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ebullition process in forced convection boiling

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Title:
ebullition process in forced convection boiling
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ebullition process in forced convection boiling
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Zeng, Ling-Zhong,
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Gainesville FL
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University of Florida
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Subjects / Keywords:
Boiling ( jstor )
Diameters ( jstor )
Film thickness ( jstor )
Heat transfer ( jstor )
Liquids ( jstor )
Modeling ( jstor )
Nucleation ( jstor )
Sensors ( jstor )
Vapors ( jstor )
Velocity ( jstor )

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University of Florida
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University of Florida
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Copyright Zeng Ling-Zhong. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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30947296 ( oclc )

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THE EBULLITION PROCESS
IN FORCED CONVECTION BOILING


















By

LING-ZHONG ZENG


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1993


UhsvfYSrrY OF FLORIDA LIERIMItS
























TO MY WIFE TANG YONG














ACKNOWLEDGEMENTS

My greatest appreciation goes to Professor James

Klausner, chairman of the supervisory committee, for all the

support and encouragement during the course of this research.

Dr. Klausner, a mentor and role model, has spent a great deal

of time and effort in helping me with the fabrication of the

experimental facility, analysis of the experimental data, as

well as editing this dissertation. I also want to extend my

appreciation to Professor Renwei Mei, member of the

supervisory committee. Dr. Mei has always been accessible and

has provided many useful suggestions throughout the course of

this research. I would also like to thank professors C.K.

Hsieh, D.Y. Goswami, and S. Anghaie for serving on the

supervisory committee. Their useful suggestions have improved

this dissertation.

I also want to thank Dave Bernhard and Boby Warren,

fellow graduate students and friends. Dave and Bob have

provided substantial support in calibrating instrumentation

and planning experiments.

I can not express enough love and appreciation to my

wife, Tang Yong. Without her support, understanding, and

sacrifice, I would not have finished my Ph.D. program.

Finally, I want to thank my parents, brothers, and sisters for


iii








their support throughout the entire course of my education.

It is my parents who inspired me to pursue the education I

have obtained.















TABLE OF CONTENTS

ACKNOWLEDGEMENTS ........................................iii

LIST OF TABLES ........................................ iii

LIST OF FIGURES ........................................ ix

NOMENCLATURE ...........................................xiii

ABSTRACT ...............................................xvii

CHAPTERS

1 INTRODUCTION ....................................1

2 EXPERIMENTAL FACILITIES .........................5

2.1 Flow Boiling Test Loop .....................5
2.2 Construction of Transparent Test Section ..10
2.3 Development of Capacitance Based
Film Thickness Sensors ....................11
2.3.1 Introduction .......................11
2.3.2 Design and Fabrication of
Film Thickness Sensor .............. 13
2.3.3 Instrumentation and Calibration ....15
2.4 Data Acquisition System ...................24

3 HEAT TRANSFER AND PRESSURE DROP
IN SATURATED FLOW BOILING ......................28

3.1 Introduction ............................. 28
3.2 Experimental Results and Discussions ......30
3.3 Conclusions ...............................37

4 INCIPIENCE AND HYSTERESIS .................... 38

4.1 Introduction and Literature Survey ........38
4.2 Experimental Results ......................42
4.3 Theoretical Analysis for Boiling
Incipience ......................... ......44
4.3.1 Boiling Initiation ................. 44
4.3.2 Sustaining Incipience Superheat ....54
4.3.3 Hysteresis of Boiling Incipience ...56
4.4 Conclusions ..................... ........ 57









5 NUCLEATION SITE DENSITY .....................59

5.1 Literature Survey ......................59
5.2 Optical Facility and Measuring
Technique .................................64
5.3 Experimental Results ......................66
5.4 Discussion of Results ..................... 78
5.5 Conclusions ...............................83

6 A UNIFIED MODEL FOR VAPOR BUBBLE DETACHMENT ....84

6.1 Introduction ..............................84
6.2 Literature Survey ......................... 86
6.2.1 Pool Boiling Departure Diameter
Correlations ....................86
6.2.2 Flow Boiling Detachment Diameter
Correlations ....................... 92
6.3 Development of Departure and Lift-off
Model .....................................94
6.3.1 Formulation ........................ 94
6.3.2 Expressions for Bubble Departure
and Lift-off Diameter ............. 105
6.4 Comparison with Experimental Data ........107
6.4.1 Pool Boiling Data ................. 108
6.4.2 Flow Boiling Data ................. 119
6.5 Conclusions ...........................127

7 PROBABILITY DENSITY FUNCTIONS OF VAPOR
BUBBLE DETACHMENT DIAMETER .................... 130

7.1 Introduction ............................. 130
7.2 Formulation ..............................132
7.3 Comparison with Experimental Data ........134
7.4 Conclusions ...........................138

8 VAPOR BUBBLE GROWTH RATE ...................... 140

8.1 Introduction .............................140
8.2 Facility and Methodology ................. 141
8.3 Results and Discussions .................. 144
8.4 Conclusions ........................... 156

9 CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH ...........................157

9.1 Accomplishments and Findings ............. 157
9.2 Suggestions for Future Research ..........159

APPENDICES
A HEAT TRANSFER COEFFICIENT, PRESSURE DROP,
AND LIQUID FILM THICKNESS IN STRATIFIED
TWO-PHASE FLOW ................................161









B NUCLEATION SITE DENSITY IN FORCED
CONVECTION BOILING ............................164

REFERENCES .................................. .......... ..... 167

BIOGRAPHICAL SKETCH ...................................... 177


vii














LIST OF TABLES


Table

6-1 Summary of forces appearing in momentum
equations ..........................................106

6-2 Mean deviation tabulated for present bubble model
as well as other correlations reported in
literature .................. ...... ....... .....109

6-3 Comparison of measured and predicted vapor bubble
departure diameter for elevated pressure data
using present model ................................117

6-4 Comparison of measured and predicted vapor bubble
departure diameter for reduced gravity data
using present model ............................... 118

6-5 Measured and predicted departure diameters
based on high speed cinematography data ............ 123

8-1 A summary of parameters controlling vapor bubble
growth rate in flow boiling ....................... 155


viii














LIST OF FIGURES


Figure

2-1 Schematic diagram of flow boiling facility ...........6

2-2 Calibration curve for flowmeter ......................8

2-3 Calibration curve of heat loss for preheaters ........9

2-4 Isometric view of transparent test section ..........11

2-5 Cut-away view of liquid film thickness sensor .......14

2-6 Prediction of relative film thickness vs capacitance
using model of Chun and Sung (1986) .................18

2-7 Calibration curve for film thickness sensor .........19

2-8 Temperature calibration for film thickness sensor
filled with pure liquid ............................. 21

2-9 Temperature calibration for film thickness sensor
filled with pure vapor ............................. 22

2-10 Close-up view of stratified two-phase flow using
CCD camera (flow direction is from left to right) ...23

2-11 Comparison of liquid film thickness measured with
CCD camera and capacitance sensor ...................24

2-12 A schematic diagram of data acquisition system ......26

3-1 Microconvection heat transfer for saturated forced
convection nucleate boiling ......................... 32

3-2 Macroconvection heat transfer coefficient in
saturated forced convection boiling ................. 33

3-3 Pressure drop in horizontal two-phase flow ..........34

3-4 Zuber and Findlay's (1965) correlation for void
fraction in horizontal stratified two-phase flow ....36

4-1 Nucleate pool boiling hysteresis constructed from
the data of Kim and Burgles (1988) ..................39

ix








4-2 A typical saturated flow boiling plot of q, vs
AT, for G=180 kg/m2-s, X=0.156, and 6=4.8 mm ......43

4-3 Measured saturated flow boiling incipience
wall superheat ......................................45

4-4 An idealized sketch of a vapor embryo in a
conical cavity ......................................47

4-5 Variation of vapor temperature with vapor embryo
volume during expansion inside a conical cavity .....49

4-6 An idealized sketch of a vapor embryo in a
reentry cavity ......................................52

4-7 Variation of minimum vapor temperature and
initiation superheat with cavity reservoir
mouth radius .......................................53

5-1 Pool boiling nucleation site density data from
Griffith and Wallis (1960) ..........................61

5-2 A diagram of optical facility for measurement
of nucleation site density ..........................65

5-3 A typical photograph of nucleation sites on
a boiling surface ...................................67

5-4 Nucleation site density as a function of wall
superheat for constant heat flux and saturation
temperature ........................................68

5-5 Pool boiling nucleation site density as functions
of wall superheat and heat flux .....................69

5-6 Nucleation site density as a function of vapor
Velocity for constant heat flux and liquid film
thickness ........................................ 71

5-7 Nucleation site density as a function of mass
flux ................................................ 72

5-8 Nucleation site density as a function of liquid
velocity ........................................ 73

5-9 Nucleation site density and liquid film thickness
as functions of vapor velocity ......................74

5-10 Nucleation site density as a function of liquid
film thickness ......................................75








5-11 Nucleation site density as a function of heat
flux ................... ........................... 77

5-12 Nucleation site density as a function of wall
superheat ........................................ .78

5-13 Nucleation site density as functions of saturation
temperature and wall superheat ......................79

5-14 Nucleation site density as a function of critical
radius for constant heat flux and vapor velocity ....80

5-15 Nucleation site density as a function of critical
radius for all flow boiling data ....................81

6-1 A typical picture of vapor bubble departure and
lift-off in flow boiling ............................85

6-2 A schematic sketch of vapor bubble detachment
process in flow boiling .............................95

6-3 Comparison of predicted and measured vapor bubble
departure diameter for subatmospheric pressure
data using present model ...........................112

6-4 Comparison of predicted and measured vapor bubble
departure diameter for subatmospheric pressure
data using Cole and Shulman 2 correlation ..........113

6-5 Comparison of predicted and measured vapor bubble
departure diameter for atmospheric pressure data
using present model ............................... 114

6-6 Comparison of predicted and measured vapor bubble
departure diameter for atmospheric pressure data
using Cole and Shulman 2 correlation ............... 115

6-7 Departure diameter variation with mean liquid
velocity at constant AT, .........................121

6-8 Comparison between predicted and measured
departure diameters ............................... 122

6-9 Departure diameter variation with mean liquid
velocity and AT ...................................... 125

6-10 Predicted inclination angle variation with
predicted departure diameter .......................126

6-11 Predicted inclination angle variation with
mean liquid velocity and ATt .....................127








6-12 Comparison between predicted and measured
lift-off diameter ............................ ..... 128

7-1 Statistical distribution of bubble lift-off
diameter in flow boiling ...........................135

7-2 Statistical distribution of bubble departure
diameter in flow boiling at constant AT, .........136

7-3 Statistical distribution of bubble departure
diameter in flow boiling at constant u, ............137

8-1 A schematic diagram of the high speed facility
for filming vapor bubble growth rate ..............142

8-2 Time history of bubble growth ......................145

8-3 Time history of bubble growth .............. ........146

8-4 Time history of bubble growth .....................147

8-5 Time history of bubble growth .......................148

8-6 Time history of bubble growth ......................149

8-7 Time history of bubble growth ......................150

8-8 Time history of bubble growth .......................151

8-9 Time history of bubble growth .....................152

8-10 Time history of bubble growth .......................153

8-11 Time history of bubble growth ....................154


xii














NOMENCLATURE

a, a(t) Radius of a growing vapor bubble

C Capacitance

CD Drag coefficient for a freely rising vapor bubble
in an infinite liquid

Cp Liquid specific heat

C, Empirical constant, equals 20/3

d Vapor bubble diameter

d, Diameter of contact area

D Inside dimension of the test section or diameter

F Force

g Earth gravity

G Mass flux

h Heat transfer coefficient

hfg Vaporization latent heat

Ja Jakob number

k Thermal conductivity

K Power law bubble growth constant as in a(t)=Ktn

m Mass

M Molecular weight

n Power law bubble growth index as in a(t)=Kt"

n/A Nucleation site density

P Absolute pressure or Polarization factor


xiii








p(x) Probability density function

q Heat flux

r Radius of the liquid/vapor interface

r, Mouth radius of the cavity

r2 Mouth radius of the cavity reservoir

R Engineering gas constant

Re Reynolds number

t Time

T Temperature

u Mean velocity

U(y) Velocity profile

V Volume

X Vapor quality

Greek Symbols

a Void fraction

6 Liquid film thickness

AP Pressure drop

AT Superheat

1 Liquid thermal diffusivity

0 Contact angle

0i Bubble inclination angle

A Dynamic viscosity

p Density

a Surface tension coefficient or standard deviation

Half cone angle of the cavity

e Relative permittivity


xiv








Subscripts

b Bulk or buoyancy

cp Contact pressure

d Bubble departure

da Dynamic advanced

dF Departure diameter predicted from Fritz's model

dr Dynamic receded

du Force due to bubble growth

g Non-condensible gas

G Garolite material

h Hydraulic

inc,i Incipience, initiation

inc,s Incipience, sustaining

L Bubble lift-off or lift force created by bubble
wake

e Liquid phase

m Mixture of vapor and liquid

mac Macroconvection

max Maximum

mic Microconvection

min Minimum

s Surface tension

sa Static advanced

sat Saturation

sL Shear lift

sr Static receded

24 Two-phase








v Vapor phase

w Wall

x X-direction, i.e., horizontal direction

y Y-direction, i.e., vertical direction


xvi














Abstract of Dissertation Presented to the Graduate School of
the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy


THE EBULLITION PROCESS
IN FORCED CONVECTION BOILING

By

Ling-zhong Zeng

August, 1993

Chairman: Professor James F. Klausner
Major Department: Mechanical Engineering

A forced convection boiling facility with Refrigerant

R113 was designed and fabricated in order to experimentally

study the ebullition process in horizontal flow boiling.

Capacitance sensors were developed for measuring the liquid

film thickness for stratified and annular two-phase flow.

Measurements of heat transfer coefficient, pressure drop, and

liquid film thickness in stratified two-phase flow with and

without boiling have been obtained. The experimental data

have conclusively demonstrated that microconvection, which is

the heat transfer due to the ebullition process, is

significant in almost all phases of saturated flow boiling.

The initiation and sustaining incipience superheats of

saturated flow boiling with R113 were found to be insensitive

to the fluid convection but they strongly depend on the system

pressure as well as the cooling history of the heating surface

xvii








prior to boiling. Nucleation site density of saturated

forced convection boiling was measured using a CCD camera.

The mean vapor velocity, heat flux, and system pressure appear

to exert a dominant parametric influence on the nucleation

site density. The critical cavity radius is an important

parameter in characterizing the nucleation process but by

itself it is not sufficient to correlate nucleation site

density data for saturated flow boiling. Based on

experimental observations and theoretical reasoning, an

analytical model has been developed for the prediction of

vapor bubble detachment diameters in saturated pool and flow

boiling. The vapor bubble growth rate is a necessary input to

the model. It is demonstrated that over the wide range of

conditions considered, the accuracy of the detachment

diameters predicted using the present model is significantly

improved over existing correlations. The model was also

extended to predict the probability density functions (pdf's)

of detachment diameters by specifying the pdf's of wall

superheat and liquid velocity. The vapor bubble growth rate

during saturated flow boiling was measured using a high speed

cinematography. Based on the experimental data obtained

herein, the vapor bubble radius can be expressed as a function

of time using a power law, where the exponent decreases with

increasing system pressure. The objective of this research is

to understand the fundamentals of the ebullition process in

flow boiling.


xviii














CHAPTER 1

INTRODUCTION

Forced convection boiling, also referred to as flow

boiling, has been used in a variety of engineering

applications for its high heat and mass transfer rates. In

nuclear power applications, flow boiling with water is used to

extract heat from reactors. Also flow boiling can be found in

fossil fuel fired steam generators, the chemical process

industry, refrigeration and air-conditioning industry, and

cooling of electrical distribution facilities. Other

potentially important applications include compact flow

boiling heat exchangers for use in spacecraft and cooling of

microelectronic components.

Due to its engineering importance, boiling heat transfer

has been the focus of extensive research for the past four

decades. However, to date, boiling remains one of the most

controversial subjects in the field of heat transfer. Many

questions raised four decades ago concerning boiling phenomena

remain unanswered (Lienhard, 1988). Current engineering

designs involving boiling phenomena rely heavily on empirical

correlations developed from experimental measurements.

Rohsenow (1952) first suggested that the rate of heat transfer

associated with forced convection boiling is due to two








2

additive mechanisms, that due to bulk turbulence and that due

to ebullition. Based on Rohsenow's conjecture, Chen (1966)

proposed a saturated flow boiling heat transfer correlation

which is simply the sum of the respective macroconvection and

microconvection heat transfer coefficients. The terms macro-

and microconvection respectively denote the contribution due

to heat transfer from bulk turbulent convection and that due

to the ebullition process. The macroconvection heat transfer

coefficient was calculated using a single-phase flow

correlation based on the liquid fraction flowing modified by

an enhancement factor, while the microconvection heat transfer

coefficient was calculated using a pool boiling correlation

modified by a suppression factor.

Chen's (1966) correlation or modified forms of it are

widely used throughout industry despite the fact that they

fail to accurately correlate a wide range of flow boiling heat

transfer data (Gungor and Winterton, 1986). One

characteristic of Chen's correlation is that it predicts the

microconvection contribution to flow boiling heat transfer is

always small compared to macroconvection. In contrast, Mesler

(1977) argued that the microconvection component is dominant.

Staub and Zuber (1966), Frost and Kippenhan (1967), Klausner

(1989), and Kenning and Cooper (1989) have presented flow

boiling heat transfer data which display a strong dependence

on the ebullition process. In addition, experimental data

provided by Koumoutsos et al. (1968) and Cooper et al. (1983)








3

demonstrate that the ebullition process in flow boiling cannot

be adequately modelled with pool boiling correlations. In

order to significantly improve flow boiling heat transfer

predictions over Chen's approach, it is necessary to

understand the mechanisms governing both macro- and

microconvection as well as their relative contribution to the

total heat transfer.

In this work, major efforts have focused on understanding

the physics governing vapor bubble incipience, nucleation site

density, growth and detachment in forced convection boiling.

In order to achieve this goal, a flow boiling facility with

refrigerant R113 was designed and fabricated. The boiling

test section is optically transparent thus allowing for the

visualization of the ebullition process. A CCD camera has

been used to measure nucleation site densities and high speed

cinematography was used to measure vapor bubble growth rates.

Two capacitance-based film thickness sensors were designed and

fabricated to measure the liquid film thickness on the upper

and lower surfaces of the horizontal square test section.

Since the flow boiling facility usually experiences large

temperature variations during operation, the temperature

dependence of the capacitance sensors must be accounted for.

A new and simple method has been developed to account for

temperature when using the film thickness sensor calibration

curve.

Using the current flow boiling facility, experimental








4

evidence was obtained to demonstrate that the heat transfer

contribution due to the ebullition process is significant in

almost all phase of boiling. Experimental data on the

incipience wall superheat, nucleation site density, and vapor

bubble growth rate for saturated flow boiling have been

gathered over a wide range of flow and thermal conditions.

The parametric influence of two-phase flow conditions on the

ebullition process have been analytically investigated.

An analytical model has been developed for the prediction

of vapor bubble departure and lift-off diameters for both pool

and flow boiling. The model was compared against all

experimental data available in the literature, and excellent

agreement has been achieved. Based on this bubble detachment

model, an analytical approach was proposed for predicting

vapor bubble detachment diameter probability density functions

(pdf's) for a specified wall superheat pdf and liquid velocity

pdf.














CHAPTER 2

EXPERIMENTAL FACILITIES



2.1 Flow Boiling Test Loop

A flow boiling facility, shown schematically in Figure 2-

1, was designed and fabricated. Refrigerant R113 was selected

as the boiling liquid in this facility primarily due to its

low latent heat of evaporation and boiling point. A variable

speed model 221 Micropump was used to pump R113 through the

facility. A freon dryer/filter was installed on the discharge

of the pump to filter out alien particles in the liquid and to

prevent the formation of hydrofluoric acid in the refrigerant.

The volumetric flow rate of liquid was monitored with an Erdco

Model 2521 vane type flowmeter equipped with a 4-20 ma analog

output. The flowmeter output was attached to a 500 ohm power

resistor. The voltage across the resistor was recorded with

a digital data acquisition system which will be discussed

later. The flowmeter was calibrated using a volume-time

method. A calibration curve for the volumetric flow rate vs

voltage is displayed in Figure 2-2. The standard deviation of

the experimental data from a third order polynomial least-

squares fit is 0.5%, which is equivalent to the repeatability

of the flow meter claimed by the manufacturer. At the outlet








6

of the flowmeter, five preheaters have been installed to

generate a saturated two-phase mixture. Each preheater


GEAR
PUMP


Figure 2-1. Schematic diagram of flow boiling facility.


consists of a 25 mm ID, 1.2 m long hard copper round pipe

around which 18 gauge nichrome wire has been circumferentially

wrapped. The nichrome wire is electrically insulated from the

copper pipe with ceramic beads. The preheaters are thermally

insulated using a 25 mm thick fiberglass insulation layer.








7

Each of the five preheaters is powered by a 240 volt line

through an adjustable AC autotransformer. The heat loss of

the preheaters has been calibrated as a function of

temperature difference between the outer surface of the

insulation and the ambient. A typical calibration curve is

shown in Figure 2-3. In order to allow the two-phase mixture

generated by the preheaters to be fully developed and smoothly

flow into a square transparent test section, which will be

described shortly, a 1.5 m long and 25 x 25 mm inner dimension

square copper duct has been mounted downstream of the

preheaters. The duct is also thermally insulated using

fiberglass, thus provides an adiabatic developing length for

the two-phase flow. A capacitance-based liquid film thickness

meter, which will be described in detail in section 2.3, was

installed on the either side of the test section to measure

the inlet and outlet liquid film thickness of the two-phase

mixture. Two Viatran model 2415 static pressure transducers

have been installed at the inlet and outlet of the test

section to measure the system pressure with an accuracy of

0.5% of full scale (30 psig). Two type E thermocouple probes

were also located at the same position to measure the bulk

temperature of R113. When the two-phase mixture becomes

saturated, the measured bulk temperature using thermocouples

matches that calculated from the saturation line based on the

measured system pressure to within 0.50C, which is also the

accuracy of the absolute temperature measurement from the








8

thermocouples. A precision Viatran differential pressure

transducer was installed to measure the pressure drop across


0.20

0.18

0.16

0.14

0.12

0.10

0.08

0.06

0.04


0.02 I-


0.00


0 1 2 3 4 5 6 7 8 9


Flow Meter Output (Volts)

Figure 2-2. Calibration curve for flowmeter.


the test section with an accuracy of 0.25% of full scale (120

mmH2O). A throttle valve is located downstream of the test

section, which allows the test section pressure to be adjusted

from atmospheric pressure to 30 psig, which is the maximum


I I I I I I I I


I I I I I I I 1 I

























4


I 3


2


1v



0 10 20 30 40 50

To-T (aC)


Figure 2-3. Calibration curve of heat loss for preheaters.


safe operating pressure of the square pyrex section.

Following the test section, the R113 two-phase mixture

condenses in a shell and tube water cooled heat exchanger to

return to the liquid storage tank.



2.2 Construction of Transparent Test Section

The major difficulties associated with fabricating a

transparent flow boiling refrigerant based test section and












PRYREX GLASS
TEST SECTION


HEATING -
SURFACE
(20mm x 0,127mm)


FLANGE


Figure 2-4. Isometric view of transparent test section.

connecting it with rigid copper pipes are the facts that the

pyrex glass is brittle and small stress concentrations

substantially reduce its safe operating pressure. After

testing many different designs, a satisfactory test section

was eventually fabricated. The fabrication procedures, which

have been detailed by Bernhard (1993), will not be repeated

here. A brief description of the test section is given. The

main body of the flow boiling test section is comprised of a








11

25 x 25 mm ID square pyrex glass tube that is 4 mm thick and

0.457 m long as depicted in Figure 2-4. A 0.13 mm thick and

22 mm wide nichrome strip, used as a heating and boiling

surface, has been adhered to the lower inner surface of the

square tube with epoxy. Six equally spaced 36 gauge type E

thermocouples were located underneath the nichrome strip using

high thermal conductivity epoxy. The mean wall temperature of

the nichrome strip was obtained by averaging the readings from

these six thermocouples. The test section was connected to

the facility with a brass block on either side. Each end of

the nichrome strip was bolted to the block to maintain good

electrical contact. Epoxy was used to seal gaps between the

glass tube and brass blocks. The facility was pressurized

with air to 30 psig and leak-checked prior to introducing

R113. Due to safety considerations, the facility has not been

operated at pressures above 30 psig.



2.3 Development of Capacitance Based Film Thickness Sensors

2.3.1 Introduction

It has been observed that in a horizontal saturated flow

boiling system, vapor-liquid flow is usually in a stratified

or annular flow regime due to the influence of gravity.

Research involving this flow regime requires knowledge of the

liquid film thickness distribution along the wall of a duct.

Many of the techniques used to measure liquid film thickness

and volume fraction were summarized by Hewitt (1978) and Jones








12

(1983). Of these, the only non-intrusive measuring

techniques, applicable to dielectric fluids, which capture the

liquid film thickness and volume fraction with a very rapid

response time are capacitance and radiation absorption

techniques. The implementation of the radiation absorption

technique requires expensive, bulky equipment with which

special safety precautions must be adhered to. In contrast,

the capacitance sensors used to measure liquid film thickness

and volume fraction are compact, safe, and inexpensive and

thus were selected for this research. Ozgu and Chen (1973)

used a capacitance sensor to measure liquid film thickness for

axisymmetric two-phase flow while Abouelwafa and Kendall

(1979), Sami et al. (1980), Irons and Chang (1983), Chun and

Sung (1986), and Gaerates and Borst (1988) used a capacitance

sensor to measure volume fraction. A summary of these

investigations can be found in Delil (1986). All of the

capacitance probes and measuring techniques reported by these

investigators were used only for adiabatic flow; there was

very little mention made of the temperature dependence of

capacitance sensors. Furthermore, the ring-type capacitance

sensor described by Ozgu and Chen (1973) may only be used to

measure symmetric two-phase duct flow, such as vertical up-

flow or down-flow. The sensor is not applicable for use with

horizontal two-phase flow, which is usually asymmetric due to

the gravitational stratification of the phases.

Since a forced convection boiling system undergoes large








13

variations in temperature, the calibration of the capacitance

sensor must account for its temperature dependence in order to

obtain accurate liquid film thickness measurements. Both the

permittivity of the liquid and the material of construction

are temperature dependent. Therefore, either the sensor must

be calibrated over the range of temperatures for which it will

operate or a suitable temperature correction scheme must be

employed when the sensor is calibrated at a fixed temperature.

The latter approach has been successfully used in this work.



2.3.2 Design and Fabrication of Film Thickness Sensor

The liquid film thickness sensor was designed to match

the inner dimension of the test section for a smooth

transition of the flow. Therefore, four Garolite sheets (152

x 38 x 6 mm) were machined and bonded together with Conap

epoxy to form a body which has a 25 x 25 mm inner square cross

section as shown in Figure 2-5. Garolite material was chosen

for the fabrication of the film thickness sensor body because

it has good dielectric properties and is corrosion resistant

to refrigerants. Two parallel grooves, 7.9 mm wide and 3.2 mm

deep were machined on both the outer upper and lower halves of

the sensor body for placement of the capacitance strips. The

distance separating two adjacent grooves is 7.9 mm. This

distance was chosen because Ozgu and Chen (1973) reported the

optimum thickness and distance between the parallel ring

sensors is equal to the film thickness at which the highest















GAROLITE
FLANGE ~-- -




S25 m



BNC --
CONNECTOR -

ALUMINUM LOWER COPPER
SHIELDING CAPACITANCE
STRIPS


15,24 cm

Figure 2-5. Cut-away view of liquid film thickness sensor.

resolution is expected. It shall be demonstrated that the
best resolution is obtained with liquid film thickness of 5 to
6 mm and poor resolution is observed near the centerline.
Copper strips with a thickness of 0.1 mm were bonded into the
grooves with epoxy. An aluminum chassis was fabricated around
the sensor body. The purpose of the chassis is twofold: it
shields extraneous electromagnetic radiation and also
compresses the sensor body so that it is pressure resistant.








15

Four BNC connectors, each of which were connected to a copper

strip using unshielded wire, were electrically insulated and

mounted on the chassis. Two square Garolite flanges (10.2 x

10.2 cm), which were used to mount the film thickness sensor

in the flow boiling facility, were bonded to the two ends of

the body with epoxy. The film thicknesses in the lower and

upper half of the duct were determined from the capacitance

between the respective pair of lower and upper parallel copper

strips. Two identical sensors were fabricated in this manner.



2.3.3 Instrumentation and Calibration

In order to obtain good performance from the film

thickness sensors, a high resolution capacitance meter must be

used to measure the capacitance across the parallel strips.

For this purpose, a Keithley 590 digital CV analyzer, which

has a resolution of 0.1 Ff, an accuracy and repeatability of

0.1% of full scale, and a frequency response of 45 kHz, as

reported by the manufacturer, was used to measure the

capacitance. The analog output of this instrument was

connected to a 12 bit analog to digital converter (A/D) which

will be described in section 2.4.

An accurate analytic relation between the capacitance and

liquid film thickness is extremely difficult to determine due

to the three-dimensional nature of the sensor. Therefore, the

sensor must be calibrated. The difficulty associated

calibrating the sensor for use in a variable temperature








16

environment is that the permittivity of both the solid and

liquid is temperature dependent. A complete calibration is

obtained only when the liquid film thickness and temperature

are varied over the full range. Such a calibration is tedious

and impractical. Therefore, an innovative scheme is proposed

which allows the sensor to be used based on its calibration at

a fixed temperature

A crude model for predicting the capacitance as a

function of film thickness or volume fraction for a known

material permittivity was introduced by Chun and Sung (1986)

by considering the sensor as a network of parallel and series

equivalent plate-type capacitors. This type of modeling was

attempted for the sensor described above. The relative

permittivity of R113 vapor was taken to be unity. The

relative permittivity of liquid R113 as a function of

temperature was determined from the Clausius-Mosotti equation

as reported by Downing (1988):

M+Pp,
et Pp1 (2-1)
SM-Pp,


where et is the liquid relative permittivity, M is the

molecular weight, P is the polarization, and p, is the liquid

density. The temperature dependence of permittivity comes

from the fact that the liquid density varies with temperature.

Published values of permittivity could not be found for

Garolite material. However, Garolite is a composite material








17

manufactured from E-glass and a phenolic based epoxy resin,

and based on the data of Leeds (1972), the relative

permittivity of Garolite was approximated over a range of

temperature of 25 to 200 OC using

eG=4.213+0.0023T (2-2)

where T is temperature in degrees Celsius. Using the crude

model of Chun and Sung (1986) the relative film thickness, 6',

for horizontal stratified flow is shown in Figure 2-6 as a

function of the relative capacitance C* for both the upper and

lower section of the sensor at 25 and 80 OC. Here C* is

defined by

c-c
C*- (2-3)
Cl-C,


where C is the capacitance across the sensor for two-phase

flow, C, is the sensor capacitance for purely liquid flow, and

C, is that for purely vapor flow; all these capacitances are

temperature dependent. For the lower section, 6'=6/h, and for

the upper section, 6'=6/h-1, where 6 is the liquid film

thickness and h=12.7 mm is the distance from the sensor inside

wall to the centerline. The results displayed in Fig. 2.6

reveal that the functional relationship between 6' and C* is

essentially independent of temperature over the 25-80 C range

investigated.

Guided by the fact that the relationship between C* and

6' is not temperature dependent, it was decided to calibrate

















1.0 I I--

v Upper section, 25C
o Upper section, 80C
S0.8-



o 0.6 -



0.4



0.2 Lower section, 250C
Sv Lower section, 80C


0.0 1 1 1
0.0 0.2 0.4 0.6 0.8 1.0

Relative Capacitance C'



Figure 2-6. Prediction of relative film thickness versus
capacitance using model of Chun and Sung
(1986).


the sensor for the stratified flow regime at room temperature

on a bench top under carefully controlled conditions. The

results of the calibration for sensor #1 were tabulated in

terms of 6' and C' and are shown in Figure 2-7. It is noted

that for the lower section of the sensor, 6' was normalized by

0.75h rather than h since the full scale of the measurement

for this section is 0.75h. There was no modification for the
















Meter #1, calibrated at 25 OC
1.0 1 1 -
Upper section
Lower section
0.8


0.6 -



0.4



0.2 -



0.0 I I
0.0 0.2 0.4 0.6 0.8 1.0

Relative Capacitance C'




Figure 2-7. Calibration curve for film thickness sensor.


upper section. It is seen from Figure 2-7 that the resolution

is good when the film thickness is well below the centerline

for the lower section and well above the centerline for the

upper section. There exists a small region near the

centerline where the film thickness can not be resolved.

However, for the current study with saturated forced

convection boiling, this does not pose a severe problem

because the liquid film is always well below the centerline








20

when the two-phase mixture is at saturated conditions.

In order to determine the liquid film thickness from the

calibration curves shown in Figure 2-7, C, and C, must be

determined as a function of temperature when the two-phase

mixture is at a temperature other than the calibration

temperature. The functions were determined after the sensors

had been installed in the facility. To do so, pure liquid

R113 was circulated through the facility and was heated. When

a steady temperature was reached, the capacitances across the

lower and upper pairs of copper strips were recorded. This

procedure was repeated for a series of increments of

temperature while the throttle valve was adjusted to elevate

the system pressure to avoid vapor generation. The results

obtained have been displayed in Figure 2-8. Similar

procedures were followed to obtain the capacitance for pure

vapor as a function of temperature as shown in Figure 2-9.

Because pure vapor flow could only be achieved by

depressurizing the boiling facility after two-phase flow had

been established, it was difficult to obtain the measurement

over a wide range of temperature. In this work only four

different temperatures were obtained. By incorporating the

calibration curves shown in Figures 2-7, 2-8, and 2-9, the

liquid film thickness may be determined as a function of

capacitance and temperature of any two-phase mixture.

In order to evaluate the performance of the liquid film

thickness sensor developed here, a CCD camera was set up for















1.85 1111

v meter #1, upper section
1.80 meter #1, lower section


1.75


S 1.70


S1.65

S1.60 -



1.55


1.50
20 30 40 50 60 70

Temperature (C)

Figure 2-8. Temperature calibration for film thickness
sensor filled with full liquid.

optically measuring the liquid film thickness for stratified

flow. The camera was focused normal to the transparent test

section to avoid optical distortion. A typical picture of

two-phase stratified flow obtained with the CCD camera used

for comparison is displayed in Figure 2-10. Liquid film

thickness is determined from the scale placed on the test















1.75 1 1

v meter #1, upper section
1.70 meter #1, lower section


1.65


) 1.60


1.55
4

o I1.50


1.45 -


1.40 I I i
20 30 40 50 60 70 80

Temperature (C)

Figure 2-9. Temperature calibration for film thickness
sensor filled with full vapor.

section. The length measurement from the pictures is accurate

to 0.1 mm. Since the liquid/vapor interface was wavy in

almost all cases considered, the instantaneous photograph of

the flow structure had to be synchronized with an

instantaneous capacitance and temperature measurement in order

to obtain a reliable comparison. The degree of waviness of













































Figure 2-10. Close-up view of stratified two-phase flow
using CCD camera (flow direction is from left
to right).


the liquid/vapor interface depends on flow conditions. The

two-phase mixture bulk temperature ranged from 50-70 OC. The

use of the digital data acquisition system, which will be

described shortly, greatly facilitated the synchronization

process. The liquid film thickness data measured using the

CCD camera have been compared against that measured by sensor

















25



20 meter #1













0 II
n S








0 5 10 15 20 25
Measured Film Thickness 6 (mm)
CCD Camera



Figure 2-11. Comparison of liquid film thickness measured
with CCD camera and capacitance sensor.


#1 and the results are illustrated in Figure 2-11. It can be

seen that over the entire range of film thickness and

temperature considered, the comparison is good. The average

error based on the data shown in Figure 2-11 is within 2% of

the full scale.



2.4 Data Acquisition System

A digital data acquisition system has been assembled for








25

this investigation, which is used for recording measurements

of pressure, temperature, flow rate, and capacitance for this

investigation. A schematic diagram of the data acquisition

system is displayed in Figure 2-12. The data acquisition

system is comprised of two Acces 16-channel multiplexer cards

(AIM-16) interfaced with one Acces 12-bit 8-channel analog-to-

digital converter (AD12-8), mounted in an I/O slot of a

Northgate PC/AT computer. The AD12-8 has a maximum conversion

speed of 40 kHz and input voltage range of 10 Volts. Each

AIM-16 card is interfaced with one channel of the AD12-8

board. Thus there are 32 different channels available when

using this system. Channel 0 of the AIM-16 has been used to

determine the cold junction temperature using a resistance

temperature device (RTD). The temperature scale factor for

the output of the RTD is 24.4 mV/OC. Each channel of the AIM-

16 has a preamplifier with gains ranging from 0.5 to 1000 and

may be programmed through the computer. The AD12-8 board and

AIM-16 cards were calibrated according to manufacturer's

specifications. Each analog signal from the respective

instrument is connected to one of the 32 channels of the AIM-

16 cards. Appropriate gains were set up for different

channels to achieve maximum resolution. Since two-phase flows

are inherently unstable, all measurements were time-averaged

to obtain repeatable values. Using this system, an average of

500 sampling points were collected over a time period of 30

seconds in order to obtain repeatable measurements. Quick

















RESISTORS


_- 12-MHZ 286-AT
ACCESS AD12-8
A/D INPUT CARD
THERMOCOUPLES TO TEST
FACILITY, (SURFACE PROBES,
INFLOW PROBES, AND HEAT LOSS
PROBES)
VALIDYNE MAGNETIC RELUCTANCE
- DIFF. PRESS, TRANSDUCER


Figure 2-12. A schematic diagram of data acquisition system.


BASIC software routines have been developed for all data

acquisition operations.

A summary of the design operating conditions of the

facility are as follows: mass flux, G=80-350 kg/m2-s; quality,

X=0-0.35; system pressure, P=1.0-2.3 bars; and test section

heat flux, q,=0-40 kW/m2. The operating constraints of the








27

facility are primarily due to the maximum flow rate of the

Micropump, the strength of the pyrex glass, and the

temperature limitation of the E-poxy used in the test section.

All the experiments performed in this investigation have been

confined to the system design conditions.














CHAPTER 3

HEAT TRANSFER AND PRESSURE DROP
IN SATURATED FLOW BOILING



3.1 Introduction

In this section of the investigation, measurements of

heat transfer coefficient with and without boiling are

described which have been obtained for a saturated two-phase

mixture flowing through the test section. The purpose of

these measurements is to elucidate the importance of the

microconvection contribution to the total heat transfer in

flow boiling. The pressure drop and liquid film thickness for

stratified two-phase flow without boiling have also been

measured over a wide range of mass flux, G, and quality, X.

The parametric trends of the heat transfer coefficient and

pressure drop for horizontal two-phase flow are displayed and

compared against those observed for single phase flows.

The total two-phase heat transfer coefficient with and

without boiling is defined by


=qw (3-1)
T,- Tb


where T, is the mean wall temperature, Tb is the two-phase bulk

temperature, and q, is the wall heat flux. Since this work








29

only deals with saturated flow boiling, Tb is equivalent to

the saturation temperature, Tt. In order to sort out the

contribution of heat transfer between macro- and

microconvection during flow boiling, the following

experimental procedure was closely adhered to. The Micropump

and preheaters were adjusted to obtain a fixed G, X, and T,

at the inlet of the test section. The nichrome strip was

heated up gradually until boiling was initiated. During this

process the heat flux and temperature were recorded. The

pressure drop, AP, across the test section and liquid film

thickness 6 at the inlet and outlet of the test section were

also recorded. As heat flux q, was further increased, vapor

bubble generation at the heating surface was generated and

sustained with increasing q,. Further measurements of h2, were

made until q, was increased up to 40 kW/m2. The range of flow

conditions over which measurements were made was G=125-280

kg/m2-s and X=0.04-0.30. As had been expected, it is observed

that for a fixed G, X, and T,, the measured two-phase heat

transfer coefficient, h2, without boiling is independent of

the heat flux, q,. Hence, it was assumed that the non-boiling

two-phase heat transfer is equivalent to that of the

macroconvection heat transfer coefficient in flow boiling and

is herein denoted by hc. As has been discussed in Chapter 1,

Rohsenow (1952) first suggested that the rate of heat transfer

associated with forced convection boiling is due to two

additive mechanisms, that due to bulk turbulence and that due








30

to ebullition. Using Rohsenow's superposition hypothesis, the

heat transfer coefficient attributed to microconvection during

saturated flow boiling may be calculated from

hmC=h2 -hmac. (3-2)





3.2 Experimental Results and Discussions

Prior to discussing the details of the experimental

results, it is necessary to define several parameters. For

two-phase stratified horizontal flow, the mean velocity of the

liquid film may be calculated from

uG(1-X)D (33)


and mean vapor velocity by

GXD
Uv p D (3-4)
p,(D-8)

where u is mean velocity, 6 is liquid film thickness, p is

density and D is the inside dimension of the horizontal square

test section for which only the lower surface is covered with

a liquid film; subscripts t and v denote the liquid and vapor

phases, respectively. The Reynolds number for liquid and

vapor phases are defined by


Re,= PuDa (3-5)
III


and











Rev= pvUPhv (3-6)
Pv


respectively, where Re is Reynolds, Dh is the hydraulic

diameter, and j is the dynamic viscosity.

Microconvective heat transfer coefficients were obtained

for the nucleate flow boiling regime using the methodology

described above. The flow boiling heat transfer data were


organized by plotting h./h2, against hcincs as shown in




Figure 3-1. It is very significant that all the experimental

data have been collapsed into a single curve. Here ATmc,.

denotes the sustaining incipience wall superheat. These data

conclusively demonstrate that microconvection is important in

almost all phases of saturated flow boiling heat transfer and

its contribution becomes dominant at high heat fluxes. This

conclusion distinctly contests most forced convection boiling

heat transfer correlations reported in the literature which

predict that macroconvection is always dominant. The curve

presented in Figure 3-1 may also be viewed as a "flow boiling

curve". As is well known, the conventional heat flux vs wall

superheat plot used for pool boiling cannot collapse the flow

boiling data due to the large variation of macroconvection

heat transfer.

Further consideration was given to the macroconvection














1.0 i 1 i 1

ATn =-8.7 OC (average)
G=1-5-266 kg/m2-s
0.8 X=0.04-0.30
6=1.6-8.8 mm

V7 V





t 0.4 -



0.2



0.0 I I I
1 2 3 4 5 6 7 8

q/(hmacATine,s)

Figure 3-1. Microconvection heat transfer for saturated
forced convection nucleate boiling.


heat transfer component, h,. Figure 3-2 shows h. as a

function of liquid Reynolds number, Ret, and vapor Reynolds

number, Rev. If h., is approximated as a linear function of

Reynolds number over the limited range of data, the standard

deviation based on Re, is 0.165 and that based on Rev is 0.093,

and thus it is seen that h. is better correlated with Rev than

Re,. This result is fundamentally different from that in















Vapor Reynolds Number Re (xlO )

2 4 6 8 10


Liquid Reynolds Number Re, (xlO-)


Figure 3-2.


Macroconvective heat transfer coefficient in
saturated forced convection boiling.


single-phase forced convection and may possibly be due to the

enhanced turbulence caused by strong interfacial waves.

Considering that most flow boiling correlations for h. are

simply modified single-phase heat transfer correlations

applied to the liquid, there remains considerable room for

improved modelling of both hn. as well as h. in flow boiling

heat transfer correlations.


.tI
0



U
4a
a


4.4
U
u
a
h


u
a,
1
42


* hmac vs Re1
V ho vs Re




*ao vv





VV S
vle.Q57


I~iw0 r


1.0 C-


0.5 F-













-4
Vapor Reynolds Number Re (xlO )

2 4 6 8 10


50



40 -


30 -



20 -


AP vs Re,
V AP vs Rev




*0 7q v
v *

Sve


1I




7 1 I
VP j~Vl

I Ii! -4


Liquid Reynolds Number Re, (10- )


Figure 3-3. Pressure drop in horizontal two-phase flow.


Figure 3-3 displays the pressure drop, AP, as a function

of Re, and Rev. In contrast to the case of h,, AP is found to

be better correlated with Re, rather than Rev. This result

suggests that the principle of analogous energy and momentum

transport in incompressible single phase flow may not be

appropriate for stratified two-phase flow in a boiling system

where strong interfacial waves are observed. For two-phase

flow with strong interfacial waves, Andritsos and Hanratty








35

(1987) have provided extensive experimental evidence that the

mean vapor velocity is a controlling parameter on the

interfacial shear stress. Recently, Maciejewski and Moffat

(1992) measured the velocity and temperature distributions in

the near wall region for flow over a flat plate and found that

the strong turbulence intensity in the free stream could

substantially alter the near-wall temperature profile while

the velocity profile maintains a relatively uniform shape.

Therefore, the dissimilarity between heat transfer and

pressure drop observed in this research may be due to the

strong turbulence intensity at the interface which may

influence the temperature profile in a manner significantly

different from that of the velocity profile.

In stratified two-phase flow, the thickness of the liquid

film along the lower surface can be converted to void fraction

a by


=1-- (3-8)
D

Using Zuber and Findlay's (1965) correlation, all the

experimental data obtained in this research were collapsed

into a straight line as shown in Figure 3-4. u, is the

superficial velocity of vapor phase defined by

GX
u-,G (3-9)
Pv

and um is the two-phase mixture velocity which is defined by











(3-10)


U -GX G(X-1)
Pv Pe


It is noted that the observed void fraction for saturated flow

boiling system in this work is always larger than 0.7. Since

the conversion of liquid film thickness to void fraction in

this range has greatly reduced the relative error of the

results, the collapse of the data does not necessarily imply


2 3

Drift Flux um (m/s)


Figure 3-4


Zuber and Findlay's (1965) correlation for
void fraction in horizontal stratified two-
phase flow.








37

that Zuber and Findlay's (1965) correlation captured the

correct physics governing the void fraction distribution in

two-phase flow.



3.3 Conclusions

Measurements of two-phase heat transfer coefficients with

and without boiling have demonstrated that the microconvection

component of heat transfer in saturated flow boiling is

significant in almost all phases of boiling and its

contribution to the total heat transfer becomes dominant as

heat flux increases. The macroconvection heat transfer in

saturated flow boiling with strong interfacial waves is not

well correlated by simply using an analogy between momentum

and heat transport. Therefore, the development of a

significantly improved heat transfer correlation for flow

boiling, which has not been attempted in this study, will

require improved modelling of both the micro- and

macroconvection processes.














CHAPTER 4

INCIPIENCE AND HYSTERESIS



4.1 Introduction and Literature Survey

The development of modern electronics packaging requires

the ability to remove large amounts of heat from

microelectronic chips. The use of nucleate boiling heat

transfer of many dielectric liquids has been investigated for

this purpose due to their high heat transfer rates. Since

dielectric liquids usually have a high wettability on most

solid surfaces, the large overshoot of incipience superheat,

i.e. boiling hysteresis, has prevented their wide

applications. The experimental observation of boiling

incipience and hysteresis for highly wetting liquids is

clearly displayed in Figure 4-1 which was reconstructed from

the experimental data of Kim and Bergles (1988). Figure 4-1

is a typical heat flux vs wall superheat plot. The initiation

incipience point A is the point at which vapor bubbles just

begin appearing on the heating surface with increasing heat

flux. The sustaining incipience point B in Figure 4-1 is the

point just before vapor bubbles disappear from the heating

surface with decreasing heat flux. The overshoot of wall

superheat at the initiation incipience point is generally








39

referred as boiling hysteresis. Incipience and hysteresis in

pool boiling have been the focus of numerous experimental


106






105


103
0.


1


1 10
T -Tat (K)


100


Figure 4-1.


Nucleate pool boiling hysteresis constructed
from the data of Kim and Burgles (1988).


investigations. It has been observed that the sustaining

incipience point for specified liquids and surface conditions

is predictable and is basically independent of the boiling

history (Yin and Abdelmessih, 1976). In contrast, the

initiation incipience point for highly wetting liquids depends

on initial system conditions as well as the history of various


V Increasing Heat Flux
V Decreasing Heat Flux
Pool Boiling with
R113 on Plain Copper
T a=46.4 C


A Initiation point
B Sustaining point


v


104








40

heating, cool-down, and surface drying procedures (You, et

al., 1990; Marto and Lepere, 1982; Bergles and Chyu, 1982).

Recently, the effects of flow on boiling incipience have been

examined by various investigators. In subcooled flow boiling

with highly wetting liquids, such as R113 and F72, mass

velocity showed little effect on boiling incipience (Hino and

Ueda, 1985; Marsh and Mudawwar, 1989). In flow boiling with

water under both subcooled and saturated conditions, Sudo et

al. (1986) and Marsh and Mudawwar (1989) observed a strong

influence of the liquid velocity on boiling incipience. Flow

boiling incipience measurements of R113 at saturated

conditions are not available in the literature.

Numerous models and correlations have been proposed for

the prediction of boiling incipience, which have recently been

reviewed by Brauer and Mayinger (1992). The majority of

models were categorized as being either thermal or mechanical.

Thermal models are those which consider the bubble embryo to

sit at the mouth of a cavity and protrude into a superheated

thermal liquid layer. Once thermal equilibrium at the embryo

interface is exceeded by the superheated liquid, bubble growth

is initiated. Experimental data have verified that for poorly

wetting liquids, such as water, the initiation and sustaining

incipience points almost coincide and these models are useful

for predicting the incipience superheat. Models proposed by

Hsu (1962), Han and Griffith (1965), Bergles and Rohsenow

(1964), Sato and Matsumura (1964), and Davis and Anderson








41

(1966) belong to the thermal category. Mechanical models

consider a stable bubble nucleus resides inside a cavity.

When both the wall and liquid are subcooled, the interface is

required to be concave toward the cavity due to condensation

of vapor. For highly wetting liquids, this kind of concave

interface is possible only with reentrant shaped cavities

because contact angles are usually less than 90 degrees. The

radius of the bubble nucleus for highly wetting liquids is

substantially smaller than that of the cavity mouth.

Therefore, a higher wall superheat is required to initiate

boiling than is required to sustain it. According to

mechanical models, the radius of the interface inside the

cavity is determined by the liquid-solid contact angle, shape

of the cavity, and the degree of subcooling at the wall.

Therefore, the incipience wall superheat is dependent on the

surface conditions, liquid wettability, and the pressure-

temperature history prior to boiling. Incipience models

proposed by Mizukami et al. (1990) and Tong et al. (1990)

belong to the mechanical category.

The difficulties associated with predicting the boiling

incipience points are summarized as follows: 1) lack of

detailed information concerning cavity shapes and sizes on

commercial surfaces, 2) difficulties in determining the

dynamic and static contact angles on a microscale, 3) lack of

knowledge concerning the shape and size of the superheated

thermal layer, especially when two-phase flows are involved,








42

and 4) lack of knowledge of the embryo expansion and recession

process inside a cavity.

In this work, the initiation and sustaining incipience

wall superheats were measured for saturated flow boiling with

refrigerant R113 using the facility described in chapter 2.

The motivation for these measurements is to investigate the

dependence of the initiation and sustaining incipience points

on two-phase flow conditions and the surface heating and

cooling history. The saturated two-phase mixture flowing

through the transparent test section was varied over a range

of G and X at constant pressure. The measurements of the

initial incipience points were obtained by slowly increasing

q, until fully developed nucleate boiling was achieved. Then

measurements of sustaining incipience points were obtained by

gradually reducing the heat flux to return to the two-phase

forced convection regime. Measurements of both initiation and

sustaining points were also performed for variable heating and

cooling cycles at a fixed G and X. A theoretical analysis

which takes into account the hysteresis of the liquid-solid

contact angle and cavity geometry is presented which explains

the incipience process and hysteresis of boiling with highly

wetting liquids.



4.2 Experimental Results

A typical saturated flow boiling plot of q, vs AT, for a

fixed G, X, and 6 is shown in Figure 4-2. A description of








43





40
V Increasing ql from T nm =20'
35 boiling initiated at A.
V Decreasing q,,
boiling sustained at B.
30 A Increasing q% from T r-=63*C
boiling initiated at A'.
0 Increasing qw from Twm=67C
25 boiling reversible. B, A"coincide. 7
T =580C, T =200C
sat room
20- -


15 7A

,o 2f A'
10 I
^r^\ BPA"
5 ABA



0 5 10 15
T --Tsat (C)


Figure 4-2. A typical saturated flow boiling plot of q,
versus AT, for G=180 kg/m2-s, X=0.156, and
6=4.8 mm.


Figure 4-2 is as follows. With a quasi-steady saturated two-

phase mixture flowing through the test section, the heat flux

is increased from zero until the initiation incipience

superheat is reached, which is denoted by point A. Here the

minimum temperature prior to boiling is room temperature,

approximately 20 OC. The heat flux is increased further until

fully developed nucleate boiling is achieved. The heat flux








44

is then decreased until the sustaining superheat is reached,

which is denoted by point B. The heat flux is further reduced

until Tw,-=63 OC. The heat flux is then increased until the

new initiation superheat is reached which is denoted by A'.

Thus is seen that Twn influences the initiation superheat.

The cycle is repeated for Twn=67 OC and A" denotes the

initiation superheat, which coincides with the sustaining

superheat. Thus, hysteresis is fully suppressed provided

Twmn>67 OC. Many experiments were conducted over a variety of

flow conditions to examine the influence of forced convection

on both the initiation and sustaining incipience points.

Figure 4-3 has been prepared for this purpose, where it is

seen that both the initiation and sustaining incipience wall

superheats remain essentially constant (although slightly

scattered) over a wide variety of flow conditions. h., has

been used in Figure 4-3 as a comprehensive parameter to

characterize the bulk turbulence. These results are

consistent with those obtained for subcooled flow boiling with

highly wetting liquids (Hino and Ueda, 1985; Marsh and

Mudawwar, 1989).



4.3 Theoretical Analysis for Boiling Incipience

4.3.1 Boiling Initiation

Effect of Non-condensible Gases. Since non-condensible

gases (usually air) are always trapped in cavities during the

process of a liquid filling over a surface, it is necessary to








45

understand their influence on the initiation of boiling. The

air trapping process has been detailed by Lorenz (1972) and

recently by Tong et al. (1990). Mizukami (1977) investigated

the effect of non-condensible gases on the stability criterion

of the embryo and found that the existence of gas stabilizes

the vapor bubble nucleus but accelerates its nucleation when

the liquid is superheated. However, quantitative


20 -


Vy V


10 -


5
0.


I I I


0


0.5 1.0 1.5

Macroconvection hm (kW/me-C)


2.0


Figure 4-3.


Measured saturated flow boiling incipience
wall superheat.


v Measured Initiation Superheat
V Measured Sustaining Superheat
-- Predicted Sustaining Superheat
Based on Tsat=59 OC, rl=0.66x1O- m





I V I








46

considerations regarding the effect of the gas mass on the

initiation superheat have not been reported in the literature.

It is worthwhile to proceed with such calculations in order to

further understand the nucleating process of a vapor bubble

containing a non-condensible gas.

Consideration is given to an embryo, consisting of a non-

condensible gas and saturated vapor, trapped in a conical

cavity as shown in Figure 4-4. The gas is taken to be air and

the mass is specified. The embryo is initially at static and

thermal equilibrium with its surroundings. Therefore, the

following relations are satisfied,


P+PP,-P 2a (4-1)


T= TV= Tsa (Pv) (4-2)


PgV=mgRTv (4-3)

where r is radius of the liquid/vapor interface, a is surface

tension, R is an engineering gas constant, and the subscripts

v, , and g respectively denote the vapor, liquid, and gas.

The liquid pressure, P,, is typically taken to be the system

pressure. Since air is assumed to be the only non-condensible

gas in the cavity the ideal gas law is obeyed. V is the

volume of an embryo, and for a conical cavity is given by

(Lorenz, 1972)


V=_ r3 (2- (2+cos2 (-)) sin (6-) + cos3 ( ) (4-4)
3 tan(w)









































Figure 4-4. An idealized sketch of a vapor embryo in a
conical cavity.

where 0 is the contact angle and i is the half cone angle of

the cavity. First, consideration is given to the effect of

non-condensible gas on incipience, and for this purpose a

conical cavity with a specified geometry, ri=0.69 pm and *=5,

is considered. The contact hysteresis, which is important for

boiling incipience, has been discussed in detail in the

literature (Johnson and Dettre, 1969; Schwartz and Tejada,








48

1972; Tong, et al., 1990). According to these investigations,

as the liquid/vapor interface gradually moves toward the vapor

phase, a maximum contact angle is reached and is referred to

as the static advancing contact angle, O. Similarly, as the

interface gradually moves toward the liquid phase, a minimum

contact angle, referred to as the static receding contact

angle, 0,, is reached. Assuming the embryo expansion follows

a quasi-equilibrium process, the contact angle 0 lies between

0, and 0, which are determined by liquid wettability and

surface conditions. Based on the data supplied by Tong et al.

(1990), 0,r~2 for R113, while 0, is usually less than 900.

For calculation purposes, here it is assumed that the initial

static contact angle is equal to the static advancing contact

angle and 08,80. Tong et al. (1990) have suggested that when

the cavity is heated, during the first expansion stage the

embryo interface adjusts such that the initial static contact

angle recedes until the static receding contact angle is

reached. Then during the second expansion stage the

liquid/vapor interface moves toward the cavity mouth, with

constant contact angle, 0,. During the first expansion stage,

the contact angle, 0, may be calculated from,


cos(0-9) =-d (4-5)
r

where rd, which remains constant, is the cavity radius at the

initial triple interface. rd may be calculated by specifying

the initial 0, T,, Pt, and mg and solving equations (4-1)

















100

90

80 -

70
v.max
60

50 -- mg =1.0xl0-' kg
m =0.25x10-" k
40 --- m =O.lxlO- kg

30 For Tsat=58 C
8 =2, +=5
sr
20 -

10 I I I I
0.001 0.01 0.1 1 10 100
V (x10-1" mO)


Figure 4-5. Variation of vapor temperature with vapor
embryo volume during expansion inside a
conical cavity.


through (4-5) simultaneously. Once rd is obtained, a Tv vs. V

plot can be constructed by solving equations (4-1) through (4-

5) assuming a quasi-equilibrium expansion process. Figure 4-5

shows three different T, vs. V curves, each for a different mg.

It is seen that as V increases there exists a maximum vapor

temperature, T,nx, which will satisfy equations (4-1) through

(4-5). Based on quasi-equilibrium considerations, it is








50

assumed that T,-T,. When T, exceeds T,,., equation (4-1) will

be violated and vapor bubble growth will be initiated. Thus

the initiation incipience superheat is evaluated from

Ajinc, i=rTvmax- r () (4-6)

It is clear that the initiation incipience superheat increases

with decreasing mg. For the conditions in Figure 4-5, the

assumed value of 0, does not significantly influence the

incipience superheat. Since it is expected that non-

condensible gas will be purged from the cavity during the

vapor bubble departure process, the amount of gas inside the

cavity should decrease as ebullition continues. As the

heating surface is degassed, ATm,i should increase. This trend

has been observed with the current facility. After the test

section is filled with liquid R113, it is necessary to sustain

fully developed nucleate boiling for approximately two hours

in order to obtain a repeatable ATmc,i. This observation is

consistent with those of Griffith and Wallis (1960). They

suggested that fully developed nucleate boiling with water

must be sustained for 1.5 hours to degas conical cavities, and

two hours is required for reentry type cavities. Thus it is

concluded that non-condensible gas trapped in cavities during

liquid flooding of the boiling surface exerts a strong

influence on ATc,i only during the initial stage of boiling.

Provided fully developed nucleate boiling is sustained for a

sufficient period of time, the embryo in active cavities










should consist of pure vapor.


Cavities with Pure Vapor. Mizukami (1990) concluded

that conical cavities with pure vapor can not survive

subcooled conditions and thus are not useful for initiating

boiling. However, even if conical cavities are initially

filled with liquid and can not initiate boiling, they can

become active nucleation sites if vapor is deposited in the

cavity from a neighboring nucleation site as has been

suggested by Calka and Judd (1985).

Mizukami (1990) also pointed out that the most favorable

cavities for surviving subcooled conditions are reentry type

ones. Thus it is likely that boiling is first initiated from

reentry cavities. Now consideration is given to reentry type

cavities, one of which is depicted in Figure 4-6. As is the

case for conical cavities, provided nucleate boiling is

sustained for a sufficient period, a vapor embryo will recede

in the cavity when the surface is cooled. Unlike conical

cavities, a reentry one will allow the liquid vapor interface

of highly wetting liquids to be concave toward the cavity

reservoir. Therefore, the vapor embryo can survive when Pt>Pv.

Following the analysis of Griffith and Wallis (1960) and

Mizukami (1975), for 0,,<4, the maximum curvature that the

liquid vapor interface can achieve is 1/r2, where r2 is the

mouth radius of the cavity reservoir. Thus the initiation

superheat can be obtained from,









































Figure 4-6. An idealized sketch of a vapor embryo in a
reentry cavity.


A Tn i Tsat (p+ ) Tsat (p) (4-7)


For 0,<90, the minimum curvature of the interface is


nsa The minimum curvature determines a minimum vapor
r2

temperature below which the vapor embryo cannot be sustained,












2osinea4
Tv, min=Tsat (Pt 2sinsa
Tz


50

45

40

35

30

25

20

15

10

5

0
0.;


36 0.38 0.40


Figure 4-7.


Variation of minimum vapor temperature and
initiation superheat with cavity reservoir
mouth radius.


T,.n and ATc,i calculated from equations (4-7) and (4-8) over

a range of r2 for R113 at a pressure of 1.45 bars (the no-flow

system pressure of the current facility) are displayed in

Figure 4-7. As shown in Figure 4-3, the measured initiation

incipience superheat for the current facility is approximately


0.32 0.34 0.

r, (gm)


-inci v.min
For T =58 C, a=80
sat sa












I
- I
--


0.42





(4-8)


--


-
r
_I
30








54

14.70 C which corresponds to cavities with r2< 0.31 pm.

Assuming that reentry cavities initiate boiling and r2-0.31

pm, they would be able to sustain their vapor embryos provided

the wall temperature is maintained above 15 OC. The ambient

temperature of the laboratory where the boiling facility is

housed is maintained at 200 C. The fact that the vapor embryo

can be sustained may explain why the initiation incipience

superheats in Figure 4-3 are relatively uniform. The above

analysis suggests that if the heating surface is cooled down

well below 15 OC or if the system is pressurized well above

1.45 bars, AT0c,1 should increase. Experiments have been

performed when the system was pressurized to 2.26 bar with

Twm,=20 OC for about half an hour. ATii measured immediately

following depressurization was found to increase to 19.1 OC,

which is consistent with the above prediction. Further

measurements revealed that AT.i was dropping down toward its

original value as boiling continued but it required several

days for AT,,,i to recover.



4.3.2 Sustaining Incipience Superheat

A vapor bubble departing a cavity which has been active

will likely leave vapor behind at the cavity mouth in the form

of an embryo. Provided sufficient superheat is available to

the embryo, it will readily expand and vapor bubble growth

will again result. This process will continue until the

superheat available to the embryo is insufficient to promote








55

bubble growth. Following bubble departure, the liquid moves

toward the cavity, and the liquid/vapor interface will acquire

an advancing dynamic contact angle, 0,, which is usually

larger than 0,. According to Cole's analysis (1974), for

either conical or reentry cavities with half cone angle, 0,

less than 0,, the maximum curvature the interface can attain

is the reciprocal of the cavity mouth radius, r,. Thus, prior

to bubble growth the interface protrudes the cavity mouth into

the superheated liquid thermal layer. Both the cavity mouth

radius and the temperature profile in the liquid thermal layer

control whether or not bubble growth will result. Assuming

bulk turbulence alone controls the liquid thermal layer, and

the temperature profile is linear in the vicinity of the vapor

embryo, the liquid temperature at the top of the embryo is

given by


T =Tw- (Tw-Ta) (4-9)


where kt is the liquid thermal conductivity. Starting from

the Clayperon equation and the perfect gas approximation for

vapor, Bergles and Rohsenow (1966) derived an equation for the

embryo vapor temperature,


Tv- Tsa TTasRvl n(1+ 20 ) (4-10)
hfg rlp,


They further proposed the criterion for boiling incipience

that T, at the top of the embryo must exceed T,. Based on this








56

criterion, the sustaining superheat ATmc,. (=Tw-Tt) can be

obtained as a function of rl, h., and Tt numerically from

equations (4-9) and (4-10). For constant r,, ATc,, has been

calculated over a range of h, as shown in Figure 4-3. It is

seen that the effect of convection on incipience superheat is

negligible which is in agreement with experimental

observations.


4.3.3 Hysteresis of Boiling Incipience

Hysteresis is the difference between the initial and

sustaining superheats. According to the preceding incipience

analysis, the initiation point depends on the minimum heating

surface temperature, while the sustaining point does not. In

fact, an explanation for incipience hysteresis is provided by

equation (4-8); as T,, decreases, potentially active

incipience nucleation sites are deactivated due to the

collapse of the vapor embryo. Assuming that the heating

surface contains reentry cavities with a large size range,

equation (4-8) predicts that incipience hysteresis will

increase with decreasing Tv,a. Such behavior is exactly what

has been observed with the present R113 flow boiling facility.

It is seen from Figure 4-2 that when T,,n is greater than Tt

and less than the sustaining point, the hysteresis declines

when compared to heating from subcooled conditions.

Furthermore, once fully developed boiling has been established

and T,,mm is maintained above the sustaining point, the boiling








57

process is completely reversible, which indicates that

hysteresis has been suppressed. However, one puzzling result

is that when T,,
may be because the size of the reentry cavities along the

heating surface are fairly uniform, r2~0.31 Am. If this were

the case, only when Tv,<15 OC would ATii be influenced. Such

a test has yet to be conducted. Electron microscope

photographs did not add any further insight.



4.4 Conclusions

Based on the experimental observations and theoretical

analysis presented herein regarding the incipience and

hysteresis associated with saturated forced convection boiling

of R113, two comments are in order:

1) Non-condensible gases trapped in cavities tend to reduce

the initiation superheat, but they will be purged from

cavities after boiling is sustained for a sufficient period.

For highly wetting liquids, the liquid flow could exert a

slight effect on the sustaining incipience superheat but not

on the initiation superheat. Gas-free conical cavities are

not useful for initiating boiling but can become activated

from adjacent nucleation sites. The initiation incipience

likely occurs in reentry cavities.

2) The incipience hysteresis is related to the minimum

heating surface temperature prior to boiling. Once fully

developed boiling has been established, the boiling process is








58

reversible if the heating surface temperature is maintained

above the sustaining point.

3) For the flow conditions investigated herein using R113,

both the initiation and sustaining superheats were not

noticeably influenced by bulk turbulence.














CHAPTER 5

NUCLEATION SITE DENSITY



5.1 Literature Survey

Due to its governing influence on heat transfer, the

nucleation site density has been the focus of numerous

investigations in pool boiling (Clark et al., 1959; Griffith

and Wallis, 1960; Kurihara and Myers, 1960; Gaertner and

Westwater, 1960; Hsu, 1962; Gaertner, 1963; Gaertner, 1965;

Nishikawa et al., 1967; Singh et al., 1976). The general

consensus from these investigations is that the formation of

nucleation sites is highly dependent on surface roughness,

geometry of microscopic scratches and pits on the heating

surface, the wettability of the fluid, the amount of foreign

contaminants on the surface, as well as the material from

which the surface was fabricated. Because of the large number

of variables which are difficult to control, none of these

investigators were successful in developing a general

correlation for nucleation site density. Griffith and Wallis

(1960) suggested that for a given surface the critical cavity

radius, re, is the only length scale pertinent to incipience

provided the wall superheat is uniform. Although they

realized the wall superheat is nonuniform in pool boiling,








60

they used r, to correlate the nucleation site density as

follows,


n=( )m (5-1)
A rc

where n/A is the nucleation site density, Ci and m are

empirically determined constants, and when p, >> p,


S 2Tsat (5-2)
PvhfgAsat


where T, is the saturation temperature, a is the surface

tension, hg is the latent heat of evaporation, and AT=Tw-T.t

is the wall superheat.

Nucleation site density data of Griffith and Wallis

(1960) for pool boiling of water on a copper surface is shown

in Figure 5-1 as a function of ATt. For n/A < 4 cm-2 the

nucleation site density increases smoothly with increasing

AT.. However for n/A > 4 cm2 no correlation exists between

n/A and ATt. Moore and Mesler (1961) used a fast response

thermocouple to demonstrate the heating surface temperature

directly beneath a nucleation site in pool boiling experiences

rapid fluctuations. Recently, Kenning (1992) used

thermochromic liquid crystals to measure the spatial variation

of wall superheat with pool boiling of water on a 0.13 mm

thick stainless steel heater. It was demonstrated that the

wall superheat was very nonuniform and |TIata/T-Ta varied
















12



1 0 V Water on 3/0 Finished Copper O
o0 ] Water on 3/0 Finshed Copper
N- from Griffith and Vallis [1]





6


>-4
U) 4

0
4-)-

CE
2

Z
0


0 5 10 15 20 25 30

Wall Superheat ATsat (OC)


Figure 5-1. Pool boiling nucleation site density data from
Griffith and Wallis (1960).


from 0.25 to 1.5 over a distance of a few mm, where ()

implies a spatial average and (') denotes a spatial variation

from the mean. Using a conduction analysis, it was also shown

that in the presence of ebullition, the spatial non-uniformity

of wall superheat on the surface of "thick plates" may also be

significant depending on geometry and thermal conductivity of








62

the plate. Kenning's (1992) result suggests that a Micro-

length scale which is related to the spatial temperature field

may also be important in characterizing incipience of vapor

bubbles. In addition, according to the suggestion of

Eddington, et al. (1978) and the experimental findings of

Calka and Judd (1985), at low n/A where nucleation sites are

sparsely distributed, neighboring nucleation sites do not

thermally interact. However at large n/A where nucleation

sites are closely packed, thermal interference among

neighboring sites exists. Since it has been demonstrated that

ATU is highly nonuniform in the presence of nucleation sites,

a question arises as to whether at large n/A the average wall

superheat is sufficient for characterizing the local wall

superheat experienced by individual nucleation sites. The

data displayed in Figure 5-1 suggest that is not.

Few similar studies on nucleation site density in flow

boiling have been reported. In one such investigation

Eddington and Kenning (1978) measured the nucleation site

density with subcooled flow boiling of water for a narrow

range of flow conditions. It was suggested that n/A is

related to rc. The objectives of the present work are

twofold: 1) to study the influence of flow and thermal

conditions on the nucleation site density in saturated

convection boiling, and 2) to determine whether or not the

nucleation site density in flow boiling is solely a function

of the critical radius, re, as has been suggested for pool








63

boiling. Measurements of nucleation site density have been

obtained for flow boiling of refrigerant R113 in a 25 x 25 mm

inner square transparent test section. These measurements

have been obtained for an isolated bubble regime with

stratified flow. In general, the vapor/liquid interface was

wavy and periodic slugs of liquid were observed passing

through the test section. No flow regime transitions were

observed. The liquid phase Reynolds number based on the mean

liquid velocity, which is defined by equation (3-5), ranged

from 12,000 to 27,000 and that for the vapor phase as defined

by (3-6) ranged from 24,000 to 80,000. The flow conditions

are characterized by the mass flux, G, liquid film thickness,

6, vapor quality, X, mean liquid velocity, ut, and mean vapor

velocity, uy. Thermal conditions are characterized by the

heat flux, q,, the wall superheat, ATt and saturation

condition (saturation temperature, Tt, or saturation pressure,

Pt). The controllable inputs of the flow boiling facility are

G, X, P, (or Tt), and q,. Of the flow parameters considered,

only two are independent since the mean liquid and vapor

velocities were calculated from equations (3-3) and (3-4),

respectively, based on measured liquid film thickness at a

given G, X, and T,. For the convenience of discussion,

equations (3-3) and (3-4) are rewritten here,

G(1-X)D (3)
u= (5-3)P8


and










GXD
u D (5-4)
pv(D-8)

Therefore, when investigating the influence of one of the flow

parameters on nucleation site density at constant saturation

conditions, only one other flow parameter can be held

constant, which introduced complexities in interpreting the

data. The range of the flow and thermal parameters covered in

these measurements, which to a large extent were limited by

the ability to visualize nucleation sites, are as follows:

G=125-290 kg/m2-s, u,=1.6-4.7 m/s, u,=0.35-0.68 m/s, 6=3.5-9.5

mm, q,=14.0-23.0 kW/m2, ATt=13.0-18.0 C, and T,=55.0-75 OC.


5.2 Optical Facility and Measuring Technique

The nucleation site density was measured optically using

a digital imaging facility shown in Figure 5-2. The facility

consists of a Videk Megaplus CCD camera with a 1320 x 1035

pixel resolution. The CCD camera is equipped with a Vivitar

50 mm macro lens with high magnification and low optical

distortion and a Videk power supply. The output of the CCD

camera is connected to an Epix 4 megabyte framegrabber which

is mounted in an I/O slot of a 386 Zenith computer. The

framegrabber allows for either high resolution (1320 x 1035)

or low resolution (640 x 480) imaging. The images are

displayed on a Sony analog monitor with 1000 lines per inch

resolution, and may also be printed out on an HP Laser Jet III

laser printer or may be saved on floppy disk for future




















ZSONY HIGH RESOLUTION
B/W MONITOR


VIDEK MEGAPLUS
CCD CAMERA
WITH MACRO
LENS I


VIDEK CAMERA
POWER SUPPLY


Z-386/20 COMPUTER

EPIX FRAME GRABBER


Figure 5-2.


A diagram of optical facility for measurement
of nucleation site density.


analysis. Computer software written in Microsoft C has been

developed for the image acquisition and processing. Due to

the strong vapor-liquid entrainment and waviness at the

interface of the two-phase mixture, it is not possible to

obtain a clear view of nucleation sites from the direction

normal to the heating surface. Therefore, the camera was

focused on the boiling surface through the side wall. A 500

Watt light illuminates the heating surface at an appropriate








66

angle from the opposite side wall. An opaque plastic sheet is

placed between the light and the object to diffuse the

incident light. Exposure time and lens aperture are properly

adjusted to obtain a clear image of the nucleation sites. A

typical picture of the nucleation sites is displayed in Figure

5-3 which was taken from the Sony monitor image. In order to

reduce the non-uniformities caused by the heater edge effect,

only nucleation sites in the middle 2/3 of the strip were

counted for measuring purposes. Thus the effective

measurement area was 1.4 cm wide by 2.2 cm. The nucleation

site density measured from an ensemble average of fifty images

was compared against that based on an average of ten images;

identical results were obtained. Therefore, all nucleation

site density measurements reported herein are based on an

ensemble average of ten images. Presumably intermittent sites

are accounted for. As has been demonstrated in Figure 3-2,

hysteresis can be avoided once the fully developed boiling has

been established. The measurements of nucleation site density

here were only made for the fully developed boiling regime

with increasing heat flux and increasing vapor velocity.


5.3 Experimental Results

Nucleation site density measurements were obtained for a

constant heat flux, q,=19.3 kW/m2, and saturation temperature,

T,=58 OC, over a range of flow conditions in which either the

mass flux, G, liquid film thickness, 6, liquid velocity, u,,









































Figure 5-3. A typical photograph of nucleation sites on a
boiling surface (flow direction is from left
to right).

or vapor velocity, U, was maintained constant. The

nucleation site density, n/A, is shown as a function of wall

superheat, ATt, in Figure 5-4. It is seen from Figure 5-4

that the n/A data can not be correlated with AT,. In light

of Figure 5-1 and equations (5-1) and (5-2), the behavior of

n/A with AT, is considered to be anomalous. In order to

demonstrate that the observed behavior is not simply due to














15


qw= 19.3kW/m2, T t=58C
o G=215 kg/m -s
V 6=6.3 mm
10 Au u=0.48 m/s
10 1
Su =3.6 m/s E

V



5 V



0)
(D



A
o 0

0 1 1 1 1
8 10 12 14 16 18 20
Wall Superheat ATsat (OC)



Figure 5-4. Nucleation site density as a function of wall
superheat for constant heat flux and
saturation temperature.

the experimental error, pool boiling nucleation site density

data were obtained using the current facility by filling the

test section with liquid and heating the nichrome strip while

the circulation pump was off. Therefore, the only net flow

was induced by the natural convection currents. The n/A data

for pool boiling are also displayed as functions of wall












Heat Flux qw (kW/m2)

8 10 12 14 16


18 20

Wall


Figure 5-5.


18 20


22 24 26 28 30 32

Superheat ATsat (OC)


Pool boiling nucleation site density as
functions of wall superheat and heat flux.


superheat, AT,, as well as heat flux, qw, in Figure 5.5. It

is seen that n/A increases smoothly with increasing AT, and

q, in a similar fashion to the data shown in Figure 5-1. As

seen from Figure 5-4, parameters other than AT, alone appear

to exert an influence on n/A in flow boiling.

In order to examine the influence of the flow parameters


10 H


Pool Boiling Data, Tsat=57.5 C
V n/A versus ATat
E n/A versus q


I I I I I I I











70

on n/A, measurements of nucleation site density were made

while the saturation temperature was maintained constant. The

nucleation site density is first plotted against vapor

velocity at a fixed heat flux, q,, and fixed liquid film

thickness, 6, as shown in Figure 5-6. It is seen that n/A

decreases markedly with increasing vapor velocity, u,. At a


10 I


5k


Vapor Velocity uv (m/s)


Figure 5-6.


Nucleation site density as a function of vapor
velocity for constant heat flux and liquid
film thickness.


O 6=6.3 mm, q= 19.3 kW/m'
V 6=7.7 mm, qw=14.5 kW/mp
Tsa=58 C





0





V
V7
V

V
V
V


I I I I








71

fixed heat flux and liquid film thickness, the data appear to

fall on a single curve. As the heat flux is increased, the

curve shifts toward higher nucleation site density.

Therefore, when investigating the influence of the flow

parameters on n/A the heat flux will be maintained constant.

Upon examination of equations (5-3) and (5-4) it is possible

that the trend shown in Figure 5-6 is due to either increasing

G or ut instead of increasing u. To sort out whether G, u,,

or u, has a controlling influence on n/A figures 5-7 and 5-8

have been prepared. In Figure 5-7, n/A is shown to increase

with increasing G when u, and q, are fixed, and decreases with

increasing G when S and q, are fixed, and thus it appears that

parameters other than G are controlling n/A. In Figure 5-8

n/A is shown to decrease with increasing u, for a fixed G and

q,. For the case of a fixed 6 and q, n/A also decreases with

increasing ut but the shape of the curve is significantly

different. When comparing Figures 5-6 and 5-8, it appears

that n/A is better behaved when displayed as a function of u,.

Further evidence of this supposition is provided in Figure 5-9

where n/A is displayed as a function of u, for q,=19.3 kW/m2,

T.=58 oC, G=215 kg/m2-s, and u,=0.58 and 0.48 m/s. It is seen

that all of the data approximately fall on a single curve,

thus demonstrating the governing influence of the mean vapor

velocity on nucleation site density. The liquid film

thickness is also shown as a function of u,. Thus, the effect

of liquid film thickness on n/A might also be included in








72







15 ,

o u1=0.48 m/s
Sqw= 19.3 kW/m"
o V 6=6.3 mm
q= 19.3 kW/m"
< 0 T =58 C
10 sat



vO






0~ ~~~~ v-------- I --------
z O
0
0 I I
100 150 200 250 300

Mass Flux G (kg/me-s)


Figure 5-7. Nucleation site density as a function of mass
flux.


Figure 5-9. Therefore, it is necessary to investigate the

influence of 6 on n/A.

In pool boiling, Nishikawa et al. (1967) demonstrated

that the nucleation site density increases with declining

liquid film thickness. Mesler (1976) postulated that the same

behavior should follow for flow boiling and used it to explain
















15

V G=215 kg/mn-s
q= 19.3 kW/m2
S0 5= 6.3 mm
qw= 19.3 kW/m2

S 10- T=58 aC


SV


5 l V
0O




z

0 I






Figure 5-8. Nucleation site density as a function of
liquid velocity.


the measured increase in flow boiling heat transfer

coefficient with declining liquid film thickness for

stratified or annular flow. To the best of the author's

knowledge direct evidence supporting or refuting Mesler's

claim has yet to be presented. To sort out the direct

influence of liquid film thickness on the nucleation site








74







15 I I 14
%=19.3 kW/m", T =58 C
Sn/A 6
Q G=215 kg/m2-s 12
] * u=0.58 m/s
A A u,=0.48 m/s
10
S10 -

8
QC



S5 v
o A 4 a
,4 '-
O 7

2
o


0 II Ii 0
0 1 2 3 4 5

Vapor Velocity uv (m/s)



Figure 5-9. Nucleation site density and liquid film
thickness as functions of vapor velocity.


density, Figure 5-9 suggests that it is necessary to maintain

a fixed u,, q,, and T.. Figure 5-10 shows n/A as a function

of liquid film thickness at uv=3.6 m/s, q,=20.7 kW/m2, and

T,=58 OC. It is seen that n/A indeed increases with declining

film thickness, which tends to support Mesler's claim

regarding n/A as a function of film thickness, provided that

















15




o u =3.6 m/s
Sqw=20.7 kW/m"
0 Tsa=58 oC








.4
(r
0
54->








2 4 6 8

Liquid Film Thickness 6 (mm)



Figure 5-10. Nucleation site density as a function of
liquid film thickness.


u,, q,, and Tt are fixed. However, over the range of film

thickness investigated (3-6 mm) the increase in n/A is only

marginal. Because n/A was obtained using a visualization

technique it was not possible to obtain data for 6<3 mm. As

6-0 the behavior of n/A is uncertain. To determine whether

uy or 6 has stronger influence on n/A, Figure 5-9 is re-








76

examined where it is seen that n/A decreases with declining 6,

which is primarily caused by increasing u,. Therefore, it

appears that u, has a governing influence on the nucleation

site density. An explanation and significance of this finding

will be discussed later.

When testing the influence of thermal conditions on n/A,

it is necessary to control Uy. In Figure 5-11, n/A is shown

as a function of q, for three different values of u, at Te=57

C. It is seen that n/A increases smoothly with increasing

heat flux at a fixed u,. As u, increases, the curves shift

toward decreasing n/A. This trend is consistent with that

observed in Figure 5-6. The n/A data in Figure 5-11 are shown

as a function of AT, in Figure 5-12. The data display

an anomalous behavior similar to that in Figure 5-4.

To examine the dependence of n/A on the critical radius

it was decided that a constant heat flux and vapor velocity

would be maintained, and r, would be controlled by raising the

system pressure. Doubling the system pressure has the effect

of essentially doubling the vapor density and increasing Tt

by only several percent. The nucleation site density was

measured for fixed U, and q, over a range of system pressure

from 1.4 to 2.3 bars which gave a 20 OC increase of saturation

temperature. Figures 5-13 and 5-14 have been prepared from

these measurements. It is seen from Figure 5-13 that n/A

increases with increasing T, while AT, is dropping during this

process. Nevertheless, Figure 5-14 shows that this increase

















15 1

Ts =57 C
sat
D u =2.15 m/s
SA u =2.67 m/s
o V u =3.64 m/s

S10


--4



Ui 5
l.u





i id I i

12 14 16 18 20 22 24

Heat Flux qr (kW/mr)



Figure 5-11. Nucleation site density as a function of heat
flux.


of n/A can be attributed to an increase of 1/r,. Since the

only physically sound explanation for the increase of n/A with

increasing T. is due to a decrease in r,, these data suggest

that r, is an important parameter in characterizing flow

boiling nucleation site density.















15 I I -
Tsat=57 C
0 u =2.15 m/s
SAu =2.67 m/s
SV u =3.64 m/s

10 -










0 D A



10 12 14 16 18 20 22 24
/ \














Figure 5-12. Nucleation site density as a function of wall
superheat.

5.4 Discussion of Results

Although the data shown in Figure 5-14, as well as

theoretical considerations, suggest that r, is an important

parameter for flow boiling nucleation site density, it is by
/


o a

0 I-I--I-II------ -- -------I-
10 12 14 16 18 20 22 24









Waitself insufficient to correlate n/A. In Figure 5-15, allC)

Figure 5-12. Nucleation site density measurements a function of wall
superheat.

5.4 Discussion of Results

Although the data shown in Figure 5-14, as well as

theoretical considerations, suggest that r, is an important

parameter for flow boiling nucleation site density, it is by

itself insufficient to correlate n/A. In Figure 5-15, all

nucleation site density measurements in this work are








79




Wall Superheat ATsat (C)

10 15 20


55 60 65 70 75


Figure 5-13.


Saturation Temperature Tsat (C)



Nucleation site density as
saturation temperature and wall


functions of
superheat.


displayed as a function of r,. All data seem to be collapsed,

but a correlation in the form of equation (5-1) would not be

useful because the slope is too steep. The pool boiling

nucleation site density data also show a similar behavior for

large n/A.

In an attempt to understand this behavior, consideration


n/A vs ATsat n/A vs T at
A uv=3.0 m/s V u =3.0 m/s
A uv=3.5 m/s v u =3.5 m/s
q =17.3 kW/mr


15 -


10 -


0
5(


)


I I I I I















100

Q
V u =3.0 m/s
< V u =3.5 m/s
Sq =17.3 kW/m2




( 10 V


oV


V V7
V



1 --
1 3 5 10
-8
Critical Radius, 1/re (xl 0m-')


Figure 5-14. Nucleation site density as a function of
critical radius.


is first given to the pool boiling analysis of Hsu (1962) in

which it was demonstrated that the nonuniform liquid

temperature field seen by a vapor embryo attempting to grow is

important when considering incipience behavior. If linear

temperature profile is assumed for the liquid layer, a minimum

cavity radius required for incipience may be expressed solely
















100



^All Data for Constant
Saturation Temperature
STsa1=58 C




'5 10 -




o 1
Ssat









a rd

z A
A,

1 3 5 10
Critical Radius, 1/r. (x10lO6m')



Figure 5-15. Nucleation site density as a function of
critical radius.


as a function of wall superheat AT, or heat flux q, provided

the fluid properties are maintained constant. Figure 5-4

demonstrates that AT, or q, alone is insufficient to correlate

the flow boiling n/A data. Bergles and Rohsenow (1964)

applied a similar analysis for flow boiling and the assumption

of a linear temperature profile in the liquid layer also leads








82

to a definition of critical cavity radius which is solely

dependent on AT, or q, for constant fluid properties. One

shortcoming of these analyses is the assumption of a linear

temperature profile in the liquid thermal layer. Certainly,

the strength of heat flux and the intensity of bulk turbulence

will have a strong influence on the shape of the thermal

layer. Nevertheless, the experimental data presented here and

these theoretical analyses suggest that in addition to the

critical radius based on equation (5-2), a length scale

related to the shape of the thermal layer may also be

important in characterizing n/A.

In addition, it is emphasized that r, has been calculated

using equation (5-2) by taking the wall superheat to be the

average value, AT.. As mentioned earlier, Kenning (1992) used

liquid crystal thermography to show that IAat|/Tga could



be as large as 1.5 for pool boiling. In this study the liquid

crystal test section was used in conjunction with a Panasonic

video recorder to record the flow boiling wall temperature

field at conditions of U,=3.0 m/s, qw=18.1 kW/m2, and Tw=58.3

OC. It was found that temperature field was very nonuniform

in both spatial and temporal scales. Therefore, it appears

the average wall superheat is insufficient for characterizing

the local wall superheat experienced by individual sites.

The experimental data of n/A presented here have revealed




Full Text
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
L
s F. Klausner, Chair
istant Professor of
chanical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor, of/Philosophy.
C.K. Hsieh
Professor of
Mechanical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
D.Y. Goswami
Professor of
Mechanical Engineering


119
dimensional flow disturbances. The zero-gravity pool boiling
photographs provided by Siegel and Usiskin (1959) tend to
support this prediction.
6.4.2 Flow Boiling Data
No experimental data with both vapor bubble detachment
diameter and growth rate are available for flow boiling in the
literature. Verification of the bubble detachment model for
flow boiling at this time can only be made using the departure
and lift-off data obtained by Bernhard (1993). The
measurements of bubble diameter were made from instantaneous
images obtained using a CCD photography facility. The
uncertainty in the departure and lift-off diameter is 0.03mm.
It is not currently possible to measure the bubble detachment
diameter and growth rate simultaneously using the CCD imaging
facility. However, for each fixed flow and thermal condition,
the departure and lift-off diameters are represented by their
mean values as well as the bubble detachment probability
density functions (pdf's) which were constructed from at least
200 bubbles. Vapor bubble growth rates in flow boiling have
also been obtained using high speed cinematography with a
speed of 5000 frames per second and will be discussed in
detail in the following chapter. Using high speed
cinematography, a few bubbles were captured over their life
span. These bubbles were used to check the accuracy of the
present model for the departure diameter prediction of


137
u
a>
H
is
Figure 7-3. Statistical distribution of bubble departure
diameter in flow boiling at constant u,.
diameter increases with increasing wall superheat. For
various wall superheats considered herein, the model
prediction is in good agreement with the experimental data.
The model was further compared against Bernhard's (1993)
experimental pdf data for flow boiling departure diameter,
where both liquid velocity and wall temperature have been


92
6.2.2 Flow Boiling Bubble Detachment Diameter Correlations
Although there have been a large number of studies
investigating pool boiling vapor bubble departure, few similar
studies have followed for flow boiling. Chang (1963) proposed
one of the first expressions for the vapor bubble detachment
diameter in flow boiling. He assumed the point at which a
vapor bubble detaches the heating surface is the point where
the net forces acting on a vapor bubble (including forces
acting parallel and normal to the heating surface) just
balance each other. The forces considered were the buoyancy
force, surface tension force, and dynamic forces normal and
tangential to the heating surface. Sliding bubbles were not
considered and the expression was not experimentally verified.
Hsu and Graham (1963) conducted a visual study for upflow
boiling of water in various flow regimes. Based on the
trajectory of a typical vapor bubble, it appears that the
bubble slides along the heating surface prior to lifting off,
although this phenomenon was not discussed in their work.
Levy (1967) obtained a vertical upflow subcooled forced
convection boiling bubble departure diameter correlation which
considered the buoyancy force, drag force, and surface tension
force. It was empirically deduced that the buoyancy force
does not contribute to bubble departure diameter which is
given by


5 NUCLEATION SITE DENSITY 59
5.1 Literature Survey 59
5.2 Optical Facility and Measuring
Technique 64
5.3 Experimental Results 66
5.4 Discussion of Results 78
5.5 Conclusions 83
6 A UNIFIED MODEL FOR VAPOR BUBBLE DETACHMENT ....84
6.1 Introduction 84
6.2 Literature Survey 86
6.2.1 Pool Boiling Departure Diameter
Correlations 86
6.2.2 Flow Boiling Detachment Diameter
Correlations 92
6.3 Development of Departure and Lift-off
Model 94
6.3.1 Formulation 94
6.3.2 Expressions for Bubble Departure
and Lift-off Diameter 105
6.4 Comparison with Experimental Data 107
6.4.1 Pool Boiling Data 108
6.4.2 Flow Boiling Data 119
6.5 Conclusions 127
7 PROBABILITY DENSITY FUNCTIONS OF VAPOR
BUBBLE DETACHMENT DIAMETER 130
7.1 Introduction 130
7.2 Formulation 132
7.3 Comparison with Experimental Data 134
7.4 Conclusions 138
8 VAPOR BUBBLE GROWTH RATE 140
8.1 Introduction 140
8.2 Facility and Methodology 141
8.3 Results and Discussions 144
8.4 Conclusions 156
9 CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH 157
9.1 Accomplishments and Findings 157
9.2 Suggestions for Future Research 159
APPENDICES
A HEAT TRANSFER COEFFICIENT, PRESSURE DROP,
AND LIQUID FILM THICKNESS IN STRATIFIED
TWO-PHASE FLOW 161
vi


170
Geraets, J.J.M., and Borst, J.C., 1988, "A Capacitance Sensor
for Two-Phase Void Fraction Measurement and Flow Pattern
Identification," Int. J. Multiphase Flow. Vol. 14, No. 3, pp.
305-320.
Griffith, P., 1958, "Bubble Growth Rates in Boiling," ASME
Trans.. Vol. 80, pp. 721-727.
Griffith, P. and Wallis, J.D., 1960, "The Role of Surface
Conditions in Nucleate Boiling," AIChE Symposium Series. No.
30, Vol. 56, pp. 49-63.
Gungor, K.E. and Winterton, R.H.S., 1986, "A General
Correlation for Flow Boiling in Tubes and Annuli," Int. J.
Heat Mass Transfer. Vol. 29, No. 3, pp. 351-358.
Han, C.Y. and Griffith, P., 1962, "The Mechanism of Heat
Transfer in Nucleate Pool Boiling," Rept. 7613-19, MIT,
Cambridge, Mass.
Han, C.Y. and Griffith, P., 1965, "The Mechanism of Heat
Transfer in Nucleate Pool Boiling, Part I: Bubble Initiation,
Growth and Departure," Int. J. Heat Mass Transfer. Vol. 8,
pp. 887-904.
Hewitt, G.F., Measurement of Two-Phase Flow Parameters,
Academic Press, London, 1978.
Hio, R. and Ueda, T., 1985, "Studies on Heat Transfer and
Flow Characteristics in Subcooled Flow Boiling: Part I,
Boiling Characteristics," Int. J. Multiphase Flow. 11, pp.
269-281.
Hosier, E.R., 1965, "Visual Study of Boiling at High
Pressure," Chemical Engineering Symposium Series. No. 57,
Vol. 61, pp. 269-279.
Hsu, Y.Y., 1962, "On the Size Range of Active Nucleation
Cavities on a Heating Surface," J. of Heat Transfer. Trans.
ASME, Vol. 84C, pp. 207-216.
Hsu, Y.Y. and Graham, R.W., 1963, "A Visual Study of Two-phase
Flow in a Vertical Tube with Heat Addition," NASA TN-D-1564.
Hsu, Y.Y. and Graham, R.W., Transport Processes in Boiling and
Two-phase Systems, Including Near-critical Fluids, Chapter 1,
Hemisphere Publishing Corporation, 1976.
Irons, G.A. and Chang, J.S., 1983, "Particle Fraction and
Velocity Measurement in Gas-Powder Streams by Capacitance
Transducers," Int. J. Multiphase Flow. Vol. 9, No. 3, pp. 289-
297.


103
force. Thus the growth force components in the x- and in
directions are given by
Fdux=Fdu Sin0i (6-30)
and
Fduy=FducosQi (6-31)
In order to accurately estimate the growth force, information
on the bubble growth rate is reguired. Since the general
prediction of the bubble growth rate in flow and pool boiling
remains unsolved, a(t) must be specified for a given set of
boiling conditions.
So far, all the forces appearing on the left hand side of
equations (6-17) and (6-18) have been approximated except the
lift force Fl caused by the preceding departed bubble. A
gross estimation for this force using potential flow is given
by Zeng et al. (1993) and was found to be generally four
orders of magnitude smaller than the growth force and thus is
negligible. Therefore, the dominant forces at the point of
bubble detachment are the buoyancy, quasi-steady drag, shear
lift, and growth force, all of which are proportional to the
liquid density. The terms on the right hand sides of
equations (6-18) and (6-19) are the forces associated with the
vapor mass acceleration which are proportional to the vapor
density. Since pvp, and du^/dt is finite at the point of
bubble detachment for most cases of practical interest, the
acceleration forces can be neglected.


70
on n/A, measurements of nucleation site density were made
while the saturation temperature was maintained constant. The
nucleation site density is first plotted against vapor
velocity at a fixed heat flux, qw/ and fixed liquid film
thickness, S, as shown in Figure 5-6. It is seen that n/A
decreases markedly with increasing vapor velocity, Uy. At a
6
o
<
\
t
ri
m
t
n
o
-4->
rH
CO
t
o
H
ct
73
t
5z;
15
10 -
5 -
0
0
<5=6.3 mm, qw= 19.3 kW/m*
V <5=7.7 mm, q =14.5 kW/ms
T =58 C
sat
V
V

V


Vapor Velocity u (m/s)
Figure 5-6. Nucleation site density as a function of vapor
velocity for constant heat flux and liquid
film thickness.


23
Figure 2-10. Close-up view of stratified two-phase flow
using CCD camera (flow direction is from left
to right).
the liquid/vapor interface depends on flow conditions. The
two-phase mixture bulk temperature ranged from 50-70 C. The
use of the digital data acguisition system, which will be
described shortly, greatly facilitated the synchronization
process. The liguid film thickness data measured using the
CCD camera have been compared against that measured by sensor


120
individual bubbles. The experimental data from high speed
films show that the diffusion controlled bubble growth
solution proposed by Zuber (1959) can adequately correlate the
ensemble average of bubble growth rate. This growth rate
solution can be expressed as
a(t) =Jav/rft (6-39)
where
Ja= p'Cp'^Ts*t (6-40)
PvAfgr
and Ja is the Jacob number, tj is the thermal diffusivity, cp<
is the liquid specific heat, and b is an empirical constant
which is supposed to account for asphericity. For most
observed bubble growth rates with flow boiling at atmospheric
pressure measured in this work, it is found that b=l gives the
best fit to the experimental data. Therefore, equation (6-39)
with b=l has been used to estimate the bubble growth rates for
the present bubble departure and lift-off diameter models.
Departure Diameter and Inclination Angle. From the
analysis of the present bubble departure model, the vapor
bubble departure diameter is a function of only the mean
liquid velocity when the wall superheat, which controls the
bubble growth rate, is fixed. Measurements of mean departure
diameter over a range of u, and ATMt obtained by Bernhard


Table 6-5. Measured and Predicted Departure Diameters
Based on High Speed Cinematography Data.
^d,mcas
mm
^d,prcd
mm
Relative
Error (%)
K(xl03)
n
m/s
AT^
C
C
0.256
0.259
1.2
1.94
0.435
0.240
0.220
8.4
1.29
0.382
0.221
0.218
1.3
1.84
0.450
0.30
8.2
67.0
0.245
0.243
0.8
1.79
0.429
0.240
0.220
8.4
1.16
0.362
0.121
' 0.115
4.6
0.97
0.428
0.123
0.115
6.8
0.57
0.334
0.142
0.138
2.8
1.07
0.421
0.28
10.0
71.0
0.150
0.153
2.2
1.10
0.410
0.138
0.148
6.9
0.94
0.386
123


31
Re
v
P v^yDhv
(3-6)
respectively, where Re is Reynolds, Dh is the hydraulic
diameter, and /x is the dynamic viscosity.
Microconvective heat transfer coefficients were obtained
for the nucleate flow boiling regime using the methodology
described above. The flow boiling heat transfer data were
organized by plotting hmic/h2i> against ^ as shown in
Anac^ -vine, s
Figure 3-1. It is very significant that all the experimental
data have been collapsed into a single curve. Here AT^,
denotes the sustaining incipience wall superheat. These data
conclusively demonstrate that microconvection is important in
almost all phases of saturated flow boiling heat transfer and
its contribution becomes dominant at high heat fluxes. This
conclusion distinctly contests most forced convection boiling
heat transfer correlations reported in the literature which
predict that macroconvection is always dominant. The curve
presented in Figure 3-1 may also be viewed as a "flow boiling
curve". As is well known, the conventional heat flux vs wall
superheat plot used for pool boiling cannot collapse the flow
boiling data due to the large variation of macroconvection
heat transfer.
Further consideration was given to the macroconvection


42
and 4) lack of knowledge of the embryo expansion and recession
process inside a cavity.
In this work, the initiation and sustaining incipience
wall superheats were measured for saturated flow boiling with
refrigerant R113 using the facility described in chapter 2.
The motivation for these measurements is to investigate the
dependence of the initiation and sustaining incipience points
on two-phase flow conditions and the surface heating and
cooling history. The saturated two-phase mixture flowing
through the transparent test section was varied over a range
of G and X at constant pressure. The measurements of the
initial incipience points were obtained by slowly increasing
qw until fully developed nucleate boiling was achieved. Then
measurements of sustaining incipience points were obtained by
gradually reducing the heat flux to return to the two-phase
forced convection regime. Measurements of both initiation and
sustaining points were also performed for variable heating and
cooling cycles at a fixed G and X. A theoretical analysis
which takes into account the hysteresis of the liquid-solid
contact angle and cavity geometry is presented which explains
the incipience process and hysteresis of boiling with highly
wetting liquids.
4.2 Experimental Results
A typical saturated flow boiling plot of qw vs ATMt for a
fixed G, X, and S is shown in Figure 4-2. A description of


171
Jakob, M., Heat Transfer, Vol. 1, Chapter 29, John Wiley &
Sons, Inc., 1949.
Jayanti, S., Hewitt, G.F., and White, S.P., 1990, "Time-
Dependent Behavior of the Liquid Film in Horizontal Annular
Flow," Int. J. Multiphase Flow. Vol. 16, No. 6, pp. 1097-
1116.
Johnson, M.A., Jr., Pena, Javier De La, and Mesler, R.B.,
1966, "Bubble Shapes in Nucleate Boiling," AIChE J.. Vol. 12,
No. 2, pp. 344-348.
Johnson, R.E., Dettre, R.H., and Brandreth, D.A., 1977,
"Dynamic Contact Angles and Contact Angle Hysteresis," J. of
Colloid and Interface Science. Vol. 62, No. 2, pp. 205-212.
Jones, O.C., 1983, "Two-Phase Flow Measurement Techniques in
Gas-Liquid Systems," in Fluid Mechanics Measurements, ed. R.J.
Goldstein, pp. 479-558, Hemisphere, New York, 1983.
Kenning, D.B.R., 1992, "Wall Temperature Patterns in Nucleate
Boiling," Int. J. Heat Mass Transfer. Vol. 35, No. 1, pp. 73-
86.
Kenning, D.B.R. and Cooper, M.G., 1989, "Saturated Flow
Boiling of Water in Vertical Tubes," Int. J. Heat Mass
Transfer. Vol. 32, No. 3, pp. 445-458.
Kenning, D.B.R., and Del Valle M., V.H., 1981, "Fully-
developed Nucleate Boiling: Overlap of Areas of Influence and
Interference between Bubble Sites," Int. J. Heat Mass
Transfer. Vol. 24, No. 6, pp. 1025-1032.
Keshock, E.G., and Siegel, R., 1964, "Forces Acting on Bubbles
in Nucleate Boiling under Normal and Reduced Gravity
Conditions," NASA Tech. Note TN D-2299, August.
Kim, C.-J., and Bergles, A.E., 1988, "Incipient Boiling
Behavior of Porous Boiling Surface Used for Cooling of
Microelectronic Chips," in Particulate Phenomena and
Multiphase Transport. Vol. 2, T.N. Veziroglu, Ed., Hemisphere,
Washington, D.C., pp. 3-18.
Klausner, J.F., 1989, "The Influence of Gravity on Pressure
Drop and Heat Transfer in Flow Boiling," Ph.D. thesis,
University of Illinois at Urbana-Champaign.
Klausner, J.F., Chao, B.T., and Soo, S.L., 1991, "An Improved
Correlation for Two-phase Frictional Pressure Drop in Boiling
and Adiabatic Downflow in the Annular Flow Regime," Proc
Instn Mech Encrrs Vol 205, Part C: Journal of Mechanical
Engineering Science, pp. 317-328.


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81
w
t
Q
O
4->
* II
m
o
13
t
55
100
10
1
All Data for Constant
Saturation Temperature
T =58 DC
sat

o
1 3 5 10
Critical Radius, 1/r (xlO
-6
m *)
Figure 5-15. Nucleation site density as a function of
critical radius.
as a function of wall superheat ATt or heat flux qw provided
the fluid properties are maintained constant. Figure 5-4
demonstrates that ATMt or qw alone is insufficient to correlate
the flow boiling n/A data. Bergles and Rohsenow (1964)
applied a similar analysis for flow boiling and the assumption
of a linear temperature profile in the liquid layer also leads


33
a
¡*
t>
*
JA
t
B
u
O
o
o
h
'a
a
i
ti
a
X
4
Vapor Reynolds Number Rey (xlO )
0 2 + 6 8 10 12
Liquid Reynolds Number Re, (xlO )
Figure 3-2. Macroconvective heat transfer coefficient in
saturated forced convection boiling.
single-phase forced convection and may possibly be due to the
enhanced turbulence caused by strong interfacial waves.
Considering that most flow boiling correlations for h^ are
simply modified single-phase heat transfer correlations
applied to the liguid, there remains considerable room for
improved modelling of both h^ as well as h^c in flow boiling
heat transfer correlations.


90
dd= 0.00127
P|~Pv^ o.9
Pv
(6-10)
The pressure dependence of dd is accounted for through pv.
Compared to surface tension controlled bubble departure,
little consideration has been given to inertia controlled
departure. Ruckenstein (1961), who was the first to propose
an inertia controlled departure model, regarded the surface
tension force as relatively unimportant in the bubble
departure process. He suggested the departure diameter could
be calculated from
(6-11)
where AT^^-T, is the wall superheat, Cp and ij are the
respective liquid specific heat and thermal diffusivity, and
hfg is the latent heat of vaporization. Roll and Myers (1964)
also argued that the surface tension force does not contribute
to the bubble departure process. Based on a balance between
the inertial force caused by the bubble growth and that due to
buoyancy, they derived an expression to estimate the bubble
departure diameter,
(6-12)
where CD is the drag coefficient on a vapor bubble and was
estimated based on data for a freely rising vapor bubble in an


29
only deals with saturated flow boiling, Tb is equivalent to
the saturation temperature, TMt. In order to sort out the
contribution of heat transfer between macro- and
microconvection during flow boiling, the following
experimental procedure was closely adhered to. The Micropump
and preheaters were adjusted to obtain a fixed G, X, and TMt
at the inlet of the test section. The nichrome strip was
heated up gradually until boiling was initiated. During this
process the heat flux and temperature were recorded. The
pressure drop, AP, across the test section and liquid film
thickness S at the inlet and outlet of the test section were
also recorded. As heat flux qw was further increased, vapor
bubble generation at the heating surface was generated and
sustained with increasing qw. Further measurements of h2 were
made until qw was increased up to 40 kW/m2. The range of flow
conditions over which measurements were made was G=125-280
kg/m2-s and X=0.04-0.30. As had been expected, it is observed
that for a fixed G, X, and TMt, the measured two-phase heat
transfer coefficient, h2(M without boiling is independent of
the heat flux, qw. Hence, it was assumed that the non-boiling
two-phase heat transfer is equivalent to that of the
macroconvection heat transfer coefficient in flow boiling and
is herein denoted by h^. As has been discussed in Chapter 1,
Rohsenow (1952) first suggested that the rate of heat transfer
associated with forced convection boiling is due to two
additive mechanisms, that due to bulk turbulence and that due


10
connecting it with rigid copper pipes are the facts that the
pyrex glass is brittle and small stress concentrations
substantially reduce its safe operating pressure. After
testing many different designs, a satisfactory test section
was eventually fabricated. The fabrication procedures, which
have been detailed by Bernhard (1993), will not be repeated
here. A brief description of the test section is given. The
main body of the flow boiling test section is comprised of a


172
Klausner, J.F., Mei, R., Bernhard, D.M., and Zeng, L.Z., 1993,
"Vapor Bubble Departure in Forced Convection Boiling," Int. J.
Heat Mass Transfer. Vol. 36, pp. 651-662.
Klausner, J.F., Zeng, L.Z., and Bernhard, D.M., 1992,
"Development of a Film Thickness Probe Using Capacitance for
Asymmetrical Two-Phase Flow with Heat Addition," Rev. Sci.
Instrum.. Vol. 63, No. 5, pp. 3147-3152.
Kocamustafaogullari, G., 1983, "Pressure Dependence of Bubble
Departure Diameter for Water," Int. Comm. Heat Mass Transfer.
Vol. 10, pp. 501-509.
Koumoutsos, N., Moissis, R., and Spyridonos, A., 1968, "A
Study of Bubble Departure in Forced-Convection Boiling," J.
of Heat Transfer. Trans. ASME, Vol. 90, pp. 223-230.
Kurihara, H.M., and Myers, J.E., 1960, "The Effects of
Superheat and Surface Roughness on Boiling Coefficients,"
AIChE J.. Vol. 6, No. 1, pp. 83-91.
Lee, R.C., and Nydahl, J.E., 1989, "Numerical Calculation of
Bubble Growth in Nucleate Boiling From Inception Through
Departure," J. of Heat Transfer. Trans. ASME, Vol. Ill, pp.
474-479.
Leeds, M.A., 1972, "Electronic Properties of Composite
Materials," in Handbook of Electronic Materials. Vol. 9,
Plenum, New York.
Levy, S., 1967, "Forced Convection Subcooled Boiling
Prediction of Vapor Volumetric Fraction," Int. J. Heat Mass
Transfer. Vol. 10, pp. 951-965.
Lienhard, J.H., 1988, "Things We Don't Know about Boiling Heat
Transfer," Int. Comm. Heat and Mass Transfer. Vol. 15, No. 4,
pp. 401-428.
Lockhart, R.W., and Martinilli, R.C., 1949, "Proposed
Correlation of Data for Isothermal Two-Phase, Two-Component
Flow in Pipes," Chemical Engineering Progress. Vol. 45, No.l,
pp. 39-48.
Lorenz, J.J., 1972, "The Effects of Surface Conditions on
Boiling Characteristics," Ph.D Thesis, Mechanical Engineering
Department, MIT, Cambridge, Massachusetts.
Maciejewski, P.K. and Moffat, R.J., 1992, "Heat Transfer with
Very High Free-Stream Turbulence: Part I, Experimental Data,"
J. of Heat Transfer. Trans. ASME, Vol. 114, pp. 827-833.
Marsh, W.J. and Mudawwar, I.,
1989, "Predicting the Onset of


Radius a(t) (mm)
148
Time t (ms)
Figure 8-5. Time history of bubble growth


173
Nucleate Boiling in Wavy Free-falling Turbulent Liquid Films,"
Int. J. Heat Mass Transfer. Vol. 32, No. 2, pp. 361-378.
Marto, P.J., and Lepere, V.J., 1982, "Heat Exchange in
Structured Surfaces for Boiling Dielectric Liquid in a Large
Volume," Trans. ASME Series C.. Vol. 104, No. 2, pp. 72-79.
Mei, R., and Klausner, J.F., 1992, "Unsteady Force on a
Spherical Bubble at Finite Reynolds Number with Small
Fluctuations in the Free-stream Velocity," Physics of Fluids
A, Vol. 4, No. 1, pp. 63-70.
Mei, R., and Klausner, J.F., 1993, "Shear Lift Force on
Spherical Bubbles," to appear in Int. J. Heat Fluid Flow.
Mesler, R.B., 1976, "A Mechanism Supported by Extensive
Experimental Evidence to Explain High Heat Fluxes Observed
During Nucleate Boiling," AIChE J.. Vol. 22, No. 2, pp. 246-
252.
Mesler, R.B., 1977, "An Alternate to the Dengler and Addoms
Convection Concept of Forced Convection Boiling Heat
Transfer," AIChE J.. Vol. 23, No. 4, pp. 448-452.
Mizukami, K., 1975, "Entrapment of Vapor in Reentrant
Cavities," Letters in Heat and Mass Transfer. Vol. 2, pp.
279-284.
Mizukami, K., Abe, F., and Futagami, K., 1990, "A Mechanical
Model for Prediction of Boiling Inception Condition," Proc.
9th Int. Heat Transfer Conf.. Jerusalem, paper 1-B0-20.
Moore, F.M., and Mesler, R.B., 1961, "The Measurement of Rapid
Surface Temperature Fluctuations during Nucleate Boiling of
Water," AIChE J.. Vol. 7, No. 4, pp. 620-624.
Nishikawa, K., Kusuda, H., Yamasaki, K., and Tanaka, K., 1967,
"Nucleate Boiling at Low Liquid Levels," Bulletin of JSME.
Vol. 10, No. 38, pp. 328-338.
Nishikawa, K., and Urakawa, K., 1960, "An Experiment of
Nucleate Boiling under Reduced Pressure," Mem. Fac. Eng.
Kvushu Univ.. 19, pp. 63-71.
zg, M.R., and Chen, J.C., 1973, "A Capacitance Method for
Measurement of Film Thickness in Two-Phase Flow," Rev. Sci.
Instrum.. Vol. 44, No. 12, pp. 1714-1716.
Puzyrev, Y.M, Kuz'min, A.V., and Salomatov, V.V., 1980, "The
Shapes of Bubbles during Boiling," Heat TransferSoviet
Research, Vol. 12, No. 2, pp. 11-15.


57
process is completely reversible, which indicates that
hysteresis has been suppressed. However, one puzzling result
is that when T^-cT,*, AT^ does not substantially vary. This
may be because the size of the reentry cavities along the
heating surface are fairly uniform, r2~0.31 /xm. If this were
the case, only when Tvmin<15 C would AT^j be influenced. Such
a test has yet to be conducted. Electron microscope
photographs did not add any further insight.
4.4 Conclusions
Based on the experimental observations and theoretical
analysis presented herein regarding the incipience and
hysteresis associated with saturated forced convection boiling
of R113, two comments are in order:
1) Non-condensible gases trapped in cavities tend to reduce
the initiation superheat, but they will be purged from
cavities after boiling is sustained for a sufficient period.
For highly wetting liquids, the liquid flow could exert a
slight effect on the sustaining incipience superheat but not
on the initiation superheat. Gas-free conical cavities are
not useful for initiating boiling but can become activated
from adjacent nucleation sites. The initiation incipience
likely occurs in reentry cavities.
2) The incipience hysteresis is related to the minimum
heating surface temperature prior to boiling. Once fully
developed boiling has been established, the boiling process is


Radius a(t) (mm)
145
Time t (ms)
Figure 8-2. Time history of bubble growth


63
boiling. Measurements of nucleation site density have been
obtained for flow boiling of refrigerant R113 in a 25 x 25 mm
inner square transparent test section. These measurements
have been obtained for an isolated bubble regime with
stratified flow. In general, the vapor/liquid interface was
wavy and periodic slugs of liquid were observed passing
through the test section. No flow regime transitions were
observed. The liquid phase Reynolds number based on the mean
liquid velocity, which is defined by equation (3-5), ranged
from 12,000 to 27,000 and that for the vapor phase as defined
by (3-6) ranged from 24,000 to 80,000. The flow conditions
are characterized by the mass flux, G, liquid film thickness,
, vapor quality, X, mean liquid velocity, u,, and mean vapor
velocity, Uy. Thermal conditions are characterized by the
heat flux, qw, the wall superheat, ATMt and saturation
condition (saturation temperature, TMt, or saturation pressure,
PMt) The controllable inputs of the flow boiling facility are
G, X, PMt (or TMt) and qw. Of the flow parameters considered,
only two are independent since the mean liquid and vapor
velocities were calculated from equations (3-3) and (3-4),
respectively, based on measured liquid film thickness at a
given G, X, and TMt. For the convenience of discussion,
equations (3-3) and (3-4) are rewritten here,
_G(1-X)D
r P,6
(5-3)
and


APPENDIX B
NUCLEATION SITE DENSITY IN FORCED CONVECTION BOILING
n/A
Tt
G
X
S
u,
Vtv
Qw
ATMt
cur2
C
kg/m2-s
mm
m/s
m/s
kW/m2
C
0.64
59.1
214.9
.20
3.5
.85
4.65
19.3
14.4
1.28
58.9
214.1
.16
4.3
.72
3.98
19.3
15.6
3.00
58.7
214.5
.13
5.3
.60
3.53
19.3
16.4
4.92
58.3
215.0
.12
6.1
.53
3.24
19.3
17.2
6.00
57.9
214.3
.10
7.1
.47
2.83
19.3
17.6
7.28
57.9
214.4
.08
7.8
.43
2.49
19.3
17.7
9.42
57.8
214.4
.05
9.5
.37
1.71
19.3
17.6
3.41
60.1
273.1
.10
6.2
.68
3.27
19.3
14.3
5.15
59.6
250.9
.09
6.3
.62
2.97
19.3
15.2
7.05
59.3
226.1
.10
6.3
.55
2.98
19.3
15.5
8.10
58.5
188.4
.11
6.3
.46
2.56
19.3
17.3
9.09
58.1
150.7
.12
6.4
.35
2.39
19.3
18.0
1.18
58.0
154.4
.23
4.2
.48
4.22
19.3
15.6
1.93
58.0
175.7
.17
5.2
.48
3.75
19.3
15.9
3.46
58.1
214.4
.11
6.8
.48
3.14
19.3
16.9
4.39
58.5
236.3
.09
7.6
.49
2.91
19.3
16.5
5.59
58.8
261.9
.06
8.7
.48
2.35
19.3
15.9
5.16
56.1
121.1
.24
3.3
.47
3.55
20.7
17.2
4.95
56.3
140.9
.20
3.8
.50
3.61
20.7
17.6
4.66
56.8
162.3
.17
4.0
.57
3.51
20.7
16.9
4.18
58.3
224.4
.13
4.4
.76
3.57
20.7
15.8
164


54
14.7 C which corresponds to cavities with r2< 0.31 jum.
Assuming that reentry cavities initiate boiling and r2~0.31
/xm, they would be able to sustain their vapor embryos provided
the wall temperature is maintained above 15 C. The ambient
temperature of the laboratory where the boiling facility is
housed is maintained at 20 C. The fact that the vapor embryo
can be sustained may explain why the initiation incipience
superheats in Figure 4-3 are relatively uniform. The above
analysis suggests that if the heating surface is cooled down
well below 15 "C or if the system is pressurized well above
1.45 bars, ATjoci should increase. Experiments have been
performed when the system was pressurized to 2.26 bar with
TWn,in=20 C for about half an hour. AT^ measured immediately
following depressurization was found to increase to 19.1 C,
which is consistent with the above prediction. Further
measurements revealed that AT^ was dropping down toward its
original value as boiling continued but it required several
days for AT^j to recover.
4.3.2 Sustaining Incipience Superheat
A vapor bubble departing a cavity which has been active
will likely leave vapor behind at the cavity mouth in the form
of an embryo. Provided sufficient superheat is available to
the embryo, it will readily expand and vapor bubble growth
will again result. This process will continue until the
superheat available to the embryo is insufficient to promote


7
Each of the five preheaters is powered by a 240 volt line
through an adjustable AC autotransformer. The heat loss of
the preheaters has been calibrated as a function of
temperature difference between the outer surface of the
insulation and the ambient. A typical calibration curve is
shown in Figure 2-3. In order to allow the two-phase mixture
generated by the preheaters to be fully developed and smoothly
flow into a square transparent test section, which will be
described shortly, a 1.5 m long and 25 x 25 mm inner dimension
square copper duct has been mounted downstream of the
preheaters. The duct is also thermally insulated using
fiberglass, thus provides an adiabatic developing length for
the two-phase flow. A capacitance-based liquid film thickness
meter, which will be described in detail in section 2.3, was
installed on the either side of the test section to measure
the inlet and outlet liquid film thickness of the two-phase
mixture. Two Viatran model 2415 static pressure transducers
have been installed at the inlet and outlet of the test
section to measure the system pressure with an accuracy of
0.5% of full scale (30 psig) Two type E thermocouple probes
were also located at the same position to measure the bulk
temperature of R113. When the two-phase mixture becomes
saturated, the measured bulk temperature using thermocouples
matches that calculated from the saturation line based on the
measured system pressure to within 0.5C, which is also the
accuracy of the absolute temperature measurement from the


47
Figure 4-4. An idealized sketch of a vapor embryo in a
conical cavity.
where 6 is the contact angle and \p is the half cone angle of
the cavity. First, consideration is given to the effect of
non-condensible gas on incipience, and for this purpose a
conical cavity with a specified geometry, rx=0.69 nm and ^=5,
is considered. The contact hysteresis, which is important for
boiling incipience, has been discussed in detail in the
literature (Johnson and Dettre, 1969; Schwartz and Tejada,


82
to a definition of critical cavity radius which is solely
dependent on ATMt or qw for constant fluid properties. One
shortcoming of these analyses is the assumption of a linear
temperature profile in the liquid thermal layer. Certainly,
the strength of heat flux and the intensity of bulk turbulence
will have a strong influence on the shape of the thermal
layer. Nevertheless, the experimental data presented here and
these theoretical analyses suggest that in addition to the
critical radius based on equation (5-2), a length scale
related to the shape of the thermal layer may also be
important in characterizing n/A.
In addition, it is emphasized that rc has been calculated
using equation (5-2) by taking the wall superheat to be the
average value, ATMt. As mentioned earlier, Kenning (1992) used
liquid crystal thermography to show that |Al^at|/ATsat could
be as large as 1.5 for pool boiling. In this study the liquid
crystal test section was used in conjunction with a Panasonic
video recorder to record the flow boiling wall temperature
field at conditions of 11^=3.0 m/s, qw=18.1 kW/m2, and TMt=58.3
C. It was found that temperature field was very nonuniform
in both spatial and temporal scales. Therefore, it appears
the average wall superheat is insufficient for characterizing
the local wall superheat experienced by individual sites.
The experimental data of n/A presented here have revealed


18
m
w
v
l
f¡
o
£
a
S
TJ
0
cr
3
J:
d
r-H
K
Relative Capacitance C"
Figure 2-6. Prediction of relative film thickness versus
capacitance using model of Chun and Sung
(1986).
the sensor for the stratified flow regime at room temperature
on a bench top under carefully controlled conditions. The
results of the calibration for sensor #1 were tabulated in
terms of S' and C* and are shown in Figure 2-7. It is noted
that for the lower section of the sensor, 6* was normalized by
0.75h rather than h since the full scale of the measurement
for this section is 0.75h. There was no modification for the


12
(1983). Of these, the only non-intrusive measuring
techniques, applicable to dielectric fluids, which capture the
liquid film thickness and volume fraction with a very rapid
response time are capacitance and radiation absorption
techniques. The implementation of the radiation absorption
technique requires expensive, bulky equipment with which
special safety precautions must be adhered to. In contrast,
the capacitance sensors used to measure liquid film thickness
and volume fraction are compact, safe, and inexpensive and
thus were selected for this research. Ozgu and Chen (1973)
used a capacitance sensor to measure liquid film thickness for
axisymmetric two-phase flow while Abouelwafa and Kendall
(1979), Sami et al. (1980), Irons and Chang (1983), Chun and
Sung (1986), and Gaerates and Borst (1988) used a capacitance
sensor to measure volume fraction. A summary of these
investigations can be found in Delil (1986) All of the
capacitance probes and measuring techniques reported by these
investigators were used only for adiabatic flow; there was
very little mention made of the temperature dependence of
capacitance sensors. Furthermore, the ring-type capacitance
sensor described by Ozgu and Chen (1973) may only be used to
measure symmetric two-phase duct flow, such as vertical up-
flow or down-flow. The sensor is not applicable for use with
horizontal two-phase flow, which is usually asymmetric due to
the gravitational stratification of the phases.
Since a forced convection boiling system undergoes large


27
facility are primarily due to the maximum flow rate of the
Micropump, the strength of the pyrex glass, and the
temperature limitation of the E-poxy used in the test section.
All the experiments performed in this investigation have been
confined to the system design conditions.


65
VIDEK MEGAPLUS
Figure 5-2. A diagram of optical facility for measurement
of nucleation site density.
analysis. Computer software written in Microsoft C has been
developed for the image acquisition and processing. Due to
the strong vapor-liquid entrainment and waviness at the
interface of the two-phase mixture, it is not possible to
obtain a clear view of nucleation sites from the direction
normal to the heating surface. Therefore, the camera was
focused on the boiling surface through the side wall. A 500
Watt light illuminates the heating surface at an appropriate


ACKNOWLEDGEMENTS
My greatest appreciation goes to Professor James
Klausner, chairman of the supervisory committee, for all the
support and encouragement during the course of this research.
Dr. Klausner, a mentor and role model, has spent a great deal
of time and effort in helping me with the fabrication of the
experimental facility, analysis of the experimental data, as
well as editing this dissertation. I also want to extend my
appreciation to Professor Renwei Mei, member of the
supervisory committee. Dr. Mei has always been accessible and
has provided many useful suggestions throughout the course of
this research. I would also like to thank professors C.K.
Hsieh, D.Y. Goswami, and S. Anghaie for serving on the
supervisory committee. Their useful suggestions have improved
this dissertation.
I also want to thank Dave Bernhard and Boby Warren,
fellow graduate students and friends. Dave and Bob have
provided substantial support in calibrating instrumentation
and planning experiments.
I can not express enough love and appreciation to my
wife, Tang Yong. Without her support, understanding, and
sacrifice, I would not have finished my Ph.D. program.
Finally, I want to thank my parents, brothers, and sisters for
iii


135
d
v
N
a
IB
55
a
a
3
m
h
a>
6
p
Figure 7-1. Statistical distribution of bubble lift-off
diameter in flow boiling.
where dj is the detachment diameter (departure or lift-off)
under consideration and Ad is the diameter range.
Comparisons were first made for the bubble lift-off
diameters in flow boiling and results are shown in Figure 7-2.
The prediction of pdf is based on assumed Gaussian
distribution of wall superheat with a standard deviation of


32
a /(h AT. )
' mac inc.s''
Figure 3-1. Microconvection heat transfer for saturated
forced convection nucleate boiling.
heat transfer component, h^. Figure 3-2 shows h^,,. as a
function of liquid Reynolds number, Re,, and vapor Reynolds
number, Rev. If h^ is approximated as a linear function of
Reynolds number over the limited range of data, the standard
deviation based on Re, is 0.165 and that based on Rev is 0.093,
and thus it is seen that h^ is better correlated with Rev than
Re,. This result is fundamentally different from that in


40
heating, cool-down, and surface drying procedures (You, et
al., 1990; Marto and Lepere, 1982; Bergles and Chyu, 1982).
Recently, the effects of flow on boiling incipience have been
examined by various investigators. In subcooled flow boiling
with highly wetting liquids, such as R113 and F72, mass
velocity showed little effect on boiling incipience (Hino and
Ueda, 1985; Marsh and Mudawwar, 1989). In flow boiling with
water under both subcooled and saturated conditions, Sudo et
al. (1986) and Marsh and Mudawwar (1989) observed a strong
influence of the liquid velocity on boiling incipience. Flow
boiling incipience measurements of R113 at saturated
conditions are not available in the literature.
Numerous models and correlations have been proposed for
the prediction of boiling incipience, which have recently been
reviewed by Brauer and Mayinger (1992). The majority of
models were categorized as being either thermal or mechanical.
Thermal models are those which consider the bubble embryo to
sit at the mouth of a cavity and protrude into a superheated
thermal liquid layer. Once thermal equilibrium at the embryo
interface is exceeded by the superheated liquid, bubble growth
is initiated. Experimental data have verified that for poorly
wetting liquids, such as water, the initiation and sustaining
incipience points almost coincide and these models are useful
for predicting the incipience superheat. Models proposed by
Hsu (1962), Han and Griffith (1965), Bergles and Rohsenow
(1964), Sato and Matsumura (1964), and Davis and Anderson


86
which a vapor bubble detaches from its nucleation site was
referred to as the point of departure and the instant it
detaches from the heating surface was referred to as the lift
off point. In pool boiling systems the departure and lift-off
points coincide and for the remaining of this work will be
referred to as the departure point. In this work, the
existing vapor bubble departure models and correlations for
nucleate pool and flow boiling in the literature were
examined. Based on experimental observations and theoretical
reasoning, an analytical model was developed for the
prediction of vapor bubble detachment diameters for both pool
and flow boiling. When compared with experimental data, the
model is found to yield significant improvement in the
accuracy of predicting vapor bubble detachment diameters when
compared with existing correlations.
6.2 Literature Survey
6.2.1 Pool Boiling Departure Diameter Correlations
Numerous vapor bubble departure diameter correlations and
models have been proposed for nucleate pool boiling, many of
them were summarized by Zuber (1964), Cole and Shulman (1966),
Hsu and Gramham (1976) and Kocamustafaogullari (1983) These
correlations and models may be categorized into three types:
surface tension controlled departure; inertia controlled
departure; and purely empirical correlations. For the surface
tension controlled bubble departure, it was assumed that the


Radius a(t) (mm)
146
Tme t (ms)
Figure 8-3. Time history of bubble growth


Radius a(t) (:
147
Time t (ms)
Figure 8-4. Time history of bubble growth.


98
is given by Hinze (1975) as
yu* yu*
exp(-0.33^Hl))
v
(6-23)
where k=0.4, x=Hf and c=7.4. It is noted that the bulk
turbulence for two-phase flow is more intense than that for
single-phase flow, and u'/u^O.OS has been assumed when
equation (6-23) is used to approximate the liquid velocity
profile in stratified two-phase flow. Here u, is the mean
liquid velocity of the two-phase mixture and is given by
equation (3-3) Both the quasi-steady drag and shear lift are
important when AU is large.
Surface Tension. Contact Pressure, and Hvdrodvnamic
Pressure Forces. Considering a vapor bubble growing on a
horizontal heating surface in a liquid pool, the surface
tension force in the y-direction can be calculated from
Fsy=-ndwosin0
(6-24)
where is the contact diameter, cr is the surface tension
coefficient, and 6 is the contact angle. Many believe that
the major obstacle in developing a reliable correlation for
vapor bubble departure diameters in boiling is due to the
inability to predict and 6 accurately. As shown by the
measurements of Keshock and Siegel (1964), both contact
diameter and contact angle vary appreciably during the bubble


25
this investigation, which is used for recording measurements
of pressure, temperature, flow rate, and capacitance for this
investigation. A schematic diagram of the data acquisition
system is displayed in Figure 2-12. The data acquisition
system is comprised of two Acces 16-channel multiplexer cards
(AIM-16) interfaced with one Acces 12-bit 8-channel analog-to-
digital converter (AD12-8), mounted in an I/O slot of a
Northgate PC/AT computer. The AD12-8 has a maximum conversion
speed of 40 kHz and input voltage range of 10 Volts. Each
AIM-16 card is interfaced with one channel of the AD12-8
board. Thus there are 32 different channels available when
using this system. Channel 0 of the AIM-16 has been used to
determine the cold junction temperature using a resistance
temperature device (RTD). The temperature scale factor for
the output of the RTD is 24.4 mV/C. Each channel of the AIM-
16 has a preamplifier with gains ranging from 0.5 to 1000 and
may be programmed through the computer. The AD12-8 board and
AIM-16 cards were calibrated according to manufacturer's
specifications. Each analog signal from the respective
instrument is connected to one of the 32 channels of the AIM-
16 cards. Appropriate gains were set up for different
channels to achieve maximum resolution. Since two-phase flows
are inherently unstable, all measurements were time-averaged
to obtain repeatable values. Using this system, an average of
500 sampling points were collected over a time period of 30
seconds in order to obtain repeatable measurements. Quick


50
assumed that TV~TW. When Tw exceeds Tvmax/ equation (4-1) will
be violated and vapor bubble growth will be initiated. Thus
the initiation incipience superheat is evaluated from
^lnCti=TVtmax-Tsat(P() (4-6)
It is clear that the initiation incipience superheat increases
with decreasing n^. For the conditions in Figure 4-5, the
assumed value of does not significantly influence the
incipience superheat. Since it is expected that non
condensible gas will be purged from the cavity during the
vapor bubble departure process, the amount of gas inside the
cavity should decrease as ebullition continues. As the
heating surface is degassed, AT^; should increase. This trend
has been observed with the current facility. After the test
section is filled with liquid R113, it is necessary to sustain
fully developed nucleate boiling for approximately two hours
in order to obtain a repeatable AT^j. This observation is
consistent with those of Griffith and Wallis (1960). They
suggested that fully developed nucleate boiling with water
must be sustained for 1.5 hours to degas conical cavities, and
two hours is required for reentry type cavities. Thus it is
concluded that non-condensible gas trapped in cavities during
liquid flooding of the boiling surface exerts a strong
influence on AT^; only during the initial stage of boiling.
Provided fully developed nucleate boiling is sustained for a
sufficient period of time, the embryo in active cavities


20
when the two-phase mixture is at saturated conditions.
In order to determine the liquid film thickness from the
calibration curves shown in Figure 2-7, C, and Cv must be
determined as a function of temperature when the two-phase
mixture is at a temperature other than the calibration
temperature. The functions were determined after the sensors
had been installed in the facility. To do so, pure liquid
R113 was circulated through the facility and was heated. When
a steady temperature was reached, the capacitances across the
lower and upper pairs of copper strips were recorded. This
procedure was repeated for a series of increments of
temperature while the throttle valve was adjusted to elevate
the system pressure to avoid vapor generation. The results
obtained have been displayed in Figure 2-8. Similar
procedures were followed to obtain the capacitance for pure
vapor as a function of temperature as shown in Figure 2-9.
Because pure vapor flow could only be achieved by
depressurizing the boiling facility after two-phase flow had
been established, it was difficult to obtain the measurement
over a wide range of temperature. In this work only four
different temperatures were obtained. By incorporating the
calibration curves shown in Figures 2-7, 2-8, and 2-9, the
liquid film thickness may be determined as a function of
capacitance and temperature of any two-phase mixture.
In order to evaluate the performance of the liquid film
thickness sensor developed here, a CCD camera was set up for


62
the plate. Kenning's (1992) result suggests that a Micro
length scale which is related to the spatial temperature field
may also be important in characterizing incipience of vapor
bubbles. In addition, according to the suggestion of
Eddington, et al. (1978) and the experimental findings of
Calka and Judd (1985), at low n/A where nucleation sites are
sparsely distributed, neighboring nucleation sites do not
thermally interact. However at large n/A where nucleation
sites are closely packed, thermal interference among
neighboring sites exists. Since it has been demonstrated that
ATMt is highly nonuniform in the presence of nucleation sites,
a question arises as to whether at large n/A the average wall
superheat is sufficient for characterizing the local wall
superheat experienced by individual nucleation sites. The
data displayed in Figure 5-1 suggest that is not.
Few similar studies on nucleation site density in flow
boiling have been reported. In one such investigation
Eddington and Kenning (1978) measured the nucleation site
density with subcooled flow boiling of water for a narrow
range of flow conditions. It was suggested that n/A is
related to rc. The objectives of the present work are
twofold: 1) to study the influence of flow and thermal
conditions on the nucleation site density in saturated
convection boiling, and 2) to determine whether or not the
nucleation site density in flow boiling is solely a function
of the critical radius, rc, as has been suggested for pool


115
8
S
e
T3
T?
Ih
V


S-4

A

a

o
T3

£h
Oh
0
Atmospheric Pressure Data
Water, Staniszewski (1959)
V Methanol, Staniszewski(1959)
O Water, Han & Griffith(1985)
A Aqueous-Sucrose Solution,
Keshock Si Siegel (1964)
Water, Fritz & Ende (1936)
nPentane,
Cole & Shuhnan (1966)
Bubble Departure Correlation
of Cole & Shulman 2, (1966)
0 2 4 6 8
Experimental Departure Diameter dd (mm)
Figure 6-6. Comparison of predicted and measured vapor
bubble departure diameter for atmospheric
pressure data using Cole and Shulman 2
correlation.
relative deviation for the present model as seen in Table 6-2
is 15%. A similar comparison for the Cole and Shulman 2
correlation is displayed in Figure 6-6. The Cole and Shulman
2 correlation which was satisfactory for subatmospheric
pressure data is also adequate for atmospheric pressure data
and has a relative deviation of 31%. However, when comparing
Figures 6-5 and 6-6, the present model appears more accurate.


Radius a
151
B
B
0.15
0.10 -
0.05 -
0.00
0.0
G=184.6 kg/m8s
X=0.155
T =67.0 C
sat
qw=8.67 kW/m
AT =7.8 C
sat
A
M
V
0.5 1.0
Time t (ms)
K=0.086
n=0.46
1.5
Figure 8-8. Time history of bubble growth.
2.0


55
bubble growth. Following bubble departure, the liquid moves
toward the cavity, and the liquid/vapor interface will acquire
an advancing dynamic contact angle, 9^, which is usually
larger than 0M. According to Cole's analysis (1974), for
either conical or reentry cavities with half cone angle, \f/,
less than 0^, the maximum curvature the interface can attain
is the reciprocal of the cavity mouth radius, rt. Thus, prior
to bubble growth the interface protrudes the cavity mouth into
the superheated liquid thermal layer. Both the cavity mouth
radius and the temperature profile in the liquid thermal layer
control whether or not bubble growth will result. Assuming
bulk turbulence alone controls the liquid thermal layer, and
the temperature profile is linear in the vicinity of the vapor
embryo, the liquid temperature at the top of the embryo is
given by
(4-9)
where k, is the liquid thermal conductivity. Starting from
the Clayperon equation and the perfect gas approximation for
vapor, Bergles and Rohsenow (1966) derived an equation for the
embryo vapor temperature,
rrJ2,
ln(i+-l2_
rlpt
(4-10)
They further proposed the criterion for boiling incipience
that T( at the top of the embryo must exceed Tv. Based on this


107
since the mean liquid velocity is generally zero, the momentum
equation at the point of departure is identical to (6-34),
which can be solved for the vapor bubble departure diameter.
It is noted that although the departure criteria for pool
boiling is identical to that of lift-off in flow boiling, the
lift-off diameter is typically smaller than the pool boiling
departure diameter. This is so because the wall superheat,
which controls the vapor bubble growth rate, is smaller for
flow boiling due to the additional energy transport from the
wall to the bulk liquid provided by the bulk turbulence. It
is seen that the bubble departure diameter dd is determined
from a balance between the buoyancy and growth forces as
opposed to the buoyancy and surface tension force.
6.4 Comparison with Experimental Data
Since the growth force is dependent on the vapor bubble
growth rate, comparisons were made only for experimental data
in which both the bubble detachment diameter and growth rate
were measured. The experimental data depicted here are either
based on those found in the literature or those measured by
Bernhard (1993) using the flow boiling facility described in
chapter 2. A useful statistical parameter, referred to here
as the relative deviation (r.d.), is used to evaluate the
performance of the present departure and lift-off model
against existing correlations and models, and is defined by


49
>
E-
100
90 -
80
70
60
50
40
30
20
10
0.001
_L
0.01 0.1 1
V (x 10-10 ma)
10
100
Figure 4-5. Variation of vapor temperature with vapor
embryo volume during expansion inside a
conical cavity.
through (4-5) simultaneously. Once rd is obtained, a Tv vs. V
plot can be constructed by solving eguations (4-1) through (4-
5) assuming a quasi-eguilibrium expansion process. Figure 4-5
shows three different Tv vs. V curves, each for a different itig.
It is seen that as V increases there exists a maximum vapor
temperature, Tvmax, which will satisfy equations (4-1) through
(4-5). Based on quasi-equilibrium considerations, it is


REFERENCES
Abouelwafa, M.S.A., and Kendall, E.J.M., 1979, "Analysis and
Design of Helical Capacitance Sensors for Volume Fraction
Determination," Rev. Sci. Instrum.. Vol. 50, No. 7, pp. 872-
878.
Andritsos, N., and Hanratty, T.J., 1987, "Influence of
Interfacial Waves in Stratified Gas-Liquid Flows," AIChE J..
Vol. 33, No. 3, pp. 444-454.
Bergles, P.J. and Chyu, M.C., 1982, "Characteristics of
Nucleate Boiling in a Large Volume in Porous Metallic Covers,"
Trans. ASME. Series C. Vol 104, No. 2, pp. 56-65.
Bergles, A.E. and Rohsenow, W.M., 1964, "The Determination of
Forced-Convection Surface Boiling Heat Transfer," J. of Heat
Transfer. Trans. ASME, Vol. 86, pp. 365-372.
Bernhard, D.M., 1993, "Experimental Investigation of Vapor
Bubble Departure and Lift-off in Forced Convection Boiling,"
Master's thesis, University of Florida, Gainesville, Florida.
Bontozoglou, V., and Hanratty, T.J., 1989, "Wave Height
Estimation in Stratified Gas-Liquid Flows," AIChE J.. Vol.
35, No. 8, pp. 1346-1350.
Brauer, H. and Mayinger, F., 1992, "Onset of Nucleate Boiling
and Hysteresis Effects under Forced Convection and Pool
Boiling," Pool and External Flow Boiling, eds. V.K. Dhir and
A.E. Bergles, pp. 15-35, ASME publication, New York, NY.
Brouillette, J., 1992, "Vapor Bubble Growth in Forced
Convection Boiling," personal communication.
Calka, A., and Judd, R., 1985, "Some Aspects of the
Interaction among Nucleation Sites during Saturated Nucleate
Boiling," Int. J. Heat Mass Transfer. Vol. 28, No. 12, pp.
2331-2342.
Chang, Y.P., 1963, "Some Possible Critical Conditions in
Nucleate Boiling," J. of Heat Transfer. Trans. ASME, Vol. 85,
No. 2, pp. 89-100.
Chen, J.C.,1966, "Correlation for Boiling Heat Transfer to
167


114
s
a
TJ
Tj
P

"
a
-i-H
Q

u
d
-*->
¡3
a.

Q
TJ

-M
O
TJ

I-,
a.
8
1 1
Atmospheric Pressure Data
# Water, Staniszewaki (1959)
V Methanol, Staniszewsld(1959)
O Water. Han & Griffith(1965)
A AqueousSucrose Solution,
Keshock & Siegel(l964)
Water, Fritz & Ende(1936)]
nPentane,
Cole & Shulman (1966)
6 -
4 -
2 -
Bubble Departure Model
of This Work
0 2 4 6 8
Experimental Departure Diameter (mm)
Figure 6-5. Comparison of predicted and measured vapor
bubble departure diameter for atmospheric
pressure data using the present model.
comprised of four different fluids and 67 data points. The
experimental departure diameters were obtained from
Staniszewski (1959), Han and Griffith (1965), Keshock and
Siegel (1964), Fritz and Ende (1936), and Cole and Shulman
(1966). A comparison between the measured and predicted
departure diameter using the present model is shown in Figure
6-5. It is seen that the prediction is also excellent. The


66
angle from the opposite side wall. An opaque plastic sheet is
placed between the light and the object to diffuse the
incident light. Exposure time and lens aperture are properly
adjusted to obtain a clear image of the nucleation sites. A
typical picture of the nucleation sites is displayed in Figure
5-3 which was taken from the Sony monitor image. In order to
reduce the non-uniformities caused by the heater edge effect,
only nucleation sites in the middle 2/3 of the strip were
counted for measuring purposes. Thus the effective
measurement area was 1.4 cm wide by 2.2 cm. The nucleation
site density measured from an ensemble average of fifty images
was compared against that based on an average of ten images;
identical results were obtained. Therefore, all nucleation
site density measurements reported herein are based on an
ensemble average of ten images. Presumably intermittent sites
are accounted for. As has been demonstrated in Figure 3-2,
hysteresis can be avoided once the fully developed boiling has
been established. The measurements of nucleation site density
here were only made for the fully developed boiling regime
with increasing heat flux and increasing vapor velocity.
5.3 Experimental Results
Nucleation site density measurements were obtained for a
constant heat flux, qw=19.3 kW/m2, and saturation temperature,
TMt=58 C, over a range of flow conditions in which either the
mass flux, G, liquid film thickness, S, liquid velocity, ut,


73
a
o
<
\
t
w
Cl
0)
n
4->
co
t
o
fH
-->
t
0)
v
t
$5
15
10
0.2
£
V G=215 kg/mss
qw=19.3 kW/mz
6=6.3 mm
q =19.3 kW/mB
T =58 C
sat

V




0.4
0.6

0.8
1.0
Liquid Velocity u. (m/s)
Figure 5-8. Nucleation site density as a function of
liquid velocity.
the measured increase in flow boiling heat transfer
coefficient with declining liquid film thickness for
stratified or annular flow. To the best of the author's
knowledge direct evidence supporting or refuting Mesler's
claim has yet to be presented. To sort out the direct
influence of liquid film thickness on the nucleation site


106
Table 6-1. Summary of Forces Appearing in Momentum Equations.
Forces in Momentum
Equations
Symbols
Forces
Negligible
Estimated
from Eqs.
Surface Tension
x-direction
F
1 sx
yes
Quasi-steady Drag
x-direction
F
rqs
no
(6-21) and
(6-23)
Growth Force
x-direction
Fdux
no
(6-29) and
(6-30)
Surface Tension
y-direction
F
ry
yes
Growth Force
y-direction
Fduy
no
(6-29) and
(6-31)
Shear Lift Force
y-direction
FsL
only when
considering
lift-off
(6-22) and
(6-23)
Buoyancy Force
y-direction
Fb
no
(6-20)
Hydrodynamic
Pressure Force
y-direction
Fh
yes
Contact Pressure
Force
y-direction
Fcp
yes
Lift Force Created
by Bubble Wake
y-direction
Fl
yes
there do not exist simple explicit expressions for dd and 6it
they can be easily solved through iteration. The y-momentum
equation at the point of lift-off is
Fdu+Fb=0 (6-34)
and can be solved for the lift-off diameter dL.
In the case of pool boiling from a horizontal surface,


4-2 A typical saturated flow boiling plot of qw vs
AT,^ for G=180 kg/m2-s, X=0.156, and i=4.8 mm 43
4-3 Measured saturated flow boiling incipience
wall superheat 45
4-4 An idealized sketch of a vapor embryo in a
conical cavity 47
4-5 Variation of vapor temperature with vapor embryo
volume during expansion inside a conical cavity 49
4-6 An idealized sketch of a vapor embryo in a
reentry cavity 52
4-7 Variation of minimum vapor temperature and
initiation superheat with cavity reservoir
mouth radius 53
5-1 Pool boiling nucleation site density data from
Griffith and Wallis (1960) 61
5-2 A diagram of optical facility for measurement
of nucleation site density 65
5-3 A typical photograph of nucleation sites on
a boiling surface 67
5-4 Nucleation site density as a function of wall
superheat for constant heat flux and saturation
temperature 68
5-5 Pool boiling nucleation site density as functions
of wall superheat and heat flux 69
5-6 Nucleation site density as a function of vapor
Velocity for constant heat flux and liquid film
thickness 71
5-7 Nucleation site density as a function of mass
flux 72
5-8 Nucleation site density as a function of liquid
velocity 73
5-9 Nucleation site density and liquid film thickness
as functions of vapor velocity 74
5-10 Nucleation site density as a function of liquid
film thickness 75
x


132
diameters have been calculated for specified pdf's of wall
superheat and liquid velocity, and the results are compared
with experimental data.
7.2 Formulation
According to the preceding bubble detachment model, the
bubble departure diameter increases with increasing wall
superheat and decreases with increasing liquid velocity in
flow boiling. Therefore, the probability distribution
function of departure diameter can be expressed as
Prob[0]
(7-1)
where d, AT, and u are the departure diameter, wall superheat,
and mean liquid velocity, respectively. The subscripts for
these three variables have been eliminated to avoid confusion.
Assuming the wall superheat and liquid velocity are
statistically independent, equation (7-1) can be expressed in
integral form as,
J^aTU)pd(0 d{=J*TpAT(i\) dx)fpu(l) d£ (7-2)
where p denotes probability density function. pd(d) is
obtained by differentiating equation (7-2) with respect to d,
pd(d)-p4T(ADpt,(u)-^|H (7-3)
dAr
dd
du
dd
are evaluated using
where partial derivatives
and


136
T
V
N
a
sf
¡z;
.o
£¡
3
m
u
V
1
3
'Z.
Bubble Departure Diameter dd (mm)
Figure 7-2. Statistical distribution of bubble departure
diameter in flow boiling at constant ATt.
one eighth of its mean value. The assumed standard deviation
was chosen such that the predicted pdf's best fit to those of
the experiment. The experimental data were obtained by
Bernhard (1993) and each pdf was constructed from more than
200 observations of bubble diameter. It is shown that both
the mean value and standard deviation of bubble lift-off


156
8.4 Conclusions and Discussions
From the limited number of experimental data obtained
here, it is seen that in flow boiling the growth exponent n
decreases with increasing system pressure. A liquid or vapor
velocity influence on n has not been observed. Since the
measurement did not include an ensemble average of many
bubbles, a comparison concerning the amplitude of the growth
rate can not be made from these data.
Since the vapor bubble growth in saturated flow boiling
typically follows a diffusion-controlled growth model, the
analysis of heat transfer during the bubble growth would be
helpful in understanding the influence of liquid turbulence on
the growth rate. A gross estimation has been made for the
heat flux transmitted from the surrounding liquid to the vapor
bubble due to the bulk convection and the latent heat
transport due to bubble growth. The bulk convection to the
bubble was estimated using a heat transfer correlation for
flow over a sphere. For a boiling condition of G=184.6 kg/m2-
s, X=0.155, TMt=67.0 C, qw=8.67 kW/m2, and ATMt=7.8 C, the
latent heat transport was found to be typically two orders of
magnitude larger than the bulk convection based on measured
bubble growth rate. Therefore, the bulk turbulence is not
expected to exert an appreciable influence on the vapor bubble
growth in saturated flow boiling. This crude analysis is
consistent with the present experimental observations.


19
cn
w
Q)

o
3
E-
B
£
I

os
Meter #1, calibrated at 25 C
Relative Capacitance C*
Figure 2-7. Calibration curve for film thickness sensor.
upper section. It is seen from Figure 2-7 that the resolution
is good when the film thickness is well below the centerline
for the lower section and well above the centerline for the
upper section. There exists a small region near the
centerline where the film thickness can not be resolved.
However, for the current study with saturated forced
convection boiling, this does not pose a severe problem
because the liquid film is always well below the centerline


118
Table 6-4. Comparison of Measured and Predicted Vapor
Bubble Departure Diameter for Reduced Gravity
Data Using Present Model.
Percentage
of Earth
Gravity
dd (mm)
Measured
dd (mm)
Predicted
K
n
42.9
3.84
4.50
0.00993
0.42
22.9
3.79
3.28
0.00430
0.22
12.6
4.90
5.63
0.00932
0.37
6.1
3.38
3.87
0.00605
0.36
1.4
5.21
6.28
0.00552
0.22
Atmospheric Pressure. Reduced Gravity. For the reduced
gravity data, only five data points are available in which the
gravitational field varies from 0.04 to 0.43 of earth gravity.
These data indicate that the vapor bubble growth rate
decreases with decreasing gravity. Table 6-4 displays the
predicted departure diameters using the current model compared
with the measured values as well as the values for K and n to
be used in equation (6-38). It is seen that n decreases with
gravitational field. For these five data points the relative
deviation is 16%. The present model is the only one which is
in satisfactory agreement with the reduced gravity data,
besides that of Nishikawa and Urakawa (1960) It is also
expected from equation (6-38) that when g approaches zero the
vapor bubble will not depart the heating surface unless there
is some external mechanism to induce an inertial force to
remove the bubble, such as system vibration or three


64
U
v
GXP
?v(D-b)
(5-4)
Therefore, when investigating the influence of one of the flow
parameters on nucleation site density at constant saturation
conditions, only one other flow parameter can be held
constant, which introduced complexities in interpreting the
data. The range of the flow and thermal parameters covered in
these measurements, which to a large extent were limited by
the ability to visualize nucleation sites, are as follows:
G=125-290 kg/m2-s, 1^=1.6-4.7 m/s, U;=0.35-0.68 m/s, 5=3.5-9.5
mm, gw=14.0-23.0 kw/m2, ATt=13.0-18.0 C, and TMt=55.0-75 C.
5.2 Optical Facility and Measuring Technique
The nucleation site density was measured optically using
a digital imaging facility shown in Figure 5-2. The facility
consists of a Videk Megaplus CCD camera with a 1320 x 1035
pixel resolution. The CCD camera is eguipped with a Vivitar
50 mm macro lens with high magnification and low optical
distortion and a Videk power supply. The output of the CCD
camera is connected to an Epix 4 megabyte framegrabber which
is mounted in an I/O slot of a 386 Zenith computer. The
framegrabber allows for either high resolution (1320 x 1035)
or low resolution (640 x 480) imaging. The images are
displayed on a Sony analog monitor with 1000 lines per inch
resolution, and may also be printed out on an HP Laser Jet III
laser printer or may be saved on floppy disk for future


142
Figure 8-1. A schematic diagram of the high speed facility
for filming vapor bubble growth rate.
possible on an active nucleation site in order to achieve
maximum magnification. The camera is typically mounted at an
angle of approximately 30 degrees with the horizontal. The
motion picture camera was usually set at 6000 frames per
second and is adjustable by controlling the input voltage with
an autotransformer. Adequate illumination of the nucleation
site is crucial for obtaining quality images. Therefore,
considerable effort was put forth in testing the influence of
different lighting directions, diffusion, and intensity in
order to achieve optimum illumination. The illumination
system that was found to give the best quality images includes


117
Table 6-3. Comparison of Measured and Predicted Bubble
Departure Diameter for Elevated Pressure Data
Using Present Model.
Boiling
Liquids
Pressure
bar
dd(mm)
Meas.
dd(mm)
Pred.
K
n
Water
1.93
2.20
1.43
0.00444
0.38
1.58
1.12
0.00388
0.37
1.41
1.10
0.00254
0.29
1.86
1.30
0.00259
0.26
1.13
1.18
0.00202
0.22
1.73
1.27
0.00209
0.24
2.76
1.83
1.07
0.00301
0.34
1.77
1.04
0.00282
0.33
Methanol
1.93
1.24
1.03
0.00250
0.30
0.69
0.57
0.00256
0.38
2.76
1.01
0.83
0.00216
0.31
best correlation is that of Staniszewski (1959) which has a
relative deviation of 18%. The relative deviation for the
Cole and Shulman 2 correlation is 25%. It is interesting to
note that since the vapor bubble growth rate decreases with
increasing pressure, the present model predicts that the
departure diameter should decrease with increasing pressure,
under otherwise similar conditions. The elevated pressure
bubble departure data of Tolubinsky and Ostrovsky (1966)
definitively support this prediction. Unfortunately, their
data do not provide enough information for comparison against
the present bubble departure model because growth rate data
were not specified.


144
measurement is 0.05 mm and that of the magnification factor
is about 2%. Therefore, the uncertainty of the resultant
equivalent radius of the bubble is approximately 7%.
8.3 Results and Discussions
Experimental data of bubble growth rate were presented in
the form of bubble radius vs growth time as shown in Figures
8-2 through 8-11. The data obtained from the same roll of
film were placed in one figure in which each symbol represents
a growth history of a single bubble. It can be seen that the
bubble growth rates are scattered which is similar to the
observations by many investigators of pool boiling. Ensemble
averages of the growth rate were made for the bubbles at each
set of conditions, and may be represented in the form of
equation (8-1) In order to examine the parametric influences
of pressure, wall superheat, and fluid flow on bubble growth,
the values of K and n were tabulated in Table 8-1. It is seen
from the table that the exponent n is about 0.5 at the system
pressure of about 1.5 bar and decreases as the pressure is
elevated. This trend is consistent with that in pool boiling.
The influence of other conditions on n is not clear from these
data. It is not possible to draw any conclusion from the data
concerning the amplitude of bubble growth rate. It has been
recognized that wall superheat is the driving force for bubble
growth and the measured mean wall superheat may not be the one
that an individual nucleation site sees. In fact, the wall


76
examined where it is seen that n/A decreases with declining S,
which is primarily caused by increasing Uy. Therefore, it
appears that Uy has a governing influence on the nucleation
site density. An explanation and significance of this finding
will be discussed later.
When testing the influence of thermal conditions on n/A,
it is necessary to control Uy. In Figure 5-11, n/A is shown
as a function of qw for three different values of Uy at TMt=57
C. It is seen that n/A increases smoothly with increasing
heat flux at a fixed Uy. As u, increases, the curves shift
toward decreasing n/A. This trend is consistent with that
observed in Figure 5-6. The n/A data in Figure 5-11 are shown
as a function of ATMt in Figure 5-12. The data display
an anomalous behavior similar to that in Figure 5-4.
To examine the dependence of n/A on the critical radius
it was decided that a constant heat flux and vapor velocity
would be maintained, and rc would be controlled by raising the
system pressure. Doubling the system pressure has the effect
of essentially doubling the vapor density and increasing T^
by only several percent. The nucleation site density was
measured for fixed Uy and qw over a range of system pressure
from 1.4 to 2.3 bars which gave a 20 C increase of saturation
temperature. Figures 5-13 and 5-14 have been prepared from
these measurements. It is seen from Figure 5-13 that n/A
increases with increasing Tsat while ATMt is dropping during this
process. Nevertheless, Figure 5-14 shows that this increase


100
computational study of Lee and Nydahl (1989) predicts that the
surface tension force is an order of magnitude less than the
buoyancy and growth forces near the departure point.
Therefore, the approach taken in this work is to assume the
surface tension force approaches zero at the point of
departure. It is emphasized that this assumption does not
imply that the surface tension force is generally negligible.
For the early stages of bubble growth, the surface tension
force may be finite. However, if a condition arises where the
bubble growth rate is very small, it may be possible for the
surface tension force to be at the same order as the growth
force. It is only near the point of the departure that the
assumption of a small surface tension force is employed. The
same argument is also applicable to the case of flow boiling
since the surface tension forces in x- and y-direction are
proportional to the contact diameter The major
contribution of surface tension to the bubble departure is to
maintain the bubble shape.
The hydrodynamic pressure force acting on a vapor bubble
may be estimated based on ideal flow over a truncated sphere.
Based on a potential flow analysis, the hydrodynamic force is
given by
(6-25)
h 8f< 4
where AU is the relative velocity between the bubble center of


THE EBULLITION PROCESS
IN FORCED CONVECTION BOILING
By
LING-ZHONG ZENG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993
UJgVERSITY OF FLORIDA LIBRARIES


138
demonstrated to have a controlling influence. Figure 7-3 was
prepared for various liquid velocities and relatively constant
wall superheat. Gaussian distributions of liquid velocity and
wall superheat were assumed as well as standard deviations of
one eighth of their means. It is seen that the mean value of
departure diameter declines as liquid velocity increases while
its standard deviation increases with increasing liquid
velocity. Good agreement with measurements were also obtained
as shown in Figure 7-3. For constant liquid velocity, the
effect of wall superheat on the departure diameter is shown in
Figure 7-4. Based on the same Gaussian distributions of
liquid velocity and wall superheat, as used previously, the
predicted pdf's of departure diameter agree well with the
experimental data.
7.4 Conclusions and Discussions
The present model has successfully connected the pdf of
detachment diameter to those of liquid velocity and wall
superheat in flow boiling, which are assumed to be Gaussian
with standard deviations of one eighth of their means.
Although direct experimental data for the pdf's of liquid
velocity and wall superheat are not available at this time,
physical justifications for the assumed distributions is
possible. It has be hypothesized that the standard deviation
of liquid velocity increases with the mean velocity. Since,
the turbulent intensity increases with increasing Reynolds


127
a>
'5b
C
o
-|J
5
a
TJ
03
4->

'S
a>
Sh
Pu,
50
45
40
35
30
25
20
15
10
5
0
0.0 0.2 0.4 0.6 0.8 1.0
T
Flow Bolling Vapor
Bubble Departure
T=60 C
a 0^=20 C
v AT_t=16 C
AT =10 C
v V v
A A A A A
vvvvvvvvv^
JL
Mean Liquid Velocity u (m/s)
Figure 6-11 Predicted inclination angle variation with
mean liquid velocity and ATMt.
which is also acceptable. The relative deviations of
prediction for the departure and lift-off diameters are
comparable to those for the pool boiling data.
6.5 Conclusions
A general model has been developed for predicting vapor
bubble detachment diameters in pool and flow boiling. It has
been demonstrated that the model is in good agreement with


79
a
o
<
t
fcs
+->
*rH
W
t
Q
d>
CO
t
o
a¡
rH
o

Wall Superheat ATgat (C)
5 10 15 20 25
Saturation Temperature T,at (C)
Figure 5-13. Nucleation site density as functions of
saturation temperature and wall superheat.
displayed as a function of rc. All data seem to be collapsed,
but a correlation in the form of equation (5-1) would not be
useful because the slope is too steep. The pool boiling
nucleation site density data also show a similar behavior for
large n/A.
In an attempt to understand this behavior, consideration


102
while Roll and Myers used
Pduy=-9^CD%a2 --*a3 (l+-g
(6-28)
8 dt
where ub is the bubble velocity and was taken to be 2 .
Ruckenstein (1961) assumed CD was unity while Roll and Myers
(1964) evaluated CD from experimental data for freely rising
bubbles in liquid.
Klausner et al. (1993) modelled the growth force by
considering a hemispherical bubble expanding in an inviscid
liquid. Here, the same form of the expression is used except
that an empirical constant, Cs, is introduced which attempts
to primarily account for the presence of a wall,
FdU=_Pi7ta2(-|c^2+aS)
(6-29)
Based on 190 pool boiling data points considered herein, it
has been found that Cs=20/3 gives the best fit to the bubble
departure data based on a least squares regression analysis.
Although equation (6-29) provides excellent agreement with the
data, it is recognized that it is only an approximation of the
growth force based on a finite number of experimental data
sets, and there exists room for improved modelling.
In flow boiling, prior to departing their nucleation
sites, vapor bubbles are inclined toward the flow direction
with an inclination angle due to the quasi-steady drag


52
Figure 4-6. An idealized sketch of a vapor embryo in a
reentry cavity.
Pt) (4-7)
X2
For 0m<9O, the minimum curvature of the interface is
s ixiO
The minimum curvature determines a minimum vapor
temperature below which the vapor embryo cannot be sustained,


V
Vapor phase
w
Wall
X
X-direction,
i.e.,
horizontal direction
y
Y-direction,
i.e.,
vertical direction
xvi


Radius a(t) (mm)
149
Time t (ms)
Figure 8-6. Time history of bubble growth.


58
reversible if the heating surface temperature is maintained
above the sustaining point.
3) For the flow conditions investigated herein using R113,
both the initiation and sustaining superheats were not
noticeably influenced by bulk turbulence.


LIST OF TABLES
Table
6-1 Summary of forces appearing in momentum
equations 106
6-2 Mean deviation tabulated for present bubble model
as well as other correlations reported in
literature 109
6-3 Comparison of measured and predicted vapor bubble
departure diameter for elevated pressure data
using present model 117
6-4 Comparison of measured and predicted vapor bubble
departure diameter for reduced gravity data
using present model 118
6-5 Measured and predicted departure diameters
based on high speed cinematography data 123
8-1 A summary of parameters controlling vapor bubble
growth rate in flow boiling 155
viii


129
data lends credence to the hypothesis that the growth force is
dominant compared to the surface tension force at the point of
detachment. The bounds of validity of this hypothesis have
yet to be explored.
In theory, the present model is also applicable to
boiling with different orientations although calibration of
the model would be required for some situations. For
instance, it is assumed that u*/u,=0.05 for horizontal flow
boiling when equation (6-23) is used to evaluate the liquid
velocity profile near the wall. If equation (6-23) is even
applicable to vertical flow, it is expected that u*/u, may be
greater than 0.05 due to enhanced bulk turbulence.


41
(1966) belong to the thermal category. Mechanical models
consider a stable bubble nucleus resides inside a cavity.
When both the wall and liquid are subcooled, the interface is
required to be concave toward the cavity due to condensation
of vapor. For highly wetting liquids, this kind of concave
interface is possible only with reentrant shaped cavities
because contact angles are usually less than 90 degrees. The
radius of the bubble nucleus for highly wetting liquids is
substantially smaller than that of the cavity mouth.
Therefore, a higher wall superheat is required to initiate
boiling than is required to sustain it. According to
mechanical models, the radius of the interface inside the
cavity is determined by the liquid-solid contact angle, shape
of the cavity, and the degree of subcooling at the wall.
Therefore, the incipience wall superheat is dependent on the
surface conditions, liquid wettability, and the pressure-
temperature history prior to boiling. Incipience models
proposed by Mizukami et al. (1990) and Tong et al. (1990)
belong to the mechanical category.
The difficulties associated with predicting the boiling
incipience points are summarized as follows: 1) lack of
detailed information concerning cavity shapes and sizes on
commercial surfaces, 2) difficulties in determining the
dynamic and static contact angles on a microscale, 3) lack of
knowledge concerning the shape and size of the superheated
thermal layer, especially when two-phase flows are involved,


CHAPTER 4
INCIPIENCE AND HYSTERESIS
4.1 Introduction and Literature Survey
The development of modern electronics packaging requires
the ability to remove large amounts of heat from
microelectronic chips. The use of nucleate boiling heat
transfer of many dielectric liquids has been investigated for
this purpose due to their high heat transfer rates. Since
dielectric liquids usually have a high wettability on most
solid surfaces, the large overshoot of incipience superheat,
i.e. boiling hysteresis, has prevented their wide
applications. The experimental observation of boiling
incipience and hysteresis for highly wetting liquids is
clearly displayed in Figure 4-1 which was reconstructed from
the experimental data of Kim and Bergles (1988). Figure 4-1
is a typical heat flux vs wall superheat plot. The initiation
incipience point A is the point at which vapor bubbles just
begin appearing on the heating surface with increasing heat
flux. The sustaining incipience point B in Figure 4-1 is the
point just before vapor bubbles disappear from the heating
surface with decreasing heat flux. The overshoot of wall
superheat at the initiation incipience point is generally
38


15
Four BNC connectors, each of which were connected to a copper
strip using unshielded wire, were electrically insulated and
mounted on the chassis. Two square Garolite flanges (10.2 x
10.2 cm), which were used to mount the film thickness sensor
in the flow boiling facility, were bonded to the two ends of
the body with epoxy. The film thicknesses in the lower and
upper half of the duct were determined from the capacitance
between the respective pair of lower and upper parallel copper
strips. Two identical sensors were fabricated in this manner.
2.3.3 Instrumentation and Calibration
In order to obtain good performance from the film
thickness sensors, a high resolution capacitance meter must be
used to measure the capacitance across the parallel strips.
For this purpose, a Keithley 590 digital CV analyzer, which
has a resolution of 0.1 Ff, an accuracy and repeatability of
0.1% of full scale, and a frequency response of 45 kHz, as
reported by the manufacturer, was used to measure the
capacitance. The analog output of this instrument was
connected to a 12 bit analog to digital converter (A/D) which
will be described in section 2.4.
An accurate analytic relation between the capacitance and
liquid film thickness is extremely difficult to determine due
to the three-dimensional nature of the sensor. Therefore, the
sensor must be calibrated. The difficulty associated
calibrating the sensor for use in a variable temperature


6
of the flowmeter, five preheaters have been installed to
generate a saturated two-phase mixture. Each preheater
Figure 2-1. Schematic diagram of flow boiling facility.
consists of a 25 mm ID, 1.2 m long hard copper round pipe
around which 18 gauge nichrome wire has been circumferentially
wrapped. The nichrome wire is electrically insulated from the
copper pipe with ceramic beads. The preheaters are thermally
insulated using a 25 mm thick fiberglass insulation layer.


THE EBULLITION PROCESS
IN FORCED CONVECTION BOILING
By
LING-ZHONG ZENG
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1993
UJgVERSITY OF FLORIDA LIBRARIES

TO MY WIFE TANG YONG

ACKNOWLEDGEMENTS
My greatest appreciation goes to Professor James
Klausner, chairman of the supervisory committee, for all the
support and encouragement during the course of this research.
Dr. Klausner, a mentor and role model, has spent a great deal
of time and effort in helping me with the fabrication of the
experimental facility, analysis of the experimental data, as
well as editing this dissertation. I also want to extend my
appreciation to Professor Renwei Mei, member of the
supervisory committee. Dr. Mei has always been accessible and
has provided many useful suggestions throughout the course of
this research. I would also like to thank professors C.K.
Hsieh, D.Y. Goswami, and S. Anghaie for serving on the
supervisory committee. Their useful suggestions have improved
this dissertation.
I also want to thank Dave Bernhard and Boby Warren,
fellow graduate students and friends. Dave and Bob have
provided substantial support in calibrating instrumentation
and planning experiments.
I can not express enough love and appreciation to my
wife, Tang Yong. Without her support, understanding, and
sacrifice, I would not have finished my Ph.D. program.
Finally, I want to thank my parents, brothers, and sisters for
iii

their support throughout the entire course of my education.
It is my parents who inspired me to pursue the education I
have obtained.
iv

TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
LIST OF TABLES viii
LIST OF FIGURES ix
NOMENCLATURE xiii
ABSTRACT XV
CHAPTERS
1 INTRODUCTION 1
2 EXPERIMENTAL FACILITIES 5
2.1 Flow Boiling Test Loop 5
2.2 Construction of Transparent Test Section ..10
2.3 Development of Capacitance Based
Film Thickness Sensors 11
2.3.1 Introduction 11
2.3.2 Design and Fabrication of
Film Thickness Sensor 13
2.3.3 Instrumentation and Calibration .... 15
2.4 Data Acquisition System 24
3 HEAT TRANSFER AND PRESSURE DROP
IN SATURATED FLOW BOILING 28
3.1 Introduction 28
3.2 Experimental Results and Discussions 30
3.3 Conclusions 37
4 INCIPIENCE AND HYSTERESIS 38
4.1 Introduction and Literature Survey 38
4.2 Experimental Results 42
4.3 Theoretical Analysis for Boiling
Incipience 44
4.3.1 Boiling Initiation 44
4.3.2 Sustaining Incipience Superheat .... 54
4.3.3 Hysteresis of Boiling Incipience ...56
4.4 Conclusions 57
v

5 NUCLEATION SITE DENSITY 59
5.1 Literature Survey 59
5.2 Optical Facility and Measuring
Technique 64
5.3 Experimental Results 66
5.4 Discussion of Results 78
5.5 Conclusions 83
6 A UNIFIED MODEL FOR VAPOR BUBBLE DETACHMENT ....84
6.1 Introduction 84
6.2 Literature Survey 86
6.2.1 Pool Boiling Departure Diameter
Correlations 86
6.2.2 Flow Boiling Detachment Diameter
Correlations 92
6.3 Development of Departure and Lift-off
Model 94
6.3.1 Formulation 94
6.3.2 Expressions for Bubble Departure
and Lift-off Diameter 105
6.4 Comparison with Experimental Data 107
6.4.1 Pool Boiling Data 108
6.4.2 Flow Boiling Data 119
6.5 Conclusions 127
7 PROBABILITY DENSITY FUNCTIONS OF VAPOR
BUBBLE DETACHMENT DIAMETER 130
7.1 Introduction 130
7.2 Formulation 132
7.3 Comparison with Experimental Data 134
7.4 Conclusions 138
8 VAPOR BUBBLE GROWTH RATE 140
8.1 Introduction 140
8.2 Facility and Methodology 141
8.3 Results and Discussions 144
8.4 Conclusions 156
9 CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH 157
9.1 Accomplishments and Findings 157
9.2 Suggestions for Future Research 159
APPENDICES
A HEAT TRANSFER COEFFICIENT, PRESSURE DROP,
AND LIQUID FILM THICKNESS IN STRATIFIED
TWO-PHASE FLOW 161
vi

B NUCLEATION SITE DENSITY IN FORCED
CONVECTION BOILING 164
REFERENCES 167
BIOGRAPHICAL SKETCH 177
vii

LIST OF TABLES
Table
6-1 Summary of forces appearing in momentum
equations 106
6-2 Mean deviation tabulated for present bubble model
as well as other correlations reported in
literature 109
6-3 Comparison of measured and predicted vapor bubble
departure diameter for elevated pressure data
using present model 117
6-4 Comparison of measured and predicted vapor bubble
departure diameter for reduced gravity data
using present model 118
6-5 Measured and predicted departure diameters
based on high speed cinematography data 123
8-1 A summary of parameters controlling vapor bubble
growth rate in flow boiling 155
viii

LIST OF FIGURES
Figure
2-1 Schematic diagram of flow boiling facility 6
2-2 Calibration curve for flowmeter 8
2-3 Calibration curve of heat loss for preheaters 9
2-4 Isometric view of transparent test section 11
2-5 Cut-away view of liquid film thickness sensor 14
2-6 Prediction of relative film thickness vs capacitance
using model of Chun and Sung (1986) 18
2-7 Calibration curve for film thickness sensor 19
2-8 Temperature calibration for film thickness sensor
filled with pure liquid 21
2-9 Temperature calibration for film thickness sensor
filled with pure vapor 22
2-10 Close-up view of stratified two-phase flow using
CCD camera (flow direction is from left to right) ...23
2-11 Comparison of liquid film thickness measured with
CCD camera and capacitance sensor 24
2-12 A schematic diagram of data acquisition system 26
3-1 Microconvection heat transfer for saturated forced
convection nucleate boiling 32
3-2 Macroconvection heat transfer coefficient in
saturated forced convection boiling 33
3-3 Pressure drop in horizontal two-phase flow 34
3-4 Zuber and Findlay's (1965) correlation for void
fraction in horizontal stratified two-phase flow ....36
4-1 Nucleate pool boiling hysteresis constructed from
the data of Kim and Burgles (1988) 39
ix

4-2 A typical saturated flow boiling plot of qw vs
AT,^ for G=180 kg/m2-s, X=0.156, and i=4.8 mm 43
4-3 Measured saturated flow boiling incipience
wall superheat 45
4-4 An idealized sketch of a vapor embryo in a
conical cavity 47
4-5 Variation of vapor temperature with vapor embryo
volume during expansion inside a conical cavity 49
4-6 An idealized sketch of a vapor embryo in a
reentry cavity 52
4-7 Variation of minimum vapor temperature and
initiation superheat with cavity reservoir
mouth radius 53
5-1 Pool boiling nucleation site density data from
Griffith and Wallis (1960) 61
5-2 A diagram of optical facility for measurement
of nucleation site density 65
5-3 A typical photograph of nucleation sites on
a boiling surface 67
5-4 Nucleation site density as a function of wall
superheat for constant heat flux and saturation
temperature 68
5-5 Pool boiling nucleation site density as functions
of wall superheat and heat flux 69
5-6 Nucleation site density as a function of vapor
Velocity for constant heat flux and liquid film
thickness 71
5-7 Nucleation site density as a function of mass
flux 72
5-8 Nucleation site density as a function of liquid
velocity 73
5-9 Nucleation site density and liquid film thickness
as functions of vapor velocity 74
5-10 Nucleation site density as a function of liquid
film thickness 75
x

5-11 Nucleation site density as a function of heat
flUX 77
5-12 Nucleation site density as a function of wall
superheat 78
5-13 Nucleation site density as functions of saturation
temperature and wall superheat 79
5-14 Nucleation site density as a function of critical
radius for constant heat flux and vapor velocity ....80
5-15 Nucleation site density as a function of critical
radius for all flow boiling data 81
6-1 A typical picture of vapor bubble departure and
lift-off in flow boiling 85
6-2 A schematic sketch of vapor bubble detachment
process in flow boiling 95
6-3 Comparison of predicted and measured vapor bubble
departure diameter for subatmospheric pressure
data using present model 112
6-4 Comparison of predicted and measured vapor bubble
departure diameter for subatmospheric pressure
data using Cole and Shulman 2 correlation 113
6-5 Comparison of predicted and measured vapor bubble
departure diameter for atmospheric pressure data
using present model 114
6-6 Comparison of predicted and measured vapor bubble
departure diameter for atmospheric pressure data
using Cole and Shulman 2 correlation 115
6-7 Departure diameter variation with mean liquid
velocity at constant ATMt 121
6-8 Comparison between predicted and measured
departure diameters 122
6-9 Departure diameter variation with mean liquid
velocity and ATt 125
6-10 Predicted inclination angle variation with
predicted departure diameter 126
6-11 Predicted inclination angle variation with
mean liquid velocity and ATMt 127
xi

6-12 Comparison between predicted and measured
lift-off diameter 128
7-1 Statistical distribution of bubble lift-off
diameter in flow boiling 135
7-2 Statistical distribution of bubble departure
diameter in flow boiling at constant ATMt 136
7-3 Statistical distribution of bubble departure
diameter in flow boiling at constant uf 137
8-1 A schematic diagram of the high speed facility
for filming vapor bubble growth rate 142
8-2 Time history of bubble growth 145
8-3 Time history of bubble growth 146
8-4 Time history of bubble growth 147
8-5 Time history of bubble growth 148
8-6 Time history of bubble growth 149
8-7 Time history of bubble growth 150
8-8 Time history of bubble growth 151
8-9 Time history of bubble growth 152
8-10 Time history of bubble growth 153
8-11 Time history of bubble growth 154
xii

NOMENCLATURE
a, a(t)
Radius of a growing vapor bubble
C
Capacitance
^D
Drag coefficient for a freely rising vapor bubble
in an infinite liquid
CP
Liquid specific heat
Cs
Empirical constant, equals 20/3
d
Vapor bubble diameter
dw
Diameter of contact area
D
Inside dimension of the test section or diameter
F
Force
g
Earth gravity
G
Mass flux
h
Heat transfer coefficient
hfg
Vaporization latent heat
Ja
Jakob number
k
Thermal conductivity
K
Power law bubble growth constant as in a(t)=Kt
m
Mass
M
Molecular weight
n
Power law bubble growth index as in a(t)=Ktn
n/A
Nucleation site density
P
Absolute pressure or Polarization factor
xiii

p(x) Probability density function
q Heat flux
r Radius of the liquid/vapor interface
rt Mouth radius of the cavity
r2 Mouth radius of the cavity reservoir
R Engineering gas constant
Re Reynolds number
t Time
T Temperature
u Mean velocity
U(y) Velocity profile
V Volume
X Vapor quality
Greek Symbols
a Void fraction
S Liquid film thickness
AP Pressure drop
AT Superheat
ij Liquid thermal diffusivity
0 Contact angle
0¡ Bubble inclination angle
H Dynamic viscosity
p Density
a Surface tension coefficient or standard deviation
Half cone angle of the cavity
e Relative permittivity
xiv

Subscripts
b
Bulk or buoyancy
cp
Contact pressure
d
Bubble departure
da
Dynamic advanced
dF
Departure diameter predicted from Fritzs model
dr
Dynamic receded
du
Force due to bubble growth
g
Non-condensible gas
G
Garolite material
h
Hydraulic
inc, i
Incipience, initiation
inc, s
Incipience, sustaining
L
Bubble lift-off or lift force created by bubble
wake
l
Liquid phase
m
Mixture of vapor and liquid
mac
Macroconvection
max
Maximum
mic
Microconvection
min
Minimum
s
Surface tension
sa
Static advanced
sat
Saturation
sL
Shear lift
sr
Static receded
20
Two-phase
xv

V
Vapor phase
w
Wall
X
X-direction,
i.e.,
horizontal direction
y
Y-direction,
i.e.,
vertical direction
xvi

Abstract of Dissertation Presented to the Graduate School of
the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
THE EBULLITION PROCESS
IN FORCED CONVECTION BOILING
By
Ling-zhong Zeng
August, 1993
Chairman: Professor James F. Klausner
Major Department: Mechanical Engineering
A forced convection boiling facility with Refrigerant
R113 was designed and fabricated in order to experimentally
study the ebullition process in horizontal flow boiling.
Capacitance sensors were developed for measuring the liquid
film thickness for stratified and annular two-phase flow.
Measurements of heat transfer coefficient, pressure drop, and
liquid film thickness in stratified two-phase flow with and
without boiling have been obtained. The experimental data
have conclusively demonstrated that microconvection, which is
the heat transfer due to the ebullition process, is
significant in almost all phases of saturated flow boiling.
The initiation and sustaining incipience superheats of
saturated flow boiling with R113 were found to be insensitive
to the fluid convection but they strongly depend on the system
pressure as well as the cooling history of the heating surface
xvii

prior to boiling. Nucleation site density of saturated
forced convection boiling was measured using a CCD camera.
The mean vapor velocity, heat flux, and system pressure appear
to exert a dominant parametric influence on the nucleation
site density. The critical cavity radius is an important
parameter in characterizing the nucleation process but by
itself it is not sufficient to correlate nucleation site
density data for saturated flow boiling. Based on
experimental observations and theoretical reasoning, an
analytical model has been developed for the prediction of
vapor bubble detachment diameters in saturated pool and flow
boiling. The vapor bubble growth rate is a necessary input to
the model. It is demonstrated that over the wide range of
conditions considered, the accuracy of the detachment
diameters predicted using the present model is significantly
improved over existing correlations. The model was also
extended to predict the probability density functions (pdf's)
of detachment diameters by specifying the pdf's of wall
superheat and liquid velocity. The vapor bubble growth rate
during saturated flow boiling was measured using a high speed
cinematography. Based on the experimental data obtained
herein, the vapor.bubble radius can be expressed as a function
of time using a power law, where the exponent decreases with
increasing system pressure. The objective of this research is
to understand the fundamentals of the ebullition process in
flow boiling.
xviii

CHAPTER 1
INTRODUCTION
Forced convection boiling, also referred to as flow
boiling, has been used in a variety of engineering
applications for its high heat and mass transfer rates. In
nuclear power applications, flow boiling with water is used to
extract heat from reactors. Also flow boiling can be found in
fossil fuel fired steam generators, the chemical process
industry, refrigeration and air-conditioning industry, and
cooling of electrical distribution facilities. Other
potentially important applications include compact flow
boiling heat exchangers for use in spacecraft and cooling of
microelectronic components.
Due to its engineering importance, boiling heat transfer
has been the focus of extensive research for the past four
decades. However, to date, boiling remains one of the most
controversial subjects in the field of heat transfer. Many
questions raised four decades ago concerning boiling phenomena
remain unanswered (Lienhard, 1988). Current engineering
designs involving boiling phenomena rely heavily on empirical
correlations developed from experimental measurements.
Rohsenow (1952) first suggested that the rate of heat transfer
associated with forced convection boiling is due to two
1

2
additive mechanisms, that due to bulk turbulence and that due
to ebullition. Based on Rohsenow's conjecture, Chen (1966)
proposed a saturated flow boiling heat transfer correlation
which is simply the sum of the respective macroconvection and
microconvection heat transfer coefficients. The terms macro-
and microconvection respectively denote the contribution due
to heat transfer from bulk turbulent convection and that due
to the ebullition process. The macroconvection heat transfer
coefficient was calculated using a single-phase flow
correlation based on the liquid fraction flowing modified by
an enhancement factor, while the microconvection heat transfer
coefficient was calculated using a pool boiling correlation
modified by a suppression factor.
Chen's (1966) correlation or modified forms of it are
widely used throughout industry despite the fact that they
fail to accurately correlate a wide range of flow boiling heat
transfer data (Gungor and Winterton, 1986). One
characteristic of Chen's correlation is that it predicts the
microconvection contribution to flow boiling heat transfer is
always small compared to macroconvection. In contrast, Mesler
(1977) argued that the microconvection component is dominant.
Staub and Zuber (1966), Frost and Kippenhan (1967), Klausner
(1989), and Kenning and Cooper (1989) have presented flow
boiling heat transfer data which display a strong dependence
on the ebullition process. In addition, experimental data
provided by Koumoutsos et al. (1968) and Cooper et al. (1983)

3
demonstrate that the ebullition process in flow boiling cannot
be adequately modelled with pool boiling correlations. In
order to significantly improve flow boiling heat transfer
predictions over Chen's approach, it is necessary to
understand the mechanisms governing both macro- and
microconvection as well as their relative contribution to the
total heat transfer.
In this work, major efforts have focused on understanding
the physics governing vapor bubble incipience, nucleation site
density, growth and detachment in forced convection boiling.
In order to achieve this goal, a flow boiling facility with
refrigerant R113 was designed and fabricated. The boiling
test section is optically transparent thus allowing for the
visualization of the ebullition process. A CCD camera has
been used to measure nucleation site densities and high speed
cinematography was used to measure vapor bubble growth rates.
Two capacitance-based film thickness sensors were designed and
fabricated to measure the liquid film thickness on the upper
and lower surfaces of the horizontal square test section.
Since the flow boiling facility usually experiences large
temperature variations during operation, the temperature
dependence of the capacitance sensors must be accounted for.
A new and simple method has been developed to account for
temperature when using the film thickness sensor calibration
curve.
Using the current flow boiling facility, experimental

4
evidence was obtained to demonstrate that the heat transfer
contribution due to the ebullition process is significant in
almost all phase of boiling. Experimental data on the
incipience wall superheat, nucleation site density, and vapor
bubble growth rate for saturated flow boiling have been
gathered over a wide range of flow and thermal conditions.
The parametric influence of two-phase flow conditions on the
ebullition process have been analytically investigated.
An analytical model has been developed for the prediction
of vapor bubble departure and lift-off diameters for both pool
and flow boiling. The model was compared against all
experimental data available in the literature, and excellent
agreement has been achieved. Based on this bubble detachment
model, an analytical approach was proposed for predicting
vapor bubble detachment diameter probability density functions
(pdf's) for a specified wall superheat pdf and liquid velocity
pdf.

CHAPTER 2
EXPERIMENTAL FACILITIES
2.1 Flow Boiling Test Loop
A flow boiling facility, shown schematically in Figure 2-
1, was designed and fabricated. Refrigerant R113 was selected
as the boiling liquid in this facility primarily due to its
low latent heat of evaporation and boiling point. A variable
speed model 221 Micropump was used to pump R113 through the
facility. A freon dryer/filter was installed on the discharge
of the pump to filter out alien particles in the liquid and to
prevent the formation of hydrofluoric acid in the refrigerant.
The volumetric flow rate of liquid was monitored with an Erdco
Model 2521 vane type flowmeter equipped with a 4-20 ma analog
output. The flowmeter output was attached to a 500 ohm power
resistor. The voltage across the resistor was recorded with
a digital data acquisition system which will be discussed
later. The flowmeter was calibrated using a volume-time
method. A calibration curve for the volumetric flow rate vs
voltage is displayed in Figure 2-2. The standard deviation of
the experimental data from a third order polynomial least-
squares fit is 0.5%, which is equivalent to the repeatability
of the flow meter claimed by the manufacturer. At the outlet
5

6
of the flowmeter, five preheaters have been installed to
generate a saturated two-phase mixture. Each preheater
Figure 2-1. Schematic diagram of flow boiling facility.
consists of a 25 mm ID, 1.2 m long hard copper round pipe
around which 18 gauge nichrome wire has been circumferentially
wrapped. The nichrome wire is electrically insulated from the
copper pipe with ceramic beads. The preheaters are thermally
insulated using a 25 mm thick fiberglass insulation layer.

7
Each of the five preheaters is powered by a 240 volt line
through an adjustable AC autotransformer. The heat loss of
the preheaters has been calibrated as a function of
temperature difference between the outer surface of the
insulation and the ambient. A typical calibration curve is
shown in Figure 2-3. In order to allow the two-phase mixture
generated by the preheaters to be fully developed and smoothly
flow into a square transparent test section, which will be
described shortly, a 1.5 m long and 25 x 25 mm inner dimension
square copper duct has been mounted downstream of the
preheaters. The duct is also thermally insulated using
fiberglass, thus provides an adiabatic developing length for
the two-phase flow. A capacitance-based liquid film thickness
meter, which will be described in detail in section 2.3, was
installed on the either side of the test section to measure
the inlet and outlet liquid film thickness of the two-phase
mixture. Two Viatran model 2415 static pressure transducers
have been installed at the inlet and outlet of the test
section to measure the system pressure with an accuracy of
0.5% of full scale (30 psig) Two type E thermocouple probes
were also located at the same position to measure the bulk
temperature of R113. When the two-phase mixture becomes
saturated, the measured bulk temperature using thermocouples
matches that calculated from the saturation line based on the
measured system pressure to within 0.5C, which is also the
accuracy of the absolute temperature measurement from the

8
thermocouples. A precision Viatran differential pressure
transducer was installed to measure the pressure drop across
m
\
o
->->
cti
05
£
o
Em
O
rH
Eh
-iJ
Q>
6
p
o
>
Flow Meter Output (Volts)
Figure 2-2. Calibration curve for flowmeter.
the test section with an accuracy of 0.25% of full scale (120
mmH20). A throttle valve is located downstream of the test
section, which allows the test section pressure to be adjusted
from atmospheric pressure to 30 psig, which is the maximum

9
O 10 20 30 40 50
tb-t. (c)
Figure 2-3. Calibration curve of heat loss for preheaters.
safe operating pressure of the square pyrex section.
Following the test section, the R113 two-phase mixture
condenses in a shell and tube water cooled heat exchanger to
return to the liquid storage tank.
2.2 Construction of Transparent Test Section
The major difficulties associated with fabricating a
transparent flow boiling refrigerant based test section and

10
connecting it with rigid copper pipes are the facts that the
pyrex glass is brittle and small stress concentrations
substantially reduce its safe operating pressure. After
testing many different designs, a satisfactory test section
was eventually fabricated. The fabrication procedures, which
have been detailed by Bernhard (1993), will not be repeated
here. A brief description of the test section is given. The
main body of the flow boiling test section is comprised of a

11
25 x 25 mm ID square pyrex glass tube that is 4 mm thick and
0.457 m long as depicted in Figure 2-4. A 0.13 mm thick and
22 mm wide nichrome strip, used as a heating and boiling
surface, has been adhered to the lower inner surface of the
square tube with epoxy. Six equally spaced 36 gauge type E
thermocouples were located underneath the nichrome strip using
high thermal conductivity epoxy. The mean wall temperature of
the nichrome strip was obtained by averaging the readings from
these six thermocouples. The test section was connected to
the facility with a brass block on either side. Each end of
the nichrome strip was bolted to the block to maintain good
electrical contact. Epoxy was used to seal gaps between the
glass tube and brass blocks. The facility was pressurized
with air to 30 psig and leak-checked prior to introducing
R113. Due to safety considerations, the facility has not been
operated at pressures above 30 psig.
2.3 Development of Capacitance Based Film Thickness Sensors
2.3.1 Introduction
It has been observed that in a horizontal saturated flow
boiling system, vapor-liquid flow is usually in a stratified
or annular flow regime due to the influence of gravity.
Research involving this flow regime requires knowledge of the
liquid film thickness distribution along the wall of a duct.
Many of the techniques used to measure liquid film thickness
and volume fraction were summarized by Hewitt (1978) and Jones

12
(1983). Of these, the only non-intrusive measuring
techniques, applicable to dielectric fluids, which capture the
liquid film thickness and volume fraction with a very rapid
response time are capacitance and radiation absorption
techniques. The implementation of the radiation absorption
technique requires expensive, bulky equipment with which
special safety precautions must be adhered to. In contrast,
the capacitance sensors used to measure liquid film thickness
and volume fraction are compact, safe, and inexpensive and
thus were selected for this research. Ozgu and Chen (1973)
used a capacitance sensor to measure liquid film thickness for
axisymmetric two-phase flow while Abouelwafa and Kendall
(1979), Sami et al. (1980), Irons and Chang (1983), Chun and
Sung (1986), and Gaerates and Borst (1988) used a capacitance
sensor to measure volume fraction. A summary of these
investigations can be found in Delil (1986) All of the
capacitance probes and measuring techniques reported by these
investigators were used only for adiabatic flow; there was
very little mention made of the temperature dependence of
capacitance sensors. Furthermore, the ring-type capacitance
sensor described by Ozgu and Chen (1973) may only be used to
measure symmetric two-phase duct flow, such as vertical up-
flow or down-flow. The sensor is not applicable for use with
horizontal two-phase flow, which is usually asymmetric due to
the gravitational stratification of the phases.
Since a forced convection boiling system undergoes large

13
variations in temperature, the calibration of the capacitance
sensor must account for its temperature dependence in order to
obtain accurate liquid film thickness measurements. Both the
permittivity of the liquid and the material of construction
are temperature dependent. Therefore, either the sensor must
be calibrated over the range of temperatures for which it will
operate or a suitable temperature correction scheme must be
employed when the sensor is calibrated at a fixed temperature.
The latter approach has been successfully used in this work.
2.3.2 Design and Fabrication of Film Thickness Sensor
The liquid film thickness sensor was designed to match
the inner dimension of the test section for a smooth
transition of the flow. Therefore, four Garolite sheets (152
x 38 x 6 mm) were machined and bonded together with Conap
epoxy to form a body which has a 25 x 25 mm inner square cross
section as shown in Figure 2-5. Garolite material was chosen
for the fabrication of the film thickness sensor body because
it has good dielectric properties and is corrosion resistant
to refrigerants. Two parallel grooves, 7.9 mm wide and 3.2 mm
deep were machined on both the outer upper and lower halves of
the sensor body for placement of the capacitance strips. The
distance separating two adjacent grooves is 7.9 mm. This
distance was chosen because Ozgu and Chen (1973) reported the
optimum thickness and distance between the parallel ring
sensors is equal to the film thickness at which the highest

14
Figure 2-5. Cut-away view of liquid film thickness sensor.
resolution is expected. It shall be demonstrated that the
best resolution is obtained with liquid film thickness of 5 to
6 mm and poor resolution is observed near the centerline.
Copper strips with a thickness of 0.1 mm were bonded into the
grooves with epoxy. An aluminum chassis was fabricated around
the sensor body. The purpose of the chassis is twofold: it
shields extraneous electromagnetic radiation and also
compresses the sensor body so that it is pressure resistant.

15
Four BNC connectors, each of which were connected to a copper
strip using unshielded wire, were electrically insulated and
mounted on the chassis. Two square Garolite flanges (10.2 x
10.2 cm), which were used to mount the film thickness sensor
in the flow boiling facility, were bonded to the two ends of
the body with epoxy. The film thicknesses in the lower and
upper half of the duct were determined from the capacitance
between the respective pair of lower and upper parallel copper
strips. Two identical sensors were fabricated in this manner.
2.3.3 Instrumentation and Calibration
In order to obtain good performance from the film
thickness sensors, a high resolution capacitance meter must be
used to measure the capacitance across the parallel strips.
For this purpose, a Keithley 590 digital CV analyzer, which
has a resolution of 0.1 Ff, an accuracy and repeatability of
0.1% of full scale, and a frequency response of 45 kHz, as
reported by the manufacturer, was used to measure the
capacitance. The analog output of this instrument was
connected to a 12 bit analog to digital converter (A/D) which
will be described in section 2.4.
An accurate analytic relation between the capacitance and
liquid film thickness is extremely difficult to determine due
to the three-dimensional nature of the sensor. Therefore, the
sensor must be calibrated. The difficulty associated
calibrating the sensor for use in a variable temperature

16
environment is that the permittivity of both the solid and
liquid is temperature dependent. A complete calibration is
obtained only when the liquid film thickness and temperature
are varied over the full range. Such a calibration is tedious
and impractical. Therefore, an innovative scheme is proposed
which allows the sensor to be used based on its calibration at
a fixed temperature
A crude model for predicting the capacitance as a
function of film thickness or volume fraction for a known
material permittivity was introduced by Chun and Sung (1986)
by considering the sensor as a network of parallel and series
equivalent plate-type capacitors. This type of modeling was
attempted for the sensor described above. The relative
permittivity of R113 vapor was taken to be unity. The
relative permittivity of liquid R113 as a function of
temperature was determined from the Clausius-Mosotti equation
as reported by Downing (1988):
_ Af+Pp,
*" Ai-Pp,
(2-1)
where et is the liquid relative permittivity, M is the
molecular weight, P is the polarization, and pt is the liquid
density. The temperature dependence of permittivity comes
from the fact that the liquid density varies with temperature.
Published values of permittivity could not be found for
Garolite material. However, Garolite is a composite material

17
manufactured from E-glass and a phenolic based epoxy resin,
and based on the data of Leeds (1972), the relative
permittivity of Garolite was approximated over a range of
temperature of 25 to 200 C using
eG=4.213+0.0023T (2-2)
where T is temperature in degrees Celsius. Using the crude
model of Chun and Sung (1986) the relative film thickness, 5',
for horizontal stratified flow is shown in Figure 2-6 as a
function of the relative capacitance C* for both the upper and
lower section of the sensor at 25 and 80 C. Here C* is
defined by
C*=
ocy
q-cy
(2-3)
where C is the capacitance across the sensor for two-phase
flow, Ct is the sensor capacitance for purely liquid flow, and
Cv is that for purely vapor flow; all these capacitances are
temperature dependent. For the lower section, 6'=6/h, and for
the upper section, 5'=i/h-l, where S is the liquid film
thickness and h=12.7 mm is the distance from the sensor inside
wall to the centerline. The results displayed in Fig. 2.6
reveal that the functional relationship between 5' and C* is
essentially independent of temperature over the 25-80 C range
investigated.
Guided by the fact that the relationship between C* and
5' is not temperature dependent, it was decided to calibrate

18
m
w
v
l
f¡
o
£
a
S
TJ
0
cr
3
J:
d
r-H
K
Relative Capacitance C"
Figure 2-6. Prediction of relative film thickness versus
capacitance using model of Chun and Sung
(1986).
the sensor for the stratified flow regime at room temperature
on a bench top under carefully controlled conditions. The
results of the calibration for sensor #1 were tabulated in
terms of S' and C* and are shown in Figure 2-7. It is noted
that for the lower section of the sensor, 6* was normalized by
0.75h rather than h since the full scale of the measurement
for this section is 0.75h. There was no modification for the

19
cn
w
Q)

o
3
E-
B
£
I

os
Meter #1, calibrated at 25 C
Relative Capacitance C*
Figure 2-7. Calibration curve for film thickness sensor.
upper section. It is seen from Figure 2-7 that the resolution
is good when the film thickness is well below the centerline
for the lower section and well above the centerline for the
upper section. There exists a small region near the
centerline where the film thickness can not be resolved.
However, for the current study with saturated forced
convection boiling, this does not pose a severe problem
because the liquid film is always well below the centerline

20
when the two-phase mixture is at saturated conditions.
In order to determine the liquid film thickness from the
calibration curves shown in Figure 2-7, C, and Cv must be
determined as a function of temperature when the two-phase
mixture is at a temperature other than the calibration
temperature. The functions were determined after the sensors
had been installed in the facility. To do so, pure liquid
R113 was circulated through the facility and was heated. When
a steady temperature was reached, the capacitances across the
lower and upper pairs of copper strips were recorded. This
procedure was repeated for a series of increments of
temperature while the throttle valve was adjusted to elevate
the system pressure to avoid vapor generation. The results
obtained have been displayed in Figure 2-8. Similar
procedures were followed to obtain the capacitance for pure
vapor as a function of temperature as shown in Figure 2-9.
Because pure vapor flow could only be achieved by
depressurizing the boiling facility after two-phase flow had
been established, it was difficult to obtain the measurement
over a wide range of temperature. In this work only four
different temperatures were obtained. By incorporating the
calibration curves shown in Figures 2-7, 2-8, and 2-9, the
liquid film thickness may be determined as a function of
capacitance and temperature of any two-phase mixture.
In order to evaluate the performance of the liquid film
thickness sensor developed here, a CCD camera was set up for

Liquid Capacitance (pf)
21
Temperature (DC)
Figure 2-8. Temperature calibration for film thickness
sensor filled with full liquid.
optically measuring the liquid film thickness for stratified
flow. The camera was focused normal to the transparent test
section to avoid optical distortion. A typical picture of
two-phase stratified flow obtained with the CCD camera used
for comparison is displayed in Figure 2-10. Liquid film
thickness is determined from the scale placed on the test

Vapor Capacitance (pf)
22
Temperature (C)
Figure 2-9. Temperature calibration for film thickness
sensor filled with full vapor.
section. The length measurement from the pictures is accurate
to 0.1 mm. Since the liquid/vapor interface was wavy in
almost all cases considered, the instantaneous photograph of
the flow structure had to be synchronized with an
instantaneous capacitance and temperature measurement in order
to obtain a reliable comparison. The degree of waviness of

23
Figure 2-10. Close-up view of stratified two-phase flow
using CCD camera (flow direction is from left
to right).
the liquid/vapor interface depends on flow conditions. The
two-phase mixture bulk temperature ranged from 50-70 C. The
use of the digital data acguisition system, which will be
described shortly, greatly facilitated the synchronization
process. The liguid film thickness data measured using the
CCD camera have been compared against that measured by sensor

24
B
B
CO
CO
Q>
A
o
a
E-<
J
* H
fin
-O
W
S3
a>
3
Measured Film Thickness 6 (mm)
CCD Camera
Figure 2-11. Comparison of liquid film thickness measured
with CCD camera and capacitance sensor.
#1 and the results are illustrated in Figure 2-11. It can be
seen that over the entire range of film thickness and
temperature considered, the comparison is good. The average
error based on the data shown in Figure 2-11 is within 2% of
the full scale.
2.4 Data Acquisition System
A digital data acquisition system has been assembled for

25
this investigation, which is used for recording measurements
of pressure, temperature, flow rate, and capacitance for this
investigation. A schematic diagram of the data acquisition
system is displayed in Figure 2-12. The data acquisition
system is comprised of two Acces 16-channel multiplexer cards
(AIM-16) interfaced with one Acces 12-bit 8-channel analog-to-
digital converter (AD12-8), mounted in an I/O slot of a
Northgate PC/AT computer. The AD12-8 has a maximum conversion
speed of 40 kHz and input voltage range of 10 Volts. Each
AIM-16 card is interfaced with one channel of the AD12-8
board. Thus there are 32 different channels available when
using this system. Channel 0 of the AIM-16 has been used to
determine the cold junction temperature using a resistance
temperature device (RTD). The temperature scale factor for
the output of the RTD is 24.4 mV/C. Each channel of the AIM-
16 has a preamplifier with gains ranging from 0.5 to 1000 and
may be programmed through the computer. The AD12-8 board and
AIM-16 cards were calibrated according to manufacturer's
specifications. Each analog signal from the respective
instrument is connected to one of the 32 channels of the AIM-
16 cards. Appropriate gains were set up for different
channels to achieve maximum resolution. Since two-phase flows
are inherently unstable, all measurements were time-averaged
to obtain repeatable values. Using this system, an average of
500 sampling points were collected over a time period of 30
seconds in order to obtain repeatable measurements. Quick

26
ERDCD SERIES
E500 FLOW
METER
^RESISTORS
V_ KEITHLEY
590 CV Analyzer
12-MHZ 286-AT
t,
ACCESS AD12-8
A/D INPUT CARD
THERMOCOUPLES TO TEST
FACILITY, (SURFACE PROBES,
INFLOW PROBES, AND HEAT LOSS
PROBES)
VALIDYNE
CARRIER rn
DEMODULATOR <|Scp
,VALIDYNE MAGNETIC RELUCTANCE
DIFF. PRESS, TRANSDUCER
Figure 2-12. A schematic diagram of data acquisition system.
BASIC software routines have been developed for all data
acquisition operations.
A summary of the design operating conditions of the
facility are as follows: mass flux, G=80-350 kg/m2-s; quality,
X=0-0.35; system pressure, P=1.0-2.3 bars; and test section
heat flux, qw=0-40 kW/m2. The operating constraints of the

27
facility are primarily due to the maximum flow rate of the
Micropump, the strength of the pyrex glass, and the
temperature limitation of the E-poxy used in the test section.
All the experiments performed in this investigation have been
confined to the system design conditions.

CHAPTER 3
HEAT TRANSFER AND PRESSURE DROP
IN SATURATED FLOW BOILING
3.1 Introduction
In this section of the investigation, measurements of
heat transfer coefficient with and without boiling are
described which have been obtained for a saturated two-phase
mixture flowing through the test section. The purpose of
these measurements is to elucidate the importance of the
microconvection contribution to the total heat transfer in
flow boiling. The pressure drop and liquid film thickness for
stratified two-phase flow without boiling have also been
measured over a wide range of mass flux, G, and quality, X.
The parametric trends of the heat transfer coefficient and
pressure drop for horizontal two-phase flow are displayed and
compared against those observed for single phase flows.
The total two-phase heat transfer coefficient with and
without boiling is defined by
(3-i>
1w 1b
where Tw is the mean wall temperature, Tb is the two-phase bulk
temperature, and qw is the wall heat flux. Since this work
28

29
only deals with saturated flow boiling, Tb is equivalent to
the saturation temperature, TMt. In order to sort out the
contribution of heat transfer between macro- and
microconvection during flow boiling, the following
experimental procedure was closely adhered to. The Micropump
and preheaters were adjusted to obtain a fixed G, X, and TMt
at the inlet of the test section. The nichrome strip was
heated up gradually until boiling was initiated. During this
process the heat flux and temperature were recorded. The
pressure drop, AP, across the test section and liquid film
thickness S at the inlet and outlet of the test section were
also recorded. As heat flux qw was further increased, vapor
bubble generation at the heating surface was generated and
sustained with increasing qw. Further measurements of h2 were
made until qw was increased up to 40 kW/m2. The range of flow
conditions over which measurements were made was G=125-280
kg/m2-s and X=0.04-0.30. As had been expected, it is observed
that for a fixed G, X, and TMt, the measured two-phase heat
transfer coefficient, h2(M without boiling is independent of
the heat flux, qw. Hence, it was assumed that the non-boiling
two-phase heat transfer is equivalent to that of the
macroconvection heat transfer coefficient in flow boiling and
is herein denoted by h^. As has been discussed in Chapter 1,
Rohsenow (1952) first suggested that the rate of heat transfer
associated with forced convection boiling is due to two
additive mechanisms, that due to bulk turbulence and that due

30
to ebullition. Using Rohsenow's superposition hypothesis, the
heat transfer coefficient attributed to microconvection during
saturated flow boiling may be calculated from
(3 2)
3.2 Experimental Results and Discussions
Prior to discussing the details of the experimental
results, it is necessary to define several parameters. For
two-phase stratified horizontal flow, the mean velocity of the
liquid film may be calculated from
_G(1-X)D
l~ Pfi
and mean vapor velocity by
(3-3)
GXD
Uv~'pv(D~b)
(3-4)
where u is mean velocity, S is liquid film thickness, p is
density and D is the inside dimension of the horizontal square
test section for which only the lower surface is covered with
a liquid film; subscripts £ and v denote the liquid and vapor
phases, respectively. The Reynolds number for liquid and
vapor phases are defined by
Ret=
PtuPht
Hi
(3-5)
and

31
Re
v
P v^yDhv
(3-6)
respectively, where Re is Reynolds, Dh is the hydraulic
diameter, and /x is the dynamic viscosity.
Microconvective heat transfer coefficients were obtained
for the nucleate flow boiling regime using the methodology
described above. The flow boiling heat transfer data were
organized by plotting hmic/h2i> against ^ as shown in
Anac^ -vine, s
Figure 3-1. It is very significant that all the experimental
data have been collapsed into a single curve. Here AT^,
denotes the sustaining incipience wall superheat. These data
conclusively demonstrate that microconvection is important in
almost all phases of saturated flow boiling heat transfer and
its contribution becomes dominant at high heat fluxes. This
conclusion distinctly contests most forced convection boiling
heat transfer correlations reported in the literature which
predict that macroconvection is always dominant. The curve
presented in Figure 3-1 may also be viewed as a "flow boiling
curve". As is well known, the conventional heat flux vs wall
superheat plot used for pool boiling cannot collapse the flow
boiling data due to the large variation of macroconvection
heat transfer.
Further consideration was given to the macroconvection

32
a /(h AT. )
' mac inc.s''
Figure 3-1. Microconvection heat transfer for saturated
forced convection nucleate boiling.
heat transfer component, h^. Figure 3-2 shows h^,,. as a
function of liquid Reynolds number, Re,, and vapor Reynolds
number, Rev. If h^ is approximated as a linear function of
Reynolds number over the limited range of data, the standard
deviation based on Re, is 0.165 and that based on Rev is 0.093,
and thus it is seen that h^ is better correlated with Rev than
Re,. This result is fundamentally different from that in

33
a
¡*
t>
*
JA
t
B
u
O
o
o
h
'a
a
i
ti
a
X
4
Vapor Reynolds Number Rey (xlO )
0 2 + 6 8 10 12
Liquid Reynolds Number Re, (xlO )
Figure 3-2. Macroconvective heat transfer coefficient in
saturated forced convection boiling.
single-phase forced convection and may possibly be due to the
enhanced turbulence caused by strong interfacial waves.
Considering that most flow boiling correlations for h^ are
simply modified single-phase heat transfer correlations
applied to the liguid, there remains considerable room for
improved modelling of both h^ as well as h^c in flow boiling
heat transfer correlations.

34
Vapor Reynolds Number Rey (xlO )
o
Du
<1
Oh
O
m
ra
£
Oh
0 2 4 6 8 10 12
4
Liquid Reynolds Number Ret (xlO )
Figure 3-3. Pressure drop in horizontal two-phase flow.
Figure 3-3 displays the pressure drop, AP, as a function
of Re, and Rev. In contrast to the case of h^., AP is found to
be better correlated with Re, rather than Rev. This result
suggests that the principle of analogous energy and momentum
transport in incompressible single phase flow may not be
appropriate for stratified two-phase flow in a boiling system
where strong interfacial waves are observed. For two-phase
flow with strong interfacial waves, Andritsos and Hanratty

35
(1987) have provided extensive experimental evidence that the
mean vapor velocity is a controlling parameter on the
interfacial shear stress. Recently, Maciejewski and Moffat
(1992) measured the velocity and temperature distributions in
the near wall region for flow over a flat plate and found that
the strong turbulence intensity in the free stream could
substantially alter the near-wall temperature profile while
the velocity profile maintains a relatively uniform shape.
Therefore, the dissimilarity between heat transfer and
pressure drop observed in this research may be due to the
strong turbulence intensity at the interface which may
influence the temperature profile in a manner significantly
different from that of the velocity profile.
In stratified two-phase flow, the thickness of the liquid
film along the lower surface can be converted to void fraction
a by
Using Zuber and Findlay's (1965) correlation, all the
experimental data obtained in this research were collapsed
into a straight line as shown in Figure 3-4. Uy, is the
superficial velocity of vapor phase defined by
uvs=^' (3-9)
P V
and is the two-phase mixture velocity which is defined by

36
GX^ G(X-l)
(3-10)
Pv Pi
It is noted that the observed void fraction for saturated flow
boiling system in this work is always larger than 0.7. Since
the conversion of liquid film thickness to void fraction in
this range has greatly reduced the relative error of the
results, the collapse of the data does not necessarily imply
o
0
Drift Flux u (m/s)
Zuber and Findlay's (1965) correlation for
void fraction in horizontal stratified two-
phase flow.
Figure 3-4

37
that Zuber and Findlay's (1965) correlation captured the
correct physics governing the void fraction distribution in
two-phase flow.
3.3 Conclusions
Measurements of two-phase heat transfer coefficients with
and without boiling have demonstrated that the microconvection
component of heat transfer in saturated flow boiling is
significant in almost all phases of boiling and its
contribution to the total heat transfer becomes dominant as
heat flux increases. The macroconvection heat transfer in
saturated flow boiling with strong interfacial waves is not
well correlated by simply using an analogy between momentum
and heat transport. Therefore, the development of a
significantly improved heat transfer correlation for flow
boiling, which has not been attempted in this study, will
require improved modelling of both the micro- and
macroconvection processes.

CHAPTER 4
INCIPIENCE AND HYSTERESIS
4.1 Introduction and Literature Survey
The development of modern electronics packaging requires
the ability to remove large amounts of heat from
microelectronic chips. The use of nucleate boiling heat
transfer of many dielectric liquids has been investigated for
this purpose due to their high heat transfer rates. Since
dielectric liquids usually have a high wettability on most
solid surfaces, the large overshoot of incipience superheat,
i.e. boiling hysteresis, has prevented their wide
applications. The experimental observation of boiling
incipience and hysteresis for highly wetting liquids is
clearly displayed in Figure 4-1 which was reconstructed from
the experimental data of Kim and Bergles (1988). Figure 4-1
is a typical heat flux vs wall superheat plot. The initiation
incipience point A is the point at which vapor bubbles just
begin appearing on the heating surface with increasing heat
flux. The sustaining incipience point B in Figure 4-1 is the
point just before vapor bubbles disappear from the heating
surface with decreasing heat flux. The overshoot of wall
superheat at the initiation incipience point is generally
38

39
referred as boiling hysteresis. Incipience and hysteresis in
pool boiling have been the focus of numerous experimental
T -T (K)
tr sat v '
Figure 4-1. Nucleate pool boiling hysteresis constructed
from the data of Kim and Burgles (1988).
investigations. It has been observed that the sustaining
incipience point for specified liquids and surface conditions
is predictable and is basically independent of the boiling
history (Yin and Abdelmessih, 1976). In contrast, the
initiation incipience point for highly wetting liquids depends
on initial system conditions as well as the history of various

40
heating, cool-down, and surface drying procedures (You, et
al., 1990; Marto and Lepere, 1982; Bergles and Chyu, 1982).
Recently, the effects of flow on boiling incipience have been
examined by various investigators. In subcooled flow boiling
with highly wetting liquids, such as R113 and F72, mass
velocity showed little effect on boiling incipience (Hino and
Ueda, 1985; Marsh and Mudawwar, 1989). In flow boiling with
water under both subcooled and saturated conditions, Sudo et
al. (1986) and Marsh and Mudawwar (1989) observed a strong
influence of the liquid velocity on boiling incipience. Flow
boiling incipience measurements of R113 at saturated
conditions are not available in the literature.
Numerous models and correlations have been proposed for
the prediction of boiling incipience, which have recently been
reviewed by Brauer and Mayinger (1992). The majority of
models were categorized as being either thermal or mechanical.
Thermal models are those which consider the bubble embryo to
sit at the mouth of a cavity and protrude into a superheated
thermal liquid layer. Once thermal equilibrium at the embryo
interface is exceeded by the superheated liquid, bubble growth
is initiated. Experimental data have verified that for poorly
wetting liquids, such as water, the initiation and sustaining
incipience points almost coincide and these models are useful
for predicting the incipience superheat. Models proposed by
Hsu (1962), Han and Griffith (1965), Bergles and Rohsenow
(1964), Sato and Matsumura (1964), and Davis and Anderson

41
(1966) belong to the thermal category. Mechanical models
consider a stable bubble nucleus resides inside a cavity.
When both the wall and liquid are subcooled, the interface is
required to be concave toward the cavity due to condensation
of vapor. For highly wetting liquids, this kind of concave
interface is possible only with reentrant shaped cavities
because contact angles are usually less than 90 degrees. The
radius of the bubble nucleus for highly wetting liquids is
substantially smaller than that of the cavity mouth.
Therefore, a higher wall superheat is required to initiate
boiling than is required to sustain it. According to
mechanical models, the radius of the interface inside the
cavity is determined by the liquid-solid contact angle, shape
of the cavity, and the degree of subcooling at the wall.
Therefore, the incipience wall superheat is dependent on the
surface conditions, liquid wettability, and the pressure-
temperature history prior to boiling. Incipience models
proposed by Mizukami et al. (1990) and Tong et al. (1990)
belong to the mechanical category.
The difficulties associated with predicting the boiling
incipience points are summarized as follows: 1) lack of
detailed information concerning cavity shapes and sizes on
commercial surfaces, 2) difficulties in determining the
dynamic and static contact angles on a microscale, 3) lack of
knowledge concerning the shape and size of the superheated
thermal layer, especially when two-phase flows are involved,

42
and 4) lack of knowledge of the embryo expansion and recession
process inside a cavity.
In this work, the initiation and sustaining incipience
wall superheats were measured for saturated flow boiling with
refrigerant R113 using the facility described in chapter 2.
The motivation for these measurements is to investigate the
dependence of the initiation and sustaining incipience points
on two-phase flow conditions and the surface heating and
cooling history. The saturated two-phase mixture flowing
through the transparent test section was varied over a range
of G and X at constant pressure. The measurements of the
initial incipience points were obtained by slowly increasing
qw until fully developed nucleate boiling was achieved. Then
measurements of sustaining incipience points were obtained by
gradually reducing the heat flux to return to the two-phase
forced convection regime. Measurements of both initiation and
sustaining points were also performed for variable heating and
cooling cycles at a fixed G and X. A theoretical analysis
which takes into account the hysteresis of the liquid-solid
contact angle and cavity geometry is presented which explains
the incipience process and hysteresis of boiling with highly
wetting liquids.
4.2 Experimental Results
A typical saturated flow boiling plot of qw vs ATMt for a
fixed G, X, and S is shown in Figure 4-2. A description of

43
5
40
35
30
25
20
15
10
5
0
0
Increasing from Twttit>=20C
boiling initiated at A.
V Decreasing q^.,
boiling sustained at B.
A Increasing qw from Tw.mJn=63C
boiling initiated at A'.
Increasing qw from TWTntT>=67aC
boiling reversible. B, Acoincide.
T =58QC, T =20C
sat room
V
*
'a
v
Vi
Va
b,a
V
&
^A'
T -T .
w sat
10
(C)
15
Figure 4-2. A typical saturated flow boiling plot of qw
versus ATMt for G=180 kg/m2-s, X=0.156, and
5=4.8 mm.
Figure 4-2 is as follows. With a quasi-steady saturated two-
phase mixture flowing through the test section, the heat flux
is increased from zero until the initiation incipience
superheat is reached, which is denoted by point A. Here the
minimum temperature prior to boiling is room temperature,
approximately 20 C. The heat flux is increased further until
fully developed nucleate boiling is achieved. The heat flux

44
is then decreased until the sustaining superheat is reached,
which is denoted by point B. The heat flux is further reduced
until Twmin=63 C. The heat flux is then increased until the
new initiation superheat is reached which is denoted by A'.
Thus is seen that Twmin influences the initiation superheat.
The cycle is repeated for Twmin=67 C and A" denotes the
initiation superheat, which coincides with the sustaining
superheat. Thus, hysteresis is fully suppressed provided
Tw,mm>67 c* Many experiments were conducted over a variety of
flow conditions to examine the influence of forced convection
on both the initiation and sustaining incipience points.
Figure 4-3 has been prepared for this purpose, where it is
seen that both the initiation and sustaining incipience wall
superheats remain essentially constant (although slightly
scattered) over a wide variety of flow conditions. h,^ has
been used in Figure 4-3 as a comprehensive parameter to
characterize the bulk turbulence. These results are
consistent with those obtained for subcooled flow boiling with
highly wetting liquids (Hino and Ueda, 1985; Marsh and
Mudawwar, 1989).
4.3 Theoretical Analysis for Boiling Incipience
4.3.1 Boiling Initiation
Effect of Non-condensible Gases. Since non-condensible
gases (usually air) are always trapped in cavities during the
process of a liquid filling over a surface, it is necessary to

45
understand their influence on the initiation of boiling. The
air trapping process has been detailed by Lorenz (1972) and
recently by Tong et al. (1990). Mizukami (1977) investigated
the effect of non-condensible gases on the stability criterion
of the embryo and found that the existence of gas stabilizes
the vapor bubble nucleus but accelerates its nucleation when
the liquid is superheated. However, quantitative
O
t
H
EH
<1
bO
t
i-H
t
rt
(S
m
t
xn
t
03
t
o
H
C0
.(H
t
25
20 -
15
10 -
0.0
Measured Initiation Superheat
v Measured Sustaining Superheat
Predicted Sustaining Superheat
Based on T =59 C, ^=0.66x10"* m
sat 1
V
V ^
0.5 1.0 1.5 2.0
Macroconvection h (kfWYmeC)
mnn v f '
Figure 4-3.
Measured saturated flow boiling incipience
wall superheat.

46
considerations regarding the effect of the gas mass on the
initiation superheat have not been reported in the literature.
It is worthwhile to proceed with such calculations in order to
further understand the nucleating process of a vapor bubble
containing a non-condensible gas.
Consideration is given to an embryo, consisting of a non
condensible gas and saturated vapor, trapped in a conical
cavity as shown in Figure 4-4. The gas is taken to be air and
the mass is specified. The embryo is initially at static and
thermal equilibrium
following relations
with its surroundings.
are satisfied,
Therefore, the
(4-1)
T,=Tv=Tc(Pv)
(4-2)
V'WV
(4-3)
where r is radius of the liquid/vapor interface, a is surface
tension, Rg is an engineering gas constant, and the subscripts
v, £, and g respectively denote the vapor, liquid, and gas.
The liquid pressure, Pf, is typically taken to be the system
pressure. Since air is assumed to be the only non-condensible
gas in the cavity the ideal gas law is obeyed. V is the
volume of an embryo, and for a conical cavity is given by
(Lorenz, 1972)
V=7tr3 (2- (2+cos2 (0i|r)) sin (0-i|O (4-4)
3 tan(i|0

47
Figure 4-4. An idealized sketch of a vapor embryo in a
conical cavity.
where 6 is the contact angle and \p is the half cone angle of
the cavity. First, consideration is given to the effect of
non-condensible gas on incipience, and for this purpose a
conical cavity with a specified geometry, rx=0.69 nm and ^=5,
is considered. The contact hysteresis, which is important for
boiling incipience, has been discussed in detail in the
literature (Johnson and Dettre, 1969; Schwartz and Tejada,

48
1972; Tong, et al., 1990). According to these investigations,
as the liquid/vapor interface gradually moves toward the vapor
phase, a maximum contact angle is reached and is referred to
as the static advancing contact angle, 0M. Similarly, as the
interface gradually moves toward the liquid phase, a minimum
contact angle, referred to as the static receding contact
angle, 0,r, is reached. Assuming the embryo expansion follows
a quasi-equilibrium process, the contact angle 0 lies between
0sr and 0 which are determined by liquid wettability and
surface conditions. Based on the data supplied by Tong et al.
(1990), 0sr~2 for R113, while 0M is usually less than 90.
For calculation purposes, here it is assumed that the initial
static contact angle is equal to the static advancing contact
angle and 0~8O. Tong et al. (1990) have suggested that when
the cavity is heated, during the first expansion stage the
embryo interface adjusts such that the initial static contact
angle recedes until the static receding contact angle is
reached. Then during the second expansion stage the
liquid/vapor interface moves toward the cavity mouth, with
constant contact angle, 0sr. During the first expansion stage,
the contact angle, 0, may be calculated from,
cos (0-iJi) = (4-5)
r
where rd, which remains constant, is the cavity radius at the
initial triple interface. rd may be calculated by specifying
the initial 0, Tv, P
49
>
E-
100
90 -
80
70
60
50
40
30
20
10
0.001
_L
0.01 0.1 1
V (x 10-10 ma)
10
100
Figure 4-5. Variation of vapor temperature with vapor
embryo volume during expansion inside a
conical cavity.
through (4-5) simultaneously. Once rd is obtained, a Tv vs. V
plot can be constructed by solving eguations (4-1) through (4-
5) assuming a quasi-eguilibrium expansion process. Figure 4-5
shows three different Tv vs. V curves, each for a different itig.
It is seen that as V increases there exists a maximum vapor
temperature, Tvmax, which will satisfy equations (4-1) through
(4-5). Based on quasi-equilibrium considerations, it is

50
assumed that TV~TW. When Tw exceeds Tvmax/ equation (4-1) will
be violated and vapor bubble growth will be initiated. Thus
the initiation incipience superheat is evaluated from
^lnCti=TVtmax-Tsat(P() (4-6)
It is clear that the initiation incipience superheat increases
with decreasing n^. For the conditions in Figure 4-5, the
assumed value of does not significantly influence the
incipience superheat. Since it is expected that non
condensible gas will be purged from the cavity during the
vapor bubble departure process, the amount of gas inside the
cavity should decrease as ebullition continues. As the
heating surface is degassed, AT^; should increase. This trend
has been observed with the current facility. After the test
section is filled with liquid R113, it is necessary to sustain
fully developed nucleate boiling for approximately two hours
in order to obtain a repeatable AT^j. This observation is
consistent with those of Griffith and Wallis (1960). They
suggested that fully developed nucleate boiling with water
must be sustained for 1.5 hours to degas conical cavities, and
two hours is required for reentry type cavities. Thus it is
concluded that non-condensible gas trapped in cavities during
liquid flooding of the boiling surface exerts a strong
influence on AT^; only during the initial stage of boiling.
Provided fully developed nucleate boiling is sustained for a
sufficient period of time, the embryo in active cavities

51
should consist of pure vapor.
Cavities with Pure Vapor. Mizukami (1990) concluded
that conical cavities with pure vapor can not survive
subcooled conditions and thus are not useful for initiating
boiling. However, even if conical cavities are initially
filled with liquid and can not initiate boiling, they can
become active nucleation sites if vapor is deposited in the
cavity from a neighboring nucleation site as has been
suggested by Calka and Judd (1985).
Mizukami (1990) also pointed out that the most favorable
cavities for surviving subcooled conditions are reentry type
ones. Thus it is likely that boiling is first initiated from
reentry cavities. Now consideration is given to reentry type
cavities, one of which is depicted in Figure 4-6. As is the
case for conical cavities, provided nucleate boiling is
sustained for a sufficient period, a vapor embryo will recede
in the cavity when the surface is cooled. Unlike conical
cavities, a reentry one will allow the liquid vapor interface
of highly wetting liquids to be concave toward the cavity
reservoir. Therefore, the vapor embryo can survive when P,>PV.
Following the analysis of Griffith and Wallis (1960) and
Mizukami (1975), for 6<9, the maximum curvature that the
liquid vapor interface can achieve is l/r2, where r2 is the
mouth radius of the cavity reservoir. Thus the initiation
superheat can be obtained from,

52
Figure 4-6. An idealized sketch of a vapor embryo in a
reentry cavity.
Pt) (4-7)
X2
For 0m<9O, the minimum curvature of the interface is
s ixiO
The minimum curvature determines a minimum vapor
temperature below which the vapor embryo cannot be sustained,

(4-8)
T
* v, mm
=T.
sat
(P,~
2osin8aa)
*2
r2 (/xm)
Figure 4-7. Variation of minimum vapor temperature and
initiation superheat with cavity reservoir
mouth radius.
Tvmin and AT^j calculated from equations (4-7) and (4-8) over
a range of r2 for R113 at a pressure of 1.45 bars (the no-flow
system pressure of the current facility) are displayed in
Figure 4-7. As shown in Figure 4-3, the measured initiation
incipience superheat for the current facility is approximately

54
14.7 C which corresponds to cavities with r2< 0.31 jum.
Assuming that reentry cavities initiate boiling and r2~0.31
/xm, they would be able to sustain their vapor embryos provided
the wall temperature is maintained above 15 C. The ambient
temperature of the laboratory where the boiling facility is
housed is maintained at 20 C. The fact that the vapor embryo
can be sustained may explain why the initiation incipience
superheats in Figure 4-3 are relatively uniform. The above
analysis suggests that if the heating surface is cooled down
well below 15 "C or if the system is pressurized well above
1.45 bars, ATjoci should increase. Experiments have been
performed when the system was pressurized to 2.26 bar with
TWn,in=20 C for about half an hour. AT^ measured immediately
following depressurization was found to increase to 19.1 C,
which is consistent with the above prediction. Further
measurements revealed that AT^ was dropping down toward its
original value as boiling continued but it required several
days for AT^j to recover.
4.3.2 Sustaining Incipience Superheat
A vapor bubble departing a cavity which has been active
will likely leave vapor behind at the cavity mouth in the form
of an embryo. Provided sufficient superheat is available to
the embryo, it will readily expand and vapor bubble growth
will again result. This process will continue until the
superheat available to the embryo is insufficient to promote

55
bubble growth. Following bubble departure, the liquid moves
toward the cavity, and the liquid/vapor interface will acquire
an advancing dynamic contact angle, 9^, which is usually
larger than 0M. According to Cole's analysis (1974), for
either conical or reentry cavities with half cone angle, \f/,
less than 0^, the maximum curvature the interface can attain
is the reciprocal of the cavity mouth radius, rt. Thus, prior
to bubble growth the interface protrudes the cavity mouth into
the superheated liquid thermal layer. Both the cavity mouth
radius and the temperature profile in the liquid thermal layer
control whether or not bubble growth will result. Assuming
bulk turbulence alone controls the liquid thermal layer, and
the temperature profile is linear in the vicinity of the vapor
embryo, the liquid temperature at the top of the embryo is
given by
(4-9)
where k, is the liquid thermal conductivity. Starting from
the Clayperon equation and the perfect gas approximation for
vapor, Bergles and Rohsenow (1966) derived an equation for the
embryo vapor temperature,
rrJ2,
ln(i+-l2_
rlpt
(4-10)
They further proposed the criterion for boiling incipience
that T( at the top of the embryo must exceed Tv. Based on this

56
criterion, the sustaining superheat AT^, (=Tw-TMt) can be
obtained as a function of r,, h^, and Tt numerically from
equations (4-9) and (4-10) For constant r,, has been
calculated over a range of h^ as shown in Figure 4-3. It is
seen that the effect of convection on incipience superheat is
negligible which is in agreement with experimental
observations.
4.3.3 Hysteresis of Boiling Incipience
Hysteresis is the difference between the initial and
sustaining superheats. According to the preceding incipience
analysis, the initiation point depends on the minimum heating
surface temperature, while the sustaining point does not. In
fact, an explanation for incipience hysteresis is provided by
equation (4-8); as Tvmin decreases, potentially active
incipience nucleation sites are deactivated due to the
collapse of the vapor embryo. Assuming that the heating
surface contains reentry cavities with a large size range,
equation (4-8) predicts that incipience hysteresis will
increase with decreasing Tvmin. Such behavior is exactly what
has been observed with the present R113 flow boiling facility.
It is seen from Figure 4-2 that when Tvmin is greater than TMt
and less than the sustaining point, the hysteresis declines
when compared to heating from subcooled conditions.
Furthermore, once fully developed boiling has been established
and Tvmin is maintained above the sustaining point, the boiling

57
process is completely reversible, which indicates that
hysteresis has been suppressed. However, one puzzling result
is that when T^-cT,*, AT^ does not substantially vary. This
may be because the size of the reentry cavities along the
heating surface are fairly uniform, r2~0.31 /xm. If this were
the case, only when Tvmin<15 C would AT^j be influenced. Such
a test has yet to be conducted. Electron microscope
photographs did not add any further insight.
4.4 Conclusions
Based on the experimental observations and theoretical
analysis presented herein regarding the incipience and
hysteresis associated with saturated forced convection boiling
of R113, two comments are in order:
1) Non-condensible gases trapped in cavities tend to reduce
the initiation superheat, but they will be purged from
cavities after boiling is sustained for a sufficient period.
For highly wetting liquids, the liquid flow could exert a
slight effect on the sustaining incipience superheat but not
on the initiation superheat. Gas-free conical cavities are
not useful for initiating boiling but can become activated
from adjacent nucleation sites. The initiation incipience
likely occurs in reentry cavities.
2) The incipience hysteresis is related to the minimum
heating surface temperature prior to boiling. Once fully
developed boiling has been established, the boiling process is

58
reversible if the heating surface temperature is maintained
above the sustaining point.
3) For the flow conditions investigated herein using R113,
both the initiation and sustaining superheats were not
noticeably influenced by bulk turbulence.

CHAPTER 5
NUCLEATION SITE DENSITY
5.1 Literature Survey
Due to its governing influence on heat transfer, the
nucleation site density has been the focus of numerous
investigations in pool boiling (Clark et al., 1959; Griffith
and Wallis, 1960; Kurihara and Myers, 1960; Gaertner and
Westwater, 1960; Hsu, 1962; Gaertner, 1963; Gaertner, 1965;
Nishikawa et al., 1967; Singh et al., 1976). The general
consensus from these investigations is that the formation of
nucleation sites is highly dependent on surface roughness,
geometry of microscopic scratches and pits on the heating
surface, the wettability of the fluid, the amount of foreign
contaminants on the surface, as well as the material from
which the surface was fabricated. Because of the large number
of variables which are difficult to control, none of these
investigators were successful in developing a general
correlation for nucleation site density. Griffith and Wallis
(1960) suggested that for a given surface the critical cavity
radius, rc, is the only length scale pertinent to incipience
provided the wall superheat is uniform. Although they
realized the wall superheat is nonuniform in pool boiling,
59

60
they used rc to correlate the nucleation site density as
follows,
-^=C1 ( )
A 1 rc
where n/A is the nucleation site density, Cx and
empirically determined constants, and when pt py
(5-1)
m are
2 O Tg.f.
(5-2)
where TMt is the saturation temperature, a is the surface
tension, hfg is the latent heat of evaporation, and ATsat=Tw-Tsat
is the wall superheat.
Nucleation site density data of Griffith and Wallis
(1960) for pool boiling of water on a copper surface is shown
in Figure 5-1 as a function of ATMt. For n/A < 4 cm"2 the
nucleation site density increases smoothly with increasing
ATMt. However for n/A > 4 cm"2 no correlation exists between
n/A and ATMt. Moore and Mesler (1961) used a fast response
thermocouple to demonstrate the heating surface temperature
directly beneath a nucleation site in pool boiling experiences
rapid fluctuations. Recently, Kenning (1992) used
thermochromic liquid crystals to measure the spatial variation
of wall superheat with pool boiling of water on a 0.13 mm
thick stainless steel heater. It was demonstrated that the
wall superheat was very nonuniform and |Al^at|/Arsat
varied

61
m
t
P
0)
ff
00
t
O
cd
a>
t
¡z¡
Figure 5-1. Pool boiling nucleation site density data from
Griffith and Wallis (1960).
from 0.25 to 1.5 over a distance of a few mm, where (-)
implies a spatial average and (') denotes a spatial variation
from the mean. Using a conduction analysis, it was also shown
that in the presence of ebullition, the spatial non-uniformity
of wall superheat on the surface of "thick plates" may also be
significant depending on geometry and thermal conductivity of

62
the plate. Kenning's (1992) result suggests that a Micro
length scale which is related to the spatial temperature field
may also be important in characterizing incipience of vapor
bubbles. In addition, according to the suggestion of
Eddington, et al. (1978) and the experimental findings of
Calka and Judd (1985), at low n/A where nucleation sites are
sparsely distributed, neighboring nucleation sites do not
thermally interact. However at large n/A where nucleation
sites are closely packed, thermal interference among
neighboring sites exists. Since it has been demonstrated that
ATMt is highly nonuniform in the presence of nucleation sites,
a question arises as to whether at large n/A the average wall
superheat is sufficient for characterizing the local wall
superheat experienced by individual nucleation sites. The
data displayed in Figure 5-1 suggest that is not.
Few similar studies on nucleation site density in flow
boiling have been reported. In one such investigation
Eddington and Kenning (1978) measured the nucleation site
density with subcooled flow boiling of water for a narrow
range of flow conditions. It was suggested that n/A is
related to rc. The objectives of the present work are
twofold: 1) to study the influence of flow and thermal
conditions on the nucleation site density in saturated
convection boiling, and 2) to determine whether or not the
nucleation site density in flow boiling is solely a function
of the critical radius, rc, as has been suggested for pool

63
boiling. Measurements of nucleation site density have been
obtained for flow boiling of refrigerant R113 in a 25 x 25 mm
inner square transparent test section. These measurements
have been obtained for an isolated bubble regime with
stratified flow. In general, the vapor/liquid interface was
wavy and periodic slugs of liquid were observed passing
through the test section. No flow regime transitions were
observed. The liquid phase Reynolds number based on the mean
liquid velocity, which is defined by equation (3-5), ranged
from 12,000 to 27,000 and that for the vapor phase as defined
by (3-6) ranged from 24,000 to 80,000. The flow conditions
are characterized by the mass flux, G, liquid film thickness,
, vapor quality, X, mean liquid velocity, u,, and mean vapor
velocity, Uy. Thermal conditions are characterized by the
heat flux, qw, the wall superheat, ATMt and saturation
condition (saturation temperature, TMt, or saturation pressure,
PMt) The controllable inputs of the flow boiling facility are
G, X, PMt (or TMt) and qw. Of the flow parameters considered,
only two are independent since the mean liquid and vapor
velocities were calculated from equations (3-3) and (3-4),
respectively, based on measured liquid film thickness at a
given G, X, and TMt. For the convenience of discussion,
equations (3-3) and (3-4) are rewritten here,
_G(1-X)D
r P,6
(5-3)
and

64
U
v
GXP
?v(D-b)
(5-4)
Therefore, when investigating the influence of one of the flow
parameters on nucleation site density at constant saturation
conditions, only one other flow parameter can be held
constant, which introduced complexities in interpreting the
data. The range of the flow and thermal parameters covered in
these measurements, which to a large extent were limited by
the ability to visualize nucleation sites, are as follows:
G=125-290 kg/m2-s, 1^=1.6-4.7 m/s, U;=0.35-0.68 m/s, 5=3.5-9.5
mm, gw=14.0-23.0 kw/m2, ATt=13.0-18.0 C, and TMt=55.0-75 C.
5.2 Optical Facility and Measuring Technique
The nucleation site density was measured optically using
a digital imaging facility shown in Figure 5-2. The facility
consists of a Videk Megaplus CCD camera with a 1320 x 1035
pixel resolution. The CCD camera is eguipped with a Vivitar
50 mm macro lens with high magnification and low optical
distortion and a Videk power supply. The output of the CCD
camera is connected to an Epix 4 megabyte framegrabber which
is mounted in an I/O slot of a 386 Zenith computer. The
framegrabber allows for either high resolution (1320 x 1035)
or low resolution (640 x 480) imaging. The images are
displayed on a Sony analog monitor with 1000 lines per inch
resolution, and may also be printed out on an HP Laser Jet III
laser printer or may be saved on floppy disk for future

65
VIDEK MEGAPLUS
Figure 5-2. A diagram of optical facility for measurement
of nucleation site density.
analysis. Computer software written in Microsoft C has been
developed for the image acquisition and processing. Due to
the strong vapor-liquid entrainment and waviness at the
interface of the two-phase mixture, it is not possible to
obtain a clear view of nucleation sites from the direction
normal to the heating surface. Therefore, the camera was
focused on the boiling surface through the side wall. A 500
Watt light illuminates the heating surface at an appropriate

66
angle from the opposite side wall. An opaque plastic sheet is
placed between the light and the object to diffuse the
incident light. Exposure time and lens aperture are properly
adjusted to obtain a clear image of the nucleation sites. A
typical picture of the nucleation sites is displayed in Figure
5-3 which was taken from the Sony monitor image. In order to
reduce the non-uniformities caused by the heater edge effect,
only nucleation sites in the middle 2/3 of the strip were
counted for measuring purposes. Thus the effective
measurement area was 1.4 cm wide by 2.2 cm. The nucleation
site density measured from an ensemble average of fifty images
was compared against that based on an average of ten images;
identical results were obtained. Therefore, all nucleation
site density measurements reported herein are based on an
ensemble average of ten images. Presumably intermittent sites
are accounted for. As has been demonstrated in Figure 3-2,
hysteresis can be avoided once the fully developed boiling has
been established. The measurements of nucleation site density
here were only made for the fully developed boiling regime
with increasing heat flux and increasing vapor velocity.
5.3 Experimental Results
Nucleation site density measurements were obtained for a
constant heat flux, qw=19.3 kW/m2, and saturation temperature,
TMt=58 C, over a range of flow conditions in which either the
mass flux, G, liquid film thickness, S, liquid velocity, ut,

67
Figure 5-3. A typical photograph of nucleation sites on a
boiling surface (flow direction is from left
to right).
or vapor velocity, uv, was maintained constant. The
nucleation site density, n/A, is shown as a function of wall
superheat, AT^, in Figure 5-4. It is seen from Figure 5-4
that the n/A data can not be correlated with AT^. In light
of Figure 5-1 and equations (5-1) and (5-2), the behavior of
n/A with ATMt is considered to be anomalous. In order to
demonstrate that the observed behavior is not simply due to

68
N
£
<
a
(*
CO
t
a>
o
a>
*4
W
t
O
* iI
-t->
(t
r <
a
t
£
15
10
5
0
qw=19.3kW/mz, T at=58C
G=215 kg/m^-s
5=6.3 mm
A u^O.48 m/s
u =3.6 m/s

A
A


4
A
S
8 10 12 14 16 18 20
Wall Superheat ATgat (C)
Figure 5-4. Nucleation site density as a function of wall
superheat for constant heat flux and
saturation temperature.
the experimental error, pool boiling nucleation site density
data were obtained using the current facility by filling the
test section with liquid and heating the nichrome strip while
the circulation pump was off. Therefore, the only net flow
was induced by the natural convection currents. The n/A data
for pool boiling are also displayed as functions of wall

69
a
o
-p
H
m
t
O
Q
xn
a
O
i-H
3
P-H

2
Z
Heat Flux qw (kW/m2)
8 10 12 14 16 18 20
Figure 5-5. Pool boiling nucleation site density as
functions of wall superheat and heat flux.
superheat, ATMt, as well as heat flux, qw, in Figure 5.5. It
is seen that n/A increases smoothly with increasing ATMt and
qw in a similar fashion to the data shown in Figure 5-1. As
seen from Figure 5-4, parameters other than AT^ alone appear
to exert an influence on n/A in flow boiling.
In order to examine the influence of the flow parameters

70
on n/A, measurements of nucleation site density were made
while the saturation temperature was maintained constant. The
nucleation site density is first plotted against vapor
velocity at a fixed heat flux, qw/ and fixed liquid film
thickness, S, as shown in Figure 5-6. It is seen that n/A
decreases markedly with increasing vapor velocity, Uy. At a
6
o
<
\
t
ri
m
t
n
o
-4->
rH
CO
t
o
H
ct
73
t
5z;
15
10 -
5 -
0
0
<5=6.3 mm, qw= 19.3 kW/m*
V <5=7.7 mm, q =14.5 kW/ms
T =58 C
sat
V
V

V


Vapor Velocity u (m/s)
Figure 5-6. Nucleation site density as a function of vapor
velocity for constant heat flux and liquid
film thickness.

71
fixed heat flux and liquid film thickness, the data appear to
fall on a single curve. As the heat flux is increased, the
curve shifts toward higher nucleation site density.
Therefore, when investigating the influence of the flow
parameters on n/A the heat flux will be maintained constant.
Upon examination of equations (5-3) and (5-4) it is possible
that the trend shown in Figure 5-6 is due to either increasing
G or uf instead of increasing Uy. To sort out whether G, ut,
or Uy has a controlling influence on n/A figures 5-7 and 5-8
have been prepared. In Figure 5-7, n/A is shown to increase
with increasing G when u, and qw are fixed, and decreases with
increasing G when S and qw are fixed, and thus it appears that
parameters other than G are controlling n/A. In Figure 5-8
n/A is shown to decrease with increasing uf for a fixed G and
qw. For the case of a fixed S and qw n/A also decreases with
increasing u, but the shape of the curve is significantly
different. When comparing Figures 5-6 and 5-8, it appears
that n/A is better behaved when displayed as a function of Uy.
Further evidence of this supposition is provided in Figure 5-9
where n/A is displayed as a function of Uy for qw=19.3 kW/m2,
TMt=58 C, G=215 kg/m2-s, and u,=0.58 and 0.48 m/s. It is seen
that all of the data approximately fall on a single curve,
thus demonstrating the governing influence of the mean vapor
velocity on nucleation site density. The liquid film
thickness is also shown as a function of Uy. Thus, the effect
of liquid film thickness on n/A might also be included in

72
e
o
t
-4->
pH
co
t
a>
Q
V
-4->
H
m
t
o
-I-!
(t
tu
o
t
S5
15
10
100


1^=0.48 m/s
qw=19.3 kW/mE
V 5=6.3 mm
qw=19.3 kW/mz
T =58 C
sat
V


150
200
250
300
Mass Flux G (kg/mz-s)
Figure 5-7. Nucleation site density as a function of mass
flux.
Figure 5-9. Therefore, it is necessary to investigate the
influence of S on n/A.
In pool boiling, Nishikawa et al. (1967) demonstrated
that the nucleation site density increases with declining
liquid film thickness. Mesler (1976) postulated that the same
behavior should follow for flow boiling and used it to explain

73
a
o
<
\
t
w
Cl
0)
n
4->
co
t
o
fH
-->
t
0)
v
t
$5
15
10
0.2
£
V G=215 kg/mss
qw=19.3 kW/mz
6=6.3 mm
q =19.3 kW/mB
T =58 C
sat

V




0.4
0.6

0.8
1.0
Liquid Velocity u. (m/s)
Figure 5-8. Nucleation site density as a function of
liquid velocity.
the measured increase in flow boiling heat transfer
coefficient with declining liquid film thickness for
stratified or annular flow. To the best of the author's
knowledge direct evidence supporting or refuting Mesler's
claim has yet to be presented. To sort out the direct
influence of liquid film thickness on the nucleation site

74
15
S
o
d
>
-ij
CO
d
o
P
m
d
o
cd
o
d
2;
10 -
5 -
0
%-
19.3 kW/ms, T =58 C
n/A
v
6

G=215 kg/m8s


ut=0.58 m/s
A

uz=0.48 m/s
<-
>-
14
12
10
8
0
6

*>^
O
CO
CO
CD
d
M

i-4
t
E-H
'd
H
d
cT
0
4
Vapor Velocity u (m/s)
Figure 5-9. Nucleation site density and liquid film
thickness as functions of vapor velocity.
density, Figure 5-9 suggests that it is necessary to maintain
a fixed uv, qw/ and T^. Figure 5-10 shows n/A as a function
of liquid film thickness at ^=3.6 m/s, qw=20.7 kW/m2, and
TMt=58 C. It is seen that n/A indeed increases with declining
film thickness, which tends to support Mesler's claim
regarding n/A as a function of film thickness, provided that

75
B
o
t
r-H
CO
t
0)
Q
0)
-u
w
o
o
!*
-tJ
t
t
II
o
t
£
Liquid Film Thickness (mm)
Figure 5-10. Nucleation site density as a function of
liquid film thickness.
Uy, qw, and TMt are fixed. However, over the range of film
thickness investigated (3-6 mm) the increase in n/A is only
marginal. Because n/A was obtained using a visualization
technique it was not possible to obtain data for 5<3 mm. As
6-+ 0 the behavior of n/A is uncertain. To determine whether
Uy or S has stronger influence on n/A, Figure 5-9 is re-

76
examined where it is seen that n/A decreases with declining S,
which is primarily caused by increasing Uy. Therefore, it
appears that Uy has a governing influence on the nucleation
site density. An explanation and significance of this finding
will be discussed later.
When testing the influence of thermal conditions on n/A,
it is necessary to control Uy. In Figure 5-11, n/A is shown
as a function of qw for three different values of Uy at TMt=57
C. It is seen that n/A increases smoothly with increasing
heat flux at a fixed Uy. As u, increases, the curves shift
toward decreasing n/A. This trend is consistent with that
observed in Figure 5-6. The n/A data in Figure 5-11 are shown
as a function of ATMt in Figure 5-12. The data display
an anomalous behavior similar to that in Figure 5-4.
To examine the dependence of n/A on the critical radius
it was decided that a constant heat flux and vapor velocity
would be maintained, and rc would be controlled by raising the
system pressure. Doubling the system pressure has the effect
of essentially doubling the vapor density and increasing T^
by only several percent. The nucleation site density was
measured for fixed Uy and qw over a range of system pressure
from 1.4 to 2.3 bars which gave a 20 C increase of saturation
temperature. Figures 5-13 and 5-14 have been prepared from
these measurements. It is seen from Figure 5-13 that n/A
increases with increasing Tsat while ATMt is dropping during this
process. Nevertheless, Figure 5-14 shows that this increase

77
"s
a
-t-3
CO
t
Q
CO
t
o
H
Cti
Q>
o
t
¡z;
Heat Flux (kW/mE)
Figure 5-11. Nucleation site density as a function of heat
flux.
of n/A can be attributed to an increase of l/rc. Since the
only physically sound explanation for the increase of n/A with
increasing TMt is due to a decrease in rc, these data suggest
that rc is an important parameter in characterizing flow
boiling nucleation site density.

78
t
H
w
t
O)
Q
cu
m
t
o
rH
-u
cfl
0)
o
t
Sz¡
Wall Superheat ATgat (C)
Figure 5-12. Nucleation site density as a function of wall
superheat.
5.4 Discussion of Results
Although the data shown in Figure 5-14, as well as
theoretical considerations, suggest that rc is an important
parameter for flow boiling nucleation site density, it is by
itself insufficient to correlate n/A. In Figure 5-15, all
nucleation site density measurements in this work are

79
a
o
<
t
fcs
+->
*rH
W
t
Q
d>
CO
t
o
a¡
rH
o

Wall Superheat ATgat (C)
5 10 15 20 25
Saturation Temperature T,at (C)
Figure 5-13. Nucleation site density as functions of
saturation temperature and wall superheat.
displayed as a function of rc. All data seem to be collapsed,
but a correlation in the form of equation (5-1) would not be
useful because the slope is too steep. The pool boiling
nucleation site density data also show a similar behavior for
large n/A.
In an attempt to understand this behavior, consideration

80
6
o
<
t
&
H
w
fl

Q
O
+J
H
m
t
o
-ij
(C
0)
t
¡2;
Figure 5-14. Nucleation site density as a function of
critical radius.
is first given to the pool boiling analysis of Hsu (1962) in
which it was demonstrated that the nonuniform liquid
temperature field seen by a vapor embryo attempting to grow is
important when considering incipience behavior. If linear
temperature profile is assumed for the liquid layer, a minimum
cavity radius required for incipience may be expressed solely

81
w
t
Q
O
4->
* II
m
o
13
t
55
100
10
1
All Data for Constant
Saturation Temperature
T =58 DC
sat

o
1 3 5 10
Critical Radius, 1/r (xlO
-6
m *)
Figure 5-15. Nucleation site density as a function of
critical radius.
as a function of wall superheat ATt or heat flux qw provided
the fluid properties are maintained constant. Figure 5-4
demonstrates that ATMt or qw alone is insufficient to correlate
the flow boiling n/A data. Bergles and Rohsenow (1964)
applied a similar analysis for flow boiling and the assumption
of a linear temperature profile in the liquid layer also leads

82
to a definition of critical cavity radius which is solely
dependent on ATMt or qw for constant fluid properties. One
shortcoming of these analyses is the assumption of a linear
temperature profile in the liquid thermal layer. Certainly,
the strength of heat flux and the intensity of bulk turbulence
will have a strong influence on the shape of the thermal
layer. Nevertheless, the experimental data presented here and
these theoretical analyses suggest that in addition to the
critical radius based on equation (5-2), a length scale
related to the shape of the thermal layer may also be
important in characterizing n/A.
In addition, it is emphasized that rc has been calculated
using equation (5-2) by taking the wall superheat to be the
average value, ATMt. As mentioned earlier, Kenning (1992) used
liquid crystal thermography to show that |Al^at|/ATsat could
be as large as 1.5 for pool boiling. In this study the liquid
crystal test section was used in conjunction with a Panasonic
video recorder to record the flow boiling wall temperature
field at conditions of 11^=3.0 m/s, qw=18.1 kW/m2, and TMt=58.3
C. It was found that temperature field was very nonuniform
in both spatial and temporal scales. Therefore, it appears
the average wall superheat is insufficient for characterizing
the local wall superheat experienced by individual sites.
The experimental data of n/A presented here have revealed

83
a strong parametric influence of vapor velocity on the
incipience process in saturated flow boiling. The similar
effect of vapor velocity has also been found on the heat
transfer coefficient in a stratified two-phase flow as shown
in chapter 3. It has been argued that vapor velocity has a
controlling effect on the intensity of turbulence at the
interface which would substantially modify the temperature
profile in the thermal layer. The same argument is applied
here to explain the effect of vapor velocity on the incipience
process. Increasing Uy results in enhanced turbulence, and
therefore a variation of Uy should have a significant impact
on the heating surface temperature field as well as the
thermal layer temperature profile which, in turn, influences
the boiling incipience process.
5.5 Conclusions
The nucleation site density n/A of saturated flow boiling
has been measured over a wide range of flow and thermal
conditions and the parametric effects of these conditions on
n/A have been examined closely. Of the flow and thermal
parameters investigated, Uy, qw, and TMt appear to have a
governing influence on n/A. Nucleation site density of
saturated flow boiling displays a dependance on the critical
radius rc, but by itself rc is insufficient to correlate n/A.
Pool boiling n/A correlations based on rc are not applicable
to flow boiling.

CHAPTER 6
A UNIFIED MODEL
FOR VAPOR BUBBLE DETACHMENT
6.1 Introduction
The detachment of vapor bubbles in nucleate boiling is
crucial in maintaining the high heat transfer rate of the
boiling process. In fact, the vapor bubble detachment
diameter has been incorporated into most boiling heat transfer
correlations. Although numerous models and correlations for
vapor bubble detachment diameter have been developed over the
past six decades (back to Fritz's model in 1935), a reliable
model for the prediction of bubble detachment diameters has
yet to be developed. Several factors which have posed
difficulties in accurately predicting the detachment diameters
are due to lack of adequate understanding of the surface
tension force and the inertial force induced by bubble growth
as well as their relative importance in the detachment
process. Due to the difficulties related to the prediction of
vapor bubble detachment diameters as well as other vapor
bubble parameters such as nucleation site density and growth
rate, it is not unexpected that the heat transfer coefficient
can not be accurately calculated for many boiling systems of
practical interest.
84

85
Figure 6-1. A typical picture of vapor bubble detachment
in flow boiling (flow direction is from left
to right).
Generally, the shape of a vapor bubble in boiling is not
strictly spherical. Thus, the bubble diameter is usually
defined as that of a sphere with an equivalent volume of the
bubble. Klausner et al. (1993) demonstrated that in forced
convection boiling systems, vapor bubbles typically detach
from the nucleation site via sliding and lift off the heating
surface downstream of the nucleation site. This process can
be clearly illustrated by a picture taken from the flow
boiling heating surface shown in Figure 6-1. The instant at

86
which a vapor bubble detaches from its nucleation site was
referred to as the point of departure and the instant it
detaches from the heating surface was referred to as the lift
off point. In pool boiling systems the departure and lift-off
points coincide and for the remaining of this work will be
referred to as the departure point. In this work, the
existing vapor bubble departure models and correlations for
nucleate pool and flow boiling in the literature were
examined. Based on experimental observations and theoretical
reasoning, an analytical model was developed for the
prediction of vapor bubble detachment diameters for both pool
and flow boiling. When compared with experimental data, the
model is found to yield significant improvement in the
accuracy of predicting vapor bubble detachment diameters when
compared with existing correlations.
6.2 Literature Survey
6.2.1 Pool Boiling Departure Diameter Correlations
Numerous vapor bubble departure diameter correlations and
models have been proposed for nucleate pool boiling, many of
them were summarized by Zuber (1964), Cole and Shulman (1966),
Hsu and Gramham (1976) and Kocamustafaogullari (1983) These
correlations and models may be categorized into three types:
surface tension controlled departure; inertia controlled
departure; and purely empirical correlations. For the surface
tension controlled bubble departure, it was assumed that the

87
departure arises from a balance between the surface tension
and buoyancy forces acting normal to the heating surface, and
other forces such as the inertial force due to the bubble
growth may be included as a correction factor. In contrast to
the surface tension controlled departure, the inertia
controlled departure assumes that the departure arises from a
balance between the inertial force and the buoyancy force.
Perhaps the most widely used and earliest bubble
departure model is that of Fritz (1935) which was derived from
a balance between the buoyancy and surface tension forces.
According to his model, the departure diameter may be
estimated from,
dd=0.02080. .
d N ^(PrPv)
(6-1)
where 8 is the contact angle in degrees, a is the surface
tension coefficient, g is the gravitational acceleration, p is
the density, and subscripts l and v respectively refer to the
liquid and vapor phases. Since the contact angle during the
bubble departure is very difficult to determine, 8 is an
empirical constant. Following Fritz's approach, Zuber (1959)
suggested that if the contact diameter, d^ remains constant
and the contact angle is 90, the bubble departure diameter
may be calculated from
dd=(
6 dwo
Sr(PrPv)
)
(6-2)

88
Staniszewski (1959) measured the bubble departure diameter and
growth rate over a range of heat flux and system pressure.
The influence of the bubble growth rate on the departure
diameter was observed from the data. Therefore, a correlation
for bubble departure diameter which accounts for the bubble
growth rate was obtained by modifying Fritz's model as
dd=0.00710 (tr) (1+34.3) (6-3)
d sr(PrPv)
where a is the bubble radius with units of m, and (') implies
differentiation with respect to time. Similar modified forms
of Fritz's (1935) model were made by Han and Griffith (1962)
and Cole and Shulman (1966) The correlation of Han and
Griffith (1962) may be expressed as
dd=2.828.
(1-
llPi
^ ^(PrPv) 48g(p,-pv) a
(2+a))
(6-4)
and that of Cole and Shulman (1966) takes the form of
dd=ddF( 1+223.62) (65)
where ddF denotes the departure diameter predicted by Fritz1s
(1935) model and the correction factor for growth rate used
here was based on a larger database than that used by
Staniszewski (1959). Cole and Shulman (1966) also modified
Fritz's model by taking into account the influence of pressure
and obtained another empirical correlation for bubble
departure diameter,

89
dd=
1.32
P
)
s^PrPv)
_i
2
(6-6)
where P is the system pressure with units of (atm) Cole
(1967) generalized equation (6-6) by taking into account the
contact angle and recognized that the system pressure could be
accounted for by the variation of vapor density through the
Jakob number. He also realized that the contact angle is
difficult to measure and for most boiling systems it does not
typically deviate by more than 20% from an average value of
50. Based on these considerations, he proposed the
correlation,
where
dd=(
o
^(prPv)
i
) 2 Ja
(6-7)
ja= p PA*
(6-8)
A modified form of Cole's (1967) correlation was proposed by
Cole and Rohsenow (1969),
dd=C( 7 g )^(,r^PCP)~f (6-9)
^(Pl-Pv) P yhfg
where C=1.5xl04 for water and 4.65X10"4 for other fluids.
Recently, Kocamustafaogullari (1983) attempted to correlate
vapor bubble departure diameters over a wide range of
pressures. He modified Fritz's model and proposed,

90
dd= 0.00127
P|~Pv^ o.9
Pv
(6-10)
The pressure dependence of dd is accounted for through pv.
Compared to surface tension controlled bubble departure,
little consideration has been given to inertia controlled
departure. Ruckenstein (1961), who was the first to propose
an inertia controlled departure model, regarded the surface
tension force as relatively unimportant in the bubble
departure process. He suggested the departure diameter could
be calculated from
(6-11)
where AT^^-T, is the wall superheat, Cp and ij are the
respective liquid specific heat and thermal diffusivity, and
hfg is the latent heat of vaporization. Roll and Myers (1964)
also argued that the surface tension force does not contribute
to the bubble departure process. Based on a balance between
the inertial force caused by the bubble growth and that due to
buoyancy, they derived an expression to estimate the bubble
departure diameter,
(6-12)
where CD is the drag coefficient on a vapor bubble and was
estimated based on data for a freely rising vapor bubble in an

91
infinite liquid.
Nishikawa and Urakawa (1960) recognized that the system
pressure has a profound influence on vapor bubble departure
diameters. Based on the bubble departure diameters measured
over a range of pressure from 300 to 760 mmHg they proposed an
empirical bubble departure diameter correlation which is
solely a function of pressure,
dd=0.00364P0,575 ( 6-13)
where P is the system pressure in units of (atm) and dd has
units of (m) Semeria (1961, 1963) proposed two correlations
which are similar to that of Nishikawa and Urakawa. The first
one is given by
dd=0.00160P'0,5 (6-14)
which was obtained from experimental data in the range of 2 to
20 atm pressure. The second one was obtained from data in
which the pressure range was extended to approximately 140 atm
and is given by
dd=0.0121P1,5 (6-15)
All of these models and correlations have been compared
with experimental data which include six different liquids,
subatmospheric, atmospheric and elevated pressures, and
reduced gravity. The relative errors of the predictions and
number of the data points considered are summarized in Table
6-2. These results will be commented on later.

92
6.2.2 Flow Boiling Bubble Detachment Diameter Correlations
Although there have been a large number of studies
investigating pool boiling vapor bubble departure, few similar
studies have followed for flow boiling. Chang (1963) proposed
one of the first expressions for the vapor bubble detachment
diameter in flow boiling. He assumed the point at which a
vapor bubble detaches the heating surface is the point where
the net forces acting on a vapor bubble (including forces
acting parallel and normal to the heating surface) just
balance each other. The forces considered were the buoyancy
force, surface tension force, and dynamic forces normal and
tangential to the heating surface. Sliding bubbles were not
considered and the expression was not experimentally verified.
Hsu and Graham (1963) conducted a visual study for upflow
boiling of water in various flow regimes. Based on the
trajectory of a typical vapor bubble, it appears that the
bubble slides along the heating surface prior to lifting off,
although this phenomenon was not discussed in their work.
Levy (1967) obtained a vertical upflow subcooled forced
convection boiling bubble departure diameter correlation which
considered the buoyancy force, drag force, and surface tension
force. It was empirically deduced that the buoyancy force
does not contribute to bubble departure diameter which is
given by

93
dd~C0^
OD
(6-16)
where D is the hydraulic pipe diameter, tw is the wall shear
stress, and C0=O.O15 is an empirically determined constant.
Sliding bubbles were not considered. Koumoutsos et al. (1968)
studied the detachment of vapor bubble at an artificial
nucleation site in forced convection boiling. They observed
that soon after incipience vapor bubbles begin to slide along
the heating surface until they lift off at some finite
distance downstream. They measured the lift-off diameters and
arrived at the following correlation,
(6-17)
where dL is the lift-off diameter, d^ is the departure
diameter for pool boiling, U is the mean liquid velocity, and
epyp/a=0.015 s/m and m=4 were determined empirically. It is
noted that when U becomes sufficiently large, equation (6-17)
predicts negative lift-off diameters which casts doubt on its
ability to correctly capture the physics governing vapor
bubble lift-off. Cooper et al. (1983) study the growth and
departure of vapor bubbles with laminar upflow of n-hexane
over a flat plate. They also reported that vapor bubbles
typically slide or roll along the heating surface prior to
lifting off and concluded the departure point was not well
defined. They also suggested that the simple force balances

94
used by Levy (1967) and Koumoutsos et al. (1968) were
insufficient for describing their observed departure data.
Recently, Klausner et al. (1993) developed a model for both
departure and lift-off diameters of vapor bubbles in flow
boiling. They demonstrated that while a vapor bubble is
attached to its nucleation site it grows asymmetrically due to
the hydrodynamic drag force posed by the flow. The asymmetric
growth was modelled by considering a vapor bubble growing at
an inclined angle to the flow direction. In order to evaluate
the force due to bubble growth acting in the direction of flow
or normal to the heating surface, knowledge of the inclination
angle is required. In addition, the contact area between the
bubble and heating surface as well as the receding and
advancing contact angles are also required in the model. Due
to the difficulties in determining the contact area and
contact angles, the model has limited practical value.
6.3 Development of Departure and Lift-off Model
6.3.1 Formulation
As has been mentioned previously, vapor bubbles in forced
convection boiling systems typically detach from their
nucleation site via sliding and lift off the heating surface
downstream of the nucleation site. Based on many observations
made with a CCD camera, the vapor bubble detachment process in
horizontal flow boiling may be depicted schematically as shown
in Figure 6-2. The bubble detachment model is based on force

95
Figure 6-2. A schematic diagram of the vapor bubble
detachment process in flow boiling.
balances in the horizontal and vertical directions. First,
consideration is given to the bubble departing from its
nucleation site. Following a similar form adopted by Klausner
et al. (1993), the x- and y-momentum equations for a bubble
attached to its nucleation site in flow boiling may be
expressed as

96
EF =F +F +Fw =p Vh dUbcx (6-18)
x x sx qs dux r'vrb '
and
ctu
E ,Vb-g3- ( 6-19)
where F, is the surface tension force, Fqs is the quasi-steady
drag in the flow direction, F*. is the unsteady drag due to
asymmetric growth, FsL is the shear lift force, FL is the lift
force created by the wake of preceding departed vapor bubble,
Fb is the buoyancy force, Fh is the hydrodynamic pressure
force, and F^ is the contact pressure force which effectively
includes the reaction of the wall to the vapor bubble, u^ is
velocity of the bubble at its center of mass, Vb is the bubble
volume, and pv is the vapor density. Equations (6-18) and (6-
19) are valid throughout the vapor bubble growth process.
Keshock and Siegel (1964) demonstrated that many of the forces
acting on a growing bubble vary significantly during different
stages of the growth process. In order to obtain a useful
vapor bubble detachment model, it is important to identify
which of those forces acting on a growing bubble are dominant
near the point of departure. The following is a detailed
analysis considering each of the forces appearing in equations
(6-18) and (6-19). For simplicity, a truncated sphere has
been assumed for the shape of a bubble growing on the heating
surface

97
Buovancv. Ouasi-steadv drag, and Shear Lift Forces. The
buoyancy force acting on a bubble immersed in liquid under
varied gravity may be calculated from
Fb=Vb(prpv) Cgg (6-20)
where Vb is the volume of the bubble, g is the gravitational
acceleration on the earth, and Cg is the ratio of reduced
gravity to the normal gravity on the earth. The buoyancy
force has typically been considered important in the removal
of vapor bubbles from pool boiling heating surfaces.
Based on the results obtained by Mei and Klausner (1992,
1993) the quasi-steady drag and shear lift acting on a bubble
in shear flow can be estimated from
QS
, Ar t=4+( (4^)n+-796n)
6nptvaUa 3 Re
n,n=0.6 5
(6-21)
and
pi 1
CL= =3.877Gs2 (2?e_2+0.014Gs2) 4 (6-22)
|p,AU**a*
where AU is the relative velocity between the bubble mass
center and liquid, a is the bubble radius, Re=2AUa/p is the
bubble Reynolds number, and v is the liquid kinematic
viscosity. In forced convection boiling, the vapor bubble
remains within the liquid boundary layer during its growth
cycle. For single phase turbulent flow, an estimation for the
velocity profile near the wall was proposed by Reichardt and

98
is given by Hinze (1975) as
yu* yu*
exp(-0.33^Hl))
v
(6-23)
where k=0.4, x=Hf and c=7.4. It is noted that the bulk
turbulence for two-phase flow is more intense than that for
single-phase flow, and u'/u^O.OS has been assumed when
equation (6-23) is used to approximate the liquid velocity
profile in stratified two-phase flow. Here u, is the mean
liquid velocity of the two-phase mixture and is given by
equation (3-3) Both the quasi-steady drag and shear lift are
important when AU is large.
Surface Tension. Contact Pressure, and Hvdrodvnamic
Pressure Forces. Considering a vapor bubble growing on a
horizontal heating surface in a liquid pool, the surface
tension force in the y-direction can be calculated from
Fsy=-ndwosin0
(6-24)
where is the contact diameter, cr is the surface tension
coefficient, and 6 is the contact angle. Many believe that
the major obstacle in developing a reliable correlation for
vapor bubble departure diameters in boiling is due to the
inability to predict and 6 accurately. As shown by the
measurements of Keshock and Siegel (1964), both contact
diameter and contact angle vary appreciably during the bubble

99
growth process. According to Cooper and Chandratilleke
(1981), Cooper et al. (1983), and Zysin et al. (1980), the
contact diameter at the base of a growing bubble embedded in
a superheated thermal layer is not easily measured. There
exists an index of refraction gradient in the thermal boundary
layer which creates a mirage of the bubble near its base.
Therefore, those investigators who relied on visual
measurements without taking into account this phenomenon have
severely overestimated the contact diameter as well as the
surface tension force. The hypothesis by Moore and Mesler
(1961) that a liquid microlayer exists beneath a growing vapor
bubble has been substantiated by various investigators and was
discussed in detail by Cooper and Lloyd (1969). Due to the
existence of the liquid microlayer it is probable that the
contact diameter is very small. Unfortunately, "very small"
is difficult to quantify because reliable measurements of the
contact diameter are not available to date. Although the
contact diameter continually changes during the growth cycle
of a vapor bubble, it is reasonable to suggest that the
contact diameter approaches zero near the point of departure
due to the necking phenomenon which has been clearly
identified by Jakob (1959), Johnson et al. (1966), and Van
Stralen et al. (1975). Direct experimental evidence can be
found in the measurements of Keshock and Siegel (1964), in
which the contact diameter is observed to decline sharply as
the vapor bubble is departing from the heating surface. The

100
computational study of Lee and Nydahl (1989) predicts that the
surface tension force is an order of magnitude less than the
buoyancy and growth forces near the departure point.
Therefore, the approach taken in this work is to assume the
surface tension force approaches zero at the point of
departure. It is emphasized that this assumption does not
imply that the surface tension force is generally negligible.
For the early stages of bubble growth, the surface tension
force may be finite. However, if a condition arises where the
bubble growth rate is very small, it may be possible for the
surface tension force to be at the same order as the growth
force. It is only near the point of the departure that the
assumption of a small surface tension force is employed. The
same argument is also applicable to the case of flow boiling
since the surface tension forces in x- and y-direction are
proportional to the contact diameter The major
contribution of surface tension to the bubble departure is to
maintain the bubble shape.
The hydrodynamic pressure force acting on a vapor bubble
may be estimated based on ideal flow over a truncated sphere.
Based on a potential flow analysis, the hydrodynamic force is
given by
(6-25)
h 8f< 4
where AU is the relative velocity between the bubble center of

101
mass and the liquid. Again, since the contact diameter
approaches zero near the point of departure as argued for the
surface tension force, the hydrodynamic pressure force is also
negligibly small.
The contact pressure force may be calculated from
ndl 2o
Fcp 4 Xi
(6-26)
where rr is the radius of curvature at the base of the bubble.
Photographs of growing vapor bubbles from Van Stralen et al.
(1975) suggest d/rTl, and it is clear that the contact
pressure force may be neglected at the point of departure
since it is small compared to the surface tension force given
by equation (6-23).
Growth Force. Although the effect of the bubble growth
rate on vapor bubble departure has been empirically accounted
for in various bubble departure correlations, an accurate
expression for the growth force is not available in the
literature. Ruckenstein (1961) and Roll and Myers (1964) gave
estimates of the vapor bubble growth force for pool boiling,
but when used in their bubble departure model unsatisfactory
results were obtained. Ruckenstein estimated the growth force
from,
(6-27)

102
while Roll and Myers used
Pduy=-9^CD%a2 --*a3 (l+-g
(6-28)
8 dt
where ub is the bubble velocity and was taken to be 2 .
Ruckenstein (1961) assumed CD was unity while Roll and Myers
(1964) evaluated CD from experimental data for freely rising
bubbles in liquid.
Klausner et al. (1993) modelled the growth force by
considering a hemispherical bubble expanding in an inviscid
liquid. Here, the same form of the expression is used except
that an empirical constant, Cs, is introduced which attempts
to primarily account for the presence of a wall,
FdU=_Pi7ta2(-|c^2+aS)
(6-29)
Based on 190 pool boiling data points considered herein, it
has been found that Cs=20/3 gives the best fit to the bubble
departure data based on a least squares regression analysis.
Although equation (6-29) provides excellent agreement with the
data, it is recognized that it is only an approximation of the
growth force based on a finite number of experimental data
sets, and there exists room for improved modelling.
In flow boiling, prior to departing their nucleation
sites, vapor bubbles are inclined toward the flow direction
with an inclination angle due to the quasi-steady drag

103
force. Thus the growth force components in the x- and in
directions are given by
Fdux=Fdu Sin0i (6-30)
and
Fduy=FducosQi (6-31)
In order to accurately estimate the growth force, information
on the bubble growth rate is reguired. Since the general
prediction of the bubble growth rate in flow and pool boiling
remains unsolved, a(t) must be specified for a given set of
boiling conditions.
So far, all the forces appearing on the left hand side of
equations (6-17) and (6-18) have been approximated except the
lift force Fl caused by the preceding departed bubble. A
gross estimation for this force using potential flow is given
by Zeng et al. (1993) and was found to be generally four
orders of magnitude smaller than the growth force and thus is
negligible. Therefore, the dominant forces at the point of
bubble detachment are the buoyancy, quasi-steady drag, shear
lift, and growth force, all of which are proportional to the
liquid density. The terms on the right hand sides of
equations (6-18) and (6-19) are the forces associated with the
vapor mass acceleration which are proportional to the vapor
density. Since pvp, and du^/dt is finite at the point of
bubble detachment for most cases of practical interest, the
acceleration forces can be neglected.

104
Now consideration is given to the bubble lift-off
process. Based on photographic visualization of vapor bubbles
in flow boiling using a CCD camera, it may be reasonable to
postulate that immediately following departure the bubble
attempts to right itself such that the inclination angle
approaches zero. Therefore, once the bubble departs its
nucleation site it slides along the surface in the flow
direction with zero inclination angle until it lifts off the
heating surface some distance downstream. It is also
hypothesized that once it departs from its nucleation site the
vapor bubble will rapidly accelerate to the speed of liquid
around it due to the low inertia of the bubble. Direct
experimental evidence for this hypothesis is not available at
this point since it requires measuring the liquid velocity
profile and bubble trajectory simultaneously. However, high
speed cinematography, using a Hycam camera operating at 5000
frames per second, was used to measure the sliding velocity of
departed vapor bubbles. The estimated error is 0.01 m/s.
For boiling conditions of u,=0.47 m/s, ATMt=9.3 C, and TMt=71.6
C the average measured sliding velocity based on an
observation of 4 bubbles is 0.14 m/s. The average liquid
velocity at the bubble center of mass, calculated from
equation (3-3), is also 0.14 m/s. The fact that the
velocities are identical is coincidental because an
observation of 4 bubbles is not sufficient to obtain a
statistically reliable average. Nevertheless,
this

105
measurement indicates that the average velocity of the bubble
and that of the liquid are at least close, and it provides
valuable evidence supporting the above hypothesis. The
hypothesis that the velocities of the sliding bubble and
surrounding liquid are approximately the same is supported by
the experimental data of bubble lift-off in flow boiling
obtained by Bernhard (1993) which shows that the liquid
velocity basically exerts no influence on the average vapor
bubble lift-off diameter.
Based on the preceding force analysis, a summary of all
forces acting on a vapor bubble growing on a horizontal
heating surface is given in Table 6-1.
6.3.2 Expressions for Bubble Departure and Lift-off Diameters
Based on the proceeding discussion, the x- and y-momentum
equations for a vapor bubble at the point of departure are
approximately
Fgs+Fdu sine^O (6-32)
and
F^COSe^F^+F^O, (6-33)
where Fqs, F*,, FsL, and Fb are determined by equations (6-21) ,
(6-29), (6-22), and (6-20), respectively. The departure
diameter dd and inclination angle 0¡ are unknown and can be
obtained by solving equations (6-32) and (6-33) simultaneously
for a known growth rate a(t) and liquid velocity u,. Although

106
Table 6-1. Summary of Forces Appearing in Momentum Equations.
Forces in Momentum
Equations
Symbols
Forces
Negligible
Estimated
from Eqs.
Surface Tension
x-direction
F
1 sx
yes
Quasi-steady Drag
x-direction
F
rqs
no
(6-21) and
(6-23)
Growth Force
x-direction
Fdux
no
(6-29) and
(6-30)
Surface Tension
y-direction
F
ry
yes
Growth Force
y-direction
Fduy
no
(6-29) and
(6-31)
Shear Lift Force
y-direction
FsL
only when
considering
lift-off
(6-22) and
(6-23)
Buoyancy Force
y-direction
Fb
no
(6-20)
Hydrodynamic
Pressure Force
y-direction
Fh
yes
Contact Pressure
Force
y-direction
Fcp
yes
Lift Force Created
by Bubble Wake
y-direction
Fl
yes
there do not exist simple explicit expressions for dd and 6it
they can be easily solved through iteration. The y-momentum
equation at the point of lift-off is
Fdu+Fb=0 (6-34)
and can be solved for the lift-off diameter dL.
In the case of pool boiling from a horizontal surface,

107
since the mean liquid velocity is generally zero, the momentum
equation at the point of departure is identical to (6-34),
which can be solved for the vapor bubble departure diameter.
It is noted that although the departure criteria for pool
boiling is identical to that of lift-off in flow boiling, the
lift-off diameter is typically smaller than the pool boiling
departure diameter. This is so because the wall superheat,
which controls the vapor bubble growth rate, is smaller for
flow boiling due to the additional energy transport from the
wall to the bulk liquid provided by the bulk turbulence. It
is seen that the bubble departure diameter dd is determined
from a balance between the buoyancy and growth forces as
opposed to the buoyancy and surface tension force.
6.4 Comparison with Experimental Data
Since the growth force is dependent on the vapor bubble
growth rate, comparisons were made only for experimental data
in which both the bubble detachment diameter and growth rate
were measured. The experimental data depicted here are either
based on those found in the literature or those measured by
Bernhard (1993) using the flow boiling facility described in
chapter 2. A useful statistical parameter, referred to here
as the relative deviation (r.d.), is used to evaluate the
performance of the present departure and lift-off model
against existing correlations and models, and is defined by

(6-35)
1 /
r.d. = meas^k xl0Q
N
where N is the number of data points, the subscripts "meas"
and "pred" refer to the respective measured and predicted
detachment diameters.
6.4.1 Pool Boiling Data
Experimental data obtained from the literature for pool
boiling were subdivided into four categories: subatmospheric
pressure, atmospheric pressure, elevated pressure, and reduced
gravity. Boiling liquids, pressure range, and gravitational
field of the departure data as well as the references from
which the data were obtained are summarized in Table 6-2. The
measured bubble growth rate, a(t), found in the literature
could generally be expressed in terms of a power law
a(t)=Ktn (6-36)
where K and n are usually determined by curve-fitting the
growth history. Equation (6-36) is useful to evaluate and
a which are required to calculate the growth force. In
situations where only the departure diameter and the growth
rate at the point of departure or the growth time are
specified in the experimental data, the growth constant can be
estimated using equation (6-36) by specifying a growth

Table 6-2. Mean Deviation Tabulated for Present Bubble Model as well as Other
Correlations Reported in the Literature.
Boiling
Conditions
Boiling
Liquids
Number
of Data
Points
This
Work
Fritz
(1935)
(6-1)
Zuber
(1959)
(6-2)
Stanisz-
ewski
(1959)
(6-3)
Nishikawa
& Urakawa
(1960)
(6-13)
Acetone
15
6.8
80.9
85.2
67.8
36.5
Sub-
Carbon Terr.
10
7.3
83.0
86.5
73.3
57.1
atmospheric
Methanol
43
9.5
73.0
76.3
63.5
26.3
Pressure
n-Pentane
5
18.6
23.7
43.7
28.0
127.1
one-g
Toluene
5
9.2
94.5
94.6
87.0
21.3
Water
27
11.9
90.5
90.9
81.7
57.1
Combined
105
10.0
78.3
81.6
69.2
43.2
Methanol
8
18.9
16.3
52.2
8.8
157.1
Atmospheric
n-Pentane
2
14.8
28.6
54.3
29.1
69.6
Pressure
Aqueous-sucrose
Solution
6
14.7
30.7
44.5
66.5
11.1
one-g
Water
51
14.9
16.9
56.8
34.2
43.6
Combined
67
15.3
18.4
55.1
33.9
55.0
Elevated
Methanol
3
17.3
55.0
37.5
15.6
156.0
Pressure
Water
8
28.8
39.9
41.5
18.5
47.7
one-g
Combined
11
25.7
44.1
40.4
17.7
77.3
Atmospheric
Pressure
Micro-g
Aqueous-sucrose
Solution
5
16.2
106.7
33.7
49.4
14.5
109

Table 6-2. (Continued)
Roll &
Rucke-
Han &
Semeria
Semeria
Cole &
Cole &
Cole
Cole &
Kocam-
Myers
nstein
Griffi.
1
2
Shulman
Shulman
(1967)
Rohse.
ustaf.
(1964)
(1961)
(1962)
(1961)
(1963)
1 (1966)
2 (1966)
(6-7)
(1979)
(1983)
(6-12)
(6-11)
(6-4)
(6-14)
(6-15)
(6-5)
(6-6)
(6-9)
(6-10)
81.6
85.1
76.1
69.2
547.1
16.3
32.6
86.9
93.7
91.8
99.2
98.1
185.5
52.2
2167.0
27.8
54.4
97.4
99.2
95.8
34.9
38.6
140.9
57.5
691.4
25.6
16.1
59.3
64.1
86.5
167.9
118.3
196.5
7.6
963.4
57.4
56.2
49.4
12.7
85.9
96.7
97.0
13.4
71.8
3265.0
46.4
66.2
96.6
96.4
99.2
372.1
279.0
34.3
83.5
845.8
31.1
29.6
43.6
30.6
58.4
143.7
119.3
106.2
63.7
986.5
28.4
29.0
64.1
62.2
81.5
33.9
31.6
371.3
20.2
753.1
116.8
49.5
13.6
20.7
57.6
36.9
26.9
235.1
25.3
482.9
59.1
6.0
39.1
43.8
89.9
555.0
140.4
130.6
52.7
256.8
30.7
6.6
48.4
21.1
32.6
138.4
94.1
110.8
38.0
366.8
73.2
31.7
38.6
16.6
17.6
160.2
88.8
147.4
36.8
406.0
74.1
30.8
36.5
18.3
25.9
85.6
67.0
330.0
26.3
333.7
110.1
32.2
63.7
29.8
69.1
51.0
33.6
91.3
32.0
156.0
86.5
22.7
34.3
33.8
30.5
60.4
42.7
158.8
30.5
204.1
93.0
25.3
42.3
32.7
41.0
440.4
345.0
283.1
61.0
194.1
106.7
186.9
338.8
132.3
102.0
110

Ill
exponent n. For subatmospheric and atmospheric pressure pool
boiling, Cole and Shulman (1966) and Van Stralen et al. (1975)
demonstrated that it is satisfactory to assume n is 0.5. For
high pressure and reduced gravity data, n is found to be less
than 0.5 and depends on pressure and gravity, thus more
information is required to estimate K and n. Using equation
(6-36) to approximate the bubble growth rate, the growth force
Fdu may be estimated from
2 2
Fdu=-ptnKn (^C^+nin-D) a* n. (6-37)
Z
A balance between Fj,, and Fb results in an explicit expression
for predicting the vapor bubble departure diameter,
dd=2 (-7- (^-Csn2+n(n-l))) (6-38)
4 g 2 ^
This equation has been used for the following comparison with
pool boiling experimental data.
Subatmospheric Pressure. Earth Gravity. A comparison
between the measured and predicted departure diameters for
subatmospheric pressure, earth gravity pool boiling is shown
in Figure 6-3. Experimental departure diameters were obtained
from Cole and Shulman (1966) and Van Stralen et al. (1975).
For the 105 data points considered, which encompass six
different fluids and a pressure range of 0.02-0.7 atm and span
two order of magnitude in departure diameter, the comparison

112
Figure 6-3. Comparison of predicted and measured vapor
bubble departure diameter for subatmospheric
pressure data using the present model.
is excellent. The relative deviation, displayed in Table 6-2,
is 10%. It is also shown from Table 6-2 that the only
correlations which give comparable predictions to the present
model are those of Cole and Shulman which are referred to as
Cole and Shulman 1 and 2. The relative error for these two
correlations are about 29%. A comparison between the measured
departure diameter and the prediction of Cole and Shulman 2 is

113
6
6
u
o
6
£0

Q
s_
2
S-,
<0
ex

TO
O
+J
o
fI
TO
O
S-.
ex
100
10
1 10 100
Experimental Departure Diameter d (mm)
Figure 6-4.
Comparison of predicted and measured vapor
bubble departure diameter for subatmospheric
pressure data using Cole and Shulman 2
correlation.
displayed in Figure 6-4. It is noted that in preparing Table
6-2, the present model is the only one in which the measured
bubble growth rate data were used in predicting departure
diameter.
Atmospheric Pressure. Earth Gravity. The atmospheric
pressure earth gravity pool boiling departure data are

114
s
a
TJ
Tj
P

"
a
-i-H
Q

u
d
-*->
¡3
a.

Q
TJ

-M
O
TJ

I-,
a.
8
1 1
Atmospheric Pressure Data
# Water, Staniszewaki (1959)
V Methanol, Staniszewsld(1959)
O Water. Han & Griffith(1965)
A AqueousSucrose Solution,
Keshock & Siegel(l964)
Water, Fritz & Ende(1936)]
nPentane,
Cole & Shulman (1966)
6 -
4 -
2 -
Bubble Departure Model
of This Work
0 2 4 6 8
Experimental Departure Diameter (mm)
Figure 6-5. Comparison of predicted and measured vapor
bubble departure diameter for atmospheric
pressure data using the present model.
comprised of four different fluids and 67 data points. The
experimental departure diameters were obtained from
Staniszewski (1959), Han and Griffith (1965), Keshock and
Siegel (1964), Fritz and Ende (1936), and Cole and Shulman
(1966). A comparison between the measured and predicted
departure diameter using the present model is shown in Figure
6-5. It is seen that the prediction is also excellent. The

115
8
S
e
T3
T?
Ih
V


S-4

A

a

o
T3

£h
Oh
0
Atmospheric Pressure Data
Water, Staniszewski (1959)
V Methanol, Staniszewski(1959)
O Water, Han & Griffith(1985)
A Aqueous-Sucrose Solution,
Keshock Si Siegel (1964)
Water, Fritz & Ende (1936)
nPentane,
Cole & Shuhnan (1966)
Bubble Departure Correlation
of Cole & Shulman 2, (1966)
0 2 4 6 8
Experimental Departure Diameter dd (mm)
Figure 6-6. Comparison of predicted and measured vapor
bubble departure diameter for atmospheric
pressure data using Cole and Shulman 2
correlation.
relative deviation for the present model as seen in Table 6-2
is 15%. A similar comparison for the Cole and Shulman 2
correlation is displayed in Figure 6-6. The Cole and Shulman
2 correlation which was satisfactory for subatmospheric
pressure data is also adequate for atmospheric pressure data
and has a relative deviation of 31%. However, when comparing
Figures 6-5 and 6-6, the present model appears more accurate.

116
Apart from the present model the best correlations are those
of Fritz (1936) and Cole and Rohsenow (1969) which have
relative deviations of 18%.
Elevated Pressure. Earth Gravity. The elevated pressure
and reduced gravity departure results are not conclusive since
the number of data points available are small. Nevertheless,
as long as the growth rate is specified satisfactory results
can be obtained using the present model. For the elevated
pressure case 11 departure data points are available which
were obtained by Staniszewski (1959) using two fluids. The
pressure ranges from 1.9 to 2.8 atms. The experimental growth
rate data available are difficult to analyze since at certain
times the bubble diameters appear to have a step change in
magnitude. Nevertheless, equation (6-38) is used to solve for
the departure diameter using the specified growth rate, and
the predicted departure diameters are compared with the
measured values in Table 6-3. Also shown in Table 6-3 are the
experimentally determined values of K and n which were used
with equation (6-38) It is seen that at the elevated
pressures the value for n ranges from 0.24 to 0.38 which
represents a decrease in bubble growth rate. This trend is in
agreement with Griffith's (1958) bubble growth model. As is
seen from Table 6-2, the relative deviation for this set of
data using the present model is 26%, which is high compared
with the subatmospheric and atmospheric pressure data. The

117
Table 6-3. Comparison of Measured and Predicted Bubble
Departure Diameter for Elevated Pressure Data
Using Present Model.
Boiling
Liquids
Pressure
bar
dd(mm)
Meas.
dd(mm)
Pred.
K
n
Water
1.93
2.20
1.43
0.00444
0.38
1.58
1.12
0.00388
0.37
1.41
1.10
0.00254
0.29
1.86
1.30
0.00259
0.26
1.13
1.18
0.00202
0.22
1.73
1.27
0.00209
0.24
2.76
1.83
1.07
0.00301
0.34
1.77
1.04
0.00282
0.33
Methanol
1.93
1.24
1.03
0.00250
0.30
0.69
0.57
0.00256
0.38
2.76
1.01
0.83
0.00216
0.31
best correlation is that of Staniszewski (1959) which has a
relative deviation of 18%. The relative deviation for the
Cole and Shulman 2 correlation is 25%. It is interesting to
note that since the vapor bubble growth rate decreases with
increasing pressure, the present model predicts that the
departure diameter should decrease with increasing pressure,
under otherwise similar conditions. The elevated pressure
bubble departure data of Tolubinsky and Ostrovsky (1966)
definitively support this prediction. Unfortunately, their
data do not provide enough information for comparison against
the present bubble departure model because growth rate data
were not specified.

118
Table 6-4. Comparison of Measured and Predicted Vapor
Bubble Departure Diameter for Reduced Gravity
Data Using Present Model.
Percentage
of Earth
Gravity
dd (mm)
Measured
dd (mm)
Predicted
K
n
42.9
3.84
4.50
0.00993
0.42
22.9
3.79
3.28
0.00430
0.22
12.6
4.90
5.63
0.00932
0.37
6.1
3.38
3.87
0.00605
0.36
1.4
5.21
6.28
0.00552
0.22
Atmospheric Pressure. Reduced Gravity. For the reduced
gravity data, only five data points are available in which the
gravitational field varies from 0.04 to 0.43 of earth gravity.
These data indicate that the vapor bubble growth rate
decreases with decreasing gravity. Table 6-4 displays the
predicted departure diameters using the current model compared
with the measured values as well as the values for K and n to
be used in equation (6-38). It is seen that n decreases with
gravitational field. For these five data points the relative
deviation is 16%. The present model is the only one which is
in satisfactory agreement with the reduced gravity data,
besides that of Nishikawa and Urakawa (1960) It is also
expected from equation (6-38) that when g approaches zero the
vapor bubble will not depart the heating surface unless there
is some external mechanism to induce an inertial force to
remove the bubble, such as system vibration or three

119
dimensional flow disturbances. The zero-gravity pool boiling
photographs provided by Siegel and Usiskin (1959) tend to
support this prediction.
6.4.2 Flow Boiling Data
No experimental data with both vapor bubble detachment
diameter and growth rate are available for flow boiling in the
literature. Verification of the bubble detachment model for
flow boiling at this time can only be made using the departure
and lift-off data obtained by Bernhard (1993). The
measurements of bubble diameter were made from instantaneous
images obtained using a CCD photography facility. The
uncertainty in the departure and lift-off diameter is 0.03mm.
It is not currently possible to measure the bubble detachment
diameter and growth rate simultaneously using the CCD imaging
facility. However, for each fixed flow and thermal condition,
the departure and lift-off diameters are represented by their
mean values as well as the bubble detachment probability
density functions (pdf's) which were constructed from at least
200 bubbles. Vapor bubble growth rates in flow boiling have
also been obtained using high speed cinematography with a
speed of 5000 frames per second and will be discussed in
detail in the following chapter. Using high speed
cinematography, a few bubbles were captured over their life
span. These bubbles were used to check the accuracy of the
present model for the departure diameter prediction of

120
individual bubbles. The experimental data from high speed
films show that the diffusion controlled bubble growth
solution proposed by Zuber (1959) can adequately correlate the
ensemble average of bubble growth rate. This growth rate
solution can be expressed as
a(t) =Jav/rft (6-39)
where
Ja= p'Cp'^Ts*t (6-40)
PvAfgr
and Ja is the Jacob number, tj is the thermal diffusivity, cp<
is the liquid specific heat, and b is an empirical constant
which is supposed to account for asphericity. For most
observed bubble growth rates with flow boiling at atmospheric
pressure measured in this work, it is found that b=l gives the
best fit to the experimental data. Therefore, equation (6-39)
with b=l has been used to estimate the bubble growth rates for
the present bubble departure and lift-off diameter models.
Departure Diameter and Inclination Angle. From the
analysis of the present bubble departure model, the vapor
bubble departure diameter is a function of only the mean
liquid velocity when the wall superheat, which controls the
bubble growth rate, is fixed. Measurements of mean departure
diameter over a range of u, and ATMt obtained by Bernhard

121
b
a
'll
QJ
Q)
B
cti
r*4
n
CL)
(h
3
(0
O*
O
Mean Liquid Velocity uz (m/s)
Figure 6-7. Departure diameter variation with mean liquid
velocity at approximately same ATMt.
(1993) are used here for comparison. Figure 6-7 shows the
measured departure diameters as a function of mean liquid
velocity in which the wall superheat was maintained in a range
of 14-16 C. Also shown are the predicted departure diameters
using the present departure model for ATsat=15C and the model
presented by Klausner et al. (1993) for ATMt=15C and <^=0. It
is seen that good agreement exists with the present model. A

122
comparison between the measured and predicted departure
diameters, obtained under various flow and thermal conditions
by Bernhard (1993), is shown in Figure 6-8. The relative
deviation of the present model is 18% which is acceptable
considering the departure diameter is sensitive to the vapor
a
a

&
U
cd
ft
P
-t->
O
U
OU
Measured Departure Diameter dd (mm)
Figure 6-8. Comparison between predicted and measured
departure diameters for flow boiling.
bubble growth rate which was evaluated using equation (6-39).
It seems that when the present model is compared to that

Table 6-5. Measured and Predicted Departure Diameters
Based on High Speed Cinematography Data.
^d,mcas
mm
^d,prcd
mm
Relative
Error (%)
K(xl03)
n
m/s
AT^
C
C
0.256
0.259
1.2
1.94
0.435
0.240
0.220
8.4
1.29
0.382
0.221
0.218
1.3
1.84
0.450
0.30
8.2
67.0
0.245
0.243
0.8
1.79
0.429
0.240
0.220
8.4
1.16
0.362
0.121
' 0.115
4.6
0.97
0.428
0.123
0.115
6.8
0.57
0.334
0.142
0.138
2.8
1.07
0.421
0.28
10.0
71.0
0.150
0.153
2.2
1.10
0.410
0.138
0.148
6.9
0.94
0.386
123

124
reported by Klausner et al. (1993) who assumed a finite d and
constant 0¡ no improvement is gained in the prediction of the
departure diameter. However, it should be recognized that the
present model is more useful since empirical data concerning
and advancing and receding contact angles are not
required. In addition, the performance of the departure model
is improved when the vapor bubble growth rate is known, and
the evidence of such is provided by Table 6-5. Table 6-5
compares the present bubble departure model against departure
diameters measured using high speed cinematography in which
the growth rate was simultaneously measured (Brouillette,
1992) It is seen that the prediction is significantly
improved, and the relative deviation for the predicted
departure diameters in Table 6-5 is 4%.
Figure 6-9 shows the predicted mean departure diameter
using the present model as a function of liquid velocity and
wall superheat. The observed trend, departure diameter
decreases with increasing velocity and increases with
increasing wall superheat, is consistent with that reported by
Klausner et al. (1993). Figure 6-10 shows the predicted
inclination angle as a function of the predicted departure
diameter. It is seen that the predicted inclination angle
varies from about 5 to 25 degrees. Although an accurate
measurement of the inclination angle with the present
experimental facility is not currently achievable, the
predicted inclination angle falls in a range which is

125
B
B
2
(d
p.
QJ
Q
tu
+j
o
xl
0)
(h
Oh
1.0
0.8 -
0.6
0.4 -
0.2 -
Flow Boiling Vapor
Bubble Departure
TMt=60 C
* AT -10 C
Mi
V ATmt=15 C
AT-t=20 'C
A A
A A
0.0
0.0 0.2 0.4 0.6 0.8
Mean Liquid Velocity ut (m/s)
1.0
Figure 6-9. Departure diameter variation with mean liquid
velocity and ATMt.
consistent with experimental observations. In addition,
Figure 6-10 shows that the departure diameter decreases with
increasing inclination angle. This trend is expected since
the inclination angle should increase with increasing u, and
the trend in Figure 6-7 shows the departure diameter decreases
with increasing velocity. In Figure 6-11 the predicted
inclination angle is shown as a function of liquid velocity at

126

t
iH
on
%
CJ
o
-4->
t
1=1
o
fl
t
+J
O
xl
t
u,
Oh
50
45
40
35
30
25
20
15
10
5
0
0.0 0.2 0.4 0.6 0.8 1.0
Predicted Departure Diameter d (mm)
Flow Bolling Bubble Departure
Totally 32 Data Points
V
v
X?
V ^7
V V V
v
w
Figure 6-10. Predicted inclination angle variation with
predicted departure diameter.
various wall superheats. While 0t increases with increasing
velocity, it decreases with increasing wall superheat.
Lift-off Diameter. Figure 6-12 shows the predicted lift
off diameters against the measured values of Bernhard (1993).
The relative deviation for the data in Figure 6-12 is 19%

127
a>
'5b
C
o
-|J
5
a
TJ
03
4->

'S
a>
Sh
Pu,
50
45
40
35
30
25
20
15
10
5
0
0.0 0.2 0.4 0.6 0.8 1.0
T
Flow Bolling Vapor
Bubble Departure
T=60 C
a 0^=20 C
v AT_t=16 C
AT =10 C
v V v
A A A A A
vvvvvvvvv^
JL
Mean Liquid Velocity u (m/s)
Figure 6-11 Predicted inclination angle variation with
mean liquid velocity and ATMt.
which is also acceptable. The relative deviations of
prediction for the departure and lift-off diameters are
comparable to those for the pool boiling data.
6.5 Conclusions
A general model has been developed for predicting vapor
bubble detachment diameters in pool and flow boiling. It has
been demonstrated that the model is in good agreement with

128
Measured Lift-Off Diameter dL (mm)
Figure 6-12. Comparison between predicted and measured
lift-off diameter.
pool boiling departure diameters measured under subatmospheric
and atmospheric pressure for different substances. Based on
a limited number of experimental data, the model is also in
good agreement with elevated pressure and microgravity pool
boiling departure diameter data. The model is in good
agreement with the limited number of flow boiling data
available. The only required input is the vapor bubble growth
rate. The good agreement between the model and experimental

129
data lends credence to the hypothesis that the growth force is
dominant compared to the surface tension force at the point of
detachment. The bounds of validity of this hypothesis have
yet to be explored.
In theory, the present model is also applicable to
boiling with different orientations although calibration of
the model would be required for some situations. For
instance, it is assumed that u*/u,=0.05 for horizontal flow
boiling when equation (6-23) is used to evaluate the liquid
velocity profile near the wall. If equation (6-23) is even
applicable to vertical flow, it is expected that u*/u, may be
greater than 0.05 due to enhanced bulk turbulence.

CHAPTER 7
PROBABILITY DENSITY FUNCTIONS OF
VAPOR BUBBLE DETACHMENT DIAMETER
7.1 Introduction
The statistical nature of the boiling process was first
discussed by Fritz and Ende (1936) who made quantitative
measurements of vapor bubble growth rate and departure
diameter in pool boiling using photographic techniques. Since
then numerous investigators have made boiling measurements
under a variety of conditions and similar statistical
variations were observed. Among them are Staniszewski (1959) ,
Strenge et al. (1961), Han and Griffith (1963), Cole and
Shulman (1966) and Tolubinsky and Ostrovsky (1966) However,
few measurements of probability density functions (pdf's) of
bubble growth rate and departure diameter were made in these
investigations. Strenge et al. (1961) gave pdf's of bubble
departure diameter and growth rate for pool boiling with ether
and pentane. Tolubinsky and Ostrovsky (1966) presented pdf's
of departure diameter for boiling with water. These
experimentally determined pdf's resemble a Gaussian
distribution. Recently, Bernhard (1993) measured vapor bubble
departure and lift-off diameters for saturated flow boiling
with refrigerant R113. pdf's of detachment diameters were
130

131
obtained over a wide range of flow and thermal conditions.
These experimentally measured departure and lift-off diameter
pdf's also resemble Gaussian distributions.
Although it has been realized that the statistical
characteristics of boiling are important in understanding the
boiling heat transfer process, theoretical analysis devoted to
these statistical characteristics is lacking. Strenge et al.
(1961) and Tolubinsky and Ostrovsky (1966) believed that the
statistical distribution of bubble departure diameters may be
caused by random factors involved in boiling systems which
have not been reliably quantified through experiments.
Recently, Kenning (1992) obtained spatial distributions of
wall temperature in pool boiling using a liquid crystal
thermography technique. The variation in wall superheat was
approximately displayed as Gaussian. The preceding bubble
detachment model indicates that in addition to the liquid
velocity, the wall superheat, which controls the bubble growth
rate, is important in predicting the bubble departure and
lift-off diameters in flow boiling. The observed statistical
variation of bubble departure and lift-off diameters is likely
caused by the apparently randomly distributed wall temperature
and turbulent fluctuations in the liquid film. In what
follows, the analytical relationship between pdf's of
detachment diameters and those of wall superheat and liquid
velocity in flow boiling are established through a unified
bubble detachment model. The pdf's of departure and lift-off

132
diameters have been calculated for specified pdf's of wall
superheat and liquid velocity, and the results are compared
with experimental data.
7.2 Formulation
According to the preceding bubble detachment model, the
bubble departure diameter increases with increasing wall
superheat and decreases with increasing liquid velocity in
flow boiling. Therefore, the probability distribution
function of departure diameter can be expressed as
Prob[0]
(7-1)
where d, AT, and u are the departure diameter, wall superheat,
and mean liquid velocity, respectively. The subscripts for
these three variables have been eliminated to avoid confusion.
Assuming the wall superheat and liquid velocity are
statistically independent, equation (7-1) can be expressed in
integral form as,
J^aTU)pd(0 d{=J*TpAT(i\) dx)fpu(l) d£ (7-2)
where p denotes probability density function. pd(d) is
obtained by differentiating equation (7-2) with respect to d,
pd(d)-p4T(ADpt,(u)-^|H (7-3)
dAr
dd
du
dd
are evaluated using
where partial derivatives
and

133
the bubble departure model, i.e. equations (6-32) and (6-33).
Equation (7-3) is used to calculate the pdf of departure
diameter in flow boiling for specified pdf's of wall superheat
and liquid velocity.
Based on the bubble detachment model, the bubble
departure diameter in pool boiling and lift-off diameter in
flow boiling do not depend on liquid velocity. Thus the
detachment diameter pdf's for these two cases are only due to
the statistical distribution of wall superheat. The pdf's of
bubble departure diameter in pool boiling and lift-off
diameter in flow boiling may be evaluated from
pd(d)=pAr(AT)^ (7-4)
for a specified pAT(AT) .
A liquid crystal thermography technique was used to
visualize the wall temperature variations in the present flow
boiling facility. Videotape recordings of the underside of
the boiling surface displayed temporal and spatial
fluctuations of wall temperature. Instantaneous pictures were
also obtained using a 4X5 format camera. The videotape is
available from the author upon request. Kenning's (1992)
liquid crystal measurements of wall temperature in pool
boiling showed an approximately Gaussian temperature
distribution. Therefore, it may be reasonable to assume a
Gaussian probability density function for wall superheat in
flow and pool boiling,

134
1 ( AT-Ara)2
(7-5)
where AT is local wall superheat, ATm is mean wall superheat,
and ctax is the standard deviation of wall superheat.
The fluctuation of liquid velocity in flow boiling
systems may be caused by interfacial waves and bulk
turbulence, both of which are stochastic in time and space.
Experimental data of liquid velocity fluctuations around a
bubble in boiling are not currently available. Here the pdf
of liquid velocity is also assumed, for simplicity, to be
Gaussian,
(7-6)
where u is instantaneous local horizontal liquid velocity,
is mean liquid velocity, and ctu is the standard deviation of
liquid velocity.
7.3 Comparison with Experimental Data
Experimental data on the statistical distribution of
bubble detachment diameters are usually obtained in the form
of histograms in terms of the normalized number of bubbles.
The normalized number n/N can be calculated from the pdf of
detachment diameter using,
(7-7)

135
d
v
N
a
IB
55
a
a
3
m
h
a>
6
p
Figure 7-1. Statistical distribution of bubble lift-off
diameter in flow boiling.
where dj is the detachment diameter (departure or lift-off)
under consideration and Ad is the diameter range.
Comparisons were first made for the bubble lift-off
diameters in flow boiling and results are shown in Figure 7-2.
The prediction of pdf is based on assumed Gaussian
distribution of wall superheat with a standard deviation of

136
T
V
N
a
sf
¡z;
.o
£¡
3
m
u
V
1
3
'Z.
Bubble Departure Diameter dd (mm)
Figure 7-2. Statistical distribution of bubble departure
diameter in flow boiling at constant ATt.
one eighth of its mean value. The assumed standard deviation
was chosen such that the predicted pdf's best fit to those of
the experiment. The experimental data were obtained by
Bernhard (1993) and each pdf was constructed from more than
200 observations of bubble diameter. It is shown that both
the mean value and standard deviation of bubble lift-off

137
u
a>
H
is
Figure 7-3. Statistical distribution of bubble departure
diameter in flow boiling at constant u,.
diameter increases with increasing wall superheat. For
various wall superheats considered herein, the model
prediction is in good agreement with the experimental data.
The model was further compared against Bernhard's (1993)
experimental pdf data for flow boiling departure diameter,
where both liquid velocity and wall temperature have been

138
demonstrated to have a controlling influence. Figure 7-3 was
prepared for various liquid velocities and relatively constant
wall superheat. Gaussian distributions of liquid velocity and
wall superheat were assumed as well as standard deviations of
one eighth of their means. It is seen that the mean value of
departure diameter declines as liquid velocity increases while
its standard deviation increases with increasing liquid
velocity. Good agreement with measurements were also obtained
as shown in Figure 7-3. For constant liquid velocity, the
effect of wall superheat on the departure diameter is shown in
Figure 7-4. Based on the same Gaussian distributions of
liquid velocity and wall superheat, as used previously, the
predicted pdf's of departure diameter agree well with the
experimental data.
7.4 Conclusions and Discussions
The present model has successfully connected the pdf of
detachment diameter to those of liquid velocity and wall
superheat in flow boiling, which are assumed to be Gaussian
with standard deviations of one eighth of their means.
Although direct experimental data for the pdf's of liquid
velocity and wall superheat are not available at this time,
physical justifications for the assumed distributions is
possible. It has be hypothesized that the standard deviation
of liquid velocity increases with the mean velocity. Since,
the turbulent intensity increases with increasing Reynolds

139
number such a hypothesis is consistent with current
understanding of turbulent phenomena, although it is doubtful
that the actual standard deviation of liquid velocity will be
exactly one eighth the mean. It is also believed that the
stochastic distribution of wall superheat is due to the
distribution of nucleation sites. As has been demonstrated in
chapter 5, the nucleation site density typically increases
with increasing wall superheat. As the number of nucleation
sites increases, thermal interaction among neighboring sites
is likely, and thus it is expected that the standard deviation
of wall superheat increases with the mean wall superheat.
Whether or not the standard deviation of wall superheat is
actually one eighth the mean remains uncertain. Certainly,
further experimental investigation and analysis are required
to resolve this uncertainty.

CHAPTER 8
VAPOR BUBBLE GROWTH
8.1 Introduction
Numerous measurements of vapor bubble growth rates in
nucleate pool boiling have been reported in the literature
(Fritz and Ende, 1936; Staniszewski, 1959; Strenge et al.,
1961; Cole and Shulman, 1966a; Van Stralen et al., 1975;
Cooper and Chandratilleke, 1981; etc.) In general, the
experimental data of bubble radius can be curve-fitted using
a power law,
a (t) =Ktn (8-1)
where t is growth time. At otherwise identical conditions K
and n vary with different bubbles and display some stochastic
characteristics. The ensemble average of K for a large bulk
of bubbles at given conditions appears to depend on system
pressure, wall superheat, and boiling liquids, n is found to
be system pressure dependent. Typically n is approximately
0.5 for subatmospheric and atmospheric pressure and decreases
as the system pressure increases above one atmosphere. No
general bubble growth model is currently available to account
for such variations.
In contrast to pool boiling, few similar measurements of
140

141
vapor bubble growth rate under saturated flow boiling
condition were found in the literature. Cooper et al. (1983)
measured vapor bubble growth rate in boiling with water under
controlled liquid velocity. They found the growth rate
follows a power law and the exponent of the power law is
approximately 0.5. The system pressure effect was not
investigated. In this work, vapor bubble growth rates in
saturated flow boiling with R113 were measured using high
speed cinematography. The parametric influence of flow rate
and system pressure were examined from the experimental data.
The purpose of the measurements is to generate a data base for
flow boiling bubble growth rate and examine its dependence on
various flow and thermal parameters.
8.2 Facility and Methodology
The measurement of the bubble growth rate was performed
using the transparent flow boiling test section which was
described in detail in chapter 2. The boiling conditions of
the bulk two-phase mixture at the test section entrance is
controlled by the preheaters and the throttle valve downstream
of the test section. The procedures for obtaining the desired
boiling conditions have also been detailed in chapter 5. A
schematic diagram of the high speed cinematography arrangement
and illumination is displayed in Figure 8-1. The Hycam motion
picture camera equipped with a Vivitar 55 mm macro lens is
mounted on a tripod and is focused as close as physically

142
Figure 8-1. A schematic diagram of the high speed facility
for filming vapor bubble growth rate.
possible on an active nucleation site in order to achieve
maximum magnification. The camera is typically mounted at an
angle of approximately 30 degrees with the horizontal. The
motion picture camera was usually set at 6000 frames per
second and is adjustable by controlling the input voltage with
an autotransformer. Adequate illumination of the nucleation
site is crucial for obtaining quality images. Therefore,
considerable effort was put forth in testing the influence of
different lighting directions, diffusion, and intensity in
order to achieve optimum illumination. The illumination
system that was found to give the best quality images includes

143
four 500 Watt lamps positioned for front-lighting. Two lamps
provide a line source and two other lamps provide a point
source. The lighting angle was set at about the viewing angle
of the macro lens. The light intensity incident on the
bubbles was adjusted by carefully moving lamps toward or away
from the test section to match the illumination requirement
which was determined with a lightmeter.
The measurements of bubble size were made from the film
negative using a microfilm reader. Two dimensions were
measured for each bubble: horizontal and vertical chords. The
shape of the bubble was assumed to be an oblate sphere so that
the equivalent radius of a sphere with the same volume is
given by
a ( t) (djtijjidytdy) 2) ^ (8-2)
where d is the chord length of a bubble measured on the
projection and M is the magnification factor; subscripts H and
V denote the horizontal and vertical dimensions, respectively.
Magnification factors are determined based on the principle of
geometric optics and using a scale placed at the location of
the bubble. The high speed film was analyzed frame by frame.
The time interval between two consecutive frames can be
interpolated from a film speed chart provided by the
manufacturer of the Hycam camera. The bubble was assumed to
be initiated from the frame prior to the one in which the
bubble is just measurable. The uncertainty of the length

144
measurement is 0.05 mm and that of the magnification factor
is about 2%. Therefore, the uncertainty of the resultant
equivalent radius of the bubble is approximately 7%.
8.3 Results and Discussions
Experimental data of bubble growth rate were presented in
the form of bubble radius vs growth time as shown in Figures
8-2 through 8-11. The data obtained from the same roll of
film were placed in one figure in which each symbol represents
a growth history of a single bubble. It can be seen that the
bubble growth rates are scattered which is similar to the
observations by many investigators of pool boiling. Ensemble
averages of the growth rate were made for the bubbles at each
set of conditions, and may be represented in the form of
equation (8-1) In order to examine the parametric influences
of pressure, wall superheat, and fluid flow on bubble growth,
the values of K and n were tabulated in Table 8-1. It is seen
from the table that the exponent n is about 0.5 at the system
pressure of about 1.5 bar and decreases as the pressure is
elevated. This trend is consistent with that in pool boiling.
The influence of other conditions on n is not clear from these
data. It is not possible to draw any conclusion from the data
concerning the amplitude of bubble growth rate. It has been
recognized that wall superheat is the driving force for bubble
growth and the measured mean wall superheat may not be the one
that an individual nucleation site sees. In fact, the wall

Radius a(t) (mm)
145
Time t (ms)
Figure 8-2. Time history of bubble growth

Radius a(t) (mm)
146
Tme t (ms)
Figure 8-3. Time history of bubble growth

Radius a(t) (:
147
Time t (ms)
Figure 8-4. Time history of bubble growth.

Radius a(t) (mm)
148
Time t (ms)
Figure 8-5. Time history of bubble growth

Radius a(t) (mm)
149
Time t (ms)
Figure 8-6. Time history of bubble growth.

Radius a(t) (mm)
150
Time t (ms)
Figure 8-7. Time history of bubble growth

Radius a
151
B
B
0.15
0.10 -
0.05 -
0.00
0.0
G=184.6 kg/m8s
X=0.155
T =67.0 C
sat
qw=8.67 kW/m
AT =7.8 C
sat
A
M
V
0.5 1.0
Time t (ms)
K=0.086
n=0.46
1.5
Figure 8-8. Time history of bubble growth.
2.0

Radius a(t) (mm)
152
Time t (ms)
Figure 8-9. Time history of bubble growth.

Radius a(t) (mm)
Figure 8-10. Time history of bubble growth.

Radius a(t) (mm)
154
Time t (ms)
Figure 8-11. Time history of bubble growth.

155
Table 8-1. A Summary of Parameters Controlling Vapor
Bubble Growth Rate in Flow Boiling.
Run
P
bar
Ja
U,
m/s
Uy
m/s
K
n
1
1.40
13.26
0.28
2.80
0.101
0.49
2
1.50
8.64
0.44
2.54
0.091
0.51
3
1.52
8.03
0.57
3.42
0.082
0.48
4
1.55
8.00
0.55
3.42
0.079
0.50
5
1.65
7.17
0.50
2.89
0.080
0.48
6
1.72
6.55
0.49
2.89
0.089
0.47
7
1.85
6.36
0.46
2.90
0.086
0.46
8
2.06
6.18
0.38
2.67
0.080
0.44
9
2.18
5.00
0.32
2.64
0.076
0.44
10
2.51
4.53
0.27
2.46
0.068
0.44
superheat beneath a growing bubble not only varies with time
but also is probably dependent on the growth rate. In order
for the experimental data to be more useful, measurements
should be made for bubbles from an ensemble of nucleation
sites on the surface to account for the spatial non
uniformity. And more data are required to discriminate
statistical variations.

156
8.4 Conclusions and Discussions
From the limited number of experimental data obtained
here, it is seen that in flow boiling the growth exponent n
decreases with increasing system pressure. A liquid or vapor
velocity influence on n has not been observed. Since the
measurement did not include an ensemble average of many
bubbles, a comparison concerning the amplitude of the growth
rate can not be made from these data.
Since the vapor bubble growth in saturated flow boiling
typically follows a diffusion-controlled growth model, the
analysis of heat transfer during the bubble growth would be
helpful in understanding the influence of liquid turbulence on
the growth rate. A gross estimation has been made for the
heat flux transmitted from the surrounding liquid to the vapor
bubble due to the bulk convection and the latent heat
transport due to bubble growth. The bulk convection to the
bubble was estimated using a heat transfer correlation for
flow over a sphere. For a boiling condition of G=184.6 kg/m2-
s, X=0.155, TMt=67.0 C, qw=8.67 kW/m2, and ATMt=7.8 C, the
latent heat transport was found to be typically two orders of
magnitude larger than the bulk convection based on measured
bubble growth rate. Therefore, the bulk turbulence is not
expected to exert an appreciable influence on the vapor bubble
growth in saturated flow boiling. This crude analysis is
consistent with the present experimental observations.

CHAPTER 9
CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH
This chapter summarizes the major research
accomplishments in this work and provides suggestions for
future research of flow boiling phenomena.
9.1 Accomplishments and Findings
The research contained herein has advanced the
understanding of flow boiling fundamentals in the following
manner:
1. Measurements of two-phase heat transfer coefficients
with and without boiling were made over a wide range of
conditions. The heat transfer of flow boiling has been
decomposed into two components: macroconvection due to the
bulk turbulence, which is equivalent to the heat transfer of
the two-phase mixture without boiling, and microconvection due
to the ebullition process, which is the total heat transfer
less that of macroconvection. The experimental data have
conclusively demonstrated that the microconvection component
of saturated flow boiling heat transfer is significant in
almost all phases of boiling and its contribution to the total
heat transfer becomes dominant as heat flux increases.
2. The initiation and sustaining incipience superheats
157

158
were found to be insensitive to the bulk turbulence for
saturated flow boiling with R113 but they strongly depend on
the system pressure as well as the cooling history of the
heating surface prior to boiling. The hysteresis can be
eliminated if the minimum temperature of the liquid prior to
boiling is maintained above a threshold. Existing incipience
models have been modified and applied to explain the
experimental results.
3. Nucleation site density in saturated forced
convection boiling was measured over a wide range of flow and
thermal conditions. The mean vapor velocity, heat flux, and
system pressure appear to exert a dominant parametric
influence on the nucleation site density. Nucleation site
density is also observed to increase with decreasing liquid
film thickness but the change is marginal. The critical
radius of the cavity is an important parameter in
characterizing the nucleation process but by itself it is not
sufficient to correlate nucleation site density for saturated
flow boiling.
4. Based on experimental observations and theoretical
reasoning, an analytical model was developed for the
prediction of vapor bubble detachment diameters in flow and
pool boiling. The model utilizes a force balance which
follows a similar form as that used by Klausner et al. (1993) .
For an upward facing heating surface, the model has been
tested over the following range of conditions: pressure, 0.02-

159
2.8 bar; Jakob number, 4-869; gravity, 0.014-lg; wall
superheat, 5.5-18.0 C; and liquid velocity, 0.35-1.0 m/s. It
was demonstrated that over the wide range of conditions
considered, the accuracy of the detachment diameters predicted
using the present model is significantly improved over
existing correlations. The only required input is the vapor
bubble growth rate. The good agreement between the model and
experimental data lends credence to the hypothesis that the
growth force is dominant compared to the surface tension force
at the point of detachment. The bounds of validity of this
hypothesis have yet to be explored.
5. Using the present bubble detachment model, the pdf of
vapor bubble detachment diameters in saturated flow boiling
can be successfully predicted from the specified pdf's of wall
superheat and liquid velocity.
6. Measurements of saturated flow boiling vapor bubble
growth rate have been obtained. Based on a limited number of
experimental data obtained herein, the vapor bubble growth
rate can be expressed as a function of time using a power law.
The exponent of the power law decreases with increasing system
pressure. Any effects of liquid velocity on the vapor bubble
growth rate could not be distinguished.
9.2 Suggestions for Future Research
The motivation for the present research is that with
sufficient understanding of the flow boiling ebullition

160
process it should be possible to construct a universally valid
flow boiling heat transfer correlation. Although significant
progress toward this goal has been achieved in this work, many
uncertainties remain. In order to build on the present
research future investigations should concentrate on:
1. Developing reliable vapor bubble growth rate models
for pool and flow boiling.
2. Developing a model for predicting the nucleation site
density for flow boiling based on the knowledge of heating
surface characteristics.
3. Expanding the validity of the bubble detachment model
to include boiling with different heating surface
orientations, i.e. vertical upflow and downflow. Testing the
bounds of validity of the hypothesis that the surface tension
force is negligible at the point of vapor bubble detachment.
4. Developing a reliable heat transfer correlation due
to macroconvection in saturated flow boiling.
5. Developing a model for predicting the incipience
superheat of boiling with highly wetting liquids based on a
non-linear temperature profile near the wall.
6. Developing a generalized flow boiling heat transfer
correlation based on an empirical understanding of vapor
bubble incipience, growth, and detachment.

APPENDIX A
HEAT TRANSFER COEFFICIENT, PRESSURE DROP, AND
LIQUID FILM THICKNESS IN STRATIFIED TWO-PHASE FLOW
AP
S
G
X
Uy
kW/m2-C
mmH20
iron
c
kg/m2-s
m/s
m/s
0.947
16.58
5.5
59.3
203.2
.134
0.55
3.31
0.924
17.08
5.4
59.0
203.4
.133
0.56
3.30
0.674
5.58
5.6
58.5
140.9
.157
0.36
2.76
0.712
5.42
5.4
58.0
141.3
.154
0.38
2.72
0.979
24.04
5.9
59.8
254.6
.094
0.67
2.92
0.977
25.26
5.9
59.5
258.6
.089
0.68
2.84
0.715
21.47
6.6
58.5
214.6
.053
0.53
1.50
0.758
17.72
6.6
59.4
218.3
.047
0.54
1.32
1.308
37.95
3.0
60.7
221.8
.191
1.05
4.39
0.802
12.33
6.4
58.1
196.2
.096
0.48
2.47
0.799
14.79
6.0
58.5
195.3
.096
0.50
2.39
0.636
17.80
6.9
57.5
192.4
.062
0.45
1.64
0.674
23.71
7.0
58.0
192.0
.058
0.44
1.52
0.446
7.93
7.0
57.3
126.0
.054
0.29
0.94
0.485
10.17
6.8
56.6
126.5
.056
0.30
0.99
0.631
5.80
5.1
57.5
131.1
.140
0.38
2.30
0.652
6.56
5.0
57.0
131.5
.137
0.38
2.28
0.446
7.93
7.0
57.3
126.0
.054
0.29
0.94
0.485
10.17
6.8
56.6
126.5
.056
0.30
0.99
0.631
5.80
5.1
57.5
131.1
.140
0.38
2.30
0.652
6.56
5.0
57.0
131.5
.137
0.38
2.28
161

162
(Continued)
*w
AP
S
Tt
G
X
U,
Uy
kW/m2-C
mmH20
mm
C
kg/m2-s
m/s
m/s
0.824
7.57
3.0
58.9
135.7
.202
0.61
2.99
0.844
8.43
2.9
58.2
135.9
.200
0.64
3.01
1.077
19.05
1.8
58.8
135.8
.298
0.92
4.20
1.066
18.44
1.8
59.6
135.8
.297
0.89
4.10
1.084
18.94
1.8
59.3
135.7
.296
0.91
4.12
0.620
13.47
7.8
57.4
159.0
.069
0.33
1.58
0.608
13.53
7.5
57.4
159.2
.069
0.34
1.57
0.754
7.65
6.3
58.1
163.1
.124
0.39
2.65
0.726
8.95
6.2
59.0
162.8
.123
0.40
2.54
0.849
10.63
4.3
58.6
163.0
.167
0.55
3.17
0.851
10.85
4.2
58.4
163.2
.167
0.55
3.19
0.886
11.20
4.1
58.6
163.1
.166
0.57
3.13
1.184
28.57
2.1
59.5
167.7
.267
0.99
4.62
1.212
29.67
2.1
59.8
167.1
.268
1.02
4.58
0.658
16.03
8.8
58.0
200.9
.041
0.37
1.24
0.654
17.12
8.8
57.8
200.2
.042
0.37
1.28
0.784
16.86
6.6
58.3
203.4
.089
0.48
2.39
0.807
14.94
6.6
58.0
203.3
.090
0.48
2.44
0.988
18.16
3.9
58.9
204.1
.143
0.77
3.31
0.966
18.10
4.0
58.7
204.0
.143
0.74
3.36
1.246
36.08
2.2
60.0
206.9
.206
1.30
4.35
1.253
35.15
2.3
60.3
207.0
.204
1.25
4.29
1.235
38.07
2.6
60.4
228.7
.176
1.26
4.14
1.292
38.81
2.6
60.7
228.9
.173
1.26
4.04
0.821
22.57
6.9
59.0
229.2
.051
0.54
1.54
0.780
23.57
7.1
57.9
229.3
.056
0.52
1.76
0.895
19.25
6.4
58.9
232.8
.094
0.56
2.82

163
(Continued)
^mac
AP
S
T
xsat
G
X
U,
Uy
kW/m2-s
ltunH20
mm
c
kg/m2-s
m/s
m/s
0.893
19.30
6.7
58.8
232.8
.095
0.54
2.89
1.055
25.20
3.8
59.4
232.8
.133
0.91
3.46
1.045
27.08
4.1
59.8
232.5
.133
0.84
3.46
0.818
27.10
8.8
58.7
261.9
.044
0.49
1.71
0.807
28.33
8.7
58.8
262.0
.042
0.49
1.62
0.970
23.13
7.9
59.6
265.4
.072
0.54
2.62
0.979
24.03
7.1
59.5
265.2
.071
0.59
2.48
1.162
31.02
4.3
60.1
265.0
.118
0.92
3.51
1.125
32.92
4.4
60.8
265.3
.114
0.91
3.35
1.335
48.58
2.5
61.1
265.1
.163
1.51
4.35
1.363
49.44
2.5
61.4
265.0
.163
1.50
4.31
0.870
23.42
7.1
58.8
253.0
.076
0.57
2.57
0.908
22.03
7.1
58.7
252.8
.075
0.57
2.54
0.636
15.09
6.8
57.2
179.6
.056
0.43
1.39
0.667
17.37
6.7
57.5
177.3
.056
0.43
1.35
0.536
11.41
7.1
56.5
125.6
.065
0.28
1.17
0.524
11.62
6.9
56.7
125.7
.063
0.29
1.11
1.232
37.40
3.4
60.4
250.4
.144
1.07
3.85
1.210
36.97
3.4
60.3
250.3
.144
1.07
3.86
1.210
39.36
3.3
60.6
250.4
.143
1.12
3.78
1.221
38.19
3.3
60.5
250.4
.143
1.10
3.80

APPENDIX B
NUCLEATION SITE DENSITY IN FORCED CONVECTION BOILING
n/A
Tt
G
X
S
u,
Vtv
Qw
ATMt
cur2
C
kg/m2-s
mm
m/s
m/s
kW/m2
C
0.64
59.1
214.9
.20
3.5
.85
4.65
19.3
14.4
1.28
58.9
214.1
.16
4.3
.72
3.98
19.3
15.6
3.00
58.7
214.5
.13
5.3
.60
3.53
19.3
16.4
4.92
58.3
215.0
.12
6.1
.53
3.24
19.3
17.2
6.00
57.9
214.3
.10
7.1
.47
2.83
19.3
17.6
7.28
57.9
214.4
.08
7.8
.43
2.49
19.3
17.7
9.42
57.8
214.4
.05
9.5
.37
1.71
19.3
17.6
3.41
60.1
273.1
.10
6.2
.68
3.27
19.3
14.3
5.15
59.6
250.9
.09
6.3
.62
2.97
19.3
15.2
7.05
59.3
226.1
.10
6.3
.55
2.98
19.3
15.5
8.10
58.5
188.4
.11
6.3
.46
2.56
19.3
17.3
9.09
58.1
150.7
.12
6.4
.35
2.39
19.3
18.0
1.18
58.0
154.4
.23
4.2
.48
4.22
19.3
15.6
1.93
58.0
175.7
.17
5.2
.48
3.75
19.3
15.9
3.46
58.1
214.4
.11
6.8
.48
3.14
19.3
16.9
4.39
58.5
236.3
.09
7.6
.49
2.91
19.3
16.5
5.59
58.8
261.9
.06
8.7
.48
2.35
19.3
15.9
5.16
56.1
121.1
.24
3.3
.47
3.55
20.7
17.2
4.95
56.3
140.9
.20
3.8
.50
3.61
20.7
17.6
4.66
56.8
162.3
.17
4.0
.57
3.51
20.7
16.9
4.18
58.3
224.4
.13
4.4
.76
3.57
20.7
15.8
164

165
(Continued)
n/A
Tt
G
X
S
Uy
<3w
AT .
sat
cm'2
C
kg/m2-s
mm
m/s
m/s
kW/m2
c
4.78
57.8
192.0
.15
4.1
.69
3.54
20.7
15.9
0.97
59.1
261.7
.09
7.9
.52
3.10
13.8
13.0
1.62
58.8
243.4
.07
7.6
.51
2.50
13.8
14.0
2.26
58.4
218.3
.09
7.3
.47
2.68
13.8
14.7
3.24
57.8
195.3
.08
7.8
.39
2.36
13.8
16.1
4.21
57.6
175.6
.08
8.0
.35
1.99
13.8
16.5
5.50
57.2
151.6
.09
7.7
.31
1.89
13.8
17.3
6.15
56.9
125.7
.10
7.4
.26
1.87
13.8
18.0
2.44
57.2
202.7
.07
7.6
.42
2.14
13.8
14.0
3.72
57.3
202.8
.07
7.5
.43
2.15
14.1
15.2
5.47
57.3
202.9
.07
7.6
.42
2.16
15.8
17.9
9.17
57.4
202.8
.07
7.7
.42
2.16
17.9
16.8
6.76
57.5
202.5
.07
7.3
.44
2.13
16.7
16.5
2.15
57.3
199.4
.10
6.5
.47
2.70
14.4
14.8
3.53
57.3
199.3
.10
6.6
.47
2.75
15.4
15.6
4.60
57.4
202.4
.09
6.5
.48
2.70
16.5
16.5
7.20
57.4
203.1
.09
6.6
.48
2.65
17.7
16.6
8.96
57.3
202.8
.09
6.2
.52
2.65
19.1
17.2
1.60
56.4
209.8
.12
6.1
.52
3.63
17.7
16.3
3.12
56.6
209.9
.12
6.0
.52
3.58
19.9
18.1
5.34
56.6
210.2
.12
6.3
.50
3.69
21.2
18.5
8.45
56.8
208.4
.12
5.8
.53
3.58
23.2
17.6
14.39
75.9
217.2
.16
6.4
.50
2.95
17.3
11.3
12.17
72.9
225.3
.14
6.1
.55
2.85
17.3
11.6
8.67
69.6
235.7
.12
5.8
.63
2.86
17.3
12.3
6.20
65.8
243.3
.12
4.9
.76
2.95
17.3
13.4
4.19
60.8
254.3
.10
4.4
.91
2.96
17.3
14.2

166
(Continued)
n/A
T*
G
X
S
Uy
qw
cm'2
C
kg/m2-s
mm
m/s
m/s
kW/m2
C
2.39
56.5
254.7
.09
4.5
.89
3.01
17.3
15.2
10.38
73.3
171.3
.25
4.4
.51
3.46
17.3
11.3
8.05
70.5
179.5
.22
4.4
.55
3.46
17.3
12.0
6.40
68.1
183.7
.20
4.4
.58
3.47
17.3
12.5
4.50
65.1
187.0
.18
4.2
.63
3.41
17.3
13.5
3.75
62.3
195.3
.16
4.4
.63
3.44
17.3
14.1
2.65
60.1
192.0
.16
4.3
.65
3.50
17.3
14.4
2.11
58.0
199.0
.14
4.4
.67
3.44
17.3
15.0
1.73
55.5
206.7
.13
4.4
.70
3.52
17.3
16.0

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BIOGRAPHICAL SKETCH
Ling-Zhong (L.Z.) Zeng was born on February 26, 1965, in
Guangxi, China. He was enrolled in Tsinghua University,
Beijing, in 1981. He majored in fluid mechanics, and received
his Bachelor of Science degree in 1986. He received his
master's degree from Tsinghua University in 1989. He married
Tang Yong in February 1990 and joined the Ph.D. program in
mechanical engineering at the University of Florida in May
1990. Since then he has been working as a research and
teaching assistant in the department of mechanical
engineering.
177

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
L
s F. Klausner, Chair
istant Professor of
chanical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor, of/Philosophy.
C.K. Hsieh
Professor of
Mechanical Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
D.Y. Goswami
Professor of
Mechanical Engineering

I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree ofJDoctor of Philosophy.
//Xei
Reiwei Mei
Assistant Professor of
Aerospace Engineering,
Mechanics and Engineering
Science
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
GIwn
aie in
S. Anghaie
Professor of
Nuclear Engineering Sciences
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
August 1993
Winfred M. Phillips
Dean, College of Engineering
Dean, Graduate School

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34
Vapor Reynolds Number Rey (xlO )
o
Du
<1
Oh
O
m
ra
£
Oh
0 2 4 6 8 10 12
4
Liquid Reynolds Number Ret (xlO )
Figure 3-3. Pressure drop in horizontal two-phase flow.
Figure 3-3 displays the pressure drop, AP, as a function
of Re, and Rev. In contrast to the case of h^., AP is found to
be better correlated with Re, rather than Rev. This result
suggests that the principle of analogous energy and momentum
transport in incompressible single phase flow may not be
appropriate for stratified two-phase flow in a boiling system
where strong interfacial waves are observed. For two-phase
flow with strong interfacial waves, Andritsos and Hanratty


Ill
exponent n. For subatmospheric and atmospheric pressure pool
boiling, Cole and Shulman (1966) and Van Stralen et al. (1975)
demonstrated that it is satisfactory to assume n is 0.5. For
high pressure and reduced gravity data, n is found to be less
than 0.5 and depends on pressure and gravity, thus more
information is required to estimate K and n. Using equation
(6-36) to approximate the bubble growth rate, the growth force
Fdu may be estimated from
2 2
Fdu=-ptnKn (^C^+nin-D) a* n. (6-37)
Z
A balance between Fj,, and Fb results in an explicit expression
for predicting the vapor bubble departure diameter,
dd=2 (-7- (^-Csn2+n(n-l))) (6-38)
4 g 2 ^
This equation has been used for the following comparison with
pool boiling experimental data.
Subatmospheric Pressure. Earth Gravity. A comparison
between the measured and predicted departure diameters for
subatmospheric pressure, earth gravity pool boiling is shown
in Figure 6-3. Experimental departure diameters were obtained
from Cole and Shulman (1966) and Van Stralen et al. (1975).
For the 105 data points considered, which encompass six
different fluids and a pressure range of 0.02-0.7 atm and span
two order of magnitude in departure diameter, the comparison


93
dd~C0^
OD
(6-16)
where D is the hydraulic pipe diameter, tw is the wall shear
stress, and C0=O.O15 is an empirically determined constant.
Sliding bubbles were not considered. Koumoutsos et al. (1968)
studied the detachment of vapor bubble at an artificial
nucleation site in forced convection boiling. They observed
that soon after incipience vapor bubbles begin to slide along
the heating surface until they lift off at some finite
distance downstream. They measured the lift-off diameters and
arrived at the following correlation,
(6-17)
where dL is the lift-off diameter, d^ is the departure
diameter for pool boiling, U is the mean liquid velocity, and
epyp/a=0.015 s/m and m=4 were determined empirically. It is
noted that when U becomes sufficiently large, equation (6-17)
predicts negative lift-off diameters which casts doubt on its
ability to correctly capture the physics governing vapor
bubble lift-off. Cooper et al. (1983) study the growth and
departure of vapor bubbles with laminar upflow of n-hexane
over a flat plate. They also reported that vapor bubbles
typically slide or roll along the heating surface prior to
lifting off and concluded the departure point was not well
defined. They also suggested that the simple force balances


121
b
a
'll
QJ
Q)
B
cti
r*4
n
CL)
(h
3
(0
O*
O
Mean Liquid Velocity uz (m/s)
Figure 6-7. Departure diameter variation with mean liquid
velocity at approximately same ATMt.
(1993) are used here for comparison. Figure 6-7 shows the
measured departure diameters as a function of mean liquid
velocity in which the wall superheat was maintained in a range
of 14-16 C. Also shown are the predicted departure diameters
using the present departure model for ATsat=15C and the model
presented by Klausner et al. (1993) for ATMt=15C and <^=0. It
is seen that good agreement exists with the present model. A


165
(Continued)
n/A
Tt
G
X
S
Uy
<3w
AT .
sat
cm'2
C
kg/m2-s
mm
m/s
m/s
kW/m2
c
4.78
57.8
192.0
.15
4.1
.69
3.54
20.7
15.9
0.97
59.1
261.7
.09
7.9
.52
3.10
13.8
13.0
1.62
58.8
243.4
.07
7.6
.51
2.50
13.8
14.0
2.26
58.4
218.3
.09
7.3
.47
2.68
13.8
14.7
3.24
57.8
195.3
.08
7.8
.39
2.36
13.8
16.1
4.21
57.6
175.6
.08
8.0
.35
1.99
13.8
16.5
5.50
57.2
151.6
.09
7.7
.31
1.89
13.8
17.3
6.15
56.9
125.7
.10
7.4
.26
1.87
13.8
18.0
2.44
57.2
202.7
.07
7.6
.42
2.14
13.8
14.0
3.72
57.3
202.8
.07
7.5
.43
2.15
14.1
15.2
5.47
57.3
202.9
.07
7.6
.42
2.16
15.8
17.9
9.17
57.4
202.8
.07
7.7
.42
2.16
17.9
16.8
6.76
57.5
202.5
.07
7.3
.44
2.13
16.7
16.5
2.15
57.3
199.4
.10
6.5
.47
2.70
14.4
14.8
3.53
57.3
199.3
.10
6.6
.47
2.75
15.4
15.6
4.60
57.4
202.4
.09
6.5
.48
2.70
16.5
16.5
7.20
57.4
203.1
.09
6.6
.48
2.65
17.7
16.6
8.96
57.3
202.8
.09
6.2
.52
2.65
19.1
17.2
1.60
56.4
209.8
.12
6.1
.52
3.63
17.7
16.3
3.12
56.6
209.9
.12
6.0
.52
3.58
19.9
18.1
5.34
56.6
210.2
.12
6.3
.50
3.69
21.2
18.5
8.45
56.8
208.4
.12
5.8
.53
3.58
23.2
17.6
14.39
75.9
217.2
.16
6.4
.50
2.95
17.3
11.3
12.17
72.9
225.3
.14
6.1
.55
2.85
17.3
11.6
8.67
69.6
235.7
.12
5.8
.63
2.86
17.3
12.3
6.20
65.8
243.3
.12
4.9
.76
2.95
17.3
13.4
4.19
60.8
254.3
.10
4.4
.91
2.96
17.3
14.2


101
mass and the liquid. Again, since the contact diameter
approaches zero near the point of departure as argued for the
surface tension force, the hydrodynamic pressure force is also
negligibly small.
The contact pressure force may be calculated from
ndl 2o
Fcp 4 Xi
(6-26)
where rr is the radius of curvature at the base of the bubble.
Photographs of growing vapor bubbles from Van Stralen et al.
(1975) suggest d/rTl, and it is clear that the contact
pressure force may be neglected at the point of departure
since it is small compared to the surface tension force given
by equation (6-23).
Growth Force. Although the effect of the bubble growth
rate on vapor bubble departure has been empirically accounted
for in various bubble departure correlations, an accurate
expression for the growth force is not available in the
literature. Ruckenstein (1961) and Roll and Myers (1964) gave
estimates of the vapor bubble growth force for pool boiling,
but when used in their bubble departure model unsatisfactory
results were obtained. Ruckenstein estimated the growth force
from,
(6-27)


4
evidence was obtained to demonstrate that the heat transfer
contribution due to the ebullition process is significant in
almost all phase of boiling. Experimental data on the
incipience wall superheat, nucleation site density, and vapor
bubble growth rate for saturated flow boiling have been
gathered over a wide range of flow and thermal conditions.
The parametric influence of two-phase flow conditions on the
ebullition process have been analytically investigated.
An analytical model has been developed for the prediction
of vapor bubble departure and lift-off diameters for both pool
and flow boiling. The model was compared against all
experimental data available in the literature, and excellent
agreement has been achieved. Based on this bubble detachment
model, an analytical approach was proposed for predicting
vapor bubble detachment diameter probability density functions
(pdf's) for a specified wall superheat pdf and liquid velocity
pdf.


105
measurement indicates that the average velocity of the bubble
and that of the liquid are at least close, and it provides
valuable evidence supporting the above hypothesis. The
hypothesis that the velocities of the sliding bubble and
surrounding liquid are approximately the same is supported by
the experimental data of bubble lift-off in flow boiling
obtained by Bernhard (1993) which shows that the liquid
velocity basically exerts no influence on the average vapor
bubble lift-off diameter.
Based on the preceding force analysis, a summary of all
forces acting on a vapor bubble growing on a horizontal
heating surface is given in Table 6-1.
6.3.2 Expressions for Bubble Departure and Lift-off Diameters
Based on the proceeding discussion, the x- and y-momentum
equations for a vapor bubble at the point of departure are
approximately
Fgs+Fdu sine^O (6-32)
and
F^COSe^F^+F^O, (6-33)
where Fqs, F*,, FsL, and Fb are determined by equations (6-21) ,
(6-29), (6-22), and (6-20), respectively. The departure
diameter dd and inclination angle 0¡ are unknown and can be
obtained by solving equations (6-32) and (6-33) simultaneously
for a known growth rate a(t) and liquid velocity u,. Although


B NUCLEATION SITE DENSITY IN FORCED
CONVECTION BOILING 164
REFERENCES 167
BIOGRAPHICAL SKETCH 177
vii


71
fixed heat flux and liquid film thickness, the data appear to
fall on a single curve. As the heat flux is increased, the
curve shifts toward higher nucleation site density.
Therefore, when investigating the influence of the flow
parameters on n/A the heat flux will be maintained constant.
Upon examination of equations (5-3) and (5-4) it is possible
that the trend shown in Figure 5-6 is due to either increasing
G or uf instead of increasing Uy. To sort out whether G, ut,
or Uy has a controlling influence on n/A figures 5-7 and 5-8
have been prepared. In Figure 5-7, n/A is shown to increase
with increasing G when u, and qw are fixed, and decreases with
increasing G when S and qw are fixed, and thus it appears that
parameters other than G are controlling n/A. In Figure 5-8
n/A is shown to decrease with increasing uf for a fixed G and
qw. For the case of a fixed S and qw n/A also decreases with
increasing u, but the shape of the curve is significantly
different. When comparing Figures 5-6 and 5-8, it appears
that n/A is better behaved when displayed as a function of Uy.
Further evidence of this supposition is provided in Figure 5-9
where n/A is displayed as a function of Uy for qw=19.3 kW/m2,
TMt=58 C, G=215 kg/m2-s, and u,=0.58 and 0.48 m/s. It is seen
that all of the data approximately fall on a single curve,
thus demonstrating the governing influence of the mean vapor
velocity on nucleation site density. The liquid film
thickness is also shown as a function of Uy. Thus, the effect
of liquid film thickness on n/A might also be included in


9
O 10 20 30 40 50
tb-t. (c)
Figure 2-3. Calibration curve of heat loss for preheaters.
safe operating pressure of the square pyrex section.
Following the test section, the R113 two-phase mixture
condenses in a shell and tube water cooled heat exchanger to
return to the liquid storage tank.
2.2 Construction of Transparent Test Section
The major difficulties associated with fabricating a
transparent flow boiling refrigerant based test section and


11
25 x 25 mm ID square pyrex glass tube that is 4 mm thick and
0.457 m long as depicted in Figure 2-4. A 0.13 mm thick and
22 mm wide nichrome strip, used as a heating and boiling
surface, has been adhered to the lower inner surface of the
square tube with epoxy. Six equally spaced 36 gauge type E
thermocouples were located underneath the nichrome strip using
high thermal conductivity epoxy. The mean wall temperature of
the nichrome strip was obtained by averaging the readings from
these six thermocouples. The test section was connected to
the facility with a brass block on either side. Each end of
the nichrome strip was bolted to the block to maintain good
electrical contact. Epoxy was used to seal gaps between the
glass tube and brass blocks. The facility was pressurized
with air to 30 psig and leak-checked prior to introducing
R113. Due to safety considerations, the facility has not been
operated at pressures above 30 psig.
2.3 Development of Capacitance Based Film Thickness Sensors
2.3.1 Introduction
It has been observed that in a horizontal saturated flow
boiling system, vapor-liquid flow is usually in a stratified
or annular flow regime due to the influence of gravity.
Research involving this flow regime requires knowledge of the
liquid film thickness distribution along the wall of a duct.
Many of the techniques used to measure liquid film thickness
and volume fraction were summarized by Hewitt (1978) and Jones


143
four 500 Watt lamps positioned for front-lighting. Two lamps
provide a line source and two other lamps provide a point
source. The lighting angle was set at about the viewing angle
of the macro lens. The light intensity incident on the
bubbles was adjusted by carefully moving lamps toward or away
from the test section to match the illumination requirement
which was determined with a lightmeter.
The measurements of bubble size were made from the film
negative using a microfilm reader. Two dimensions were
measured for each bubble: horizontal and vertical chords. The
shape of the bubble was assumed to be an oblate sphere so that
the equivalent radius of a sphere with the same volume is
given by
a ( t) (djtijjidytdy) 2) ^ (8-2)
where d is the chord length of a bubble measured on the
projection and M is the magnification factor; subscripts H and
V denote the horizontal and vertical dimensions, respectively.
Magnification factors are determined based on the principle of
geometric optics and using a scale placed at the location of
the bubble. The high speed film was analyzed frame by frame.
The time interval between two consecutive frames can be
interpolated from a film speed chart provided by the
manufacturer of the Hycam camera. The bubble was assumed to
be initiated from the frame prior to the one in which the
bubble is just measurable. The uncertainty of the length


160
process it should be possible to construct a universally valid
flow boiling heat transfer correlation. Although significant
progress toward this goal has been achieved in this work, many
uncertainties remain. In order to build on the present
research future investigations should concentrate on:
1. Developing reliable vapor bubble growth rate models
for pool and flow boiling.
2. Developing a model for predicting the nucleation site
density for flow boiling based on the knowledge of heating
surface characteristics.
3. Expanding the validity of the bubble detachment model
to include boiling with different heating surface
orientations, i.e. vertical upflow and downflow. Testing the
bounds of validity of the hypothesis that the surface tension
force is negligible at the point of vapor bubble detachment.
4. Developing a reliable heat transfer correlation due
to macroconvection in saturated flow boiling.
5. Developing a model for predicting the incipience
superheat of boiling with highly wetting liquids based on a
non-linear temperature profile near the wall.
6. Developing a generalized flow boiling heat transfer
correlation based on an empirical understanding of vapor
bubble incipience, growth, and detachment.


67
Figure 5-3. A typical photograph of nucleation sites on a
boiling surface (flow direction is from left
to right).
or vapor velocity, uv, was maintained constant. The
nucleation site density, n/A, is shown as a function of wall
superheat, AT^, in Figure 5-4. It is seen from Figure 5-4
that the n/A data can not be correlated with AT^. In light
of Figure 5-1 and equations (5-1) and (5-2), the behavior of
n/A with ATMt is considered to be anomalous. In order to
demonstrate that the observed behavior is not simply due to


116
Apart from the present model the best correlations are those
of Fritz (1936) and Cole and Rohsenow (1969) which have
relative deviations of 18%.
Elevated Pressure. Earth Gravity. The elevated pressure
and reduced gravity departure results are not conclusive since
the number of data points available are small. Nevertheless,
as long as the growth rate is specified satisfactory results
can be obtained using the present model. For the elevated
pressure case 11 departure data points are available which
were obtained by Staniszewski (1959) using two fluids. The
pressure ranges from 1.9 to 2.8 atms. The experimental growth
rate data available are difficult to analyze since at certain
times the bubble diameters appear to have a step change in
magnitude. Nevertheless, equation (6-38) is used to solve for
the departure diameter using the specified growth rate, and
the predicted departure diameters are compared with the
measured values in Table 6-3. Also shown in Table 6-3 are the
experimentally determined values of K and n which were used
with equation (6-38) It is seen that at the elevated
pressures the value for n ranges from 0.24 to 0.38 which
represents a decrease in bubble growth rate. This trend is in
agreement with Griffith's (1958) bubble growth model. As is
seen from Table 6-2, the relative deviation for this set of
data using the present model is 26%, which is high compared
with the subatmospheric and atmospheric pressure data. The


125
B
B
2
(d
p.
QJ
Q
tu
+j
o
xl
0)
(h
Oh
1.0
0.8 -
0.6
0.4 -
0.2 -
Flow Boiling Vapor
Bubble Departure
TMt=60 C
* AT -10 C
Mi
V ATmt=15 C
AT-t=20 'C
A A
A A
0.0
0.0 0.2 0.4 0.6 0.8
Mean Liquid Velocity ut (m/s)
1.0
Figure 6-9. Departure diameter variation with mean liquid
velocity and ATMt.
consistent with experimental observations. In addition,
Figure 6-10 shows that the departure diameter decreases with
increasing inclination angle. This trend is expected since
the inclination angle should increase with increasing u, and
the trend in Figure 6-7 shows the departure diameter decreases
with increasing velocity. In Figure 6-11 the predicted
inclination angle is shown as a function of liquid velocity at


6-12 Comparison between predicted and measured
lift-off diameter 128
7-1 Statistical distribution of bubble lift-off
diameter in flow boiling 135
7-2 Statistical distribution of bubble departure
diameter in flow boiling at constant ATMt 136
7-3 Statistical distribution of bubble departure
diameter in flow boiling at constant uf 137
8-1 A schematic diagram of the high speed facility
for filming vapor bubble growth rate 142
8-2 Time history of bubble growth 145
8-3 Time history of bubble growth 146
8-4 Time history of bubble growth 147
8-5 Time history of bubble growth 148
8-6 Time history of bubble growth 149
8-7 Time history of bubble growth 150
8-8 Time history of bubble growth 151
8-9 Time history of bubble growth 152
8-10 Time history of bubble growth 153
8-11 Time history of bubble growth 154
xii


BIOGRAPHICAL SKETCH
Ling-Zhong (L.Z.) Zeng was born on February 26, 1965, in
Guangxi, China. He was enrolled in Tsinghua University,
Beijing, in 1981. He majored in fluid mechanics, and received
his Bachelor of Science degree in 1986. He received his
master's degree from Tsinghua University in 1989. He married
Tang Yong in February 1990 and joined the Ph.D. program in
mechanical engineering at the University of Florida in May
1990. Since then he has been working as a research and
teaching assistant in the department of mechanical
engineering.
177


159
2.8 bar; Jakob number, 4-869; gravity, 0.014-lg; wall
superheat, 5.5-18.0 C; and liquid velocity, 0.35-1.0 m/s. It
was demonstrated that over the wide range of conditions
considered, the accuracy of the detachment diameters predicted
using the present model is significantly improved over
existing correlations. The only required input is the vapor
bubble growth rate. The good agreement between the model and
experimental data lends credence to the hypothesis that the
growth force is dominant compared to the surface tension force
at the point of detachment. The bounds of validity of this
hypothesis have yet to be explored.
5. Using the present bubble detachment model, the pdf of
vapor bubble detachment diameters in saturated flow boiling
can be successfully predicted from the specified pdf's of wall
superheat and liquid velocity.
6. Measurements of saturated flow boiling vapor bubble
growth rate have been obtained. Based on a limited number of
experimental data obtained herein, the vapor bubble growth
rate can be expressed as a function of time using a power law.
The exponent of the power law decreases with increasing system
pressure. Any effects of liquid velocity on the vapor bubble
growth rate could not be distinguished.
9.2 Suggestions for Future Research
The motivation for the present research is that with
sufficient understanding of the flow boiling ebullition


68
N
£
<
a
(*
CO
t
a>
o
a>
*4
W
t
O
* iI
-t->
(t
r <
a
t
£
15
10
5
0
qw=19.3kW/mz, T at=58C
G=215 kg/m^-s
5=6.3 mm
A u^O.48 m/s
u =3.6 m/s

A
A


4
A
S
8 10 12 14 16 18 20
Wall Superheat ATgat (C)
Figure 5-4. Nucleation site density as a function of wall
superheat for constant heat flux and
saturation temperature.
the experimental error, pool boiling nucleation site density
data were obtained using the current facility by filling the
test section with liquid and heating the nichrome strip while
the circulation pump was off. Therefore, the only net flow
was induced by the natural convection currents. The n/A data
for pool boiling are also displayed as functions of wall


139
number such a hypothesis is consistent with current
understanding of turbulent phenomena, although it is doubtful
that the actual standard deviation of liquid velocity will be
exactly one eighth the mean. It is also believed that the
stochastic distribution of wall superheat is due to the
distribution of nucleation sites. As has been demonstrated in
chapter 5, the nucleation site density typically increases
with increasing wall superheat. As the number of nucleation
sites increases, thermal interaction among neighboring sites
is likely, and thus it is expected that the standard deviation
of wall superheat increases with the mean wall superheat.
Whether or not the standard deviation of wall superheat is
actually one eighth the mean remains uncertain. Certainly,
further experimental investigation and analysis are required
to resolve this uncertainty.


26
ERDCD SERIES
E500 FLOW
METER
^RESISTORS
V_ KEITHLEY
590 CV Analyzer
12-MHZ 286-AT
t,
ACCESS AD12-8
A/D INPUT CARD
THERMOCOUPLES TO TEST
FACILITY, (SURFACE PROBES,
INFLOW PROBES, AND HEAT LOSS
PROBES)
VALIDYNE
CARRIER rn
DEMODULATOR <|Scp
,VALIDYNE MAGNETIC RELUCTANCE
DIFF. PRESS, TRANSDUCER
Figure 2-12. A schematic diagram of data acquisition system.
BASIC software routines have been developed for all data
acquisition operations.
A summary of the design operating conditions of the
facility are as follows: mass flux, G=80-350 kg/m2-s; quality,
X=0-0.35; system pressure, P=1.0-2.3 bars; and test section
heat flux, qw=0-40 kW/m2. The operating constraints of the


17
manufactured from E-glass and a phenolic based epoxy resin,
and based on the data of Leeds (1972), the relative
permittivity of Garolite was approximated over a range of
temperature of 25 to 200 C using
eG=4.213+0.0023T (2-2)
where T is temperature in degrees Celsius. Using the crude
model of Chun and Sung (1986) the relative film thickness, 5',
for horizontal stratified flow is shown in Figure 2-6 as a
function of the relative capacitance C* for both the upper and
lower section of the sensor at 25 and 80 C. Here C* is
defined by
C*=
ocy
q-cy
(2-3)
where C is the capacitance across the sensor for two-phase
flow, Ct is the sensor capacitance for purely liquid flow, and
Cv is that for purely vapor flow; all these capacitances are
temperature dependent. For the lower section, 6'=6/h, and for
the upper section, 5'=i/h-l, where S is the liquid film
thickness and h=12.7 mm is the distance from the sensor inside
wall to the centerline. The results displayed in Fig. 2.6
reveal that the functional relationship between 5' and C* is
essentially independent of temperature over the 25-80 C range
investigated.
Guided by the fact that the relationship between C* and
5' is not temperature dependent, it was decided to calibrate


CHAPTER 1
INTRODUCTION
Forced convection boiling, also referred to as flow
boiling, has been used in a variety of engineering
applications for its high heat and mass transfer rates. In
nuclear power applications, flow boiling with water is used to
extract heat from reactors. Also flow boiling can be found in
fossil fuel fired steam generators, the chemical process
industry, refrigeration and air-conditioning industry, and
cooling of electrical distribution facilities. Other
potentially important applications include compact flow
boiling heat exchangers for use in spacecraft and cooling of
microelectronic components.
Due to its engineering importance, boiling heat transfer
has been the focus of extensive research for the past four
decades. However, to date, boiling remains one of the most
controversial subjects in the field of heat transfer. Many
questions raised four decades ago concerning boiling phenomena
remain unanswered (Lienhard, 1988). Current engineering
designs involving boiling phenomena rely heavily on empirical
correlations developed from experimental measurements.
Rohsenow (1952) first suggested that the rate of heat transfer
associated with forced convection boiling is due to two
1


141
vapor bubble growth rate under saturated flow boiling
condition were found in the literature. Cooper et al. (1983)
measured vapor bubble growth rate in boiling with water under
controlled liquid velocity. They found the growth rate
follows a power law and the exponent of the power law is
approximately 0.5. The system pressure effect was not
investigated. In this work, vapor bubble growth rates in
saturated flow boiling with R113 were measured using high
speed cinematography. The parametric influence of flow rate
and system pressure were examined from the experimental data.
The purpose of the measurements is to generate a data base for
flow boiling bubble growth rate and examine its dependence on
various flow and thermal parameters.
8.2 Facility and Methodology
The measurement of the bubble growth rate was performed
using the transparent flow boiling test section which was
described in detail in chapter 2. The boiling conditions of
the bulk two-phase mixture at the test section entrance is
controlled by the preheaters and the throttle valve downstream
of the test section. The procedures for obtaining the desired
boiling conditions have also been detailed in chapter 5. A
schematic diagram of the high speed cinematography arrangement
and illumination is displayed in Figure 8-1. The Hycam motion
picture camera equipped with a Vivitar 55 mm macro lens is
mounted on a tripod and is focused as close as physically


36
GX^ G(X-l)
(3-10)
Pv Pi
It is noted that the observed void fraction for saturated flow
boiling system in this work is always larger than 0.7. Since
the conversion of liquid film thickness to void fraction in
this range has greatly reduced the relative error of the
results, the collapse of the data does not necessarily imply
o
0
Drift Flux u (m/s)
Zuber and Findlay's (1965) correlation for
void fraction in horizontal stratified two-
phase flow.
Figure 3-4


2
additive mechanisms, that due to bulk turbulence and that due
to ebullition. Based on Rohsenow's conjecture, Chen (1966)
proposed a saturated flow boiling heat transfer correlation
which is simply the sum of the respective macroconvection and
microconvection heat transfer coefficients. The terms macro-
and microconvection respectively denote the contribution due
to heat transfer from bulk turbulent convection and that due
to the ebullition process. The macroconvection heat transfer
coefficient was calculated using a single-phase flow
correlation based on the liquid fraction flowing modified by
an enhancement factor, while the microconvection heat transfer
coefficient was calculated using a pool boiling correlation
modified by a suppression factor.
Chen's (1966) correlation or modified forms of it are
widely used throughout industry despite the fact that they
fail to accurately correlate a wide range of flow boiling heat
transfer data (Gungor and Winterton, 1986). One
characteristic of Chen's correlation is that it predicts the
microconvection contribution to flow boiling heat transfer is
always small compared to macroconvection. In contrast, Mesler
(1977) argued that the microconvection component is dominant.
Staub and Zuber (1966), Frost and Kippenhan (1967), Klausner
(1989), and Kenning and Cooper (1989) have presented flow
boiling heat transfer data which display a strong dependence
on the ebullition process. In addition, experimental data
provided by Koumoutsos et al. (1968) and Cooper et al. (1983)


61
m
t
P
0)
ff
00
t
O
cd
a>
t
¡z¡
Figure 5-1. Pool boiling nucleation site density data from
Griffith and Wallis (1960).
from 0.25 to 1.5 over a distance of a few mm, where (-)
implies a spatial average and (') denotes a spatial variation
from the mean. Using a conduction analysis, it was also shown
that in the presence of ebullition, the spatial non-uniformity
of wall superheat on the surface of "thick plates" may also be
significant depending on geometry and thermal conductivity of


(4-8)
T
* v, mm
=T.
sat
(P,~
2osin8aa)
*2
r2 (/xm)
Figure 4-7. Variation of minimum vapor temperature and
initiation superheat with cavity reservoir
mouth radius.
Tvmin and AT^j calculated from equations (4-7) and (4-8) over
a range of r2 for R113 at a pressure of 1.45 bars (the no-flow
system pressure of the current facility) are displayed in
Figure 4-7. As shown in Figure 4-3, the measured initiation
incipience superheat for the current facility is approximately


72
e
o
t
-4->
pH
co
t
a>
Q
V
-4->
H
m
t
o
-I-!
(t
tu
o
t
S5
15
10
100


1^=0.48 m/s
qw=19.3 kW/mE
V 5=6.3 mm
qw=19.3 kW/mz
T =58 C
sat
V


150
200
250
300
Mass Flux G (kg/mz-s)
Figure 5-7. Nucleation site density as a function of mass
flux.
Figure 5-9. Therefore, it is necessary to investigate the
influence of S on n/A.
In pool boiling, Nishikawa et al. (1967) demonstrated
that the nucleation site density increases with declining
liquid film thickness. Mesler (1976) postulated that the same
behavior should follow for flow boiling and used it to explain


112
Figure 6-3. Comparison of predicted and measured vapor
bubble departure diameter for subatmospheric
pressure data using the present model.
is excellent. The relative deviation, displayed in Table 6-2,
is 10%. It is also shown from Table 6-2 that the only
correlations which give comparable predictions to the present
model are those of Cole and Shulman which are referred to as
Cole and Shulman 1 and 2. The relative error for these two
correlations are about 29%. A comparison between the measured
departure diameter and the prediction of Cole and Shulman 2 is


78
t
H
w
t
O)
Q
cu
m
t
o
rH
-u
cfl
0)
o
t
Sz¡
Wall Superheat ATgat (C)
Figure 5-12. Nucleation site density as a function of wall
superheat.
5.4 Discussion of Results
Although the data shown in Figure 5-14, as well as
theoretical considerations, suggest that rc is an important
parameter for flow boiling nucleation site density, it is by
itself insufficient to correlate n/A. In Figure 5-15, all
nucleation site density measurements in this work are


74
15
S
o
d
>
-ij
CO
d
o
P
m
d
o
cd
o
d
2;
10 -
5 -
0
%-
19.3 kW/ms, T =58 C
n/A
v
6

G=215 kg/m8s


ut=0.58 m/s
A

uz=0.48 m/s
<-
>-
14
12
10
8
0
6

*>^
O
CO
CO
CD
d
M

i-4
t
E-H
'd
H
d
cT
0
4
Vapor Velocity u (m/s)
Figure 5-9. Nucleation site density and liquid film
thickness as functions of vapor velocity.
density, Figure 5-9 suggests that it is necessary to maintain
a fixed uv, qw/ and T^. Figure 5-10 shows n/A as a function
of liquid film thickness at ^=3.6 m/s, qw=20.7 kW/m2, and
TMt=58 C. It is seen that n/A indeed increases with declining
film thickness, which tends to support Mesler's claim
regarding n/A as a function of film thickness, provided that


Radius a(t) (mm)
150
Time t (ms)
Figure 8-7. Time history of bubble growth


96
EF =F +F +Fw =p Vh dUbcx (6-18)
x x sx qs dux r'vrb '
and
ctu
E ,Vb-g3- ( 6-19)
where F, is the surface tension force, Fqs is the quasi-steady
drag in the flow direction, F*. is the unsteady drag due to
asymmetric growth, FsL is the shear lift force, FL is the lift
force created by the wake of preceding departed vapor bubble,
Fb is the buoyancy force, Fh is the hydrodynamic pressure
force, and F^ is the contact pressure force which effectively
includes the reaction of the wall to the vapor bubble, u^ is
velocity of the bubble at its center of mass, Vb is the bubble
volume, and pv is the vapor density. Equations (6-18) and (6-
19) are valid throughout the vapor bubble growth process.
Keshock and Siegel (1964) demonstrated that many of the forces
acting on a growing bubble vary significantly during different
stages of the growth process. In order to obtain a useful
vapor bubble detachment model, it is important to identify
which of those forces acting on a growing bubble are dominant
near the point of departure. The following is a detailed
analysis considering each of the forces appearing in equations
(6-18) and (6-19). For simplicity, a truncated sphere has
been assumed for the shape of a bubble growing on the heating
surface


(6-35)
1 /
r.d. = meas^k xl0Q
N
where N is the number of data points, the subscripts "meas"
and "pred" refer to the respective measured and predicted
detachment diameters.
6.4.1 Pool Boiling Data
Experimental data obtained from the literature for pool
boiling were subdivided into four categories: subatmospheric
pressure, atmospheric pressure, elevated pressure, and reduced
gravity. Boiling liquids, pressure range, and gravitational
field of the departure data as well as the references from
which the data were obtained are summarized in Table 6-2. The
measured bubble growth rate, a(t), found in the literature
could generally be expressed in terms of a power law
a(t)=Ktn (6-36)
where K and n are usually determined by curve-fitting the
growth history. Equation (6-36) is useful to evaluate and
a which are required to calculate the growth force. In
situations where only the departure diameter and the growth
rate at the point of departure or the growth time are
specified in the experimental data, the growth constant can be
estimated using equation (6-36) by specifying a growth


3
demonstrate that the ebullition process in flow boiling cannot
be adequately modelled with pool boiling correlations. In
order to significantly improve flow boiling heat transfer
predictions over Chen's approach, it is necessary to
understand the mechanisms governing both macro- and
microconvection as well as their relative contribution to the
total heat transfer.
In this work, major efforts have focused on understanding
the physics governing vapor bubble incipience, nucleation site
density, growth and detachment in forced convection boiling.
In order to achieve this goal, a flow boiling facility with
refrigerant R113 was designed and fabricated. The boiling
test section is optically transparent thus allowing for the
visualization of the ebullition process. A CCD camera has
been used to measure nucleation site densities and high speed
cinematography was used to measure vapor bubble growth rates.
Two capacitance-based film thickness sensors were designed and
fabricated to measure the liquid film thickness on the upper
and lower surfaces of the horizontal square test section.
Since the flow boiling facility usually experiences large
temperature variations during operation, the temperature
dependence of the capacitance sensors must be accounted for.
A new and simple method has been developed to account for
temperature when using the film thickness sensor calibration
curve.
Using the current flow boiling facility, experimental


45
understand their influence on the initiation of boiling. The
air trapping process has been detailed by Lorenz (1972) and
recently by Tong et al. (1990). Mizukami (1977) investigated
the effect of non-condensible gases on the stability criterion
of the embryo and found that the existence of gas stabilizes
the vapor bubble nucleus but accelerates its nucleation when
the liquid is superheated. However, quantitative
O
t
H
EH
<1
bO
t
i-H
t
rt
(S
m
t
xn
t
03
t
o
H
C0
.(H
t
25
20 -
15
10 -
0.0
Measured Initiation Superheat
v Measured Sustaining Superheat
Predicted Sustaining Superheat
Based on T =59 C, ^=0.66x10"* m
sat 1
V
V ^
0.5 1.0 1.5 2.0
Macroconvection h (kfWYmeC)
mnn v f '
Figure 4-3.
Measured saturated flow boiling incipience
wall superheat.


Radius a(t) (mm)
154
Time t (ms)
Figure 8-11. Time history of bubble growth.


113
6
6
u
o
6
£0

Q
s_
2
S-,
<0
ex

TO
O
+J
o
fI
TO
O
S-.
ex
100
10
1 10 100
Experimental Departure Diameter d (mm)
Figure 6-4.
Comparison of predicted and measured vapor
bubble departure diameter for subatmospheric
pressure data using Cole and Shulman 2
correlation.
displayed in Figure 6-4. It is noted that in preparing Table
6-2, the present model is the only one in which the measured
bubble growth rate data were used in predicting departure
diameter.
Atmospheric Pressure. Earth Gravity. The atmospheric
pressure earth gravity pool boiling departure data are


88
Staniszewski (1959) measured the bubble departure diameter and
growth rate over a range of heat flux and system pressure.
The influence of the bubble growth rate on the departure
diameter was observed from the data. Therefore, a correlation
for bubble departure diameter which accounts for the bubble
growth rate was obtained by modifying Fritz's model as
dd=0.00710 (tr) (1+34.3) (6-3)
d sr(PrPv)
where a is the bubble radius with units of m, and (') implies
differentiation with respect to time. Similar modified forms
of Fritz's (1935) model were made by Han and Griffith (1962)
and Cole and Shulman (1966) The correlation of Han and
Griffith (1962) may be expressed as
dd=2.828.
(1-
llPi
^ ^(PrPv) 48g(p,-pv) a
(2+a))
(6-4)
and that of Cole and Shulman (1966) takes the form of
dd=ddF( 1+223.62) (65)
where ddF denotes the departure diameter predicted by Fritz1s
(1935) model and the correction factor for growth rate used
here was based on a larger database than that used by
Staniszewski (1959). Cole and Shulman (1966) also modified
Fritz's model by taking into account the influence of pressure
and obtained another empirical correlation for bubble
departure diameter,


CHAPTER 2
EXPERIMENTAL FACILITIES
2.1 Flow Boiling Test Loop
A flow boiling facility, shown schematically in Figure 2-
1, was designed and fabricated. Refrigerant R113 was selected
as the boiling liquid in this facility primarily due to its
low latent heat of evaporation and boiling point. A variable
speed model 221 Micropump was used to pump R113 through the
facility. A freon dryer/filter was installed on the discharge
of the pump to filter out alien particles in the liquid and to
prevent the formation of hydrofluoric acid in the refrigerant.
The volumetric flow rate of liquid was monitored with an Erdco
Model 2521 vane type flowmeter equipped with a 4-20 ma analog
output. The flowmeter output was attached to a 500 ohm power
resistor. The voltage across the resistor was recorded with
a digital data acquisition system which will be discussed
later. The flowmeter was calibrated using a volume-time
method. A calibration curve for the volumetric flow rate vs
voltage is displayed in Figure 2-2. The standard deviation of
the experimental data from a third order polynomial least-
squares fit is 0.5%, which is equivalent to the repeatability
of the flow meter claimed by the manufacturer. At the outlet
5


44
is then decreased until the sustaining superheat is reached,
which is denoted by point B. The heat flux is further reduced
until Twmin=63 C. The heat flux is then increased until the
new initiation superheat is reached which is denoted by A'.
Thus is seen that Twmin influences the initiation superheat.
The cycle is repeated for Twmin=67 C and A" denotes the
initiation superheat, which coincides with the sustaining
superheat. Thus, hysteresis is fully suppressed provided
Tw,mm>67 c* Many experiments were conducted over a variety of
flow conditions to examine the influence of forced convection
on both the initiation and sustaining incipience points.
Figure 4-3 has been prepared for this purpose, where it is
seen that both the initiation and sustaining incipience wall
superheats remain essentially constant (although slightly
scattered) over a wide variety of flow conditions. h,^ has
been used in Figure 4-3 as a comprehensive parameter to
characterize the bulk turbulence. These results are
consistent with those obtained for subcooled flow boiling with
highly wetting liquids (Hino and Ueda, 1985; Marsh and
Mudawwar, 1989).
4.3 Theoretical Analysis for Boiling Incipience
4.3.1 Boiling Initiation
Effect of Non-condensible Gases. Since non-condensible
gases (usually air) are always trapped in cavities during the
process of a liquid filling over a surface, it is necessary to


TABLE OF CONTENTS
ACKNOWLEDGEMENTS iii
LIST OF TABLES viii
LIST OF FIGURES ix
NOMENCLATURE xiii
ABSTRACT XV
CHAPTERS
1 INTRODUCTION 1
2 EXPERIMENTAL FACILITIES 5
2.1 Flow Boiling Test Loop 5
2.2 Construction of Transparent Test Section ..10
2.3 Development of Capacitance Based
Film Thickness Sensors 11
2.3.1 Introduction 11
2.3.2 Design and Fabrication of
Film Thickness Sensor 13
2.3.3 Instrumentation and Calibration .... 15
2.4 Data Acquisition System 24
3 HEAT TRANSFER AND PRESSURE DROP
IN SATURATED FLOW BOILING 28
3.1 Introduction 28
3.2 Experimental Results and Discussions 30
3.3 Conclusions 37
4 INCIPIENCE AND HYSTERESIS 38
4.1 Introduction and Literature Survey 38
4.2 Experimental Results 42
4.3 Theoretical Analysis for Boiling
Incipience 44
4.3.1 Boiling Initiation 44
4.3.2 Sustaining Incipience Superheat .... 54
4.3.3 Hysteresis of Boiling Incipience ...56
4.4 Conclusions 57
v


CHAPTER 3
HEAT TRANSFER AND PRESSURE DROP
IN SATURATED FLOW BOILING
3.1 Introduction
In this section of the investigation, measurements of
heat transfer coefficient with and without boiling are
described which have been obtained for a saturated two-phase
mixture flowing through the test section. The purpose of
these measurements is to elucidate the importance of the
microconvection contribution to the total heat transfer in
flow boiling. The pressure drop and liquid film thickness for
stratified two-phase flow without boiling have also been
measured over a wide range of mass flux, G, and quality, X.
The parametric trends of the heat transfer coefficient and
pressure drop for horizontal two-phase flow are displayed and
compared against those observed for single phase flows.
The total two-phase heat transfer coefficient with and
without boiling is defined by
(3-i>
1w 1b
where Tw is the mean wall temperature, Tb is the two-phase bulk
temperature, and qw is the wall heat flux. Since this work
28


TO MY WIFE TANG YONG


Abstract of Dissertation Presented to the Graduate School of
the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
THE EBULLITION PROCESS
IN FORCED CONVECTION BOILING
By
Ling-zhong Zeng
August, 1993
Chairman: Professor James F. Klausner
Major Department: Mechanical Engineering
A forced convection boiling facility with Refrigerant
R113 was designed and fabricated in order to experimentally
study the ebullition process in horizontal flow boiling.
Capacitance sensors were developed for measuring the liquid
film thickness for stratified and annular two-phase flow.
Measurements of heat transfer coefficient, pressure drop, and
liquid film thickness in stratified two-phase flow with and
without boiling have been obtained. The experimental data
have conclusively demonstrated that microconvection, which is
the heat transfer due to the ebullition process, is
significant in almost all phases of saturated flow boiling.
The initiation and sustaining incipience superheats of
saturated flow boiling with R113 were found to be insensitive
to the fluid convection but they strongly depend on the system
pressure as well as the cooling history of the heating surface
xvii


89
dd=
1.32
P
)
s^PrPv)
_i
2
(6-6)
where P is the system pressure with units of (atm) Cole
(1967) generalized equation (6-6) by taking into account the
contact angle and recognized that the system pressure could be
accounted for by the variation of vapor density through the
Jakob number. He also realized that the contact angle is
difficult to measure and for most boiling systems it does not
typically deviate by more than 20% from an average value of
50. Based on these considerations, he proposed the
correlation,
where
dd=(
o
^(prPv)
i
) 2 Ja
(6-7)
ja= p PA*
(6-8)
A modified form of Cole's (1967) correlation was proposed by
Cole and Rohsenow (1969),
dd=C( 7 g )^(,r^PCP)~f (6-9)
^(Pl-Pv) P yhfg
where C=1.5xl04 for water and 4.65X10"4 for other fluids.
Recently, Kocamustafaogullari (1983) attempted to correlate
vapor bubble departure diameters over a wide range of
pressures. He modified Fritz's model and proposed,


APPENDIX A
HEAT TRANSFER COEFFICIENT, PRESSURE DROP, AND
LIQUID FILM THICKNESS IN STRATIFIED TWO-PHASE FLOW
AP
S
G
X
Uy
kW/m2-C
mmH20
iron
c
kg/m2-s
m/s
m/s
0.947
16.58
5.5
59.3
203.2
.134
0.55
3.31
0.924
17.08
5.4
59.0
203.4
.133
0.56
3.30
0.674
5.58
5.6
58.5
140.9
.157
0.36
2.76
0.712
5.42
5.4
58.0
141.3
.154
0.38
2.72
0.979
24.04
5.9
59.8
254.6
.094
0.67
2.92
0.977
25.26
5.9
59.5
258.6
.089
0.68
2.84
0.715
21.47
6.6
58.5
214.6
.053
0.53
1.50
0.758
17.72
6.6
59.4
218.3
.047
0.54
1.32
1.308
37.95
3.0
60.7
221.8
.191
1.05
4.39
0.802
12.33
6.4
58.1
196.2
.096
0.48
2.47
0.799
14.79
6.0
58.5
195.3
.096
0.50
2.39
0.636
17.80
6.9
57.5
192.4
.062
0.45
1.64
0.674
23.71
7.0
58.0
192.0
.058
0.44
1.52
0.446
7.93
7.0
57.3
126.0
.054
0.29
0.94
0.485
10.17
6.8
56.6
126.5
.056
0.30
0.99
0.631
5.80
5.1
57.5
131.1
.140
0.38
2.30
0.652
6.56
5.0
57.0
131.5
.137
0.38
2.28
0.446
7.93
7.0
57.3
126.0
.054
0.29
0.94
0.485
10.17
6.8
56.6
126.5
.056
0.30
0.99
0.631
5.80
5.1
57.5
131.1
.140
0.38
2.30
0.652
6.56
5.0
57.0
131.5
.137
0.38
2.28
161


24
B
B
CO
CO
Q>
A
o
a
E-<
J
* H
fin
-O
W
S3
a>
3
Measured Film Thickness 6 (mm)
CCD Camera
Figure 2-11. Comparison of liquid film thickness measured
with CCD camera and capacitance sensor.
#1 and the results are illustrated in Figure 2-11. It can be
seen that over the entire range of film thickness and
temperature considered, the comparison is good. The average
error based on the data shown in Figure 2-11 is within 2% of
the full scale.
2.4 Data Acquisition System
A digital data acquisition system has been assembled for


99
growth process. According to Cooper and Chandratilleke
(1981), Cooper et al. (1983), and Zysin et al. (1980), the
contact diameter at the base of a growing bubble embedded in
a superheated thermal layer is not easily measured. There
exists an index of refraction gradient in the thermal boundary
layer which creates a mirage of the bubble near its base.
Therefore, those investigators who relied on visual
measurements without taking into account this phenomenon have
severely overestimated the contact diameter as well as the
surface tension force. The hypothesis by Moore and Mesler
(1961) that a liquid microlayer exists beneath a growing vapor
bubble has been substantiated by various investigators and was
discussed in detail by Cooper and Lloyd (1969). Due to the
existence of the liquid microlayer it is probable that the
contact diameter is very small. Unfortunately, "very small"
is difficult to quantify because reliable measurements of the
contact diameter are not available to date. Although the
contact diameter continually changes during the growth cycle
of a vapor bubble, it is reasonable to suggest that the
contact diameter approaches zero near the point of departure
due to the necking phenomenon which has been clearly
identified by Jakob (1959), Johnson et al. (1966), and Van
Stralen et al. (1975). Direct experimental evidence can be
found in the measurements of Keshock and Siegel (1964), in
which the contact diameter is observed to decline sharply as
the vapor bubble is departing from the heating surface. The


Radius a(t) (mm)
Figure 8-10. Time history of bubble growth.


175
Siegel, R., and Usiskin, C., 1959, "A Photographic Study of
Boiling in the Absence of Gravity," J. of Heat Transfer.
Trans. ASME, Vol. 81, No. 3, pp. 230-236.
Singh, A., Mikic, B.B., and Rohsenow, W.M., 1976, "Active
Sites in Boiling," J. of Heat Transfer. Trans. ASME, Vol. 98C,
pp. 401-406.
Staniszewski, B.E., 1959, "Bubble Growth and Departure in
Nucleate Boiling," Tech. Rept. No. 16, MIT, Cambridge, Mass.
Staub, F.W. and Zuber, N., 1966, "Void Fraction Profiles, Flow
Mechanisms, and Heat Transfer Coefficients for Refrigerant 22
Evaporating in a Vertical Tube," ASHRAE Trans.. Vol. 72, Part
I, pp. 130-146.
Strenge, P.H., Orell, A., and Westwater, J.W., 1961,
"Microscopic Study of Bubble Growth During Nucleate Boiling,"
AIChE J.. Vol. 7, No. 4, pp. 578-583.
Sudo, Y., Miyata, K., Ikawa, H., and Kaminaga, M., 1986,
"Experimental Study of Incipient Nucleate Boiling in Narrow
Vertical Rectangular Channel Simulating Subchannel of Upgraded
JRR-3," J. of Nuclear Science and Technology. 23(1), pp. 73-
82.
Taitel, Y., and Dukler, A.E., 1976, "A Theoretical Approach to
the Lockhart-Martinelli Correlation for Stratified Flow,"
Int. J. Multiphase Flow. Vol. 2, pp. 591-595.
Tien, C.L., 1962, "A Hydrodynamic Model for Nucleate Pool
Boiling," Int. J. Heat Mass Transfer. Vol. 5, 533-540.
Tolubinsky, V.I., and Ostrovsky, J.N., 1966, "On the Mechanism
of Boiling Heat Transfer (Vapor Bubbles Growth Rate in the
Process of Boiling of Liquids, Solutions, and Binary
Mixtures)," Int. J. Heat Mass Transfer. Vol. 9, pp. 1463-
1470.
Tong, W., Bar-Cohen, A., Simon, T.W., and You, S.M., 1990,
"Contact Angle Effects on Boiling Incipience of Highly-wetting
Liquids," Int. J. Heat Mass Transfer. Vol. 33, No. 1, pp. 91-
103.
Van Stralen, S.J.D., Sohal, M.S., Cole, R., and Sluyter, W.M.,
1975, "Bubble Growth Rates in Pure and Binary Systems:
Combined Effect of Relaxation and Evaporation Microlayers,"
Int. J. Heat Mass Transfer. Vol. 18, pp. 453-467.
Van Stralen, S.J.D., Cole, R., Sluyter, W.M. and Sohal, M.S.,
1975, "Bubble Growth Rates in Nucleate Boiling of Water at
Subatmospheric Pressures," Int. J. Heat Mass Transfer. Vol.


75
B
o
t
r-H
CO
t
0)
Q
0)
-u
w
o
o
!*
-tJ
t
t
II
o
t
£
Liquid Film Thickness (mm)
Figure 5-10. Nucleation site density as a function of
liquid film thickness.
Uy, qw, and TMt are fixed. However, over the range of film
thickness investigated (3-6 mm) the increase in n/A is only
marginal. Because n/A was obtained using a visualization
technique it was not possible to obtain data for 5<3 mm. As
6-+ 0 the behavior of n/A is uncertain. To determine whether
Uy or S has stronger influence on n/A, Figure 5-9 is re-


8
thermocouples. A precision Viatran differential pressure
transducer was installed to measure the pressure drop across
m
\
o
->->
cti
05
£
o
Em
O
rH
Eh
-iJ
Q>
6
p
o
>
Flow Meter Output (Volts)
Figure 2-2. Calibration curve for flowmeter.
the test section with an accuracy of 0.25% of full scale (120
mmH20). A throttle valve is located downstream of the test
section, which allows the test section pressure to be adjusted
from atmospheric pressure to 30 psig, which is the maximum


p(x) Probability density function
q Heat flux
r Radius of the liquid/vapor interface
rt Mouth radius of the cavity
r2 Mouth radius of the cavity reservoir
R Engineering gas constant
Re Reynolds number
t Time
T Temperature
u Mean velocity
U(y) Velocity profile
V Volume
X Vapor quality
Greek Symbols
a Void fraction
S Liquid film thickness
AP Pressure drop
AT Superheat
ij Liquid thermal diffusivity
0 Contact angle
0¡ Bubble inclination angle
H Dynamic viscosity
p Density
a Surface tension coefficient or standard deviation
Half cone angle of the cavity
e Relative permittivity
xiv


166
(Continued)
n/A
T*
G
X
S
Uy
qw
cm'2
C
kg/m2-s
mm
m/s
m/s
kW/m2
C
2.39
56.5
254.7
.09
4.5
.89
3.01
17.3
15.2
10.38
73.3
171.3
.25
4.4
.51
3.46
17.3
11.3
8.05
70.5
179.5
.22
4.4
.55
3.46
17.3
12.0
6.40
68.1
183.7
.20
4.4
.58
3.47
17.3
12.5
4.50
65.1
187.0
.18
4.2
.63
3.41
17.3
13.5
3.75
62.3
195.3
.16
4.4
.63
3.44
17.3
14.1
2.65
60.1
192.0
.16
4.3
.65
3.50
17.3
14.4
2.11
58.0
199.0
.14
4.4
.67
3.44
17.3
15.0
1.73
55.5
206.7
.13
4.4
.70
3.52
17.3
16.0


prior to boiling. Nucleation site density of saturated
forced convection boiling was measured using a CCD camera.
The mean vapor velocity, heat flux, and system pressure appear
to exert a dominant parametric influence on the nucleation
site density. The critical cavity radius is an important
parameter in characterizing the nucleation process but by
itself it is not sufficient to correlate nucleation site
density data for saturated flow boiling. Based on
experimental observations and theoretical reasoning, an
analytical model has been developed for the prediction of
vapor bubble detachment diameters in saturated pool and flow
boiling. The vapor bubble growth rate is a necessary input to
the model. It is demonstrated that over the wide range of
conditions considered, the accuracy of the detachment
diameters predicted using the present model is significantly
improved over existing correlations. The model was also
extended to predict the probability density functions (pdf's)
of detachment diameters by specifying the pdf's of wall
superheat and liquid velocity. The vapor bubble growth rate
during saturated flow boiling was measured using a high speed
cinematography. Based on the experimental data obtained
herein, the vapor.bubble radius can be expressed as a function
of time using a power law, where the exponent decreases with
increasing system pressure. The objective of this research is
to understand the fundamentals of the ebullition process in
flow boiling.
xviii


14
Figure 2-5. Cut-away view of liquid film thickness sensor.
resolution is expected. It shall be demonstrated that the
best resolution is obtained with liquid film thickness of 5 to
6 mm and poor resolution is observed near the centerline.
Copper strips with a thickness of 0.1 mm were bonded into the
grooves with epoxy. An aluminum chassis was fabricated around
the sensor body. The purpose of the chassis is twofold: it
shields extraneous electromagnetic radiation and also
compresses the sensor body so that it is pressure resistant.


104
Now consideration is given to the bubble lift-off
process. Based on photographic visualization of vapor bubbles
in flow boiling using a CCD camera, it may be reasonable to
postulate that immediately following departure the bubble
attempts to right itself such that the inclination angle
approaches zero. Therefore, once the bubble departs its
nucleation site it slides along the surface in the flow
direction with zero inclination angle until it lifts off the
heating surface some distance downstream. It is also
hypothesized that once it departs from its nucleation site the
vapor bubble will rapidly accelerate to the speed of liquid
around it due to the low inertia of the bubble. Direct
experimental evidence for this hypothesis is not available at
this point since it requires measuring the liquid velocity
profile and bubble trajectory simultaneously. However, high
speed cinematography, using a Hycam camera operating at 5000
frames per second, was used to measure the sliding velocity of
departed vapor bubbles. The estimated error is 0.01 m/s.
For boiling conditions of u,=0.47 m/s, ATMt=9.3 C, and TMt=71.6
C the average measured sliding velocity based on an
observation of 4 bubbles is 0.14 m/s. The average liquid
velocity at the bubble center of mass, calculated from
equation (3-3), is also 0.14 m/s. The fact that the
velocities are identical is coincidental because an
observation of 4 bubbles is not sufficient to obtain a
statistically reliable average. Nevertheless,
this


43
5
40
35
30
25
20
15
10
5
0
0
Increasing from Twttit>=20C
boiling initiated at A.
V Decreasing q^.,
boiling sustained at B.
A Increasing qw from Tw.mJn=63C
boiling initiated at A'.
Increasing qw from TWTntT>=67aC
boiling reversible. B, Acoincide.
T =58QC, T =20C
sat room
V
*
'a
v
Vi
Va
b,a
V
&
^A'
T -T .
w sat
10
(C)
15
Figure 4-2. A typical saturated flow boiling plot of qw
versus ATMt for G=180 kg/m2-s, X=0.156, and
5=4.8 mm.
Figure 4-2 is as follows. With a quasi-steady saturated two-
phase mixture flowing through the test section, the heat flux
is increased from zero until the initiation incipience
superheat is reached, which is denoted by point A. Here the
minimum temperature prior to boiling is room temperature,
approximately 20 C. The heat flux is increased further until
fully developed nucleate boiling is achieved. The heat flux


Liquid Capacitance (pf)
21
Temperature (DC)
Figure 2-8. Temperature calibration for film thickness
sensor filled with full liquid.
optically measuring the liquid film thickness for stratified
flow. The camera was focused normal to the transparent test
section to avoid optical distortion. A typical picture of
two-phase stratified flow obtained with the CCD camera used
for comparison is displayed in Figure 2-10. Liquid film
thickness is determined from the scale placed on the test


174
Rallis, C.J., and Jawurek, H.H., 1964, "Latent Heat Transport
in Saturated Nucleate Boiling," Int. J. Heat Mass Transfer.
Vol. 7, pp. 1051-1068.
Rayleigh, L., 1917, "On the Pressure Developed in a Liquid
during the Collapse of a Spherical Cavity," Phil. Mag.. 34,
94-98.
Rohsenow, W.M., 1952, "Heat Transfer, A Symposium,"
Engineering Research Institute, University of Michigan, Ann
Arbor, MI.
Roll, J.B. and Myers, J.E., 1964, "The Effect of Surface
Tension on Factors in Boiling Heat Transfer," AIChE J.. Vol.
10, pp. 530-534.
Ruckenstein, E., 1961, "A Physical Model for Nucleate Boiling
Heat Transfer from a Horizontal Surface," Bui. Institutului
Politech. Bucaresti. Vol. 33, No. 3, pp. 79; AMR 16 (1963),
Rev. 6055.
Russell, T.W.F., Etchells, A.W., Jensen, R.H., and Arruda,
P.J., 1974, "Pressure Drop and Holdup in Stratified Gas-Liquid
Flow," AIChE J.. Vol. 20, No. 4, pp. 664-669.
Sami, M., Abouelwafa, M.S.A., and Kendal, E.J.M., 1980, "The
Use of Capacitance Sensors for Phase Percentage Determination
in Multiphase Pipelines," IEEE Trans, on Instrum, and Measur..
Vol. IM-29, No. 1, pp. 24-27.
Sato, T. and Matsumura H., 1964, "On the Conditions of
Incipient Subcooled Boiling with Forced Convection," Bulletin
Of JSME. Vol. 7, No. 26, pp. 392-398.
Schwartz, A.M. and Tejada, S.B., 1972, "Studies of Dynamic
Contact Angle on Solids," J. of Colloid Interface Science.
Vol. 38, No. 2, pp. 359-375.
Semeria, R., 1961, "Une Method de Determination de la
Population de Cebtres Generateurs de Bulles sur une Surface
Chauffante Daus l'eau Bouiliante," Comotes Rendus. Acad.
Sci., Paris, 252, pp. 675-677.
Semeria, R., 1963, "Charateristiques des Bulles de Vapeur sur
une Paroic Chauffante dans l'eau en Ebullition a Haute
Pression," Comotes Rendus. Acad. Sci., Paris, 256, pp. 1227-
1230.
Shoham, O., and Taitel, Y., 1984, "Stratified Turbulent-
Turbulent Gas-Liquid Flow in Horizontal and Inclined Pipes,"
AIChE J.. Vol. 30, No. 3, pp. 377-385.


97
Buovancv. Ouasi-steadv drag, and Shear Lift Forces. The
buoyancy force acting on a bubble immersed in liquid under
varied gravity may be calculated from
Fb=Vb(prpv) Cgg (6-20)
where Vb is the volume of the bubble, g is the gravitational
acceleration on the earth, and Cg is the ratio of reduced
gravity to the normal gravity on the earth. The buoyancy
force has typically been considered important in the removal
of vapor bubbles from pool boiling heating surfaces.
Based on the results obtained by Mei and Klausner (1992,
1993) the quasi-steady drag and shear lift acting on a bubble
in shear flow can be estimated from
QS
, Ar t=4+( (4^)n+-796n)
6nptvaUa 3 Re
n,n=0.6 5
(6-21)
and
pi 1
CL= =3.877Gs2 (2?e_2+0.014Gs2) 4 (6-22)
|p,AU**a*
where AU is the relative velocity between the bubble mass
center and liquid, a is the bubble radius, Re=2AUa/p is the
bubble Reynolds number, and v is the liquid kinematic
viscosity. In forced convection boiling, the vapor bubble
remains within the liquid boundary layer during its growth
cycle. For single phase turbulent flow, an estimation for the
velocity profile near the wall was proposed by Reichardt and


133
the bubble departure model, i.e. equations (6-32) and (6-33).
Equation (7-3) is used to calculate the pdf of departure
diameter in flow boiling for specified pdf's of wall superheat
and liquid velocity.
Based on the bubble detachment model, the bubble
departure diameter in pool boiling and lift-off diameter in
flow boiling do not depend on liquid velocity. Thus the
detachment diameter pdf's for these two cases are only due to
the statistical distribution of wall superheat. The pdf's of
bubble departure diameter in pool boiling and lift-off
diameter in flow boiling may be evaluated from
pd(d)=pAr(AT)^ (7-4)
for a specified pAT(AT) .
A liquid crystal thermography technique was used to
visualize the wall temperature variations in the present flow
boiling facility. Videotape recordings of the underside of
the boiling surface displayed temporal and spatial
fluctuations of wall temperature. Instantaneous pictures were
also obtained using a 4X5 format camera. The videotape is
available from the author upon request. Kenning's (1992)
liquid crystal measurements of wall temperature in pool
boiling showed an approximately Gaussian temperature
distribution. Therefore, it may be reasonable to assume a
Gaussian probability density function for wall superheat in
flow and pool boiling,


35
(1987) have provided extensive experimental evidence that the
mean vapor velocity is a controlling parameter on the
interfacial shear stress. Recently, Maciejewski and Moffat
(1992) measured the velocity and temperature distributions in
the near wall region for flow over a flat plate and found that
the strong turbulence intensity in the free stream could
substantially alter the near-wall temperature profile while
the velocity profile maintains a relatively uniform shape.
Therefore, the dissimilarity between heat transfer and
pressure drop observed in this research may be due to the
strong turbulence intensity at the interface which may
influence the temperature profile in a manner significantly
different from that of the velocity profile.
In stratified two-phase flow, the thickness of the liquid
film along the lower surface can be converted to void fraction
a by
Using Zuber and Findlay's (1965) correlation, all the
experimental data obtained in this research were collapsed
into a straight line as shown in Figure 3-4. Uy, is the
superficial velocity of vapor phase defined by
uvs=^' (3-9)
P V
and is the two-phase mixture velocity which is defined by


169
Delil, A.A.M., 1986, "Sensors for a System to Control the
Liquid Flow into and Evaporative Cold Plate of a Two-Phase
Heat Transport System for Large Spacecraft," National
Aerospace Laboratory Report NLR TR 86001 U, the Netherlands.
Downing, R.C., Fluorocarbon Refrigerant Handbook, Prentice
Hall, Englewood Cliffs, New Jersey, 1988.
Eddington, R.I. and Kenning, D.B.R., 1978, "The Prediction of
Flow Boiling Bubble Populations from Gas Bubble Nucleation
Experiments," Proc. 6th Int. Heat Transfer Conf.. Vol. 1, pp.
275-280.
Eddington, R.I. and Kenning, D.B.R., 1979, "The Effect of
Contact Angle on Bubble Nucleation," Int. J. Heat Mass
Transfer. Vol. 22, pp. 1231-1236.
Eddington, R.I., Kenning, D.B.R., and Korneichev, A.I., 1978,
"Comparison of Gas and Vapor Bubble Nucleation on a Brass
Surface in Water," Int. J. Heat Mass Transfer. Vol. 21, pp.
855-862.
Fritz, W., 1935, "Bereshnung des Maximalvolume von
Dampfblasen," Physci. Zeitschr. Vol. 36, pp. 379-384.
Fritz, W. and Ende, W., 1936, "Uber den Verdampfungsvorgang
nach kinematographischen Aufnahmen an Dampfblasen," Phvsci.
Zeitschr. Vol. 37, pp. 391-401.
Frost, W. and Kippenhan, C.J., 1967, "Bubble Growth and Heat
Transfer Mechanic\sms in the Forced Convection Boiling of
Water Containing a Surface Active Agent," Int. J. Heat Mass
Transfer. Vol. 10., pp. 931-949.
Gaerates, J.J.M. and Borst, J.C., 1988, "A Capacitance Sensor
for Two-Phase Void Fraction Measurement and Flow Pattern
Identification," Int. J. Multiphase Flow. Vol. 14, No. 3, pp.
305-320.
Gaertner, R.F., 1963, "Distribution of Active Sites in the
Nucleate Boiling of Liquids," Chemical Engineering Progress
Symposium Series. No. 41, Vol. 59, pp. 52-61.
Gaertner, R.F., 1965, "Photographic Study of Nucleate Boiling
on a Horizontal Surface," J. of Heat Transfer. Trans. ASME,
Vol. 87, pp. 17-29.
Gaertner, R.F., and Westwater, J.W., 1960, "Population of
Active Sites in Nucleate Boiling Heat Transfer," Chemical
Engineering Progress Symposium Series. No. 30, Vol. 56, pp.
39-48.


NOMENCLATURE
a, a(t)
Radius of a growing vapor bubble
C
Capacitance
^D
Drag coefficient for a freely rising vapor bubble
in an infinite liquid
CP
Liquid specific heat
Cs
Empirical constant, equals 20/3
d
Vapor bubble diameter
dw
Diameter of contact area
D
Inside dimension of the test section or diameter
F
Force
g
Earth gravity
G
Mass flux
h
Heat transfer coefficient
hfg
Vaporization latent heat
Ja
Jakob number
k
Thermal conductivity
K
Power law bubble growth constant as in a(t)=Kt
m
Mass
M
Molecular weight
n
Power law bubble growth index as in a(t)=Ktn
n/A
Nucleation site density
P
Absolute pressure or Polarization factor
xiii


5-11 Nucleation site density as a function of heat
flUX 77
5-12 Nucleation site density as a function of wall
superheat 78
5-13 Nucleation site density as functions of saturation
temperature and wall superheat 79
5-14 Nucleation site density as a function of critical
radius for constant heat flux and vapor velocity ....80
5-15 Nucleation site density as a function of critical
radius for all flow boiling data 81
6-1 A typical picture of vapor bubble departure and
lift-off in flow boiling 85
6-2 A schematic sketch of vapor bubble detachment
process in flow boiling 95
6-3 Comparison of predicted and measured vapor bubble
departure diameter for subatmospheric pressure
data using present model 112
6-4 Comparison of predicted and measured vapor bubble
departure diameter for subatmospheric pressure
data using Cole and Shulman 2 correlation 113
6-5 Comparison of predicted and measured vapor bubble
departure diameter for atmospheric pressure data
using present model 114
6-6 Comparison of predicted and measured vapor bubble
departure diameter for atmospheric pressure data
using Cole and Shulman 2 correlation 115
6-7 Departure diameter variation with mean liquid
velocity at constant ATMt 121
6-8 Comparison between predicted and measured
departure diameters 122
6-9 Departure diameter variation with mean liquid
velocity and ATt 125
6-10 Predicted inclination angle variation with
predicted departure diameter 126
6-11 Predicted inclination angle variation with
mean liquid velocity and ATMt 127
xi


CHAPTER 6
A UNIFIED MODEL
FOR VAPOR BUBBLE DETACHMENT
6.1 Introduction
The detachment of vapor bubbles in nucleate boiling is
crucial in maintaining the high heat transfer rate of the
boiling process. In fact, the vapor bubble detachment
diameter has been incorporated into most boiling heat transfer
correlations. Although numerous models and correlations for
vapor bubble detachment diameter have been developed over the
past six decades (back to Fritz's model in 1935), a reliable
model for the prediction of bubble detachment diameters has
yet to be developed. Several factors which have posed
difficulties in accurately predicting the detachment diameters
are due to lack of adequate understanding of the surface
tension force and the inertial force induced by bubble growth
as well as their relative importance in the detachment
process. Due to the difficulties related to the prediction of
vapor bubble detachment diameters as well as other vapor
bubble parameters such as nucleation site density and growth
rate, it is not unexpected that the heat transfer coefficient
can not be accurately calculated for many boiling systems of
practical interest.
84


30
to ebullition. Using Rohsenow's superposition hypothesis, the
heat transfer coefficient attributed to microconvection during
saturated flow boiling may be calculated from
(3 2)
3.2 Experimental Results and Discussions
Prior to discussing the details of the experimental
results, it is necessary to define several parameters. For
two-phase stratified horizontal flow, the mean velocity of the
liquid film may be calculated from
_G(1-X)D
l~ Pfi
and mean vapor velocity by
(3-3)
GXD
Uv~'pv(D~b)
(3-4)
where u is mean velocity, S is liquid film thickness, p is
density and D is the inside dimension of the horizontal square
test section for which only the lower surface is covered with
a liquid film; subscripts £ and v denote the liquid and vapor
phases, respectively. The Reynolds number for liquid and
vapor phases are defined by
Ret=
PtuPht
Hi
(3-5)
and


155
Table 8-1. A Summary of Parameters Controlling Vapor
Bubble Growth Rate in Flow Boiling.
Run
P
bar
Ja
U,
m/s
Uy
m/s
K
n
1
1.40
13.26
0.28
2.80
0.101
0.49
2
1.50
8.64
0.44
2.54
0.091
0.51
3
1.52
8.03
0.57
3.42
0.082
0.48
4
1.55
8.00
0.55
3.42
0.079
0.50
5
1.65
7.17
0.50
2.89
0.080
0.48
6
1.72
6.55
0.49
2.89
0.089
0.47
7
1.85
6.36
0.46
2.90
0.086
0.46
8
2.06
6.18
0.38
2.67
0.080
0.44
9
2.18
5.00
0.32
2.64
0.076
0.44
10
2.51
4.53
0.27
2.46
0.068
0.44
superheat beneath a growing bubble not only varies with time
but also is probably dependent on the growth rate. In order
for the experimental data to be more useful, measurements
should be made for bubbles from an ensemble of nucleation
sites on the surface to account for the spatial non
uniformity. And more data are required to discriminate
statistical variations.


168
Saturated Fluids in Convective Flow," I&EC Process Pesian and
Development. Vol. 5 No. 3, pp. 322-329.
Chun, M.H., and Sung, C.K., 1986, "Parametric Effect on Void
Fraction Measurement," Int. J. Multiphase Flow. Vol. 12, pp.
627-640.
Clark, H.B., Strenge, P.S., and Westwater, J.W., 1959, "Active
Sites for Nucleate Boiling," Chemical Engineering Progress
Symposium Series. Vol. 55, No. 29, pp. 103-110.
Cole, R., 1967, "Bubble Frequencies and Departure Volumes at
Subatmospheric Pressure," AIChE J.. Vol. 13, No. 4, pp. 779-
783.
Cole, R., 1974, "Boiling Nucleation," Advances in Heat
Transfer. Vol. 10, pp. 86-166.
Cole, R. and Rohsenow, W.M., 1969, "Correlation of Bubble
Departure Diameters for Boiling of Saturated Liquids,"
Chemical Engineering Progress Symposium Series. No., 92, Vol.
65, pp. 211-213.
Cole, R. and Shulman, H.L., 1966, "Bubble Departure Diameters
at Subatmospheric Pressures," Chemical Engineering Progress
Symposium Series, no. 64, Vol. 62, pp. 6-16.
Cole, R., and Shulman, H.L., 1966a, "Bubble Growth Rate of
High Jacob Numbers," Int. J. Heat Mass Transfer. Vol. 9, pp.
1377-1390.
Cooper, M.G., 1969, "The Microlayer and Bubble Growth in
Nucleate Pool Boiling," Int. J. Heat Mass Transfer. Vol. 12,
pp. 915-933.
Cooper, M.G. and Chandratilleke, T.T., 1981, "Growth of
Diffusion-controlled Vapor Bubbles at a Wall in a Known
Temperature Gradient," Int. J. Heat Mass Transfer. Vol. 24,
No. 9, pp. 1475-1492.
Cooper, M.G., and Lloyd, A.J.P., 1969, "The Microlayer in
Nucleate Pool Boiling," Int. J. Heat Mass Transfer. Vol. 12,
pp. 895-913.
Cooper, M.G., Mori, K., and Stone, C.R., 1983, "Behavior of
Vapor Bubbles Growing at a Wall with Forced Flow," Int. J.
Heat Mass Transfer. Vol. 26, No. 10, pp. 1489-1507.
Davis, E.J., and Anderson, G.H., 1966, "The Incipience of
Nucleate Boiling in Forced Convection Flow," AIChE J.. Vol.
12, No. 4, pp. 774-780.


83
a strong parametric influence of vapor velocity on the
incipience process in saturated flow boiling. The similar
effect of vapor velocity has also been found on the heat
transfer coefficient in a stratified two-phase flow as shown
in chapter 3. It has been argued that vapor velocity has a
controlling effect on the intensity of turbulence at the
interface which would substantially modify the temperature
profile in the thermal layer. The same argument is applied
here to explain the effect of vapor velocity on the incipience
process. Increasing Uy results in enhanced turbulence, and
therefore a variation of Uy should have a significant impact
on the heating surface temperature field as well as the
thermal layer temperature profile which, in turn, influences
the boiling incipience process.
5.5 Conclusions
The nucleation site density n/A of saturated flow boiling
has been measured over a wide range of flow and thermal
conditions and the parametric effects of these conditions on
n/A have been examined closely. Of the flow and thermal
parameters investigated, Uy, qw, and TMt appear to have a
governing influence on n/A. Nucleation site density of
saturated flow boiling displays a dependance on the critical
radius rc, but by itself rc is insufficient to correlate n/A.
Pool boiling n/A correlations based on rc are not applicable
to flow boiling.


CHAPTER 8
VAPOR BUBBLE GROWTH
8.1 Introduction
Numerous measurements of vapor bubble growth rates in
nucleate pool boiling have been reported in the literature
(Fritz and Ende, 1936; Staniszewski, 1959; Strenge et al.,
1961; Cole and Shulman, 1966a; Van Stralen et al., 1975;
Cooper and Chandratilleke, 1981; etc.) In general, the
experimental data of bubble radius can be curve-fitted using
a power law,
a (t) =Ktn (8-1)
where t is growth time. At otherwise identical conditions K
and n vary with different bubbles and display some stochastic
characteristics. The ensemble average of K for a large bulk
of bubbles at given conditions appears to depend on system
pressure, wall superheat, and boiling liquids, n is found to
be system pressure dependent. Typically n is approximately
0.5 for subatmospheric and atmospheric pressure and decreases
as the system pressure increases above one atmosphere. No
general bubble growth model is currently available to account
for such variations.
In contrast to pool boiling, few similar measurements of
140


134
1 ( AT-Ara)2
(7-5)
where AT is local wall superheat, ATm is mean wall superheat,
and ctax is the standard deviation of wall superheat.
The fluctuation of liquid velocity in flow boiling
systems may be caused by interfacial waves and bulk
turbulence, both of which are stochastic in time and space.
Experimental data of liquid velocity fluctuations around a
bubble in boiling are not currently available. Here the pdf
of liquid velocity is also assumed, for simplicity, to be
Gaussian,
(7-6)
where u is instantaneous local horizontal liquid velocity,
is mean liquid velocity, and ctu is the standard deviation of
liquid velocity.
7.3 Comparison with Experimental Data
Experimental data on the statistical distribution of
bubble detachment diameters are usually obtained in the form
of histograms in terms of the normalized number of bubbles.
The normalized number n/N can be calculated from the pdf of
detachment diameter using,
(7-7)


Table 6-2. (Continued)
Roll &
Rucke-
Han &
Semeria
Semeria
Cole &
Cole &
Cole
Cole &
Kocam-
Myers
nstein
Griffi.
1
2
Shulman
Shulman
(1967)
Rohse.
ustaf.
(1964)
(1961)
(1962)
(1961)
(1963)
1 (1966)
2 (1966)
(6-7)
(1979)
(1983)
(6-12)
(6-11)
(6-4)
(6-14)
(6-15)
(6-5)
(6-6)
(6-9)
(6-10)
81.6
85.1
76.1
69.2
547.1
16.3
32.6
86.9
93.7
91.8
99.2
98.1
185.5
52.2
2167.0
27.8
54.4
97.4
99.2
95.8
34.9
38.6
140.9
57.5
691.4
25.6
16.1
59.3
64.1
86.5
167.9
118.3
196.5
7.6
963.4
57.4
56.2
49.4
12.7
85.9
96.7
97.0
13.4
71.8
3265.0
46.4
66.2
96.6
96.4
99.2
372.1
279.0
34.3
83.5
845.8
31.1
29.6
43.6
30.6
58.4
143.7
119.3
106.2
63.7
986.5
28.4
29.0
64.1
62.2
81.5
33.9
31.6
371.3
20.2
753.1
116.8
49.5
13.6
20.7
57.6
36.9
26.9
235.1
25.3
482.9
59.1
6.0
39.1
43.8
89.9
555.0
140.4
130.6
52.7
256.8
30.7
6.6
48.4
21.1
32.6
138.4
94.1
110.8
38.0
366.8
73.2
31.7
38.6
16.6
17.6
160.2
88.8
147.4
36.8
406.0
74.1
30.8
36.5
18.3
25.9
85.6
67.0
330.0
26.3
333.7
110.1
32.2
63.7
29.8
69.1
51.0
33.6
91.3
32.0
156.0
86.5
22.7
34.3
33.8
30.5
60.4
42.7
158.8
30.5
204.1
93.0
25.3
42.3
32.7
41.0
440.4
345.0
283.1
61.0
194.1
106.7
186.9
338.8
132.3
102.0
110


80
6
o
<
t
&
H
w
fl

Q
O
+J
H
m
t
o
-ij
(C
0)
t
¡2;
Figure 5-14. Nucleation site density as a function of
critical radius.
is first given to the pool boiling analysis of Hsu (1962) in
which it was demonstrated that the nonuniform liquid
temperature field seen by a vapor embryo attempting to grow is
important when considering incipience behavior. If linear
temperature profile is assumed for the liquid layer, a minimum
cavity radius required for incipience may be expressed solely


Table 6-2. Mean Deviation Tabulated for Present Bubble Model as well as Other
Correlations Reported in the Literature.
Boiling
Conditions
Boiling
Liquids
Number
of Data
Points
This
Work
Fritz
(1935)
(6-1)
Zuber
(1959)
(6-2)
Stanisz-
ewski
(1959)
(6-3)
Nishikawa
& Urakawa
(1960)
(6-13)
Acetone
15
6.8
80.9
85.2
67.8
36.5
Sub-
Carbon Terr.
10
7.3
83.0
86.5
73.3
57.1
atmospheric
Methanol
43
9.5
73.0
76.3
63.5
26.3
Pressure
n-Pentane
5
18.6
23.7
43.7
28.0
127.1
one-g
Toluene
5
9.2
94.5
94.6
87.0
21.3
Water
27
11.9
90.5
90.9
81.7
57.1
Combined
105
10.0
78.3
81.6
69.2
43.2
Methanol
8
18.9
16.3
52.2
8.8
157.1
Atmospheric
n-Pentane
2
14.8
28.6
54.3
29.1
69.6
Pressure
Aqueous-sucrose
Solution
6
14.7
30.7
44.5
66.5
11.1
one-g
Water
51
14.9
16.9
56.8
34.2
43.6
Combined
67
15.3
18.4
55.1
33.9
55.0
Elevated
Methanol
3
17.3
55.0
37.5
15.6
156.0
Pressure
Water
8
28.8
39.9
41.5
18.5
47.7
one-g
Combined
11
25.7
44.1
40.4
17.7
77.3
Atmospheric
Pressure
Micro-g
Aqueous-sucrose
Solution
5
16.2
106.7
33.7
49.4
14.5
109


Radius a(t) (mm)
152
Time t (ms)
Figure 8-9. Time history of bubble growth.


95
Figure 6-2. A schematic diagram of the vapor bubble
detachment process in flow boiling.
balances in the horizontal and vertical directions. First,
consideration is given to the bubble departing from its
nucleation site. Following a similar form adopted by Klausner
et al. (1993), the x- and y-momentum equations for a bubble
attached to its nucleation site in flow boiling may be
expressed as


162
(Continued)
*w
AP
S
Tt
G
X
U,
Uy
kW/m2-C
mmH20
mm
C
kg/m2-s
m/s
m/s
0.824
7.57
3.0
58.9
135.7
.202
0.61
2.99
0.844
8.43
2.9
58.2
135.9
.200
0.64
3.01
1.077
19.05
1.8
58.8
135.8
.298
0.92
4.20
1.066
18.44
1.8
59.6
135.8
.297
0.89
4.10
1.084
18.94
1.8
59.3
135.7
.296
0.91
4.12
0.620
13.47
7.8
57.4
159.0
.069
0.33
1.58
0.608
13.53
7.5
57.4
159.2
.069
0.34
1.57
0.754
7.65
6.3
58.1
163.1
.124
0.39
2.65
0.726
8.95
6.2
59.0
162.8
.123
0.40
2.54
0.849
10.63
4.3
58.6
163.0
.167
0.55
3.17
0.851
10.85
4.2
58.4
163.2
.167
0.55
3.19
0.886
11.20
4.1
58.6
163.1
.166
0.57
3.13
1.184
28.57
2.1
59.5
167.7
.267
0.99
4.62
1.212
29.67
2.1
59.8
167.1
.268
1.02
4.58
0.658
16.03
8.8
58.0
200.9
.041
0.37
1.24
0.654
17.12
8.8
57.8
200.2
.042
0.37
1.28
0.784
16.86
6.6
58.3
203.4
.089
0.48
2.39
0.807
14.94
6.6
58.0
203.3
.090
0.48
2.44
0.988
18.16
3.9
58.9
204.1
.143
0.77
3.31
0.966
18.10
4.0
58.7
204.0
.143
0.74
3.36
1.246
36.08
2.2
60.0
206.9
.206
1.30
4.35
1.253
35.15
2.3
60.3
207.0
.204
1.25
4.29
1.235
38.07
2.6
60.4
228.7
.176
1.26
4.14
1.292
38.81
2.6
60.7
228.9
.173
1.26
4.04
0.821
22.57
6.9
59.0
229.2
.051
0.54
1.54
0.780
23.57
7.1
57.9
229.3
.056
0.52
1.76
0.895
19.25
6.4
58.9
232.8
.094
0.56
2.82


87
departure arises from a balance between the surface tension
and buoyancy forces acting normal to the heating surface, and
other forces such as the inertial force due to the bubble
growth may be included as a correction factor. In contrast to
the surface tension controlled departure, the inertia
controlled departure assumes that the departure arises from a
balance between the inertial force and the buoyancy force.
Perhaps the most widely used and earliest bubble
departure model is that of Fritz (1935) which was derived from
a balance between the buoyancy and surface tension forces.
According to his model, the departure diameter may be
estimated from,
dd=0.02080. .
d N ^(PrPv)
(6-1)
where 8 is the contact angle in degrees, a is the surface
tension coefficient, g is the gravitational acceleration, p is
the density, and subscripts l and v respectively refer to the
liquid and vapor phases. Since the contact angle during the
bubble departure is very difficult to determine, 8 is an
empirical constant. Following Fritz's approach, Zuber (1959)
suggested that if the contact diameter, d^ remains constant
and the contact angle is 90, the bubble departure diameter
may be calculated from
dd=(
6 dwo
Sr(PrPv)
)
(6-2)


158
were found to be insensitive to the bulk turbulence for
saturated flow boiling with R113 but they strongly depend on
the system pressure as well as the cooling history of the
heating surface prior to boiling. The hysteresis can be
eliminated if the minimum temperature of the liquid prior to
boiling is maintained above a threshold. Existing incipience
models have been modified and applied to explain the
experimental results.
3. Nucleation site density in saturated forced
convection boiling was measured over a wide range of flow and
thermal conditions. The mean vapor velocity, heat flux, and
system pressure appear to exert a dominant parametric
influence on the nucleation site density. Nucleation site
density is also observed to increase with decreasing liquid
film thickness but the change is marginal. The critical
radius of the cavity is an important parameter in
characterizing the nucleation process but by itself it is not
sufficient to correlate nucleation site density for saturated
flow boiling.
4. Based on experimental observations and theoretical
reasoning, an analytical model was developed for the
prediction of vapor bubble detachment diameters in flow and
pool boiling. The model utilizes a force balance which
follows a similar form as that used by Klausner et al. (1993) .
For an upward facing heating surface, the model has been
tested over the following range of conditions: pressure, 0.02-


48
1972; Tong, et al., 1990). According to these investigations,
as the liquid/vapor interface gradually moves toward the vapor
phase, a maximum contact angle is reached and is referred to
as the static advancing contact angle, 0M. Similarly, as the
interface gradually moves toward the liquid phase, a minimum
contact angle, referred to as the static receding contact
angle, 0,r, is reached. Assuming the embryo expansion follows
a quasi-equilibrium process, the contact angle 0 lies between
0sr and 0 which are determined by liquid wettability and
surface conditions. Based on the data supplied by Tong et al.
(1990), 0sr~2 for R113, while 0M is usually less than 90.
For calculation purposes, here it is assumed that the initial
static contact angle is equal to the static advancing contact
angle and 0~8O. Tong et al. (1990) have suggested that when
the cavity is heated, during the first expansion stage the
embryo interface adjusts such that the initial static contact
angle recedes until the static receding contact angle is
reached. Then during the second expansion stage the
liquid/vapor interface moves toward the cavity mouth, with
constant contact angle, 0sr. During the first expansion stage,
the contact angle, 0, may be calculated from,
cos (0-iJi) = (4-5)
r
where rd, which remains constant, is the cavity radius at the
initial triple interface. rd may be calculated by specifying
the initial 0, Tv, P

LIST OF FIGURES
Figure
2-1 Schematic diagram of flow boiling facility 6
2-2 Calibration curve for flowmeter 8
2-3 Calibration curve of heat loss for preheaters 9
2-4 Isometric view of transparent test section 11
2-5 Cut-away view of liquid film thickness sensor 14
2-6 Prediction of relative film thickness vs capacitance
using model of Chun and Sung (1986) 18
2-7 Calibration curve for film thickness sensor 19
2-8 Temperature calibration for film thickness sensor
filled with pure liquid 21
2-9 Temperature calibration for film thickness sensor
filled with pure vapor 22
2-10 Close-up view of stratified two-phase flow using
CCD camera (flow direction is from left to right) ...23
2-11 Comparison of liquid film thickness measured with
CCD camera and capacitance sensor 24
2-12 A schematic diagram of data acquisition system 26
3-1 Microconvection heat transfer for saturated forced
convection nucleate boiling 32
3-2 Macroconvection heat transfer coefficient in
saturated forced convection boiling 33
3-3 Pressure drop in horizontal two-phase flow 34
3-4 Zuber and Findlay's (1965) correlation for void
fraction in horizontal stratified two-phase flow ....36
4-1 Nucleate pool boiling hysteresis constructed from
the data of Kim and Burgles (1988) 39
ix


Subscripts
b
Bulk or buoyancy
cp
Contact pressure
d
Bubble departure
da
Dynamic advanced
dF
Departure diameter predicted from Fritzs model
dr
Dynamic receded
du
Force due to bubble growth
g
Non-condensible gas
G
Garolite material
h
Hydraulic
inc, i
Incipience, initiation
inc, s
Incipience, sustaining
L
Bubble lift-off or lift force created by bubble
wake
l
Liquid phase
m
Mixture of vapor and liquid
mac
Macroconvection
max
Maximum
mic
Microconvection
min
Minimum
s
Surface tension
sa
Static advanced
sat
Saturation
sL
Shear lift
sr
Static receded
20
Two-phase
xv


69
a
o
-p
H
m
t
O
Q
xn
a
O
i-H
3
P-H

2
Z
Heat Flux qw (kW/m2)
8 10 12 14 16 18 20
Figure 5-5. Pool boiling nucleation site density as
functions of wall superheat and heat flux.
superheat, ATMt, as well as heat flux, qw, in Figure 5.5. It
is seen that n/A increases smoothly with increasing ATMt and
qw in a similar fashion to the data shown in Figure 5-1. As
seen from Figure 5-4, parameters other than AT^ alone appear
to exert an influence on n/A in flow boiling.
In order to examine the influence of the flow parameters


16
environment is that the permittivity of both the solid and
liquid is temperature dependent. A complete calibration is
obtained only when the liquid film thickness and temperature
are varied over the full range. Such a calibration is tedious
and impractical. Therefore, an innovative scheme is proposed
which allows the sensor to be used based on its calibration at
a fixed temperature
A crude model for predicting the capacitance as a
function of film thickness or volume fraction for a known
material permittivity was introduced by Chun and Sung (1986)
by considering the sensor as a network of parallel and series
equivalent plate-type capacitors. This type of modeling was
attempted for the sensor described above. The relative
permittivity of R113 vapor was taken to be unity. The
relative permittivity of liquid R113 as a function of
temperature was determined from the Clausius-Mosotti equation
as reported by Downing (1988):
_ Af+Pp,
*" Ai-Pp,
(2-1)
where et is the liquid relative permittivity, M is the
molecular weight, P is the polarization, and pt is the liquid
density. The temperature dependence of permittivity comes
from the fact that the liquid density varies with temperature.
Published values of permittivity could not be found for
Garolite material. However, Garolite is a composite material


124
reported by Klausner et al. (1993) who assumed a finite d and
constant 0¡ no improvement is gained in the prediction of the
departure diameter. However, it should be recognized that the
present model is more useful since empirical data concerning
and advancing and receding contact angles are not
required. In addition, the performance of the departure model
is improved when the vapor bubble growth rate is known, and
the evidence of such is provided by Table 6-5. Table 6-5
compares the present bubble departure model against departure
diameters measured using high speed cinematography in which
the growth rate was simultaneously measured (Brouillette,
1992) It is seen that the prediction is significantly
improved, and the relative deviation for the predicted
departure diameters in Table 6-5 is 4%.
Figure 6-9 shows the predicted mean departure diameter
using the present model as a function of liquid velocity and
wall superheat. The observed trend, departure diameter
decreases with increasing velocity and increases with
increasing wall superheat, is consistent with that reported by
Klausner et al. (1993). Figure 6-10 shows the predicted
inclination angle as a function of the predicted departure
diameter. It is seen that the predicted inclination angle
varies from about 5 to 25 degrees. Although an accurate
measurement of the inclination angle with the present
experimental facility is not currently achievable, the
predicted inclination angle falls in a range which is


85
Figure 6-1. A typical picture of vapor bubble detachment
in flow boiling (flow direction is from left
to right).
Generally, the shape of a vapor bubble in boiling is not
strictly spherical. Thus, the bubble diameter is usually
defined as that of a sphere with an equivalent volume of the
bubble. Klausner et al. (1993) demonstrated that in forced
convection boiling systems, vapor bubbles typically detach
from the nucleation site via sliding and lift off the heating
surface downstream of the nucleation site. This process can
be clearly illustrated by a picture taken from the flow
boiling heating surface shown in Figure 6-1. The instant at


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree ofJDoctor of Philosophy.
//Xei
Reiwei Mei
Assistant Professor of
Aerospace Engineering,
Mechanics and Engineering
Science
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
GIwn
aie in
S. Anghaie
Professor of
Nuclear Engineering Sciences
This dissertation was submitted to the Graduate Faculty
of the College of Engineering and to the Graduate School and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
August 1993
Winfred M. Phillips
Dean, College of Engineering
Dean, Graduate School


CHAPTER 7
PROBABILITY DENSITY FUNCTIONS OF
VAPOR BUBBLE DETACHMENT DIAMETER
7.1 Introduction
The statistical nature of the boiling process was first
discussed by Fritz and Ende (1936) who made quantitative
measurements of vapor bubble growth rate and departure
diameter in pool boiling using photographic techniques. Since
then numerous investigators have made boiling measurements
under a variety of conditions and similar statistical
variations were observed. Among them are Staniszewski (1959) ,
Strenge et al. (1961), Han and Griffith (1963), Cole and
Shulman (1966) and Tolubinsky and Ostrovsky (1966) However,
few measurements of probability density functions (pdf's) of
bubble growth rate and departure diameter were made in these
investigations. Strenge et al. (1961) gave pdf's of bubble
departure diameter and growth rate for pool boiling with ether
and pentane. Tolubinsky and Ostrovsky (1966) presented pdf's
of departure diameter for boiling with water. These
experimentally determined pdf's resemble a Gaussian
distribution. Recently, Bernhard (1993) measured vapor bubble
departure and lift-off diameters for saturated flow boiling
with refrigerant R113. pdf's of detachment diameters were
130


their support throughout the entire course of my education.
It is my parents who inspired me to pursue the education I
have obtained.
iv


37
that Zuber and Findlay's (1965) correlation captured the
correct physics governing the void fraction distribution in
two-phase flow.
3.3 Conclusions
Measurements of two-phase heat transfer coefficients with
and without boiling have demonstrated that the microconvection
component of heat transfer in saturated flow boiling is
significant in almost all phases of boiling and its
contribution to the total heat transfer becomes dominant as
heat flux increases. The macroconvection heat transfer in
saturated flow boiling with strong interfacial waves is not
well correlated by simply using an analogy between momentum
and heat transport. Therefore, the development of a
significantly improved heat transfer correlation for flow
boiling, which has not been attempted in this study, will
require improved modelling of both the micro- and
macroconvection processes.


Vapor Capacitance (pf)
22
Temperature (C)
Figure 2-9. Temperature calibration for film thickness
sensor filled with full vapor.
section. The length measurement from the pictures is accurate
to 0.1 mm. Since the liquid/vapor interface was wavy in
almost all cases considered, the instantaneous photograph of
the flow structure had to be synchronized with an
instantaneous capacitance and temperature measurement in order
to obtain a reliable comparison. The degree of waviness of


77
"s
a
-t-3
CO
t
Q
CO
t
o
H
Cti
Q>
o
t
¡z;
Heat Flux (kW/mE)
Figure 5-11. Nucleation site density as a function of heat
flux.
of n/A can be attributed to an increase of l/rc. Since the
only physically sound explanation for the increase of n/A with
increasing TMt is due to a decrease in rc, these data suggest
that rc is an important parameter in characterizing flow
boiling nucleation site density.


60
they used rc to correlate the nucleation site density as
follows,
-^=C1 ( )
A 1 rc
where n/A is the nucleation site density, Cx and
empirically determined constants, and when pt py
(5-1)
m are
2 O Tg.f.
(5-2)
where TMt is the saturation temperature, a is the surface
tension, hfg is the latent heat of evaporation, and ATsat=Tw-Tsat
is the wall superheat.
Nucleation site density data of Griffith and Wallis
(1960) for pool boiling of water on a copper surface is shown
in Figure 5-1 as a function of ATMt. For n/A < 4 cm"2 the
nucleation site density increases smoothly with increasing
ATMt. However for n/A > 4 cm"2 no correlation exists between
n/A and ATMt. Moore and Mesler (1961) used a fast response
thermocouple to demonstrate the heating surface temperature
directly beneath a nucleation site in pool boiling experiences
rapid fluctuations. Recently, Kenning (1992) used
thermochromic liquid crystals to measure the spatial variation
of wall superheat with pool boiling of water on a 0.13 mm
thick stainless steel heater. It was demonstrated that the
wall superheat was very nonuniform and |Al^at|/Arsat
varied


CHAPTER 5
NUCLEATION SITE DENSITY
5.1 Literature Survey
Due to its governing influence on heat transfer, the
nucleation site density has been the focus of numerous
investigations in pool boiling (Clark et al., 1959; Griffith
and Wallis, 1960; Kurihara and Myers, 1960; Gaertner and
Westwater, 1960; Hsu, 1962; Gaertner, 1963; Gaertner, 1965;
Nishikawa et al., 1967; Singh et al., 1976). The general
consensus from these investigations is that the formation of
nucleation sites is highly dependent on surface roughness,
geometry of microscopic scratches and pits on the heating
surface, the wettability of the fluid, the amount of foreign
contaminants on the surface, as well as the material from
which the surface was fabricated. Because of the large number
of variables which are difficult to control, none of these
investigators were successful in developing a general
correlation for nucleation site density. Griffith and Wallis
(1960) suggested that for a given surface the critical cavity
radius, rc, is the only length scale pertinent to incipience
provided the wall superheat is uniform. Although they
realized the wall superheat is nonuniform in pool boiling,
59


13
variations in temperature, the calibration of the capacitance
sensor must account for its temperature dependence in order to
obtain accurate liquid film thickness measurements. Both the
permittivity of the liquid and the material of construction
are temperature dependent. Therefore, either the sensor must
be calibrated over the range of temperatures for which it will
operate or a suitable temperature correction scheme must be
employed when the sensor is calibrated at a fixed temperature.
The latter approach has been successfully used in this work.
2.3.2 Design and Fabrication of Film Thickness Sensor
The liquid film thickness sensor was designed to match
the inner dimension of the test section for a smooth
transition of the flow. Therefore, four Garolite sheets (152
x 38 x 6 mm) were machined and bonded together with Conap
epoxy to form a body which has a 25 x 25 mm inner square cross
section as shown in Figure 2-5. Garolite material was chosen
for the fabrication of the film thickness sensor body because
it has good dielectric properties and is corrosion resistant
to refrigerants. Two parallel grooves, 7.9 mm wide and 3.2 mm
deep were machined on both the outer upper and lower halves of
the sensor body for placement of the capacitance strips. The
distance separating two adjacent grooves is 7.9 mm. This
distance was chosen because Ozgu and Chen (1973) reported the
optimum thickness and distance between the parallel ring
sensors is equal to the film thickness at which the highest


163
(Continued)
^mac
AP
S
T
xsat
G
X
U,
Uy
kW/m2-s
ltunH20
mm
c
kg/m2-s
m/s
m/s
0.893
19.30
6.7
58.8
232.8
.095
0.54
2.89
1.055
25.20
3.8
59.4
232.8
.133
0.91
3.46
1.045
27.08
4.1
59.8
232.5
.133
0.84
3.46
0.818
27.10
8.8
58.7
261.9
.044
0.49
1.71
0.807
28.33
8.7
58.8
262.0
.042
0.49
1.62
0.970
23.13
7.9
59.6
265.4
.072
0.54
2.62
0.979
24.03
7.1
59.5
265.2
.071
0.59
2.48
1.162
31.02
4.3
60.1
265.0
.118
0.92
3.51
1.125
32.92
4.4
60.8
265.3
.114
0.91
3.35
1.335
48.58
2.5
61.1
265.1
.163
1.51
4.35
1.363
49.44
2.5
61.4
265.0
.163
1.50
4.31
0.870
23.42
7.1
58.8
253.0
.076
0.57
2.57
0.908
22.03
7.1
58.7
252.8
.075
0.57
2.54
0.636
15.09
6.8
57.2
179.6
.056
0.43
1.39
0.667
17.37
6.7
57.5
177.3
.056
0.43
1.35
0.536
11.41
7.1
56.5
125.6
.065
0.28
1.17
0.524
11.62
6.9
56.7
125.7
.063
0.29
1.11
1.232
37.40
3.4
60.4
250.4
.144
1.07
3.85
1.210
36.97
3.4
60.3
250.3
.144
1.07
3.86
1.210
39.36
3.3
60.6
250.4
.143
1.12
3.78
1.221
38.19
3.3
60.5
250.4
.143
1.10
3.80


94
used by Levy (1967) and Koumoutsos et al. (1968) were
insufficient for describing their observed departure data.
Recently, Klausner et al. (1993) developed a model for both
departure and lift-off diameters of vapor bubbles in flow
boiling. They demonstrated that while a vapor bubble is
attached to its nucleation site it grows asymmetrically due to
the hydrodynamic drag force posed by the flow. The asymmetric
growth was modelled by considering a vapor bubble growing at
an inclined angle to the flow direction. In order to evaluate
the force due to bubble growth acting in the direction of flow
or normal to the heating surface, knowledge of the inclination
angle is required. In addition, the contact area between the
bubble and heating surface as well as the receding and
advancing contact angles are also required in the model. Due
to the difficulties in determining the contact area and
contact angles, the model has limited practical value.
6.3 Development of Departure and Lift-off Model
6.3.1 Formulation
As has been mentioned previously, vapor bubbles in forced
convection boiling systems typically detach from their
nucleation site via sliding and lift off the heating surface
downstream of the nucleation site. Based on many observations
made with a CCD camera, the vapor bubble detachment process in
horizontal flow boiling may be depicted schematically as shown
in Figure 6-2. The bubble detachment model is based on force


176
18, pp. 655669.
Yin, S.T. and Abdelmessih, A.H., 1976, "Prediction of
Incipient Flow Boiling from a Uniformly Heated Surface," AIChE
Symposium Series. No. 164, Vol. 33, No. 1, pp. 91-103.
You, S.M., Simon, T.W., Bar-Cohen, A., and Tong, W., 1990,
"Experimental Investigation of Nucleate Boiling Incipience
with a Highly-wetting Dielectric Fluid (R-113)," Int. J. Heat
Mass Transfer. Vol. 33, No. 1, pp. 105-117.
Zeng, L.Z., and Klausner, J.F., 1993, "Nucleation Site Density
in Forced Convection Boiling," J. of Heat Transfer. Trans.
ASME, Vol. 115, pp. 215-221.
Zeng, L.Z., and Klausner, J.F., 1993, "Heat Transfer,
Incipience, and Hysteresis in Saturated Flow Boiling," to be
presented at the 29th National Heat Transfer Conf.. Atlanta.
Zeng, L.Z., Klausner, J.F., and Mei, R., 1993a, "A Unified
Model for the Prediction of Bubble Detachment Diameters in
Boiling Systems: Part I Pool Boiling," Int. J. Heat Mass
Transfer. Vol. 36, No. 9, pp. 2261-2270.
Zeng, L.Z., Klausner, J.F., Bernhard, D.M., and Mei, R.,
1993b, "A Unified Model for the Prediction of Bubble
Detachment Diameters in Boiling Systems: Part I Flow Boiling,"
Int. J. Heat Mass Transfer. Vol. 36, No. 9, pp. 2271-2279.
Zuber, N., 1959, "Hydrodynamic Aspects of Boiling Heat
Transfer," U.S. AEC Rep. AECU 4439, Tech. Inf. Serv., Oak
Ridge, Tenn.
Zuber, N., 1961, "The Dynamics of Vapor Bubbles in Nonuniform
Temperature Fields," Int. J. Heat Mass Transfer. Vol. 2, pp.
83-98.
Zuber, N., 1964, "Recent Trend in Boiling Heat Transfer
Research, Part I: Nucleate Pool Boiling," Applied Mechanics
Reviews. Vol. 17, No. 9, pp. 663-672.
Zuber, N. and Findlay, J.A., 1965, "Average Volumetric
Concentration in Two-Phase Flow Systems," J. of Heat Transfer.
Trans. ASME, Vol. 87C, pp. 453-468.


CHAPTER 9
CONCLUSIONS AND RECOMMENDATIONS
FOR FUTURE RESEARCH
This chapter summarizes the major research
accomplishments in this work and provides suggestions for
future research of flow boiling phenomena.
9.1 Accomplishments and Findings
The research contained herein has advanced the
understanding of flow boiling fundamentals in the following
manner:
1. Measurements of two-phase heat transfer coefficients
with and without boiling were made over a wide range of
conditions. The heat transfer of flow boiling has been
decomposed into two components: macroconvection due to the
bulk turbulence, which is equivalent to the heat transfer of
the two-phase mixture without boiling, and microconvection due
to the ebullition process, which is the total heat transfer
less that of macroconvection. The experimental data have
conclusively demonstrated that the microconvection component
of saturated flow boiling heat transfer is significant in
almost all phases of boiling and its contribution to the total
heat transfer becomes dominant as heat flux increases.
2. The initiation and sustaining incipience superheats
157


131
obtained over a wide range of flow and thermal conditions.
These experimentally measured departure and lift-off diameter
pdf's also resemble Gaussian distributions.
Although it has been realized that the statistical
characteristics of boiling are important in understanding the
boiling heat transfer process, theoretical analysis devoted to
these statistical characteristics is lacking. Strenge et al.
(1961) and Tolubinsky and Ostrovsky (1966) believed that the
statistical distribution of bubble departure diameters may be
caused by random factors involved in boiling systems which
have not been reliably quantified through experiments.
Recently, Kenning (1992) obtained spatial distributions of
wall temperature in pool boiling using a liquid crystal
thermography technique. The variation in wall superheat was
approximately displayed as Gaussian. The preceding bubble
detachment model indicates that in addition to the liquid
velocity, the wall superheat, which controls the bubble growth
rate, is important in predicting the bubble departure and
lift-off diameters in flow boiling. The observed statistical
variation of bubble departure and lift-off diameters is likely
caused by the apparently randomly distributed wall temperature
and turbulent fluctuations in the liquid film. In what
follows, the analytical relationship between pdf's of
detachment diameters and those of wall superheat and liquid
velocity in flow boiling are established through a unified
bubble detachment model. The pdf's of departure and lift-off


122
comparison between the measured and predicted departure
diameters, obtained under various flow and thermal conditions
by Bernhard (1993), is shown in Figure 6-8. The relative
deviation of the present model is 18% which is acceptable
considering the departure diameter is sensitive to the vapor
a
a

&
U
cd
ft
P
-t->
O
U
OU
Measured Departure Diameter dd (mm)
Figure 6-8. Comparison between predicted and measured
departure diameters for flow boiling.
bubble growth rate which was evaluated using equation (6-39).
It seems that when the present model is compared to that


91
infinite liquid.
Nishikawa and Urakawa (1960) recognized that the system
pressure has a profound influence on vapor bubble departure
diameters. Based on the bubble departure diameters measured
over a range of pressure from 300 to 760 mmHg they proposed an
empirical bubble departure diameter correlation which is
solely a function of pressure,
dd=0.00364P0,575 ( 6-13)
where P is the system pressure in units of (atm) and dd has
units of (m) Semeria (1961, 1963) proposed two correlations
which are similar to that of Nishikawa and Urakawa. The first
one is given by
dd=0.00160P'0,5 (6-14)
which was obtained from experimental data in the range of 2 to
20 atm pressure. The second one was obtained from data in
which the pressure range was extended to approximately 140 atm
and is given by
dd=0.0121P1,5 (6-15)
All of these models and correlations have been compared
with experimental data which include six different liquids,
subatmospheric, atmospheric and elevated pressures, and
reduced gravity. The relative errors of the predictions and
number of the data points considered are summarized in Table
6-2. These results will be commented on later.


51
should consist of pure vapor.
Cavities with Pure Vapor. Mizukami (1990) concluded
that conical cavities with pure vapor can not survive
subcooled conditions and thus are not useful for initiating
boiling. However, even if conical cavities are initially
filled with liquid and can not initiate boiling, they can
become active nucleation sites if vapor is deposited in the
cavity from a neighboring nucleation site as has been
suggested by Calka and Judd (1985).
Mizukami (1990) also pointed out that the most favorable
cavities for surviving subcooled conditions are reentry type
ones. Thus it is likely that boiling is first initiated from
reentry cavities. Now consideration is given to reentry type
cavities, one of which is depicted in Figure 4-6. As is the
case for conical cavities, provided nucleate boiling is
sustained for a sufficient period, a vapor embryo will recede
in the cavity when the surface is cooled. Unlike conical
cavities, a reentry one will allow the liquid vapor interface
of highly wetting liquids to be concave toward the cavity
reservoir. Therefore, the vapor embryo can survive when P,>PV.
Following the analysis of Griffith and Wallis (1960) and
Mizukami (1975), for 6<9, the maximum curvature that the
liquid vapor interface can achieve is l/r2, where r2 is the
mouth radius of the cavity reservoir. Thus the initiation
superheat can be obtained from,


56
criterion, the sustaining superheat AT^, (=Tw-TMt) can be
obtained as a function of r,, h^, and Tt numerically from
equations (4-9) and (4-10) For constant r,, has been
calculated over a range of h^ as shown in Figure 4-3. It is
seen that the effect of convection on incipience superheat is
negligible which is in agreement with experimental
observations.
4.3.3 Hysteresis of Boiling Incipience
Hysteresis is the difference between the initial and
sustaining superheats. According to the preceding incipience
analysis, the initiation point depends on the minimum heating
surface temperature, while the sustaining point does not. In
fact, an explanation for incipience hysteresis is provided by
equation (4-8); as Tvmin decreases, potentially active
incipience nucleation sites are deactivated due to the
collapse of the vapor embryo. Assuming that the heating
surface contains reentry cavities with a large size range,
equation (4-8) predicts that incipience hysteresis will
increase with decreasing Tvmin. Such behavior is exactly what
has been observed with the present R113 flow boiling facility.
It is seen from Figure 4-2 that when Tvmin is greater than TMt
and less than the sustaining point, the hysteresis declines
when compared to heating from subcooled conditions.
Furthermore, once fully developed boiling has been established
and Tvmin is maintained above the sustaining point, the boiling


126

t
iH
on
%
CJ
o
-4->
t
1=1
o
fl
t
+J
O
xl
t
u,
Oh
50
45
40
35
30
25
20
15
10
5
0
0.0 0.2 0.4 0.6 0.8 1.0
Predicted Departure Diameter d (mm)
Flow Bolling Bubble Departure
Totally 32 Data Points
V
v
X?
V ^7
V V V
v
w
Figure 6-10. Predicted inclination angle variation with
predicted departure diameter.
various wall superheats. While 0t increases with increasing
velocity, it decreases with increasing wall superheat.
Lift-off Diameter. Figure 6-12 shows the predicted lift
off diameters against the measured values of Bernhard (1993).
The relative deviation for the data in Figure 6-12 is 19%


128
Measured Lift-Off Diameter dL (mm)
Figure 6-12. Comparison between predicted and measured
lift-off diameter.
pool boiling departure diameters measured under subatmospheric
and atmospheric pressure for different substances. Based on
a limited number of experimental data, the model is also in
good agreement with elevated pressure and microgravity pool
boiling departure diameter data. The model is in good
agreement with the limited number of flow boiling data
available. The only required input is the vapor bubble growth
rate. The good agreement between the model and experimental


46
considerations regarding the effect of the gas mass on the
initiation superheat have not been reported in the literature.
It is worthwhile to proceed with such calculations in order to
further understand the nucleating process of a vapor bubble
containing a non-condensible gas.
Consideration is given to an embryo, consisting of a non
condensible gas and saturated vapor, trapped in a conical
cavity as shown in Figure 4-4. The gas is taken to be air and
the mass is specified. The embryo is initially at static and
thermal equilibrium
following relations
with its surroundings.
are satisfied,
Therefore, the
(4-1)
T,=Tv=Tc(Pv)
(4-2)
V'WV
(4-3)
where r is radius of the liquid/vapor interface, a is surface
tension, Rg is an engineering gas constant, and the subscripts
v, £, and g respectively denote the vapor, liquid, and gas.
The liquid pressure, Pf, is typically taken to be the system
pressure. Since air is assumed to be the only non-condensible
gas in the cavity the ideal gas law is obeyed. V is the
volume of an embryo, and for a conical cavity is given by
(Lorenz, 1972)
V=7tr3 (2- (2+cos2 (0i|r)) sin (0-i|O (4-4)
3 tan(i|0


39
referred as boiling hysteresis. Incipience and hysteresis in
pool boiling have been the focus of numerous experimental
T -T (K)
tr sat v '
Figure 4-1. Nucleate pool boiling hysteresis constructed
from the data of Kim and Burgles (1988).
investigations. It has been observed that the sustaining
incipience point for specified liquids and surface conditions
is predictable and is basically independent of the boiling
history (Yin and Abdelmessih, 1976). In contrast, the
initiation incipience point for highly wetting liquids depends
on initial system conditions as well as the history of various