experimental investigation of gravity...

EXPERIMENTAL INVESTIGATION OF GRAVITY-INDEPENDENT FLOW

BOILING REGIMES

By

JASON SCOTT BOWER

A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2003

Copyright 2003

by

Jason Scott Bower

ACKNOWLEDGMENTS

Over the course of my time at the University of Florida, I have been blessed with

great technical mentors and significant personal support. I would like to express my

foremost gratitude to Dr. James Klausner, my graduate advisor during my studies. His

patience and support never wavered during my studies, and he has left a lasting

impression regarding the practical critical thinking skills that an engineer must cultivate

to grow in our profession. I would also like to thank Dr. Renwei Mei and Dr. William

Lear for their guidance while serving on my supervisory committee. I also must express

my gratitude to NASA for financially supporting my experimental work.

My fellow graduate students, Chris Velat, Yusen Qi, Mohamed Darwish, and

Siddartha Sathyanarayan, have been instrumental through their daily friendship and have

made lasting contributions to my life and understanding beyond the academic realm.

John Terlizzi, who was brought in during the homestretch, made invaluable contributions

to the final product and has earned much appreciation.

Finally, I would like to thank my Mom and Dad, my sister Erin, and my wife

Becky for providing years of support, through all the highs, lows, and in-betweens, as

only family can.

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................................................................................. iii

LIST OF TABLES............................................................................................................. vi

LIST OF FIGURES .......................................................................................................... vii

NOMENCLATURE ............................................................................................................x

ABSTRACT..................................................................................................................... xiii

CHAPTER 1 INTRODUCTION ........................................................................................................1

1.1 Current Two-Phase Flow Boiling Understanding ..................................................1 1.1.1 Two-Phase Flow Boiling Process .............................................................2 1.1.2 Two-Phase Flow Boiling Modeling..........................................................4 1.1.3 Critical Heat Flux......................................................................................6

1.2 Microgravity Effects on Flow Boiling Heat Transfer.............................................7 1.3 Scope of Current Research .....................................................................................8

2 EXPERIMENTAL FACILITY ..................................................................................11

2.1 Flow Boiling Facility Overview ...........................................................................11 2.2 Heat Exchanger Test Section Design ...................................................................13

2.2.1 Polycarbonate Test Section ........................................................................14 2.2.2 Brass Test Section ......................................................................................16 2.2.3 Test Section Angular Support ....................................................................18

2.3 High Speed Digital Camera ..................................................................................20 2.4 Instrumentation and Calibration ...........................................................................21

2.4.1 Temperature Measurement .........................................................................21 2.4.4 Flow Measurement .....................................................................................21 2.4.3 Differential Pressure Measurement ............................................................23 2.4.2 Static Pressure Measurement......................................................................23 2.4.5 Preheat Section Heat Loss ..........................................................................23 2.4.6 Test Section Heat Loss ...............................................................................25 2.4.7 Temperature Correction..............................................................................27

2.6 Data Acquisition and Processing ..........................................................................29

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3 GRAVITATIONAL EFFECTS ON VAPOR BUBBLE DYNAMICS .....................31

3.1 Introduction and Literature Survey.......................................................................31 3.2 Experimental Procedure........................................................................................38 3.3 Results...................................................................................................................40 3.4 Discussion.............................................................................................................51

4 GRAVITATIONAL EFFECT ON TWO-PHASE HEAT TRANSFER....................53


5 GRAVITATIONAL EFFECT ON CRITICAL HEAT FLUX...................................77


6 CONCLUSIONS AND RECOMMENDATIONS.....................................................94

6.1 Accomplishments and Findings............................................................................94 6.2 Recommendations for Future Research................................................................96

APPENDIX A PROPERTIES OF FC-87 ...........................................................................................99

B BUBBLE LIFT-OFF DATA ....................................................................................102

C HEAT TRANSFER COEFFICIENT DATA............................................................108

LIST OF REFERENCES.................................................................................................134

BIOGRAPHICAL SKETCH ...........................................................................................139

v

LIST OF TABLES

Table page 3.1. Results of experimental bubble lift-off measurements ..............................................41

5.1. Critical heat flux data.................................................................................................85

vi

LIST OF FIGURES

Figure page 2.1. Schematic diagram of two-phase flow boiling facility ..............................................12

2.2. Polycarbonate test section assembly...........................................................................15

2.3. Exploded view of polycarbonate test section..............................................................17

2.4. Brass heat exchanger..................................................................................................18

2.5. Angular positioning system using linear motion components...................................19

2.6. Typical test orientations, φ, with respect to gravity...................................................20

2.7. ERDCO 2521-02T0 flow meter calibration...............................................................22

2.8. Calibration of venturi discharge coefficient ...............................................................23

2.9. Validyne Model 3-32 pressure transducer calibration curves....................................24

2.10. Viatran static pressure transducer calibration curves...............................................24

2.11. Preheat heat loss calibration.....................................................................................25

2.12. Polycarbonate test section heat loss calibration........................................................26

2.13. Brass test section heat loss calibration......................................................................26

2.14. Temperatures in test section......................................................................................27

3.1. Growth, departure, sliding, and lift-off of a vapor bubble on an inclined flow boiling surface. .....................................................................................................................34

3.2. Variation of vapor bubble departure diameter with bulk fluid velocity ....................35

3.3. Variation of vapor bubble lift-off diameter with bulk fluid velocity.........................36

3.4. Gravity independent/dependent flow regime map for vapor bubble lift-off..............37

3.5. Photographs of bubble lift-off at Ja = 30, ψ = 0.02, and φ = 45° upflow ..................43

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3.9. Photographs of bubble lift-off at Ja = 30, ψ = 0.02, and φ = 225° downflow ...........44

3.10. Photographs of bubble lift-off at Ja = 30, ψ = 0.04, and φ = 225° downflow .........44



3.13. Variation of bubble lift-off diameter with ψ at φ = 0° .............................................45

3.14. Variation of bubble lift-off diameter with ψ at φ = 45° ...........................................46

3.15. Variation of lift-off diameter with ψ at φ = 90° .......................................................46

3.16. Variation of bubble lift-off diameter with ψ at φ = 315° .........................................47

3.17. Variation of bubble lift-off diameter with ψ at φ = 270° .........................................47

3.18. Bubble lift-off diameter vs. ψ at Ja = 24..................................................................49



4.1. Polycarbonate test section boiling curves at ψ = 0.025 .............................................58

4.2. Variation of Nusselt number with ψ for Ja = 16 and different flow orientations ......59








4.10. Variation of Nusselt number with ψ for Ja = 32 and different flow orientations ....63

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4.15. Coefficient of variation at different ψ for Ja = 16 to 22 ..........................................68



4.18. Coefficient of variation for different ψ with buoyancy assisted flow orientations..70

4.19. Coefficient of variation for different ψ with buoyancy resisted flow orientations ..71

4.20. Effect of subcooling on gravity dependence for Ja = 32 .........................................72

4.21. Experimental gravity dependence map in comparison to theoretical gravity dependence curve for bubble lift-off diameter .........................................................73

5.1. Critical heat flux vs. ψ for all orientations.................................................................87

5.2. Coefficient of variation vs. ψ .....................................................................................88

5.3. Comparison of CHF vs. ψ data with model of Brusstar and Merte (1997b) for upflow and horizontal orientations...........................................................................90

5.4. Comparison of CHF vs. ψ data with model of Brusstar and Merte (1997b) for downflow orientations..............................................................................................90

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NOMENCLATURE

Cf – venturi discharge coefficient

Cp – specific heat (kJ/kg/K)

D – test section flow channel height used as hydraulic diameter (mm)

growthFr

– growth force (N)

bulkgrowthF ,r

– bulk growth force (N)

BodyFr

– body force (N)

BFr

– buoyancy force (N)

SFr

– shear force (N)

CPFr

– contact pressure force (N)

FSFr

– free stream acceleration force (N)

AMFr

– added mass force (N)

QSFr

– quasi-static drag force (N)

SLFr

– shear lift force (N)

g& – power generation within heater (W/m3)

g – gravitational acceleration (9.81 m/s2)

h – convection heat transfer coefficient (W/m2K)

hlv – latent heat of vaporization (J/kg)

x

Ja – Jacob number

k – thermal conductivity (W/mK)

mb – mass of the bubble (kg)

Nu – Nusselt number

P – pressure (Pa, bar, or psi)

Q – volumetric flow rate (L/min)

q″s – heat flux provided from the heater surface to the bulk fluid (W/m2)

q″loss – heat loss (W/m2)

q″c – critical heat flux (kW/m2)

q″L&D – critical heat flux correlation by Brusstar and Merte (1997) based on Leinhard and

Dhir (1973), (kW/m2)

Rr

– reaction force (N)

Re – bulk Reynolds number

t – thickness (mm or cm)

T – temperature (°C or K)

U – bulk fluid velocity (m/s)

u – base flow velocity in perturbation flow field (m/s)

V – bubble sliding velocity (m/s)

Vb – vapor bubble volume (m3)

We – Weber number

Greek

µ --- dynamic viscosity (Ns/m2)

xi

µψ, Ja --- average of data from different orientations at a specified Ja and ψ

ρ -- density (kg/m3)

φ --- heater surface inclination angle

θ --- bubble inclination angle

σ --- liquid/vapor surface tension (N/m)

σ ψ,Ja --- standard deviation of data from different orientations at a specified Ja and ψ

α --- Fourier disturbance wave frequency in perturbation flow field

∆Tsat -- wall superheat (°C)

∆Tsub – bulk liquid subcooling (ºC)

ψ – dimensionless parameter reflecting bulk flow velocity

Subscripts

b – bulk

br – brass

ep – epoxy

junc – junction

l – liquid

meas - measured

s - surface

v – vapor

w - wall

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Abstract of Thesis Presented to the Graduate School

of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science

EXPERIMENTAL INVESTIGATION OF GRAVITY-INDEPENDENT FLOW BOILING REGIMES

By

Jason Scott Bower

December 2003

Chair: James F. Klausner Major Department: Mechanical and Aerospace Engineering

An existing two-phase flow boiling facility has been upgraded and recalibrated to

experimentally study the effect of gravitational forces on boiling heat transfer with the

motivation of elucidating a gravity dependent/independent flow regime map. It is

envisioned that such a map would be utilized for the fabrication of two-phase heat

exchange systems to be deployed in variable gravity environments. A transparent

polycarbonate test section has been constructed to perform visual observations and gather

heat transfer data examined in this study. The flow facility incorporates a linear bearing

system for angular positioning of the test section at various orientations to terrestrial

gravity in order to evaluate the consequences of varying the magnitude of gravitational

forces parallel and normal to the flow direction.

Video sequences have been captured to determine bubble lift-off diameter at

various thermal and hydrodynamic conditions and at different test section orientations.

These data exhibit trends towards gravity independence at low imposed heat flux, and at

xiii

increasingly higher flow velocities for increasing heat flux. The trends in the empirical

data validate the analytical bubble dynamics model that suggests the existence of a

gravity independent flow-boiling regime.

Heat transfer coefficients have been investigated and it appears that a consequence

of gravity independence of ebullition phenomena is a corresponding gravity independent

thermal transport two-phase flow-boiling regime. The dependent/independent regime

map constructed from experimental data suggests that the analytical bubble dynamics

model prescribes a conservative design criterion for the gravity-independent regime.

The problem of heat exchanger component burnout has been addressed in the study

by measuring the critical heat flux at differing orientations relative to gravity. The data

exhibit a strong influence of orientation and suggest that flow orientations without

sufficient means to sweep and lift vapor away from the heat transfer surface are subject to

considerably lower critical heat fluxes. However, at high velocities, the differences

among flow orientations are sharply reduced, suggesting there exists a high velocity

region where the critical heat flux is gravity-independent.

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CHAPTER 1 INTRODUCTION

The efficiency of heat removal associated with forced convection boiling has

promoted the implementation of two-phase heat exchange service loops in many thermal

management applications where power loads are sufficiently high to render single-phase

heat exchange ineffective. Benefits of boiling heat transfer are a consequence of the

large latent heat energy absorption that is requisite for the liquid-to-vapor phase change

process. This phase change, and thus the heat transfer to the fluid, can occur at

significantly lower operating temperatures than single-phase systems with similar heat

removal capacities. As power requirements grow during the evolution of space systems,

where single-phase heat transport has previously been used successfully to relocate heat

to deep space radiators, there is a growing impetus among NASA and other organizations

to investigate and develop two-phase systems applicable to space environments. Zhang

et al. (2002) suggest that implementing these systems may offer better than an order of

magnitude reduction in heat-load-to-weight ratio in comparison with their single-phase

predecessors.

1.1 Current Two-Phase Flow Boiling Understanding

To adequately describe microgravity boiling heat transfer, a general discussion of

two-phase flow boiling is required. A depiction of forces on a growing bubble and of the

bubble’s rate of growth are necessary to quantify heat transfer. Thus, an examination of

these parameters for gravitational effects can illuminate the influence of a microgravity

environment on the heat transfer performance of a thermal management system. In

1

2

particular, Thorncroft et al. (2001) has proposed a computational model that suggests that

vapor bubble departure and liftoff sizes collapse to a single value at high bulk fluid

velocities, regardless of the magnitude or direction of the buoyancy force on the bubble.

1.1.1 Two-Phase Flow Boiling Process

While the practical benefits offered by two-phase flow boiling heat management

have been identified and have led to widespread utilization of such systems, the

underlying phenomena have not yet been modeled with acceptable accuracy. Boiling

heat transfer characteristics can be attributed to the aggregate heat removal associated

with ebullition and enhanced convective heat transfer due to increased turbulent mixing

of the two-phase flow. These boiling and convective terms are referred to as

microconvection and macroconvection, respectively. The microconvective ebullition

process can involve a number of distinct stages that will be discussed below: incipience,

growth, detachment, sliding, departure, and waiting time. Microconvective heat transfer

can be extended from an isolated bubble’s ebullition process to a practical boiling surface

involving multiple ebullition sites with knowledge of the nucleation site density of the

surface.

Incipience, which provides the microconvective portion of two-phase heat transfer,

occurs in a cavity on the boiling surface when vapor trapped in the cavity is supplied with

sufficient energy from the solid heater to vaporize adjacent liquid in the cavity. It has

been recognized that vapor trapping is dependent on the cavity geometry and the wetting

characteristics of the boiling fluid, establishing a minimum cavity radius for nucleation.

The nascent bubble’s continued growth from the nucleation site is contingent on the

continual provision of energy to vaporize additional liquid. However, due to turbulent

motion that characterizes two-phase flow, a smaller thermal boundary layer may expose

3

the growing bubble to cool liquid in a subcooled bulk flow. If the vapor temperature is

lowered enough due to growth into the thermal boundary layer, the bubble will condense.

This criterion establishes a maximum cavity radius governing incipience.

Once a nucleation site has been activated, growth proceeds in a fashion dependent

upon several factors, including the superheat available from the boiling surface and the

bulk fluid flow. Expansion of the bubble is resisted by the inertia of the liquid from

above and the solid surface below, causing the bubble to deform into a hemispherical

dome. As the bubble expands around the nucleation cavity, the engine for its growth

becomes the evaporation of a thin, wedge shaped liquid microlayer that lies between the

solid heater and the liquid-vapor boundary. This microlayer is evaporated by absorbing

heat from the heater surface and is replenished by liquid surrounding the bubble.

Vapor bubbles will depart from their nucleation cavity by detaching from the site

and moving into the bulk flow, or by sliding away from the site along the heated surface.

In the case of pool boiling with an upward facing heated surface, a vapor bubble that has

grown to sufficient size will lift directly off the nucleation site. As observed by Zeng et

al. (1993a), vapor bubbles on an upward facing heated surface exposed to low velocity

bulk flow lift directly off the boiling surface and are then carried away with the bulk

liquid. However, as the bulk velocity increases above some threshold value, the

influence of hydrodynamic forces will cause the bubble to depart the nucleation site and

slide along the heating surface. During sliding, the vapor bubble will continue to absorb

energy from the surface and will continue to grow until a sufficient buoyancy force is

present to lift the bubble into the flow stream. Thorncroft et al. (2001) have observed

bubble dynamics during vertical upflow and downflow. In vertical upflow, bubbles

4

depart the heating surface by sliding upward and typically remain attached to the heating

surface. In contrast, bubbles in downflow can depart by sliding either upward or

downward along the heating surface as dictated by interaction of hydrodynamic forces

and buoyancy forces on the bubble. Bubbles departing from nucleation sites in low bulk

velocity fields will tend to slide upward, while those departing in higher liquid velocity

fields will slide downward due to drag.

The waiting time is the time between the departure of a bubble from a nucleation

site and the incipience of a subsequent bubble from the same site. The large amount of

heat required by the growth of the initial bubble is extracted from the heater surface in the

local region of nucleation, creating temperature contours in the solid heater. The local

heater temperature recovers during the waiting time, and the time of recovery is related to

the thermal capacity of the heater, physical properties of the solid and liquid phases, and,

ultimately, to the bubble growth rate.

1.1.2 Two-Phase Flow Boiling Modeling

Roshenow (1952) introduced a landmark concept for flow boiling heat transfer

correlations by suggesting that two-phase flow heat transfer rates are due to two

independent additive mechanisms; bulk turbulence and ebullition. Chen (1966) proposed

an extension of this model, asserting that the application of empirical suppression and

enhancement factors to alter the ebullition and bulk turbulent flow motion contributions

to heat transfer, respectively, allows the researcher to obtain agreement with experimental

observations. A number of correlations reported in the literature seek to correlate with

flow boiling data based on Chen’s technique.

Researchers’ lack of success in predicting two-phase flow characteristics with

widely used methods has led to a desire to reexamine basic principles of flow boiling.

5

The Chen approach has encountered significant criticism for failing to account for several

recently realized physical processes. Most significantly, Kenning and Cooper (1989),

among others, have demonstrated that microconvection and macroconvection

components of two-phase heat transfer are not independent and additive. Additionally,

whereas the Chen correlation predicts that microconvection does not contribute

significantly to overall heat transfer, researchers such as Cooper (1989) have shown that

microconvection can provide a large portion of heat transfer. Thorncroft and Klausner

(1999) have attributed as much as 50% of the total heat transfer to latent heat effects

during the sliding and continuing growth of a bubble after departure from the nucleation

site, a phenomenon which Chen’s correlation cannot account for.

Due to its governing influence on heat transfer, the vapor bubble growth rate has

been the subject of considerable investigation. However, fundamental shortcomings of

previously accepted theory and the inability to represent experimental growth rate data

described by researchers such as Van Stralen et al. (1975) and Mei et al. (1995a, 1995b)

led Dhir (1990) to call for a return to basic boiling heat transfer experiments with

different techniques. In particular, Kenning (1991) has identified large local variation in

wall temperature as a factor in widely varying experimental constants that fail to garner

widespread applicability. Knowledge of accurate vapor bubble growth rate

determination, which predicates valid expressions for boiling heat transfer, must be

determined from a detailed simultaneous solution of the momentum and energy equations

in the solid heater, the liquid phase, and the vapor phase. In this study, a visual

determination of the vapor bubble growth rate will be used, in the process of assessing

gravity dependence, to validate the Sathyanarayan’s (2003) current model that predicts

6

the points of vapor bubble departure from the nucleation site and lift-off from the heater

surface.

1.1.3 Critical Heat Flux

As increasing heat is dissipated to the bulk flow, considerable amounts of vapor

are formed from nucleation sites and it becomes difficult for fluid to rewet the boiling

surface. The heating surface is covered with a layer of relatively low thermal

conductivity vapor, causing the heat transfer rate to drop abruptly, and thus resulting in a

precipitous and possibly catastrophic rise in surface temperature. The destructive

consequences of exceeding this critical heat flux have led to investigations into the small-

scale physical phenomena that lead to burnout and methods of predicting this occurrence.

Early photographic evidence of pool boiling obtained by Kirby and Westwater

(1965) demonstrated that, at near-critical heat flux, coalescence of individual bubbles

forms a large vapor mass separated from the boiling surface by a very thin liquid layer.

At times, evaporation of the layer would result in temporary surface dryout before the

large vapor mass departed and allowed liquid to replenish this layer. These visual results

and the periodic nature of local dry patches called into question early modeling efforts.

Various modeling efforts can be roughly grouped into two categories; hydrodynamic

instability models and macrolayer dryout models. The hydrodynamic instability model

proposed by Zuber (1958) and extended by Lienhard and Dhir (1973) assumes the

existence of a mechanism that collapses vapor escape passages on the boiling surface due

to capillary instability between the vapor and liquid phases. Macrolayer dryout models,

credited to Haramura and Katto (1982), describe the evaporation of a uniform and thin

liquid layer beneath large vapor masses. Both models ultimately lead to dryout as vapor

volume increases coverage over the boiling surface by eliminating the cool liquid.

7

Gersey and Mudawar (1995a) provided photographic flow boiling evidence of a wavy

vapor layer propagating along the boiling surface in separated flow due to hydrodynamic

instability. Surface wetting occurred at the troughs of the wave, whose period increased

in the streamwise direction and as heat flux was increased. At critical heat flux, available

area of surface rewetting was insufficient to prevent complete dryout.

1.2 Microgravity Effects on Flow Boiling Heat Transfer

The practical difficulties of obtaining experimental data at microgravity conditions

have hindered the utilization of two-phase flow boiling systems in space applications.

Nevertheless, insight into behavior of flow boiling systems at various levels of

gravitational influence can be gained in terrestrial experiments. The magnitude and

direction of the gravitational components parallel and perpendicular to the heating

surface can be altered through the range of +/- 1g by performing tests with the boiling test

section rotated through different orientations relative to terrestrial gravity. By varying

the gravitational influence, the effect of gravity on flow boiling may be discerned.

Results of studies by researchers such as Van Helden et al. (1995) and numerical

results reported by Lee and Nydahl (1989) and Zeng et al. (1993b) indicate that the

buoyancy force can play a significant role in bubble growth dynamics. The buoyancy

force influences the heat transfer from the boiling surface by either assisting or impeding

departure and liftoff from the heater surface, depending on its orientation. At low

velocity, the buoyancy-dependent flow regime has been clearly identified by Kirk et al.

(1995), who demonstrated that vertical upflow produced significant heat transfer

enhancement when compared with horizontal flow. Researchers have also observed that

the buoyancy effect is eliminated at sufficiently high velocities, where hydrodynamic

8

forces overwhelm buoyancy forces. This is the regime that this work will attempt to

identify.

Reliable operation of flow boiling heat exchangers requires operation below the

critical heat flux to prevent an opportunity for catastrophic damage. Bulk fluid velocity

acts to remove vapor from the heating surface, postponing the onset of burnout to higher

heat fluxes. The effect of zero gravity accelerates dryout as buoyancy forces, which

normally aid in sweeping large vapor volumes from the surface to allow liquid

replenishment, become negligible. This possible propensity for reduced critical heat flux

at micro-g conditions is a severe barrier to the implementation of two-phase flow

systems. Gersey and Mudawar (1995b) developed a model for critical heat flux based on

a wavy vapor layer that breaks down on the surface due to hydrodynamic instability.

This model suggests that as bulk fluid velocity increases, buoyancy forces, and thus

critical heat flux, become independent of the orientation of gravity. Zhang et al. (2002)

also provide a visual study and CHF measurements describing the effects of the direction

of buoyancy force and notes that orientation is a factor only at lower velocities.

1.3 Scope of Current Research

Due to the very large heat fluxes available, the use of phase change heat transfer in

micro-g and reduced-g environments can have a profound impact on reducing the size,

weight, and cost of thermal management power systems to be deployed in space. As

such, there have been numerous research studies attempting to gain a fundamental

understanding and predictive capability regarding phase change heat and momentum

transfer in reduced gravity. In particular Thorncroft et al. (2001) have developed a model

that very reliably describes the dynamics of vapor bubbles during the boiling process

through inception, growth, and departure. It has been experimentally demonstrated that

9

the model correctly predicts the influence of gravity. It is particularly noteworthy that the

model suggests a subcooled flow-boiling regime in which the boiling process is

independent of the gravitational field.

Based on model predictions and experimental observations, it is hypothesized that

the development of advanced phase-change heat exchangers that utilize subcooled flow

boiling and operate in the gravity-independent regime are feasible. The advantages to

developing advanced flow boiling micro-g heat exchanger technology are: 1) high heat

flux heat exchangers may be developed for spacecraft deployment, 2) the heat exchangers

may be thoroughly tested in any orientation with respect to gravity to insure their reliable

operation independent of gravity, and 3) the heat exchanger design will be based on

extensive experimental data, and will not rely on sparse micro-g data. The

comprehensive analysis and testing that can be accomplished under 1-g conditions will

dramatically increase the reliability for the heat exchanger to operate efficaciously for

space-based applications.

The focus of the current investigation is to provide experimental verification of a

computational bubble dynamics analysis tool that can be used to identify a gravity-

independent subcooled flow-boiling regime. The regime will be experimentally

identified using prototype heat exchangers for testing thermodynamic performance for

flow directions at different orientations relative to terrestrial gravity. Development of the

experimental facility, heat exchangers, instrumentation, and data acquisition methods are

detailed in Chapter 2. The heat exchangers are thoroughly instrumented to provide

measurements related to heat transfer during boiling. The polycarbonate heat exchanger

allows for visual study of bubble dynamics and flow regime during testing. Chapter 3

10

discusses the results of the visual investigation and reconciles these results with

predictions of the computational model. Insight is also sought into the physical

phenomenon that governs the incipience, growth, departure, and flow pattern of a bubble

with respect to gravity. Assuming that the bubble dynamics governing the boiling

process in the subcooled region are independent of the gravitational field, the heat

transfer coefficient and pressure drop presumably also remain constant as orientation of

the gravitational force is changed. These flow effects and their influence on heat transfer

characteristics are explored in Chapter 4, with the motivation of verifying and describing

the existence of a gravity-independent flow regime. Because this bubble dynamics model

loses validity at some critical heat flux, the heat exchangers are to be designed to operate

with low quality, away from this critical value. At lower gravity, it may be more difficult

to promote removal of vapor from the boiling surface and heater burnout may occur at

lower-than-expected heat fluxes, thus it is important to quantify this critical value. In

Chapter 5, attempts are made to explore the critical heat bounds of the gravity

independent regime in the prototype heat exchanger. Chapter 6 offers concluding

remarks and suggests further direction for related study.

CHAPTER 2 EXPERIMENTAL FACILITY

An experimental flow boiling facility and heat exchanger were constructed to

explore the parameter space for which subcooled forced convection boiling heat transfer

is independent of the gravitational field. The experimental results will be compared with

a computational bubble dynamics model that delineates the gravity dependent and

independent flow boiling regimes. The two-phase flow boiling facility is fully

instrumented to measure the heat transfer coefficient and pressure drop in the heat

exchanger. The test section design also provides for visualization of the nucleation,

growth, departure, and lift-off of vapor bubbles under various flow and thermal

conditions. Critical heat flux conditions will also be investigated and evaluated with

regard to gravitational field.

2.1 Flow Boiling Facility Overview

An existing flow boiling facility at the University of Florida was modified to

accommodate this study. A schematic diagram of the facility is shown in Figure 2.1. A

variable speed gear pump, driven by a permanent magnet DC motor, pumps fluid through

a filter/drier. The fluid flow rate is measured with either a vane flow meter or a venturi

flow meter, depending on the flow rate range to be measured. Next, six preheater coils

bring the working fluid to the desired saturation or subcooled condition. The fluid is then

directed into the heat exchanger test section via a series of valves. The valves dictate

which side of the test section the fluid enters and exits from, allowing for arrangement of

upflow and downflow at a variety of angular orientations with respect to gravity from

11

12

vertical to horizontal. In the heat exchanger test section, which is described below, the

working fluid undergoes a boiling process when sufficient heat flux is supplied. Wall

and bulk fluid temperature measurements are made with type E thermocouples and the

heat exchanger pressure drop is measured with a Validyne differential pressure

transducer. A high-speed digital camera is used to record the ebullition phenomena

within the test section. After discharging from the heat exchanger test section, the fluid

passes through a water-cooled, shell-and-tube condenser. The condenser shell fluid

either circulates water from the city ground supply at approximately 23ºC, chilled water

circulated by a closed loop refrigeration system, or a mixture of the two to provide

sufficient condensation at high vapor qualities or to attain appropriate levels of

subcooling. The condensed liquid returns to the gear pump to complete its circuit. The

facility operates with FC-87, a perflourocarbon fluid supplied by 3M Corporation, as the

Figure 2.1. Schematic diagram of two-phase flow boiling facility

13

working fluid. The fluid is desirable for its low latent heat of vaporization that reduces

the required heat input, low boiling point allowing for lower operating temperatures, non-

toxicity, and chemical inertness.

The flow rate is controlled manually by adjusting the speed of the pump through a

pulsed-width modulated DC voltage controller. A series of autotransformers are used to

adjust the AC voltage into the preheaters, thus controlling the thermal field throughout

the flow boiling facility. A 120-amp DC variable voltage supply is connected to the heat

exchanger test section and is used to control the heat flux into the heat exchanger. Flow

rate, pressure, and temperature measurements are obtained with a 12-bit digital data

acquisition system that uses a QuickBasic source code to output conditioned data to a PC

screen in real time. The calibration of the instrumentation is described in a later section.

2.2 Heat Exchanger Test Section Design

Two heat exchanger test sections have been developed for the flow boiling

investigation: a) a transparent heat exchanger that allows for visualization of the

liquid/vapor dynamics and b) an opaque brass prototype heat exchanger. Experimental

measurements reported herein have primarily been obtained using the transparent test

section. The visual heat exchanger test section will facilitate experimental measurements

and visual study of the flow boiling characteristics, while the brass prototype heat

exchanger represents a scale model of a heat exchanger that may be used for spacecraft

thermal management deployment. The brass heat exchanger will be able to sustain more

extreme temperature and pressures, allowing for a test range that includes investigation of

burnout conditions. Both heat exchangers are designed to be subjected to similar testing

protocol in the flow boiling facility.

14

2.2.1 Polycarbonate Test Section

Several requirements dictated the design of the transparent test section. High-

resolution visual observation of the boiling phenomena must be possible to identify

nucleation centers and quantify bubble sizes during the boiling process. The heat

exchanger must also utilize channel flow, since extensive experience and understanding

of flow boiling bubble dynamics is based on channel flow. The heat exchanger design

should also be modular such that it can be easily scaled up or down for different heat load

applications. The design must also facilitate temperature and pressure measurements in

the heat exchanger. Additionally, the heat exchanger must be designed and fabricated

with sufficient structural integrity to withstand operating pressures and temperatures

without leakage.

A number of challenges were experienced in construction of the test section before

a successful design and fabrication method were developed. The visual heat exchanger

section is constructed from polycarbonate. Determining the appropriate adhesive that did

not compromise the optical clarity of the test section and that set slowly enough to allow

good adhesion and sufficient bond strength between the test section components was

critical. Selection of an appropriate method for eliminating leaks, whether through

gasketing, various sealant epoxies used after the structure’s assembly, application of a

polycarbonate weld, or improved machining, were also investigated. The final

polycarbonate test section design relies mainly on sealant epoxy to prevent fluid leaks

during operation, but it is suggested here that construction relying on gasketing methods

rather than adhesives and epoxies may provide a more reliable and less time-consuming

method of protecting the test section integrity. Gasketing would be simpler to work with,

would not obstruct visualization or distort material clarity, and would facilitate non-

15

destructive disassembly of the test section as well as the replacement of parts such as the

heating surface. This caveat should be considered when planning future test section

construction.

An assembled view of the final test section design is shown in Figure 2.2. The

walls of the test section are constructed of 1.3 cm thick polycarbonate and assembled to

form a 0.56 x 2.54 cm rectangular flow channel. Each end of the channel fits into a 3.8

cm thick flange that allows the test section to be connected into the flow facility. The

bottom polycarbonate wall is machined to accommodate the heating apparatus. A 17.8

cm long, 0.018 cm thick Nichrome strip was adhered to the bottom surface of the

channel. The strip is clamped in place at each end of the channel by wrapping around

brass tabs that protrude through the bottom surface of the polycarbonate to the outside of

the test section. A compression fitting on the outside surface of the bottom wall seals the

Figure 2.2. Polycarbonate test section assembly

16

test section at the locations where these tabs protrude. The remainder of the threaded

length is used to secure power connections that allow for the resistance heating of the

nichrome strip heater. All polycarbonate components are bonded with a clear acrylic

plastic adhesive. The Nichrome heating strip is secured to the polycarbonate using a

silicone adhesive.

The bottom surface of the test section must be machined to allow for

thermocouples to measure the temperature of the nichrome heating strip over which

boiling takes place. Type E (Chromel-Constantan) thermocouples are adhered to the

nichrome strips at 3.8 cm. intervals along the heating surface. The leading upstream

thermocouple is located approximately 25 channel diameters from the entrance

connection to the test section, allowing for the assumption of fully developed flow at the

point where measurements begin. The process by which the thermocouples and heater

were assembled with the polycarbonate and the interior detail of the assembly is

illustrated by the exploded view of the test section shown in Figure 2.3. The

thermocouples were first attached to the bottom of the Nichrome heater before the heater

was adhered to the polycarbonate. Electrically insulating epoxy was used to prevent

interference in temperature measurements associated with the current traveling through

the heater. The thermocouples were then passed through the small holes machined in the

test section bottom surface. The adhesive was applied to the Nichrome strip and the

thermocouples were pulled through as the strip was lowered into contact with the

polycarbonate. The thermocouple holes were then filled to seal the test section and to

provide strain relief to the thermocouple junction.

2.2.2 Brass Test Section

Brass was chosen for the heat exchanger construction, shown in Figure 2.4., and the

17

Thermocouples

b

Figure 2.3. Exploded view of polycarbonate test se

channel geometry was retained as it provided for ea

transfer devices. Two machined brass sheets have

form a four-channel flow area, with each channel m

polycarbonate test section, flanged end pieces allow

the flow facility. Heat will be provided to the brass

heaters measuring 23.25 inches long by 1.5 inches

to 80 kW/m2 heat flux and will be mounted to the b

flow channel by means of mounting tabs. The bott

the strip heaters’ power into the fluid channel.

The polycarbonate and brass heat exchangers

means of a brass flanged expansion header bolted t

Brass Ta

Nichrome Heater

ction

sy scaling to larger or smaller heat

been machined and braised together to

easuring 5.0 x 24 mm. As with the

the heat exchanger to connect with

using three Watlow 375 Series strip

wide. The 240-volt heaters provide up

ottom side of the heat exchanger’s

om surface is then insulated to direct

are connected to the flow facility by

o each test section or heat exchanger

18

Brass Expansion Header

Flanged End Piece

Terminal Posts

Strip Heaters

Figure 2.4. Brass

flange. These bra

tested in various o

gradually change

the test section an

experienced by th

and outlet pressur

2.2.3 Test Sectio

The test sec

the theoretical pre

facility was modi

a wide variety of

Thermocouples

heat exchanger

ss ends connect to flexible piping that allows the test section to be

rientations. The flow channel within the brass expansion header

s from a path the size of the piping to a rectangular opening the size of

d heat exchanger channel openings in order to reduce the pressure drop

e fluid. Pressure taps are machined on each brass end piece so that inlet

e can be measured.

n Angular Support

tion must be tested in various orientations relative to gravity to validate

diction that a gravity-independent flow-boiling regime exists. The flow

fied to create a method that would allow the test sections to be moved to

different angular positions without disconnecting them from the flow

19

facility. Figure 2.5 illustrates the method used to obtain the angular positioning. Four

linear motion guide rails are added to the existing facility construction, with one pair

positioned vertically and one pair horizontally. A hinge on the flanged face of the brass

connector piece attaches to the linear bearings that slide along these rails. The test

sections can be rotated by simultaneously sliding the horizontal and vertical rail blocks.

A hand brake on each block allows the test sections to be secured into position. This

configuration allows for the test section to be positioned at any angular orientation with

respect to gravity. Typically, investigators have considered up to eight positions in

seeking to test gravity-dependent behavior. Test section orientation, upward or

downward flow, and an upward or downward facing heater describe these positions,

shown in Figure 2.6. Flow direction is indicated by the direction of the arrow. The flat

line adjacent to the rectangular test section body symbol represents the heater strip.

Figure 2.5. Angular positioning system using linear motion components

20

Figure 2.6. Typical test orientations, φ, with respect to gravity

2.3 High Speed Digital Camera

A high-speed digital camera was purchased to capture images of the ebullition

process and to measure bubble sizes during growth, departure, and lift-off. A HiDcam II

from NAC Image Technology can capture images with a resolution of 1280 x 1024 at

500 frames per second (full resolution) to 1280 x 64 at 8000 partial frames per second.

The camera images can be stored and analyzed on a PC using Motion Analysis Video

Viewer software provided with the camera. It was determined that 3000 frames per

second provided sufficient clarity for conducting bubble measurements at all but the

21

highest flow velocities, for which 4000 frames per second was adequate. At these

speeds, approximately 3 seconds of recording time was available.

2.4 Instrumentation and Calibration

The flow boiling facility used for the investigation is fully instrumented to provide

reliable and accurate measurements of key physical parameters during operation. The

following sections detail instruments used to capture data, the construction of new

thermocouples for determination of relevant temperatures, and the calibration of all new

and existing measurement and data acquisition devices.

2.4.1 Temperature Measurement

Temperature measurements are recorded at a number of locations during testing.

The bulk fluid temperature is monitored at the entrance to the preheater section, the inlet

of the heat exchanger, and the exit of the heat exchanger. Heat loss from the insulated

piping at the preheat section is calculated by recording the temperatures at the outer

surface of the insulation. Temperature data on the surface of the Nichrome heater are

recorded at four locations in the test section flow channel. Finally, the suction line

temperature between the condenser and the pump is measured with a thermocouple on

the outside of the tubing to ensure that the pump does not cavitate. All thermocouples are

36-gauge, fast responding Type-E thermocouples that were constructed in the laboratory.

Thermocouple probes inserted into the flow stream were encased in 1.6 mm brass tube.

Thermocouples were inserted into the tubing and sealed with epoxy at either end. They

were then sealed into the facility using a brass compression fitting.

2.4.4 Flow Measurement

The flow rate is measured using two different meters corresponding to different

flow rate ranges. An Erdco model 2521-02T0 vane flow meter is installed to measure 0.4

22

to 4.0 gpm. The vane meter is equipped with a 4-20 mA analog output connected to a

500-ohm power resistor. The voltage drop across the resistor is recorded by the data

acquisition system and calibrated against the volumetric flow rate. A third order

polynomial is used to fit the experimental data: the calibration curve for the vane flow

meter is shown in Figure 2.7.

Q = 0.0024V3 - 0.0165V2 + 1.1862V + 1.0324

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Voltage (V)

Flow

Rat

e (l/

min

)

Figure 2.7. ERDCO 2521-02T0 flow meter calibration

A venturi flow meter is used to measure flow rates above 4.0 gpm. The discharge

coefficient was experimentally determined so that the differential pressure measurement

across the venturi could be translated into a flow rate. A specified volume of the working

fluid was pumped into the facility storage tank as the time was measured to determine the

mass flowrate. The discharge coefficient is defined as the ratio of this actual mass

flowrate to the theoretical mass flowrate proscribed by applying Bernoulli’s equation to

the venturi. The variation of the discharge coefficient with flow Reynolds number is

shown in Figure 2.8. An average discharge coefficient of CD = 0.556 was obtained from

the calibration.

23

0.0000.1000.2000.3000.4000.5000.6000.7000.8000.9001.000

0 10000 20000 30000 40000 50000

Reynolds Number

Dis

char

ge C

oeffi

cien

t

Figure 2.8. Calibration of venturi discharge coefficient

2.4.3 Differential Pressure Measurement

The differential pressure across the venturi is measured using a Validyne model

DP15 variable reluctance differential pressure transducer. A Validyne DP15 is also used

to measure the pressure drop across the test section. To calibrate the transducers, the

output voltage was compared to the pressure difference applied to a liquid manometer. A

linear calibration curve is depicted in Figure 2.9 for the two transducers.

2.4.2 Static Pressure Measurement

The static pressure at the inlet and outlet of the test section was measured by two

Viatran model 2416 static pressure transducers and used to calculate thermophysical

properties of the fluid. The calibration data and linear curve fit equation are shown in

Figure 2.10.

2.4.5 Preheat Section Heat Loss

The preheat section heats the fluid from a subcooled liquid state to the desired

vapor quality or subcooled state at the heat exchanger test section inlet. Four 1000W

24

heaters are coiled around the 3/8” copper pipe, through which the fluid flows, to comprise

the preheater section. The power input is controlled via autotransformers and measured

manually during testing. The system is insulated from the preheat section to either

entrance of the heat exchanger test section using 25 mm thick fiberglass pipe insulation.

Heat loss through the insulation is considered negligible except at the preheat section.

The heat lost in this section is calibrated by draining the system and providing a known

P1 = 1.2165V + 0.3936

P2 = 1.2248V + 0.3805

0

2

4

6

8

10

12

14

0 2 4 6 8 10 12Voltage (V)

Pres

sure

(kPa

)

Figure 2.9. Validyne Model 3-32 pressure transducer calibration curves

P1 = 69079V - 5604

P2 = 41662V - 1037.4

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

4.0E+05

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Voltage (V)

Pres

sure

(Pa)

Figure 2.10. Viatran static pressure transducer calibration curves

25

power to the preheat coils. When the system settles to steady state, the heat lost through

the insulation is equal to the heat input to the system. Thermocouples record the

insulation surface temperature TS and the ambient temperature TA. By repeating

measurements at various power inputs, the variation of the heat loss with surface-ambient

temperature difference can be determined. The calibration results are shown in

Figure2.11, along with the polynomial curve fit to describe the heat loss relation.

Q1 = -0.0002dT3 + 0.0183dT2 + 0.8897dTQ2 = -3E-05dT3 + 0.0072dT2 + 0.886dT

Q3 = -0.0002dT3 + 0.016dT2 + 1.0108dTQ4 = -7E-05dT3 + 0.0123dT2 + 0.91dT

0

10

20

30

40

50

60

70

0 10 20 30 40 50 60

Average Surface Temp - Ambient Temp (oC)

Hea

t Los

s (W

)

Preheater 1

Preheater 2

Preheater 3

Preheater 4

Figure 2.11. Preheat heat loss calibration

2.4.6 Test Section Heat Loss

Unless the bottom surface of the test sections can be perfectly insulated to provide

an adiabatic boundary condition, some heat generated by the polycarbonate nichrome

heater strip and the brass test section heaters will be lost to the ambient. Thus, the test

section heat loss must be corrected for in order to accurately determine the heat input to

the working fluid during testing.

The calibration scheme for both test sections is similar. The test section is drained

and sealed at either end and a small voltage is applied to the test section heaters. It is

assumed that, once steady state conditions have been established, all heat will pass

26

through the bottom polycarbonate surface or the bottom insulation for the polycarbonate

and brass test sections, respectively, and then to the ambient. With knowledge of this

heat flux and measured temperatures in the interior of the test sections and at the exterior

surfaces exposed to the ambient, the overall heat transfer coefficient could be determined.

This heat transfer coefficient, in conjunction with the real time interior and exterior

measurements during operation, can be used to determine the heat lost from the test

dT = 3.9839Q - 1.2613

-5

0

5

10

15

20

25

0 1 2 3 4 5 6

Heat Loss (W)

Surf

ace

Tem

p - J

unct

ion

Tem

p (C

)

Figure 2.12. Polycarbonate test section heat loss calibration

y = 0.2403x

0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Heat Loss (W)

Surf

ace

Tem

p - J

unct

ion

Tem

p (C

)

Figure 2.13. Brass test section heat loss calibration

27

section. The calibration curves obtained for the heat loss from the polycarbonate and

brass test sections are shown in Figures 2.12 and 2.13.

2.4.7 Temperature Correction

Due to the construction of the polycarbonate heat exchanger test section and brass

prototype heat exchanger, the temperature of the surface exposed to the flow cannot be

directly measured. In order to obtain an accurate determination of the boiling surface

temperature, the measured temperatures must be corrected unless sufficient insulation is

achieved to justify an assumption of an adiabatic test section. In these experiments,

correction is necessary and is implemented as described below.

In the case of the polycarbonate heat exchanger test section, the temperature of the

bottom surface of the heater is being measured through a thickness of electrically

insulating epoxy, as detailed in Figure 2.14, across which a temperature difference exists.

The temperature gradient through the epoxy and the thickness of the heater should be

accounted for to correct the measured temperature and yield an accurate value for the

surface temperature exposed to the fluid flow. The one-dimensional Laplace equation

with heat generation from the power supplied to the heater appropriately describes the

situation. The appropriate boundary conditions that complete the specification of the

Thermocouple

i

b

Figure 2.14. Temperatures in test section

Ts
TN
T

Tmeas

(bottom of epoxy)

28

problem are the known temperature Tmeas and the heat loss escaping through the bottom

of the polycarbonate.

02

2=+

∂∂

kg

yT &

(2.1)

BC1 : 0| =∂∂

=′′ yloss yTkq (2.2)

BC2 : 0| == ymeas TT (2.3)

Solution of the above differential equation and application of the boundary

conditions yields:

NiNi

Niloss

Ni

NiS T

ktq

ktg

T +′′

+−=2

2&. (2.4)

In addition, Fourier’s Law for conduction of the lost heat through the bottom of the

test section,

( )

ep

measNieploss t

TTkq

−=′′ , (2.5)

can be used to eliminate the unknown temperature TNi, yielding the final relation

for correcting the polycarbonate heater surface temperatures:

measep

ep

Ni

Niloss

Ni

NiS T

kt

kt

qktg

T +

+′′+−=

2

2&. (2.6)

Upon fabrication, the thickness of the nichrome strip and the insulating epoxy layer

measured 0.007” and 0.005”, respectively. Nichrome and epoxy thermal conductivity

was 12 W/mK and 95 W/mK, respectively.

29

In a similar manner, considering Fourier’s conduction law applied between the

measured temperature at the embedded thermocouple and the surface of the flow channel

yields the desired temperature correction for the brass heat exchanger:

( )

Br

BrlossmeasS k

tqqTT

′′−′′−= . (2.7)

The thickness and thermal conductivity of brass used in this correction is 0.075”

and 110 W/mK, respectively.

2.6 Data Acquisition and Processing

An existing data acquisition system has been modified for monitoring and

recording the temperatures, pressures, and flow rates during the experiment and

calculating relevant quantities such as heat flux, vapor quality, and pertinent

dimensionless parameters. The data acquisition hardware is an ACCES AD12-8, 12-bit,

8-channel analog-to-digital converter board interfaced with two ACCES AIM-16, 16-

channel multiplexer cards, allowing for a total of 32 channels to be sampled. One

channel on each multiplexer uses a thermistor that is used as the reference temperature

for thermocouple measurements. The analog-to-digital board and the multiplexer cards

were calibrated according to the manufacturer’s guidelines.

A QuickBASIC computer program was developed to process data during operation

of the facility and to control acquisition of data by the A/D board. Appropriate gain

values are set to maximize signal resolution from the system instrumentation. The

program provides for continuous output of time-averaged data to the monitor, typically

sampling 200 data points per second. All measured instrument voltages are converted to

temperature, pressure, and flowrate data based upon calibration correlations discussed in

Section 2.4. Once the user has zeroed the system and specified the applied preheat and

30

test section heat fluxes, a set of data may be saved in ASCII format and then imported to

a spreadsheet for further analysis.

CHAPTER 3 GRAVITATIONAL EFFECTS ON VAPOR BUBBLE DYNAMICS

3.1 Introduction and Literature Survey

Vapor bubbles in flow boiling will typically depart from their nucleation cavity by

sliding away from the site along the heated surface. A number of visual studies have

sought to document and quantify bubble behavior, including Cooper et al. (1983), who

obtained bubble growth and displacement in terrestrial gravity and short duration

microgravity flow, and van Helden et al. (1995). It is apparent from previous work that

bubble dynamics and detachment are influenced by bulk flow velocity and subcooling,

flow regime, heat flux, flow direction, heater surface orientation relative to gravity, and

the strength of the gravitational field. In pool boiling systems, as the bubble grows, a

buoyancy force will become sufficiently large to cause the bubble to detach from its

nucleation site. As observed by Zeng et al. (1993a), vapor bubbles on an upward heated

surface exposed to low velocity bulk flow will lift directly off the boiling surface and are

then carried away with the bulk liquid. However, as the bulk liquid velocity increases to

some some critical value, hydrodynamic forces will compel bubbles to depart the

nucleation site by sliding along the heated surface. Heat is absorbed during sliding and

bubble growth continues until the bubble lifts off the surface due to the influence of

buoyancy and shear lift forces. Thorncroft and Klausner (1997) reported mean departure

and lift off diameters measured in vertical upward and downward flow boiling of FC-87.

In vertical upflow, bubbles depart the heating surface by sliding upward and typically

31

32

remain attached to the heating surface. In contrast, bubbles in downflow can depart by

sliding either upward or downward along the heating surface as dictated by interaction of

hydrodynamic forces and buoyancy forces on the bubble. Bubbles departing from

nucleation sites in low bulk velocity fields will tend to slide upward against the bulk flow

as buoyancy forces are large relative to opposing drag force. The buoyancy force is

overcome at higher flow velocities and the bubble slides downward. The dependence of

bubble dynamics upon the buoyancy force indicates a corresponding dependence upon

the gravitational field.

Mikic and Roshenow (1970) developed an early model for bubble growth in a

uniformly superheated liquid under inertia and diffusion controlled growth conditions and

extended their results to bubble growth in non-uniform temperature fields. Van Stralen et

al. (1975) and Mei et al. (1995a) identified clear discrepancies between many such early

modeling efforts and extensive data available at the time. Mei et al. submitted a

numerical analysis detailing bubble growth in saturated heterogeneous boiling

determined by considering the simultaneous energy balance on the vapor bubble, a liquid

microlayer under the bubble, and the heater. A vapor bubble shape parameter and

microlayer wedge parameter are empirically determined to provide agreement with

experimental results. In the second part of the study, Mei et al. (1995b), present insight

into the dependence of bubble growth rate and the thermal field within the heater on four

governing dimensionless parameters; Jacob number, Fourier number, solid-liquid thermal

conductivity ratio, and solid-liquid thermal diffusivity ratio. Klausner et al. (1993)

created a model to predict vapor bubble departure based on the onset of imbalance

between a quasi-steady drag force, the unsteady component of the drag due to

33

asymmetrical bubble growth, and the surface tension force in the flow direction. A

significant dependence on wall superheat and bulk liquid velocity was noted, with

departure diameters increasing and decreasing, respectively, with increases in these

quantities. An updated version of this model offered by Zeng et al. (1993a) includes

determination of the bubble inclination angle as part of the solution rather than as a

required input to the model. The surface tension force at departure and lift-off is

neglected, and the bubble contact area and contact angles are not required. The model

agreed well with available experimental data.

The current model proposed by Thorncroft et al. (2001) and discussed in Bower et

al. (2002) in conjunction with this experimental work was constructed from first

principles and related the forces affecting a vapor bubble during its life through Newton’s

Law as

dtdVmRFFFFFFFFF bSLQSAMFSCPBSBody =++++++++=

rrrrrrrrrr. (3.1)

Thorncroft et al. (2001) extensively detail these forces as they apply to a bubble

growing in a bulk liquid flow parallel to a heater surface oriented at some angle relative

to the direction of gravity, as shown in Figure 3.1. BodyFr

represents the body force of the

bubble. SFr

is the surface tension force integrated around the base of the bubble using a

simplified third order polynomial to approximate the contact angle of the bubble as it

moves from the advancing to receding value. BFr

is the buoyancy force due to the liquid-

vapor density difference. The contact pressure force, CPFr

, is due to the pressure

difference inside and outside the top of the liquid-vapor interface over the bubble contact

area. SLFr

represents a shear lift force due to pressure gradients in the velocity field

34

around a growing bubble. QSFr

is a quasi-steady drag force of the bulk fluid on the

growing bubble. Solving the inviscid flow problem for a growing sphere in a uniform

unsteady flow using the unsteady Bernoulli equation yields the added mass force, AMFr

,

and the freestream acceleration force, FSFr

, which is composed of a growth force and a

bulk growth force. A reaction force at the heated surface, Rr

, approaches zero as the

bubble detaches. The velocity field at the center of the bubble, the bubble inclination

angle, and the bubble growth rate must be input to the model of Thorncroft et al. (2001)

to solve for the bubble detachment diameters. Reichardt’s expression, found in Hinze

(1975), is used to estimate the velocity of the bulk liquid at the bubble center of mass.

Growth rates are approximated by the diffusion-controlled bubble growth solution for

saturated pool boiling under one-g subatmospheric and atmospheric conditions as

described by Zuber (1961). The inclination angle is not readily determined due to the

deformable nature of the bubble interface. Thus, the inclination angle is approximated at

45 degrees in horizontal and upflow. In downflow, if the buoyancy force is greater than

Figure 3.1. Growth, departure, sliding, and lift-off of a vapor bubble on an inclined flow boiling surface.

35

the drag force, the inclination angle is –45 degrees, against the flow. Otherwise the

contact angle is 45 degrees, with the flow.

At the condition imposed to determine departure diameter, Thorncroft et al. (2001)

express the x-momentum equation as

. (3.2) 0~sinsinsin ,, φφφ GrowthbulkGrowthQSxSBBody FFFFFF +++++

Similarly, the y-momentum balance describing the condition for bubble lift-off is

0~coscos , GrowthSLySBBody FFFFF ++++ φφ . (3.3)

The comparison of the departure and lift-off diameters generated from

computational solutions of this model at various conditions compares well with

experimental measurements. In addition, by imposing different orientations on the

heated surface, the analytical dependence of bubble departure and lift-off diameter is

illustrated. Bower et al. (2002) show in Figure 3.2 that as bulk flow velocity is increased

for a particular Jacob number, the departure diameter for various orientations becomes

Bulk Liquid Velocity (m/s)

0.0 0.2 0.4 0.6 0.8 1.0

Dep

artu

re D

iam

eter

(mm

)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Horizontal FlowUpflowDownflowZero GravityJa = 13.5

Figure 3.2. Variation of vapor bubble departure diameter with bulk fluid velocity

36

Bulk Liquid Velocity (m/s)

0.0 0.2 0.4 0.6 0.8 1.0

Lift-

Off

Dia

met

er (m

m)

0.18

0.19

0.20

0.21

0.22

0.23

Horizontal FlowUpflowDownflowZero GravityJa = 13.5

Figure 3.3. Variation of vapor bubble lift-off diameter with bulk fluid velocity

independent of flow orientation with respect to gravity. Figure 3.3 depicts a similar trend

for bubble lift-off diameter.

The computational model is solved to yield lift-off diameters for a number of fluids

at a range of Jacob numbers. The point at which bulk velocity is high enough to attain

gravity independence, framed within a correlating parameter ψ , is plotted versus Jacob

number, as in Figure 3.4. These correlating parameters are defined as follows:

fgv

satlpl

hTc

Jaρ

ρ ∆= , (3.4)

vl

l

vl

ll WeUρρ

ρρρ

ρσ

µψ

−=

−=

Re. (3.5)

A similar graph is obtained for bubble departure diameter conditions. It is apparent that a

flow boiling system operating to the right of the curve fitting these data points operates in

a gravity independent regime, as far as bubble lift-off conditions are concerned.

37

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Ja

0

20

40

60

80

100

R-113R-12FC-87R-22

Gravity Dependent

Gravity Independent

vl

llUρρ

ρσ

µψ

−=

Figure 3.4. Gravity independent/dependent flow regime map for vapor bubble lift-off

Due to its governing influence on heat transfer, the vapor bubble growth rate and

the related departure and lift-off phenomena have been the subject of considerable

investigation. Knowledge of accurate vapor bubble growth rate determination, which

predicates valid expressions for boiling heat transfer, must be determined from a detailed

simultaneous solution of the momentum and energy equations in the solid heater, liquid

phase, and the vapor phase. Although this study does not report growth rate, bubble

dynamics critical to assessing the nature of a varying gravitational field on boiling heat

transfer are investigated. In this study, a visual determination of vapor bubble lift off will

be used, in the process of assessing the gravity dependence suggested by Figure 3.4, to

elucidate the reliability of the current model, which predicts the points of vapor bubble

departure from the nucleation site and lift-off from the heater surface. If the

hypothesized existence of a gravity independent bubble lift-off regime can be confirmed,

it is expected that a gravity independent boiling heat transfer regime can be similarly

described.

38

3.2 Experimental Procedure

The experimental flow-boiling facility and polycarbonate test section described in

Chapter 2 were used to capture bubble images and collect bubble dynamics data. The

flow orientations investigated to assess gravitational influence on the boiling process

were as follows: 0° horizontal, 45° upflow, 90° upflow, 315° downflow, and 270°

downflow. All tests were performed with the heater surface facing upward.

Before testing at a specified system flow rate, the bulk single-phase conditions at

the test section entrance must be established. These conditions are controlled by

moderation of the refrigeration cooling system at the condenser in conjunction with the

system preheat. Once steady flow conditions are established at the appropriate velocity

and inlet conditions and vigorous boiling from the test section has been observed, power

to the test section heater is reduced to suppress nucleation and thus assure degassing of

the heater surface. It has been shown that boiling data is sensitive to the order in which

the data is taken due to boiling hysteresis. Therefore, the heat flux is always raised to

generate the ensuing test condition following completion of one set of data.

The NAC HiDCam is used to capture video sequences for bubble lift-off analysis.

The camera is mounted on a gimbaled tripod that allows the viewing area to be squared

with the flow channel at all test section orientations. The flow channel is viewed through

the side of the clear test section at a slight angle above the heater. The test section was

backlit with three 500W halogen lights. The image is focused using a 50 mm/f1.4 lense

and a 20 mm extension tube. The camera is operated at either 3000 or 4000 frames per

second and with the maximum exposure time for each case. At 3000 fps, better lighting

was available, but some high-speed flow conditions dictated capturing images at a higher

speed. The sequences length was approximately 3.28 s, and the test section area viewed

39

is 11.0 mm x 4.5 mm to 19.5 mm x 8.0 mm. In order to calibrate the camera software’s

measurement tool once appropriate focusing had been obtained for a test, the camera was

aimed at a flat surface and an object of known width was moved towards the lens until it

was focused properly. At this point, the object was measured in terms of pixels, and

based upon its known width, translated into a pixel-per-mm calibration value.

After obtaining appropriate inlet conditions and identifying a clearly focused

stream of vapor bubbles, the HiDCam software is used to trigger the camera and a video

sequence is captured and saved. This video sequence can be replayed frame-by-frame to

monitor the characteristics of individual vapor bubbles passing within the viewing area.

When an instance of bubble lift-off was observed in a frame, the bubble diameter was

measured by an average of the horizontal and vertical chords through the estimated

centroid of the bubble. Measurement resolution ranged from 0.009 mm/pixel to 0.015

mm/pixel, depending on the specific focal length of the camera for each test.

It was inappropriate to measure many of the vapor bubbles observed in video

sequences and several factors were considered to attain consistency in measurement

technique. At times of vigorous boiling, the turbulent flow pattern in the test section

forced bubbles from the freestream flow down to the heated surface for a moment;

similarly, a small portion of growing vapor bubbles exhibited a brief and slight separation

from the surface followed by a return to the heater. For measurement purposes, an

occurrence of bubble lift-off was defined as the lifting of the bubble from the surface for

a prolonged period of time interrupted only by swift and momentary returns to the heater

that were not consistent with the previous trajectory of the bubble. In addition, a number

of bubbles, particularly at high heat fluxes and flow rates, merged with other bubbles,

40

causing large fluctuation in the bubble shape, and at times accruing sufficient volume to

immediately lift the bubble from the surface. Merged bubbles were only considered once

short-term transient distortions in the bubble shape were eliminated and the bubble had

traveled four to five diameters further along the surface. Some bubbles exhibit necking

that elongates the bubble as the contact area at the heater shrinks, indicating imminent

lift-off. Once the bubble detaches, surface tension returns the interface to a spherical

shape. It was assumed that relatively little bubble growth occurred during the brief

necking period, and bubbles were measured at a point where the liquid-vapor interface

was more spherical, either immediately before necking or immediately after detachment.

3.3 Results

Vapor bubble lift-off diameters have been measured for Jacob numbers of 24, 30,

and 36 at bulk flow rates corresponding to values of ψ ranging from 0.02 to 0.05. Each

test has been performed at five orientations relative to gravity: 0°, 45°, 90°, 270°, and

315°. Tests involved identifying, ideally, ten vapor bubbles from the captured video

sequence, although at some conditions, as discussed below, lift-off phenomenon was only

sporadically observed and fewer data points were recorded. Average values of measured

bubble lift-off diameters are shown in Table 3.1. All data taken during this portion of the

study is catalogued in Appendix B.

A discussion of the forces affecting bubble dynamics at lift-off is helpful in an

initial examination of the parametric effects of heat flux, velocity, and, particularly,

orientation on lift-off diameter. The buoyancy force acts to lift the vapor bubble from a

horizontal surface and is larger at high bubble growth rates, as in high heat flux

conditions. This lifting influence is reduced as the surface is rotated to a vertical

position, where buoyancy acts completely in the flow direction parallel to the

41

Table 3.1. Results of experimental bubble lift-off measurements

Bubble Lift-off Diameter (mm) Avg. Ja Avg. ψ 0 deg 45 deg 90 deg 315 deg 270 deg

24.0 0.0200 0.258 0.339 0.422 0.310 0.376 0.0250 0.222 0.280 0.335 0.282 0.310 0.0300 0.218 0.255 0.247 0.238 0.230 0.0350 0.184 0.214 0.217 0.207 0.195 0.0400 0.156 0.199 0.173 0.177 0.151

30.0 0.0200 0.397 0.427 No lift-off 0.3158 0.285 0.0249 0.379 0.396 No lift-off 0.2836 0.226 0.0301 0.344 0.357 No lift-off 0.2538 0.225 0.0350 0.344 0.317 0.567 0.2235 0.201 0.0400 0.308 0.306 0.383 0.2258 0.166 0.0451 0.281 0.273 0.324 0.1884 0.154 0.0500 0.264 0.243 0.239 0.1439 0.132

36.0 0.0200 0.417 0.557 No lift-off 0.3417 0.330 0.0250 0.392 0.496 No lift-off 0.3143 0.292 0.0300 0.343 0.446 No lift-off 0.2884 0.228 0.0350 0.309 0.394 No lift-off 0.2667 0.216 0.0400 0.270 0.333 No lift-off 0.2538 0.181 0.0450 0.226 0.304 No lift-off 0.2321 0.181 0.0500 0.214 0.270 No lift-off 0.2148 0.161

heater. The body force exerts itself opposite the buoyancy force, albeit in much weaker

fashion. Surface tension and growth forces deter lift-off at all orientations. The shear lift

force acts to remove the bubble from the surface and its magnitude depends upon the

difference between the bulk fluid velocity and the velocity of the bubble center of mass

after departure from its nucleation site. In the case of upflow, this velocity difference is

small at low bulk liquid velocities due to cooperative influences of buoyancy and quasi-

steady drag. This leads to an unfavorable condition for lift-off in vertical flow

orientations and provides explanation for the lack of lift-off phenomena observed at

higher Jacob numbers or low velocities where increased buoyancy effects associated with

larger vapor bubbles exacerbate the condition. In downflow, however, buoyancy resists

the bulk flow direction, and lift-off is promoted. In fact, some vapor bubbles lift directly

42

from the nucleation site without sliding along the heater surface. For all orientations,

higher flowrate should result in decreased lift-off diameter.

Frames from selected video sequences are shown in Figures 3.5 through 3.12 for

selected values of Ja = 30 and 36, ψ = 0.02 and 0.04, and φ = 45° upflow and 225°

downflow. The frames are taken 0.01s apart and show the lift-off and movement of a

vapor bubble with the aid of an arrow at the leading edge of the bubble approximately

indicating its current trajectory. An arrow directed downward perpendicular towards the

heater identifies a bubble that is not moving in the current frame. The arrow in the top

left corner of each figure indicates the flow direction. The frame where lift-off is

observed denotes t = 0 s, with images preceding lift-off marked with negative time

values. The image resolution in transferring photographs to this report format is

somewhat poor and is not indicative of the clarity obtained in the image measurement

software. Due to the poor resolution of the image, a circle is drawn about the bubble that

is lifting off in each figure. Because these pictures were obtained using different focal

lengths, it is inappropriate to compare the sizes of vapor bubbles from one figure to

another. It is apparent that in upflow conditions, vapor bubbles slide along the heater in

the flow direction before lifting off the surface. In downflow, vapor bubbles slide along

the heater against the flow before lifting off, and in some conditions, lift directly from the

heater without sliding. In downflow, many bubbles were swept with the flow after lift-

off, but at low velocity and high Jacob number, some bubbles moved upstream against

the flow or lifted perpendicular to the heater for a short distance before being swept

downstream. This behavior is shown in Figure 3.11. It is suggested that this occurs

because of the weakening drag force acting on bubbles near the surface due to the

43

existence of a velocity boundary layer over the heater. At high heat fluxes it should be

noted that nucleation site density was sufficiently high and waiting time sufficiently low

to cause almost certain bubble collision, and lift-off was often suddenly induced by

agglomeration of two or more vapor bubbles. A similar effect was observed during

sliding; as a fast moving bubble overtook a slower moving bubble, their combination

often lead to the lift-off of the entire vapor mass. Sliding bubbles also swept growing

bubbles from their nucleation sites before they had departed. Upon collision, bubbles are

temporarily deformed, as indicated in the first two frames of Figure 3.7, which indicates

an example of lift-off due to agglomeration of sliding vapor bubbles.

Figure 3.5. Photographs of bubble lift-off at Ja = 30, ψ = 0.02, and φ = 45° upflow


t = -0.01s t = 0 s t = 0.01s t = 0.02s

t = -0.01s t = 0 s t = 0.01s t = 0.02s

t = -0.01s t = 0 s t = 0.01s t = 0.02s


44


Figure 3.9. Photographs of bubble lift-off at Ja = 30, ψ = 0.02, and φ = 225° downflow


t = -0.01s t = 0 s t = 0.01s t = 0.02s

t = -0.01s t = 0 s t = 0.01s t = 0.02s

t = -0.01s t = 0 s t = 0.01s t = 0.02s


45

t = -0.01s t = 0 s t = 0.01s t = 0.02s


The variation of the vapor bubble lift-off diameter with the dimensionless bulk

flow parameter ψ is depicted in Figures 3.13 through 3.17 for each flow orientation at

each Jacob number condition. Also included in Figures 3.13 and 3.17 is the analytical

lift-off diameter predictions provided by Sathyanarayan (2003) based on the model of

Thorncroft (2001) using the growth rate correlation model of Zuber (1961). It should be

noted that the analytical solution predicted that lift-off would not occur in vertical

upflow. In all cases the empirical data show, as expected, a decrease in lift-off diameter

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bubb

le L

ift-o

ff D

iam

eter

(mm

)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Ja = 24, experimentalJa = 30, experimentalJa = 36, experimentalJa = 24, analyticalJa = 30, analyticalJa = 36, analytical

Figure 3.13. Variation of bubble lift-off diameter with ψ at φ = 0°

46

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bub

ble

Lift-

off D

iam

eter

(mm

)

0.1

0.2

0.3

0.4

0.5

0.6

Ja = 24Ja = 30Ja = 36


ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bub

ble

Lift-

off D

iam

eter

(mm

)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ja = 24Ja =30

Figure 3.15. Variation of lift-off diameter with ψ at φ = 90°

47

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bub

ble

Lift-

off D

iam

eter

(mm

)

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Ja = 24Ja = 30Ja = 36


ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bubb

le L

ift-o

ff D

iam

eter

(mm

)

0.0

0.2

0.4

0.6

0.8

1.0

Ja = 24, experimentalJa = 30, experimentalJa = 36, experimentalJa = 24, analyticalJa = 30, analyticalJa = 36, analytical


48

as the bulk velocity is increased. Also, decreasing heat flux seems, as expected, to

decrease lift-off diameter, although this is not the case for a portion of the curve at the

horizontal orientation. It is notable that in all cases, the analytical model results based on

the Zuber growth correlation significantly overestimate the lift-off diameter. This will be

discussed below.

The influence of bulk flow velocity on the variation of bubble lift-off diameter with

test section orientation is shown in Figures 3.18 through 3.20 for each Jacob number test

condition. Based on the discussion above, it is expected that 90° upflow should exhibit

the largest lift-off diameters, followed by 45° upflow, 0° horizontal flow, 315° downflow,

and finally 270° downflow. Data presented in Figure 3.18 for the lowest Jacob number,

Ja = 24, exhibits similar behavior at low velocity, although measured departure diameters

in downflow are unexpectedly high. In this case, horizontal lift-off diameters are the

smallest at low velocity. As velocity increases, the difference between data at different

orientations is reduced and the predicted effects of orientation, as stated above, are less

evident. In Figure 3.19, at Ja = 30, lift-off diameter is ordered in the expected manner

relative to test section orientation. No convergence is observed as velocity increases

other than that displayed in the vertical data set. At Ja = 36, shown in Figure 3.20, the

expected spread is again observed and some convergence seems to occur at higher

velocity, although no lift-off was observed at any velocity for the vertical upflow

orientation.

Examining the data for expected effects of orientation, as described above, can

assess gravity dependence at a certain test condition. If lift-off diameter for upflow data

does not present larger lift-off diameters due to the effect of buoyancy, it is reasonable to

49

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045

Bub

ble

Lift-

off D

iam

eter

(mm

)

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0O Horizontal Flow45O Upflow90O Upflow315O Downflow270O Downflow

Figure 3.18. Bubble lift-off diameter vs. ψ at Ja = 24

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bubb

le L

ift-o

ff D

iam

eter

(mm

)

0.0

0.2

0.4

0.6

0.8



50

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Bubb

le L

ift-o

ff D

iam

eter

(mm

)

0.1

0.2

0.3

0.4

0.5

0.6



suspect that bubble dynamics are governed by hydrodynamic considerations. At this

point, shear lift has become the dominant mechanism responsible for removing the vapor

bubble from the heater due to the high flow velocity and the relatively small influence of

the buoyancy force. Conditions displayed in Figure 3.18 suggest gravity independence in

this manner due to the downflow bubble lift-off data that is inexplicably larger than

expected at the lowest flow rate, ψ = 0.02. As the flow rate increases, disorganization

among the test orientations becomes more apparent; for instance at ψ = 0.04, the vertical

upflow lift-off diameters are no longer the largest. Although these considerations suggest

an influence of gravity that does not reconcile with expected one-g effects, it is difficult

to make a clear judgement of gravity independence in this manner from the limited data.

This type of observation is much less apparent at the higher Jacob numbers tested,

although at Ja = 30, in Figure 3.19, the orientations where buoyancy tends to apply in the

51

bulk flow direction merge at high velocity. By ψ = 0.05, the 0° orientation exhibits the

largest lift-off diameter, followed by 45° and 90°, respectively, in the reverse order that

would be expected.

3.4 Discussion

Approximately 750 vapor bubble lift-off measurements have been taken and 95

video sequences have been captured for Ja = 24, 30, and 36 and from ψ = 0.02 to 0.05.

This corresponds to heat flux of approximately 4.5 to 33 kW/m2 and a bulk flow velocity

of 0.39 to 1.08 m/s. Bubble lift-off diameter generally decreases with increased heat flux

and increased bulk flow velocity, as expected. The expected consequences of orientation

are clearly evident in the data for Ja = 36, exhibiting a reduction in lift-off diameter in

vertical downflow and a gradual increase with test section rotation towards vertical

upflow, where lift-off was not observed. For lower Jacob numbers tested, this trend is

not as apparent. The model created by Thorncroft (2001) has been compared with the

data. Acceptable agreement between the model and experimental results validates the

analytical prediction of a gravity independent bubble dynamics flow regime and suggests

the existence of a similarly gravity independent heat transfer regime. However, only

limited tendencies toward gravity independence are observed in the current experimental

results. Ultimately, additional bubble lift-off measurements will be required over a

broader range of test conditions to experimentally verify gravity independence.

During the initial stages of bubble growth, the surrounding liquid is highly

superheated and the rapid emergence of the vapor embryo from the surface cavity is

resisted by the inertia of the surrounding liquid. Heat transfer may become the limiting

factor to bubble growth at later stages as the liquid superheat is locally depleted about the

bubble, suggesting a thermal diffusion-controlled portion of growth. Use of the

52

diffusion-controlled growth rate of Zuber (1961) may be responsible for the considerable

discrepancy between bubble lift-off diameters predicted by Sathyanarayan’s (2003)

model and those measured in this study. Higher Jacob number predictions yield

increased error in Figures 3.13 and 3.17 because the temperature field in the solid heater

is not included in Zuber’s solution. As the growing bubble locally depletes the heater

temperature near its nucleation site, less energy is available to fuel bubble growth. Thus,

if the effect of energy depletion within the heater is ignored, the predicted growth rate is

overstated. This in turn inflates the growth force that tends to hold the vapor bubble to

the heater surface and then requires a larger vapor bubble diameter for sufficient

buoyancy to commence lift-off. Also, Zuber’s model pertains to saturated conditions,

and would again overestimate growth rate and bubble lift-off diameter in subcooled flow

conditions that have been utilized in this study. Currently, a satisfactory growth rate

expression for subcooled boiling does not exist. The preceding line of reasoning suggests

that a more accurate model of the vapor bubble growth rate may further reconcile

predictions of Sathyanarayan (2003) using the model of Thorncroft (2001) with the

observed data.

CHAPTER 4 GRAVITATIONAL EFFECT ON TWO-PHASE HEAT TRANSFER


Due to the very large heat fluxes available, the use of phase change heat transfer in

micro-gravity and reduced-gravity environments can have a profound impact on reducing

the size, weight, and cost of thermal management power systems to be deployed in space.

As such, numerous research studies have attempted to gain a fundamental understanding

and predictive capability regarding phase-change heat transfer in reduced gravity

environments. Heat transfer associated with two-phase flow depends upon phenomena

described as microconvection and macroconvection. Microconvection refers to the heat

transfer due to the liquid vaporization during the bubble nucleation and the subsequent

growth of the vapor bubble until it detaches from the heating surface. Heat transfer

facilitated by the bulk two-phase turbulent flow is referred to as macroconvection. Both

processes, and thus the overall heat transfer rate, are dependent upon the dynamics and

detachment of vapor bubbles on the heated surface. If, as suggested, in Chapter 3, bubble

dynamics governing the boiling process in the subcooled region are independent of the

gravitational field, the heat transfer coefficient should also remain constant as orientation

of the gravitational force is changed.

Roshenow (1952) introduced a landmark concept for flow boiling heat transfer

correlations by suggesting that two-phase flow heat transfer rates are due to two

independent and additive mechanisms; bulk turbulence and ebullition. Chen (1966)

53

54

proposed an extension of this model, asserting that the application of empirical

suppression and enhancement factors to alter the ebullition and bulk turbulent flow

motion contributions to heat transfer, respectively, allows the researcher to obtain

agreement with experimental observations. A number of correlations reported in the

literature seek to correlate with flow boiling data based on Chen’s technique.

Researcher’s lack of success in predicting two-phase flow characteristics with

widely utilized methods has led to a desire to reexamine basic principles of flow boiling.

The Chen approach has encountered significant criticism for failing to account for several

recently realized physical processes. Gungor and Winterton (1986) introduce a

dependence on heat flux to their expression for the convective portion of boiling heat

transfer, reasoning that the generation of vapor results in significant disturbance of flow

at the wall that determines convective transport. Kenning and Cooper (1989), while

declaring this effect to be overstated by Gungor and Winterton, has demonstrated that

microconvection and macroconvection components of two-phase heat transfer are not

independent and additive by correlating convective heat transfer data based on a small

dependence on heat flux. Kenning, along with Shah (1982), among others, has asserted

that the proper heat transfer coefficient is the larger of the convective or nucleate terms

and not the sum of the two.

Two-phase flow thermal transport data concerned with micro-gravity conditions are

scarce and what does exist is inconclusive. Standley and Fairchild (1991) conducted

micro-g experiments using a KC-135 aircraft and refrigerant R-11 as the working fluid.

Due to large systematic variations in temperature and pressure, the results are difficult to

interpret. Crowley and Sam (1991) used a KC-135 to make measurements of bulk

55

temperature and wall temperature in a condensing section at micro-g. Their results

indicate that the heat transfer coefficient increases at micro-g when compared to one-g

environments. However, steady-state conditions were never reached during the entire 20-

second micro-g window and the systematic variations in time were so large that

meaningful interpretation of the results cannot be made. The condensation heat transfer

data obtained by Hill and Best (1991) appear to be carefully measured and Baranek et al.

(1994) used the data to construct a micro-g condensation heat transfer model. Also using

a KC-135 aircraft, Rite and Rezkallah (1993) measured the two-phase heat transfer

coefficient for various air-fluid combinations with no phase change in one- and micro-g.

It was found that the differences between the one-g and micro-g heat transfer data were

typically less than 10% and within the uncertainty of the available heat transfer

correlations. Kirk et al. (1995) found that heat transfer is enhanced when the heating

surface is rotated from horizontal towards vertical upflow. At very low heat fluxes,

enhancement was also observed for a downward facing heater where velocity was

sufficient to sweep away vapor bubbles. Sliding of vapor bubbles along the heated

surface was credited with bolstering the heat transfer rate. A reduced effect of test

section orientation was observed at the highest tested bulk flow velocity of 0.32 m/s.

Rite and Rezkallah (1997) performed one-g experiments and micro-g experiments aboard

a KC-135 and observed lower heat transfer coefficients in micro-g. Heat transfer

coefficients dropped along the length of the heating surface in micro-g while they

increased in one-g. The investigators determined that liquid-vapor slip that reduces the

thermal and flow entry lengths in one-g flow was not present in micro-g flow due to the

56

absence of buoyancy forces, causing a reduction in heat transfer. This influence was

observed to weaken at higher velocities.

When considering the totality of the prior reduced gravity experimental efforts in

flow boiling, there appears to be significant confusion and insufficient data to reliably

design heat exchangers for reduced-gravity applications that cover all boiling and two-

phase flow regimes. However, it is very significant that Miller et al. (1993) and Rite and

Rezkallah (1993) operated in flow and boiling regimes in which the pressure drop and

heat transfer coefficient appear to be independent of gravity. The purpose of this

investigation is to investigate the bounds of gravity independent heat transfer and assess

the predictive capabilities of the detailed bubble dynamics model that analytically

exhibits the diminishing effects of gravity.


Heat transfer data were gathered using the experimental flow-boiling facility

described in Chapter 2. The polycarbonate test section was used so that visual inspection

of the boiling flow regime was possible during testing. The flow orientations

investigated to assess gravitational influence on the boiling process were as follows: 0°

horizontal, 45° upflow, 90° upflow, 315° downflow, 270° downflow. All tests were

performed with the heater surface facing upward.




system preheat. Once steady flow conditions are established at the appropriate velocity

and inlet condition and vigorous boiling from the test section has been observed, power

to the test section heater is reduced to suppress nucleation and thus assure degassing of

57

the heater surface. It has been shown that boiling data is sensitive to the order in which

the data is taken due to boiling hysteresis. Therefore, the heat flux was always raised to

generate the ensuing test conditions following completion of one set of data.

After degassing the heater surface and obtaining appropriate inlet conditions, heat

flux was increased to achieve a certain Jacob number at the lowest system velocity. Data

was recorded at the establishment of steady state conditions, the pump speed was

increased to the next velocity data point, and the power to the heater was increased to

maintain the current Jacob number. This procedure continued through the range of

velocities and then the Jacob number was increased. Data was gathered in this manner

for each flow orientation.

4.3 Results

The totality of the data collected during this portion of the study can be examined

in Appendix C. Prior to commencing the investigation into gravity dependence, boiling

curves were generated at two levels of subcooling, ∆Tsub = 0.75ºC and 3.8ºC, and at ψ =

0.025. As shown in Figure 4.1, the boiling curves provide a means of verifying the

operation of the facility and providing a basis for determining the correct scale of wall

superheat to be expected during subsequent testing at various heat fluxes. As shown in

the figure, the boiling curve obtained for the higher subcooling condition initially

indicates a higher heat flux is necessary to obtain comparable wall superheats with the

case close to saturated boiling. The boiling curves, however, become similar at higher

heat flux approaching the observed boiling suppression points at approximately ∆Tsat =

16ºC. This is because, following suppression, the correct temperature potential driving

heat transfer is ∆Tb = Tw – Tb, where Tb is the bulk liquid temperature that dictates the

58

subcooling. In the regime where the bubble ebullition dominates the heat transfer process

the driving potential is ∆Tsat. In the case considered here, the degree of subcooling has

very little influence on the heat transfer.

∆Tsat (ºC)

0 5 10 15 20 25 30

Hea

t Flu

x (k

W/m

2 )

-10

0

10

20

30

40

50

∆Tsub = 3.8 C∆Tsub = 0.75 C

Suppression Point (both curves)

Figure 4.1. Polycarbonate test section boiling curves at ψ = 0.025

Figures 4.2 through 4.14 depict the heat transfer data gathered during gravity

dependence testing. Each figure illustrates the variation of heat transfer coefficient with

the dimensionless variable ψ (defined in Equation 3.5). The Nusselt number is defined as

lk

hDNu = (4.1)

where

sat

s

Tq

h∆

′′= . (4.2)

59

Each figure corresponds to a specific Jacob number. The range of ψ is from 0.02 to 0.06,

corresponding to a velocity range of 0.39 to 1.17 m/s and a Reynolds number from 9105

to 28062. At lower Jacob number testing proceeded only to ψ = 0.05. Jacob number

was varied from 16 to 40. For all of the data, the wall superheat exceeded that required

for incipience. The flow orientations discussed below are defined in Figure 2.6.

It is expected that flow orientations that encourage vapor bubble sliding along the

heated surface should exhibit greater heat transfer rates than others. Kirk et al. (1995)

and Thorncroft and Klausner (1999) observed such enhancement. In addition Thorncroft

and Klausner (1999) obtained data from the injection of air bubbles at a heated surface

suggesting that bubble sliding enhances bulk liquid turbulence at the wall and thereby

contributes extensively to the total macroscale heat transfer. Kirk (1995) observed

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Nus

selt

Num

ber

20

40

60

80

100

120

140

160

180

200


Figure 4.2. Variation of Nusselt number with ψ for Ja = 16 and different flow orientations

60

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Nus

selt

Num

ber

20

40

60

80

100

120

140

160

180

200



ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Nus

selt

Num

ber

20

40

60

80

100

120

140

160



61

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Nus

selt

Num

ber

20

40

60

80

100

120

140

160



ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Nus

selt

Num

ber

20

40

60

80

100

120

140

160



62

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Nus

selt

Num

ber

20

40

60

80

100

120

140

160



ψ

0.01 0.02 0.03 0.04 0.05 0.06

Nus

selt

Num

ber

40

60

80

100

120

140

160

180



63

ψ

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Nus

selt

Num

ber

40

60

80

100

120

140

160

180

200



ψ

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Nus

selt

Num

ber

80

100

120

140

160

180

200

220

240

260



64

ψ

0.01 0.02 0.03 0.04 0.05 0.06

Nus

selt

Num

ber

60

80

100

120

140

160

180

200

220

240



ψ

0.01 0.02 0.03 0.04 0.05 0.06

Nus

selt

Num

ber

100

120

140

160

180

200

220

240



65

ψ

0.01 0.02 0.03 0.04 0.05 0.06

Nus

selt

Num

ber

140

160

180

200

220

240

260



ψ

0.01 0.02 0.03 0.04 0.05 0.06

Nus

selt

Num

ber

180

200

220

240

260

280



66

that sliding vapor bubbles that continue to absorb energy from the surface deactivated

downstream nucleation sites. Kirk conjectured that increased agitation of the bulk liquid

flow associated with large nucleation site densities typical of orientations where bubble

sliding is not observed was not a source for heat transfer enhancement, contrary to the

result of Jung et al. (1987). Kirk instead attributed heat transfer enhancement in sliding

orientations to continued evaporation of a liquid microlayer beneath and in the path of the

bubbles. Bouyancy aids in lifting the bubble from the heated surface in all flow

orientations where the heater faces upward, and thus limits bubble sliding along the

surface. The shear lift force can prevent lift-off in low velocity upflow orientations

where a bubble’s buoyancy causes its velocity to lead that of the bulk flow. At high bulk

fluid velocities the bubble will lag the flow, and shear lift will aid lift-off. The bubble

lags the bulk flow in downflow, and the shear lift aids in lift-off and restricts

enhancement due to bubble sliding. With these effects in consideration, it would be

expected that gravitational influence would present itself in higher heat transfer

coefficients at the vertical upflow, or 90 degree, condition and in lower heat transfer

coefficients in downflow and horizontal conditions at low velocities. Examination of

Figures 4.2 through 4.14 shows that this suspected trend is not evident until Ja = 32, as

shown in Figure 4.10. In this case, heat transfer coefficients at 0° and 315° are

significantly lower than those at other test orientations. The trend continues and becomes

more apparent at higher Jacob numbers, with heat transfer coefficients at upflow

conditions considerably larger at the lowest registered velocity. As the bulk liquid

velocity is increased, the effect of orientation at Ja < 32 remains indiscriminate. At

higher Jacob numbers, when velocity is increased, heat transfer coefficients seem to

67

segregate into two merging regions. The first region consists of orientations φ = 0°, 45°,

and 90°, where buoyancy provides either some or no assistance to the hydrodynamic

forces sweeping bubbles from the nucleation sites. In this region, measured values of Nu

merge at large ψ as displayed in Figures 4.10 through 4.14. In the second region, φ =

315° and 270°, buoyancy resists bulk flow motion. At high values of ψ, values of Nu

merge, but at lower values than observed for region one.

In order to obtain a more quantitative description of the influence of gravity

manifest in the heat transfer coefficient data presented, the coefficient of variation of data

gathered at each Jacob number is presented in Figures 4.15 through 4.17. The coefficient

of variation is defined as the standard deviation of Nusselt numbers, measured at a

specified Ja and ψ over each orientation tested, normalized by the mean Nusselt number

value:

Ja

Javc,

,..ψ

ψ

µσ

= . (4.3)

where the subscripts ψ and Ja indicate constant ψ and Ja. The standard deviation, defined

for each orientation m in a set of M orientations tested at the specified Ja and ψ, is

( )

11

2,,,

, −

−

=∑

=

M

NuM

mJamJa

Ja

ψψ

ψ

µ

σ (4.4)

and the mean value of the data set is

M

NuM

mmJa

Ja

∑== 1

,,

,

ψ

ψµ . (4.5)

In general, increasing the flow velocity acts to reduce the orientation-induced

variation among the Jacob numbers presented. In some cases, the coefficient of variation

68

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Coe

ffici

ent o

f Var

iatio

n

0

2

4

6

8

10

12

14

16

Ja = 16Ja = 18Ja = 20Ja = 22

Figure 4.15. Coefficient of variation at different ψ for Ja = 16 to 22

ψ

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Coe

ffice

nt o

f Var

iatio

n

0

2

4

6

8

10

12

14

16

18

20

Ja = 24Ja = 26Ja = 28Ja = 30


69

ψ

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Coe

ffice

nt o

f Var

iatio

n

2

4

6

8

10

12

14

16

18

20

22

24

Ja = 32Ja = 34Ja = 36Ja = 38Ja = 40


drops rapidly to a value below 4%, and in some instances as low as 1 %. Figure 4.17

depicts a more complicated trend as the bulk fluid velocity increases. For Ja = 32 to 36,

however, the coefficient of variation approaches a minimum value at some threshold

velocity, which remains relatively steady with any further increases in ψ. At the highest

Jacob numbers, Ja = 38 and Ja = 40, there is no evidence that increasing flow

velocity acts to decrease the coefficient of variation. The steady values reached in these

higher Jacob number cases ultimately present larger discrepancies in heat transfer

coefficients, with data lying between 5.4% and 9.1% variation. While hydrodynamic

forces were sufficient to mitigate gravity-induced conditions at low heat fluxes, these

data suggest that the capability of flow velocity to overcome buoyancy forces at these

higher heat fluxes is limited by the bulk flow rate attainable in the current study. As

noted in the examination of the heat transfer coefficients presented in Figures 4.2 to 4.14,

70

at high heat flux, the data seem to converge in two distinct orientation groupings; those in

which the vapor bubble buoyancy force resists the hydrodynamic drag, and those where it

does not. The coefficients of variation for the high Jacob numbers that approach constant

values are plotted again, this time for each of these groups, in Figures 4.18 and 4.19.

These graphs illustrate the degree of separation between heat transfer coefficients in the

two groups identified. When compared with one another, buoyancy assisted flow

orientations present heat transfer coefficients whose dependence upon orientation is

sharply reduced as velocity increases. The coefficients of variation obtained in buoyancy

resisted flow orientations show, however, an initially low value and little additional

reduction at any increasing flowrate. Data at Ja = 32 is included because it seems, at high

velocities, to follow this pattern of a steadying coefficient of variation. The implication is

Psi

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Coe

ffici

ent o

f Var

iatio

n

0

5

10

15

20

25

30

Ja = 32Ja = 34Ja = 36Ja = 38Ja = 40

Figure 4.18. Coefficient of variation for different ψ with buoyancy assisted flow orientations

71

Psi

0.01 0.02 0.03 0.04 0.05 0.06 0.07

Coe

ffici

ent o

f Var

iatio

n

0

2

4

6

8

10

12

14

16

18

Ja = 32Ja = 34Ja = 36Ja = 38Ja = 40

Figure 4.19. Coefficient of variation for different ψ with buoyancy resisted flow orientations

that, based on similarities within flow regimes grouped as in Figures 4.18 and 4.19, heat

transfer performance may behave similarly with respect to gravity within the grouping,

although the flow condition may not be in the gravity-independent regime.

An additional set of tests were performed at Ja = 32 to assess the influence of

subcooling on the coefficient of variation. The results are reported in Figure 4.20 for

subcooling of approximately 1°C and 4°C. The data indicate that highly subcooled flow

is more dependent upon the effects of buoyancy than slightly subcooled flow at otherwise

similar flow conditions.

The aim of this empirical work is to examine the validity of a proposed gravity-

independent flow regime. In order to prescribe such a regime; the meaning of gravity

dependence must be defined for this study. One qualitative perspective in defining

72

Psi

0.01 0.02 0.03 0.04 0.05 0.06

Coe

ffici

ent o

f Var

iatio

n

4

6

8

10

12

14

16

18

∆ Tsub = 4 C∆ Tsub = 1 C

Figure 4.20. Effect of subcooling on gravity dependence for Ja = 32

gravity independence is to identify flow regimes where predicted orientation effects are

not present, as in data for Ja = 16 to Ja = 30. If upflow orientations exhibit lower heat

transfer coefficients than downflow orientations that are expected to be less efficient

methods of removing energy from the heated surface due to vapor bubble sliding, then

gravity-independence is suggested. Figure 4.5 depicts a clear example of this behavior;

45° and 90° upflow exhibit lower Nu than 90° horizontal flow and 270° downflow at ψ =

0.02. As a more quantitative method of comparison is preferred, it is reasoned that

gravity-independence is experienced when the coefficient of variation describing

orientation effects is less than the uncertainty in the heat transfer measurements. This

uncertainty, based upon measurement error in heat flux, bulk temperature, and heater

surface geometry, varies somewhat throughout the data but peaks at a value of nearly 5%.

73

When the coefficient of variation is 5% or lower, the data acquired at a particular Jacob

number and flow rate is judged to be gravity independent. A threshold of 6% was

chosen, however, because a number of coefficient of variation values are between 5%

and 6%, and using a criterion of 6% to determine gravity independence provided

significantly improved reconciliation between the analytical bubble lift-off prediction and

the empirical heat transfer determination. Figure 4.21 shows those data judged to be

gravity dependent and independent as well as the analytically predicted gravity dependent

and independent regime based on vapor bubble lift-off. From examination of this figure,

it appears that gravitational influence on heat transfer coefficients varies in a similar

manner to the influence on bubble dynamics, as expected. As velocity is increased, more

uniform two-phase thermal transport characteristics are realized. If larger quantities of

heat are to be managed, a further increase in velocity is required to operate in a gravity

ψ

0.00 0.02 0.04 0.06

Jaco

b N

umbe

r

0

10

20

30

40

50

independent datadependent data

experimental

Gravity Independent Lift-off

Gravity Dependent Lift-off

analytical

Figure 4.21. Experimental gravity dependence map in comparison to theoretical gravity dependence curve for bubble lift-off diameter

74

independent flow regime. Although the heat transfer coefficient may follow a boundary

of similar shape to that for bubble lift-off, it is apparent that this boundary is shifted

towards lower bulk flow rates, as illustrated by the approximated experimental curve in

the figure, indicating that gravity independence will be manifest for the heat transfer

coefficient with a smaller influence of hydrodynamic forces than for vapor bubble

dynamics.

4.4 Discussion

Heat transfer coefficients have been measured from Ja = 16 to 40 and flow rate

parameter ψ = 0.02 to 0.06. This corresponds to a heat flux of approximately 4 to 55

kW/m2 and a bulk flow velocity of 0.39 to 1.17 m/s. As expected, buoyancy forces that

are responsible for the dependence of the boiling heat transfer coefficient through their

influence on vapor bubble dynamics become less influential at higher velocities where

hydrodynamic forces become relatively large. The lower Jacob numbers investigated do

not exhibit the predicted influence of orientation and are judged to be in the gravity

independent regime. Increased velocities are required at progressively larger heat fluxes

to generate comparable reductions in the variation between data gathered at different

orientations. At high Jacob numbers, the effect of velocity on coefficient of variation

seems to be absent and disparities in data at different orientations tend towards constant,

and relatively low, values at high flow rates. Of considerable interest is the separate

comparison of orientations in which vapor bubble buoyancy assists hydrodynamic drag

and those in which buoyancy resists hydrodynamic drag. When viewed separately, each

set of data converges to a low coefficient of variation. Based on the coefficient of

variation, a gravity dependence map has been created that mimics the behavior of the

75

analytical gravity dependence criterion for bubble lift-off diameter. It is significant that

the highest Jacob number unexpectedly exhibits gravity independence at low velocity.

Further study and additional experimental data may be required to investigate whether

these flow conditions represent gravity independence due to a heat transfer mechanism

unexpectedly independent of gravitational influence, or whether experimental error in the

current study has caused these points to suggest gravity independent behavior. At the

highest Jacob numbers studied in Chapter 3, the bubble detachment and lift-off

mechanisms no longer depended on the growth of an individual bubble, but, due the large

quantity of bubbles at the heater surface, depended on the agglomeration of bubbles into

large vapor masses that were immediately removed from the surface. This change in

vapor bubble dynamics may be responsible for the high Jacob number heat transfer

measurements presented here.

The heat transfer coefficient over the heating surface is a result of both large and

small-scale phenomenon, described by researchers many times as the aforementioned

convective and nucleate contributions. While the heat transfer coefficient reported here

is a macroscopic property of the entire heater, it is expected that heat transfer coefficients

at all points along the heater will vary spatially and temporally over the ebullition time

scale. Klausner et al (1997) discussed researchers’ recognition of stochastic features in

boiling that are important in predicting the heat transfer rate and postulated that observed

statistical variations in bubble dynamics are due to apparently randomly distributed wall

superheat and turbulent velocity fluctuations in the liquid film. It is suggested that the

average macroscale heat transfer coefficient reported here is relatively insensitive to

stochastic fluctuations in microscale phenomenon, rather being an aggregate value based

76

upon the totality of the variation in conditions such as bubble lift-off. For this reason, it

is expected that the heat transfer coefficient will exhibit gravity independence at lower

velocities than bubble lift-off diameter, as depicted by data in Figure 4.20. Thus, if the

analytical bubble lift-off model is utilized in microgravity heat exchanger design, it will

serve as a conservative criterion for establishing gravity independent operation.

Additionally, although the coefficient of variation is suitable for comparison of

gravity independent trends relative to velocity, there are shortcomings associated with its

use as a criterion for gravity dependence as shown in Figure 4.21. This is because data

was not taken at all intervals of a 360° rotation. By neglecting to take data between 180°

and 270°, the standard deviation used to define the coefficient of variation may not be

completely applicable in defining the difference in orientation over all orientations in the

360° degree range of interest.

CHAPTER 5 GRAVITATIONAL EFFECT ON CRITICAL HEAT FLUX


Critical heat flux and burnout are phase-change heat transfer conditions defined by

a precipitous reduction in heat transfer coefficient realized by the system and a

corresponding increase of system wall temperatures. The damaging effects of excessive

temperatures are reflected in the terminology “burnout”, suggesting the possibility of the

catastrophic failure of the heat transfer surface. In subcooled flow boiling critical heat

flux (CHF) is the manifestation of the transition from the nucleate boiling mechanism to

the film boiling mechanism. Upon the departure from nucleate boiling, vapor crowds the

heated surface and curtails enhanced heat transfer coefficients realized through the

ebullition process. As local wall temperatures exceed the Liedenfrost temperature, fluid

is unable to rewet the surface and a dry spot can begin to grow. Kirby and Westwater

(1965) provided one of the initial visual studies of near-CHF conditions and noted the

appearance of a thin liquid microlayer under large vapor masses near burnout. High

speed photographic evidence offered by Katto and Yokoya (1967) a short time later

provided a view of vapor stems within the microlayer feeding large vapor masses and

noted that local dryout was a periodic event, contrary to the static nature of existing

theories. Both early studies confirmed the continuous spread of a vapor blanket along the

heated surface at CHF conditions. Current attempts to reconcile analytical models with

experimental observations such as these remain uncertain and predictive capabilities are

77

78

largely confined to empirical correlations. If two-phase boiling heat transfer devices are

to be deployed in microgravity environments, the behavior of CHF and its relation to

gravitational effects must be clarified.

Early research efforts led to postulation of three general mechanisms as the trigger

for the CHF phenomenon; vapor crowding, hydrodynamic instability models, and

macrolayer dry out models. Although considerable experimental research has failed to

clarify the underlying phenomenon governing the critical heat flux transition, significant

light has been shed on these possible mechanisms. Each model results in a scenario

where vapor blankets the heater surface, leading to abrupt rise in thermal resistance and a

subsequent increase in wall superheat.

As described by Carey (1992), the premise of vapor crowding, which is analogous

to bubble-packing models in pool boiling CHF, involves the accretion of vapor bubbles

from individual nucleation sites into a large vapor mass that inhibits liquid flow to the

surface. The quantity of active nucleation sites increases with heat flux, and it is

suggested that some critical bubble packing occurs that causes liquid trapped beneath the

packed bubbles to be evaporated, thus blanketing the heater surface with vapor. The

logical merit of this model, however, is abrogated by visual evidence suggesting that, at

high heat fluxes, rapid vapor generation leads to the formation of vapor jets rather than a

packed blanket. In addition, quantitative perusal of this model requires detailed

predictive capability regarding the nucleation phenomena on the heated surface that does

not exist at this time. Thus, bubble packing has received relatively less attention in

comparison to the other models.

79

Hydrodynamic instability models of the CHF mechanism, as introduced by Zuber

(1959), include consideration of Taylor wave motion and Kelvin-Helmholtz instability as

important elements. Such instability analysis suggests that perturbations of some

frequency along a flowing liquid-vapor interface may become unstable, dramatically

changing the characteristics of the flow. The velocity differential between the liquid and

vapor phases acts to destabilize the wave propagating along the interface, while surface

tension provides a stabilizing influence. Gravity stabilizes the interface for a liquid

region below a vapor region, destabilizes the interface for a liquid region below a vapor

region, and has no effect for a vertical liquid-vapor interface. Zuber (1959) proposed that

CHF occurs when the oscillating disturbance wave becomes unstable, distorting vapor

jets atop the heater and preventing liquid flow from cooling the surface. Leinhard and

Dhir (1973) refined Zuber’s model, assuming a rectangular array of vapor jets leaving the

heated surface with a spacing equal to the most dangerous wavelength as dictated by

Taylor instability. The jets have a diameter equal to half of this wavelength and CHF is

attained when the interface of these columns becomes Helmholtz unstable. Lienhard and

Dhir cite evidence that the critical wavelength causing instability is also equal to the most

dangerous wavelength.

The macrolayer dryout model developed by Haramura and Katto (1982) focuses on

the liquid layer residing beneath a large conglomeration of vapor collected from an area

of nucleation sites on the heated surface. Their work contends that the thickness of this

liquid layer must be smaller than the Helmholtz-unstable wavelength to assure the

stability of the vapor jets feeding the large mass. Vapor will accumulate until it is large

enough to depart due to its buoyancy. If the liquid film is not continually refreshed from

80

the bulk flow stream, then it is suggested that CHF will occur when the entire liquid film

is evaporated during the hovering time of the large vapor mass. Haramura and Katto

(1982) developed a CHF relation that agreed well with the hydrodynamic instability

analysis of Zuber and was readily extended from pool boiling to flow boiling. Yet

despite success in generating useful CHF correlations, Carey (1992) asserts that both

hydrodynamic and macrolayer dryout mechanisms have both been widely questioned

regarding significant idealizations or assumptions in the works that may not be

justifiable.

Recent studies have offered a more detailed morphological description of the two-

phase flow regime approaching and at the CHF condition. Galloway and Mudawar

(1993) identified the coalescence of vapor bubbles at high heat fluxes into a wave of

vapor which propogated downstream with the bulk flow in the vertical upflow boiling of

FC-87. Vigorous boiling occurred at the troughs of this wave, allowing liquid to

periodically replenish the surface and provide sufficient cooling. CHF coincided with the

observation of the lifting of the most upstream wetting front, resulting in the subsequent

lifting of the remaining wave troughs as vapor blanketing spread along the heated

surface. Gersey and Mudawar (1995a) provided the first photographic evidence of vapor

waves traveling along heaters with a variable wavelength characteristic of Kelvin-

Helmholtz instability at the upstream edge and growing in the stream-wise direction due

to wave stretching and merging. In a subsequent effort, Gersey and Mudawar (1995b)

developed a separated two-phase flow model to determine the critical interface

wavelength for stability while accounting for heater length and orientation. In testing

bulk flow velocities from 25 to 200 cm/s, little variation of CHF was observed with

81

orientation and it was proposed that vapor velocity increased rapidly enough that Kelvin-

Helmholtz instability dominates Taylor instability in characterizing interfacial features.

The model predicted a diminishing influence of gravity as flow rate was increased, with

this effect becoming negligible around a bulk fluid velocity of 0.25 m/s. In a later

investigation, Brusstar et al. (1997a) found no visual evidence of vapor stems, Kelvin-

Helmholtz instability, or a liquid microlayer beneath large vapor patches moving along a

heated surface near CHF while compiling data that validated aspects of models

predicated on these phenomena acting as the CHF trigger. Brusstar et al. (1997a) present

data suggesting that the energy flux leaving the heater surface during the residence time

of a large vapor mass is independent of the orientation of gravity, proposing a CHF

mechanism common to all heater orientations which did not rely on physical descriptions

not validated by their experimental results. Although the authors refrain from assuming

the validity of a macrolayer, Brusstar and Merte (1997b) develop a model based on the

concept of energy flux evaporating a volume of liquid that is equivalent to the

vaporization of a uniformly thick macrolayer. This model, requiring empirical evaluation

of the characteristic energy flux term for closure of the energy and momentum equations,

adequately correlates with experimental data that demonstrates a reduction in orientation

effects as velocity is increased. At a bulk flow velocity of 0.55 m/s, CHF varies +/- 20%

by orientation and is deemed to closely approach the buoyancy-independent limit. Zhang

et al. (2002) provided visualization of the liquid-vapor interface at various orientations

and flow velocities, identifying six regimes describing vapor layer characteristics. Data

in this study also indicated a deteriorating effect of gravity noticeable at 0.5 m/s.

82

In the CHF trigger mechanisms discussed above, gravitational forces seem to play

an integral role through either buoyancy forces sweeping large bubbles from the surface

or in determining the stability of interfacial liquid-vapor wave formations. Yet

agreement on a physically accurate depiction of CHF that correctly incorporates

parametric effects such as orientation with respect to gravity remains elusive. In order to

reliably implement microgravity boiling heat exchangers, gravitational influence, in

particular, and the degree to which the effect is mitigated by other flow considerations,

must be clarified. Data presented in the following section attempt to clarify the influence

of bulk fluid velocity on gravitational effects by recording maximum heat flux at various

flow orientations.


Critical heat flux testing was performed using the experimental flow-boiling

facility described in Chapter 2. Although the brass test section, due to its ability to

withstand high temperatures, is more appropriate for investigating critical heat flux and

transition boiling regimes that result from the spread of CHF, the polycarbonate test

section was chosen for these tests. Based on evidence from Chapter 4, it was thought that

higher velocities possible with the smaller flow channel of the polycarbonate test section

would be necessary to approach the gravity-dependent regime. As CHF is initially a very

localized phenomenon, close monitoring during testing would prevent destructive

overheating of the polycarbonate test section. The facility is operated to achieve

appropriate test conditions for the eight orientations detailed in Figure 2.6, comprising

45-degree incremental rotations of the test section through a full revolution. Rotating the

test section in this manner allows for testing in upflow and downflow modes as well as

with the heater surface facing upward and downward. For each angular position of the

83

test section, critical heat flux measurements are taken incrementally through the velocity

range of the system.




system preheat. Due to the large heat fluxes often required to commence CHF conditions

during these tests and the substantial influence of these heat fluxes on bulk inlet

subcooling, the test section heater is operated at a value approaching the CHF predicted

from previous testing to accurately establish initial subcooling values. Once steady flow

conditions are established at the appropriate velocity and inlet condition and vigorous

boiling from the test section has been observed, power to the test section heater is

reduced to suppress the majority of nucleation in order to eliminate boiling hysteresis

effects.

Incrementally increasing heat flux provided by the test section heater induces CHF

on the heated surface. Once steady state conditions are established at a given heat flux,

the system is monitored for CHF conditions. If these conditions are not present, heat flux

is increased again. Typically, power to the test section was increased in 5-10 W

increments, constituting a 1.4% to 4.2% increase relative to recorded CHF values. In

situations where a significantly lower CHF value was expected, such as lower velocity

conditions with the test section heater facing downward, care was taken to increment the

power supply by smaller quantities. Once CHF is attained, a set of data is saved to retain

bulk fluid information and instrument settings, power to the test section heater is quickly

shut off, and the process is repeated at the next set of conditions.

84

Monitoring heater surface temperature data and visually observing flow regime

changes are two methods of identifying CHF. In the former case, realization of CHF is

signaled by the rapid increase of heater surface temperature caused by the spreading of

the low conductivity vapor dry spot along the heater. It is expected that each

thermocouple in turn should experience extreme temperature rise as the dry spot extends

into the proximity of the thermocouple. However, it appeared during testing that the

design of the polycarbonate test section did not lend itself to accurately reporting

temperature rise at the commonly observed location of the initial dry spot growth.

Although critical heat flux was often observed to occur first at the ends of the test section

heater strip, thermocouples in the center were the first to exhibit sharp temperature

increases as the vapor blanket extended towards them. This may be due to thermal

conduction to the brass heater tabs and the connected power cabling outside the test

section in close vicinity to the thermocouples located at the ends of the heater strip. CHF

could also be identified by visually confirming the sustained growth of a dry spot on the

heater surface, although the objectivity of this measurement is questionable. Two CHF

tests were performed at fifteen conditions, identifying CHF by both of these means at

each condition to assess which method may provide greater accuracy. The difference in

comparing temperature-observed onset and visually observed onset was 2.91%, with

maximum and minimum deviations of 5.18% and 0.29%, respectively. This small value

gives credibility to the use of temperature-observed onset by suggesting that, at a variety

of conditions, the influence of CHF spreads rapidly enough to more centrally located

thermocouples to allow the use of these data for comparative purposes.

85

5.3 Results

The critical heat flux (CHF) data obtained is shown in Table 5.1 for each test

section orientation and the range of system velocities, represented by the parameter ψ.

Measurements were performed at a bulk liquid subcooling of approximately 1.5°C.

Table 5.1. Critical heat flux data ψ CHF (kW/m2)

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0 82.6 86.6 87.6 94.3 99.1 110.1 119.3 45 91.2 93.5 94.3 98.0 103.1 110.3 118.4 90 96.8 99.5 103.4 107.4 107.8 110.7 116.8

135 81.3 83.2 82.5 86.0 89.6 92.8 97.7 180 73.6 68.3 74.0 80.0 88.5 92.8 98.5 225 12.1 29.9 41.1 56.3 65.6 75.6 n/a 270 39.2 47.6 57.5 67.0 74.5 84.1 98.4

Orie

ntat

ion

315 79.1 86.8 91.3 93.0 97.3 105.5 113.5

The onset of CHF was observed for each of these tests in order to compare any

noticeable trigger mechanism with those suggested in previous studies. As heat flux is

increased, the single-phase convective flow moves into the nucleate boiling flow regime.

Incipience is initially observed only on a downstream portion of the heater, as the

subcooled fluid is heated to the critical temperature for nucleation over a thermal entry

length at the upstream edge of the heater. It appears that heat is effectively routed

downstream to the portion of the heater undergoing more effective two-phase thermal

transport, and all surface thermocouple measurements are reduced. As velocity is

increased, the onset of nucleation is delayed until a further downstream location along the

heater. Increases in heat flux reduce the length of the heater experiencing single-phase

heat transfer. When the heat flux approaches CHF, vigorous boiling occurs over the

entire heater surface, leaving only a small sliver of the single-phase regime at the leading

edge.

86

Very near CHF, intermittent localized areas of reduced ebullition could be observed

moving over the surface, possibly due to a restriction of liquid supply to the heater.

Three to four patches appeared on the heater at one time, and the approximated length of

the areas was on the order of 1 cm in the flow direction. This occurrence was observed

primarily on the upstream portion of the heater, although once patches of suppressed

nucleation were formed, they moved in an irregular fashion but with a general

downstream direction for a short period of time before disappearing. The third of four

thermocouples in the downstream direction tended to increase above the others at this

time. It may be possible that the fourth and most downstream thermocouple remained at

a lower temperature due to heat transfer out of the test section through the brass heater

post connecting to the power supply. Individual nucleation sites formed jets that seemed

to periodically accumulate into large vapor masses that departed from the surface when

the heater faced upward relative to gravity. In low velocity downflow conditions, these

large vapor bubbles moved counter to the bulk flow. At some intermediate velocity, they

seemed to stagnate on the surface for a long period of time before being swept away, and

at higher velocities they detached and departed downstream with the bulk flow. Test

orientations with the heater facing downward produced large vapor masses that seemed to

flatten against the heater and slide away along its surface. As velocity increased, the

inception of larger vapor masses diminished.

Additional increases in heat flux prompted onset of CHF, noted by a dry spot

apparent at the upstream edge of the heater. This spot quicky spread in the downstream

direction and thermocouples below the spreading vapor blanket registered sharp

temperature increases before the power supply to the heater was interrupted. In some

87

cases, a small patch of reduced nucleation, mentioned above, formed a dry spot on the

heater surface in the approximate area of the most upstream thermocouple, about 3 cm

from the leading heater edge. This dry spot began to grow and CHF proceeded from this

mechanism rather than from the leading heater edge.

Figure 5.1 depicts the polar representation of the variation of CHF with ψ at each

test section orientation. The data exhibit significant buoyancy-related effects,

100

35

180180o

o

o

o

Figure 5.1. Criti

1135

0

20

40

60

80

204060801000

20

40

60

80

100225

ψ = 0.020ψ = 0.025ψ = 0.030ψ = 0.035ψ = 0.040ψ = 0.045ψ = 0.050

225o

cal heat flux vs. ψ for all or

9090

0 20 40 60 800

270270o

ientations

4545

1000

315

315o

0o

CH(kW/m

F 2)

88

particularly at orientations in which the heater faces downward relative to gravity or in

vertical downflow. At low velocity, CHF at 225° is nearly an order of magnitude smaller

than at upflow orientations. Gravitational effects are alleviated somewhat as velocity is

increased; this is particularly evident at the 225° orientation. It is also apparent that

increasing the inlet velocity can reduce CHF by more readily replenishing the surface

with cool liquid and sweeping away bubbles intent on conglomerating into a large vapor

mass.

The discrepancy in CHF for each orientation tested is quantitatively compared

using the coefficient of variation, as defined in Chapter 4. The relationship between the

coefficient of variation and the flow parameter ψ is illustrated in Figure 5.2. It is clear

that increased inertial effects promote a dramatic weakening of buoyancy effects relevant

to CHF. The trend suggests that a flow regime that is gravity independent relative to the

CHF trigger mechanism is approachable.

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Coe

ffici

ent o

f Var

iatio

n

0

10

20

30

40

50

Figure 5.2. Coefficient of variation vs. ψ

89

The instability mechanism that is a common consideration in the CHF trigger

mechanisms discussed in section 5.1 is based upon a perturbation analysis of the flow

field subject to a Fourier component wave disturbance at the liquid vapor interface

(Carey, 1992). The analysis dictates that the amplitude of the interface wavelength will

grow with time and destabilize the interface if the following condition holds:

( )[ ]( ) 21

+−+

>−vl

vlvlvl

guu

ρρρραρρσα (5.1)

As evident in the above criterion, surface tension promotes stability, the difference

between liquid and vapor phase velocities degrades stability, and gravity can assume

either effect based upon its direction of influence. At low velocities, the stability of the

interface can be sensitive to variations in body force, but in low gravity conditions of

particular concern to this study, high velocity leads to a buoyancy independent balance

between inertial and surface tension effects. It is reasonable to hypothesize that CHF

would exhibit a reduced dependence on gravitational forces. In consideration of the CHF

trigger mechanism, Zhang et al. (2002) noted that the wavy vapor layer CHF regime

detailed by Gersey and Mudawar (1995a) was evident at all orientations at high

velocities, but that at low velocities, the trigger mechanism seemed to vary. This gives

physically observed credence to the possible independence of CHF to gravitational

considerations at high velocities.

Figures 5.3 and 5.4 compare the empirically determined CHF with the correlation

of Brusstar and Merte (1997b) that attempts to model the effects of subcooling and

orientation for pool boiling and low velocity flow boiling, defined as velocities below

0.55 m/s, or approximately ψ = 0.03. The model predicts a deleterious effect on CHF for

orientations between 90° and 270°, but no effect for others. The original correlation

90

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Crit

ical

Hea

t Flu

x (k

W/m

2 )

70

80

90

100

110

120

130

0O experimental45O experimental90O experimental0O Brusstar & Merte45O Brusstar & Merte90O Brusstar & Merte

Figure 5.3. Comparison of CHF vs. ψ data with model of Brusstar and Merte (1997b) for upflow and horizontal orientations

ψ

0.015 0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055

Crit

ical

Hea

t Flu

x (k

W/m

2 )

0

20

40

60

80

100

120

225O experimental270O experimental225O Brusstar & Merte270O Brusstar & Merte

Figure 5.4. Comparison of CHF vs. ψ data with model of Brusstar and Merte (1997b) for downflow orientations

91

modified Zuber’s (1958) initial hydrodynamic instability model for saturated pool boiling

on a horizontal surface. For the current comparison, the improved correlation of

Leinhard and Dhir (1973) is substituted. The model is as follows:

214

1

& sin102.01 φρρ

+′′=′′ Jaqq

lv

DLc (5.2)

( ) 41

2& 149.0

−=′′

v

vllvvDL

ghq

ρ

ρρσρ (5.3)

where the bracketed portion of equation 5.2 represents the subcooling correction credited

to Ivey and Morris (1962) and equation 5.3 is formulated by Leinhard and Dhir. The low

velocity portion of the CHF test seems to approach the low velocity solution offered by

Brusstar and Merte for the horizontal orientation only. It appears that even at low

velocities, the simple model proposed above does not adequately encorporate effects of

velocity or orientation.

5.4 Discussion

Critical heat flux measurements have been taken at eight orientations with respect

to terrestrial gravity and at velocities within the range of 0.39 m/s to 0.98 m/s with 1.5°C

subcooling. These data exhibit an increase in CHF as velocity is increased, and a

considerable consolidation of data at different orientations at the highest velocity. The

coefficient of variation reported at 0.98 m/s, 9.4%, is relatively low and consistent with

the similarity observed by Zhang (2002), but no criteria was established to deem this

gravity dependent or independent.

The CHF inception at the leading edge of the heater is unlike the mechanism

suggested by Haramura and Katto (1982) in the extension of their pool boiling

macrolayer dryout model to flow boiling. They suggested that the macrolayer film would

92

decrease in thickness in the flow direction due to aggregation of vapor produced by

feeder jets at the surface. In this situation, fluid would more easily replenish the liquid

macrolayer at the upstream edge and CHF was expected to occur at the downstream edge

of the large vapor masses over the surface. This is inconsistent with the observation of

CHF proceeding from the front of the heater.

Observations corroborated some details of the trigger mechanism proposed by

Gersey and Mudawar (1995a), though a cohesive and defined wavy vapor layer could not

be identified as in their study. The slow downstream progression of intermittently

formed, short duration areas of reduced ebullition occurring primarily on the upstream

portion of the heater do suggest the possibility of a wave-like flow instability altering

surface conditions. Additionally, CHF was observed to commence at the leading edge of

the heater, as in Gersey and Mudawar. Gersey and Mudawar pronounced orientation

insignificant from 0° to 90° above 0.25 m/s; the data from this study exhibited a

coefficient of variation of 7.9% at these orientations and a velocity of 0.39 m/s, which is

somewhat high to be considered insignificant but certainly approaching gravity

independence within reasonable experimental error.

Zhang (2002) stresses the vast discrepancies in physical characterizations of the

CHF phenomenon reported at different orientations and suggests that one model may not

adequately encompass all conditions. The observations in this study, similar to those

reported by Zhang, of liquid-vapor counterflow, concurrent flow, and stagnant flow two-

phase flow regimes and the accuracy of pool boiling correlations at very low velocities

suggest that a number of models will be needed to account for variations in CHF trigger

mechanisms. It is apparent that more strenuous and detailed observations of the CHF

93

trigger mechanism and two-phase flow regime near CHF must be recorded. In order to

offer a predictive capability of gravity dependence, the regime must be clearly identified

and defined based on similarities in trigger mechanism and verified with experimental

CHF data.

CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS

This study has experimentally examined the behavior of two-phase flow boiling

heat transfer coefficients, bubble dynamics, and critical heat flux phenomenon in the

presence of various gravitational fields through manipulation of the test section

orientation. The extent to which gravity-dependent buoyancy forces supersede

hydrodynamic forces and govern flow-boiling characteristics has been investigated in

order to provide a more reliable predictive capability regarding microgravity heat

exchanger design and performance. The significant accomplishments of this work and

recommendations for future study are discussed in this chapter.

6.1 Accomplishments and Findings

Chapter 3 presents a photographic study of vapor bubble lift-off across a range of

heat fluxes, bulk flow velocities, and test section orientations in order to clarify the

interaction of bouyancy forces and hyrdrodynamic forces in determining vapor bubble

dynamics. The visual investigation indicates that bubble lift-off diameter generally

decreases with decreased heat flux and increased bulk flow velocity, as expected. The

consequences of orientation are clearly evident at high heat flux, exhibiting a reduction in

lift-off diameter in vertical downflow and a gradual increase with test section rotation

towards vertical upflow, where lift-off was seldom observed. However, as heat flux is

reduced, limited tendencies toward gravity independence are observed at increasingly

lower velocities. The trends evident in the model created by Thorncroft et al. (2001)

94

95

have been compared with the data and acceptable agreement validates the analytical

prediction of a gravity independent bubble dynamics flow regime, suggesting the

existence of a similarly gravity independent heat transfer regime.

In Chapter 4, a study of heat transfer coefficients at various test section orientations

has elucidated the influence of gravity on two-phase boiling heat transfer and investigated

the degree to which the vapor bubble dynamics model, validated by experimental

measurements in Chapter 3, can be used to describe gravity independence of thermal

data. Heat transfer coefficients obtained here display similar trends as the vapor bubble

lift-off measurements when heat flux, velocity, and orientation effects are investigated.

Examination of the data suggests that heat exchanger operation can occur in a gravity

independent heat transfer regime. Increased velocities are required at progressively

larger heat fluxes to generate comparable reductions in the variation between data

gathered at different orientations. The coefficient of variation among orientations

recorded at each test condition is used to construct an empirical Ja vs. ψ gravity

dependent/independent flow regime map. The dependence criterion suggested by this

data is similar in shape to the analytical dependence in bubble dynamics suggested by

Bower et al. (2002). The gravity independence occurs at slightly lower velocities in heat

transfer measurements due to the minimal effect of microscale bubble dynamics

variations in the general large scale heat transfer coefficient applied to the entire test

section heater. Thus, the model of Thorncroft et al. (2001) would be a conservative tool

in design of heat exchangers to provide reliable microgravity heat transfer.

The dependence of flow-boiling critical heat flux (CHF) on gravity has been

studied in Chapter 5 to assess the possible dangers of destructive burnout at low heat flux

96

in microgravity conditions where bouyancy is not present to prevent vapor accumulation

on the heat transfer surface. As velocity increased, cool fluid more readily flushed the

heater surface and higher CHF was attained. The effect of orientation was most evident

in test section positions in which the heater surface faced downward and stagnation of

vapor above the surface was promoted by downflow conditions which balanced

bouyancy and hydrodynamic forces. The reported coefficients of variation show the

CHF data consolidates considerably at high velocities, though, and suggests a regime

where the CHF trigger mechanism, and thus maximum operating heat fluxes, may not

depend on gravity.

6.2 Recommendations for Future Research

Several aspects of the information provided herein may be extended or further

substantiated by additional experimental observations and increasingly efficacious

methodologies suggested by the results of this study. Also, a number of key

considerations remain unresolved.

1. Future test section construction should involve gasketing methods to facilitate

modular use in heat transfer testing. The current test section design proved to

be unexpectedly difficult to fabricate, epoxy sealant was somewhat unreliable,

and damage to one part of the test section led to recreation of the entire

assembly. With a gasketed design, additional testing considerations could more

easily be investigated without significant fabrication downtime, such as the

dependence of nucleation and bubble dynamics on heater surface material and

finish, or the effect of heater length in CHF phenomena.

2. Improved visual quality of vapor bubble dynamics measurements should be

obtained. Additional photographic capabilities would provide increased

97

resolution, limiting error in bubble measurement, and provide increased

magnification of the viewing area to allow for empirical determination of

bubble growth rates. It is evident that the discrepancy between bubble lift-off

diameter data obtained in this study and the analytical predictions of Thorncroft

et al. (2001) may be due primarily to the inadequacy of the bubble growth rate

model used in the analysis. At this time, no adequate subcooled bubble growth

rate model exists.

3. Investigation of heat transfer coefficients must be extended to a larger portion

of the proposed gravity dependent/independent regime map, particularly into

the analytical gravity independent regime. Additionally, further investigation

of the gravity independence exhibited by high heat flux measurements in this

study even at low velocities is needed.

4. A detailed investigation is needed to study the vapor bubble dynamics behavior

observed at high heat fluxes where agglomeration of bubbles appeared to be the

driving factor influencing lift-off phenomena. This mechanism suggests a heat

transfer regime in which the current model cannot describe bubble dynamics.

The relationship between this mechanism and gravity dependent heat transfer

should be determined in further detail.

5. Future study must incorporate visual investigation of CHF trigger mechanism

as a means to determine gravity dependence. It is apparent that one model does

not fit CHF data at all orientations, but that the CHF trigger regime may be

specified at each flow conditions. The extent to which the high velocity trigger

mechanism regime represents gravity independent CHF values should be

98

clarified and the location of the onset of this independence specified for design

purposes. In addition, an updated data acquisition system has been purchased

that can provide substantial improvements in the capability to analyze data over

the progression through the CHF regime.

6. Although extensive study of the thermal transport phenomenon has been

undertaken, hydrodynamic transport is also an area of interest. Two-phase

pressure drop data should be acquired and analyzed to determine whether

gravity independence suggested by bubble dynamics models and measurements

extends to flow hydrodynamics. This consideration will be critical in forming

accurate estimates of pumping costs associated with high velocities needed to

obtain gravity independent thermal transport.

7. Ultimately, the feasible development of heat exchangers operating in the

proposed gravity independent regime must be examined. Although the

theoretical advantages of utilizing flow-boiling heat transfer in space-deployed

systems are clear, solar power generation aboard space systems provides a

restrictive power budget that precludes large allowances for pumping power, as

discussed by Zhang (2002). Whether low velocities available are sufficient to

operate in a gravity independent heat transfer regime that obviates the concern

of low heat flux burnout remains to be investigated.

APPENDIX A PROPERTIES OF FC-87

The following relations used during data acquisition and analysis were generated

from empirical curve fits of fluid property data provided by 3M Corporation, with the

exception of the relation for vapor dynamic viscosity. The vapor viscosity is

approximated using Lucas’ method as shown in the equation below. All data are valid in

the range 20>T>80ºC. The pressure and temperature in the following expressions are in

bars and ºC, respectively.

1. Saturation Temperature, Tsat(P) :

Tsat(ºC) = - 8.58181276 + 49.9516086 P - 15.06236247 P2

+ 2.717311907 P3 - 0.1962241098 P4 (A.1)

2. Saturation Pressure, Psat(T) :

Psat(bar) = 0.2495501529 + 0.01885309262 T

+ 0.0001239063032 T2 + 4.18978433 x 10-6 T3 (A.2)

3. Density, liquid, ρf :

ρf (kg/m3) = 1949.52224 - 10.16562488 T + 0.1692868739 T2

- 0.002136889443 T3 + 8.045897135 x 10-6 T4 (A.3)

99

100

4. Density, vapor, ρg:

ρg (kg/m3) = 2.281459716 + 0.3231243337 T

- 0.00126417128 T2 + 7.361978099 x105 T3 (A.4)

5. Enthalpy, liquid, hf :

hf (kJ/kg) = - 0.01769359364 + 1.12231746 T

- 0.00230599836 T2 + 1.846219316 x 10-5 T3 (A.5)

6. Enthalpy of vaporization, hfg :

hfg (kJ/kg) = 101.3279152 – 0.507085092 T

+ 0.003288716463 T2 - 2.258900124 x 10-5 T3 (A.6)

7. Enthalpy, vapor, hg :

hg(kJ/kg) = 100.9158578 + 0.6436365089 T

+ 0.000376818698 T2 (A.7)

8. Coefficient of Surface Tension, σ :

σ x 103 (N/m) = 12.55031729 - 0.1220063458 T (A.8)

9. Liquid Thermal Conductivity, kf :

kf x 103 (W/m K) = 59.90037017 - 0.1564500264 T (A.9)

101

10. Liquid Dynamic Viscosity, µf :

µf x 106 (kg/m s) = 697.382533 - 10.65949228 T

+ 0.09782017889 T2 - 0.0004165597581 T3 (A.10)

11. Liquid Specific Heat, CP,f :

CP,f (kJ/kg K) = 1.03617927 + 0.001805922792 T (A.11)

12. Vapor Dynamic Viscosity, µg :

µg (kg/m s) = 1.061691986 x 10-5 + 3.870019716 x 10-8 T (A.12)

APPENDIX B BUBBLE LIFT-OFF DATA

The following appendix contains raw bubble lift-off data obtained during this study

and discussed in Chapter 3. All bubble lift-off measurements made at a specified Ja and

ψ flow condition are presented in pixels. The mm/pixel conversion rate is included along

with the final average bubble lift-off diameter in mm. If no entry is present, vapor bubble

lift-off was not observed.

102

0° HORIZONTAL FLOW

Ja Psi D1 (pixel)

D2 (pixel)

D3 (pixel)

D4 (pixel)

D5 (pixel)

D6 (pixel)

D7 (pixel)

D8 (pixel)

D9 (pixel)

D10 (pixel)

Calibration (mm/pixel)

D(avg) (mm)

24.0 0.020 20 15 21 23 18 21 25 16 0.0130 0.25824.0

0.025 20 21 19 13 20 15 13 14 19 0.0130 0.22224.0 0.030 14 18 16 15 19 15 19 15 20 0.0130 0.21824.0 0.035 14 14 12 17 16 12 14 0.0130 0.18424.0 0.040 11 12 16 11 10 0.0130 0.156

30.0 0.020 26 22 25 28 26 24 30 27 27 25 0.0153 0.39730.0 0.025 27 24 22 24 25 29 25 27 23 22 0.0153 0.37930.0 0.030 23 18 20 21 23 25 21 26 22 26 0.0153 0.34430.0 0.035 22 21 20 24 22 18 0.0153 0.34430.0 0.040 18 19 24 22 20 20 18 20 0.0153 0.30830.0 0.045 17 16 19 17 17 20 18 23 0.0153 0.28130.0 0.050 20 15 18 15 15 15 22 18 0.0153 0.26430.0 0.055 19 16 18 12 13 14 14 18 15 16 0.0153 0.237

36.0 0.020 32 33 36 35 28 37 32 27 31 30 0.0130 0.41736.0 0.025 31 27 36 30 29 29 30 34 29 27 0.0130 0.39236.0 0.030 28 26 24 26 27 26 30 30 24 23 0.0130 0.34336.0 0.035 28 24 30 22 20 21 22 23 25 23 0.0130 0.30936.0 0.040 21 24 23 23 16 23 21 17 20 20 0.0130 0.27036.0 0.045 21 18 17 15 17 20 14 15 20 17 0.0130 0.22636.0 0.050 14 14 17 21 12 16 20 17 18 16 0.0130 0.214

45° UPFLOW Ja Psi D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) Calibration

(mm/pixel)D(avg) (mm)

24.0 0.020 28 26 26 22 23 27 25 35 27 29 0.0127 0.339

103

104

24.0 0.025 27 20 21 19 23 24 26 18 21 0.0127 0.28024.0 0.030 22 18 23 18 17 22 21 20 0.0127 0.25524.0 0.035 12 16 17 15 17 18 18 22 0.0127 0.21424.0 0.040 13 15 14 20 20 14 15 15 0.0127 0.199

30.0 0.020 27 26 24 27 31 25 31 36 37 25 0.0148 0.42730.0 0.025 35 27 21 25 27 20 24 24 34 31 0.0148 0.39630.0 0.030 15 19 24 25 27 21 31 22 22 36 0.0148 0.35730.0 0.035 26 25 19 19 18 24 20 23 20 21 0.0148 0.31730.0 0.040 18 25 26 23 20 24 16 17 17 21 0.0148 0.30630.0 0.045 17 12 18 22 20 15 19 16 21 25 0.0148 0.27330.0 0.050 15 15 14 13 22 18 21 17 13 0.0148 0.243

36.0 0.020 41 47 39 42 48 49 38 48 0.0127 0.55736.0 0.025 36 31 40 42 39 40 43 44 38 0.0127 0.49636.0 0.030 31 36 38 32 33 32 34 35 46 0.0127 0.44636.0 0.035 29 33 35 33 27 31 33 27 32 0.0127 0.39436.0 0.040 28 31 26 28 27 18 23 29 27 0.0127 0.33336.0 0.045 28 22 25 24 27 23 23 20 0.0127 0.30436.0

0.050

18

21

26

23

21

23

21

19

20

0.0127

0.270

90° UPFLOW Ja Psi D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) Calibration


24.0 0.020 29 31 34 33 40 43 33 49 29 38 0.0086 0.31024.0

0.025 33 40 35 24 40 35 31 20 36 32 0.0086 0.28224.0 0.030 25 26 23 25 34 30 26 26 32 28 0.0086 0.23824.0 0.035 20 28 20 32 22 30 25 19 23 20 0.0086 0.20724.0 0.040 25 22 22 18 20 22 16 22 22 16 0.0086 0.177

30.0 0.020 20 19 23 21 28 20 22 22 19 25 0.0144 0.316

105

30.0 0.025 16 23 19 19 20 21 19 17 23 20 0.0144 0.28430.0 0.030 16 18 18 22 19 14 15 17 17 20 0.0144 0.25430.0 0.035 18 18 14 16 15 17 13 15 15 14 0.0144 0.22330.0 0.040 17 17 18 22 20 16 14 19 16 22 0.0125 0.22630.0 0.045 13 15 14 21 17 15 12 17 14 13 0.0125 0.18830.0 0.050 10 7 7 11 8 11 8 14 12 10 0.0147 0.144

36.0 0.020 25 24 21 23 22 21 25 21 28 27 0.0144 0.34236.0 0.025 25 18 22 19 25 23 23 20 24 19 0.0144 0.31436.0 0.030 19 22 19 17 19 23 21 17 22 21 0.0144 0.28836.0 0.035 18 17 16 24 20 19 17 19 19 16 0.0144 0.26736.0 0.040 19 14 15 19 17 17 20 18 19 18 0.0144 0.25436.0 0.045 17 13 16 17 13 17 15 20 16 17 0.0144 0.23236.0

0.050

16

12

16

16

15

16

17

14

14

13

0.0144

0.215

225° DOWNFLOW Ja Psi D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) Calibration


24.0 0.020 28 33 34 30 31 30 34 26 24 33 0.0124 0.37624.0

0.025 22 27 26 26 24 29 19 24 28 0.0124 0.31024.0 0.030 20 19 21 16 20 18 20 18 15 0.0124 0.23024.0 0.035 15 17 16 15 0.0124 0.19524.0 0.040 12 13 11 14 12 11 0.0124 0.151

30.0 0.020 26 24 24 25 41 40 29 25 35 32 0.0095 0.28530.0 0.025 25 23 19 26 20 20 27 22 33 37 0.0095 0.22630.0 0.030 25 21 25 27 33 22 25 19 22 19 0.0095 0.22530.0 0.035 24 17 18 21 17 20 29 24 20 22 0.0095 0.20130.0 0.040 15 18 16 18 19 13 21 19 21 16 0.0095 0.16630.0 0.045 14 17 16 18 17 16 17 15 15 18 0.0095 0.15430.0 0.050 14 13 13 19 13 17 15 11 11 14 0.0095 0.132

106

36.0 0.020 39 33 31 30 40 38 30 32 36 40 0.0095 0.33036.0 0.025 25 36 31 30 30 28 25 35 39 30 0.0095 0.29236.0 0.030 30 27 24 31 22 33 27 26 31 30 0.0095 0.22836.0 0.035 29 25 22 22 20 18 27 23 24 31 0.0095 0.21636.0 0.040 21 22 24 21 24 31 23 24 18 20 0.0095 0.18136.0 0.045 18 17 18 17 18 19 24 21 19 20 0.0095 0.18136.0

0.050

18

19

14

18

15

19

17

15

20

15

0.0095

0.161

270° DOWNFLOW Ja Psi D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) D (pixel) Calibration


24.0 0.020 33 0.0128 0.422 24.0

0.025 24 25 28 27 27 0.0128 0.33524.0 0.030 22 23 14 19 20 18 0.0128 0.24724.0 0.035 17 20 20 16 11 12 20 18 21 15 0.0128 0.21724.0 0.040 11 14 12 11 17 13 13 15 17 12 0.0128 0.173

30.0 0.020 - -30.0 0.025 - -30.0 0.030 - -30.0 0.035 44 41 46 50 49 0.0123 0.56730.0 0.040 30 32 22 29 34 38 32 32 34 28 0.0123 0.38330.0 0.045 32 32 24 26 27 29 21 20 34 18 0.0123 0.32430.0 0.050 22 25 23 22 20 19 17 21 13 12 0.0123 0.239

36.0 0.020 - -36.0 0.025 - -36.0 0.030 - -36.0 0.035 - -36.0 0.040 - -

D (pixel)

107

36.0 0.045 - -36.0 0.050 - -

APPENDIX C HEAT TRANSFER COEFFICIENT DATA

The heat transfer data discussed in Chapter 4 is included in this appendix. All

parameters discussed withing the work were calculated from this data. Properties of FC-

87 were calculated based on the test section bulk inlet temperature, TTS in, and the

property relations listed in Appendix A. The bulk inlet temperature, the average heater

temperature corrected as discussed in Section 2.4.7, and the test section inlet saturation

temperature, Tsat, TS in, are used to determine superheat and subcooling. Data used for the

high ∆Tsub tests and the boiling curves are included as well.

108

Ja = 16

Angle° h (W/m2K) Re We TS Power

(W) mdot''

(kg/m2s) Flow Rate

(L/min) TTS in (°C)

TTS out (°C)

Heater avg, corrected

(°C) Tsat, TS in (°C) P(TS in) P(TS out)

ψ = 0.020 0 409.8

9553 195.8 19.49 706 3.88 27.60 25.62 38.13 29.32 6.91 7.080 404.0 9553 195.8 19.13 706 3.88 27.59 25.60 38.07 29.32 6.92 7.1145 364.4 9502 193.0 16.88 698 3.85 27.97 26.26 38.23 29.32 6.95 7.1190 407.4 9700 199.6 18.05 706 3.90 28.72 26.40 38.53 29.32 7.41 7.53

225 393.2 9601 197.5 18.65 708 3.90 27.75 29.44 38.25 29.33 7.81 7.65270 367.4 9565 196.3 17.49 706 3.89 27.63 29.36 38.17 29.33 7.64 7.46ψ = 0.025

0 535.1 11516 284.7 25.70 851 4.69 27.54 25.82 38.17 29.31 6.83 7.0045 596.5 11506 284.6 28.69 852 4.69 27.41 25.98 38.06 29.31 6.80 6.9190 537.0 11369 275.4 24.19 832 4.59 28.28 26.27 38.26 29.32 6.87 7.00

225 529.4 11305 273.9 25.22 834 4.59 27.70 29.29 38.25 29.34 8.06 7.89270 539.0 11802 298.5 25.50 870 4.79 27.72 29.17 38.20 29.33 7.94 7.79ψ = 0.030

0 661.8 13797 407.7 31.26 1017 5.60 27.76 26.33 38.22 29.32 7.11 7.2645 736.8 13820 408.7 34.09 1017 5.60 27.87 26.32 38.11 29.32 7.09 7.1790 727.4 13635 397.9 34.02 1004 5.53 27.85 26.14 38.20 29.31 6.85 6.95

225 696.3 13814 408.8 32.84 1018 5.61 27.73 29.13 38.18 29.34 8.48 8.31270 713.3 14135 428.2 33.89 1042 5.74 27.72 29.09 38.24 29.34 8.33 8.15ψ = 0.035

0 922.7 16303 570.9 44.54 1206 6.64 27.49 26.13 38.18 29.32 7.27 7.3545 938.3 16124 555.8 43.89 1185 6.53 27.94 26.61 38.30 29.33 7.55 7.6690 960.3 16274 569.9 46.62 1206 6.64 27.32 25.91 38.07 29.32 7.04 7.08

225 874.6 16349 572.7 41.41 1205 6.64 27.73 29.01 38.21 29.35 8.70 8.54270 836.1 16097 555.0 39.89 1186 6.53 27.77 29.02 38.33 29.35 8.60 8.42ψ = 0.040

0 1057.0 18364 725.0 50.86 1360 7.48 27.40 26.12 38.06 29.33 7.60 7.6745 1064.1 18747 750.8 49.18 1377 7.59 28.01 26.80 38.25 29.34 8.00 8.03

109

109

110

90 1119.6 18643 746.6 53.94 1379 7.59 27.49 26.20 38.16 29.33 7.57 7.58225 996.2 18436 727.5 46.79 1357 7.48 27.84 29.01 38.24 29.36 9.05 8.84270 1006.8 18711 749.1 47.69 1377 7.59 27.87 28.98 38.36 29.36 9.06 8.86ψ = 0.045

0 1274.7 20722 922.8 61.40 1534 8.44 27.44 26.22 38.10 29.34 8.09 8.1145 1267.5 21135 951.2 57.69 1546 8.53 28.34 27.21 38.41 29.35 8.63 8.6590 1301.4 20903 933.7 60.33 1536 8.46 27.99 26.48 38.26 29.34 8.17 8.14

225 1167.2 20772 923.1 54.85 1528 8.42 27.88 28.96 38.28 29.36 9.22 9.02270 1192.8 21067 949.0 56.08 1549 8.54 27.93 28.94 38.34 29.37 9.64 9.43ψ = 0.050

0 1493.6 23394 1173.8 70.98 1727 9.51 27.64 26.43 38.16 29.35 8.84 8.8145 1433.1 23214 1148.4 65.29 1699 9.37 28.26 27.09 38.35 29.35 9.02 8.9890 1562.2 23440 1175.0 73.22 1724 9.50 27.92 26.63 38.30 29.35 8.79 8.73

225 1383.6 23472 1175.7 64.54 1721 9.49 28.12 29.12 38.45 29.37 10.03 9.78270 1370.3

23211 1150.8 63.85 1704 9.40 28.03 29.04 38.35 29.38 10.40 10.18

Ja = 18


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



ψ = 0.020 0 431.6 9590

196.4 22.15 704 3.88 28.03 27.31 39.39 29.33 7.49 7.5645 424.8 9863 207.5 21.68 723 3.99 28.16 27.32 39.46 29.33 7.49 7.6090 430.5 9585 196.3 22.14 704 3.88 28.02 26.85 39.40 29.32 7.22 7.31

225 341.7 9360 187.3 17.56 688 3.79 27.97 29.85 39.35 29.33 7.72 7.57270 351.3 9415 189.5 18.18 692 3.81 27.96 29.97 39.42 29.33 7.67 7.51ψ = 0.025

28.03

0 635.9 11859 300.1 32.41 869 4.79 28.15 27.58 39.43 29.33 7.65 7.7245 558.8 11863 300.0 28.42 869 4.79 28.23 27.45 39.50 29.33 7.77 7.8390 622.3 11524 285.1 32.96 851 4.69 27.57 26.53 39.30 29.32 7.12 7.21

225 571.0 11867 300.3 29.04 869 4.79 28.21 29.75 39.47 29.34 8.22 8.06

111

270 544.5 11791 297.0 28.01 866 4.77 28.03 29.67 39.42 29.34 8.08 7.92ψ = 0.030

28.04

0 780.3 13864 410.0 39.83 1016 5.60 28.15 27.62 39.46 29.34 7.98 8.0245 741.1 14152 426.2 37.39 1034 5.71 28.39 27.65 39.56 29.34 8.03 8.0790 758.5 13747 406.5 40.23 1018 5.60 27.36 26.52 39.10 29.32 7.29 7.36

225 708.3 13896 411.3 35.86 1017 5.61 28.32 29.67 39.53 29.35 8.51 8.32270 689.4 13870 410.9 35.43 1018 5.61 28.05 29.56 39.43 29.34 8.43 8.25ψ = 0.035

28.05

0 956.3 16428 575.4 48.58 1203 6.64 28.22 27.67 39.47 29.34 8.24 8.2245 877.0 16489 577.7 43.47 1202 6.64 28.57 27.96 39.54 29.35 8.49 8.5190 926.3 16294 570.7 49.22 1206 6.64 27.43 26.63 39.20 29.33 7.80 7.81

225 864.1 16753 596.2 42.69 1221 6.74 28.58 29.84 39.52 29.35 8.99 8.82270 887.3 16405 574.4 45.61 1203 6.64 28.11 29.40 39.49 29.35 8.75 8.56ψ = 0.040

28.18

0 1150.3 18776 751.7 58.35 1375 7.59 28.21 27.60 39.44 29.35 8.52 8.4845 1072.7 18913 758.0 52.72 1374 7.59 28.82 28.11 39.70 29.35 8.85 8.8390 1140.2 18971 770.5 59.19 1397 7.70 27.80 27.12 39.30 29.34 8.45 8.45

225 1014.1 18869 755.4 50.51 1373 7.59 28.70 29.83 39.73 29.36 9.25 9.04270 1008.6 18749 751.1 51.82 1377 7.59 28.00 29.22 39.38 29.36 9.15 8.93ψ = 0.045

28.31

0 1267.1 21109 950.9 65.25 1548 8.54 28.13 27.56 39.53 29.35 8.86 8.8045 1272.1 21208 954.9 63.25 1545 8.53 28.64 28.02 39.65 29.36 9.19 9.1490 1306.5 21146 955.1 66.85 1553 8.56 28.04 27.35 39.37 29.35 8.93 8.88

225 1148.6 21207 955.6 57.33 1546 8.54 28.56 29.67 39.61 29.36 9.52 9.30270 1171.2 21221 962.2 61.14 1559 8.59 28.00 29.11 39.56 29.37 9.77 9.54ψ = 0.050

28.27

0 1542.3 23563 1182.6 78.48 1724 9.51 28.31 27.71 39.58 29.37 9.58 9.4945 1409.4 23327 1154.7 69.93 1698 9.38 28.68 28.13 39.67 29.37 9.66 9.5790 1464.3 23356 1162.2 73.77 1709 9.43 28.29 27.60 39.45 29.36 9.51 9.43

225 1338.8 23587 1182.7 67.10 1721 9.50 28.51 29.61 39.61 29.38 10.18 9.95270 1430.2 23494 1179.6 73.82 1726 9.51 27.98 29.02 39.41 29.38 10.34 10.13ψ = 0.055 28.36

112

45 1882.9 25318 1364.6 93.17 1851 10.21 28.36 27.83 39.32 29.39 10.82 10.5990 1714.7

25535 1385.2 85.31 1862 10.28 28.57 27.86 39.59 29.38 10.46 10.30

Ja = 20


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



ψ = 0.020 0 388.6

9568 196.0 22.19 705 3.88 27.79 27.60 40.43 29.32 7.09 7.2245 390.9 9574 196.2 22.17 705 3.88 27.82 27.62 40.38 29.32 7.10 7.2690 307.3 9571 195.7 17.49 703 3.88 28.00 27.78 40.61 29.32 7.12 7.32

225 328.8 9601 196.9 18.41 705 3.89 28.05 28.59 40.45 29.33 7.44 7.18270 360.1 9576 196.3 20.61 705 3.89 27.79 28.28 40.47 29.33 7.63 7.33ψ = 0.025

0 502.3 11820 299.0 28.58 870 4.79 27.85 27.65 40.45 29.32 7.36 7.4845 500.2 11319 274.4 28.52 834 4.59 27.77 27.56 40.40 29.32 7.11 7.3590 423.4 11616 287.7 23.74 851 4.69 28.22 28.05 40.63 29.33 7.52 7.68

225 462.2 11575 286.6 26.32 852 4.69 27.88 28.38 40.49 29.33 7.62 7.28270 448.4 11409 278.6 25.54 840 4.63 27.84 28.35 40.45 29.33 7.94 7.65ψ = 0.030

0 641.5 14112 425.4 36.08 1036 5.71 28.02 27.80 40.47 29.33 7.63 7.7745 623.8 13884 412.1 35.44 1021 5.63 27.95 27.70 40.53 29.32 7.38 7.6090 567.2 13899 411.4 31.52 1017 5.61 28.32 28.13 40.62 29.33 7.81 7.93

225 606.2 14090 424.7 34.38 1036 5.71 27.90 28.40 40.46 29.33 7.89 7.64270 588.7 14100 425.0 33.39 1036 5.71 27.97 28.51 40.53 29.34 8.30 8.05ψ = 0.035

0 737.3 15911 540.9 41.37 1169 6.44 28.01 27.80 40.44 29.33 7.90 8.0245 792.5 16421 576.0 44.63 1206 6.65 28.02 27.74 40.49 29.33 7.73 7.8990 766.0 16494 579.7 42.42 1207 6.66 28.27 28.02 40.53 29.34 8.10 8.24

225 700.0 16147 557.3 39.77 1187 6.54 27.97 28.48 40.55 29.34 8.19 7.93270 733.2 16420 575.8 41.38 1205 6.65 28.04 28.55 40.54 29.35 8.82 8.57

113

1360 7.50 28.10 27.87 40.58 29.34 8.22 8.35 45 890.4 1857 1360 7.50 28.22 27.90 40.69 29.34 8.03 8.22 90 870.5 18861 756.3 47.86 1376 7.60 28.51 28.24 40.68 29.34 8.22 8.36

225 831.8 18573 735.9 46.73 1362 7.51 28.16 28.68 40.60 29.35 8.73 8.40 270 850.8 18562 735.3 48.01 1361 7.51 28.13 28.64 40.62 29.36 9.19 8.87 ψ = 0.045

0 1040.6 20976 938.5 58.47 1537 8.48 28.18 27.94 40.62 29.34 8.47 8.60 45 999.1 20732 916.3 55.45 1518 8.37 28.23 27.91 40.52 29.34 8.35 8.52 90 987.5 21051 940.9 54.22 1534 8.47 28.63 28.40 40.79 29.35 8.60 8.72

225 1038.8 21228 961.9 58.05 1557 8.59 28.09 28.60 40.47 29.36 9.20 8.81 270 1023.5 21011 942.0 57.48 1541 8.50 28.13 28.66 40.57 29.37 9.65 9.26 ψ = 0.050

0 1197.9 23516 1177.4 66.94 1719 9.49 28.35 28.05 40.73 29.35 9.01 9.10 45 1137.5 23225 1149.2 63.40 1700 9.38 28.29 28.05 40.63 29.35 8.88 9.03 90 1187.7 23573 1179.5 64.93 1717 9.48 28.66 28.42 40.76 29.36 9.20 9.29

225 1172.2 23186 1145.7 66.05 1698 9.36 28.25 28.79 40.73 29.37 9.71 9.29 270 1155.1 23202 1146.6 64.90 1697 9.36 28.32 28.83 40.76 29.38 10.28 9.91

ψ = 0.040

0 886.6 18536 733.4

1 735.2 49.9650.14

Ja = 22


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



ψ = 0.020 0 427.3 9577 196.3 26.45 705 3.88 27.83 27.67 41.54 29.32 7.28 7.51 45 379.2 9611 197.1 23.21 705 3.89 28.16 27.98 41.72 29.32 7.29 7.51 90 333.4 9619 197.3 20.46 705 3.89 28.22 28.07 41.81 29.33 7.45 7.61

225 296.2 9565 196.1 18.56 706 3.89 27.67 28.13 41.55 29.33 7.94 7.59 270 402.8 9593 196.6 24.78 705 3.88 28.02 28.49 41.64 29.33 7.67 7.38

270 1011.5 21221 960.6 61.69 1555 8.58 28.16 28.63 41.67 29.37 9.89 9.53 ψ = 0.050

114

ψ = 0.025 0 517.5 11590 286.9 31.72 851 4.69 28.02 27.82 41.60 29.33 7.63 7.79 45 485.8 11603 287.3 29.63 851 4.69 28.12 27.93 41.63 29.33 7.55 7.72 90 465.8 11606 287.4 28.53 851 4.69 28.14 27.97 41.70 29.33 7.41 7.65

225 416.7 11559 286.1 25.94 851 4.69 27.79 28.25 41.58 29.34 8.25 7.93 270 461.9 11332 274.6 28.56 833 4.59 27.93 28.42 41.63 29.34 7.99 7.75 ψ = 0.030

0 643.7 14119 425.5 39.56 1036 5.71 28.11 27.94 41.72 29.33 7.92 8.07 45 654.6 14128 425.8 39.73 1036 5.71 28.17 27.96 41.60 29.33 7.78 7.94 90 589.7 13885 411.0 35.61 1017 5.61 28.23 27.99 41.60 29.33 7.71 7.94

225 569.4 14039 421.7 35.24 1033 5.69 27.86 28.29 41.57 29.34 8.44 8.04 270 587.4 14098 424.8 36.14 1036 5.71 27.96 28.49 41.59 29.34 8.29 8.05 ψ = 0.035

0 769.4 16704 594.9 46.79 1224 6.75 28.21 28.00 41.68 29.34 8.20 8.40 45 779.2 16446 576.7 47.47 1205 6.64 28.22 28.00 41.71 29.34 8.02 8.22 90 769.1 16449 576.8 46.87 1205 6.64 28.23 28.07 41.73 29.34 8.02 8.22

225 667.3 16148 558.1 41.42 1189 6.55 27.83 28.26 41.57 29.35 8.93 8.72 270 731.0 16151 557.3 45.01 1186 6.54 28.02 28.53 41.65 29.35 8.71 8.35 ψ = 0.040

0 892.2 18809 754.3 54.56 1378 7.60 28.21 27.99 41.75 29.35 8.60 8.72 45 928.6 18831 755.0 56.09 1377 7.60 28.35 28.09 41.72 29.34 8.43 8.55 90 903.2 18820 754.5 54.57 1377 7.60 28.31 28.11 41.69 29.34 8.37 8.55

225 804.7 18576 735.7 49.33 1361 7.50 28.22 28.69 41.80 29.36 9.39 9.02 270 874.1 18770 752.6 53.75 1378 7.60 28.03 28.52 41.65 29.36 9.27 8.93 ψ = 0.045

0 1028.7 20977 937.4 62.50 1535 8.47 28.29 27.94 41.74 29.35 8.81 8.94 45 1070.1 21010 939.1 64.72 1535 8.47 28.44 28.25 41.83 29.35 8.82 8.95 90 1034.2 20991 938.4 63.08 1535 8.47 28.32 28.14 41.83 29.35 8.79 8.92

225 937.7 20992 938.4 57.04 1535 8.47 28.34 28.79 41.81 29.37 9.75 9.32

29.36

0 1200.0 23223 1147.4 72.78 1696 9.36 28.43 28.22 41.86 9.26 9.34

115

0 9.28 9.37 9.93 10.20

45 1219.51199.1

232332323

1147.71147.7

73.7572.37

16961696

9.369.36

28.48 28.2828.46 28.20

41.8741.82

29.3629.36

9.27 9.3490

225 1116.1 23276 1149.4 67.48 1694 9.36 28.71 29.06 42.09 29.38 10.42270

1198.4

23445 1172.1 73.48 1718 9.47 28.20 28.72 41.78 29.38 10.62

Ja = 24

Angle° h (W/m2K) Re T (°C)We TS Power

(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)


(°C) sat, TS in P(TS in) P(TS out)

ψ = 0.020 0 335.8 9464 191.1 22.18 694 3.83 28.13 28.06 42.76

42.88 42.62 42.86 43.01

503.1 11852 299.8 33.35 869 4.79 28.11 28.09 42.79 42.80 42.73 42.92 42.78

650.9 14140 426.1 42.91 1035 5.71 28.25 28.20 42.85 42.86 42.73 43.02 42.88

779.3 16248 562.5 51.60 1189 6.56 28.28 28.19 42.94 42.92 42.77

29.33 7.48 7.7345 355.4 9621 197.3 23.48 704 3.89 28.25 28.06 29.33 7.52 7.7690 452.2 9319 186.2 30.48 687 3.79 27.69 27.73 29.33 7.78 7.52

225 298.1 9448 190.4 19.78 692 3.82 28.17 28.58 29.33 7.76 7.42270 288.6 9614 196.3 18.75 700 3.87 28.62 29.15 29.34

8.16 7.84

ψ = 0.025 0

29.33 7.73 7.93

45 449.2 11603 287.3 29.75 851 4.69 28.14 28.02 29.33 7.76 7.9590 484.8 11398 278.0 32.52 839 4.62 27.87 28.00 29.34 8.02 7.79

225 416.4 11609 287.6 27.83 851 4.69 28.12 28.54 29.34 8.05 7.69270 412.8 11610 287.5 27.20 851 4.69 28.19 28.66 29.34

8.33 8.05

ψ = 0.030 0

29.34 7.97 8.17

45 596.4 13876 410.6 39.50 1017 5.61 28.20 28.04 29.33 7.83 8.1090 646.8 13838 409.5 43.29 1018 5.61 27.91 28.00 29.34 8.23 8.03

225 565.5 14151 426.5 37.56 1035 5.71 28.31 28.76 29.35 8.52 8.18270 575.4 14133 425.9 38.13 1035 5.71 28.21 28.68 29.35

8.66 8.29

ψ = 0.035 0

29.34 8.19 8.41

45 772.0 16458 576.8 50.89 1204 6.64 28.32 28.20 29.34 8.25 8.4690 762.5 16427 575.9 50.46 1205 6.64 28.11 28.23 29.35 8.62 8.36

116

42.88 42.82

913.8 18830 754.8 60.32 1377 7.60 28.37 28.24 42.98 42.86 42.82 43.18 43.00

996.9 21014 938.9 65.20 1534 8.47 28.48 28.31 42.97 42.92 42.98 43.15 42.96

0 1196.0 23256 1148.5 77.93 1695 9.36 28.62 28.42 43.04 29.36 29.36 1 29.39 10.68 10.20 10.55

225 686.9 16481 577.9 44.84 1204 6.64 28.43 28.90 29.35 8.96 8.64270 728.0 16483 579.1 47.89 1207 6.66 28.25 28.73 29.36

9.14 8.82

ψ = 0.040 0

29.35 8.59 8.78

45 908.1 18827 754.7 59.53 1377 7.60 28.35 28.22 29.35 8.65 8.8390 855.0 18263 711.4 56.54 1338 7.38 28.17 28.32 29.35 8.90 8.75

225 803.6 18629 736.1 52.44 1355 7.49 28.73 29.18 29.36 9.36 9.03270 826.8 18546 732.9 54.99 1357 7.49 28.27 28.86 29.36

9.51 9.09

ψ = 0.045 0

29.35 8.99 9.17

45 1083.7 21272 962.8 70.98 1554 8.58 28.41 28.26 29.36 9.04 9.2190 1019.7 21249 961.8 67.60 1555 8.58 28.30 28.46 29.36 9.22 9.06

225 957.4 21356 966.7 62.06 1552 8.58 28.80 29.24 29.37 10.06 9.62270 999.9 20993 937.8 65.73 1534 8.46 28.41 28.90 29.38

10.20

9.80

ψ = 0.050 9.50 9.62

45 1226.7 23241 1148.6 80.36 1697 9.36 28.48 28.29 42.99 9.47 9.6190 1195.3

1117.8234782368

1174.21187.6

78.7272.04

17181719

9.489.50

28.3028.89

28.5629.33

42.8843.16

29.37 9.70 9.56225270

1168.1

23319 1155.7 76.77 1701 9.39 28.53 29.07 43.08 29.39 10.99

Ja = 26

Angle° h (W/m2K) Re T (°C)We TS Power

(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)


(°C) sat, TS in P(TS in) P(TS out)

ψ = 0.020 0 348.2 9105 177.0 24.90 668 3.78 28.08 27.73 43.91

44.09 43.90 44.02 44.01

29.33 7.45 7.7245 362.5 9622 197.3 25.91 704 3.79 28.26 28.16 29.34 7.61 7.8590 309.5 9569 195.7 22.29 703 3.89 27.95 27.72 29.33 7.66 7.93

225 302.0 9408 188.4 21.33 688 3.88 28.38 29.25 29.33 7.99 7.69270 311.5 9395 188.1 22.16 688 3.68 28.25 29.07 29.33 8.03 7.67

117

503.9 1161 35.87 851 4.69 28.19 27.80 43.95

43.84 43.93 44.13 43.95

605.0 1417 42.58 1035 5.62 28.45 28.06 44.04 44.10 44.09 44.15 44.15

767.4 1629 54.08 1189 6.64 28.53 28.09 44.13 43.98 44.16 44.11 44.14

909.1 1865 64.14 1358 7.50 28.66 28.25 44.29 44.02 44.13 44.19 44.18

0 1045.2 21082 72.91 1533 8.47 28.76 28.26 44.21 44.16 44.18 44.20 44.11

0 1201.3 23323 83.84 1693 9.36 28.89 28.39 44.34

ψ = 0.025 0

5 287.7 29.33 7.80 7.99

45 428.7 11742 294.0 30.25 860 4.74 28.22 27.91 29.33 7.71 7.9690 406.0 11615 287.7 28.82 851 4.69 28.21 27.85 29.33 7.82 8.14

225 456.3 11411 277.0 32.34 833 4.60 28.43 29.25 29.34 8.17 7.82270 469.0 11648 289.0 33.12 852 4.70 28.31 29.11 29.34

8.38 8.09

ψ = 0.030 0

1 427.1 29.35 7.96 8.22

45 576.4 13898 411.3 41.03 1016 5.71 28.34 28.02 29.34 7.88 8.1790 562.7 13909 411.6 39.79 1016 5.72 28.43 28.00 29.35 8.14 8.39

225 614.2 14210 429.1 43.27 1036 5.61 28.56 29.46 29.34 8.69 8.37270 600.2 13927 412.9 42.77 1018 5.61 28.37 29.17 29.33

8.64 8.24

ψ = 0.035 0

3 564.2 29.34 8.40 8.57

45 706.0 16189 557.7 49.63 1183 6.65 28.41 28.01 29.36 8.31 8.5190 705.4 16501 578.5 49.68 1203 6.65 28.56 28.13 29.35 8.30 8.59

225 757.7 16524 580.2 53.24 1205 6.53 28.55 29.44 29.34 9.01 8.60270 746.2 16521 579.9 52.50 1205 6.56 28.56 29.35 29.34

9.21 8.88

ψ = 0.040 0

1 738.3 29.35 8.67 8.87

45 848.1 18573 734.0 59.76 1357 7.60 28.42 28.02 29.35 8.59 8.8190 842.2 18891 757.3 58.73 1375 7.61 28.69 28.28 29.37 8.67 8.91

225 846.5 18642 737.6 59.37 1357 7.49 28.66 29.53 29.35 9.43 9.05270 878.2 18909 759.2 61.75 1378 7.50 28.62 29.37 29.36

9.67 9.24

ψ = 0.045 942.4 29.36 9.09 9.24

45 993.3 21071 942.3 69.46 1534 8.48 28.67 28.25 29.37 9.04 9.2690 1013.3 21069 941.7 70.75 1533 8.48 28.72 28.27 29.38 9.04 9.25

225 968.8 21077 942.9 68.01 1535 8.47 28.65 29.57 29.36 9.92 9.51270 1019.6 21063 942.6 71.59 1536 8.47 28.56 29.39 29.36

10.32 9.91

ψ = 0.050 1152.0 29.37 9.65 9.76

118

44.29 44.14 9.54 9.74

0 44.24 44.25

45 1165.5 23547 1176.0 81.87 1713 9.46 28.74 28.29 29.3729.36

9.64 9.8090 1185.2

225 1141.4 235502334

1176.61154.6

82.6179.56

17141696

9.479.37

28.7128.81

28.2529.64 29.38 10.56 10.11

270

1175.7

23591 1180.8 82.52 1717 9.48 28.71 29.54 29.39 11.09 10.64

Angle° h (W/m2K) Re


(°C) We TS Power

(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C) Tsat, TS in (°C) P(TS in) P(TS out)

ψ = 0.020 0 402.7 45.06

44.49 45.37 7.78 8.04

225 705 29.04

44.93 44.61 45.36 7.82 8.09

225 565.7 1178 29.06

45.08 44.84 45.39 8.20 8.42

225 646.3 1389 29.25

45.06 44.98 45.44 8.39 8.65

9592 196.7 31.11 705 3.89 27.96 28.49 29.34 8.13 7.8745 450.7 9503 194.7 35.38 706 3.89 27.11 26.69 29.33 7.24 7.4990 464.9 9661

441.0 9587 196.5 198.2 35.13

34.09 704 3.89

3.88 28.6427.93

28.1628.87

29.3445.04 29.32 7.98 7.63

270 510.5 9614 197.3 38.98 705 3.88 28.12 45.03

29.34 8.23 7.87ψ = 0.025

0 515.2 11835 299.5 39.51 870 4.79 27.95 28.47 29.34 8.25 8.0045 579.2 11759 298.1 45.68 874 4.80 27.15 26.76 29.33 7.42 7.6690 500.3 11670 289.0

6 296.9 37.7143.38

850866

4.694.77

28.6727.98

28.1828.87

29.3344.96 29.34 8.26 7.92

270 638.1 11846 299.5 48.64 869 4.79 28.10 44.98

29.35 8.49 8.18ψ = 0.030

0 607.4 13863 410.4 46.67 1017 5.61 28.06 28.65 29.35 8.46 8.1945 665.3 13801 408.3 51.52 1018 5.61 27.70 27.24 29.34 7.70 7.9990 649.4 14205 428.2

3 411.2 48.9548.92

10341017

5.715.61

28.7028.29

28.1929.25

29.3445.05 29.33 8.58 8.25

270 729.4 13691 399.3 55.50 1002 5.53 28.30 45.15

29.35 8.78 8.40ψ = 0.035

0 776.2 16427 575.8 59.31 1205 6.64 28.14 28.67 29.35 8.82 8.5845 811.5 16150 557.0 62.00 1185 6.54 28.06 27.59 29.34 8.12 8.3790 774.5 16539 579.8 58.24 1202 6.64 28.79 28.26 29.34

Ja = 28

119

225 800.4 16461 577.0 60.78 1204 6.64 28.34 29.19 270 863.6 16467 578.0 65.92 1206 6.65 28.25 29.13 9.29 9.00 ψ = 0.040

0 894.2 18532 732.5 68.59 1358 7.49 28.18 28.69 45.17 29.35 9.15 8.92 45 916.0 18541 732.4 69.91 1357 7.59 28.29 27.79 45.19 29.37 8.65 8.84 90 896.1 18670 737.9 66.77 1355 7.59 28.92 28.32 45.42 29.37 8.77 8.96

225 910.7 18573 733.9 69.37 1357 7.48 28.42 29.32 45.29 29.35 9.40 8.94 270 970.7 18818 754.2 74.19 1377 7.49 28.32 29.38 45.24 29.36 9.81 9.40 ψ = 0.045

0 1032.7 20973 937.2 78.79 1535 8.47 28.29 28.94 45.18 29.36 9.42 9.21 45 1057.8 21019 939.1 80.24 1534 8.47 28.51 28.03 45.31 29.37 8.93 9.12 90 1049.7 21146 945.3 77.93 1532 8.47 29.06 28.45 45.50 29.36 9.20 9.37

225 1071.2 21014 939.1 81.35 1534 8.47 28.48 29.39 45.29 29.35 9.90 9.45 270 1058.0 20981 937.4 80.35 1534 8.47 28.34 29.38 45.16 29.38 10.39 9.95 ψ = 0.050

0 1217.6 23515 1176.4 92.75 1718 9.47 28.43 29.05 45.30 29.39 9.92 9.75 45 1227.2 23428 1157.8 91.09 1692 9.48 29.29 29.44 45.73 29.40 10.08 10.23 90 1228.0 23387 1156.2 91.27 1694 9.48 29.07 28.55 45.53 29.37 9.72 9.89

225 1235.7 23519 1175.5 93.35 1715 9.36 28.54 29.51 45.26 29.37 10.73 10.26 270 1213.0 23516 1176.2 91.77 1717 9.37 28.45 29.40 45.21 29.37 11.24 10.81 ψ = 0.055

0 1404.0 25813 1415.9 106.60 1883 10.40 28.55 29.21 45.36 29.38 10.61 10.50 45 1426.1 26519 1457.1 99.94 1868 10.48 31.20 30.72 46.71 29.40 11.28 11.39 90 1430.6 25993 1426.8 106.21 1880 10.39 29.18 28.62 45.61 29.40 10.44 10.56

225 1369.7 26045 1440.8 103.26 1898 10.39 28.59 29.50 45.29 29.38 11.62 11.13 270 1356.0 25515 1383.9 102.99 1862 10.28 28.51 29.45 45.33 29.41 12.15 11.67

45.1545.15

29.3529.36

8.98 8.52

Ja = 30


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



270 1080.6 18742 750.3 88.46 1376 7.59 28.03 29.02 46.16 29.38 10.21 9.90

120

ψ = 0.020 0 520.7 9641 197.4 41.87 703 3.88 28.58 27.16 46.39 29.34 8.13 8.24 45 620.6 9614 196.9 50.51 704 3.88 28.29 27.85 46.31 29.34 7.97 8.17 90 615.1 9569 195.9 50.57 704 3.88 27.85 26.46 46.05 29.32 7.31 7.45

225 568.7 9572 196.0 46.82 704 3.88 27.88 29.00 46.10 29.34 8.30 8.05 270 636.5 9577 196.4 52.29 705 3.89 27.81 28.82 46.00 29.35 8.64 8.36 ψ = 0.025

0 698.6 11585 286.5 57.09 850 4.69 28.08 26.88 46.18 29.33 7.90 8.01 45 765.5 11612 287.2 62.05 850 4.69 28.31 27.84 46.26 29.34 8.19 8.36 90 758.3 11490 284.2 63.14 852 4.69 27.30 26.17 45.73 29.32 7.25 7.39

225 715.7 11563 286.0 59.07 851 4.69 27.88 28.98 46.16 29.35 8.57 8.30 270 741.2 11819 298.8 60.68 869 4.79 27.89 28.95 46.02 29.35 8.92 8.65 ψ = 0.030

0 810.8 13818 408.5 66.38 1017 5.60 27.87 26.67 46.00 29.34 7.97 8.07 45 875.6 13903 411.2 70.67 1015 5.60 28.45 28.02 46.32 29.34 8.43 8.57 90 898.2 13801 410.7 75.13 1026 5.64 27.12 26.00 45.64 29.32 7.36 7.48

225 821.3 13820 408.6 67.31 1017 5.60 27.89 28.99 46.04 29.35 8.84 8.55 270 844.9 13815 408.4 69.32 1017 5.60 27.86 28.92 46.02 29.36 9.19 8.89 ψ = 0.035

0 979.6 16298 570.6 81.23 1205 6.63 27.48 26.02 45.84 29.34 8.03 8.12 45 1017.9 16216 559.1 81.76 1184 6.53 28.49 28.03 46.28 29.35 8.66 8.80 90 1046.8 16242 568.6 87.34 1207 6.63 27.16 26.02 45.63 29.33 7.75 7.82

225 949.9 16139 556.4 77.57 1185 6.53 28.03 29.12 46.12 29.36 9.21 8.95 270 969.5 16376 573.4 79.23 1204 6.64 27.93 28.94 46.03 29.37 9.83 9.50 ψ = 0.040

0 1072.6 18819 753.8 87.26 1376 7.59 28.38 27.03 46.39 29.35 8.80 8.84 45 1108.2 18555 732.2 89.99 1355 7.48 28.46 28.02 46.44 29.36 9.05 9.15 90 1147.5 18321 723.3 95.94 1360 7.48 27.19 26.05 45.71 29.34 8.08 8.11

225 1051.5 18504 730.4 85.66 1356 7.48 28.16 29.23 46.20 29.37 9.67 9.38

8.48

ψ = 0.045

0 1197.6 21035 940.9 96.88 1535 28.48 27.29 46.39 29.36 9.04 9.04

121

46.42 9.56 9.60 5

29.37 29.18

46.42 46.56 46.69

5 29.35

46.35 46.65 46.61

3 29.28

46.48 46.73 46.62

45 1227.290 1291.9

211042103

946.0948.1

98.78106.00

15381551

8.498.54

28.6027.73

28.1026.59

29.3745.89 29.35 8.81 8.79

225 1171.5 21027 941.8 95.24 1538 8.49 28.30 46.30 29.38 10.23 9.92270 1193.5 21027 943.3 97.32 1542 8.50 28.15 46.20

29.39 10.68 10.35

ψ = 0.050

0 1364.4 23497 1172.3 109.66 1712 9.45 28.63 27.53 29.37 9.79 9.7445 1341.4 23583 1178.6 107.52 1714 9.47 28.81 28.34 29.38 10.12

10.0810.1210.1090 1343.8

225 1290.7 235862346

1179.01171.6

108.46105.14

17141714

9.479.46

28.8228.42

28.1529.50

29.3746.46 29.39 10.86 10.52

270 1275.7 23153 1142.2 103.99 1694 9.35 28.28 46.33

29.40 11.36 11.02ψ = 0.055

0 1409.4 25690 1406.3 115.06 1880 10.37 28.27 28.87 29.39 10.81 10.8645 1476.1 25451 1372.4 118.69 1849 10.22 28.85 28.34 29.39 10.73

10.7410.6810.6990 1493.3

225 1410.8 255772601

1386.01438.1

119.75114.42

18581898

10.2710.48

28.8528.53

28.2129.62

29.3946.49 29.41 11.77 11.41

270 1417.4 25829 1421.6 115.03 1891 10.43 28.27 46.24

29.42 12.55 12.15ψ = 0.06

0 1747.8 27507 1609.5 142.33 2009 11.09 28.45 29.10 29.41 12.24 12.4345 1711.3 27717 1626.2 137.51 2011 11.12 28.94 28.45 29.41 12.06

11.9211.9011.7790 1730.6

27661 1619.8 138.31 2007 11.09 28.92 28.37 29.41

Ja = 32


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



ψ = 0.020 0 885.4 5.71

4.71 7.88 8.09

704 689

9631 197.2 75.89 703 28.51 27.8827.78

47.4947.39

29.3429.34

8.00 8.2045 1019.990 1040.6

96369615

197.8197.1

87.9889.65

705704

28.283.89 28.22 27.62 47.29 29.33 8.17 8.38

225 826.3 9565 195.8 72.08 7.49 27.86 29.08 47.17 29.35 8.44 8.20270 1048.0 9376 187.8 91.04 6.64 28.00 29.54 47.24 29.35 8.39 8.17

122

11.21

3.88 8.01 8.23 3

850 850

6.59 8.46 8.31 8.49

5 1020 1015

10.37 11.19 8.68 8.83

0 9.46 10.37 9.45 9.19

ψ = 0.040 47.69 47.58 47.49 47.30 47.29 9.98 9.71

ψ = 0.045 47.75 47.61 47.68 47.32 47.35

ψ = 0.050 47.73

ψ = 0.025

0 978.2 11637 287.8 83.55 849 28.54 27.95

27.8747.4547.49

29.4329.34

8.17 8.3545 1090.090 1093.9

116941161

291.0287.2

93.8994.58

854849

28.4210.36 28.34 27.79 47.49 29.38 8.32 8.51

225 906.5 11543 285.2 78.89 8.35 27.82 28.98 47.09 29.36 8.63 8.38270 1103.1 11575 286.2 95.75 9.46

28.02 29.39 47.24 29.37 8.64 8.39

ψ = 0.030

0 1049.9 14139 424.9 90.06 1031 28.54 27.98

28.0047.5347.61

29.3529.36

8.45 8.6145 1184.890 1185.7

141811414

427.2425.7

101.79101.97

10341033

28.597.60 28.42 27.85 47.46 29.36 8.57 8.74

225 1019.5 13874 411.5 88.84 5.70 27.96 29.07 47.26 29.35 9.00 8.74270 1162.7 13831 408.5 100.78 4.69

28.05 29.37 47.24 29.34 8.97 8.71

ψ = 0.035

0 1152.9 16526 579.5 98.37 1203 28.69 28.03

28.71 28.06 47.5847.63

29.3929.42

8.77 8.8745 1279.090 1266.4

165241639

579.3570.0

109.26108.66

12031193 28.69 28.08 47.69 29.37 8.91 9.04

225 1124.8 16374 573.0 97.92 1203 27.98 29.07 47.2647.29

29.39 9.37 9.12270 1255.6 16394

573.8

108.91

1203

11.21

28.08

29.35

29.43

0 1218.6 18565 730.8 104.13 1350 9.46 28.77 28.05 29.37 9.04 9.1145 1360.8 18626 736.1 116.10 1356 7.46 28.69 27.97 29.36 8.96 9.0790 1365.7 18876 756.9 116.70 1376 5.69 28.57 27.95 29.34 9.30 9.38

225 1208.8 18469 728.8 105.35 1357 8.46 28.00 29.09 29.36 9.70 9.43270 1312.6 18755

751.0 113.83

1376

6.64

28.08

29.34

29.35

0 1360.9 21064 940.6 116.54 1531 4.68 28.79 28.10 29.35 9.45 9.5045 1465.7 20803 917.2 124.47 1512 4.69 28.81 28.10 29.34 9.13 9.2290 1479.5 21054 940.0 126.46 1531 3.88 28.75 28.02 29.34 9.46 9.52

225 1297.9 20929 934.3 112.24 1534 3.88 28.17 29.24 29.34 10.1210.61

9.8210.33270 1402.2 21179

957.6 121.95

1554

5.62

28.09

29.33

29.35

0 1520.1 23543 1175.6 130.41 1713 8.46 28.73 28.05 29.38 10.00 10.01

123

47.73 47.70 47.47 47.38

ψ = 0.055 47.78 47.73 47.74 47.52 47.46

ψ 47.97 47.85 48.10 48.29 47.64

45 1589.1 23562 1176.0 135.40 1711 6.63 28.87 28.15 29.36 9.73 9.7790 1603.3 23547 1175.5 136.96 1712 7.48 28.78 28.05 29.37 9.97 9.98

225 1440.8 23721 1199.3 125.09 1737 10.39 28.25 29.31 29.41 10.8411.39

10.5311.09270 1453.1 23414

1169.7 126.23

1717

9.58

28.14

29.32

29.39

0 1684.1 25827 1414.2 144.55 1878 4.69 28.77 28.08 29.35 10.74 10.6745 1653.3 25830 1412.7 140.52 1875 11.18 28.91 28.16 29.46 10.39 10.3890 1686.9 25842 1414.3 143.66 1876 3.80 28.89 28.14 29.34 10.67 10.65

225 1544.9 25728 1410.6 134.31 1883 6.63 28.27 29.33 29.36 11.7312.42

11.4012.11270

= 0.06 1521.1 25700

1407.7 131.94

1882

5.60

28.25

29.37

29.35

0 2067.0 27970 1652.9 175.89 2024 8.57 29.13 28.42 29.38 12.70 12.4745 2042.7 27974 1654.6 173.47 2027 9.47 29.05 28.37 29.40 13.02 12.7790 2076.3 28062 1660.4 175.98 2026 10.38 29.34 28.54 29.42 13.31 13.00

225 1855.4 28018 1654.2 158.34 2021 7.59 29.39 30.29 29.37 14.4614.75

14.0114.34270 1760.8

27914 1658.0 152.83 2039 11.25 28.42 29.59 29.46

Ja = 34


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



ψ = 0.020 0 700.3 5.63

6.58 8.32 8.49

704 705

4.61 10.70 8.36 8.49

2

9631 197.3 63.73 703 28.45 27.9727.54

48.6048.78

29.3529.35

8.61 8.7045 1066.890 1150.1

94699557

190.4195.7

97.05105.55

690704

28.637.59 27.75 27.30 48.07 29.36 8.19 8.31

225 1071.7 9617 197.1 97.85 3.81 28.26 29.81 48.48 29.34 8.95 8.74270 1082.9 9562 196.0 99.67 4.59

27.70 29.27 48.08 29.34 9.08 8.85

ψ = 0.025

0 862.7 11459 279.1 73.61 836 28.53 28.00

27.5247.4248.64

29.3529.41

8.84 8.9145 1158.690 1276.2

113911157

275.8286.2

105.31117.34

831850

28.513.88 27.97 27.51 48.33 29.34 8.47 8.55

124

850 878 9.59 9.32

ψ = 0.030 6.55 8.65 8.77

3 29.45 29.59

48.92 48.63 8.91 8.97

6 29.87 30.00

49.12 48.58 9.15 9.17

0 29.97 29.74

49.13 48.76

9 29.66 29.65

49.23 48.88

0 225 1479.9 23220 1155.0 137.33 1711 10.46 27.76 29.25 270 1505.9 23461 1168.9 137.62 1710 8.35 28.60 29.71 48.84 29.37 12.15 11.87

225 1118.1 11591 286.8 102.78 8.359.44

28.12 29.5727.83 29.24

48.4748.28

29.3729.38

9.18 8.97270 1134.3 11929

304.6

104.79

0 1175.3 14198 427.4 106.29 1032 28.77 28.25 48.80

48.61 29.36 9.11 9.18

45 1233.690 1348.5

139801383

415.7408.9

112.32123.81

10211016

7.488.45

28.4527.99

27.5827.53

29.3648.32 29.37 8.62 8.70

225 1190.9 14110 424.8 109.16 1035 4.69 28.14 48.43 29.34 9.51 9.31270 1188.7 14144 425.9 108.39 1034 5.60 28.37 48.56

29.35 10.16 9.90

ψ = 0.035

0 1312.4 16287 561.5 118.46 1182 10.73 28.93 28.40 29.41 9.58 9.5945 1387.190 1451.4

163311621

567.2560.5

126.24132.30

11921187

3.884.61

28.4828.24

27.4827.74

29.3548.43 29.35 9.11 9.12

225 1288.2 16774 596.9 117.54 1221 9.50 28.71 48.91 29.38 10.25 10.03270 1250.1 16528 579.4 114.09 1202 10.38 28.75 48.96

29.39 10.73 10.47

ψ = 0.040

0 1416.2 18971 760.5 127.99 1373 7.59 29.11 28.61 29.37 9.87 9.8545 1469.990 1509.3

188441855

755.1732.4

133.49137.22

13761356

8.469.44

28.4728.39

27.5027.84

29.3848.52 29.39 9.45 9.44

225 1328.0 18641 736.6 120.20 1355 5.70 28.80 48.84 29.36 10.54 10.30270 1300.2 18327 713.8 118.27 1337 6.53 28.54 48.69

29.37 10.84 10.57

ψ = 0.045

0 1486.9 21147 944.3 133.92 1529 10.47 29.18 28.67 29.40 10.28

9.73 10.239.73 45 1566.8

90 1612.8 207742098

915.4936.5

141.72147.05

15121532

8.469.44

28.7328.51

27.7927.98

29.3848.70 29.41 9.89 9.87

225 1400.3 20944 934.6 128.16 1533 10.30 28.29 48.56 29.40 10.45 10.19270 1420.8 21013 938.3 129.68 1532 8.46 28.55 48.76

29.38 11.37 11.10

ψ = 0.050

0 1601.7 23652 1179.3 143.72 1707 8.46 29.36 28.78 29.38 10.89

10.4110.7710.3745 1689.0

90 1733.8 235072361

1171.51183.5

153.31158.09

17091720

8.458.46

28.7828.64

27.9328.04

29.3748.8348.30

29.40 10.4229.41 10.79 10.52

10.33

125

ψ = 0.055 0 1716.4 25833 1405.0 154.42 1861 8.46 29.49 28.85 49.41 29.40 11.58 11.44 45 1803.0 25939 1422.2 162.39 1879 9.44 29.08 28.22 49.02 29.38 11.27 11.19 90 1851.5 25822 1415.0 168.06 1880 9.44 28.68 28.10 48.78 29.39 11.12 10.98

225 1574.5 25626 1415.3 148.01 1903 9.43 27.17 28.73 47.99 29.39 11.69 11.41 270 1557.2 25477 1406.6 147.40 1905 9.50 26.65 28.64 47.61 29.38 12.19 11.95 ψ = 0.057

0 1869.7 26971 1528.2 167.98 1937 10.34 29.71 29.18 49.61 29.41 12.56 12.31 45 1890.2 26751 1511.7 170.16 1936 10.47 29.14 28.38 49.08 29.40 12.05 11.86 90 1966.0 26729 1514.2 177.51 1943 10.66 28.80 28.12 48.80 29.43 11.97 11.77

225 1643.4 26071 1466.3 153.69 1939 7.49 27.07 28.52 47.78 29.38 13.08 12.74 270 1638.1 26628 1506.6 149.70 1942 9.43 28.55 29.56 48.79 29.39 14.89 14.52

Ja = 36


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



ψ = 0.020 0 1208.6 9428 190.6 117.82 696 3.88 27.63 25.94 49.21 29.36 7.82 7.88 45 1413.8 9591 196.5 136.93 704 4.80 28.04 26.96 49.49 29.35 8.11 8.20 90 1504.4 9570 196.7 146.88 708 6.64 27.48 26.30 49.10 29.37 7.93 8.00

225 962.1 9650 197.8 92.41 704 5.71 28.57 32.45 49.84 29.36 8.97 8.82 270 1038.8 9441 193.4 103.13 707 3.88 26.54 31.21 48.52 29.35 8.12 7.96 ψ = 0.025

0 1302.9 11574 286.4 126.34 851 9.43 27.96 26.53 49.43 29.40 8.07 8.12 45 1464.9 11402 277.9 141.49 838 7.51 27.94 26.92 49.33 29.38 8.16 8.16 90 1553.7 11562 287.3 152.16 856 10.38 27.44 26.32 49.13 29.41 7.94 8.02

225 1121.8 11878 300.6 108.47 869 3.88 28.29 31.24 49.70 29.34 8.98 8.79 270 1137.2 11458 283.4 112.06 853 8.56 27.00 31.02 48.82 29.39 8.50 8.32

ψ = 0.030 0 1379.4 13793 408.0 134.07 1018 5.60 27.64 26.31 49.16 29.35 8.15 8.17

126

45 1521.8 13805 408.5 148.18 1018 6.64 27.71 26.82 49.27 29.36 8.25 8.28 90 1598.9 13759 407.2 156.65 1019 7.59 27.37 26.32 49.07 29.38 8.15 8.16

225 1214.5 14131 425.5 117.14 1034 8.57 28.28 30.88 49.64 29.39 9.34 9.14 270 1204.7 13713 405.4 118.76 1019 4.69 27.14 30.74 48.97 29.35 8.96 8.79 ψ = 0.035

0 1478.2 16176 557.7 142.53 1184 9.45 28.25 27.05 49.60 29.40 8.78 8.78 45 1610.3 16313 571.1 156.94 1205 10.39 27.58 26.62 49.16 29.42 8.47 8.48 90 1666.3 16285 570.5 163.16 1207 5.61 27.34 26.30 49.02 29.34 8.43 8.41

225 1304.5 16447 576.2 125.99 1203 4.69 28.30 30.61 49.69 29.34 9.79 9.57 270 1291.7 16315 571.5 125.96 1206 3.83 27.54 30.70 49.13 29.33 9.56 9.40 ψ = 0.040

0 1593.8 18801 753.2 154.49 1376 9.45 28.27 27.20 49.73 29.37 9.10 9.06 45 1692.0 18657 747.7 164.66 1380 10.50 27.49 26.62 49.03 29.39 8.80 8.76 90 1729.2 18338 724.1 169.63 1360 6.53 27.26 26.30 48.98 29.35 8.61 8.61

225 1384.8 18639 738.3 133.12 1360 7.59 28.54 30.63 49.82 29.36 10.40 10.19 270 1383.3 18708 749.3 134.63 1378 8.46 27.80 30.66 49.36 29.36 10.18 10.00 ψ = 0.045

0 1667.0 20935 935.0 161.66 1535 5.61 28.16 27.18 49.63 29.34 9.44 9.36 45 1773.2 20758 927.0 173.50 1538 4.62 27.34 26.54 49.01 29.34 9.06 9.02 90 1805.3 20726 925.6 177.34 1539 3.88 27.19 26.30 48.94 29.34 9.04 8.98

225 1476.8 21367 965.4 141.95 1548 6.63 29.04 30.98 50.32 29.34 11.11 10.90 270 1465.3 21153 956.6 142.51 1555 7.59 27.95 30.34 49.48 29.35 10.87 10.68 ψ = 0.050

0 1780.1 23283 1160.6 174.25 1715 4.71 27.81 26.97 49.49 29.33 9.80 9.63 45 1850.5 23480 1187.6 181.56 1743 5.61 27.22 26.38 48.95 29.34 9.63 9.53 90 1898.4 23113 1151.9 186.67 1718 10.27 27.12 26.27 48.90 29.38 9.46 9.35

225 1584.1 23474 1168.1 152.21 1707 9.58 28.78 30.37 50.06 29.37 11.42 11.17 1518.5

49 25 10 65 10 46 0

26.09

270 23295 1161.1 148.38 1714 3.90

27.87 30.11 49.51 29.33 11.46 11.26ψ = 0.055

.

. .0 1904.8

45 1953.5 258592513

1433.31361.2

185.43192.42

19071867

10.325.61

27.7027.15

26.8926.36

29.3848.97 29.34 10.28 10.11

90 1979.9 25234 1374.6 195.10 1878 6.64 27.02 48.84 29.34 10.18 10.00

127

29.78 29.65

225 1696.2 25731 1409.4 163.43 1881 7.48 28.37 49.71 29.35 12.13 11.87270

1605.8

25561 1401.6 157.27 1887 8.46 27.62 49.30 29.36 12.41 12.16

Ja = 38

Angle° h (W/m2K) Re


(°C) Tsat, TS in (°C) P(TS in) P(TS out) We TS Power

(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)

0 705

705 706 705 706 8.86 8.73

ψ = 0.025 833 851 869 870 834 9.06 8.94

ψ = 0.030 1039 1017 1017 1035 1037 9.56 9.42

ψ = 0.035 1205 1204 1186 1205 1206 9.95 9.82

1351.2 9584 196.5 137.79 4.59 27.88 27.39 50.46 29.35 8.60 8.7545 1563.7 9584 196.5 159.45 6.64 27.88 27.32 50.46 29.35 8.55 8.6690 1607.9 9627 197.9 163.95 7.60 28.08 27.41 50.66 29.36 8.55 8.66

225 1429.0 9586 196.6 146.14 3.89 27.8727.

31.0636 30.46

50.5250.09

29.3529.35

8.81 8.69270 1422.1 9530

195.3

145.97

3.89

0 1428.7 11382 275.9 145.15 10.38 28.32 27.67 50.81 29.40 8.64 8.7245 1577.9 11601 287.2 161.04 10.71 28.14 27.59 50.74 29.42 8.73 8.8190 1619.4 11876 300.6 164.72 3.89 28.25 27.74 50.78 29.35 8.67 8.75

225 1448.6 11856 300.1 147.78 8.46 28.10 30.8627.36 30.25

50.6950.20

29.3729.38

9.17 9.05270 1462.2 11261

272.8

150.83

9.40

0 1545.6 14124 426.7 157.96 6.64 27.90 27.30 50.53 29.36 8.75 8.8145 1626.9 13877 410.6 165.87 7.59 28.20 27.64 50.78 29.36 8.82 8.8790 1716.1 13885 410.9 174.73 8.47 28.24 27.69 50.79 29.37 8.89 8.95

225 1501.1 14111 425.1 152.89 4.69 28.10 30.6627.34 29.84

50.6650.20

29.3529.35

9.35 9.25270 1508.2 13998

421.6

155.73

5.61

0 1649.0 16409 575.0 168.43 4.59 28.05 27.35 50.66 29.36 9.00 9.0545 1704.4 16428 575.8 173.15 5.71 28.15 27.51 50.65 29.36 9.15 9.1790 1762.4 16144 556.9 179.51 6.64 27.99 27.47 50.55 29.37 9.06 9.06

225 1568.0 16413 575.3 159.77 10.72 28.05 30.3527.39 29.64

50.6250.22

29.4129.38

9.81 9.68270 1553.5 16291 570.7 160.17 9.44

ψ = 0.020

128

ψ = 0.040 1378 1377 1358 1378 1380 29.40 10.47 10.31

ψ = 0.045 1534 1535 1554 1556 1556

ψ = 0.050 9.45

3 29.72 29.51

50.88 50.96

29.56 29.42

51.04 51.01

29.54 29.35

0 1715.8 18778 752.7 174.69 4.80 28.11 27.49 50.65 29.36 9.37 9.3745 1791.8 18807 753.7 182.64 3.89 28.27 27.62 50.84 29.35 9.42 9.3990 1815.7 18490 730.5 185.10 7.59 28.01 27.50 50.58 29.38 9.28 9.27

225 1629.5 18753 751.4 166.35 10.39 28.0027.42

30.0429.49

50.6150.21

29.42 9.96 9.80270 1613.9 18640

746.8

166.09

9.45

0 1803.2 20916 933.7 184.33 6.64 28.11 27.50 50.75 29.37 9.70 9.7045 1861.9 20971 936.9 189.04 7.59 28.30 27.63 50.78 29.37 9.83 9.7990 1907.5 21157 956.5 195.00 9.45 27.99 27.49 50.63 29.39 9.76 9.70

225 1695.1 21164 957.7 173.55 10.698.58

27.9427.62

29.8729.51

50.6150.37

29.43 10.5729.38 10.86 10.71

10.41270 1702.9 21074

952.7

175.00

0 1888.5 23263 1154.1 192.56 1704 28.20 27.62 50.78

50.9229.40 10.34

10.4010.2610.3045 1926.9

90 1994.1 232102332

1146.11162.2

195.69203.32

16951713

9.3610.39

28.4328.01

27.8627.50

29.3850.59 29.42 10.34 10.21

225 1774.9 23324 1163.5 181.94 1715 7.59 27.91 50.61 29.38 11.18 11.01270 1740.9 23265 1160.0 178.99 1716 8.57 27.71 50.47

29.39 11.69 11.52

ψ = 0.055

0 2023.2 25728 1409.5 205.94 1881 4.80 28.34 27.79 29.36 11.29

11.2211.1311.0645 2040.0

90 2108.1 25634 1397.9

1390.4 207.55214.89

18721870

5.716.64

28.4328.26

27.8727.66

29.3625543 50.83 29.37 11.14 10.97

225 1893.3 25757 1418.9 193.56 1894 10.66 27.91 50.55 29.44 12.19 11.97270 1824.4 25606 1404.2 187.38 1886 3.89 27.78 50.52

29.35 12.77 12.55

ψ = 0.057

0 2144.3 26600 1504.2 218.21 1941 9.45 28.50 27.88 29.39 12.30

12.0212.0611.7545 2122.3

90 2166.7 26468 1489.5

1502.9 215.80220.54

19321943

10.4410.69

28.4928.32

27.8927.75

29.4126565 50.86 29.43 11.77 11.51

225 1934.7 26384 1487.9 197.83 1939 7.59 27.96 50.61 29.37 12.91 12.68270 1855.7 26274 1478.1 190.56 1935 8.58 27.80 50.54 29.38 13.69 13.47

Ja = 40

129


(°C) Tsat, TS in (°C) P(TS in) Angle° h

(W/m2K) Re We TS Power (W)

mdot'' (kg/m2s)

Flow Rate (L/min)

TTS in (°C)

TTS out (°C) P(TS out)

0 711

704 704

9.35 27 79 51.87 29.40 9.08 9.13 5

5.70 7.50 4.69

35.3 16382 573.7 207.11 1204 10.25 3.92

27.79 28.34

21268 961.4 226.52 1551 3.89 28 53 28.13

26.80 28.13 28.18

3 28.03

0 2225.6 25347 1382.4 240.56 1879 3.88 27.33 26.62 28.23

1675.0 9716 201.0 178.70 4.79 28.33 27.83 51.95 29.37 9.03 9.0845 1873.7 9574 196.1 200.97 5.65 27.88 27.26 51.63 29.37 8.73 8.7790 1730.8 9595 196.5 184.79 3.88

28.11 30.74 51.75 29.36 9.18 9.02

ψ = 0.025

.

225 1775.8270 1963.1

116111156

287.3286.1

189.23210.50

850851

28.2810.71

27.89 27.26 51.64 29.45 8.76 8.79

ψ = 0.030

0 1869.4 14109 424.8 199.69 1035 28.12 27.52 51.78 29.37 9.21 9.2445 2006.3 14068 423.4 215.18 1035 27.88 27.37 51.63 29.38 9.06 9.0890 1834.6 14095 424.2 196.57 1034 28.07

30.08 51.79

29.36

9.61

9.46

ψ = 0.035 19

225 27.95 27.29 51.64 29.43 9.33 9.32270 2090.2 16224 561.9 223.74 1190 28.09

27.52 51.80 29.36 9.44 9.40

ψ = 0.040

0 2002.7 18481 731.4 215.37 1361 6.64 27.20 51.60 29.36 9.57 9.5290 2132.7 18547 732.5 227.77 1356 8.46 27.81

51.98 29.37

9.87

9.83

ψ = 0.045 .

45 2131.4 27.92 52.06 29.35 10.36 10.27

225 1935.5 20912 933.2 207.56 1534 9.44 29.54

51.87 29.37 10.88 10.68ψ = 0.050

0 2128.9 23162 1153.4 230.00 1715 7.59 27.40 51.32 29.37 10.09 9.9745 2186.6 23199 1141.6 232.07 1688 8.56 28.72 52.22 29.38 10.90

29.39 10.70 10.55 10.77

90 2249.4 232602314

1145.61141.4

239.16210.79

16881694

9.325.60

28.9128.25

52.45225 1981.8 29.49 51.81 29.36 11.57 11.36270 1945.3 23344 1164.0 209.50 1714 6.63 29.43

51.88

29.36

12.02

11.81

ψ = 0.055 51.26 29.35 10.76 10.59

45 2265.7 25631 1391.7 241.22 1862 4.69 28.85 52.43 29.35 11.66 11.47

ψ = 0.020

130

11.17 8

11.58 12.70 11.84

7

90 2295.7225 2074.9

259182579

1432.11416.6

245.54221.80

18981886

5.7010.29

28.2228.38

27.4729.63

51.9052.05

29.36 10.9529.40 12.74 12.49

270 2022.4 25392 1373.7 216.92 1858 10.64 28.29 29.64 52.04 29.42 13.25 13.00 ψ = 0.057

0 2335.4 26205 1478.9 253.69 1945 8.46 27.23 26.54 51.29 29.38 11.3145 2338.8 26521 1489.2 248.90 1925 9.33 28.91 28.24 52.48 29.39 12.4290 2343.6

225 2165.5 264752657

1497.01502.3

250.69231.39

19441941

10.476.56

28.0528.46

27.3329.68

51.7352.12

29.39 11.5629.36 14.14 13.84

270 2083.4

26637 1508.2 223.69 1944 7.48 28.51 29.73 52.29 29.37 14.37 14.08

High ∆Tsub Test Ja = 32



ψ = 0.020 0 927.3 25.17

25.24 23.07 27.88 7.95 7.85

25.29 23.25 23.00 27.91 8.24 8.15

9 ψ = 0.030

0 1129.2 13488 398.7 103.29 1023 6.63 25.62 25.14 45.88 29.32 7.86 7.97 45 1334.2 13765 414.5 121.51 1042 7.59 25.77 23.49 45.94 29.33 6.96 6.94

9370 192.0 84.48 709 4.69 25.79 45.97 29.33 7.57 7.7045 1084.2 9376 192.1 98.38 708 6.57 25.89 45.98 29.34 7.16 7.2890 1165.9 9347 191.5 106.41 709 7.59 25.63 45.84 29.35

29.33 6.66 6.72

225 695.5270 1064.7

93759365

192.5191.9

63.6997.21

711709

3.883.88

25.6525.77

45.9228.14

45.99 29.33 8.02 7.94

ψ = 0.025

0 1001.4 11303 279.6 91.09 856 10.41 25.74 45.88 29.38 7.74 7.8245 1229.5 11504 290.8 112.75 875 10.67 25.37 45.68 29.40 6.67 6.6790 1266.4 11483 290.2 116.64 875 3.88 25.22 45.62 29.32

29.35 6.49 6.52

225 812.6270 1114.9

115681168

292.7298.8

74.18101.95

875884

8.469.43

25.7925.82

46.0127.95

46.06

29.36

8.37

8.27


(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)

131

90 1338.8 13614 410.1 124.39 1045 8.46 24.74 22.79 45.32 29.34 6.59 6.60 225 957.2 13761 414.5 87.27 1042 4.79 25.72 27.60 45.90 29.31 8.52 8.44 270 1181.4 13851 418.8 107.29 1045 5.70 25.97 27.79 46.08 29.32 8.72 8.59 ψ = 0.035

0 1255.2 15819 548.5 114.51 1200 10.71 25.60 25.10 45.80 29.39 8.27 8.31 45 1415.7 15977 559.6 129.25 1212 3.88 25.59 23.66 45.80 29.31 7.26 7.23 90 1434.4 15957 558.8 131.28 1212 4.79 25.50 23.80 45.76 29.31 7.50 7.50

225 1082.9 15986 560.1 99.32 1212 9.44 25.61 27.30 45.92 29.35 8.74 8.61 270 1260.3 15799 544.8 114.51 1192 10.25 25.99 27.69 46.11 29.36 9.05 8.92 ψ = 0.040

0 1369.2 18310 733.8 124.97 1386 7.50 25.73 25.25 45.94 29.33 8.61 8.65 45 1493.7 18266 732.0 136.64 1387 8.45 25.51 23.73 45.77 29.34 7.55 7.48 90 1536.7 18051 715.0 141.00 1371 9.33 25.49 24.03 45.81 29.35 7.88 7.82

225 1206.0 18524 752.6 110.62 1406 6.63 25.54 27.10 45.85 29.31 9.32 9.19 270 1348.5 18123 716.0 122.78 1365 6.63 26.11 27.66 46.27 29.33 9.51 9.38 ψ = 0.045

0 1474.6 20420 911.5 134.31 1544 4.79 25.85 25.35 46.02 29.34 8.83 8.81 45 1599.1 20376 909.7 146.24 1545 5.71 25.64 23.93 45.89 29.35 8.02 7.92 90 1628.5 20376 909.1 148.86 1544 10.41 25.69 24.34 45.93 29.37 8.29 8.22

225 1315.0 20679 935.4 119.93 1565 10.73 25.78 27.19 45.98 29.39 9.56 9.42 270 1409.7 20762 939.6 127.67 1564 3.89 26.11 27.50 46.17 29.34 10.26 10.12 ψ = 0.050

0 1626.5 22817 1135.8 147.69 1721 9.42 26.03 25.52 46.14 29.38 9.52 9.44 45 1729.1 22746 1134.2 157.99 1725 10.34 25.59 24.08 45.82 29.40 8.66 8.49 90 1745.2 22516 1109.2 159.00 1704 6.64 25.77 24.53 45.94 29.35 8.98 8.85

225 1436.8 22720 1129.7 131.39 1720 7.70 25.75 27.15 45.99 29.36 10.23 10.05 270 1488.9 23165 1170.4 135.60 1746 8.57 26.05 27.43 46.22 29.36 10.93 10.75 ψ = 0.055

0 1753.0 25195 1385.0 159.09 1900 4.84 26.02 25.49 46.12 29.34 10.35 10.21

45 1849.6 24734 1339.0 168.50 1873 5.73 25.73 24.35 45.91 29.35 9.47 9.25 90 1876.5 25212 1384.9 169.78 1898 6.53 26.15 25.02 46.19 29.36 10.02 9.82

225 1558.7 24989 1364.3 141.95 1888 10.75 25.90 27.17 46.06 29.41 11.19 10.95

132

270 1598.7 25306 1396.9 144.76 1908 3.88 26.04 27.34 46.09 29.34 11.91 11.73 ψ = 0.057

0 1815.7 25882 1457.2 164.23 1945 9.57 26.29 25.72 46.32 29.39 11.34 11.11 45 2004.0 25765 1457.1 183.50 1957 10.46 25.48 24.30 45.75 29.41 11.07 10.69 90 1984.5 26061 1476.0 178.48 1956 10.68 26.39 25.25 46.30 29.42 10.93 10.66

225 1646.0 26009 1476.2 150.28 1962 7.48 26.00 27.23 46.22 29.36 11.81 11.59 270 1626.9 25791 1453.4 148.00 1949 8.57 25.89 27.05 46.03 29.38 12.53 12.28

Boiling Curve Data

∆Tsub = °C

Ja h (W/m2K) Re We TS Power

(W) mdot''

(kg/m2s) Flow Rate


TTS out (°C)



40.0 1579.2 11540 292.3 876.57 174 25.49 27.52 8.32 8.16 49.92 4.80 29.34 38.2 1374.0 11782 304.6 894.88 146 25.49 27.23 8.25 8.11 48.97 4.90 29.34 36.1 1214.0 11844 307.9 899.80 123 25.48 27.09 8.35 8.20 47.89 4.92 29.34 34.0 1075.4 11281 279.4 857.15 104 25.47 26.93 8.36 8.22 46.83 4.69 29.34 32.2 1011.2 11284 279.7 858.06 93 25.41 26.81 8.21 8.06 45.85 4.69 29.34 29.7 843.0 11294 279.7 856.90 73 25.58 27.59 8.39 8.24 44.64 4.69 29.34 27.9 762.2 11295 279.6 856.45 62 25.62 27.42 8.48 8.33 43.76 4.69 29.34 26.0 796.0 11309 279.9 856.20 62 25.73 27.14 8.39 8.24 42.84 4.69 29.34 23.8 679.5 11408 285.1 864.55 49 25.66 26.94 8.46 8.30 41.66 4.73 29.34 22.0 594.1 11306 279.9 856.32 40 25.70 26.78 8.33 8.20 40.72 4.69 29.34 20.2 538.3 11246 276.9 851.68 34 25.71 26.77 8.41 8.25 39.79 4.66 29.34 18.0 509.6 11845 307.2 897.00 30 25.72 26.58 8.45 8.27 38.68 4.91 29.34 16.0

461.6 1165 18 25. 25.96

496.7 12078 319.1 913.95893.64

27 25.77 26.57 8.45 8.31 37.63 5.01 29.3413.8 464.3 11805 305.0 23 25.74 26.55

26.428.45 8.31

8.20 36.5235.30

4.895.67

29.3429.34 11.5

9.7 451.8 13671 409.4

2 297.6 1035.96883.95

20 25.6725.58

8.3326.36 8.30 8.19 34.37 4.84 29.34

7.5 607.9 19651 846.8 1491.22 21 56 26.30 8.48 8.33 33.22 8.16 29.346.3 662.4 11830 305.6 892.98 20 26.55 8.57 8.42 32.64 4.89 29.35

133

25.85 25.82 25.93

3.4 637.2 11814 305.1 893.03 15 26.54 8.64 8.45 31.13 4.89 29.351.9 719.5 11840 306.5 895.38 15 26.50 8.69 8.49 30.36 4.90 29.35

0.09 672.7 11825 305.4 892.85 11 26.62 8.59 8.45 29.39 4.89 29.35

Ja h (W/m2K) Re mdot''

(kg/m2s) We TS Power (W)

Flow Rate (L/min)

TTS in (°C)

TTS out (°C)



39.8 13324 1592.3 378.9 977.31 170 28.11 29.85 9.96 9.80 51.72 5.39 29.3738.1 12108

12667 12042 29.13 9.65 9.49 4.89

853.4 705.8 660.2 590.6 442.7 27 28.59 9.57 9.46 5.02

15.8 13.4 12.2 10.1

8 -1

1361.3 312.8 887.59 139 28.16 29.77 9.89 9.71 50.78 4.89 29.3736.2 1235.7 342.5 929.26

887.70 120101

28.1027.73

29.58 9.82 9.67 49.6948.37

5.12 29.3729.37 34.3

32.4 1078.9963.8

310.713813 407.8 1015.07 85 27.97 29.27 9.69 9.55 47.46 5.59 29.37

29.9 12083 312.4 889.17 70 27.86 29.15 9.61 9.45 46.03 4.90 29.3727.4 12076 312.1 889.08 53 27.83 28.96 9.44 9.29 44.60 4.90 29.3625.6 11879 302.0 874.49 47 27.84 28.71 9.59 9.46 43.61 4.82 29.3724.1 12141 315.4

328.4893.35911.82

40 27.8727.86

28.70 9.56 9.44 42.7641.27

4.92 29.3629.37 21.4

17.912389

308.5 12058 311.3 887.95 16 27.81 28.48 9.50 9.39 39.33 4.89 29.36232.4 12063 311.8 889.22 11 27.74 28.50 9.49 9.39 38.14 4.90 29.36186.9 13605 396.5 1002.50 8 27.77 29.29 9.68 9.61 36.80 5.52 29.37330.6 12315 324.3 905.33 12 27.94 29.39 9.82 9.71 36.15 4.99 29.37205.0 17112

1463625.8456.9

1257.381072.45

7 27.98 29.4028.20 29.10

9.909.99

9.789.89

35.0233.09

6.935.91

29.3729.37 6.6 -51.9

4.63 -228.6 20880 926.4 1522.75 -4 28.55 29.10 10.15 10.04 32.01 8.41 29.38

∆Tsub = °C

134

Galloway, J.E., and Mudawar, I., 1993, “CHF Mechanism in Flow Boiling from a Short Heated Wall – I. Examination of Near-Wall Conditions with the Aid of

LIST OF REFERENCES

Baranek, P., Marsden, K.C., and Best, F.R., 1994, “Zero-G Annular Flow and 1-G Stratified Flow Single Component Two-Phase Condensation Modeling,” Proceedings of the ASME 1994 WAM, pp. 1137-1142.

Bower, J.S., Klausner, J.F., Sathyanarayan, S., 2002, “High Heat Flux, Gravity

Independent, Two-Phase Heat Exchangers for Spacecraft Thermal Management,” SAE Journal of Aerospace, Paper 2002-01-3196, pp. 747-755

Brusstar, M.J., Merte, H., Keller, R.B., and Kirby, B.J., 1997, “Effects of Heater Surface Orientation on the Critical Heat Flux – I.,” International Journal of Heat and Mass Transfer, Vol. 40, No. 17, pp. 4007-4019.

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BIOGRAPHICAL SKETCH

Jason was born in Greensboro, North Carolina, on May 27, 1978. After receiving

his Bachelor of Science in mechanical engineering from North Carolina State University

in 2000, Jason worked in mechanical design and thermal analysis for Northrop Grumman

Electronic Systems and Sensors in Baltimore, Maryland. Jason began his studies in

pursuit of a Master of Science degree in mechanical engineering at the University of

Florida in 2002 and has plans to return to Northrop Grumman following completion of

this degree.

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experimental investigation of gravity...

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