thermal-hydraulics in nuclear systems
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1. INTRODUCTION ............................................................................ 9
1.1 Thermal-Hydraulic Processes in Nuclear Reactors .....................................................10
1.2 Power Generation in Nuclear Reactors ........................................................................12
2. THERMODYNAMICS ....................................................................17
2.1 Laws of Thermodynamics ..............................................................................................182.1.1 Zero-th Law of Thermodynamics ..............................................................................182.1.2 First Law of Thermodynamics ...................................................................................192.1.3 Second Law of Thermodynamics ...............................................................................222.1.4 Maximum Work and Exergy ......................................................................................23
2.2 Thermodynamic Processes ............................................................................................242.2.1 Ideal Gas ....................................................................................................................242.2.2 van der Waals Equation .............................................................................................282.2.3 Gas Mixtures ..............................................................................................................292.2.4 Gas Processes .............................................................................................................302.2.5 Carnot Cycle ..............................................................................................................342.2.6 Rankine Cycle ............................................................................................................352.2.7 Brayton Cycle ............................................................................................................362.2.8 Phase Change .............................................................................................................37
3. FLUID MECHANICS ................................... ..................................39
3.1 Mathematical Tools ........................................................................................................393.1.1 Coordinate System .....................................................................................................393.1.2 Scalars, Vectors and Tensors .....................................................................................413.1.3 Differential Operators ................................................................................................433.1.4 Substantial Time Derivative .......................................................................................443.1.5 Integral Theorems ......................................................................................................44
3.2 Field Equations for Single-Phase Flows .......................................................................463.2.1 Mass Conservation .....................................................................................................463.2.2 Momentum Conservation ...........................................................................................473.2.3 Energy Conservation ..................................................................................................503.2.4 Constitutive Equations ...............................................................................................533.2.5 Conservation Equations for Ideal Fluids ....................................................................543.2.6 Conservation Equations for Ideal Gas ........................................................................553.2.7 Turbulence in Incompressible Flows .........................................................................55
3.3 Field Equations for Multi-Phase Flows ........................................................................593.3.1 Local Instantaneous Conservation Equations.............................................................593.3.2 Time-Averaged Conservation Equations ...................................................................61
3.4 Single-Phase Flows in Channels ....................................................................................693.4.1 Mass Conservation Equation......................................................................................703.4.2 Momentum Conservation Equation ...........................................................................713.4.3 Energy Conservation Equation ..................................................................................763.4.4 Wall Shear Stress in Laminar Flows ..........................................................................823.4.5 Wall Shear Stress in Turbulent Flows ........................................................................843.4.6 Local Pressure Losses ................................................................................................85
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3.4.7 Total Pressure Drop ................................................................................................... 88
3.5 Multi-phase Flows in Channels .................................................................................... 883.5.1 Area-Averaged Conservation Equations ................................................................... 883.5.2 Void Fraction and Quality in Multiphase Flows ....................................................... 973.5.3 Homogeneous Equilibrium Model ............................................................................ 993.5.4 Drift Flux Model ..................................................................................................... 1003.5.5 Pressure Drop in Multiphase Flows ........................................................................ 1033.5.6 Friction Pressure Loss ............................................................................................. 1053.5.7 Gravity Pressure Gradient ....................................................................................... 1083.5.8 Acceleration Pressure Gradient ............................................................................... 1093.5.9 Local Pressure Loss ................................................................................................. 1093.5.10 Total Pressure Drop ............................................................................................. 111
4. HEAT TRANSFER ..................................... ................................ 115
4.1 Heat Conduction .......................................................................................................... 1154.1.1 Steady-State Heat Conduction with Heat Sources .................................................. 1214.1.2 Steady-State Heat Conduction in Fuel Elements ..................................................... 1234.1.3 Heat Conduction with Temperature-Dependent Conductivity ................................ 128
4.2 Convective Heat Transfer ........................................................................................... 1294.2.1 Laminar Forced Convection .................................................................................... 1324.2.2 Turbulent Forced Convection .................................................................................. 1354.2.3 Natural Convection ................................................................................................. 136
4.3 Radiative Heat Transfer ............................................................................................. 1394.3.1 Heat Transfer between Two Parallel Surfaces ........................................................ 1404.3.2 Heat Transfer in Closed Volumes ........................................................................... 1414.3.3 Radiation of Gases and Vapors ............................................................................... 142
4.4 Pool Boiling Heat Transfer ......................................................................................... 1424.4.1 Heat Transfer coefficient in Pool Boiling ............................................................... 1444.4.2 Critical Heat Flux in Pool Boiling ........................................................................... 1454.4.3 Minimum Film Boiling ........................................................................................... 1464.4.4 Transition Boiling ................................................................................................... 146
4.5 Convective Boiling in Heated Channels ..................................................................... 1474.5.1 Onset of Nucleate Boiling ....................................................................................... 1484.5.2 Subcooled Nucleate Boiling .................................................................................... 1504.5.3 Saturated Flow Boiling ........................................................................................... 1514.5.4 Forced Convective Critical Heat Flux ..................................................................... 1544.5.5 Film Boiling Heat Transfer ..................................................................................... 1564.5.6 Mist Flow Evaporation ............................................................................................ 158
5. SELECTED APPLICATIONS ............................. ........................ 163
5.1 Compressible Flows ..................................................................................................... 1635.1.1 Speed of Sound ....................................................................................................... 1635.1.2 Stationary Gas Flow in Channels ............................................................................ 1655.1.3 Discharge of Compressible Fluid from a Tank ....................................................... 1685.1.4 Two-Phase Critical Flow ......................................................................................... 171
5.2 Fluid-Structure Interactions ....................................................................................... 1755.2.1 Static Reaction Forces ............................................................................................. 1755.2.2 Hydraulic Transients in Elastic Channels ............................................................... 1775.2.3 Flow-Induced Vibrations......................................................................................... 1845.2.4 Conjugate Heat Transfer ......................................................................................... 1895.2.5 Thermal Fatigue ...................................................................................................... 191
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5.3 Plant Components ........................................................................................................1925.3.1 Pipelines and Valves ................................................................................................1925.3.2 Heat Exchangers ......................................................................................................1925.3.3 Steam Generators .....................................................................................................1955.3.4 Pumps .......................................................................................................................2025.3.5 Turbines Sets ............................................................................................................2115.3.6 Steady-State Balance of Boiling Water Reactor ......................................................214
APPENDIX A CONSTANTS AND SELECTED DATA. 219
APPENDIX B DIMENSIONLESS NUMBERS....221
APPENDIX C SELECTED STEAM-WATER DATA.. 223
APPENDIX D SCILAB THERMAL-HYDRAULIC LIBRARY...2 25
INDEX... .... 231
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