Multiphase Flow Dynamics 4 (eBook)

The motivation to write this book 7
Summary 8
Nomenclature 13
Table of contents 22
1. Heat release in the reactor core 30
1.1 Thermal power and thermal power density 30
1.2 Thermal power density and fuel material 33
1.3 Thermal power density and moderator temperature 34
1.4 Spatial distribution of the thermal power density 35
1.5 Equalizing of the spatial distribution of the thermal power density 37
1.6 Nomenclature 41
References 42
2. Temperature inside the fuel elements 43
2.1 Steady state temperature field 43
2.2 Transient temperature field 51
2.3 Influence of the cladding oxidation, hydrogen diffusion and of the corrosion product deposition 56
2.4 Nomenclature 58
References 59
3. The “simple” steady boiling flow in a pipe 60
3.1 Mass conservation 62
3.2 Mixture momentum equation 63
3.3 Energy conservation 66
3.4 The idea of mechanical and thermodynamic equilibrium 68
3.5 Relaxing the assumption of mechanical equilibrium 69
3.6 Relaxing the assumption of thermodynamic equilibrium 70
3.7 The relaxation method 72
3.8 The boundary layer treatment 77
3.9 The boundary layer treatment with considered variable effective bubble size 79
3.10 Saturated flow boiling heat transfer 83
3.11 Combining the asymptotic method with boundary layer treatment allowed for variable effective bubble size 87
3.12 Separated momentum equations and bubble dynamics 87
3.13 Nomenclature 95
References 98
4. The “simple” steady three-fluid boiling flow in a pipe 103
4.1 Flow regime transition slug to churn turbulent flow 104
4.2 Instantaneous liquid redistribution in film and droplets 105
4.3 Relaxing the assumption for instantaneous liquid redistribution in film and droplets, entrainment and deposition 107
4.4 Drift flux correlations 110
4.5 Separated momentum equation 112
4.6 Dynamic evolution of the mean droplet size 115
4.7 Heat transfer 119
4.8 Mass transfer 121
4.9 Comparison with experiments 124
4.10 Nomenclature 128
References 131
5. Core thermal hydraulic 133
5.1. Reactor pressure vessels 133
5.2. Steady state flow in heated rod bundles 140
5.3. Pressure drop for boiling flow in bundles 170
5.4. Transient boiling 173
5.5. Steady state critical heat flux 182
5.6. Outlook – towards the large scale turbulence modeling in bundles 197
5.7. Outlook – towards the fine resolution analysis 200
5.8. Core analysis 201
5.9 Nomenclature 205
References 207
6. Flow boiling and condensation stability analysis 214
6.1 State of the art 214
6.2 AREVA boiling stability data for the ATRIUM 10B fuel bundle 216
6.3 Flow condensation stability 221
References 229
7. Critical multiphase flow 232
7.1 Definition of the criticality condition 232
7.2 Grid structure 235
7.3 Iteration strategy 237
7.4 Single phase flow in pipe 237
7.5 Simple two phase cases for pipes and nozzles 246
7.6 Recent state of the knowledge for describing critical flow 294
7.7. Examples for application of the theory of the critical flow 304
7.8 Nomenclature 310
References 314
8. Steam generators 318
8.1 Introduction 318
8.2 Some popular designs of steam generators 319
8.3 Frequent problems 326
8.4 Analytical tools 327
References 329
9. Moisture separation 332
9.1 Introduction 332
9.2 Moisture characteristics 336
9.3 Simple methods for computation of the efficiency of the separation 339
9.4 Velocity fields modeling in separators 354
9.5 Experiments 362
9.6 Moisture separation in NPP with PWR’s analyzed by three fluid models 390
9.7 Nomenclature 396
References 399
10. Pipe networks 402
10.1 Some basic definitions 404
10.2 The 1983-Interatome experiments 413
References 428
11. Some auxiliary systems 429
11.1 High pressure reduction station 429
11.2 Gas release in research reactors piping 432
References 445
12. Emergency condensers 446
12.1 Introduction 446
12.2 Simple mathematical illustration of the operation of the system 447
12.3 Performance of the condenser as a function of the water level and pressure 450
12.4 Condensate removal 450
13. Core degradation 452
13.1 Processes during the core degradation depending on the structure temperature 452
13.2 Analytical tools for estimation of the core degradation 453
References 454
14. Melt-coolant interaction 457
14.1 Melt-coolant interaction analysis for the boiling water reactor KARENA 458
14.2 Pressure increase due to the vapor generation at the surface of the melt pool 467
14.3 Conditions for water penetration into melt 468
14.4 Vessel integrity during the core relocation phase 469
References 471
15. Coolability of layers of molten reactor material 475
15.1 Introduction 477
15.2 Problem definition 477
15.3 System of differential equations describing the process 478
15.4 Heat conducting structures 491
15.5 Metal layer 496
15.6 Test case 496
15.7 Gravitational flooding of hot solid horizontal surface by water 501
15.8 Nomenclature 513
15.9 Nomenclature to Sect. 15.7 515
References 517
16. External cooling of reactor vessels during severe accident 519
16.1 Introduction 519
16.2. State of the art 520
16.3. Dry core melting scenario, melt relocation, wall attack, focusing effect 522
16.4. Model assumptions and brief model description 523
16.5 Critical heat flux 547
16.6 Application examples of the model 552
16.7 Nomenclature 560
References 562
17. Thermo-physical properties for severe accident analysis 571
17.1 Introduction 573
17.2 Uranium dioxide caloric and transport properties 581
17.3 Zirconium dioxide 601
17.4 Stainless steel 610
17.5 Zirconium 626
17.6 Aluminum 637
17.7 Aluminum oxide, Al2O3 646
17.8 Silicon dioxide 658
17.9 Iron oxide 669
17.10 Molybdenum 677
17.11 Boron oxide 685
17.12 Reactor corium 694
17.13 Sodium 702
17.14 Lead, bismuth and lead-bismuth eutectic alloy 748
References 754
Index 755