually appreciated on Fig. 4.3, where Prt was reported as a function of the Peclet number for both the correlations previously mentioned.

4.1.2 Convective heat transfer correlations The convective heat transfer correlations for a liquid metal flowing inside a circular pipe can be derived analytically using one of the correlations that gives the turbulent Prandtl number (see, e.g., Taler, 2016), or it can be obtained experimentally, as in the case of well-known Lyon (1951) and Seban and Shimazaki (1950) correlations:

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Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Fig. 4.3 Turbulent Prandtl number as predicted by Aoki and Cheng and Tak correlations (Pr ¼ 0.02). Nu ¼ 7.0 + 0.025 Pe0.8 (Lyon, constant heat flux) Nu ¼ 5.0 + 0.025 Pe0.8 (Seban and Shimazaki, constant wall temperature)

In a fast reactor core, the liquid metal flows inside a complex array of fuel pins; therefore, one of the most important issues is the determination of the dependence of convective heat transfer coefficient from the Peclet number, the lattice geometry, the pitch-to-diameter (p/D) ratio, and the presence of spacer grids or wires. Many correlations are reported in literature, for example, the one developed by Ushakov et al. (1977) for the flow of liquid metal in a triangular lattice of heated rods and that of Zhukov et al. (2002) finalized to BREST lead-cooled reactor. An accurate review of the convective heat transfer correlations for liquid metals flowing in a bundle of cylindrical heated rods was performed by Mikityuk (2009); in this work, he proposed a new correlation valid for rod bundles without spacer grids and for both triangular and square lattice. More recently, El-Genk and Schriener (2017) performed a review of available experimental data and convective heat transfer correlations for parallel flow of alkali liquid metals and LBE eutectic in bundles, stating that the proposed convective heat transfer correlation found for alkali liquid metals may also be used for the LBE within an uncertainty of 20%. An important correlation developed for rod bundles is that of Kazimi and Carelli (1976), recently implemented in the RELAP5/3D code (2009). This correlation was derived using several sets of experiments performed using sodium, mercury, and sodium-potassium as working fluid. All the mentioned correlations are reported in Table 4.1 together with the conditions for their applicability. In Fig. 4.4, instead, the Nusselt number is reported, as a

References

Ushakov et al. Zhukov et al. Zhukov et al. Mikityuk El-Genk and Schriener Kazimi and Carelli

Equation  p  p 2 0:56 + 0:19 D + 0:041 Pe D D  p  p 13  p 2 0:56 + 0:19 p D Nu ¼ 7:55 D  20 + 0:041 Pe D D  p  p 5 0:64 + 0:246 D + 0:007Pe Nu ¼ 7:55 Dp  14 D  p   0:77  Pe + 250 Nu ¼ 0:047 1  exp 3:8 D  1     

Nu ¼ 10:7 Dp  7:1 + 0:024 1  exp 10:4 Dp  1 Pe0:85  p 3:8  Pe 0:86  p 5:0 + 0:16 Nu ¼ 4:0 + 0:33 D 100 D Nu ¼ 7:55 Dp  20

 p 13

p/D

Pe

Lattice

1.2–2.0

1–4000

Triangle

1.25–1.46

60–2000

Triangle

1.2–1.5

10–2500

Square

1.1–1.95

30–5000

Triangle/square

1.06–1.95

4–4000

Triangle

1.1–1.4

10–5000

Triangle

System thermal hydraulics for liquid metals

Table 4.1 Convective heat transfer correlations for a bundle of cylindrical heated rods

161

162

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Fig. 4.4 Nusselt number from different correlations for convective heat transfer of liquid metals in vertical bundles of heated rods (case with p/D ¼ 1.3 and triangular lattice).

function of the Peclet number, obtained from the five different convective heat transfer correlations for liquid metals in a vertical bundle of triangular lattice heated rods.

4.2

Hydrodynamic model for STH codes

Mathematically, there are two ways to address the concept of finite balance of a given “extensive” variable: l

The Eulerian point of view in which the different properties of a fluid passing from a welldefined “control volume” are evaluated. With this point of view, the fluid can enter or exit from the “control volume” due to advection and diffusion phenomena. Control volume

Exchanges due to fluid motion (advection) Exchanges not due to fluid motion (diffusion)

l

The Lagrangian point of view in which the different properties of a given “control mass” are evaluated while evolving/moving into the system. With this point of view, no mass exchanges can occur.

System thermal hydraulics for liquid metals

Control volume

163

No exchange due to fluid motion can occur in this case

Generally, the Lagrangian approach is more familiar (e.g., thermodynamics makes an extensive use of it), but STH and computational fluid dynamic (CFD) codes often adopt the Eulerian approach. Moreover, two-phase conditions may further complicate the problem no matter of the considered point of view. Two-phase conditions can be due to the presence of vapor of the same coolant fluid or for the presence of incondensable gases. In the case of two-phase flow, even more complicating aspects come into play, owing to the fact that at each spatial location, either phase may be present at a given time. This is customarily accounted for by the phase density function (see Todreas and Kazimi, 2012):  ! ! time t αk r , t ¼ 1, if the k  th phase is present in r at! 0, if the k  th phase is not present in r at time t The local instantaneous form of balance equations for phase k (k ¼ f for liquid phase or k ¼ g for vapor phase) is  ! ∂ ! ðρk ψ k Þ ¼ —  ρk ψ k wk —  J ψ,k + ρk Sψ,k ∂t |fflfflfflfflffl{zfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflffl{zfflfflfflfflfflffl} |fflffl{zfflffl} variation in time

convection ðadvectionÞ

diffusion

volumetric source

due to fluid motion

!

where the expression of the intensive property ψ k, diffusion flux J ψ, k , and the source term Sψ ,k depends on the particular accounted balance equation (see Table 4.2). To be used in STH codes, these equations must be subjected to. l

l

time averaging, to filter the fluctuations due to turbulence; space averaging, to operate in terms of area-averaged variables and to obtain 1-D versions of the equations.

Table 4.2 Specific terms of the differential fluid transport equations Mass balance

ψk¼1

Momentum balance Energy balance

! ψ k ¼ wk

ψ k ¼ uk + w2k /2

! J ψ,k

¼0

Sψ ,k ¼ 0 ! !

!

! !  τk

Sψ , k ¼g

! J ψ,k

¼ pk I

! J ψ,k

¼ q 00 + pk I  τk

!

! !

! !

!

00 0

!

 wk

!

!

Sψ , k ¼ qρk + g  wk

164

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

From a theoretical point of view, in the averaging process of the differential balance equations, the local instantaneous information is lost, and so, there is the need. l

l

to reintroduce information on the effect of turbulent fluctuations, to reintroduce information on local gradients and related fluxes.

For these reasons, to “close” the problem, the phasic balance equations must be also supplemented by. l

l

l

“jump conditions” expressing the continuity of mass, momentum, and energy across the liquid-gas interface; state relationships between thermodynamic variables (equation of state, EOS); constitutive laws to evaluate specific terms (friction factor, convective heat transfer coefficient, etc.).

In STH codes, one-dimensional equations are used. They are obtained averaging the 3-D balance equations on the space over a conveniently short piece of a duct with impermeable walls and variable cross section (see Fig. 4.5). As an example, the balance equations used in RELAP5 1D STH code (RELAP5/ Mod.3.3, 2003) are typically written as reported in the following: Continuity equations ∂ 1∂ ðαk ρk Þ + ðαk ρk wk AÞ ¼ Γk ðk ¼ f , gÞ ∂t A ∂z The overall continuity consideration at the interface between liquid (f ) and vapor ( g) yields to the requirement that the liquid mass generation term must be the negative of the vapor generation (Γf ¼  Γg). Momentum equations αk ρk

∂wk 1 ∂w2 ∂p 1 fk,w + αk ρk k ¼ αk  αk ρk g cos ϑ  αk ρk wk jwk j ∂z 2 ∂t 2 ∂z D + Γk ðwk,i  wk Þ + Fk,i + Fk,vm ðk ¼ f , gÞ

In the previous equation, the subscript i refers to the phase interface, and w refers to the wall. Several STH codes include the “virtual mass effect” (the term Fk,vm) that occurs

Fig. 4.5 Elementary control volume for a one-dimensional flow in a channel.

System thermal hydraulics for liquid metals

165

when there is a relative acceleration between the two phases. This contribute is important only when the velocity is close to the sound speed in the fluid: Thermal energy equations   ∂ðαk ρk uk Þ 1 ∂ðαk ρk uk wk AÞ ∂αk p ∂ αk uk k A + ¼p  ∂z ∂t A ∂z ∂t A 1 fk,w 2 w jwk j ðk ¼ f , gÞ + qk,w + qk,i + αk ρk 2 D k where uk represents the internal energy for the phase k. In the previous energy equations, qk,w and qk,i are, respectively, the phasic wall heat transfer rate and the phasic interface heat transfer rate that take also into account for the energy associated with the interface mass transfer. Non-condensable gas If the gas includes also a noncondensable gas, the mass balance equation for the noncondensable gas must be added:   1∂ ∂ αg ρnc + αg ρnc wg A ¼ 0 ∂t A ∂z in which the noncondensable gas is assumed to move with the same velocity and having the same temperature of the vapor phase. For what concerns the energy and momentum balance equations, the noncondensable gas is accounted together with the vapor phase as a Daltonian gas mixture. In the previous equations, the calculation of the mass transfer through the interface Γi, wall friction term Fw, interfacial friction term Fi, wall heat transfer qw, interfacial heat transfer qi, and virtual mass term Fk,vm requires the use of empirical correlations: constitutive laws.

4.3

Thermodynamic properties for the liquid metals to be implemented in a STH code

In STH codes, developed to cover a wide amount of working fluids, the thermodynamic property data functions are in general required as a function of both temperature and pressure. Frequently in the literature, the thermodynamic properties of a liquid metal are instead given at atmospheric pressure as temperature functions only, due to the very limited pressure dependence in common applications and the fact that frequently only liquid phase is considered. So, the reconstruction of the functional dependence from both temperature and pressure of these properties is needed to be implemented in the STH code. Moreover, a strategy for the reconstruction of the thermodynamic properties in vapor phase should be also accounted. This is mainly required to take into account the presence of noncondensable gases that may be used as cover gas and that can be mixed with the vapor phase of the used liquid-metal coolant.

166

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

In the following, the procedure adopted by the University of Pisa (UniPi) to implement the thermodynamic properties of lead, lead-bismuth, lead-lithium, and sodium in the RELAP5/Mod3.3 is reported.

4.3.1 Liquid phase From the work of Sobolev (2011), it is possible to find the density, isobaric specific heat, and sound velocity, for liquid metals of interest in the nuclear field, given as a function of the temperature at a reference pressure pref of 105 Pa. Starting from these three aforementioned properties, all the thermodynamic properties can be reconstructed analytically as a function of temperature and pressure (Kolev, 2011). Typically, the density at atmospheric pressure (reference pressure, pref) of a liquid metal is given in literature as a linear function of temperature: ρl, ref ðT Þ ¼ r0 + r1 T Sometimes, in the STH codes, the use a polynomial form for the specific volume correlation is preferred instead of density: vl, ref ðT Þ ¼ b0 + b1 T + b2 T 2 + b3 T 3 Similarly, the correlation for the isobaric specific heat can be set as a third-order polynomial of temperature: cpl, ref ðT Þ ¼ d0 + d1 T + d2 T 2 + d3 T 3 In the work of Sobolev, the sound velocity of a liquid metal is generally given by a second-order polynomial function: wsl, ref ðT Þ ¼ c0 + c1 T + c2 T 2 The specific volume of a liquid metal is generally weakly dependent from pressure; thus, a linear dependence from it can be assumed: 

vl ðT, pÞ ¼ vl, ref ðT Þ + F1 ðT Þ p  pref



  ∂vl with F1 ðT Þ ¼ ∂p T

Because the specific volume partial derivative with respect to the pressure is assumed only as a function of temperature, it can be calculated using !    2 2 T β ∂vl 1 Tβ 1 l, ref ¼ v2l + l ¼ v2l, ref + with βl, ref ∂p T w2sl cpl w2sl, ref cpl, ref ¼

1 dvl, ref vl, ref dT

System thermal hydraulics for liquid metals

167

and then 

∂vl ∂p

 ¼ F1 ð T Þ ¼  T

v2l, ref w2sl, ref



T v_ 2l, ref cpl, ref

with v_ l, ref

dvl, ref ¼ b1 + 2b2 T + 3b3 T 2 dT

Deriving again with respect to the temperature, the following correlation is obtained:   dF1 ðT Þ d ∂vl _ ¼ F 1 ðT Þ dT dT ∂p T ¼ 

2vl, ref v_ l, ref wsl, ref  2w_ sl, ref v2l, ref w3sl, ref

 v_ 2l, ref + 2T v_ l, ref v€l, ref cpl, ref  T v_ 2l, ref c_ pl, ref c2pl, ref

where: v€l, ref dcpl, ref dT

d 2 vl, ref dT 2

¼ 2b2 + 6b3 T,

w_ sl, ref

dwsl, ref dT

¼ c1 + 2c2 T,

and

c_ pl, ref

¼ d1 + 2d2 T + 3d3 T . 2

Finally, the partial derivative of the specific volume with respect to the temperature is     ∂vl ¼ v_ l, ref + F_ 1 ðT Þ p  pref ∂T p The thermal expansion coefficient and the isothermal coefficient of compressibility can be then calculated according to their definitions:     v_ l, ref ðT Þ + F_ 1 ðT Þ p  pref 1 ∂vl βl ðT, pÞ ) βl ðT, pÞ ¼ vl ðT, pÞ ∂T p vl ðT, pÞ   1 ∂vl F 1 ðT Þ κ l ðT, pÞ  ) κl ðT, pÞ ¼  vl ðT, pÞ ∂p T vl ðT, pÞ Similar derivations can be used to obtain the specific enthalpy, the specific internal energy, and the specific entropy of the liquid phase as a function of both temperature and pressure.

4.3.2 Vapor phase In principle, in STH codes, the properties of coolants in vapor phase are also needed. Apart from the sodium, the other liquid metals foreseen in the nuclear field as possible coolants (such as lead and lead-bismuth) have the boiling temperature so high that

168

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

boiling is reached only in a very severe condition in which the integrity of the structural material is compromised. For these liquid metals, the “vapor state” is then considered only if noncondensable gases are present. In the present work, the use of the van der Waals equation of state for the vapor phase of the considered metals is proposed. The equation of state (EOS) is p¼

RT a  vv  b v2v

where a¼

27R2 Tc2 RTc , b¼ , vv, c ¼ 3b 64pc 8pc

This EOS can be solved iteratively to obtain the specific volume. The thermal expansion coefficient is given by βv ðT, pÞ ¼

  1 ∂vv ¼ vv ∂T p

vv  b   2a vv  b 2 vv T  R vv

while the isothermal coefficient of compressibility follows from the following equation: κ v ðT, pÞ ¼ 

  1 ∂vv 1 # ¼ " vv ∂p T 2a RT vv 3  vv ðvv  bÞ2

Starting from the previous thermodynamic properties, the isobaric specific heat, the specific internal energy, and the specific entropy can be found for the vapor phase as a function of both temperature and pressure (Kolev, 2011).

4.4

RELAP5/Mod3.3 modified code and application

4.4.1 RELAP5/Mod3.3 modified code The University of Pisa (UniPi), from the early 2000s, was involved in the implementation of a dedicated version of the RELAP5 code, capable to simulate liquid-metalcooled systems. More specifically, UniPi, in collaboration with ANSALDO and ENEA, performed several simulations on the accelerator-driven system (ADS) cooled by heavy liquid metal using the RELAP5/Mod3.2β code. The code was modified to simulate the thermal hydraulics of lead- and LBE-cooled systems. Both the selfstanding version of the code and a version coupled with PARCS multigroup reactor kinetics code were employed (Oriolo et al., 2000; Ambrosini et al., 2000).

System thermal hydraulics for liquid metals

169

In 2002, the version of RELAP5/Mod3.2β was used in a posttest validation process of experiments conducted on CHEOPE, loop located at ENEA (Brasimone), designed to study the LBE chemical and technological aspects of heavy-liquid-metal reactors. The comparison between experimental and numerical results showed a reasonable agreement and contributed to the assessment of the code capabilities in simulating LBE in forced and natural circulation regime (Agostini et al., 2002). In 2006, an experimental campaign was performed on an LBE pool-type facility, named CIRCE, located at ENEA Brasimone, where gas-injection enhanced circulation tests were carried out. In 2007, UniPi implemented the thermodynamic properties of lead and LBE in RELAP5/Mod3.3 code version, adding the updated transport properties for viscosity, thermal conductivity, and surface tension. Subsequently, this upgraded version of RELAP5/Mod3.3 code was extensively employed in support of the experimental activities performed at ENEA (Brasimone) in the field of HLM nuclear system. In particular, two main LBE facilities, NACIE (loop-type) (Coccoluto et al., 2011) and CIRCE (pool-type) (Tarantino et al., 2013), were reproduced in order to investigate the related thermal-hydraulic phenomenology in both nominal conditions (gas enhanced circulation) and transient conditions (e.g., transition to natural circulation and ULOF). In 2012, UniPi started a research activity on the development of a coupling tool between the modified RELAP5/Mod3.3 code and the CFD Fluent code (Martelli et al., 2017). In 2016, in order to perform this activity in a rational way, the last revised liquid-metal properties available in the scientific literature were assigned to RELAP5/ Mod3.3, for sodium, lead, lead-bismuth eutectic, and lead-lithium eutectic (Angelucci et al., 2017). In particular, the equations needed to obtain temperature, pressure, specific volume, specific internal energy, thermal expansion coefficient, isothermal compressibility, specific heat at constant pressure, and specific entropy both for single- and two-phase conditions have been reviewed according to the OECD/NEA (2015), using the relationships presented in the previous section. These relationships were used to generate the external thermodynamic property file for the specific working fluid, while the upgraded transport properties (thermal conductivity, dynamic viscosity, and surface tension) were implemented directly inside the code. In addition, specific convective heat transfer correlations for a liquid metal as working fluid flowing in a pipe or in a fuel bundle have been also implemented according, respectively, to Seban and Shimazaki and Cheng and Tak correlations and to Ushakov and Mikityuk correlations (see Section 4.1.2). In particular, when a liquid metal is adopted as working fluid, a specific convective boundary condition can be set in the input file for the heat structures.

4.4.2 Application to NACIE 4.4.2.1 Facility description The NACIE facility was commissioned to perform experiments in the field of thermal hydraulics and fluid dynamics to investigate pressure drops and heat transfer correlations in prototypical fuel bundle simulators (Coccoluto et al., 2011). The NACIE

170

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Fig. 4.6 Isometric view and layout of NACIE primary loop.

experimental campaigns are intended to support Generation IV nuclear power plant design and for the qualification and development of CFD and STH codes. The facility consists of a rectangular loop made of two vertical stainless steel (AISI 304) pipes of 2½ in. acting as riser and downcomer connected by means of two horizontal pipes of the same dimension. The heat source (fuel bundle simulator) is installed in the bottom part of the riser, while the upper part of the downcomer is connected, through appropriate flanges, to a heat exchanger (see Fig. 4.6). The heat source consists of two electric pins with a nominal thermal power of about 43 kW and an active length of 0.89 m.

System thermal hydraulics for liquid metals

171

The overall height, measured between the axes of the upper and lower horizontal pipes, is 7.5 m, and the width is 1 m. The maximum inventory of LBE is in the order of 1000 kg, and the loop is designed to withstand to temperatures and pressures up to 550°C and 10 bar, respectively. The facility can work both in natural and forced circulation conditions, and the transition from forced to natural circulation can be investigated as well. Concerning the operation under natural circulation regime, the difference between the thermal center elevation of the heat source (FPS) and the heat sink (heat exchanger, HX), H, is about 5.7 m. This difference is able to provide the pressure head (ΔpDF ¼ gβΔTH) required to guarantee a suitable LBE mass flow rate even under natural circulation conditions. Under forced circulation conditions, a gas-lift technique is adopted to promote LBE mass flow rate along the loop. A pipe with an inner diameter of 10 mm is housed inside the riser connected through the expansion gas top flange to the argon feeding circuit, while at the pipe lower section, a nozzle is installed to inject argon into the riser promoting enhanced circulation inside the loop. The gas injection system is able to supply argon flow rate in the range 1–20 NL/min with a maximum injection pressure of 5.5 bar. The argon gas flows into the riser and is separated, in the gas expansion vessel, from the coolant flowing upward to the cover gas, while the LBE flows back into the heat exchanger through the upper horizontal branch. According to the described configuration, the maximum LBE mass flow rate is around 20 kg/s in gas-lift forced circulation and 5 kg/s in natural circulation conditions. Fig. 4.7 shows the NACIE loop as installed in the HLM experimental-hall laboratory at the ENEA Brasimone Research Centre. Under forced circulation isothermal conditions, the density difference between the LBE in the “downcomer” and the LBE/argon mixture in the riser can be expressed as h i  Δρ ¼ ρl  ρm ¼ ρl  ρl ð1  αÞ + αρg ¼ α ρl  ρg where ρl is the density of the LBE in the downcomer, while ρm is the average density of the two-phase mixture in the riser, defined by the void fraction α, and ρg represents the average gas density in the riser. The gas density strongly depends from pressure, which is mainly given by the LBE column mass above. Then, the pressure changes as the gas rises up in the riser. Since the gas injection line runs all along inside the riser, driving the gas to its bottom part, it is reasonable to assume the rising gas in thermal equilibrium with the liquid metal. In order to simplify the model, it is useful to define the average gas density ρg as the density calculated at the average pressure in the riser, which means the pressure at z ¼ HR/2. Since the void fraction is relatively small, the average pressure can be estimated as p ¼ p0 + ρl g

HR 2

where p0 is the cover gas pressure. Then, it is possible to write the pressure difference as  ΔpDF ¼ α ρl  ρg gHR

172

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Fig. 4.7 NACIE facility. Courtesy from ENEA.

Now, introducing the flow quality x and the slip ratio S, defined, respectively, as x

wg 1  α x ρl m_ g S ¼ α 1  x ρg wl m_ g + m_ l

the previous equation can be written as  ΔpDF ¼

ρl  ρg gHR

1+S

1  x ρg x ρl

The total pressure drop along the flow path (Δpfric) can be written as Δpfric ¼

   X    1 X L 2 HR 2 2 2 f w + Kρ w + Φ f ρ  w ρ lo l l lo lo j i j 2 De De,R l i

System thermal hydraulics for liquid metals

173

where the first term represents the distributed friction pressure losses through the single-phase region (usually negligible), the second term represents the loss localized in singularities (such as the effect of sudden expansion or contraction, valves, and orifices), and the third represents the distributed friction pressure losses along the twophase region (usually negligible). The first and the third terms are characterized by an own characteristic length, equivalent diameter, flow pattern, and then friction coefficient. Introducing the liquid flow rate and assuming a constant riser cross section AR, the previous equation can be written as Δpfric ¼

X   X  L HR m_ 2l m_ 2l 2 f + K + Φ f ffi K lo j lo t lo 2 i j De i De,r 2ρl AR 2ρl A2R

Since the single-phase and the two-phase distributed pressure losses are negligible in comparison with the singular pressure drops along the path, Kt is independent from the mass flow rate for turbulent flow regime. Moreover, under the tested conditions, it can be assumed  ΔpDF ¼

ρl  ρg gHR

1  x ρg 1+S x ρl

 ffi

ρl  ρg gHR S

m_ l ρg m_ g ρl

So, it is possible to write 

ρl  ρg gHR

m_ l ρg S m_ g ρl |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}

m_ 2l ¼ Kt 2ρl A2R |fflfflfflfflffl{zfflfflfflffl ffl} Δpfric

ΔpDF

Rearranging the previous equation, we have vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi u  2 2 u 3 2 ρl  ρg gHR ρl AR  0:33 t _ l ffi const  m _g m_ l ¼  m_ g ) m SKt ρg Moreover, the primary LBE side is coupled to the water secondary side by means of a “tube in tube” counterflow-type heat exchanger (HX) fed by liquid water at low pressure (about 1.5 bar) and designed assuming a thermal duty of 30 kW. The HX essentially consists of three coaxial tubes with different thicknesses and with an active length of 1.5 m (see Fig. 4.8). LBE flows downward into the HX inner pipe, while water flows upward in the annular region between the middle and the outer pipe allowing a countercurrent flow

174

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

Fig. 4.8 NACIE HX. Courtesy from ENEA.

heat transfer. The annular region between the inner and middle pipe is filled with a stainless steel powder. The aim of this powder gap is to ensure the thermal coupling between LBE and water and to reduce the thermal stress across the tube walls (the thermal gradient between LBE and water is localized mostly across the powder layer, as the highest thermal resistance). An air cooler completes the secondary circuit to maintain water temperature under its boiling point.

4.4.2.2 NACIE RELAP5 model and application: Isothermal and ULOF transient The RELAP5/Mod3.3 model setup for NACIE facility is shown in Fig. 4.9. This is mainly composed of several pipes and junctions to represent the main rectangular loop. Other component models (annulus and branch) have been used to model the expansion vessel and the gas injection system. Suitable time-dependent volumes and time-dependent junctions that have been employed were necessary to set the boundary conditions. Referring to Fig. 4.9, liquid metal follows an anticlockwise flow path through the loop components. The performed analysis for the isothermal test consisted in the analysis of the LBE flow rate established in the facility with varying argon inlet flow rate. This test was performed as a step-by-step increase and decrease of the argon flow rate. Fig. 4.10

System thermal hydraulics for liquid metals

175

TDV-320 (argon out)

Expansion vessel

150 152 148

170

TDV-520 (water out)

5 1 0

1.5 m

0.765 m

160 156 146

1 7 2

1 8 0 1 3 0

HX

5m

TDJ-505 TDV-500 (water in)

7.5 m

5.7 m 2 0 0

TDV-400 (argon in)

125

TDJ-405 1 2 0 2.35 m FPS 2 0 6

1 1 0 100

210 1m

Fig. 4.9 RELAP5 nodalization of the NACIE facility.

0.89 m

Thermal Hydraulics Aspects of Liquid Metal Cooled Nuclear Reactors

LBE flow rate (kg/s)

176

Time (h)

Fig. 4.10 LBE mass flow rate time trend (Test 206).

shows the comparison between the experimental data and the RELAP5 results of the LBE mass flow rate at the outlet section of the fuel pin simulator (FPS). After the argon gas injection activation, the LBE mass flow rate increases to a value of about 7.7 kg/s (argon flow rate equal to 2 NL/min), and steady-state conditions are reached in few minutes. The argon flow rate has been maintained constant for about half an hour, and then, it has been increased to 4 NL/min; as a consequence, LBE mass flow rate increased to about 9.2 kg/s. Similarly, subsequent increases of argon flow rate have been considered (5–6–8–10 NL/min), and in correspondence with a value of 10 NL/ min, the obtained LBE mass flow rate is about 13–14 kg/s. In the second part of the test, gas injection is decreased symmetrically with respect to the increasing ramp. With respect to the experimental data, the calculated LBE mass flow rate overestimates them by