Multiphase Flow Dynamics 4; Nuclear Thermal Hydraulics

Multiphase Flow Dynamics 4......Page 2
Nuclear Thermal Hydraulics......Page 4
The motivation to write this book......Page 8
Summary......Page 10
Nomenclature......Page 16
Table of contents......Page 26
1.1 Thermal power and thermal power density......Page 34
1.2 Thermal power density and fuel material......Page 37
1.3 Thermal power density and moderator temperature......Page 38
1.4 Spatial distribution of the thermal power density......Page 39
1.5 Equalizing of the spatial distribution of the thermal power density......Page 41
1.6 Nomenclature......Page 45
References......Page 46
2.1 Steady state temperature field......Page 48
2.2 Transient temperature field......Page 56
2.3.1 Cladding oxidation......Page 61
2.3.3 Deposition......Page 62
2.4 Nomenclature......Page 63
References......Page 64
3. The “simple” steady boiling flow in a pipe......Page 66
3.1 Mass conservation......Page 68
3.2 Mixture momentum equation......Page 69
3.3 Energy conservation......Page 72
3.4 The idea of mechanical and thermodynamic equilibrium......Page 74
3.5 Relaxing the assumption of mechanical equilibrium......Page 75
3.6 Relaxing the assumption of thermodynamic equilibrium......Page 76
3.7 The relaxation method......Page 78
3.8 The boundary layer treatment......Page 83
3.9 The boundary layer treatment with considered variable effective bubble size......Page 85
3.10 Saturated flow boiling heat transfer......Page 89
3.12 Separated momentum equations and bubble dynamics......Page 93
3.13 Nomenclature......Page 101
References......Page 104
Appendix 3.1: The Sani’s (1960) data for flow boiling in pipe......Page 106
4. The “simple” steady three-fluid boiling flow in a pipe......Page 110
4.1 Flow regime transition slug to churn turbulent flow......Page 111
4.2 Instantaneous liquid redistribution in film and droplets......Page 112
4.3 Relaxing the assumption for instantaneous liquid redistribution in film and droplets, entrainment and deposition......Page 114
4.4 Drift flux correlations......Page 117
4.5 Separated momentum equation......Page 119
4.6.1 Droplet size stability limit......Page 122
4.6.3 Duration of the fragmentation......Page 123
4.6.4 Collision and coalescence......Page 125
4.7 Heat transfer......Page 126
4.8 Mass transfer......Page 128
4.9 Comparison with experiments......Page 131
4.10 Nomenclature......Page 135
References......Page 138
5.1. Reactor pressure vessels......Page 140
5.2.1 The NUPEC experiment......Page 147
5.2.3. The FRIGG experiment......Page 166
5.2.4. The THTF experiments: high pressure and low mass flow......Page 172
5.3. Pressure drop for boiling flow in bundles......Page 177
5.4.1 The NUPEC transients in a channel simulating one sub-channel of a PWR fuel assembly......Page 180
5.4.2 The NUPEC transients in PWR 5 5 fuel assembly......Page 185
5.5. Steady state critical heat flux......Page 189
5.5.1 Initial 0D-guess......Page 190
5.5.2.3 Importance of the spacer grid modeling......Page 195
5.5.3.1 Interfacial drag......Page 197
5.5.3.2 Entrainment......Page 198
5.5.3.3 Deposition......Page 199
5.5.3.4 Deposition and entrainment changes due to nucleate boiling:......Page 200
5.5.3.5 Residual film thickness at DO......Page 203
5.6. Outlook – towards the large scale turbulence modeling in bundles......Page 204
5.7. Outlook – towards the fine resolution analysis......Page 207
5.8. Core analysis......Page 208
5.9 Nomenclature......Page 212
References......Page 214
Appendix 5.1: Some relevant constitutive relationship addressed in this analysis......Page 218
6.1 State of the art......Page 222
6.2 AREVA boiling stability data for the ATRIUM 10B fuel bundle......Page 224
6.3 Flow condensation stability......Page 229
References......Page 237
7.1 Definition of the criticality condition......Page 240
7.2 Grid structure......Page 243
7.4.1 No friction energy dissipation, constant cross section......Page 245
7.4.2 General case, perfect gas......Page 252
7.5 Simple two phase cases for pipes and nozzles......Page 254
7.5.1 Subcooled critical mass flow rate in short pipes, orifices and nozzles......Page 257
7.5.1 Frozen homogeneous non-developed flow......Page 258
7.5.2 Non-homogeneous developed flow without mass exchange......Page 261
7.5.3.1 Developing flow......Page 262
7.5.3.2 Developed flow......Page 276
7.5.4.1 Developing flow......Page 281
7.5.4.2 Developed flow......Page 290
7.5.5 Inhomogeneous developing flow in short pipes ans nuzzles with infinetely fast heat exchange and with limited interfacial mass transfer......Page 294
7.6.1.1 Active nucleation seeds at the surface......Page 302
7.6.1.2 Bubble departure diameter......Page 305
7.6.1.3 Heat flux transferred by turbulent conduction from the bulk to the wall, frequency of bubble generation......Page 307
7.6.1.4 Bubble growth in the bulk......Page 308
7.6.2 Bubble fragmentation......Page 309
7.6.4 Droplets origination......Page 311
7.7.1 Blow down from initially closed pipe......Page 312
7.7.2 Blow down from initially closed vessel......Page 316
7.8 Nomenclature......Page 318
References......Page 322
8.1 Introduction......Page 326
8.2.1 U-tube type......Page 327
8.3 Frequent problems......Page 334
8.4 Analytical tools......Page 335
References......Page 337
9.1 Introduction......Page 340
9.2 Moisture characteristics......Page 344
9.3 Simple methods for computation of the efficiency of the separation......Page 347
9.3.1 Cyclone separators......Page 348
9.3.2 Vane separators......Page 356
9.4.1 Kreith and Sonju solution for the decay of turbulent swirl in pipe......Page 362
9.4.2 Potential gas flow in vanes......Page 363
9.4.3 Trajectory of particles in a known continuum field......Page 364
9.4.5 CFD analyses of vane separators......Page 367
9.5.1 BWR cyclones, PWR steam generator cyclones......Page 370
9.5.2 Other cyclone types......Page 382
9.5.3 Vane dryers......Page 387
9.6 Moisture separation in NPP with PWR’s analyzed by three fluid models......Page 398
9.6.1. Separation efficiency of the specific cyclone design......Page 400
9.6.2 Efficiency of the specific vane separators design......Page 401
9.6.3 Uniformity of the flow passing the vane separators......Page 402
9.6.4 Efficiency of the condensate removal locally and integrally......Page 403
9.7 Nomenclature......Page 404
References......Page 407
10. Pipe networks......Page 410
10.1.1 Pipes......Page 412
10.1.2 Axis in the space......Page 414
10.1.3 Diameters of pipe sections......Page 415
10.1.5 Elbows......Page 416
10.1.7 Sub system network......Page 417
10.1.8 Discretization of pipes......Page 418
10.1.9 Knots......Page 419
10.2 The 1983-Interatome experiments......Page 421
10.2.1 Experiment 1.2......Page 422
10.2.2 Experiment 1.3......Page 423
10.2.3 Experiment 10.6......Page 426
10.2.4 Experiment 11.3......Page 427
10.2.5 Experiment 21......Page 429
10.2.6 Experiment 5......Page 431
10.2.7 Experiment 15......Page 433
References......Page 436
11.1 High pressure reduction station......Page 438
11.2 Gas release in research reactors piping......Page 441
11.2.1 Solubility of O2, N2 and H2 under 1 bar pressure......Page 442
11.2.2.1 Main pipe of the cleaning system up to the pump......Page 443
11.2.3 Gas release in the siphon safety pipe......Page 444
11.2.4 Radiolysis gases: generation, absorption and release......Page 445
11.2.6 Computational analyses......Page 448
11.2.6.1 Case 1 and 2: 0% and 1% gas volume fraction at the entrance of the CCS......Page 449
11.2.6.2 Case 3: 2.6% gas volume fraction at the entrance of the CCS......Page 450
References......Page 454
12.1 Introduction......Page 456
12.2 Simple mathematical illustration of the operation of the system......Page 457
12.4 Condensate removal......Page 460
13.1 Processes during the core degradation depending on the structure temperature......Page 462
13.2 Analytical tools for estimation of the core degradation......Page 463
References......Page 464
14. Melt-coolant interaction......Page 468
14.1 Melt-coolant interaction analysis for the boiling water reactor KARENA......Page 469
14.1.1 Interaction inside the guide tubes......Page 475
14.1.2 Melt-relocation through the lower core grid......Page 477
14.2 Pressure increase due to the vapor generation at the surface of the melt pool......Page 478
14.3 Conditions for water penetration into melt......Page 479
14.4 Vessel integrity during the core relocation phase......Page 480
References......Page 482
15. Coolability of layers of molten reactor material......Page 486
15.2 Problem definition......Page 488
15.3.1 Simplifying assumptions......Page 489
15.3.2 Mass conservation......Page 490
15.3.3 Gas release and gas volume faction......Page 492
15.3.4 Viscous layer......Page 493
15.3.5 Crust formation......Page 495
15.3.6 Melt energy conservation......Page 497
15.3.7 Buoyancy driven convection......Page 499
15.3.8 Film boiling......Page 501
15.4.1 Heat conduction through the structures......Page 502
15.4.2 Boundary conditions......Page 503
15.4.3 Oxide crust formation on colder heat conducting structures......Page 504
15.6 Test case......Page 507
15.6.1 Oxide over metal......Page 508
15.6.2 Oxide besides metal......Page 511
15.7 Gravitational flooding of hot solid horizontal surface by water......Page 512
15.7.1 Simplifying assumptions......Page 513
15.7.2 Conservation of mass and momentum, scaling......Page 515
15.7.3 Eigen values, eigen vectors and canonical forms......Page 518
15.7.4 Steady state......Page 522
15.8 Nomenclature......Page 524
15.9 Nomenclature to Sect. 15.7......Page 526
References......Page 528
16.1 Introduction......Page 530
16.2. State of the art......Page 531
16.3. Dry core melting scenario, melt relocation, wall attack, focusing effect......Page 533
16.4. Model assumptions and brief model description......Page 534
16.4.1 Molten pool behavior......Page 535
16.4.2 Two dimensional heat conduction through the vessel wall......Page 536
16.4.3 Boundary conditions......Page 537
16.4.4 Total heat flow from the pools into the vessel wall......Page 539
16.4.5 Vessel wall ablation......Page 540
16.4.6 Heat fluxes and crust formation......Page 541
16.4.7.1 Buoyancy convection – steel layer......Page 542
16.4.7.2 Buoyancy convection – cavity with internal heat sources......Page 547
16.4.7.3 Redistribution of the averaged heat flux at the lower head......Page 552
16.4.7.4 Comparison of the heat transfer coefficient used in different lumped parameter models......Page 554
16.4.7.5 Summary......Page 557
16.5 Critical heat flux......Page 558
16.6 Application examples of the model......Page 563
16.6.2 The effect of the lower head radius......Page 564
16.6.5 Some important parameters characterizing the process......Page 566
16.7 Nomenclature......Page 571
References......Page 573
Appendix 1: Some geometrical relations......Page 577
17. Thermo-physical properties for severeaccident analysis......Page 582
17.1.1 Summary of the properties at the melting line at atmospheric pressure......Page 584
17.1.2 Approximation of the liquid state of melts......Page 586
17.1.3 Nomenclature......Page 589
References......Page 591
17.2 Uranium dioxide caloric and transport properties......Page 592
17.2.1.1 Specific capacity at constant pressure, specific enthalpy and specific entropy......Page 593
17.2.1.2 Solid density......Page 598
17.2.1.4 Solid thermal conductivity......Page 599
17.2.1.5 Solid sonic velocity......Page 600
17.2.2.1 Caloric equation of state......Page 601
17.2.2.2 Transport properties......Page 606
17.2.3 Vapor......Page 608
References......Page 610
17.3.1.1 Solid specific capacity at constant pressure......Page 612
17.3.1.2 Solid density......Page 615
17.3.1.5 Solid sonic velocity......Page 616
17.3.2 Liquid......Page 617
References......Page 620
17.4.1.1 Solid specific capacity at constant pressure......Page 622
17.4.1.2 Solid specific enthalpy......Page 623
17.4.1.3 Solid specific entropy......Page 624
17.4.1.4 Solid density......Page 625
17.4.1.6 Solid thermal conductivity......Page 626
17.4.1.7 Solid sonic velocity......Page 627
17.4.2.1 Thermal properties......Page 629
17.4.2.2 Transport properties......Page 633
17.4.3 Vapor......Page 636
References......Page 637
17.5.1.1 Solid specific capacity at constant pressure......Page 638
17.5.1.2 Solid specific enthalpy......Page 639
17.5.1.3 Solid specific entropy......Page 640
17.5.1.4 Solid density......Page 642
17.5.1.6 Solid thermal conductivity......Page 643
17.5.2.2 Liquid density derivative with respect to temperature......Page 644
17.5.2.6 Liquid thermal conductivity......Page 645
17.5.2.9 Liquid dynamic viscosity......Page 646
17.5.2.13 Liquid temperature as a function of pressure and specific entropy......Page 647
References......Page 648
17.6.1.2 Solid specific enthalpy......Page 650
17.6.1.6 Solid thermal conductivity......Page 651
17.6.2.3 The derivative of the liquid specific enthalpy with respect to pressure at constant temperature......Page 652
17.6.2.5 Density......Page 654
17.6.2.7 Liquid density derivative with respect to pressure......Page 655
17.6.2.11 Liquid dynamic viscosity......Page 656
References......Page 657
17.7.1.1 Solid specific capacity at constant pressure......Page 660
17.7.1.2 Solid specific enthalpy......Page 661
17.7.1.3 Solid specific entropy......Page 662
17.7.1.5 The derivative of the solid density with respect to the temperature......Page 664
17.7.1.6 Solid thermal conductivity......Page 665
17.7.1.7 Solid sonic velocity......Page 666
17.7.2.6 Liquid density......Page 667
17.7.2.10 Liquid velocity of sound......Page 668
17.7.2.13 Liquid dynamic viscosity......Page 669
References......Page 670
17.8.1.1 Solid specific capacity at constant pressure......Page 672
17.8.1.3 Solid specific entropy......Page 673
17.8.1.4 Solid density......Page 675
17.8.1.6 Solid thermal conductivity......Page 676
17.8.1.7 Solid sonic velocity......Page 677
17.8.2.5 Liquid velocity of sound......Page 678
17.8.2.8 Liquid dynamic viscosity......Page 679
17.8.2.11 Liquid specific entropy......Page 680
References......Page 681
17.9.1.2 Solid specific enthalpy......Page 684
17.9.1.6 Solid thermal conductivity......Page 685
17.9.2.4 Liquid specific entropy......Page 686
17.9.2.6 Liquid density......Page 688
17.9.2.10 Liquid thermal conductivity......Page 689
17.9.2.11 Liquid surface tension......Page 690
References......Page 691
17.10.1.1 Solid specific capacity at constant pressure......Page 692
17.10.1.3 Solid specific entropy......Page 693
17.10.1.6 Solid thermal conductivity......Page 695
17.10.2.2 Liquid specific enthalpy......Page 696
17.10.2.6 Liquid density derivative with respect to pressure......Page 697
17.10.2.13 Saturation temperature......Page 698
References......Page 699
17.11.1.1 Solid specific capacity at constant pressure......Page 700
17.11.2.6 Solid thermal conductivity......Page 701
17.11.2.3 The derivative of the liquid specific enthalpy with respect to pressure at constant temperature......Page 702
17.11.2.4 Liquid specific entropy......Page 703
17.11.2.5 Liquid density......Page 704
17.11.2.8 Liquid velocity of sound......Page 705
17.11.2.9 Liquid thermal conductivity......Page 706
12.2.12 Liquid temperature as a function of pressure and specific entropy......Page 707
References......Page 708
17.12 Reactor corium......Page 710
17.12.1.4 Liquid density derivative with respect to pressure......Page 713
17.12.1.10 The derivative of the liquid specific enthalpy with respect to pressure at constant temperature......Page 714
17.12.2.4 Solid density......Page 715
References......Page 716
17.13 Sodium......Page 718
17.13.1.1 Moll mass and gas constant......Page 719
17.13.1.6 Dissociation energy for Na4 = 4Na......Page 720
17.13.1.8 Specific capacity at constant pressure for solid sodium......Page 721
17.13.1.10 Sonic velocity in solid sodium......Page 722
17.13.2.1 Velocity of sound of liquid sodium......Page 723
17.13.2.2 Density of liquid sodium......Page 724
17.13.2.3 Density of the saturated liquid sodium......Page 726
17.13.2.4 Boiling temperature at 1 bar......Page 727
17.13.2.5 Saturation pressure as a function of temperature......Page 728
17.13.2.6 Specific capacity at constant pressure of liquid sodium at atmospheric conditions......Page 730
17.13.2.8 The pressure dependence of the specific liquid capacity at constant pressure......Page 732
17.13.2.9 Specific liquid enthalpy......Page 734
17.13.2.11 The pressure dependence of the liquid density......Page 735
17.13.2.12 Thermal conductivity or liquid sodium......Page 736
17.13.2.13 Dynamic viscosity or liquid sodium......Page 737
17.13.2.14 Prandtl number of liquid sodium......Page 738
17.13.2.15 Surface tension of liquid sodium......Page 739
17.13.2.17 Solubility of argon and helium in sodium......Page 740
17.13.3.1 Constituents of the sodium vapor......Page 741
17.13.3.2 Sodium vapor density......Page 744
17.13.3.4 Evaporation enthalpy – using Clausius–Clapayron equation......Page 746
17.13.3.5 Specific enthalpy of evaporation–empirical approximations......Page 747
17.13.3.6 Specific enthalpy of evaporation – quasi-chemical approach......Page 748
17.13.3.8 Velocity of sound of sodium vapor......Page 750
17.13.3.9 The density derivative with respect to the temperature at constant pressure......Page 751
17.13.3.10 The density derivative with respect to the pressure at constant temperature......Page 752
17.13.3.11 Specific enthalpy......Page 753
17.13.3.12 Specific heat at constant pressure......Page 754
17.13.3.13 Specific entropy......Page 756
17.13.3.14 Thermal conductivity or sodium vapor......Page 758
17.13.3.15 Dynamic viscosity or sodium vapor......Page 760
References......Page 761
Appendix 1......Page 762
17.14 Lead, bismuth and lead-bismuth eutectic alloy......Page 764
References......Page 770
Index......Page 772