Heat transfer and vapor bubble dynamics in forced convective boiling

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Heat transfer and vapor bubble dynamics in forced convective boiling
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Thesis (Ph. D.)--University of Florida, 1997.
Bibliography:
Includes bibliographical references (leaves 147-152).
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by Glen Eward Thorncroft.
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Typescript.
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Vita.

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HEAT TRANSFER AND VAPOR BUBBLE DYNAMICS
IN FORCED CONVECTION BOILING
















By

GLEN EDWARD THORNCROFT













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

1997













ACKNOWLEDGMENTS


I would like to express my sincere gratitude to the many individuals who have helped

me accomplish this goal. My greatest appreciation goes to Dr. James Klausner, Chair of my

supervisory committee, for his boundless patience, encouragement, and support throughout

my education and research. His excellence in experimental and analytical research, as well

as his enthusiasm for his work, serves as an example to myself and my fellow students in the

department. Dr. Renwei Mei also provided much technical guidance and expertise, as well

as encouragement, throughout my research. I would like to thank him, along with Professors

William Tiederman, Chung K. Hsieh, and Wei Shyy, for graciously serving on my

supervisory committee and demanding the best work of this student.

My appreciation also goes to Dr. Dan Hanes, Department of Coastal and

Oceanographic Engineering, for the use of their high-speed digital imaging facility which was

crucial to my research. The 3M Corporation, Specialty Fluids Division, generously donated

the perfluorocarbon fluids used throughout this work. I wish particularly to thank Greg

Sherwood of 3M, not only for supplying the fluids, but also for providing a wealth of

technical information and property data for the fluids.

This work was accomplished through the support of the Florida Space Grant

Consortium, through which the author has been funded as a Florida Space Grant Fellow.

This research was also partially supported through the Exxon Education Foundation under

Grant No. 04/1995.








I wish to give special thanks to Becky Hoover, Graduate Secretary for the Department

of Mechanical Engineering. She has been an invaluable supporter and friend, and provided

endless administrative support, guidance, and encouragement throughout my work.

The opportunity rarely arises in one's life to give public tribute to the many

individuals who have had the greatest influence on him. To Estelle Griggs, who taught me

the three "R's", and whose discipline is sorely appreciated; Walter Bowes, who taught me

the meaning of humility, fostered my creative thinking, and showed me that learning could

be fun; Sandy Hudson and Gail Teulon, who taught me how to express my ideas in writing

and to view the world with a healthy skepticism; Doug Vining, a caring and supportive

employer who gave me extra hours when I needed money for college, and any day off I

needed to study; and Rod Henry and Michael Varney, who challenged me to think beyond

the written text and to ask "Why does this make sense?" Each of them have played a large

part in who I am today.

Finally, I want to thank my family and closest friends, without whose support and

understanding through the years this would not have been possible. I particularly thank my

mom and dad, for giving me the drive to be the best at whatever I chose to do, and the

encouragement to pursue it to the end. This document is as much a reflection of their hard

work as it is of mine.













TABLE OF CONTENTS


ACKNOWLEDGMENTS ........... ...........................

LIST OF TABLES .......... ....... ....................... vii

LIST OF FIGURES ........... .................... .......... viii

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

ABSTRACT ........... ....................... .......... xviii

CHAPTERS
1 INTRODUCTION ........... .... ............ ........... 1
1.1 Small-Scale Processes in Flow Boiling Ebullition ............... 2
1.1.1 Vapor Bubble Growth Rate ....... ....... ........ 3
1.1.2 Vapor Bubble Detachment and Motion ................. 5
1.1.3 Waiting Time .......... ........ ............. 6
1.1.4 Nucleation Site Density ........ ........ ......... 7
1.2 Outline of Current Investigation .......... ....... .......... 7

2 EXPERIMENTAL FACILITY ................. ............ 10


2.1 System Overview ...........................
2.2 Development of Test Section .....................
2.2.1 Test Section Design .....................
2.2.2 Fabrication of Heater Assembly ..............
2.3 Air Injection System ...........................
2.4 Instrumentation and Calibration ....................
2.4.1 Flow M eters ..........................
2.4.2 Preheater Heat Loss .....................
2.4.3 Test Section Heat Loss ...................
2.4.4 Test Section Pressure Drop ................
2.4.5 Static Pressure Measurements ...............
2.4.6 Temperature Measurements ................
2.5 Data Acquisition ................ ...........
2.6 Imaging Facilities ............................


3 DEVELOPMENT OF CAPACITANCE-BASED FILM THICKNESS
SEN SO R .............. .............................


ii jil








3.1 Introduction and Literature Survey .... . 30
3.2 Sensor Design and Instrumentation . 32
3.3 Methodology of Sensor Analysis ........................ 34
3.4 Results and Discussion ............................ 37
3.4.1 Stratified Film ........... ................... 37
3.4.2 Annular Flow ............................... 40

4 NUCLEATION SITE DENSITY AND SUPPRESSION ............. 44
4.1 Introduction and Literature Survey ................... ..... 44
4.2 Nucleation Sites in Flow Boiling ........................ 46
4.2.1 Estimating the Minimum and Maximum Cavity Radii ...... 48
4.2.2 Nucleation Site Density ........................ 51
4.3 Experimental Procedure ................. .............. 53
4.4 Results ... ................... .................. 54
4.5 Discussion ......... ........... .. .............. 61

5 OBSERVATION AND MEASUREMENT OF VAPOR BUBBLE
DYNAMICS ........................................ 62
5.1 Introduction and Literature Survey ....................... 62
5.2 Experimental Procedure ................ .............. 64
5.3 Flow Visualization .......... ........ .. ............ 66
5.3.1 Upflow ............... ... ................ 66
5.3.2 Downflow ............. ................... 70
5.3.3 Vertical Pool Boiling ......... ................ 74
5.4 Bubble Dynamics Measurements ........................ 74
5.4.1 Growth Rate ............ .................... 74
5.4.2 Departure and Lift-off Diameter .................. 79
5.4.3 W waiting Time ....... ........ .............. 86
5.5 Discussion ........ ............................. 89

6 VAPOR BUBBLE DYNAMICS MODEL .................... 92
6.1 Introduction and Literature Survey ....................... 92
6.2 Development of Model ......... ....... .............. 95
6.2.1 Buoyancy Force .................. ......... 96
6.2.2 Quasi-Steady Drag and Shear Lift Forces .............. 97
6.2.3 Growth Force .......... ....... .............. 99
6.2.4 Surface Tension Force ....................... 100
6.2.5 Contact Pressure and Hydrodynamic Lift Forces ......... 102
6.2.6 Free-Stream Acceleration and Added Mass Forces ........ 102
6.2.7 Departure Model ................. .......... 104
6.2.8 Sliding Trajectory and Lift-off Model ................ 104
6.3 Results ......................................... 105
6.3.1 Comparison of Model with Experimental Data ........... 105








6.3.2 Examination of Contributing Forces in Sliding and Lift-off
M odel .................... ............... 111
6.3.3 Application of Model to Horizontal Flow Boiling ......... 113
6.4 Discussion .......... ................. .... ........ 120

7 THE VAPOR BUBBLE SLIDING MECHANISM ................. 122
7.1 Introduction and Literature Survey ........................ 122
7.2 Results ...................... ....... .......... 125
7.2.1 Examination of Macroscale Heat Transfer ............. 125
7.2.2 Estimation of Sliding Heat Transfer ................. 129
7.2.3 Sliding Air Bubble Heat Transfer ................... 131
7.3 Discussion .......... ....... ........ ............ 134

8 CONCLUSIONS AND RECOMMENDATIONS .................. 136
8.1 Accomplishments and Findings ......................... 136
8.2 Recommendations for Future Research ..................... 138

APPENDIX A PROPERTIES OF FC-87 ......................... 141
A.1 Property Relations ................ ................. 141
A.2 Estimation of FC-87 Vapor Viscosity ...................... 143

APPENDIX B ESTIMATION OF SHEAR LIFT FORCE ON VAPOR BUBBLE 145

REFERENCES ................. ................ .......... 147

BIOGRAPHICAL SKETCH ................................ 153














LIST OF TABLES


Table pRee
Table 4.1 Point of suppressed nucleation heat transfer data from present
work .............. ................ .......... 57

Table 4.2 Point of suppressed nucleation from Kenning and Cooper (1989)
heat transfer data ................................. 58

Table 5.1 Forced convection nucleation data ................. 67

Table 6.1 Forced convective nucleation data ....................... 109













LIST OF FIGURES


Figure
Figure 1.1 Idealized sketch of vapor ebullition process in upflow boiling ....... 3

Figure 1.2 Sketch of pool boiling vapor bubble growth ................. 5

Figure 2.1 Schematic diagram of vertical flow boiling facility ............. 11

Figure 2.2 Exploded view of visual test section ................. .. 13

Figure 2.3 Connection of test section to system ..................... 14

Figure 2.4 Exploded view of test section heater assembly ............... 15

Figure 2.5 Cross-section of test section. Detail of heater attachment ........ 16

Figure 2.6 Detail of transparent test section with air injection nozzle ........ 16

Figure 2.7 Calibration curve for venturi flow meter ................... 19

Figure 2.8 Calibration curve for vane flow meter ................. 19

Figure 2.9 Preheater assembly ............................... 20

Figure 2.10 Preheater heat loss calibration curve ........ ......... ... 21

Figure 2.11 Control volumes for calibration of heat loss from test section ...... 22

Figure 2.12 Calibration of temperature difference between bulk flow and
heater surface ................... ... ............. 23

Figure 2.13 Calibration curve for test section differential pressure ........ 25

Figure 2.14 Calibration curve for static pressure transducer #1 ............. 26

Figure 2.15 Calibration curve for static pressure transducer #2 ............. 26

Figure 3.1 Exploded view of capacitance meter ................. .. 33

Figure 3.2 Reduction of square vapor flow geometry into composites ........ 35









Figure 3.3 Reduction of round vapor core capacitance into composites ....... 36

Figure 3.4 Percent difference in capacitance between annular flow with a
square and round vapor core .......... ........ 37

Figure 3.5 Upward and side configurations of parallel-plate capacitor in
stratified flow .......... ....................... 38

Figure 3.6 Comparison between predicted and measured film thickness for
the upward orientation .......... ....... ............. 39

Figure 3.7 Comparison between predicted and measured film thickness for
the side configuration ................ ......... .... 40

Figure 3.8 Temperature calibration of CL and C, .. ......... 41

Figure 3.9(a) Typical photograph of liquid film in annular upflow ............ 42

Figure 3.9(b) Typical photograph of liquid film in annular downflow .......... 42

Figure 3.10 Comparison of annular two-phase flow liquid film thickness
measured with capacitance sensor and CCD camera ............ 43

Figure 4.1 Ratio of microconvection heat transfer coefficient to total two-phase
heat transfer coefficient for different flow boiling configurations 45

Figure 4.2 Idealized sketch of a vapor embryo embedded in shear flow
protruding a surface cavity ................. .......... 49

Figure 4.3 Nucleation site density data of Zeng and Klausner (1993b) shown as
a function of r,_/r, ............................... 52

Figure 4.4 Boiling curves for vertical annular upflow and downflow, illustrating
nucleation suppression point ......... ........ ......... 55

Figure 4.5 Comparison of measured single-phase heat transfer coefficient to
Petukhov's (1970) model .......... ....... ........... 56

Figure 4.6 Suppression point cavity ratio, (r,,x/rm),,p as a function of mass
flux ........... ............... .............. 59

Figure 4.7 Suppression point cavity ratio, (r,./rJ),,p as a function of test
section inlet quality ................. .... ......... 59

Figure 4.8 Suppression point cavity ratio, (r,/r ), as a function of wall
heat flux ......... ................ .......... 60








Figure 4.9 Identification of two-phase heat transfer regimes based on point
of suppressed nucleation ........ .......... 60

Figure 5.1 Photographs of bubbles originating from a single nucleation site
in upflow .................. .................... 68

Figure 5.2 Photographs of bubbles originating from a nucleation site in downflow
boiling ................. ........... .......... 71

Figure 5.3 Plot of heat transfer coefficient, h, vs. wall superheat, T.-T,, for
the upflow and downflow conditions in Table 5.1 ............. 73

Figure 5.4 Photograph of bubbles originating from the same nucleation site in
vertical pool boiling ................. .......... .... 75

Figure 5.5 Typical bubble growth measurement ................. .. 76

Figure 5.6 Comparison of mean growth curves; (a) upflow, (b) downflow ..... 78

Figure 5.7 Comparison of measured mean departure diameters for (a) upflow
and (b) downflow forced convection boiling ................. 81

Figure 5.8 Comparison of measured mean lift-off diameters n downflow forced
convection and vertical pool boiling ...................... 83

Figure 5.9 Departure diameter probability density functions at various wall
superheats in upflow forced convection boiling: G=195 kg/m2-s 84

Figure 5.10 Departure diameter probability density functions at various wall
superheats in upflow forced convection boiling: G=250 kg/m2-s .... 84

Figure 5.11 Departure diameter probability density functions at various wall
superheats in upflow forced convection boiling: G=315 kg/m2-s 85

Figure 5.12 Departure diameter probability density functions for (a) G=250
kg/m'-s and (b) G=315 kg/m2-s at various wall superheats
in downflow boiling ......... ........ .............. 87

Figure 5.13 Lift-off diameter probability density functions for (a) G=250
kg/m2-s and (b) G=315 kg/m2-s at various wall superheats
in downflow ............ ...... ................. 88

Figure 5.14 Sequence of measured departure diameters and associated waiting
times for upflow boiling from the same nucleation site .......... 89

Figure 6.1 Illustration of vapor bubble stationary and sliding growth ........ 96








Figure 6.2 Comparison of measured and predicted bubble sliding trajectories:
vertical pool boiling .......... . 106

Figure 6.3 Comparison of measured and predicted bubble sliding trajectories:
upflow ........... ...... .. .. ................ 106

Figure 6.4 Comparison of measured and predicted bubble sliding trajectories:
downflow, u,=0.112 m/s ........................... 107

Figure 6.5 Comparison of measured and predicted bubble sliding trajectories:
downflow, u,=0.144 m/s ............................ 107

Figure 6.6 Comparison of measured and predicted bubble sliding trajectories:
downflow, u,=0.390 m/s ............................108

Figure 6.7 Comparison of predicted and measured (a) departure and (b) lift-off
diameters for vertical pool and flow boiling ................. 110

Figure 6.8 Comparison of forces predicted by model on sliding bubble:
upflow, u, = 0.151 m/s, AT, = 4.300C ................. 112

Figure 6.9 Comparison of forces predicted by model on sliding bubble:
downflow, u, = 0.143 m/s, AT,, = 5.01C ............ 114

Figure 6.10 Comparison of forces predicted by model on sliding bubble:
vertical pool boiling, AT., = 4.53C .................... 115

Figure 6.11 Comparison of measured and predicted departure and lift-off
diameters for horizontal stratified flow boiling of R113 .......... 117

Figure 6.12 Comparison of forces predicted by model on sliding bubble,
horizontal stratified flow boiling, u, = 0.82 m/s, 6 = 4.1 mm,
AT., = 5.2C .................................. 119

Figure 6.13 Variation of lift-off diameter in horizontal stratified flow with
liquid velocity; comparison with results of present model ........ 120

Figure 7.1 Heat transfer coefficient ratio, h/h1,, vs. nucleation site density
for upflow and downflow boiling in the isolated bubble regime ..... 127

Figure 7.2 Comparison of boiling curves for single-phase inlet upflow and
downflow .................................... 127

Figure 7.3 Comparison of heat transfer coefficient vs. wall superheat for
annular upflow and downflow boiling .................... 129








Figure 7.4 Measured heat transfer coefficient vs. bulk wall temperature
difference for single-phase inlet upflow under various air bubble
injection rates ................ ..... 133

Figure 7.5 Measured heat transfer coefficient vs. bulk wall temperature
difference for single-phase inlet upflow with air bubble injection
under varied liquid subcooling ......................... 133

Figure B.1 Shear lift coefficient CL as calculated from Equation (B.5) ... 146













NOMENCLATURE


a vapor bubble radius (m or mm)

A area (m')

C capacitance (pf, or coulombs

C* relative capacitance, (C-C,)/(CL-C,)

C, coefficient of friction

C, specific heat (J/kg K)

C, empirical constant used in Equation (6.3)

d(t) vapor bubble diameter (mm or m)

d,D width of square duct (m or mm)

dd vapor bubble departure diameter (m or mm)

dL vapor bubble lift-off diameter (m or mm)

d, surface/bubble contact diameter (m)

D, hydraulic diameter of duct (m or mm)

f,(r) probability density function for finding cavities with mouth radius r

f2(imm) probability density function for finding cavities with minimum side angle n

f farads

F force (N)

g gravitational constant (9.81 m/s2)

G mass flux (kg/m's)

h convection heat transfer coefficient (W/m'-K)








hf, latent heat of vaporization (J/kg)

H heater thickness (mm)

Ja Jacob number, pCp.tAT./phf,

k thermal conductivity (W/m-K)

K mean vapor bubble growth constant (m/s")

n mean vapor bubble growth exponent

n/A nucleation site density (cm'2)

N/A number of surface cavities per unit area (cm2)

Nu Nusselt number

P pressure (Pa, bar, or psi)

Pr Prandtl number

Q volumetric flow rate (f/min)

q" heat flux (W/m2)

q"L heat loss (W/m2)

r cavity mouth radius (mm or m)

r, maximum cavity radius allowed for nucleation (m)

r, minimum cavity radius required for nucleation (m)

R, universal gas constant (J/kg-K)

Reb bubble Reynolds number, Reb= 2AUa/Pl

Re, liquid Reynolds number, Re, = GDh/,t

t time (s or ms)

td time of bubble departure (ms or s)

t, waiting time (ms or s)

T temperature ("C or K)








T,(z) liquid temperature profile near wall ("C)


u liquid velocity (m/s)

u, mean liquid velocity (m/s)

u(y) liquid velocity profile near wall (m/s)

u* friction velocity (m/s)

U overall heat transfer coefficient (W/m2'K)

V voltage (V)

Vb bubble volume (m')

We, bubble weber number, Web = pAU22a/l,

x vapor quality

z normal distance from heating surface (m)

Greek

a vapor volume fraction

f3 receding liquid/solid contact angle

7y microlayer wedge angle

6 film thickness (m or mm)

AP pressure difference

AT temperature difference

AT, bulk wall temperature difference, T,-Tb (C)

AT., incipient wall superheat ("C)

AT., wall superheat, T,-T., (C)

AT,,b bulk liquid subcooling, T,t-Tb (C)

AU velocity difference between bubble center of mass and liquid velocity at bubble
center of mass (m/s)


XV








e, relative permittivity (C2/N m2 = f/m)

0 liquid/solid contact angle (radians)

O, bubble inclination angle (radians)

X integral length scale (m)

X* dimensionless integral time scale

J dynamic viscosity (kg/ms)

v kinematic viscosity (m2/s)

p density (kg/m3)

o surface tension (N/m)

T integral time scale (s)

O1/ minimum cavity side angle (radians)


subscripts

10

20

a

b

be

i

L, I

mac

mic

meas

pred


single-phase

two-phase

ambient, also annular flow

bulk liquid

bubble center of mass

inlet

liquid

macroconvection

microconvection

measured

predicted

surface








sat saturation

sub subcooling

sup nucleation suppression point

v vapor

w wall (heating surface)

x direction parallel to heater surface

y direction normal to heater surface













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

HEAT TRANSFER AND VAPOR BUBBLE DYNAMICS
IN FORCED CONVECTIVE BOILING

By

GLEN EDWARD THORNCROFT

August 1997




Chairperson: Dr. James F. Klausner
Major Department: Mechanical Engineering

A forced convection boiling facility has been designed, fabricated, and tested to

experimentally study small-scale heat transfer processes in vertical upflow and downflow

forced convection boiling. The facility incorporates a transparent boiling test section,

through which the ebullition process can be observed and recorded using digital single-frame

and high speed motion cameras. A capacitance-based sensor was developed and calibrated

for measurement of liquid film thickness in annular two-phase flows.

Analysis of a current model for nucleation site density has led to the development of

a new dimensionless parameter, the cavity size ratio, which is demonstrated to correlate

nucleation site density. Measurements of flow boiling suppression in annular flow has

revealed that the cavity size ratio is, to a leading order, a fundamental parameter on which

the suppression of nucleation depends. This has led to the introduction of a flow boiling

regime map which delineates the purely convective and nucleate boiling regimes.








Experimental measurements of the ebullition process in single-phase inlet upflow and

downflow boiling has yielded a wealth of data for vapor bubble growth rate, departure and

lift-off diameters, sliding trajectories, and waiting times, in the isolated bubble regime. One

very significant result of these experiments is that vastly different vapor bubble dynamics are

observed for upflow, downflow, and vertical pool boiling. It is demonstrated that the

differences in vapor bubble dynamics are responsible for a marked increase in the heat

transfer rate for upflow compared with that of downflow.

Based on these observations, a bubble dynamic model is developed which predicts

the departure diameter, sliding trajectory, and lift-off diameter in upflow, downflow, and

vertical pool boiling. The model compares well to experimental data recorded in this work,

as well as data reported in the literature. Furthermore, the model is applied to the case of

horizontal stratified flow boiling, for which it shows a marked improvement over previous

models for horizontal flow. Analysis of the model reveals, among other trends, that a

negative shear lift force is responsible for maintaining vapor bubbles at the wall in upflow

and ejecting bubbles from the wall in downflow.

Studies of sliding vapor bubbles have revealed that the sliding vapor bubble

mechanism contributes significantly to the macroscale heat transfer in forced convection

boiling. Experiments incorporating air bubble injection at the heating surface suggest that

the presence of sliding bubbles enhances the bulk turbulent heat transport from the surface,

and that turbulence enhancement is at least as important as the latent heat contribution to the

sliding bubble heat transport mechanism.













CHAPTER 1
INTRODUCTION


Forced convection boiling, or flow boiling, is one of the most widely implemented

and yet least understood modes of heat transfer. The ebullition or boiling process, subject

to countless debate over the past four decades, is coupled with the turbulence structure of the

bulk flow, a complex interaction which still defies fundamental understanding. As a result,

engineers have historically had only simplistic models available to them to predict heat

transfer rates and flow behavior. To this day engineers must rely on experience, empirical

correlations, and costly prototype testing to design and analyze flow boiling systems.

The most widely used empirical method to predict flow boiling heat transfer was first

suggested by Rohsenow (1952). The concept he introduced is that the rate of heat transfer

associated with forced convection boiling is due to two independent and additive mechanisms:

that due to bulk turbulence and that due to ebullition. Based on this concept, Chen (1966)

proposed a correlation for saturated flow boiling in which the total two-phase heat transfer

is obtained by simply adding the effects of macroconvection (i.e., bulk turbulence) and

microconvection (i.e., ebullition). Numerous correlations based on Chen's (1966)

superposition technique have been reported in the literature, many of which have been

summarized by Gungor and Winterton (1986).

There are, however, serious limitations with this method. First and foremost, the

concept presumes that the effects of bulk turbulence and ebullition are mutually independent.

The soundness of this assumption is questionable since, in reality, the growth and motion of






2

vapor bubbles likely effects the hydrodynamic and thermal boundary layers, and vice versa.

Second, correlations using the form proposed by Chen (1966) typically predict that the

macroconvection component is the dominant heat transfer mechanism, and that the

microconvection component does not contribute significantly to the total heat transfer

(Klausner, 1989). In fact, numerous investigators, such as Blatt and Adt (1964), Staub and

Zuber (1966), Cooper (1989), and Zeng and Klausner (1993a) have found microconvection

heat transfer to be significant over a range of flow and thermal conditions. Moreover,

Gungor and Winterton (1986) reported that correlations based on Chen's (1966) correlation

technique fail to accurately correlate a wide range of flow boiling heat transfer data. Despite

these limitations, the technique remains the most widely used to predict heat transfer rates

in forced convection boiling.

The development of more reliable predictions of flow boiling heat transfer requires

a thorough understanding of the fundamental mechanisms which govern the process. Forced

convection boiling is comprised of a number of complicated small-scale mechanisms,

interacting and combining to culminate in the macroscale heat transfer of interest to

engineers. The purpose of this work is to examine these small-scale mechanisms to provide

a framework for the development of future mechanistic models of the macroscale heat

transfer. In the process, the superposition technique proposed by Rohsenow (1952) and used

by Chen (1966) is critically examined based on the results of this study.


1.1 Small-Scale Processes in Flow Boiling Ebullition

The ebullition process in forced convection boiling heat transfer is comprised of a

number of small-scale processes, which are categorized and described in the discussion which

follows. Figure 1.1 illustrates an idealized vapor bubble at various stages of the ebullition






3

process for the case of saturated vertical upflow. For this ideal case, the behavior of the

vapor bubble can be subdivided into five phases: (1) the (stationary) growth phase, in which

the bubble grows while attached to the nucleation site, (2) departure (not labeled), where the

bubble begins to slide away from the nucleation site, (3) sliding, where the bubble is still

attached to the heater and continues to grow, (4) lift-off, where the bubble detaches

completely from the surface and is ejected into the bulk flow, and (5) waiting time (not

shown), defined as the time between departure and the incipience of a new bubble at the

same nucleation site. These processes, along with the active nucleation site density, are

necessary to characterize the heat transfer associated with the ebullition process in forced

convection boiling.







LIFT OFF
-(y)
(STATIONARY)
GROWTH



1 ___ SLIDING
I PHASE





Figure 1.1. Idealized sketch of vapor ebullition process in upflow boiling.



1.1.1 Vapor Bubble Growth Rate

The rate of vapor bubble growth is a measure of the latent heat transport at the

surface. To date, no adequate prediction exists for the vapor bubble growth rate in forced






4

convection boiling. However, for the simpler case of pool boiling, a great deal of progress

has been made in the past decade toward describing the fundamental mechanisms which

control bubble growth. It is therefore instructive to examine the present pool boiling concept

with the aim of understanding the complexities of forced convection boiling bubble growth.

A sketch of a vapor bubble growing in an otherwise quiescent liquid pool is depicted

in Figure 1.2. The vapor bubble begins as a tiny embryo in a cavity or defect in the surface

of the heater. Once growth is initiated, the bubble expands very rapidly, and the momentum

of the vapor is resisted on one side by the inertia of the surrounding fluid and on the other

by the heating surface. The growing bubble thus deforms into a hemispherical dome which

sandwiches a thin, wedge-shaped liquid microlayer between itself and the heating surface.

The evaporation of the liquid within this microlayer supplies the majority of vapor to the

growing bubble, and in turn removes the majority of energy from the heating surface. This

rapid and localized heat transfer consumes the energy from the heater surface, resulting in

temperature contours within the solid. In the case of subcooled boiling, the vapor at the top

of the bubble can condense due to exposure to the cooler bulk liquid, which can ultimately

lead to the collapse of the vapor bubble. In some cases evaporation and condensation may

occur simultaneously, in which case the vapor bubble acts essentially as a heat pipe.

Recently, Mei et al. (1995a and b) successfully used the above concept to develop a

highly detailed numerical analysis to describe the growth of vapor bubbles in saturated pool

boiling. But the extension of this analysis to the case of flow boiling is complicated by

several factors. First, the liquid surrounding the bubble is in motion, and is in fact turbulent

motion, which depends in part on the growth and motion of the bubble. Thus both the

hydrodynamic and thermal boundary layers surrounding the bubble are difficult to describe.

Second, a vapor bubble exposed to forced convection is tilted by the flow, so the shape of






5

the bubble and the microlayer are asymmetric. Third, when sliding is present, the

microlayer is continually exposed to a different part of the heater surface, and the microlayer

structure itself may change in response to the bubble motion. Thus an accurate description

of vapor bubble growth in flow boiling requires a detailed three-dimensional, three-phase heat

and momentum transfer analysis. It is left for future investigators to attempt to model this

complicated process. In this work, experimental vapor bubble growth rate data is obtained

which is necessary in predicting vapor bubble detachment, and to develop a better

understanding of the bubble growth process in forced convection boiling as a framework for

a future analysis.





LIQUID
POOL


GROWING
BUBBLE


IMCROLAYER


CAVITY H
/ .TEMPERATURE
CONTOURS

SOLID WALL;
HEAT IS SUPPLIED
FROM WITHIN OR BELOW

Figure 1.2. Sketch of pool boiling vapor bubble growth.



1.1.2 Vapor Bubble Detachment and Motion

The mechanisms of vapor bubble detachment in flow boiling include departure from

the nucleation site, sliding, and lift-off. Following departure from the nucleation site, vapor

bubbles typically slide and continue to grow until they lift off the surface. This sliding






6

growth continues to remove energy from the surface in two ways: First, the continued

growth of the bubbles is indicative of latent heat transport. Second, the motion of the

bubbles at the surface alters the local turbulence structure of the bulk liquid. Either of these

mechanisms augment the heat transfer from the heating surface.

The vapor bubble sliding and lift-off mechanisms have generally been ignored in flow

boiling heat transfer models reported in the literature. This is likely a result of the prevailing

use of Chen-type correlations, which typically rely on pool boiling experimental data to

predict the microconvection heat transfer. In pool boiling, vapor bubbles typically depart

directly from the nucleation site into the quiescent liquid without sliding; consequently, the

motion of the vapor bubble following departure from the site does not affect the latent heat

transport at the surface. An objective of the present work is to understand and model the

bubble dynamic processes, and to demonstrate to what extent the bubble sliding process

affects the macroscale heat transfer.


1.1.3 Waiting Time

As stated earlier, the waiting time is defined as the time between the departure of a

vapor bubble from its nucleation site and the incipience of a new bubble at the same site.

It is related, along with the vapor bubble growth rate, to the energy consumption at the

nucleation site, and is a partial measure of the rate of energy transport from the surface.

Because the waiting time is connected with the vapor bubble growth rate, its prediction is

beyond the scope of this work. Instead, an objective of this work is to experimentally

examine the waiting time as a framework for future analysis.








1.1.4 Nucleation Site Density

A nucleation site is a microscopic pit or cavity on the surface of a heater in which

vapor bubbles may be generated during boiling. Therefore the number of nucleation sites

which actively produce vapor bubbles have a substantial influence on the ebullition heat

transfer from the surface. During flow boiling, bulk turbulent convection strongly affects

the nucleation site density by removing sufficient energy from the heating surface to

deactivate nucleation sites. In fact, the bulk turbulent convection can be great enough to

suppress nucleation completely. One objective of the present investigation is to understand

the fundamental mechanisms controlling nucleation site density and suppression of sites in

flow boiling.


1.2 Outline of Current Investigation

An experimental and analytical study has been performed to examine a range of

small-scale processes in forced convection heat transfer and their influence on the macroscale

heat transfer. An experimental facility, described in Chapter 2, has been designed, tested,

and calibrated which allows visual examination of the ebullition process in upflow and

downflow boiling. Both single-phase subcooled and two-phase annular flow regimes are

attainable. The facility is fully instrumented to measure relevant heat transfer and flow

properties, and is equipped with digital single-frame and high-speed video cameras to capture

the ebullition process in a transparent boiling section. A capacitance-based sensor, described

in Chapter 3, has been developed and installed to measure liquid film thickness in annular

two-phase flows. The experimental facility has been calibrated and fully tested to ensure the

accuracy of the measurements.

In Chapter 4, an investigation is presented of nucleation site density and the

suppression of active nucleation sites in flow boiling. The nucleation site density model






8

proposed by Yang and Kim (1988) is examined, leading to the development of a

dimensionless parameter, the cavity size ratio, which is demonstrated to correlate flow

boiling nucleation site density. Furthermore, experiments conducted for annular upflow and

downflow forced convection boiling suggest that this parameter is the leading order term on

which the suppression of nucleation sites depends. Experiments in this portion of the

investigation focused on annular flow boiling because of its relevance to a majority of

industrial heat transport processes.

Chapter 5 presents an extensive experimental study of vapor bubble growth and

motion in single-phase inlet vertical upflow and downflow boiling. Using high-speed digital

imaging, a series of experiments were performed to measure vapor bubble growth rates,

departure diameters, sliding trajectories, lift-off diameters, and waiting times in subcooled

single-phase inlet upflow and downflow under various liquid mass fluxes and wall superheats.

The condition chosen for this portion of the investigation were restricted to single-phase flow

inlet to the test section, and focused primarily on the isolated bubble boiling regime. These

conditions were selected in order to facilitate high-speed photography, as well as to eliminate

the effects of adjacent sites on the dynamics of the isolated bubbles. Furthermore, the

absence of annular flow eliminates interfacial effects, which simplifies the modeling of bubble

behavior.

A thorough examination of the data is also presented in Chapter 5, providing a wealth

of insight into the ebullition process and its effect on the macroscale heat transfer in vertical

flow boiling. Photographs of ebullition reveal vastly different vapor bubble dynamic

behavior under upflow, downflow, and vertical pool boiling conditions, which helps to

explain the difference in heat transfer rates observed between upflow and downflow boiling.

Examination of the vapor bubble growth rate, departure and lift-off diameters, and waiting






9

time demonstrate the complicated interaction of the bulk flow and the energy transport at the

heater surface. From these data the mechanisms which control the growth and motion of the

vapor bubble are postulated, and a framework is developed of a phenomenological vapor

bubble dynamics model.

In Chapter 6, the knowledge obtained from experiments is used to develop a vapor

bubble dynamics model for vertical upflow and downflow. The model predicts vapor bubble

departure and lift-off diameters, as well as sliding trajectories, utilizing a force balance

similar to that of Zeng et al. (1993a and b) which was developed for horizontal flow boiling.

The model compares well to experimental data from a range of flow and thermal conditions,

including data taken from the literature. Moreover, the model is demonstrated to predict

features of bubble lift-off behavior in horizontal flow which were not captured by Zeng's

(1993a and b) model.

In Chapter 7, a detailed investigation of the vapor bubble sliding process is presented

which quantifies the contribution of vapor bubble sliding energy transport to the total heat

transfer in forced convection boiling. Experiments performed in upflow and downflow over

a range of flow conditions reveal that the vapor bubble sliding mechanism contributes

significantly to the macroscale heat transfer. Experiments using air bubble injection are

performed to isolate the effect of bulk turbulence enhancement on the bubble sliding energy

transport mechanism. The results of these tests demonstrate that bulk turbulence

enhancement may be as important as the latent heat transport in the bubble sliding energy

transport mechanism.

The work concludes in Chapter 8 with a summary of this work, as well as a

discussion of the critical phenomenological issues which remain unresolved. Finally,

recommendations are proposed for future research efforts.














CHAPTER 2
EXPERIMENTAL FACILITY


2.1 System Overview

The experimental work in this research was performed in a vertical flow boiling test

facility designed and fabricated under the direction of the author. A schematic diagram of the

system is shown in Figure 2.1. A variable speed Model 221 Micropump drives the working fluid

through the facility. Following the pump, the fluid is filtered to eliminate contaminants. The

volumetric flow rate is then measured using either a venturi- or vane-type flow meter, each

installed to measure a different range of flow rates. The fluid is preheated via four preheaters

to achieve a saturated two-phase mixture, then routed by a series of valves (la&b, 2a&b) to

obtain vertical upflow or downflow in the test section. The square test section, described in

detail in Section 2.2, features a DC-powered nichrome heating strip, and is used to measure wall

temperatures and heat fluxes, as well as to make visual observations of nucleation and

hydrodynamic phenomena using a CCD camera. A capacitance sensor, described in Chapter 3,

is used to measure film thickness in annular two-phase flows. From there the flow enters a

water-cooled, shell and tube condenser/receiver which returns the fluid to a subcooled state.

The operation of the facility is achieved through a combination of manual control and

automatic monitoring. The physical operation of the system, i.e. the pump, preheaters, test

section, and cooling via the condenser/receiver, is controlled manually. Nearly all measurements

of temperature, pressure, flow rate, etc., are made using a data acquisition system controlled by

a PC-style computer. An elaborate computer code was written which outputs both unprocessed






11

data and calculated quantities on the screen in real time, so that complete monitoring of the

system data is possible during the experiment.


Figure 2.1. Schematic diagram of vertical flow boiling facility.


FC-87, a perfluorocarbon fluid supplied by 3M Corporation, was used as the working

fluid for the system. This fluid was selected for several reasons: First, its low latent heat of

vaporization (26.9 kJ/kg @ 250C) reduces the heat input required to achieve nucleate boiling.

Second, its low boiling point (30.0 *C @ 1 atm) translates to a lower system temperature and

pressure, allowing more flexibility in the selection of working materials and the design of

components. Additionally, the fluid is nontoxic, chemically inert, and poses no threat to the

ozone layer. Finally, the properties of FC-87 are well documented; a list of thermodynamic and

physical properties is provided in Appendix A.






12

2.2 Development of Test Section


2.2.1 Test Section Design

The most critical component of the boiling facility is the transparent test section, where

nucleate boiling phenomena is measured and observed. Several requirements govern the design;

first, the test section is used with the optical imaging system to conduct high-resolution

measurements, so the section must be transparent and provide a clear and unimpeded view of the

heating/boiling surface and flow. Second, a method is needed to attach the nichrome heating strip

to an inside wall of the section, and to attach leads through the walls to an external power source.

Thermocouples must also be attached to the underside of the heater, while being electrically

insulated from the heater, and penetrate the walls of the section. Finally, the test section must

withstand the operating pressures and temperatures of the system, and attach to the rest of the

system without disturbing the flow. All of these requirements must be met while maintaining

leak-free operation.

The design of the test section underwent several iterations before success in all aspects

was achieved; the final design is depicted in Figure 2.2. The walls of the test section and the

heater assembly are constructed of 1/2-inch-thick cast Lexan plate; these are bonded together with

methacrylate resin to form a 12.7 x 12.7 mm square duct. Cast Lexan was chosen for its optical

clarity and its strength. A 30 cm long, 0.15 mm thick nichrome strip, clamped and adhered to

one wall, is used as a heating surface. A detailed discussion of the heater assembly is presented

in Section 2.2.2. Two 1-inch-thick Lexan flanges are sleeved over the ends of the duct and

bonded with the resin. The test section was leak-tested to 414 kPa (60 psig); leaks were sealed

by lowering the pressure inside the test section with a vacuum pump, and using suction to fill the

leaks with 5-Minute epoxy. The test section is installed to the boiling facility as shown in Figure

2.3. The section is connected at both ends to 12.7 x 12.7 mm ID square brass tubing, extending

approximately 1 meter above and below the test section to form a hydrodynamic development




























HEATER ASSEMBLY


Figure 2.2. Exploded view of visual test section.


length for the flow. A brass plate, soldered to the end of the square tube, is machined to form

a double O-ring face seal. This type of flange seals the joint while leaving the flow undisturbed.

A series of flange seals are also used to install the capacitance sensor, and to connect the square

tubing with the rest of the facility. In addition, a flexible tube is mounted to the top of the line

to aid in alignment, and to eliminate stresses on the test section and capacitance sensor due to

thermal expansion.

Power to the heater is supplied by a 240 volt/20 Amp/3-phase AC source, converted to

36 V/125 A DC through an autotransformer and rectifier. A rheostat and autotransformer are

manually adjusted to control the DC power input to the heater. Two digital voltmeters measure

the power into the heater: the voltage across the heater is measured directly, while the current

is determined by measuring the voltage across a 1 m1 shunt connected in series with the heater.









BUNA-N O-RINGS





0 SOLDER JOINT





TEST SECTION

BRASS TUBING:
127 X 12.7 MM
BRASS FLANGE SQUARE ID


Figure 2.3. Connection of test section to system.





2.2.2 Fabrication of Heater Assembly

The fabrication of the heater assembly is shown in Figure 2.4. The ends of the heater

are wrapped over two brass bolts, machined with flat square heads. The ends are then

sandwiched between the bolts and square brass washers, which clamp the heater in place when

attached to the Lexan base. Two hex nuts hold the clamps in place, while O-ring washers seal

the protrusions. The brass bolts, protruding outside, attach to an external DC power source. To

measure the heater surface temperature, six equally-spaced thermocouples are attached to the

underside of the nichrome strip, and lead out through holes in the base. A detailed description

of the thermocouples used in the facility are described in Section 2.4.6.

The most difficult aspect of the design is the attachment of the thermocouples to the

heater and the attachment of the heater to the Lexan base. In prior designs, numerous epoxies,

resins, and glues were used to bond the heater to the base, but thermal expansion would cause

the nichrome strip to shear off of the adhesive and detach completely from the Lexan base.

Ultimately the technique illustrated in Figure 2.5 proved successful. A high-strength, non-






15

hardening adhesive tape manufactured by 3M Corporation holds the heater to the base; it forms

a flexible bond which allows thermal expansion of the heater. The heater and base are slightly

wider than the duct, and the joining walls are machined with a 0.5 mm lip which holds the edges

of the heater in place. The heater is also pretensioned while adhered to the base to counteract

thermal expansion. The thermocouples are attached to the heater with Hysol Aerospace Epoxy,

at spots pre-coated with the epoxy to provide electrical insulation. The stripped thermocouple

wire is sealed within the base with 5-Minute epoxy. A small air space near the thermocouple

junction is provided to eliminate shear stress due to thermal expansion of the heater.



THERMOCOUPLES
NICHROME HEATER:
.3048 M LONG
12.7 MM WIDE
0.15 MM THICK







O-RING SEAL


LEXAN BASE

0B HEX NUT

Figure 2.4. Exploded view of test section heater assembly.



2.3 Air Injection System

An air injection system was installed at the entrance to the test section to allow for the

injection of air bubbles at the heater surface during certain experiments. A schematic diagram

of this system is depicted in Figure 2.6. The nozzle is constructed of 1.6 mm OD brass tubing,

crimped at the tip to provide a small (less than 100 ,m) opening. The tubing is soldered to the

square brass channel containing the working fluid, such that the nozzle tip extends into the boiling












NICHROME HEATER


7 mm


12.7

AEROSPACE
EPOXY




,\ i THERMOCOUPLE

DEVCON
5-MINUTE EPOXY




Figure 2.5. Cross-section of test section. Detail of heater attachment.



I NICHROME
THEATER
TEST SECTION \ Z



'' HEATER
N! OL TERMINAL

NOZZLE _




~~^~t : 1iI


i BRASS
Si LANGE




/ ,IIR INJECTION
SQUARE BF-
TUBING

LIQUID
FLOW


Figure 2.6. Detail of transparent test section with air injection nozzle.






17

test section just below the heater. Compressed air is supplied to the nozzle, which is adjusted

by a needle valve to obtain air flow rates ranging from zero to 50 mt/min. A capillary-tube flow

meter was constructed in the laboratory to measure air flow rate, where the pressure drop across

the 0.83 mm ID capillary tube is measured by a Validyne model DP45-16 differential pressure

transducer. The voltage output of the transducer was calibrated using a syringe pump, and the

estimated uncertainty of the air flow rate measurement is +2.0 (/min. Prior to entering the test

section, the air is first routed through approximately 2 meters of 3.2 mm OD copper tubing,

attached to the square brass tubing attached to the inlet of the test section. This technique allows

the air to be preheated by the inlet liquid flow to ensure that the air enters the test section at the

bulk fluid temperature.


2.4 Instrumentation and Calibration


2.4.1 Flow Meters

Two flow meters are installed in the facility to measure a wide range of volumetric flow

rates. A venturi meter is used to measure low flow rates (0.0-1.8 e/min). The differential

pressure from the entrance to the throat is measured with a Validyne model DP15 variable

reluctance differential pressure transducer. The electrical signal of the transducer is converted

to a voltage output using a carrier demodulator, which is then connected to a data acquisition

system discussed in Section 2.5. The voltage is calibrated directly against the volumetric flow

rate, using a volume-time method. The resulting calibration curve is depicted in Figure 2.7. A

curve fit of the form y=Ax" yields


Q = 0.54537 Vo-2017 (2.1)


where Q is the volumetric flow rate in liters per minute, and V is the voltage across the

transducer. To account for a small drift in the zero-flow-rate reading, the voltage is referenced






18

to a zero reading taken at the beginning of each test. The standard deviation of the experimental

data for the above curve fit is 0.43% of full scale, within the accuracy of the DP15 as reported

by the manufacturer.

An Erdco model 2521 vane-type flow meter is installed parallel to the venturi meter to

obtain a higher range of flow rates (3.0-9.0 /1min). Two valves installed prior to the meters

allow the user to switch between the two. The vane meter is equipped with a 4-20 ma analog

output, which is connected to a 500 ohm power resistor. The voltage across the resistor is

recorded by the data acquisition system, and calibrated against the volumetric flow rate as before.

The resulting calibration curve for this meter is depicted in Figure 2.8. A third-order polynomial

curve fit of the experimental data yields


Q = 1.067 + 1.156V 0.02354 V2 + 0.004055 V3 (2.2)


where Q is in liters per minute and V is in volts. The standard deviation of the experimental

data for this curve fit is 0.44%, which is within the limits of repeatability reported by the

manufacturer.


2.4.2 Preheater Heat Loss

Four preheaters raise the fluid from a subcooled liquid state to the desired vapor quality

prior to entering the test section. Each heater, one of which is illustrated in Figure 2.9, is coiled

around a 3/8 inch copper tube, and delivers up to 1000 Watts. Each is powered by a 240 AC

line, controlled manually through an adjustable AC autotransformer. The power input to each

of the preheaters is measured and recorded manually: a digital volt meter measures the voltage

across each heater, while a clamp-on AC current probe is used with a digital multimeter to

measure the current. The system is insulated, from the preheaters to the entrance to the

condenser/receiver, using 25 mm thick fiberglass pipe insulation. Heat loss through the

insulation is considered negligible except at the preheaters, where it must be determined. To







19


2.0

0 Data
Curvefit

1.5 -




o 1.0 0

u


2 0.5



0. 0

0 2 4 6 8 10 12

Voltage (V)

Figure 2.7. Calibration curve for venturi flow meter.






9 -

0 Data ,
8 Curve fit


S6



0
U5





3


2
1 2 3 4 5 6 7
Voltage (V)

Figure 2.8. Calibration curve for vane flow meter.






20

calibrate this heat loss, the working fluid is drained from the system, and a known power is input

to the preheaters. When thermal equilibrium has been reached so that the power input equals the

heat loss through the insulation, thermocouples record the surface temperature of the insulation,

T,, along with the ambient temperature, T.. When this is repeated over various power inputs,

a curve of heat loss versus T, T, is generated, which is depicted in Figure 2.10. A fourth-order

polynomial curve fit of the data gives


q = -0.07275 + 0.6618AT + 0.07057AT2 (2.3)
-0.002863AT3 + 0.00004101AT4




where 4L is in Watts and AT = T,-T., with T in degrees Celsius.




SURFACE
THERMOCOUPLES






127MM OD 11 4MM ID l


220 VAC
1 000 W MAX


Figure 2.9. Preheater assembly.

















20



lo /
10

5


0 5 10 15 20 25 30
T- Ta ('C)

Figure 2.10. Preheater heat loss calibration curve.





2.4.3 Test Section Heat Loss

In order to accurately measure the energy imparted to the flow in the test section, the

energy loss from the test section to the atmosphere must be taken into account. To quantify this

effect, the following procedure was used. At a flow rate of approximately 250 kg/m2-s and a

given system operating temperature, the facility was allowed to come to thermal equilibrium, and

measurements of bulk flow temperature and heater surface temperatures were recorded. Assuming

a 2-dimensional control volume depicted in Figure 2.11(a), an energy balance at the fluid/wall

interface yields


q11" = q (2.4)


or


h(T,-T) = U(T,-T,)





22

where h is the convective heat transfer coefficient of the fluid, U is the overall heat transfer

coefficient for the heat transfer from the fluid/wall interface to the atmosphere, and Tb, T,, and

T, are the bulk flow, surface, and ambient temperatures, respectively. Equation (2.5) implies

that, if the temperatures are measured and the convective heat transfer coefficient for the fluid

flow can be determined, the overall heat transfer coefficient, U, may be readily determined.


TEST SECTION
/WALL


17 ~ ~ ~ ~ T T ~~ is --.-- ---
STb. T., T


Ii-




(a) (b)


Figure 2.11. Control volumes for calibration of heat loss from test section.


A plot of (Tb-T) vs. (T,-TJ over a range of bulk fluid temperatures is illustrated in

Figure 2.12. Linear regression curve-fits of each set of data are included in the figure. The

(T T,) data were measured relative to both thermocouples which measure bulk flow

temperature, one located directly above and one below the test section. The slope of both curve-

fits are approximately equal, although a small difference in the magnitude of the two curves

(s0.4*C) is noted. This is attributed to the difference in bulk temperature, Tb, measured by the

two thermocouples; this difference is within the stated accuracy of the thermocouples. The slope

of either curve-fit is thus a measure of the ratio of U/h. To estimate h for single-phase flow, the

model by Petukhov (1970) is used for turbulent, fully developed flow through a duct,









2.U I I I I I
0 (T -Tb. above)

5 (T. -Tb. belw)
1.5
O












-5 0 5 10 15 20 25
T, Ta (C)

Figure 2.12. Calibration of temperature difference between bulk flow and heater surface.




Nu, hDh RePr(Cfl2) 10' S k 1.07+12.7(Pr 1)C/2


S= (2.236 nRe-4.639)-2 0.5



where Dh is the hydraulic diameter of the duct which is equal to the side width for a square cross-

section, Cf is the coefficient of friction, Re is the Reynolds number, and Pr is the Prandtl

number of the fluid. Estimating the properties of FC-87 to be constant, the heat transfer

coefficient for the fluid flow for these experimental data is estimated to be h = 300 W/m'-K.

Finally, from the slope of the curves in Figure 2.12, the overall heat transfer coefficient across

the test section to the atmosphere is calculated from Equation (2.5) to be U=22.0 W/m'-K.

During operation, an energy balance on the test section gives


q" q"= h(T-Tb) ,






24

where q is the power input to the heater per unit surface area of the heater, q" = U(T,-T,)

is the heat loss, and h(T,-T,) is the energy convected from the heater by the fluid flow. the

convection coefficient is not typically known a priori and must be determined using Equation

(2.8).

When power is supplied to the heater, the inner surface temperature of the test section

is no longer uniform, since only one wall of the test section is heated. Therefore in order to

estimate the heat loss, an average surface temperature is calculated by assuming the unheated

surfaces to be approximately equal to the bulk temperature. This condition is depicted in Figure

2.11(b). A weighted average of surface temperatures is then used to calculate qE in Equation

(2.8).


2.4.4 Test Section Pressure Drop

The streamwise pressure drop for the test section is measured with a Validyne model

DP15 variable reluctance differential pressure transducer, identical to the one used with the

venturi flow meter. A carrier demodulator converts the signal output of the device to a voltage,

which is recorded by the data acquisition system. The voltage signal is proportional to the

differential pressure; the calibration curve, depicted in Figure 2.13, results in the linear

expression

AP = 1.377 V (2.9)


where AP is given in kPa and V in volts. As before, some drift is encountered with the voltage

output at zero AP, so the voltage measured is referenced to a zero-AP voltage taken at the

beginning of each test. The standard deviation of the calibration data for the above curve fit is

0.05% of full scale, which is within the accuracy stated by the manufacturer.








14
0 Data )2
12 Curve Fit









a 4
<00












0 2 4 6 8 10
Voltage (V)
Figure 2.13. Calibration curve for test section differential pressure.




2.4.5 Static Pressure Measurements

Two Viatran model 2415 static pressure transducers are installed at either side of the test

section to measure inlet and outlet pressure and, in conjunction with thermocouples mounted

nearby, to calculate thermophysical properties of the working fluid. Transducers number 1 and

2, mounted below and above the test section, respectively, are calibrated in Figures 2.14 and

2.15. The resulting linear curve fits are


PI = -1.551 + 41.63 V (2.11)



below the test section, and


P = -5.502 + 69.10V (2.12)



above the test section, where P, and P2 are given as gage pressure in kPa and V is in volts. Both

calibrations are accurate to 0.12% of their respective full scale.






26


225

Transducer #1 -
Below Test Section
0
175 O Experiment

S150 -- Curve Fit

12 125
a
100 -

75 -7

50 -

25 -

0
0.0 10 20 3.0 4.0 5.0
Voltage Output (V)
Figure 2.14. Calibration curve for static pressure transducer #1.


350


300


250


200


150


100


50


0


00 10 20 30 4.0 50

Voltage (V)
Figure 2.15. Calibration curve for static pressure transducer #2.


Transducer #2 -
Above Test Section

0 Experiment
- Curve Fit



0'

a

a
0
0
0
0








2.4.6 Temperature Measurements

Numerous temperatures are monitored and/or recorded during an experimental run. The

temperature at the inlet to the preheaters establishes the subcooled liquid state. Surface

temperatures on the preheater insulation determine the heat loss at the preheaters. Temperature

probes at either inlet (depending on the flow direction) of the test section establish the bulk fluid

two-phase temperature, and are used with the temperature at the preheater inlet to evaluate the

vapor quality of the flow. Finally, temperatures on the surface of the test section heater are

monitored.

Temperature measurements throughout the system were made with Type E (Chromel-

Constantan) thermocouples, accurate to within + 1.0C. 36-gauge wire (0.005 in./0.127 mm

dia.) was selected for fast response. Thermocouple junctions were welded in the laboratory,

resulting in a typical bead size of approximately 0.44 mm. Thermocouple probes, manufactured

in the laboratory, were used to measure bulk fluid temperature. The probes were constructed of

1/16 inch brass tubing; the thermocouple wire was inserted into the tubing such that the junction

was exposed directly to the flow. The wire was sealed inside the tubing using epoxy adhesive,

and the probe was installed in the system with brass compression fittings. The voltage output of

the thermocouples was measured by the data acquisition system and converted to temperature via

operating software (described in Section 2.5).


2.5 Data Acquisition System

A digital data acquisition system has been developed for monitoring and recording

measurements of pressure, temperature, flow rate, and capacitance during the experiment. The

system is comprised of two major components: the data acquisition hardware and the operating

software. An ACCES AD12-8 12-bit, 8-channel analog-to-digital (A/D) converter board installed

in an 80386 personal computer performed the data acquisition. Two ACCES AIM-16 16-channel

multiplexer cards are interfaced to two channels on the board, allowing the system to measure






28

up to 32 different signals. Each channel of the multiplexers has a preamplifier with

programmable gains ranging from 0.5 to 1000. A thermistor located at channel 0 of the

multiplexers served as the reference temperature for thermocouple measurements. The A/D

board and the multiplexer cards were calibrated according to the manufacturer's specifications.

A QuickBASIC computer code, developed for this work, operates the data acquisition

hardware and gives continuous data output of every instrument during an experiment. The

operation of the system is as follows: each analog signal from the respective instrument was

supplied to one of the 32 channels of the multiplexers. Appropriate gains were set in the

program for each channel to achieve maximum signal resolution. Because two-phase flows are

inherently unstable, and because signals received from thermocouples and other devices carry

unwanted noise, all measurements were time-averaged to obtain repeatable values. Typically,

500 sampling points were taken for each channel over a 5-second interval and averaged to obtain

one set of data.

The operating software converts the voltage data of the sensors to pressure, temperature,

flow rate, and capacitance using standard correlations and those developed in Section 2.4. A

menu-driven screen format was developed to display the data. The software also displays film

thickness, vapor volume fraction, vapor quality, and other calculated values for monitoring during

the experiment. A keystroke changes the format of the output from converted data to

unprocessed voltages to allow verification of instrument operation. Finally, all unprocessed data,

reduced data, and calculated properties and quantities are saved at the operator's command to

ASCII file format, which is imported to spreadsheet software for further analysis and graphical

display.

2.6 Imaging Facilities

Two digital imaging facilities were used to obtain images of the flow and of nucleation

phenomena through the transparent boiling test section. The first consists of a Videk Megaplus






29

CCD single-image camera with image resolution up to 1320x1036 pixels. The camera is

equipped with a Vivitar 50 mm macro lens for high magnification and low optical distortion. The

output of the CCD camera is input to an Epix 4 megabyte frame grabber card installed in an

80386 personal computer. The frame grabber allows for either high resolution (1320x1035

pixels) or low resolution (640x480 pixels) images, displayed on a Sony monitor with 1000

lines/inch resolution. The imaging acquisition was software-controlled using a C language

algorithm, and image processing and analysis were performed using two commercial programs,

Pixfolio and SigmaScan.

A Kodak EktaPro digital high-speed motion camera was used to capture moving images

of the ebullition process. The Model VSG Intensified Imager and Controller captures images

with a resolution of 192x239 pixels at rates ranging from 1000 full-size frames per second up

to 6000 partial frames per second. Typically, half-frame images were recorded at 2000 frames

per second. The camera is equipped with a Vivitar 50 mm macro lens for high magnification and

low distortion. The lens/camera configuration results in an image field of approximately 2 x4

mm (half-frame images) with a 20 pm resolution. A typical synchronous recording is comprised

of 1600 images spanning 800 ms in real time. An EktaPro EM Motion Analyzer stores the

images, which are then downloaded to standard S-VHS video tape. A description of the image

acquisition and analysis procedure is described further in later chapters.














CHAPTER 3
DEVELOPMENT OF CAPACITANCE-BASED FILM THICKNESS SENSOR


3.1 Introduction and Literature Survey

Capacitance sensors have recently gained popularity for measuring vapor volume fraction

in two-phase flows. Their popularity is primarily due to the fact that they are non-invasive and

are simple to operate. However, the design of capacitance sensors can vary greatly depending

on the desired temporal and spatial resolution, signal-to-noise ratio, two-phase flow pattern, and

temperature variations. For this reason, prior investigators have put forth great effort in (i)

understanding those factors that dictate the performance of capacitance sensors, and (ii) improving

the performance of those sensors. Most prior work has been conducted for two-phase flows

through circular tubes, but many of the results can be generalized to other geometries. The focus

of previous work may be categorized as described below.

Sensor geometry. The sensitivity of the capacitance sensor to changes in liquid film

thickness or vapor volume fraction strongly depends on the geometry of the sensing electrodes,

and various investigators have examined the performance of different electrode configurations.

Irons and Chang (1983) and Chun and Sung (1986) tested strip and ring type electrodes for

gas/powder and liquid/vapor flows, respectively. Gregory and Mattar (1973) and Abouelwafa

and Kendall (1980) tested many different electrode configurations for liquid/vapor flows,

including helical, strips, parallel plates, and concave plates. Ozgu and Chen (1973) considered

ring-type and parallel-strip type electrodes and discussed the required spacing between electrodes

to achieve the optimum sensitivity. These studies revealed, among other things, that the

calibration of a capacitance sensor is flow regime dependant. Therefore the anticipated flow






31

regime, whether known or unknown, should be considered in choosing the electrode

configuration.

Analytical/numerical modeling. Analytical attempts have been made to estimate the

sensor output for various flows. Abouelwafa and Kendall (1979a, 1979b) estimated the output

of helical and concave-plate type sensors for homogeneous, slug, annular, and stratified flows

by assuming a uniform charge distribution on diametrically opposed electrodes as well as uniform

flux lines between them. Chun and Sung (1986) used a similar approach for ring-type electrodes.

Geraets and Borst (1988) solved for the three-dimensional potential field between helical

electrodes and developed a closed form expression for the capacitance associated with annular and

dispersed flows. Gupta et al. (1994) used a finite-difference technique to solve for the potential

field between concave plates with stratified flow. Although they used this solution to compute

the impedance, it may also be used to compute the capacitance.

Spatial sensitivity. Xie et al. (1990) conducted a detailed investigation on the effect of

electrode size, wall thickness, and the proximity of electrical shielding on the spatial sensitivity

of a concave plate capacitance sensor. Based on their analysis, they attempted to optimize the

electrode design so that the sensor output is approximately linear and independent of flow regime.

However, due to non-uniformities in the electric field with changes in flow regime, it is not

possible to design a sensor with a purely linear output. Klug and Mayinger (1994) used an eight-

electrode sensor to measure impedance in horizontal gas/liquid flows. The use of capacitance was

also considered to measure two-phase flows of nonconducting fluids. The impedance was

measured between various pairs of electrodes, each sensitive to a different region of the flow.

The impedances measured from these pairs is compared to those produced by known flow

patterns in order to identify flow regime and volume fraction.

Temporal resolution for dynamic measurements. Various authors have used the time

history of the capacitance signal output as a way of discerning information about the flow






32

structure. Geraets and Borst (1988) used the signal time history as a way of characterizing the

flow pattern in horizontal gas-liquid flows. Klausner et al. (1992) examined the power spectral

density function for the capacitance signal to study the low-frequency fluctuations of film

thickness in horizontal stratified and annular liquid-vapor flows. Keska et al. (1994) also studied

frequency and power spectral density distributions, from time traces of concentration, film

thickness, and pressure, in horizontal air-water flow.

Effect of temperature variations. Klausner et al. (1992) discussed the effect of

temperature variations on both the permittivity of the phases and the surrounding sensor body and

devised a temperature-correction scheme to account for the effect.

In this work, a capacitance-based film thickness sensor is designed, and an experimental

investigation and analysis are performed to predict its output as a function of liquid film

thickness. Both stratified and annular flow patterns are considered. Since the fluids considered

have a low relative permittivity (FC-87, e,= 1.72; FC-72, ,= 1.75), the analysis was very useful

in designing a sensor with satisfactory resolution. Furthermore, the analysis eliminates the need

for sensor calibration when measuring horizontal stratified flow or annular flow film thickness.

The analysis is validated by measurements of stratified, stationary films in the sensor. The sensor

is then installed in the vertical boiling facility, where annular flow film thickness measurements

are obtained with the digital imaging facility and compared against those measured using the

capacitance sensor. The temperature range over which the flow boiling facility operates is 20 to

80*C, and thus it is necessary to account for non-isothermal conditions, which is accomplished

by calibrating the sensor over a range of operating temperatures.


3.2 Sensor Design and Instrumentation

An exploded view of the square cross section capacitance sensor is illustrated in Figure

3.1. The sensor is constructed in a similar manner to the test section, with four 12.7 mm thick

Lexan walls, chemically welded with methacrylate resin. Two Lexan flanges welded at each end



























PARALLEL-PLATE
CAPACITOR PAIRS
BNC CONNECTORS

Figure 3.1. Exploded view of capacitance meter (wiring omitted for clarity).



of the sensor allow for connection to the flow boiling facility. Two sets of parallel brass plates,

mounted apart and rotated 90* from each other, span the width of the channel and are attached

to the inside surfaces of the walls. The result is two separate sensors, labeled as 'set 1' and 'set

2' in Figure 3.1, which are mounted in orthogonal planes. The resulting capacitances of the

respective sets are electrically connected in parallel such that the signals are combined. This

technique helps to ensure that asymmetries in the film thickness, if present, do not affect the

combined signal from the sensor. In each set, the plates comprising the capacitor are divided into

3 separate pieces, one long plate (12.7X60 mm) and two short plates (12.7X20 mm). The plates

can be wired together in different combinations, allowing different effective electrode lengths,

and therefore allowing some control over the sensitivity of the sensor. In this study, however,

only the long electrodes are used.

Surrounding the sensor are 4 aluminum plates, mounted to the sides of the flanges, each

grounded to shield the electrodes from external electromagnetic fields. The two sets of capacitors






34

are connected together (in parallel for the current configuration) with shielded cable, then

connected to BNC fittings mounted on the aluminum plate. The wiring of the sensor has been

omitted in the figure for clarity. The sensor is connected via BNC fittings and shielded cable to

a Keithley 590 digital CV analyzer. The instrument measures capacitance with a resolution of

0.1 fF and accurate to 0.1 % of full scale. An analog signal from the analyzer is input to the data

acquisition system for monitoring and recording. In order to test the adequacy of the capacitance

sensor analysis, the CCD camera is used to photograph the liquid film through a visual section.

The liquid film thicknesses measured using the capacitance sensor are compared with CCD

camera film thickness measurements.


3.3 Methodology of Sensor Analysis

An analysis is performed on two parallel plates of area A, separated by a distance d, with

a homogeneous material of relative permittivity e, in between. For the ideal case where'A > d,

the electric field is constant throughout the material, and the capacitance is given by


C = E ,A (3.1)
d

where e. = 8.85X10"12 C2/(Nm2) = 8.85 pf/m is the permittivity of free space. Due to the

linearity of the Laplace equation which governs the potential field within the sensor, the

capacitance of a composite material in the space between the plates can be analyzed by

constructing an equivalent circuit of series and parallel capacitances. For example, the composite

material shown in Figure 3.2 has a capacitance

C = C, + C c] + C1 (3.2)
1C C-3 C,2

where C,, C2, and C, are computed using Equation (3.1) applied to the equivalent geometry

shown.





35

The composite structure depicted in Figure 3.2 is equivalent to a steady two-phase annular

flow where the vapor core has a square cross section. Of course, in a real flow, the annular core

is never completely square in cross section. When the vapor volume fraction is small the annular

core approaches a circular shape, although for small vapor volume fractions annular flow is not

likely to occur. And as the volume fraction approaches unity the core shape approaches a square

with rounded corners. Given this reasoning, the calibration procedure assumes that the annular

core cross section will be square.








_i i
-- -- C, C,





LIQUID VAPOR



Figure 3.2. Reduction of square vapor core flow geometry into composites.


Nevertheless, it is of interest to determine the degree of error introduced in the vapor

volume fraction measurement when the shape of the core is circular. To address this concern,

the method of composites, described above, is repeated for the case of a round vapor core

geometry. The capacitance sensor is divided into very small composites, as demonstrated in

Figure 3.3. For the same vapor volume fraction, the computed capacitance for the round vapor

core may be compared against that of a square core. The percent difference between the

computed capacitance for the two geometries is depicted in Figure 3.4. The comparison is made






36

up to a vapor volume fraction of 0.785, which corresponds to the largest circular vapor core that

can exist in a square cross section. It is seen is that, when the vapor volume fraction is small,

the error in approximating the round vapor core as square becomes vanishingly small. As the

vapor volume fraction increases, the error increases. However, two points are worth noting.

First, as the vapor volume fraction increases, the shape of the core will begin to conform to the

shape of the square channel. Indeed, for annular flow conditions achievable in the current two-

phase flow facility (a > .80), the vapor core appears to be a square with rounded corners.

Second, the maximum error in Figure 3.4 is less than 0.30%, which is within the accuracy of

the measuring technique. It is noted, however, that the small error is partially due to the fact that

the ratio of the liquid to vapor permittivity is small, e /E,, = 1.75. Therefore for this work,

the vapor core geometry can be effectively approximated as square without the introduction of

any significant error.

















F7 LI QU ID VAPOR


Figure 3.3. Reduction of round vapor core capacitance into composites.






37

3.4 Results and Discussion


3.4.1 Stratified Film

It is desirable to test the capacitance film thickness sensor on a bench top where the liquid

film can be precisely controlled and measured. For liquid/vapor mixtures it is not possible to do

so for the annular flow regime. So instead, the sensor was tested on the bench top using FC-87

(e,= 1.72) for a stratified liquid layer. These tests validate the composite material analysis, which

will subsequently be used to evaluate the liquid film thickness for annular flow. The usefulness

of this methodology for evaluating the annular flow film thickness will be demonstrated in the

following section.


0.35

0 30 -

0.25

0.20 -

S015 -

0 10 -
/

005 -
0 785
0.00 1--
00 01 02 03 04 0.5 0.6 0.7 08
Vapor Volume Fraction

Figure 3.4. Percent difference in capacitance between annular flow with a square and round
vapor core.


The square channel may be placed in two different orientations: the upwards orientation

and the side orientation, as shown in Figure 3.5. C, and C, denote the capacitances measured

for a stratified liquid layer in the respective upward and side orientations. Assuming that (3.1)

is valid, the ratio of the liquid to vapor permittivity can be expressed as










d Cu




UPWARD
CONFIGURATION


SIDE
CONFIGURATION


[ LIQUID = VAPOR

Figure 3.5. Upward and side configurations of parallel-plate capacitor in stratified flow.


EL CL
e, C '


where CL is the measured capacitance when the sensor is filled with pure liquid and C, is the
measured capacitance when the sensor is filled with pure vapor, and the ratio of CL to C, is
referred to here as the effective permittivity ratio. Using Equations (3.1) and (3.3) and the
composite material analysis, the dimensionless capacitances for a stratified liquid layer in the
upward and side orientations, as shown in Figure 3.5, may be expressed as


.C- C- C 1 C -1
c,-C, C,- c C _
C, d C,I d }


C. c,-c, 8
C' C,, d


where 6 is the liquid film thickness and d is the channel width.


ij






39

Figures 3.6 and 3.7 show the predicted film thickness as a function of capacitance for the

upward and side orientations respectively. Also shown are the measured film thicknesses using

the CCD camera associated with the measured capacitances using the parallel plate sensor. The

capacitances were measured for only one set of parallel plates. The estimated uncertainty of the

CCD camera measurements is .01 mm. It is seen that there is good agreement between the

analysis and the experimental measurements. The standard deviations for the measured and

predicted film thickness for the upward and side orientations are 0.014 and 0.019 mm,

respectively, thus validating the composite material analysis. C, and C, may be computed using

Equations (3.4) and (3.5) for a given film thickness at any system temperature provided CL and

C, are known as a function of temperature.



0.5 1 ---------------1--
0 Experiment
Model
S04


S03
S/o

S0.2
rC

0o 1 -


001----I -
0.0 0.1 0.2 0.3 0.4
Relative Capacitance, C'

Figure 3.6. Comparison between predicted and measured film thickness for the upward
orientation. Capacitance is measured using the sensor, and film thickness is measured by the
CCD camera.








0.2
0 Experiment 0
S-- Model
04 /0
Q/

03 0


S0.2

o o
W 0.1
E /0


0.0 /
0.0 0 1 0.2 0.3 0.4 0.5
Relative Capacitance, C'

Figure 3.7. Comparison between predicted and measured film thickness for the side
configuration. Capacitance is measured using the sensor, and film thickness is measured
using the CCD camera.


3.4.2 Annular Flow

For the sensor design considered herein, using one set of parallel plates and FC-72 as the

working fluid, the calibration curves for CL and C, as a function of temperature are shown in

Figure 3.8. Over the temperature range considered, 23-60oC, C, and Cv are approximately

linear functions of temperature. The objective in this work is to measure the liquid film thickness

for annular two-phase vertical upflow or downflow using the capacitance sensor without having

to calibrate it for annular flow conditions. Utilizing the composite material analysis shown in

Figure 3.2 in conjunction with Equation (3.2), the capacitance, C" for annular flow with a

square cross section and uniform film thickness may be expressed as



C.; C= 2 + 1-2 (3.6)
C L 2(3 ), CL 1-()









4.0 i
0 Liquid only, CL
V Vapor only, C

3.5




o 3.0



25



2.0
20 30 40 50 60
Temperature, C

Figure 3.8. Temperature calibration of CL and C,.



Thus, Equation (3.6) and the calibration curves for CL and C, are used to evaluate the liquid film

thickness, 6, for a measured annular flow capacitance, C,.

The capacitance sensor was installed above the test section in the vertical flow boiling

facility charged with FC-72. For a given system pressure, two-phase flow was established by

evaporating liquid FC-72 in a preheater section. There are approximately 120 diameters of

adiabatic developing length for the liquid/vapor mixture prior to entering the capacitance sensor.

The flow boiling facility is configured such that either vertical upflow or downflow may be

established in the capacitance sensor. Both sets of electrodes were used for the annular flow

tests. Directly adjacent to the capacitance sensor is a visual test section, through which the liquid

film can be observed. The system mass flux and vapor quality are adjusted to obtain annular

two-phase flow. The liquid film in two-phase flow is inherently unstable and thus the film

displays large temporal and spacial variations. Typical CCD photographs of the annular flow

liquid film for vertical upflow and downflow are shown in Figures 3.9(a) and (b), respectively.



























Figure 3.9(a). Typical photograph of liquid film in annular upflow.


~~K


'U


Figure 3.9(b). Typical photograph of liquid film in annular downflow.






43

An ensemble of ten photographs were used to evaluate the liquid film thickness in vertical

downflow using the CCD camera; twenty photographs were taken for upflow due to the highly

variable nature of the film. A comparison between the film thickness measured from photographs

and a time-averaged measurement using the capacitance sensor is shown in Figure 3.10. The

estimated uncertainty of the photographic film thickness measurements is .014 mm for upflow

and +.019 mm for downflow. Considering the large temporal and spatial variations in film

thickness observed with two-phase flow, the comparison is satisfactory. It is seen that the largest

deviation is for vertical upflow. This is because the liquid film for upflow is considerably more

variable than that for downflow, and obtaining an accurate measurement of the film thickness

from photographs is quite difficult. It is believed that the average film thickness measurements

using the capacitance sensor are more reliable than those using the camera. The standard

deviation for the downflow comparison is 0.093 mm and that for upflow is 0.173 mm.

1.6
v Downflow A
1.4 A Upflow

E 12

S1.0



0.6



E 0.2


0.0
00 0.2 04 06 08 10 1.2 14 16
6, mm based on capacitance measurements

Figure 3.10. Comparison of annular two-phase flow liquid film thickness measured with
capacitance sensor and CCD camera.














CHAPTER 4
NUCLEATION SITE DENSITY AND SUPPRESSION


4.1 Introduction and Literature Survey

Over the past four decades, the heat transfer rates associated with forced convection

boiling have been investigated by hundreds of researchers. Perhaps the first investigators to

propose a correlation for predicting flow boiling heat transfer rates were Dengler and Addoms

(1956). Since then many other flow boiling heat transfer correlations have been proposed, many

of which have been summarized by Gungor and Winterton (1986). The type of correlation which

has been used the most was first proposed by Chen (1966) and takes the form


h2 = h, + h, (4.1)


where h. is the two-phase heat transfer coefficient, h. is the macroconvection heat transfer

coefficient due to bulk turbulent transport, and h, is the microconvection heat transfer coefficient

due to the ebullition process. Klausner (1989) examined various correlations which take the same

form as (4.1) and found they predict that the macroconvection component of heat transfer is the

dominant heat transfer mechanism, and the microconvection component of heat transfer typically

does not contribute significantly to the total two-phase heat transfer. One notable exception is

the correlation proposed by Kandlikar (1990), which predicts that microconvection can be a

considerable portion of the total heat transfer. Zeng and Klausner (1993a) measured the

microconvection component of heat transfer for horizontal flow boiling of refrigerant R113 and

demonstrated that under certain flow and thermal conditions it contributes significantly to the total

two-phase heat transfer, as demonstrated in Figure 4.1. Others who have reported finding






45

microconvection heat transfer to be significant over a range of flow and thermal conditions

include Blatt and Adt (1964), Staub and Zuber (1966), Frost and Kippenhan (1967), Kenning and

Cooper (1989), Cooper (1989), Klausner (1989), and Tran et al. (1993).


1.0 1
ATn.=8.7 *C (average)
G=125-266 kg/m' s
0.8 6=1.6-B.8 mm
X=0.04-0.30
7 v7 v

0.6 7, aS 17


S04-



0.2



0.0
1 2 3 4 5 6 7 8
qw/(hmacATinc.s)

Figure 4.1. Ratio of microconvection heat transfer coefficient to total two-phase heat transfer
coefficient for different flow boiling conditions (from Zeng and Klausner; 1993a).


In order to understand the discrepancy, it is instructive to consider the saturated vertical

upflow boiling experiments by Kenning and Cooper (1989). Over the range of flow and thermal

conditions tested, two flow boiling regimes were identified: the apparently convective regime and

the apparently nucleate boiling regime. In the apparently convective regime, the measured two-

phase heat transfer coefficient appears to be independent of the heat flux and heating surface

conditions and can be predicted within an uncertainty of approximately 10%. In this regime,

it appears that the boiling activity has been completely suppressed. In the apparently nucleate

boiling regime, the measured heat transfer coefficients are essentially independent of mass flux,

vapor quality, and flow regime. They tend not to be repeatable due to variations in surface

conditions and gas entrainment, and they are difficult to predict.






46

The importance of the two flow boiling regimes identified by Kenning and Cooper cannot

be underestimated. When nucleation sites are completely suppressed and heat transfer is

dominated by bulk turbulence and liquid film evaporation, as occurs in the convective regime,

the physics governing the heat transfer are completely different than that in the nucleate boiling

regime in which heat transfer is mainly controlled by the incipience, growth, and departure of

vapor bubbles. As demonstrated in Figure 4.1, as soon as the wall superheat is sufficient such

that incipience occurs, microconvection strongly contributes to the total two-phase heat transfer.

Moreover, without a clear distinction between the two regimes, experimental data used to

construct empirical heat transfer correlations can contain convective data interspersed with

nucleate boiling data. This can bias a correlation toward one regime, making it incapable of

satisfactorily predicting the heat transfer in the other. Therefore it is of critical importance to be

able to predict which heat transfer regime is present for a given set of flow conditions.

The objective of this work is to understand the fundamental mechanisms controlling the

suppression of nucleation sites in flow boiling inside channels or tubes with net vapor generation,

which establishes the transition point between the convective and nucleate boiling regimes. Based

on thermodynamic relations and physical reasoning, a dimensionless parameter is identified to

serve as a criterion for predicting when nucleation sites become completely suppressed. It is

tested and calibrated using experimental heat transfer data obtained in this work, flow boiling

nucleation site density data of Zeng and Klausner (1993b), and heat transfer data of Kenning and

Cooper (1989) and Jallouk (1974). The working fluids considered are water, R113, R114, and

FC-87.


4.2 Nucleation Sites in Flow Boiling

An extensive experimental investigation of nucleation site density in horizontal flow boiling

with refrigerant R113 was reported by Zeng and Klausner (1993b). They demonstrated that the

behavior of the nucleation site density is significantly different than that found in pool boiling,






47

and although the nucleation site density data show dependence on the critical (minimum) cavity

radius, it is insufficient for correlating the data. They observed a strong dependence on heat flux

and mean vapor velocity. As the mean vapor velocity increased, the nucleation site density

decreased until complete suppression of nucleation sites occurred. No generalized correlation for

the data was suggested. In general the formation of nucleation sites is highly dependent on the

size and geometry of the microscopic scratches and pits on the heating surface, the wettability

of the fluid, the amount of foreign contaminants on the surface, and the material from which the

surface was fabricated. Here, the data of Zeng and Klausner (1993b) are reexamined based on

theoretical considerations.

It has long been recognized that surface cavities which become active nucleation sites must

be capable of trapping vapor (Corty and Foust, 1955). Wang and Dhir (1993) suggested that

only those cavities with 0> ~, are capable of trapping vapor, in which 0 is the liquid-solid

contact angle and 4n. is the minimum cavity side angle, or in the case of spherical cavities, 0.,

is the mouth angle. Using this vapor trapping criterion and the nucleation site density model

proposed by Yang and Kim (1988) for pool boiling, the nucleation site density for either pool or

flow boiling may be calculated from,


N= ffNrrfdr ( (4.2)
r- 0


where n/A is the nucleation site density, N/A is the number of cavities per unit area on the

heating surface, f, is the probability density function of finding cavities with mouth radius r, f,

is the probability density function of finding cavities with minimum side angle Ve, and r. and

r, are the respective minimum and maximum mouth cavity radii within which incipience will

occur. The use of Equation (4.2) assumes a statistically homogeneous distribution of cavities on

the heating surface and statistical independence of r and 0.,.






48

Although the applicability of (4.2) to flow boiling has yet to be experimentally verified,

it is quite useful in understanding the nucleation site density data presented by Zeng and Klausner

(1993b), in which n/A is observed to decrease rapidly with increasing vapor velocity. Increasing

the mean vapor velocity results in enhanced two-phase bulk turbulence and thus reduces the

thermal boundary layer thickness. The temperature field which is seen by a vapor embryo

protruding a surface cavity, as sketched in Figure 4.2, is strongly influenced by the bulk

turbulence. A vapor embryo will grow and establish a nucleation site only if there is sufficient

energy from the surroundings to sustain growth. If a vapor embryo is too large, which might

occur in a cavity with a large diameter, it will protrude into the colder region of the liquid, which

reduces the vapor temperature to below the value required by the Clapeyron equation for the

equilibrium of the two phases. Therefore, in addition to a minimum cavity radius required for

incipience, there also exists a maximum cavity radius, above which the incipience is inhibited.

As the bulk turbulence is enhanced, the thermal boundary layer becomes thinner and r,,-ra,

and thus the nucleation sites become suppressed as suggested by (4.2). The distinct difference

in the formation of nucleation sites between pool and flow boiling lies in the fact that r in flow

boiling is typically much less than that in pool boiling due to a much thinner thermal boundary

layer. In fact, Wang and Dhir (1993) were able to adequately predict pool boiling nucleation site

density by assuming rm-o. As will be demonstrated, such an assumption is not valid for flow

boiling.


4.2.1 Estimating the Minimum and Maximum Cavity Radii

In order to estimate r,, and r,, for saturated flow boiling, consideration is given to a

hemispherical vapor embryo which protrudes a surface cavity as shown in Figure 4.2, for which

the following assumptions are made. (1) The static vapor embryo is embedded in a saturated

liquid shear flow with a temperature profile governed by macroconvection heat transfer. (2) The

embryo radius is typically much less than the liquid film thickness, and the temperature profile









Laminar Sublayer



u()



S '/ Vapor Embryo






Surface Cavity



Figure 4.2. Idealized sketch of a vapor embryo embedded in shear flow protruding a surface
cavity.


in the vicinity of the embryo may be approximated as linear. Following Zeng and Klausner

(1993a), the near-wall temperature profile, T,(z), is approximated as


k, (4.3)
Te(z) = T, A, (4.3)


where T. is the mean wall temperature, AT., is the wall superheat, and k, is the thermal

conductivity of the liquid. During vapor bubble growth under saturated conditions, energy is

transferred to the vapor through the liquid microlayer which resides beneath the bubble.

However, prior to growth no liquid microlayer can be established and thus energy is transferred

to the embryo from the surrounding liquid and the solid heating surface beneath the embryo. A

physically sound criterion for vapor embryo growth to continue is that there must exist net heat

transfer into the embryo from the surroundings. Resolution of the temperature field in the

vicinity of the embryo requires a three-dimensional, three-phase heat transfer analysis. Because

of the complexity of such an analysis, the problem is greatly simplified by approximating the

liquid temperature profile near the wall to be linear as given by (4.3), and the incipience criterion






50

proposed by Bergles and Rohsenow (1964) is instituted: vapor bubble growth will proceed only

when the liquid temperature, T, at the top of the hemispherical embryo exceeds the vapor

temperature, T. It is assumed that the vapor embryo temperature T, is uniform, which is

computed from the Clapeyron equation as


T T T In( + (4.4)
h rP,4


where R, is the engineering gas constant, a is the surface tension, P_ is the pressure in the liquid

phase, and hf is the latent heat. Thus the maximum and minimum cavity radii which can sustain

an active nucleation site may be estimated by setting T, = T, and z = r in (4.3) and solving (4.3)

and (4.4) for r. An approximation for r can be made by noting that In 1 + 2-- 2a for
SrPnml rPsa
many cases of practical interest. Implementing the perfect gas law and combining (4.3) and (4.4)

results in

h r T, 2a
1 (4.5)
kt h p AT,,r(45)

Equation (4.5) is quadratic in r, and the two solutions give the respective maximum and minimum

cavity radii, r, and r, Simplification of the solutions to (4.5) may be made by noting that

(T 2ah,/,hf pAT1 ,ke) is small compared with unity for many cases of interest, and thus

approximate expressions for r,, and r., are:

r = (4.6)


and


r.i- T a (4.7)
AT,h p,

A straightforward result of this analysis is the identification of the dimensionless parameter

r/r.r which is referred to as the cavity size ratio,








r AT7,kph
rt=~ ATkep~hA (4.8)
r h rT,T 2o "

In cases where the approximations leading to Equations (4.6)-(4.8) cannot be satisfied, it is only

necessary to use an iterative technique to simultaneously solve Equations (4.3) and (4.4) for r,,

and r,,. It is noted that variations of the Bergles-Rohsenow incipience criterion have appeared

in the literature, but inherent assumptions are used in all of these. In light of the assumptions

used in the incipience criterion, the assumptions used to arrive at Equation (4.8), and the

nonuniform geometry of most nucleation sites, r/Jr,, should be viewed as a dimensionless

variable on which the formation and suppression of nucleation sites depends.

As implied by (4.2), the probability of finding cavities on the heating surface which have

mouth radii which fall between r, and r,, decreases as r, -- r,, Specifically, it is noted that

r,/r..r = 4 is the limit allowed by the Bergles-Rohsenow incipience criterion. This suggests

that r,/r,. may serve as a useful correlating parameter for the nucleation site density. In fact,

when r /r,=4 it is not physically possible to maintain heterogeneous boiling; however, this

is too restrictive a condition to use as a suppression criterion since it is possible for nucleation

sites to become completely suppressed for r,/r, > 4, depending on the distribution of cavity

mouth radii on the heating surface. It is expected that the topography of the heating surface plays

some role, as do the wetting characteristics of the fluid. The usefulness of r,,Jr, as a

dimensionless variable to characterize nucleation suppression will be demonstrated empirically.


4.2.2 Nucleation Site Density

Figure 4.3 shows the flow boiling nucleation site density data, measured by Zeng and

Klausner (1993b) using R113 in horizontal stratified flow over a smooth nichrome heating strip,

displayed as a function of r_/r,, for two different heat fluxes, q,=19.3 and 13.8 kW/m. In

these data the mass flux, vapor quality, liquid film thickness, and wall superheat varied. The

lines through the data are merely curve fits. In computing r/r,, experimental values for h_






52

were used. It is seen that for a given heat flux the data collapse into a single curve. It is noted

that Zeng and Klausner were unable to correlate their nucleation site density data with r., alone.

For the data shown in Figure 4.3, r, does not change appreciably, while r, varies significantly.

Thus the variation in r,/rj is primarily controlled by r, which suggests that r, has a

controlling influence on flow boiling nucleation site density. This is significant because r, has

historically been ignored in correlating n/A.



14 q, = 19.3 kW/m'
0 q, = 13.8 kW/m'
12

10

S8 0

6 -

4 0 0

2

0
50 100 150 200 250 300 350 400 450 500
rmax/rm

Figure 4.3. Nucleation site density data of Zeng and Klausner (1993b) shown as a function of
r /r.,.


According to (4.2), the nucleation site density as a function of r,/r, should not be heat

flux dependent. The heat flux dependence shown in Figure 4.3 may be due to the fact that (4.3)

and (4.8) assume a uniform wall temperature. In fact, in the presence of heterogeneous boiling,

the thermal field on the heating surface is highly nonuniform with large temperature gradients

beneath nucleation sites, which are more pronounced at higher heat fluxes. As the nucleation site

density is reduced, the temperature nonuniformities should be less pronounced and the observed

convergence of the data in Figure 4.3 is expected. The heat flux dependence displayed in Figure

4.3 may also be a result of the simplified incipience criterion to used compute r_/r,.






53

When nucleation is completely suppressed, the wall temperature should be uniform (within

the length scale of the bubble size) and the two curves fitted to the data are expected to intersect

at n/A=0. Although they do not exactly intersect at n/A=0, (r /r),,=117 for q,=19.3

kW/m2, which is close to (r /r).,,= 130 for q,= 13.8 kW/m2, where the subscript sup denotes

the point of suppressed nucleation.

A result which makes clear the limitations of the Bergles-Rohsenow incipience criterion is

that (r/rd), is much greater than unity. Although the magnitude of r./r, is high, its value

as a correlating parameter will be further demonstrated. In order to further test the applicability

of correlating the cavity size ratio with the point of suppressed nucleation, a vertical forced

convection boiling facility has been constructed in which measurements of the flow boiling

nucleation suppression point have been made for vertical upflow and downflow over a wide range

of flow and thermal conditions. A perfluorocarbon fluid, FC-87, having similar surface wetting

characteristics as R113, was used as the working fluid, and nichrome was again used as the

heating surface. Suppression point data have been obtained for mass flux, G, ranging from 183

to 315 kg/m2-s; inlet quality, x ranging from 0 to 0.151; and heat flux, q,, ranging from 1.20

to 16.95 kW/m2.


4.3 Experimental Procedure

The nucleation site density suppression point data were obtained from the boiling facility

described in Chapter 2 in the following manner: for a given mass flux and inlet vapor quality

at the test section, sufficient power was applied to the heater to achieve vigorous boiling. The

power input to the test section heater was then stepped down in small increments, and

measurements of heat flux, mass flux, wall superheat, vapor quality, liquid film thickness, and

saturation pressure and temperature were obtained. Decreasing wall heat flux was used in order

to avoid boiling hysteresis. A flow boiling curve (q, vs. AT.) was generated for the given flow

conditions. Typical flow boiling curves for vertical upflow and downflow are illustrated in






54

Figures 4.4(a) and (b), respectively. The suppression point is determined from the flow boiling

curve by observing that in the convective regime the heat transfer coefficient is independent of

heat flux, and q, varies linearly with AT, The suppression point is therefore taken to be the

point at which the heat flux curve departs from linearity as shown in Figures 4.4(a) and (b). The

value of AT., for which nucleation suppression is established has an estimated uncertainty of

0.5C. The macroconvection heat transfer coefficient, h_, is the slope of the q, vs. AT,

curve in the convective regime. The macroconvection heat transfer coefficient, h,, is

determined with an uncertainty of 5%. In order to validate the heat transfer coefficient

measurements, single-phase flow heat transfer coefficients were measured over a range of

Reynolds number. The results are compared against Petukhov's (1970) single-phase flow heat

transfer correlation in Figure 4.5. It is seen that the agreement is good.


4.4 Results

In the present work, a set of 29 suppression points were determined from vertical upflow

and downflow boiling curves. Using flow conditions and properties obtained from the

experiment, the cavity size ratio at the point of suppression, (rd/r,,,, was calculated using

(4.8). In determining (r,/rJ,,) experimental values of h,,, (the slope of the q, vs. AT,

curve in the convective regime) were used. A summary of the suppression point data and thermal

and flow conditions at the point of suppression are displayed in Table 4.1.

Figures 4.6 to 4.8 show the variation of (r_/r,,,, for vertical upflow and downflow with

mass flux, inlet quality, and wall heat flux, respectively. According to (4.2), (rIrJ. should

be independent of these parameters. Furthermore, for a specific heating surface and fluid

combination, (r./rJ,,), should be invariant. As shown in Figures 4.6 to 4.8, the measured

values for (r_/r,,J, are scattered slightly over a narrow range, 40 < (r./rj3, < 60, and show

no dependence on inlet quality and very little dependence on mass flux, which qualitatively

supports the theory. However, Figure 4.8 shows a slight dependence of (r/rJ),, on heat flux,










60 I 1
Upflow:
G = 313 kg/m2 s
50 Xi = 0.044
Nucleate Boiling
Regime
40 -


30 Suppression Point



20



10
SConvective
Regime
0
0 2 4 6 8 10 12 14

AT..t (C)

(a) upflow


60

Downflow.
G = 315 kg/m2 s
50 X = 0.048

Nucleate Boiling
40 Regime



S30 -

Suppression Point
20 -


10

--- Convective Regime

0 2 4 6 8 10 12 14

ATsat (-C)

(b) downflow

Figure 4.4. Boiling curves for vertical annular upflow and downflow, illustrating nucleation
suppression point.









1200
A Upflow
V Downflow
1000 -- Petukhov



8- 00 -



S600



S400



200
5000 10000 15000 20000 25000 30000 35000
Reynolds Number

Figure 4.5. Comparison of measured single-phase heat transfer coefficient to Petukhov's
(1970) model.

particularly in upflow. Although the dependence on heat flux is not strong, it may be indicative

of some thermal phenomena which the theory does not take into account. Whether this is due

to the assumed uniform wall superheat in Equation (4.8) or the use of the Bergles-Rohsenow

incipience criterion is not currently known and requires further scrutiny. Again it is observed

that (r,/r_.,, is much greater than unity, although within the same order of magnitude of the

suppression point data of Zeng and Klausner (1993b).

The point of suppressed nucleation can also be determined from the heat transfer data of

Kenning and Cooper (1989), obtained from vertical upflow boiling of water on cupronickel

tubing. The values of (r,/r.J, based on their measured heat transfer data are summarized in

Table 4.2. Additionally, the R114 heat transfer data measured inside a copper tube by Jallouk

(1974) can be used to determine that (r./rd,.) = 112 for q,= 19 kW/m2. These (r_/rJ,

data, as well as those obtained using the current experimental facility, are summarized in Figure

4.9 as a function of the heat flux.








Table 4.1. Point of suppressed nucleation heat transfer data from present work.

G 6 q AT., h (r/r
(kg/m2-s) (mm) (kW/m2) (C) (W/moC)
upflow
200 0.045 1.60 16.18 8.60 2022 54.8
201 0.052 1.68 16.36 8.01 2043 53.2
200 0.057 1.54 16.62 8.25 2015 56.6
201 0.087 1.41 15.52 7.54 2059 50.5
201 0.120 1.21 16.23 7.75 2094 51.5
200 0.151 1.11 15.55 7.46 2084 49.5
260 0.023 1.75 16.21 7.94 2041 54.2
261 0.062 1.39 16.51 7.66 2155 50.0
260 0.087 1.31 16.27 7.58 2147 50.2
261 0.109 1.15 16.67 7.49 2225 48.7
262 0.137 1.07 13.67 8.17 2285 52.5
311 0.025 1.65 15.57 7.41 2101 50.1
314 0.044 1.48 16.36 7.58 2158 50.6
314 0.067 1.31 16.50 7.48 2206 49.5
314 0.102 1.14 17.52 7.41 2364 47.3
downflow
183 0.060 0.851 7.00 5.12 1367 51.8
202 0.062 0.829 8.15 5.07 1603 44.5
236 0.054 0.892 8.52 4.97 1714 41.2
237 0.075 0.889 6.53 4.21 1550 38.5
238 0.128 0.860 6.04 4.05 1492 39.9
237 0.151 0.829 6.82 4.43 1540 43.0
284 0.023 0.940 8.06 4.48 1798 36.0
280 0.048 0.939 7.91 4.56 1734 38.3
280 0.076 0.927 9.19 5.05 1819 39.6
280 0.109 0.900 8.23 4.82 1707 42.6
315 0.026 0.981 9.41 4.74 1986 34.6
314 0.049 0.968 8.78 4.67 1881 36.6
313 0.073 0.951 8.19 4.50 1819 37.0
311 0.106 0.919 7.73 4.30 1798 36.8






58

Table 4.2. Point of suppressed nucleation from Kenning and Cooper (1989) heat
transfer data.


(r-/r..),) qw G
(kW/m2) (kg/m' -s)
108 50 304
90 100 304
103 100 123
111 150 123
74 200 304
74 200 203
99 250 123
69 300 304
89 300 123
63 350 123


It is seen that the data demonstrate a slight dependence on heat flux, but are generally

scattered between (r I/r,). =40-120. In general, the point of suppressed nucleation will

depend on the fluid/surface combination and the wetting characteristics of the fluid; however,

despite vastly different flow configurations and fluid/surface combinations, Equation (4.8) yields

suppression point cavity size ratios within the same order of magnitude. In this study, both

highly wetting fluids (FC-87, R113, R114) and an intermediate wetting fluid (water) have been

considered. As indicated in Figure 4.9, three regimes may be identified based on r,/r,,

Regime I: r/r.< 40, Convective Regime (suppressed nucleation)

Regime II: 40 < r_/rr, 120, Regime of Uncertainty (nucleation may or may not

be sustainable)

Regime III: r,/r, > 120, Nucleate Boiling Regime (nucleation is sustained).

Thus Figure 4.9 may be used as a flow boiling regime map to determine whether the flow and

thermal conditions correspond to sustained nucleation or purely forced convection. The purpose

of the flow boiling regime map is to provide guidance to practitioners, experimenters, and

theoreticians as to which regime is most probable for specific operating conditions.











100

O Downflow
0 Upflow
80



60

0 OI

40 -







0 ---- I

150 200 250 300 350

G (kg/m' s)
Figure 4.6. Suppression point cavity ratio, (ri/r, ) as a function of mass flux.






100

Upllow Downflow
Mass Flux (kg/m' s) Mass Flux (kg/m' s)
0 G = 200 G = 200
80- v G = 261 G = 280
M G = 313 O G = 313


60 -
60



v40 o -



20 -
20



0 -------------------
0.00 0.05 0.10 0.15
X

Figure 4.7. Suppression point cavity ratio, (r ,/r as a function of test section inlet
quality.










100 I I
Upflow: Downflow:
Mass Flux (kg/m' a) Mass Flux (kg/m- ')
| G = 200 0 G = 237
0 G = 261 7 G = 280
G = 313 G = 313


60 -


V

40 O O
40 00 *



20 -
20



0 ------I I I

4 6 8 10 12 14 16 18 20

q (kW/m')

Figure 4.8. Suppression point cavity ratio, (r/r,.,, as a function of wall heat flux.






400
A Present Work, uptlow
50 v Present Work. downflow
O Zeng and Klausner (1993b), horizontal flow
0 Kenmnng and Cooper (1989), upflow
300 D Jallouk (1974). upflow


250


200 -
Nucleate Bodling Regime

150 -

100 0 O- O-

Regime of Uncertainty 0
50 & -

0 Convective Regime
0 I
1 10 100

q, (kW/m')

Figure 4.9. Identification of two-phase heat transfer regimes based on point of suppressed
nucleation.






61

4.5 Discussion

The cavity size ratio, r_/r.,, has been demonstrated to correlate nucleation site density

as well as distinguish between the convective and nucleate boiling regimes in flow boiling.

Experimental data from this work, along with data obtained from the literature, are used to

examine (rl/r), and identify the transition between the two regimes. The values of

(rJr )r are much greater than unity; however, data taken over a wide range of flow

conditions, heating surfaces, and working fluids all fall within the same order of magnitude. This

suggests that the cavity size ratio is, to the leading order, the most important dimensionless

parameter in characterizing the suppression of nucleation sites.

The cavity size ratio identified in this work is intended as a first step toward a better

understanding of flow boiling nucleation and the development of a flow boiling regime map. This

work also provides direction for future flow boiling nucleation investigations. An incipience

criterion based on conservation of energy which provides a realistic description of the thermal

boundary layer in the vicinity of the vapor embryo may give an improved estimate for r_,.

Equation (4.2) dictates that the heating surface topography and fluid/surface wetting

characteristics play a role in the formation and suppression of nucleation sites, both of which

require improved understanding.













CHAPTER 5
OBSERVATION AND MEASUREMENT OF VAPOR BUBBLE DYNAMICS


5.1 Introduction and Literature Survey

The high heat transfer rates associated with forced convection boiling are due to two

complex processes working together: bulk turbulent convection and the growth and

detachment of vapor bubbles at the heating surface. Therefore in order to develop reliable

predictive capabilities for forced convection boiling heat transfer, a fundamental

understanding of the ebullition process in the presence of a turbulent flow is essential.

However, while numerous measurements of vapor bubble growth rate and departure diameter

have been reported in the literature for nucleate pool boiling, the available flow boiling data

are limited. For this reason among others, pool boiling heat transfer correlations are often

incorporated into those for flow boiling.

In recent years, great strides have been made toward understanding vapor bubble

dynamics in horizontal flow boiling. Klausner et al. (1993) and Zeng et al. (1993) developed

a vapor bubble departure and lift-off model for horizontal flow boiling, which agrees well

with a wide range of data obtained using high-speed imaging. However, a general extension

of their model to vertical flow boiling remains uncertain. For the vertical downflow

configuration, sliding bubbles lag the liquid velocity, and the resulting shear lift could be

sufficient to lift vapor bubbles off the heating surface. However, quantifying the shear lift

force requires knowledge of the bubble sliding velocity, which is not provided by the model.

For vertical upflow, the sliding bubble velocity leads the liquid velocity, and thus the shear






63

lift pushes the bubble against the heating surface. Whether a mechanism exists to remove

vapor bubbles from the heating surface remains uncertain. In the case of microgravity flow

boiling, a mechanism for removing vapor bubbles from the heating surface has yet to be

identified, and thus it is not clear under what conditions microgravity flow boiling can be

sustained.

Several investigations have sought to visually document the ebullition process in

forced convection boiling. Gunther (1951) used high-speed cinematography to examine vapor

bubble dynamics in subcooled, upflow boiling of water. Vapor bubble radii were measured

during the growth and collapse stages in subcooled flow, and the effects of flow velocity and

subcooling were documented. Gunther observed that the vapor bubbles slide away from the

nucleation site, and remain attached to the heating surface throughout the growth and collapse

stages. Hsu and Graham (1963) performed a similar visual study with highly subcooled

water to investigate the hydrodynamic features of vertical bubbly and slug flow regimes

subjected to boiling. No measurements of bubble growth rate or departure diameter were

made. However, bubbles ejected into the bulk flow, and "ejection" diameters were

measured. The authors attributed the ejection, in part, to a lifting force imposed by the flow.

Frost and Kippenhan (1967) examined the growth and collapse of bubbles in subcooled

upflow of water containing various concentrations of a surface active agent. Bubble growth

and departure diameters were measured. Cooper et al. (1983) measured bubble growth and

displacement in supersaturated n-hexane in forced laminar upflow over a stationary wall.

Similar measurements were made for short duration microgravity flow. Recently, van

Helden et al. (1995) obtained growth and departure diameter data in saturated and

superheated upflow boiling of pure water. He reported sliding to occur following departure,

but did not record the bubble trajectory.






64

The purpose of this work is to experimentally examine the complex vapor growth and

removal process in vertical upflow and downflow forced convection boiling, with an

emphasis on understanding the role of gravity. An experimental facility which uses a

dielectric fluid, FC-87, has been designed, tested, and calibrated and allows visual

examination of the ebullition process under slightly (1.0-5.0*C) subcooled conditions. Using

a high-speed digital video imaging facility, a visual study of the bubble dynamics in the

isolated bubble regime is presented. Image analysis of the film reveals vapor bubble growth,

departure diameter, sliding trajectory, lift-off diameter, and waiting time. In Chapter 6, the

detailed forces acting on a vapor bubble are considered, and a vapor bubble departure and

lift-off model is proposed which is an extension of that developed by Zeng et al. (1993).

Included in the model is a prediction of the bubble sliding trajectory, which is also compared

to experimental data.


5.2 Experimental Procedure

The experimental facility described in Chapter 2 was operated to achieve single-phase

flow through the transparent boiling test section. The bulk single-phase conditions at the

entrance of the test section are controlled by adjusting the preheat and flow rate. Once

steady-state flow is established, power is supplied to the test section heater at a sufficient rate

to obtain vigorous boiling at the surface. The heat flux is then reduced until only isolated

nucleation sites are active. Operating the facility in this manner eliminates the effect of

boiling hysteresis.

The Ektapro high-speed digital camera is mounted on a tripod, and is aimed at the

heater from the side at approximately a 25-30* angle above the heater. The test section was

backlit (the lighting was aimed at the camera) through a gray filter to create a diffusely

illuminated flow. In order to achieve the highest possible resolution and eliminate errors in






65

calibration, the camera lens is fixed at a constant focal length, resulting in a fixed viewing

area of approximately 4x4 mm (full-frame). To view an image in the test section, the

camera is moved forward or backward using a linear traverse installed on the head of the

tripod. This technique eliminates the need to recalibrate the image magnification every time

the field of view is adjusted. Image analysis is performed manually by measuring distances

on the film as it is played back from video tape on a 20-inch video monitor with 1000 lines

per inch resolution. The lateral displacement of the vapor bubble is the distance measured

from the nucleation site to the bubble centroid. The characteristic bubble diameter is taken

to be the length of the chord measured through the centroid of the bubble and parallel to the

wall. This definition is chosen because the camera angle normal to the heater must be varied

slightly in order to achieve an unobstructed view of a nucleation site, which introduces

uncertainty as to the image magnification in the normal direction. Moreover, thermal

gradients in the boundary layer and reflection of the bubble image on the heater surface make

the location of the base of the bubble difficult to distinguish precisely. However, as will be

shown, the bubbles are very nearly spherical during the early portion of growth and sliding,

during which the diameter is measured. Therefore the bubble diameter as it is measured is

judged to be an adequate representation of the bubble size.

An important consideration in these experiments involves the temporal and spatial

variations in the heater surface temperature and liquid velocity. Specifically, it is necessary

to estimate the time scale of these variations to ensure that the film length is sufficient to

establish statistically meaningful values of mean bubble growth, departure and lift-off

diameter, and sliding trajectory. For surface temperature, variations due to ebullition can

be estimated using the time taken for growth and departure plus the waiting time. For

experimental conditions examined in this work, this time scale is typically on the order of






66

20 to 50 ms. Velocity fluctuations may be estimated as follows. From a numerical

simulation of single-phase turbulent channel flow (Lyons, 1989), the integral length scale in

the streamwise direction is on the order of X\ =-u'/vP- 500. Thus an estimate of the time

scale, assuming the frozen field hypothesis is valid, is on the order of r=(500v/u*)/u- 0 10'1

s, where u, is the mean liquid velocity in the duct. Considering both of these estimated time

scales, the 800 ms film length is judged to be sufficient to capture the statistical variations

in the measured bubble growth, departure and lift-off diameter, and trajectory. To ensure

consistency of the film data, two to three films are acquired at each condition.


5.3 Flow Visualization

Table 5.1 summarizes the experimental conditions and data collected for vertical

upflow and downflow forced convection boiling considered in this work. A total of 20

experimental conditions were studied, with mass fluxes ranging from 193 to 666 kg/m2-s and

heat fluxes ranging from 1.3 to 14.6 kW/m2. The bulk flow was slightly subcooled, with

AT, ranging from 1.9 to 5.2C. In addition, one vertical surface pool boiling condition was

studied, which is included as Exp. no. 8 in the table. All conditions examined in this work

are within the isolated bubble regime.


5.3.1 Upflow

Figure 5.1(a) depicts a photograph of a stream of vapor bubbles originating from a

single nucleation site in upflow, for G=258 kg/m2-s, AT.=3.15C (Exp. no. 2b). Bubbles

which emanate from the site are marked by the symbol "+" at the centroid. Shadows of the

bubbles appear on the surface of the heater due to the lighting and camera angle. Arrows

represent the direction in which the bubble is traveling. The behavior shown is typical of

upflow nucleation at low heat flux. At the nucleation site, the bubbles experience a short








Table 5.1. Forced convective nucleation data.

Exp. G T., AT., AT.,b q h KxlO dd d
no. (kg/m'-s) ("C) (*C) (C) (kW/m2) (m/s) (mm) (N) (mm) (N) (ms) (N)
upflow
la 195 39.9 0.54 2.98 0.73 2.83 805 1.13 0.400 0.094 (98) 2.23 (92)
lb 192 39.8 2.39 2.83 3.23 4.80 920 2.46 0.463 0.165 (44) 22.2 (42)
lc 194 39.8 4.38 2.86 5.95 7.36 1017 4.07 0.500 0.207 (8) 4.67 (6)
2a 244 40.2 0.55 3.06 0.73 3.52 976 1.03 0.361 0.105 (110) 1.58 (106)
2b 258 40.2 3.15 3.27 4.28 6.92 1077 1.69 0.400 0.147 (83) 6.38 (79)
2c 255 40.0 6.34 2.78 8.56 10.9 1201 2.15 0.400 0.199 (53) *
3a 315 40.3 1.32 2.52 1.74 3.63 945 1.26 0.419 0.112 (124) 2.23 (121)
3b 319 40.2 4.04 2.29 5.33 7.26 1147 1.58 0.408 0.160 (59) 1.31 (63)
3c 315 39.9 6.89 1.96 9.04 11.8 1338 2.05 0.404 0.204 (27) *
downflowt
4a 193 40.6 0.05 4.91 0.07 1.32 267 0.82 0.401 0.131A (4) 0.260 (4) 159.5 (2)
4b 192 40.6 4.60 4.28 6.43 4.78 538 1.23 0.374 0.157a (77) 0.324 (40) 9.29 (76)
4c 197 40.5 6.34 4.20 8.89 7.54 715 1.89 0.443 0.187A (31) 0.348 (20) 1.58 (6)
5a 246 40.8 2.95 4.78 4.15 3.24 418 1.29 0.413 0.134A (81) 0.254 (65) 5.07 (61)
5b 247 40.8 5.23 4.71 7.35 4.82 485 2.22 0.458 0.1670 (32) 0.286 (45) 2.41 (22)
5c 247 40.7 7.06 4.49 9.90 7.67 664 2.55 0.484 0.148A (59) 0.259 (56) 1.64 (14)
6a 315 41.0 3.18 5.00 4.45 3.93 469 1.00 0.384 0.1500 (20) 0.193 (34) *
6b 313 41.1 5.08 4.84 7.09 5.04 495 2.05 0.495 0.1120 (73) 0.280 (32) *
6c 311 41.1 6.30 7.79 8.79 6.66 583 2.59 0.500 0.1320 (50) 0.226 (37) *
7 666 42.3 7.17 3.89 9.40 14.6 1319 2.91 0.488 0.123v (80) 0.186 (57) 1.69 (28)
vertical pool boiling
8 0 (pool) 38.4 3.44 0.99 4.54 4.42 997 1.54 0.343 0.237 (34) 0.566 (34) 9.36 (30)
* insufficient data due to "site coalescence"
t symbols represent bubble departure and sliding direction: a =upward; v =downward; 0 =transitional, as described in Section 5.3.2






































(a) (b)


Figure 3. Photographs of bubbles originating from a single nucleation site in upflow, G = 258 kg/m2-s, ATT =
the nucleation site. (b) approximately 10 mm downstream of site. (c) approximately 30 mm downstream of site.


(c)

3.15 C (Exp. no. 2b). (a) at






69

period of stationary growth, and then depart from the site by sliding upward. Growth and

departure is very regular, and the bubbles appear to be spherical in shape. The bubbles

remain attached to the heating surface and continue to grow while sliding along the surface.

Figures 5.1(b) and (c) depict two other streams of bubbles originating from the same

nucleation site. The field of view is approximately 10 mm and 30 mm downstream of the

site, respectively. As the bubbles become larger, they become slightly distorted, assuming

a cap-like shape characteristic of bubbles rising faster than the surrounding flow. Bubbles

are observed to oscillate laterally along the surface, most likely due to vortices shed by the

bubbles, but generally remain attached to the heating surface. Bubbles that lift off the

surface do so randomly, and tend to remain close to the heating surface. The fact that the

bubbles do not typically lift off the surface is consistent with the supposition of Zeng et al.

(1993) that in upflow boiling, the sliding bubble leads the surrounding flow, and the resulting

shear lift force pushes the bubble against the wall, preventing lift-off.

Nucleation sites near the leading edge of the heater produced the majority of vapor

bubbles, and very few sites were found downstream. Even at higher heat fluxes, the most

active portion of the heater, in terms of the number of nucleation sites, was clearly the first

2 to 3 cm of the 30 cm long heater. The suppression of nucleation downstream is likely a

result of several factors. First, the bubbles do not generally lift off of the surface, and the

growth of the bubbles during sliding implies that energy is being depleted from the heating

surface through latent heat transport. Also, the flow around the sliding bubbles may enhance

bulk turbulent convection at the heater surface.

Collision and coalescence of vapor bubbles was observable at all but the lowest heat

flux conditions. For example, at G=244 kg/m2-s and q",=3.52 kW/m2 (Exp. no. 2a),

nucleation sites were sparse and ebullition was well ordered. As the heat flux is increased






70

to q",=6.92 kW/m2 (Exp. no. 2b), the nucleation site density increases, and bubbles from

neighboring sites are occasionally observed to collide and coalesce. The waiting time also

decreases. Upon further increasing the heat flux to q",=11.0 kW/m2 (Exp. no. 2c),

coalescence at a nucleation site becomes the dominant feature of the bubble dynamics. That

is, the waiting time decreases to a point where a new bubble forms and grows at the

nucleation site faster than the previous bubble can slide away, resulting in a collision and

coalescence of the two bubbles. At even higher heat fluxes this waiting time becomes

indistinguishable short, and a bubble may undergo repeated "site coalescence" before it is

large enough to finally escape under the influence of buoyancy and/or drag.

At these higher heat fluxes, the flow near the surface becomes bubbly and chaotic,

with neighboring bubbles colliding and numerous intermittent sites participating. Based on

random fluctuations in the observed bubble trajectory, the flow near the wall appears to be

highly turbulent. Under these conditions bubble lift-off was observed to occur on occasion.

It appeared that a turbulent eddy or a passing bubble in the bulk liquid flow would randomly

sweep the surface and lift off a bubble. Further downstream the entire flow field is bubbly

and highly chaotic. Because lift-off occurred infrequently except during bubbly flow, and

its occurrence appears to be random, lift-off diameters were not recorded for upflow.


5.3.2 Downflow

In downflow forced convection boiling, the buoyancy force experienced by a vapor

bubble resists the quasi-steady drag exerted by the liquid flow. As a result, three bubble

sliding conditions were observed, which depend largely on the local liquid velocity. These

conditions are demonstrated in Figure 5.2, where photographs of bubble ebullition are shown

at three different mass fluxes, G=246, 315, and 666 kg/m2-s (Exp. nos. 5a, 6a, and 7). In

Figure 5.2(a), the bubbles rise against the oncoming flow, behaving similar to that of upflow.






Q V^


*',
!.*
I
p.



I,,I


Figure 4. Photographs of bubbles originating from a nucleation site in downflow boiling. (a) G=246 kg/m2-s, AT., = 2.95C (Exp. no. 5a),
(b) G=315 kg/m'-s, AT,, = 3.18C (Exp. no. 6a), (c) G=666 kg/m2-s, AT, = 7.34C (Exp. no. 7).






72

The conditions under which this behavior is observed are marked with the symbol (a) in

Table 5.1. However, bubbles do not slide far from the nucleation site before they are lifted

off the surface into the bulk flow. Unlike in upflow, lift-off is not a result of random bulk

or bubble-induced turbulence but is continuous and regular. This is consistent with the

supposition of Zeng et al. (1993) that for the downflow configuration, the vapor bubble

velocity will lag that of the surrounding fluid, and the resulting shear lift force should lift the

bubble off the surface. As the liquid velocity is increased, the increased drag on a bubble

overcomes the buoyancy force, and as shown in Figure 5.2(c), the bubble slides downward

in the same direction as the bulk flow. This is marked in Table 1 by the symbol (v). Lift-

off occurs regularly, since the bubble still lags the surrounding flow. At elevated heat fluxes,

bubble coalescence and eddies were observed in downflow as in upflow. But regardless of

liquid velocity, the bubble sliding trajectory is much shorter in downflow compared with

upflow due to lift-off.

As expected, there exists a transitional condition in downflow where bubble sliding

was either upward or downward. This was observed in Exp. nos. 5b and 6a-c, where sliding

took place with or against the flow with no preferred direction. These are marked in Table

1 with the symbol (0). At times a bubble would simply remain attached to the site or remain

within close proximity of the site. Figure 5.2(b) depicts a single photograph of a stream of

vapor bubbles emanating from a nucleation site in which sliding is completely absent. The

liquid velocity is such that sliding does not occur; it would appear that the buoyancy, drag,

and growth forces balance. As a result, the bubble continues to grow until lifted off the

surface, presumably by the shear lift force. Under these conditions smaller bubbles were

often observed to grow in the wake of the larger coalesced bubble. It should be noted that,








while Figure 5.2(b) may represent the mean behavior under these conditions, the

instantaneous behavior of the bubbles may resemble any of Figures 5.2(a)-(c).

In Section 5.3.1, it was suggested that bubble sliding is responsible to some extent

for energy removal from the heating surface in vertical upflow. This point can be examined

further by comparing the heat transfer rates for upflow and downflow, since in downflow

boiling, bubble sliding is limited by the lift-off mechanism. Comparing the wall superheat

in Table 5.1 for similar values of mass flux and heat flux, it appears that the wall superheat

is generally lower for upflow than downflow boiling, indicative of a higher heat transfer rate.

This point can be brought into clearer focus in Figure 5.3, where values of heat transfer

coefficient, defined as h=q",/ATb, are plotted for the upflow and downflow conditions of

Table 5.1. From the figure it is clear that the heat transfer coefficient is greater for upflow

than for downflow at otherwise similar flow and thermal conditions. It is reasonable to

1800
upflow downflo
G = 195 kg/m e 0
S1600 = 250
G =315
1400




4c



600

400

200
0 2 4 6 10
T T0at (*C)

Figure 5.3. Plot of heat transfer coefficient, h, vs. wall superheat, T,-T, for the
upflow and downflow conditions in Table 5.1.
200 ---------------




upflow and downflow conditions in Table 5.1.






74

conclude that bubble sliding is responsible for the higher heat transfer rates in upflow forced

convection boiling. The importance and influence of bubble sliding on flow boiling heat

transfer will be examined in detail in Chapter 7.


5.3.3 Vertical Pool Boiling

For the purpose of comparison, one boiling condition was examined under zero bulk

flow conditions, which is listed as Exp. no. 20 in Table 1. A photograph of the ebullition

process is presented in Figure 5.4. As in downflow, the bubbles regularly lift off of the

surface. However, since there is no bulk fluid motion, the rising bubble experiences no

significant velocity gradient from the surrounding fluid. As a result, there is no shear lift,

and therefore another force must be responsible for lift-off. In Chapter 6, the hydrodynamic

pressure force, previously examined by Klausner et al. (1993), is identified as the force

responsible for vapor bubble lift-off in vertical pool boiling.


5.4 Bubble Dynamics Measurements


5.4.1 Growth Rate

Numerous investigators have attempted to model the growth of vapor bubbles in the

simpler case of nucleate pool boiling. The most recent effort was made by Mei et al.

(1995a&b), who performed a detailed numerical analysis to describe the growth of vapor

bubbles in saturated pool boiling. They solved for the localized temperature variation within

the heater surface as well as the liquid microlayer beneath the expanding bubble, and found

that the growth rate is highly dependant on the rate of energy depletion from heater surface.

By comparison, the modelling of flow boiling bubble growth is considerably more difficult

for various reasons. In flow boiling, the bubble is subjected to a shear flow and is

asymmetrically distorted. The thermal boundary layer surrounding the bubble is therefore






75

difficult to describe. Furthermore, when a bubble slides, the liquid microlayer is continually

exposed to a different part of the heater surface, and the microlayer structure itself may change

in response to the bubble's motion. Thus an accurate description of vapor bubble growth in

flow boiling requires a detailed three-dimensional, three-phase heat and momentum transfer

analysis. The purpose of this work is to collect experimental growth data, which is necessary

to develop a better understanding of vapor bubble growth in order to provide a framework for

future bubble growth models. Moreover, the experimental bubble growth data obtained in this

investigation is necessary to estimate the forces on the growing bubble, which are used to

develop the bubble dynamics model described in Chapter 6.










(V,


















nuc.

1 mm

Figure 5.4. Photograph of bubbles originating from the same nucleation site in vertical
pool boiling, AT,, = 3.440C (Exp. no. 8).






76

A typical set of experimentally measured growth curves is depicted in Figure 5.5.

A growth curve was obtained by measuring the diameter of an individual bubble from

incipience through sliding. For saturated or nearly saturated boiling, the experimental growth

rates may be curve-fit by a power law,

d(t) = Kt (5.1)

where d(t) is the diameter of the bubble and t is the growth time. Because of the stochastic

nature of the flow and thermal variations discussed in Section 5.2, a set of 5 growth curves

were measured at various points in the film set, and the constants K and n were averaged to

estimate the mean growth curve at this condition. Because in downflow the vapor bubbles

resist the motion of the flow, the growth showed more variation, so a set of 10 growth

curves were obtained at each condition. The averaged growth constants for upflow and

downflow are included in Table 5.1. The Jacob number, Ja, is included in the tables for

each condition. From the table it is observed that the growth data fit a power law ranging

from about t"3 to t"2, which is expected for slightly subcooled boiling.


0.6
Upflow.
0.5 G = 195 1 kg/m' s
AT, = 0 54 'C
E (run no la)
E 0.4 -
Curve fit v "

E o VC 0 00
023 0Vv ~ 8 S,0*o o"


02 2


0.1


00
0 10 20 30 40 50 60
Time, ms
Figure 5.5. Typical bubble growth measurement.






77

In order to verify the statistical validity of the measured growth curves, additional

growth data were obtained from the digital footage of ebullition for Exp. no. la. By

increasing the total number of measured growth curves from 5 to 20, the resulting averaged

constants K and n varied by less than 6 and 2 percent, respectively. Moreover, the scatter

in the growth curves seen in Figure 5.5 was consistent, indicating that the variation in

measured growth rate is primarily a result of statistical fluctuations in flow velocity and

surface temperature, and not a result of a change in measurement accuracy. Therefore, a

sample of 5 growth curves for upflow and 10 for downflow is judged acceptable to estimate

the mean bubble growth curve.

A graphical comparison of the growth curves reveals useful information about the

ebullition process. Figures 5.6(a) and (b) depict the mean growth curves for upflow and

downflow, respectively. On both graphs, the number assigned to each curve represents the

experiment number listed in Table 5.1. The solid triangles on both sets of curves represent

the departure diameter at each condition. The upflow growth curves end approximately at

the point where the vapor bubbles leave the field of view, except for curves Ic, 2b, 2c, 3b,

and 3c, where bubble collisions and coalescence limited the available growth data. The

downflow curves end when the bubbles lift off the heater surface, except for curve 4a, which

extends beyond the limits of the plot.

Examining both graphs, several trends are clear. First, at a given mass flux, the

bubble growth increases with increasing Ja (increasing ATT). Second, departure from the

nucleation site occurs early in the growth curves, particularly in upflow, and therefore a large

portion of bubble growth occurs during the sliding phase.













04
5' ///





0.2 -

Upflow:
G 194 (runs la-c) (kg/m'-s)
0 1 --- GZ250 (runs 2a-c)
S- G315 (runs 3a-c)
A Departure point


0 10 20 30 40
time. t (ms)

(a)


50 60


10 20 30
time. t (ms)

(b)


Figure 5.6. Comparison of mean growth curves; (a) upflow, (b) downflow. End of
upflow curves represent limits of measuring diameter, due either to end of viewfield or
coalescence. End of downflow curves represent mean lift-off point.






79

The effect of varying mass flux can be seen in both figures. In upflow it appears

that, at low AT., (or Ja), the variation of mass flux has little impact on growth, as evidenced

by curves la, 2a, and 3a in Figure 5.6(a), which represent conditions with roughly similar

AT, (Ja). At higher wall superheat/Jacob number, the growth curves appear to separate,

although this effect is less obvious since the wall superheat/Jacob number was not held

constant. What is clear, however, is that the growth at these higher wall superheats/Jacob

numbers decreases with increasing G. This is evident when comparing curves lb, 2b, and

3b, and the curves Ic, 2c, and 3c, in which the growth decreases with increasing G despite

a slight increase in ATt (Ja) in some cases. The same effect can be seen in Figure 5.6(b)

for downflow, by examining the curves 4b, 5a, and 6a, and the curves 4c, 5b and 6b. These

results suggest that the thermal boundary layer thickness is decreased with increasing G,

which results in a greater amount of condensation from the dome of the bubble.

A final observation in the downflow growth curves deserves comment. At elevated

AT, as is the case for conditions 4c, 5c, and 7 in Figure 5.6(b), all with nearly the same

value of wall superheat (approximately 7"C), the growth rates do not vary appreciably

despite large changes in G (247 to 666 kg/m'-s). Since n approaches 0.5, which is the

maximum value for diffusion-controlled growth in saturated boiling, it can be concluded that

microlayer evaporation is predominant and condensation is negligible.


5.4.2 Departure and Lift-off Diameter

The departure diameter, dd, was measured from the film footage as the diameter of

the vapor bubble in the frame immediately after the first sign of displacement from the

nucleation site. Similarly, the lift-off diameter, dL is measured in the frame immediately

after the bubble detaches from the heater surface. This method was also chosen by Klausner

et al. (1993) in their measurement of departure and lift-off diameters. A source of






80

uncertainty in the measurement of bubble departure diameter arises because departure occurs

early in the growth curve, when the bubbles are small and the diameter is increasing rapidly.

Furthermore, bubble collisions, particularly at the nucleation site as described in Section

5.3.1, limited the available departure and lift-off diameter and waiting time data under some

conditions. Mean values of dd, dL, and t, at each experimental condition are included in

Table 5.1. As discussed in Section 5.3.1, few bubbles were observed to lift off in upflow,

and therefore no data for lift-off in upflow are presented.

Comparison of mean departure and lift-off diameter data. Figure 5.7 compares

the mean values of departure diameter, dd, at various values of mean liquid velocity as a

function of wall superheat, AT.,, for (a) upflow and (b) downflow. Also included in both

plots is the mean departure diameter under vertical pool boiling, obtained in the same

experimental facility under zero flow conditions. Each mean value of dd and dL results from

a distribution of approximately 50 to 100 measurements; in the following section, the

statistical relevance of the mean values will be examined. In upflow it is seen that the

departure diameter clearly increases with increasing wall superheat; this is due to the

increased bubble growth at higher wall superheat. The expanding vapor bubble generates

a reaction force, referred to as the growth force, in the surrounding liquid which resists

bubble motion away from the heater wall. While attached to the nucleation site, the vapor

bubble is tilted due to the flowing liquid, and a component of the growth force parallel to the

heater surface resists bubble departure. The larger the growth rate, the greater the resistance

to departure, and therefore the larger the bubble will be before drag and/or buoyancy

removes the bubble from the nucleation site. The departure diameter appears to decrease

with increasing mean liquid velocity in upflow, although beyond G-250 kg/m2-s there is

little change in dd with G.










0.3






2 0.2






7. upflow

S0 G 195 kg/ma-s
E0 G Z 250
G 315
0 Vertical pool boiling
0.0 S
0 1 2 3 4 5 6 7
T T (1C)

(a)


0.3






0.2





d1 downflow:
G : 195 kg/m'-s
G = 250
S G 315
0 G z 666
Vertical pool boiling
00
0 1 2 3 4 5 6 7 8
T. T. (TC)

(b)

Figure 5.7. Comparison of measured mean departure diameters for (a) upflow and (b)
downflow forced convection boiling. Diamond (0) represents vertical pool boiling data
point.




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