## CONTENTS

Preface xv

Preface to the First Edition xvii

Symbols xix

Unit Conversions xxix

1 INTRODUCTION

1.1 Regimes of boiling 1

1.2 Two-Phase Flow 3

1.3 Flow Boiling Crisis 4

1.4 Flow Instability 4

2 POOL BOILING 7

2.1 Introduction 7

2.2 Nucleation and Dynamics of Single Bubbles 7

2.2.1 Nucleation 8

2.2.1 .1 Nucleation in a Pure Liquid 8

2.2.1 .2 Nucleation at Surfaces 10

2.2.2 Waiting Period 19

2.2.3 Isothermal Bubble Dynamics 23

2.2.4 Isobaric Bubble Dynamics 26

2.2.5 Bubble Departure from a Heated Surface 37

2.2.5.1 Bubble Size at Departure

2.2.5.2 Departure Frequency

2.2.5.3 Boiling Sound

2.2.5.4 Latent Heat Transport and Microconvection by

Departing Bubbles

2.2.5.5 Evaporation-of-Microlayer Theory

2.3 Hydrodynamics of Pool Boiling Process

2.3.1 The Helmholtz Instability

2.3.2 The Taylor Instability

2.4 Pool Boiling Heat Transfer

2.4.1 Dimensional Analysis

2.4.1.1 Commonly Used Nondimensional Groups

2.4.1.2 Boiling Models

2.4.2 Correlation of Nucleate Boiling Data

2.4.2.1 Nucleate Pool Boiling of Ordinary Liquids

2.4.2.2 Nucleate Pool Boiling with Liquid Metals

2.4.3 Pool Boiling Crisis

2.4.3.1 Pool Boiling Crisis in Ordinary Liquids

2.4.3.2 Boiling Crisis with Liquid Metals

2.4.4 Film Boiling in a Pool

2.4.4.1 Film Boiling in Ordinary Liquids

2.4.4.2 Film Boiling in Liquid Metals

2.5 Additional References for Further Study

3 HYDRODYNAMICS OF TWO-PHASE FLOW

3.1 Introduction

3.2 Flow Patterns in Adiabatic and Diabatic Flows

3.2.1 Flow Patterns in Adiabatic Flow

3.2.2 Flow Pattern Transitions in Adiabatic Flow

3.2.2.1 Pattern Transition in Horizontal Adiabatic Flow

3.2.2.2 Pattern Transition in Vertical Adiabatic Flow

3.2.2.3 Adiabatic Flow in Rod Bundles

3.2.2.4 Liquid Metal-Gas Two-Phase Systems

3.2.3 Flow Patterns in Diabatic Flow

3.3 Void Fraction and Slip Ratio in Diabatic Flow

3.3.1 Void Fraction in Subcooled Boiling Flow

3.3.2 Void Fraction in Saturated Boiling Flow

3.3.3 Diabatic Liquid Metal-Gas Two-Phase Flow

3.3.4 Instrumentation

3.3.4.1 Void Distribution Measurement

3.3.4.2 Interfacial Area Measurement

3.3.4.3 Measurement of the Velocity of a Large Particle

3.3.4.4 Measurement of Liquid Film Thickness

3.4 Modeling of Two-Phase Flow

3.4.1 Homogeneous Model/Drift Flux Model

3.4.2 Separate-Phase Model (Two-Fluid Model)

3.4.3 Models for Flow Pattern Transition

3.4.4 Models for Bubbly Flow

3.4.5 Models for Slug Flow (Taitel and Barnea, 1 990)

3.4.6 Models for Annular Flow

3.4.6.1 Falling Film Flow

3.4.6.2 Countercurrent Two-Phase Annular Flow

3.4.6.3 Inverted Annular and Dispersed Flow

3.4.7 Models for Stratified Flow (Horizontal Pipes)

3.4.8 Models for Transient Two-Phase Flow

3.4.8.1 Transient Two-Phase Flow in Horizontal Pipes

3.4.8.2 Transient Slug Flow

3.4.8.3 Transient Two-Phase Flow in Rod Bundles

3.5 Pressure Drop in Two-Phase Flow

3.5.1 Local Pressure Drop

3.5.2 Analytical Models for Pressure Drop Prediction

3.5.2.1 Bubbly Flow

3.5.2.2 Slug Flow

3.5.2.3 Annular Flow

3.5.2.4 Stratified Flow

3.5.3 Empirical Correlations

3.5.3.1 Bubbly Flow in Horizontal Pipes

3.5.3.2 Slug Flow

3.5.3.3 Annular Flow

3.5.3.4 Correlations for Liquid Metal and Other Fluid

Systems

3.5.4 Pressure Drop in Rod Bundles

3.5.4.1 Steady Two-Phase Flow

3.5.4.2 Pressure Drop in Transient Flow

3.5.5 Pressure Drop in Flow Restriction

3.5.5.1 Steady-State, Two-Phase-Flow Pressure Drop

3.5.5.2 Transient Two-Phase-Flow Pressure Drop

3.6 Critical Flow and Unsteady Flow

3.6.1 Critical Flow in Long Pipes

3.6.2 Critical Flow in Short Pipes, Nozzles, and Orifices

3.6.3 Blowdown Experiments

3.6.3.1 Experiments with Tubes

3.6.3.2 Vessel Blowdown

3.6.4 Propagation of Pressure Pulses and Waves

3.6.4.1 Pressure Pulse Propagation

3.6.4.2 Sonic Wave Propagation

3.6.4.3 Relationship Among Critical Discharge Rate,

Pressure Propagation Rate, and Sonic Velocity

3.7 Additional References for Further Study

4.2.1 Subcooled Nucleate Flow Boiling

4.2.1.1 Partial Nucleate Flow Boiling

4.2.1.2 Fully Developed Nucleate Flow Boiling

4.2.2 Saturated Nucleate Flow Boiling

4.2.2.1 Saturated Nucleate Flow Boiling of Ordinary

Liquids

4.2.2.2 Saturated Nucleate Flow Boiling of Liquid Metals

4.3 Forced-Convection Vaporization

4.3.1 Correlations for Forced-Convection Vaporization

4.3.2 Effect of Fouling Boiling Surface

4.3.3 Correlations for Liquid Metals

4.4 Film Boiling and Heat Transfer in Liquid-Deficient Regions

4.4.1 Partial Film Boiling (Transition Boiling)

4.4.2 Stable Film Boiling

4.4.2.1 Film Boiling in Rod Bundles

4.4.3 Mist Heat Transfer in Dispersed Flow

4.4.3.1 Dispersed Flow Model

4.4.3.2 Dryout Droplet Diameter Calculation

4.4.4 Transient Cooling

4.4.4.1 Blowdown Heat Transfer

4.4.4.2 Heat Transfer in Emergency Core Cooling Systems

4.4.4.3 Loss-of-Coolant Accident (LOCA) Analysis

4.4.5 Liquid-Metal Channel Voiding and Expulsion Models

4.5 Additional References for Further Study

5 FLOW BOILING CRISIS

5.1 Introduction

5.2 Physical Mechanisms of Flow Boiling Crisis in Visual Observations

5.2.1 Photographs of Flow Boiling Crisis

5.2.2 Evidence of Surface Dryout in Annular Flow

5.2.3 Summary of Observed Results

5.3 Microscopic Analysis of CHF Mechanisms

5.3.1 Liquid Core Convection and Boundary-Layer Effects

5.3.1 .1 Liquid Core Temperature and Velocity

Distribution Analysis

5.3.1.2 Boundary-Layer Separation and Reynolds Flux

5.3.1.3 Subcooled Core Liquid Exchange and Interface

Condensation

5.3.2 Bubble-Layer Thermal Shielding Analysis

5.3.2.2 Interface Mixing 336

5.3.2.3 Mass and Energy Balance in the Bubble Layer 342

5.3.3 Liquid Droplet Entrainment and Deposition in High-

Quality Flow 343

5.3.4 CHF Scaling Criteria and Correlations for Various Fluids 351

5.3.4.1 Scaling Criteria 351

5.3.4.2 CHF Correlations for Organic Coolants and

Refrigerants 357

5.3.4.3 CHF Correlations for Liquid Metals 360

5.4 Parameter Effects on CHF in Experiments 366

5.4.1 Pressure Effects 367

5.4.2 Mass Flux Effects 369

5.4.2.1 Inverse Mass Flux Effects 369

5.4.2.2 Downward Flow Effects 373

5.4.3 Local Enthalpy Effects 377

5.4.4 CHF Table of p-G-X Effects 378

5.4.5 Channel Size and Cold Wall Effects 378

5.4.5.1 Channel Size Effect 378

5.4.5.2 Effect of Unheated Wall in Proximity to the CHF

Point 379

5.4.5.3 Effect of Dissolved Gas and Volatile Additives 382

5.4.6 Channel Length and Inlet Enthalpy Effects and Orientation

Effects 383

5.4.6.1 Channel Length and Inlet Enthalpy Effects 383

5.4.6.2 Critical Heat Flux in Horizontal Tubes 387

5.4.7 Local Flow Obstruction and Surface Property Effects 391

5.4.7.1 Flow Obstruction Effects 391

5.4.7.2 Effect of Surface Roughness 391

5.4.7.3 Wall T hermal Capacitance Effects 392

5.4.7.4 Effects of Ribs or Spacers 393

5.4.7.5 Hot-Patch Length Effects 394

5.4.7.6 Effects of Rod Bowing 395

5.4.7.7 Effects of Rod Spacing 395

5.4.7.8 Coolant Property (D20 and H20) Effects on CHF 396

5.4.7.9 Effects of Nuclear Heating 397

5.4.8 Flow Instability Effects 398

5.4.9 Reactor Transient Effects 399

5.5 Operating Parameter Correlations for CHF Predictions in Reactor

Design 401

5.5.1 W-3 CHF Correlation and THINC-II Subchannel Codes 405

5.5.1.1 W-3 CHF Correlation 405

5.5.1.2 THINC II Code Verification 410

5.5.2 B & W-2 CHF Correlation (Gellerstedt et al., 1969) 415

5.5.2.1 Correlation for Uniform Heat Flux 415

5.5.2.2 Correlation for Nonuniform Heat Flux 416

5.5.3 CE-l CHF Correlation (C-E Report, 1975, 1976) 416

5.5.4 WSC-2 CHF Correlation and HAMBO Code 417

5.5.4.1 Bowring CHF Correlation for Uniform Heat Flux

(Bowring, 1972)

5.5.4.2 WSC-2 Correlation and HAMBO Code

Verification (Bowring, 1979)

5.5.5 Columbia CHF Correlation and Verification

5.5.5.1 CHF Correlation for Uniform Heat Flux

5.5.5.2 COBR A IIIC Verification (Reddy and Fighetti,

1983)

5.5.5.3 Russian Data Correlation of Ryzhov and

Arkhipow (1985)

5.5.6 Cincinnati CHF Correlation and Modified Model

5.5.6.1 Cincinnati CHF Correlation and COBR A IIIC

Verification

5.5.6.2 An Improved CHF Model for Low-Quality Flow

5.5.7 A.R.S. CHF Correlation

5.5.7.1 CHF Correlation with Uniform Heating

5.5.7.2 Extension A.R.S. CHF Correlation to Nonuniform

Heating

5.5.7.3 Comparison of A.R.S. Correlation with

Experimental Data

5.5.8 Effects of Boiling Length: CISE-l and CISE-3 CHF

Correlations

5.5.8.1 CISE- l Correlation

5.5.8.2 CISE-3 Correlation for Rod Bundles (Bertoletti

et al., 1965)

5.5.9 GE Lower-Envelope CHF Correlation and CISE-GE

Correlation

5.5.9.1 GE Lower-Envelope CHF Correlation

5.5.9.2 GE Approximate Dryout Correlation (GE Report,

1975)

5.5.10 Whalley Dryout Predictions in a Round Tube (Whalley

et al., 1973)

5.5.11 Levy’s Dryout Prediction with Entrainment Parameter

5.5.12 Recommendations on Evaluation of CHF Margin in

Reactor Design

5.6 Additional References for Further Study

6 INSTABILITY OF TWO-PHASE FLOW

6.1 Introduction

6.1.1 Classification of Flow Instabilities

6.2 Physical Mechanisms and Observations of Flow Instabilities

6.2.1 Static Instabilities

6.2.1.1 Simple Static Instability

6.2.1.2 Simple (Fundamental) Relaxation Instability

6.2.1.3 Compound Relaxation Instability

6.2.2 Dynamic Instabilities

6.2.2.1 Simple Dynamic Instability

6.2.2.2 Compound Dynamic Instability

6.2.2.3 Compound Dynamic Instabilities as Secondary

Phenomena

6.3 Observed Parametric Effects on Flow Instability

6.3.1 Effect of Pressure on Flow Instability

6.3.2 Effect of Inlet and Exit Restrictions on Flow Instability

6.3.3 Effect of Inlet Subcooling on Flow Instability

6.3.4 Effect of Channel Length on Flow Instability

6.3.5 Effects of Bypass Ratio of Parallel Channels

6.3.6 Effects of Mass Flux and Power

6.3.7 Effect of Nonuniform Heat Flux

6.4 Theoretical Analysis

6.4.1 Analysis of Static Instabilities

6.4.1.1 Analysis of Simple (Fundamental) Static

Instabilities

6.4.1.2 Analysis of Simple Relaxation Instabilities

6.4.1.3 Analysis of Compound Relaxation Instabilities

6.4.2 Analysis of Dynamic Instabilities

6.4.2.1 Analysis of Simple Dynamic Instabilities

6.4.2.2 Analysis of Compound Dynamic Instabilities

6.4.2.3 Analysis of Compound Dynamic Instabilities as

Secondary Phenomena (Pressure Drop

Oscillations)

6.5 Flow Instability Predictions and Additional References for Further

Study

6.5.1 Recommended Steps for Instability Predictions

6.5.2 Additional References for Further Study

APPENDIX Subchannel Analysis (Tong and Weisman, 1979)

A. l Mathematical Representation

A.2 Computer Solutions

REFERENCES

INDEX

## PREFACE

Since the original publication of Boiling Heat Transfer and Two-Phase Flow by L. S.

Tong almost three decades ago, studies of boiling heat transfer and two-phase

flow have gone from the stage of blooming literature to near maturity. Progress

undoubtedly has been made in many aspects, such as the modeling of two-phase

flow, the evaluation of and experimentation on the forced-convection boiling crisis

as well as heat transfer beyond the critical heat flux conditions, and extended research

in liquid-metal boiling. This book reexamines the accuracy of existing, generally

available correlations by comparing them with updated data and thereby

providing designers with more reliable information for predicting the thermal hydraulic

behavior of boiling devices. The objectives of this edition are twofold:

1 . To provide engineering students with up-to-date knowledge about boiling heat

transfer and two-phase flow from which a consistent and thorough understanding

may be formed.

2. To provide designers with formulas for predicting real or potential boiling heat

transfer behavior, in both steady and transient states.

The chapter structure remains close to that of the first edition, although significant

expansion in scope has been made, reflecting the extensive progress advanced

during this period. At the end of each chapter (except Chapter 1 ), additional,

recent references are given for researchers’ outside study.

Emphasis is on applications, so some judgments based on our respective experiences

have been applied in the treatment of these subjects. Various workers from

international resources are contributing to the advancement of this complicated

field. To them we would like to express our sincere congratulations for their valuable

contributions. We are much indebted to Professors C. L. Tien and G. F. Hewitt

for their review of the preliminary manuscript. Gratitude is also due to the

## PREFACE TO THE FIRST EDITION

In recent years, boiling heat transfer and two-phase flow have achieved worldwide

interest, primarily because of their application in nuclear reactors and rockets.

Many papers have been published and many ideas have been introduced in this

field, but some of them are inconsistent with others. This book assembles information

concerning boiling by presenting the original opinions and then investigating

their individual areas of agreement and also of disagreement, since disagreements

generally provide future investigators with a basis for the verification of truth.

The objectives of this book are

1 . To provide colleges and universities with a textbook that describes the present

state of knowledge about boiling heat transfer and two-phase flow.

2. To provide research workers with a concise handbook that summarizes literature

surveys in this field.

3 . To provide designers with useful correlations by comparing such correlations

with existing data and presenting correlation uncertainties whenever possible.

This is an engineering textbook, and it aims to improve the performance of

boiling equipment. Hence, it emphasizes the boiling crisis and flow instability. The

first five chapters, besides being important in their own right, serve as preparation

for understanding boiling crisis and flow instability.

Portions of this text were taken from lecture notes of an evening graduate

course conducted by me at the Carnegie Institute of Technology, Pittsburgh, during

1 96 1-1 964.

Of the many valuable papers and reports on boiling heat transfer and twophase

flow that have been published, these general references are recommended:

“Boiling of Liquid,” by 1. W Westwater, in Advances in Chemica l Engineering 1

## PREFACE TO THE FIRST EDITION

( 1 956) and 2 ( 1 958), edited by T. B. Drew and 1. W Hoopes, Jr. , Academic

Press, New York.

“Heat Transfer with Boiling,” by W M. Rohsenow, in Modern Developmen t in Heat

Transfer, edited by W Ibele, Academic Press ( 1 963).

” Boiling,” by G. Leppert and C. C. Pitts, and “Two-Phase Annular-Dispersed

Flow,” by Mario Silvestri, in Advances in Heat Transfer 1, edited by T. F. Irvine,

Jr. , and 1. H. Hartnett, Academic Press ( 1 964).

“Two-Phase (Gas-Liquid) System: Heat Transfer and Hydraulics, An Annotated

Bibliography,” by R. R. Kepple and T. V. Tung, ANL-6734, U SAEC Report

( 1 963).

I sincerely thank Dr. Poul S. Larsen and Messrs. Hunter B. Currin, James N.

Kilpatrick, and Oliver A. Nelson and Miss Mary Vasilakis for their careful review

of this manuscript and suggestions for many revisions; the late Prof. Charles P.

Costello, my classmate, and Dr. Y S. Tang, my brother, for their helpful criticisms,

suggestions, and encouragement in the preparation of this manuscript. I am also

grateful to Mrs. Eldona Busch for her help in typing the manuscript.