THE MECHANICS OF LARGE GAS BUBBLES IN TUBES
1 1 THERMAL POWER AND THERMAL POWER DENSITY 1 2 THERMAL POWER DENSITY AND FUEL MATERIAL 1 3 THERMAL POWER DENSITY AND MODERATOR TEMPERATURE 1 4 SPATIAL DISTRIBUTION OF THE THERMAL POWER DENSITY 1 5 EQUALIZING OF THE SPATIAL DISTRIBUTION OF THE THERMAL POWER DENSITY 1 6 NOMENCLATURE REFERENCES 2 TEMPERATURE INSIDE THE FUEL ELEMENTS 2 1 STEADY-STATE TEMPERATURE FIELD 2 2 TRANSIENT TEMPERATURE FIELD 2 3 INFLUENCE OF THE CLADDING OXIDATION, HYDROGEN DIFFUSION, AND CORROSION PRODUCT DEPOSITION 2 3 1 CLADDING OXIDATION 2 3 2 HYDROGEN DIFFUSION 2 3 3 DEPOSITION 2 4 NOMENCLATURE 3 THE “SIMPLE” STEADY BOILING FLOW IN A PIPE 3 1 MASS CONSERVATION 3 2 MIXTURE MOMENTUM EQUATION 3 3 ENERGY CONSERVATION 3 4 THE IDEA OF MECHANICAL AND THERMODYNAMIC EQUILIBRIUM 3 5 RELAXING THE ASSUMPTION OF MECHANICAL EQUILIBRIUM 3 6 RELAXING THE ASSUMPTION OF THERMODYNAMIC EQUILIBRIUM 3 7 THE RELAXATION METHOD 3 8 THE BOUNDARY LAYER TREATMENT 3 9 THE BOUNDARY LAYER TREATMENT WITH CONSIDERED VARIABLE EFFECTIVE BUBBLE SIZE 3 10 SATURATED FLOW BOILING HEAT TRANSFER 3 11 COMBINING THE ASYMPTOTIC METHOD WITH BOUNDARY LAYER TREATMENT ALLOWED FOR VARIABLE EFFECTIVE BUBBLE SIZE 3 12 SEPARATED MOMENTUM EQUATIONS AND BUBBLE DYNAMICS 3 13 NOMENCLATURE APPENDIX 3 1 SANI’S (1960) DATA FOR BOILING FLOW IN A PIPE 4 THE “SIMPLE” STEADY THREE-FLUID BOILING FLOW IN A PIPE 4 1 FLOW REGIME TRANSITION FROM SLUG TO CHURN TURBULENT FLOW 4 2 INSTANTANEOUS LIQUID REDISTRIBUTION IN FILM AND DROPLETS 4 3 RELAXING THE ASSUMPTION FOR INSTANTANEOUS LIQUID REDISTRIBUTION IN FILM AND DROPLETS, ENTRAINMENT, AND DEPOSITION 4 4 DRIFT FLUX CORRELATIONS 4 5 SEPARATED MOMENTUM EQUATION 4 6 DYNAMIC EVOLUTION OF THE MEAN DROPLET SIZE 4 6 1 DROPLET SIZE STABILITY LIMIT 4 6 2 DROPLET PRODUCTION RATE DUE TO FRAGMENTATION 4 6 3 DURATION OF THE FRAGMENTATION 4 6 4 COLLISION AND COALESCENCE 4 7 HEAT TRANSFER 4 8 MASS TRANSFER 4 9 COMPARISON WITH EXPERIMENTS 4 10 NOMENCLATURE 5 CORE THERMAL HYDRAULICS 5 1 REACTOR PRESSURE VESSELS 5 2 STEADY-STATE FLOW IN HEATED ROD BUNDLES 5 2 1 THE NUPEC EXPERIMENT 5 2 2 THE SIEMENS VOID DATA FOR THE ATRIUM 10 FUEL BUNDLE 5 2 3 THE FRIGG EXPERIMENTS 5 2 4 THE THTF EXPERIMENTS: HIGH PRESSURE AND LOW MASS FLOW 5 3 PRESSURE DROP FOR BOILING FLOW IN BUNDLES 5 4 TRANSIENT BOILING 5 4 1 THE NUPEC TRANSIENTS IN A CHANNEL SIMULATING ONE SUBCHANNEL OF A PWR FUEL ASSEMBLY 5 4 2 THE NUPEC TRANSIENTS IN PWR 5 × 5 FUEL ASSEMBLY 5 5 STEADY-STATE CRITICAL HEAT FLUX 5 5 1 INITIAL ZERO-DIMENSIONAL GUESS 5 5 2 THREE-DIMENSIONAL CHF ANALYSIS 5 5 3 UNCERTAINTIES 5 6 OUTLOOK – TOWARD LARGE-SCALE TURBULENCE MODELING IN BUNDLES 5 7 OUTLOOK – TOWARD FINE-RESOLUTION ANALYSIS 5 8 CORE ANALYSIS 5 9 NOMENCLATURE APPENDIX 5 1 SOME RELEVANT CONSTITUTIVE RELATIONSHIPS ADDRESSED IN THIS ANALYSIS 6 FLOW BOILING AND CONDENSATION STABILITY ANALYSIS 6 1 STATE OF THE ART 6 2 AREVA BOILING STABILITY DATA FOR THE ATRIUM 10B FUEL BUNDLE 6 3 FLOW CONDENSATION STABILITY 7 CRITICAL MULTIPHASE FLOW 7 1 DEFINITION OF THE CRITICALITY CONDITION 7 2 GRID STRUCTURE 7 3 ITERATION STRATEGY 7 4 SINGLE PHASE FLOW IN PIPE 7 4 1 NO FRICTION ENERGY DISSIPATION, CONSTANT CROSS SECTION 7 4 2 GENERAL CASE, PERFECT GAS 7 5 SIMPLE TWO PHASE CASES FOR PIPES AND NOZZLES 7 5 1 SUBCOOLED CRITICAL MASS FLOW RATE IN SHORT PIPES, ORIFICES AND NOZZLES 7 5 1 FROZEN HOMOGENEOUS NON-DEVELOPED FLOW 7 5 2 NON-HOMOGENEOUS DEVELOPED FLOW WITHOUT MASS EXCHANGE 7 5 3 EQUILIBRIUM HOMOGENEOUS FLOW 7 5 4 EQUILIBRIUM NON-HOMOGENEOUS FLOW 7 5 5 INHOMOGENEOUS DEVELOPING FLOW IN SHORT PIPES AND NUZZLES WITH INFINITELY FAST HEAT EXCHANGE AND WITH LIMITED INTERFACIAL MASS TRANSFER 7 6 RECENT STATE OF THE KNOWLEDGE FOR DESCRIBING CRITICAL FLOW 7 6 1 BUBBLES ORIGINATION 7 6 2 BUBBLE FRAGMENTATION 7 6 3 BUBBLE COALESCENCES 7 6 4 DROPLETS ORIGINATION 7 7 EXAMPLES FOR APPLICATION OF THE THEORY OF THE CRITICAL FLOW 7 7 1 BLOW DOWN FROM INITIALLY CLOSED PIPE 7 7 2 BLOW DOWN FROM INITIALLY CLOSED VESSEL 7 8 NOMENCLATURE 8 STEAM GENERATORS 8 1 INTRODUCTION 8 2 SOME POPULAR DESIGNS OF STEAM GENERATORS 8 2 1 U-TUBE TYPE 8 2 2 ONCE THROUGH TYPE 8 2 3 OTHER DESIGN TYPES 8 3 FREQUENT PROBLEMS, SOUND DESIGN PRACTICES 8 4 ANALYTICAL TOOLS 8 4 1 SOME PRELIMINARY REMARKS ON THE PHYSICAL PROBLEM TO BE SOLVED 8 4 2 SOME SIMPLE CONSERVATION PRINCIPLES 8 4 3 THREE-DIMENSIONAL ANALYSIS 8 5 VALIDATION EXAMPLES 8 5 1 BENCHMARK FOR HEAT EXCHANGER DESIGN WITH COMPLEX COMPUTER CODES 8 5 2 BENCHMARK FOR ONCE THROUGH STEAM GENERATOR DESIGN WITH COMPLEX COMPUTER CODES 8 5 3 THREE-DIMENSIONAL BENCHMARKS – COMPARISON WITH PREDICTIONS OF OLDER COMPUTER CODES 8 6 PRIMARY CIRCUITS OF PWRS UP TO 1976 8 7 PRIMARY CIRCUITS OF MODERN PWRS APPENDIX 1 SOME USEFUL GEOMETRICAL RELATIONS IN PREPARING GEOMETRICAL DATA FOR U-TUBE STEAM GENERATOR ANALYSIS 9 MOISTURE SEPARATION 9 1 INTRODUCTION 9 2 MOISTURE CHARACTERISTICS 9 3 SIMPLE ENGINEERING METHODS FOR COMPUTATION OF THE EFFICIENCY OF THE SEPARATION 9 3 1 CYCLONE SEPARATORS 9 3 2 VANE SEPARATORS 9 4 VELOCITY FIELD MODELING IN SEPARATORS 9 4 1 KREITH AND SONJU SOLUTION FOR THE DECAY OF TURBULENT SWIRL IN PIPES 9 4 2 POTENTIAL GAS FLOW IN VANES 9 4 3 TRAJECTORY OF PARTICLES IN A KNOWN CONTINUUM FIELD 9 4 4 COMPUTATIONAL FLUID DYNAMICS ANALYSES OF CYCLONES 9 4 5 COMPUTATIONAL FLUID DYNAMICS ANALYSES OF VANE SEPARATORS 9 5 EXPERIMENTS 9 5 1 BWR CYCLONES, PWR STEAM GENERATOR CYCLONES 9 5 2 OTHER CYCLONE TYPES 9 5 3 VANE DRYERS 9 6 MOISTURE SEPARATION IN NPP WITH PWRS ANALYZED BY THREE-FLUID MODELS 9 6 1 SEPARATION EFFICIENCY OF THE SPECIFIC CYCLONE DESIGN 9 6 2 EFFICIENCY OF THE SPECIFIC VANE SEPARATOR DESIGN 9 6 3 UNIFORMITY OF THE FLOW PASSING THE VANE SEPARATORS 9 6 4 EFFICIENCY OF THE CONDENSATE REMOVAL LOCALLY AND INTEGRALLY 9 7 NOMENCLATURE 10 PIPE NETWORKS 10 1 SOME BASIC DEFINITIONS 10 1 1 PIPES 10 1 2 AXIS IN THE SPACE 10 1 3 DIAMETERS OF PIPE SECTIONS 10 1 4 REDUCTIONS 10 1 5 ELBOWS 10 1 6 CREATING A LIBRARY OF PIPES 10 1 7 SUB SYSTEM NETWORK 10 1 8 DISCRETIZATION OF PIPES 10 1 9 KNOTS 10 2 THE 1983-INTERATOME EXPERIMENTS 10 2 1 EXPERIMENT 1 2 10 2 2 EXPERIMENT 1 3 10 2 3 EXPERIMENT 10 6 10 2 4 EXPERIMENT 11 3 10 2 5 EXPERIMENT 21 10 2 6 EXPERIMENT 5 10 2 7 EXPERIMENT 15 11 SOME AUXILIARY SYSTEMS 11 1 HIGH PRESSURE REDUCTION STATION 11 2 GAS RELEASE IN RESEARCH REACTORS PIPING 11 2 1 SOLUBILITY OF O2, N2 AND H2 UNDER 1 BAR PRESSURE 11 2 2 SOME GENERAL REMARKS ON THE GAS RELEASE- AND ABSORPTION DYNAMICS 11 2 3 GAS RELEASE IN THE SIPHON SAFETY PIPE 11 2 4 RADIOLYSIS GASES: GENERATION, ABSORPTION AND RELEASE 11 2 5 MIXING IN THE WATER POOL 11 2 6 COMPUTATIONAL ANALYSES 12 EMERGENCY CONDENSERS 12 1 INTRODUCTION 12 2 SIMPLE MATHEMATICAL ILLUSTRATION OF THE OPERATION OF THE SYSTEM 12 3 PERFORMANCE OF THE CONDENSER AS A FUNCTION OF THE WATER LEVEL AND PRESSURE 12 4 CONDENSATE REMOVAL 12 5 AIR-COOLED CONDENSER, STEAM REHEATER 12 5 1 HEAT EXCHANGER POWER 12 5 2 INTENSIFYING HEAT TRANSFER BY FINS 12 5 3 HEAT TRANSFER AT FINNED TUBES 12 5 4 HEAT CONDUCTION THROUGH FINNED PIPE 12 5 5 CONDENSATION INSIDE A PIPE 12 6 NOMENCLATURE 12 7 REFERENCES 13 CORE DEGRADATION 13 1 PROCESSES DURING THE CORE DEGRADATION DEPENDING ON THE STRUCTURE TEMPERATURE 13 2 ANALYTICAL TOOLS FOR ESTIMATION OF THE CORE DEGRADATION 14 MELT-COOLANT INTERACTION 14 1 MELT-COOLANT INTERACTION ANALYSIS FOR THE BOILING WATER REACTOR KARENA 14 1 1 INTERACTION INSIDE THE GUIDE TUBES 14 1 2 MELT-RELOCATION THROUGH THE LOWER CORE GRID 14 1 3 SIDE MELT-RELOCATION THROUGH THE CORE BARREL 14 1 4 LATE WATER INJECTION 14 2 PRESSURE INCREASE DUE TO THE VAPOR GENERATION AT THE SURFACE OF THE MELT POOL 14 3 CONDITIONS FOR WATER PENETRATION INTO MELT 14 4 VESSEL INTEGRITY DURING THE CORE RELOCATION PHASE 15 COOLABILITY OF LAYERS OF MOLTEN REACTOR MATERIAL 15 1 INTRODUCTION 15 2 PROBLEM DEFINITION 15 3 SYSTEM OF DIFFERENTIAL EQUATIONS DESCRIBING THE PROCESS 15 3 1 SIMPLIFYING ASSUMPTIONS 15 3 2 MASS CONSERVATION 15 3 3 GAS RELEASE AND GAS VOLUME FACTION 15 3 4 VISCOUS LAYER 15 3 5 CRUST FORMATION 15 3 6 MELT ENERGY CONSERVATION 15 3 7 BUOYANCY DRIVEN CONVECTION 15 3 8 FILM BOILING 15 4 HEAT CONDUCTING STRUCTURES 15 4 1 HEAT CONDUCTION THROUGH THE STRUCTURES 15 4 2 BOUNDARY CONDITIONS 15 4 3 OXIDE CRUST FORMATION ON COLDER HEAT CONDUCTING STRUCTURES 15 5 METAL LAYER 15 6 TEST CASE 15 6 1 OXIDE OVER METAL 15 6 2 OXIDE BESIDES METAL 15 7 GRAVITATIONAL FLOODING OF HOT SOLID HORIZONTAL SURFACE BY WATER 15 7 1 SIMPLIFYING ASSUMPTIONS 15 7 2 CONSERVATION OF MASS AND MOMENTUM, SCALING 15 7 3 EIGEN VALUES, EIGEN VECTORS AND CANONICAL FORMS 15 7 4 STEADY STATE 15 8 NOMENCLATURE 15 9 NOMENCLATURE TO SECT 15 7 16 EXTERNAL COOLING OF REACTOR VESSELS DURING SEVERE ACCIDENT 16 1 INTRODUCTION 16 2 STATE OF THE ART 16 3 DRY CORE MELTING SCENARIO, MELT RELOCATION, WALL ATTACK, FOCUSING EFFECT 16 4 MODEL ASSUMPTIONS AND BRIEF MODEL DESCRIPTION 16 4 1 MOLTEN POOL BEHAVIOR 16 4 2 TWO DIMENSIONAL HEAT CONDUCTION THROUGH THE VESSEL WALL 16 4 3 BOUNDARY CONDITIONS 16 4 4 TOTAL HEAT FLOW FROM THE POOLS INTO THE VESSEL WALL 16 4 5 VESSEL WALL ABLATION 16 4 6 HEAT FLUXES AND CRUST FORMATION 16 4 7 BUOYANCY CONVECTION 16 5 CRITICAL HEAT FLUX 16 6 APPLICATION EXAMPLES OF THE MODEL 16 6 1 THE EFFECT OF VESSEL DIAMETER 16 6 2 THE EFFECT OF THE LOWER HEAD RADIUS 16 6 3 THE EFFECT OF THE RELOCATION TIME 16 6 4 THE EFFECT OF THE MASS OF THE INTERNAL STRUCTURES 16 6 5 SOME IMPORTANT PARAMETERS CHARACTERIZING THE PROCESS 16 7 NOMENCLATURE APPENDIX 1: SOME GEOMETRICAL RELATIONS 17 THERMO-PHYSICAL PROPERTIES FOR SEVERE ACCIDENT ANALYSIS 17 1 INTRODUCTION 17 1 1 SUMMARY OF THE PROPERTIES AT THE MELTING LINE AT ATMOSPHERIC PRESSURE 17 1 2 APPROXIMATION OF THE LIQUID STATE OF MELTS 17 1 3 NOMENCLATURE 17 2 URANIUM DIOXIDE CALORIC AND TRANSPORT PROPERTIES 17 2 1 SOLID 17 2 2 LIQUID 17 2 3 VAPOR 17 3 ZIRCONIUM DIOXIDE 17 3 1 SOLID 17 3 2 LIQUID 17 4 STAINLESS STEEL 17 4 1 SOLID 17 4 2 LIQUID 17 4 3 VAPOR 17 5 ZIRCONIUM 17 5 1 SOLID 17 5 2 LIQUID 17 6 ALUMINUM 17 6 1 SOLID 17 6 2 LIQUID 17 7 ALUMINUM OXIDE, AL2O3 17 7 1 SOLID 17 7 2 LIQUID 17 8 SILICON DIOXIDE 17 8 1 SOLID 17 8 2 LIQUID 17 9 IRON OXIDE 17 9 1 SOLID 17 9 2 LIQUID 17 10 MOLYBDENUM 17 10 1 SOLID 17 10 2 LIQUID 17 11 BORON OXIDE 17 11 1 SOLID 17 11 2 LIQUID 17 12 REACTOR CORIUM 17 12 1 LIQUID 17 12 2 SOLID 17 13 SODIUM 17 13 1 SOME BASIC CHARACTERISTICS 17 13 2 LIQUID 17 13 3 VAPOR APPENDIX 1