Chapter 1 Introduction 1
1.1 What is Two-Phase Flow 1
1.2 Methods of Analysis 2
1.3 Notation 3
Chapter 2 Flow Pattern and Flow Pattern Map 6
2.1 Introduction 6
2.2 Flow Patterns in Vertical Flows 6
2.2.1 Flow patterns in vertical co-current flow 6
2.2.2 Flow patterns in vertical heated channels 8
2.3 Flow Patterns in Horizontal Flows 10
2.3.1 Flow patterns in horizontal co-current flow 10
2.3.2 Flow patterns in horizontal heated channel 12
2.4 Flow Pattern Maps and Transitions 12
2.4.1 Typical flow pattern maps 13
2.4.2 Criteria for flow pattern transitions 15
2.5 Flow Patterns in Other Applications 17
Chapter 3 Basic Models 18
3.1 Introduction 18
3.2 Drift Flux Model 19
3.3 Two-Fluid Model 20
3.4 Homogeneous Model 22
3.4.1 Conservation of mass 23
3.4.2 Conservation of momentum 24
3.4.3 Conservation of energy 25
3.5 Separated Flow Model 27
3.6 Overview 27
Chapter 4 Empirical Methods for Pressure Drop 28
4.1 Introduction 28
4.2 Correlations Based on the Homogeneous Model 28
4.3 Correlations Based on the Separated Flow Model 31
4.3.1 Correlations from momentum balance 31
4.3.2 Use of model to evaluate pressure loss 33
4.3.3 Determination of the two-phase multiplier 33
4.4 Pressure Losses Through Enlargements,Contractions,Orifices,Bends,and Valves 40
4.4.1 Sudden enlargement 41
4.4.2 Sudden contraction 43
4.4.3 Orifices 43
4.5 Annular Flow 45
4.6 Void Fraction 46
4.6.1 Homogeneous model 47
4.6.2 Drift-flux model 47
4.6.3 The Bankoff variable density model 49
4.6.4 The Hughmark correlation 50
4.7 Conclusions 51
Chapter 5 Two-Phase Critical Flow 52
5.1 Introduction 52
5.2 Theoretical Foundations 53
5.3 Critical Flow in Long Pipes 55
5.4 Critical Flow in Short Pipes,Nozzles and Orifices 59
5.5 Propagation of Pressure Pulses and Waves 63
Chapter 6 Introduction to Hydrodynamic Instability 64
6.1 Introduction 64
6.2 Classifications of Two-Phase Flow Instabilities 65
6.3 Physical Mechanisms of Static Instabilities 67
6.3.1 Fundamental static instability 67
6.3.2 Fundamental relaxation instability 71
6.3.3 Compound relaxationinstability 71
6.4 Physical Mechanisms of Dynamic Instabilities 73
6.4.1 Fundamental dynamic instability 73
6.4.2 Acoustic instability 74
6.4.3 Density-wave oscillations 75
6.4.4 Pressure-drop oscillations 76
6.4.5 Condensing instability 78
6.4.6 Thermal oscillations 78
6.4.7 Boiling water reactor instability 79
6.4.8 Parallel channel instability 80
6.5 Approaches in Two-Phase Flow Stability Analysis 80
6.5.1 Direct numerical analysis 81
6.5.2 Frequency-domain analysis 81
6.6 Situations Where Instability Arise 82
6.7 The Designer's Requirements 83
6.8 Problems Arising in the Application of Models and Tests to Designs 84
Chapter 7 Introduction to Nucleation in Boiling 86
7.1 Vapor-Liquid Equilibrium 86
7.1.1 Equilibrium criterion 86
7.1.2 P-v-T diagram 86
7.1.3 Equation of state 87
7.1.4 Metastable state 88
7.1.5 Clausius-Clapeyron equation 89
7.1.6 Thermodynamic equilibrium at a curved interface 90
7.2 Homogeneous Nucleation 92
7.2.1 Equilibrium condition for a embryo bubble 93
7.2.2 Mechanism of nucleation 94
7.3 Heterogeneous Nucleation 95
7.3.1 Contact angle and wettability 95
7.3.2 Nucleation at solid surfaces 97
7.3.3 Nucleation from entrapped gas or vapor in cavities 99
7.3.4 Size Range of Active Nucleation Sites 101
7.4 Bubble Dynamics 102
7.4.1 Bubble growth in an extensive liquid pool 103
7.4.2 Bubble growth near heated surfaces 107
7.4.3 Diameter and frequency of Bubble departure 110
Chapter 8 Pool Boiling 114
8.1 Nukiyama Boiling Curve 114
8.2 Regimes of Pool Boiling 116
8.3 Nucleate Boiling 120
8.3.1 Inception of boiling(Onset of Nucleate Boiling) 120
8.3.2 Heat transfer mechanisms in nucleate boiling 123
8.3.3 Nucleate Pool Boiling Correlations 125
8.4 Departure From Nucleate Pool Boiling 128
8.4.1 Transitional boiling regime and Taylor instability 128
8.4.2 Helmhohtz instability of vapor jets 130
8.4.3 Prediction of critical heat flux 131
8.5 Film Boiling 133
8.6 Minimum Heat Flux 134
Chapter 9 Flow Boiling 135
9.1 Regimes of Convective Boiling in Tubes 135
9.2 Onset of Boiling in Internal Flows 140
9.3 Subcooled Flow Boiling 143
9.3.1 Regimes of subcooled flow boiling 143
9.3.2 Methods of predicting partial subcooled flow boiling heat transfer 144
9.3.3 Void fraction and pressure drop in subcooled boiling 147
9.4 Saturated Flow Boiling 152
9.4.1 Regimes of saturated flow boiling 152
9.4.2 Heat transfer correlations for saturated flow boiling 153
9.5 Critical Heat Flux in Flow Boiling 157
9.5.1 Mechanisms 157
9.5.2 Prediction of CHF in flow boiling 159
References 167