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NATL INST OF STANDARDS & TECH R.I.C.

A1 11 02577663

Ross, Howard D/An Investigation of horiz QC100 .U56 NO.86-3450 1986 V19 C.1 NBS-P

\

f 1 ^REFEKE NBS

PUBLICATIONS

V /

-3450

An Investigation of Horizontal

Flow Boiling of Pure and Mixed

Refrigerants

Howard D. Ross

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Equipment Division

Gaithersburg, MD 20899

August 1986

Issued November 1986

,!

i; QC

100

.056

86 - 34^0

in part by;

artment of Energy

Ridge National Laboratory)

•ion, DC 20585

NBSIR 86-3450

AN INVESTIGATION OF HORIZONTAL

FLOW BOILING OF PURE AND MIXED

REFRIGERANTS

'f©S research

information CENTER NSSC.

i

• -

Howard D. Ross

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Equipment Division

Gaithersburg, MD 20899

August 1986

Issued November 1986

Sponsored in part by:

U.S. Department of Energy

(via Oak Ridge National Laboratory)

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

ABSlTlACr

The research involved determining experimental heat transfer

coefficients (HTC) and analyzing the predictive ability of available

models for both pure and mixed Rl52a/R13B1 refrigerants. Over 1,000

data points were collected, covering a range of pressure, composition,

quality, and heat and mass flux.

A current controversy regarding suppression of nucleate boiling was

resolved in favor of traditional theory. A suppression criterion for

pure refrigerants predicted quantitatively the quality at which suppression occurs. Ihe method was extended to mixed refrigerants and

partially verified.

Older pure fluid heat transfer correlations lacked general validity.

Ihe complete Qien correlation and many suggested variations were tested.

The original correlation overestimates the nucleate boiling contribution. In the nucleate boiling regime, the method of Stephan and

Abdel sal am (SA) was validated. In the evaporative regime, Bennett and

Chen's (BC) Prandtl number correction predicted BTC's for pure

refrigerants. The method incorporates the suppression criterion to

determine when to invoke the Prandtl correction. It is better grounded in

theory than recent regression-based correlations. The method predicted the

values of this and other independent data well.

i i i
The circumferential variation in HTC is opposite for mixtures than

observed for pure fluids, suggesting the existence of a circumferential

gradient in concentration and interfacial temperature. The measured

values in both the nucleate boiling and the evaporative regimes showed a

degradation in heat transfer. In the nucleate boiling regime, mass

transfer resistance caused the degradation. In the evaporative regime,

the reduction may be due to mass transfer resistance suppressing

nucleate boiling for the mixture but not for the pure component.

None of the mixtures' calculation methods achieved closure with measured

values to the same degree as was achieved with pure fluids. Closure,

however, was typical of the literature for mixtures. In the nucleate

boiling regime, the method of Thome achieved the best agreement. It

however predicted the opposite quality dependence.. In the evaporative

regime, the best fit was achieved by the evaporative portion of Chen's

original equation which neglects any mixture effect and suggests the

absence of nucleate boiling.

IV
TABLE OF CONTENTS

Page

ABSTRACT iii

LIST OF TABLES is

LIST OF FIGURES x NOMENCLATURE siii

PR£A>BLE IV

1. BACKGROUND AND SCOPE 1

1.1 Introduction and Goals 1 1.2 Text Organization 2

1.3 Nomenclature 5 1.4 Test Fluids 5 1.5 General Description of Forced Convection Boiling

(Flow Boiling) of Pure Fluids 6

1.6 TEe Differences Between Mixtures and Pure Fluids 9

1.7 Literature Review of Experiments of Annular Flow

Boiling of Mixtures 12

2. mOPERTY I«TER>IINATION 21

2.1 Introduction 21

2.2 Thermodynamic Properties and the Equation of State ... 22

2.3 Transport Properties 26

2.4 The Effect of Non- Ideal Property Behavior on the

Heat Transfer Coefficient 31

3. EIPERI>ENTS 37

3.1 Introduction and Historical Review 37

3.2 General Description of Test Rigs Used in

This Investigation 38

3.3 Testing Protocol 43

3.4 Measurement and Data Reduction Technique 44

3.5 Quality Assurance 61

3 . 6 Probl ems 6 8

3.7 Summary of Experimental Data 69

4. ON THE SUPPRESSION OF NUaEATE BOILING 93

4.1 Background 93

4.1.1 Conventional Theory of Onset and Suppression

of Nucleate Boiling 94

4.1.2 New Alternate Theory: Enhancement of

Nucleate Boiling 98

4.1.3 Suppression of Boiling with Organic Fluids .... 99

4.1.4 Problem Resolution Methods 99

4.2 Summary of Visual Evidence 100

V
4.3 Summary and Analysis of Experimental Evidence:

Dependence on Heat and Mass Flux 102

4.4 Summary of Experimental Evidence: Dependence of

Heat Transfer Coefficient on Quality 104

4.5 Summary of Experimental Evidence: Effect of

Pressure 105

4.6 Sxmunary of Experimental Evidence: Presence of

Hysteresis 106

4.7 Summary of Literature Review: Mixtures 106

4.8 Comparison of Experimental Results to Hieory 108

4.8.1 Application of Conventional Theory to

Refrigerants and Refrigerant Mixtures 108

4.8.2 Experimental Results: Pure Refrigerants 112

4.8.3 Experimental Results: Mixtures 116

4.9 Conclusions and Recommendations 118

5. A FURTHER EXAMINATION OF THE DATA 141

5.1 Introduction 141

5.2 Circumferential Variation in Heat Transfer in

Horizontal Flow Boiling 141

5.3 Effect of Equilibrium Quality on Mixture Heat

Transfer 145

5.4 Departure from Nucleate Boiling (DNB) Events 147

5.5 Comparison Betw'een Pure and Mixed Refrigerants 148

5.6 Pressure Drop in Horizontal Flow Boiling of Pure

and Mixed Refrigerants '.

. . 150

6. FREDICTION OF JURE REFRIGERANT HEAT TRANSFER 161

6.1 Introduction 161

6.2 Correlation for Annular Flow Boiling 162

6.2.1 Miscellaneous Forms 165

6.2.2 The Original Chen Method 165

6.

2

.2.1 Qosed Form Solution for Chen's

Me thod 168

6.2.3 Comparing Chen's Method to Experimental

Data: Literature Review 169

6.2.4 Modification to Nucleate Boiling

Contribution in Chen's Method 170

6.2.5 Modification of Forced Convection

contribution 171

6.2.6 Modification of Suppression Factor 172

6.2.7 Other Modifications to Chen's Method 173

6.2.8 Application of Modification to Chen's Method .. 173

6.3 Experimental Results: Comparison to Measured Data ... 175

6.3.1 comparison to Rig #1, R152a Data 176

6.3.2 Comparison to Rig #2, Preheat Data 177

6.3.3 Comparison to Rig #2, Test Section Data 178

6.4 Discussion of Findings 178

6.4.1 Nucleate Boiling Dominated Flow Situations .... 178

VI
6.4.2 Forced Convection Dominated Flow Situations ... 181

6.4.3 A Ccmplete Correlation 182

6.4.4 A Compari son w ith Other Data 185

6.5 Closing Remarks: Conclusions and Recommendations .... 186

7. PREDICTION OF HEAT TRANSFER WITH MIXED REFRIGERANTS 205

7.1 Introduction 205

7.2 Pool Boiling of Mixtures 205

7.2.1 Modelling of Single Bubbles 205

7.2.2 Boiling of Mixtures versus Pure Fluids 207

7.2.3 Mixtures Correlations for Pool Boiling 208

7.3 Forced Convection/Evaporation of Mixtures 210

7.3.1 Analytic Modelling 210

7.3.2 Simplified Predictive Modelling for Forced

Conve ctive /Evapora tion of Mixutres (Bell

and Gbaly) 212

7.4 Complete Mixtures' Correlations 213

7.4.1 Modification to Bell and Gbaly to

Include Nucleate Boiling 214

7.4.2 Modification to Bennett and Cben' s Method

to Include Mixture Effects 215

7.4.3 Other Modifications to Chen's Method to

Include Mixture Effects 217

7.4.4 Other Correlations for Flow Boiling

of Mixture's 218

7.4.5 Summary of Mixtures' Models ". . . . 219

7.5 Comparison to tieasured Data 220

7.5.1 Comparison to Preheat Data of Rig #2 220

7.5.2 Comparison to Rig #1 Data 221

7.5.3 Comparison to Rig #2: Test Section Data 223

7.6 Discussion of Findings 224

8. CONaUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH 241

8.1 Summary of Findings and Contributions 241

8.2 Further Research Needs 246

APPENDI CES

3A: Experimental Data Collection 251

4A: Alternate Suppression Criterion 289

4B: Review of Correlations with 291

4C: Review of Visual Evidence: Review of Literature 295

4D: Dependence on Heat and Mass Flux 3 01

4E: Mixtures - Literature Review 309

6A: Miscellaneous Heat Transfer Forms 317

6B : Pol ley's thod 321

7A: Development of COON (Mass Transfer Effect on Liquid Side)

in Bennett and Chen's Method 323

7B: Bennett and Chen's Inclusion of Sensible Heating of

Liquid 327

V ii
7C: Microlayer Evaporation Models 329

7D: Further Comments on Shock's Analysis 333

7E; The Bell and Ghaly Model 335

REFERENCES 343

V iii
1- LIST OF TABLES

1: Flow Boiling Experiments with Pure Refrigerants: Literature

Rev iew

2-

1: Comparison of Equation of State Values and Mole Fraction

Weighting of Pure Components

3-

la: Hardware Differences Between Rig #1 and Rig §2

3-lb: Data Reduction Differences Between [Ra83] and This Thesis (Rig

#1 )

3-2: Effect of Pressure Taps on Heat Transfer Coefficient

5-

1: Suaimary of Experimental Data

6-

1: Some Simple Correlations for Flow Boiling of Pure Refrigerants

6-2: Simple Correlations for Average Heat Transer of Flow Boiling

Refrigerant s

6-3: Comparison of Predictions to Data: Mass Fractional Deviation

6-

4: Summary of Chen-Styled Methods

7-

1: Pool Boiling Correction Factors for Binary Mixtures

7-2: Summary of Assumptions in Mixtures' Models

7-3: Comparison of Mixed Refrigerant Correlations and Experimental

Data

IX
LIST OF FIGURES

1 - 1 :

1 -2 :

1-3 :

1-

4:

2

-

1 :

3-1:

3-2:

3-3 :

3-4:

3-5:

3 -6 :.

3-7:

3-8:

3-9:

3-10:

3-11:

3-12a:

3- 12b:

3-13:

3-14:

3-15:

3-16:

Regimes of IWo Phase Flow (Reprinted from [La62]).

Temperature-Composition Diagrams for Test Fluids in Terms of

weight and Molar Fractions.

Heat Balance on Control Volume in Annular Flow of Mixtures.

Effect of Oil on Heat Transfer Coefficients of Refrigerants.

Comparison of Transport Properties as Determined by Mole Fraction

Weighting and Mixing Rules.

Typical Test Rig in the Literature.

Experimental Test Rig #1.

Experimental Test Rig #2

Thermocouple Lead Arrangement.

Thermocouple Mounting Scheme Including Electrical Isolation.

Wall and Instream Temperature Measurement.

The Simulation of Pressure Taps.

Calculated Pressure Drop via Mar tinell i-Nel son Method.

Effect of Instream Thermocouples on Single Phase Measurements.

Effect of Instream Thermocouples on Evaporative Heat Transfer

Coefficient.

Sampling Technique to Determine Mixture Composition.

Data Reduction Scheme for Pure Refrigerants.

Data Reduction Scheme for Mixtures.

Condensation Curves for Various Ccmpo si tions.

Typical Output from Test Run Data Reduction.

Comparison of Predicted to Measured Data for Single Phase Heat

Transfer Coefficients.

Pressure Drop: Predicted versus Measured.

X
3-17: Effect of Preheat Flux on Test Section Wall Temperature

Measurements.

3-

18: Effect of Preheat Flux on Heat Transfer Coefficients for

Mixture s.

4-

1: Criterion for the Onset of Nucleate Boiling.

4-2: Flow Chart for Determining Suppression Heat Flux.

4-3: Effect of Pressure and Mass Flux on Suppression Heat Flux

(R152a) .

4-4: Calculated Suppression Heat Flux for Mixtures—Isolated Bubble

The ory.

4-5: Calculated Suppression Heat Flux for Mixtures—Pool Boiling

The ory.

4-6: Effect of Heat Flux on Pure R152a at Low Pre.ssure.

4-7: Effect of Pressure on Pure R152a.

4-8: Effect of Heat Flux on Pure R13B1

4-9: Effect of Heat flux on Pure R152a and R152a/R13B1 Mixture:

Preheat Data.

4-10: Effect of Heat Flux on Pure R13B1 and R152a/R13B1 Mixture:

Preheat Data.

4-11: Effect of Heat Flux on Pure R152a—Test Section Data.

4-12: Effect of Mass Flux: Test Section Data.

4-13a: Effect of Step Change in Heat Flux: Pure Refrigerants.

4-13b: Effect of Step Change in Heat Flux; Mixtures.

4-14: Effect of Heat and Mass Flux on 0.662 wt. R13B1 Mixture.

4-15: Effect of Heat and Mass Flux on 0.706 wt. R13B1.

4-16: Effect of Heat and Mass Flux on 0.75 wt. R13B1.

4-17: Effect of Beat and Mass Flux on 0.833 wt. R13B1.

4-

18: Rig #2 Test Section Data.

5-

1: Variation in Measured Heat Transfer Coefficient.

5-2: Variation in Measured Heat Transfer Coefficient for Mixtures.

xi
5-3: Effect of Composition on Top-Bottom Wall Temperature Difference.

5-4: Indications of Probable Film Boiling for Pure R13B1 and a Mixture.

5-5: Probable Film Boiling in the Data of [Mi81] .

5-6: Comparison Between Mixtures and Pure Fluids in Evaporative Flow.

5-

7: Comparison Between Predicted and Measured Pressure Drop for

Mixture s.

6-

1: Comparison of Shah's Method with Experimental Data.

6-2: Comparison of Einpirical and Analytic Functions in Chen's Method.

6-3: Comparison of ChenrStyled Methods to Experiments.

6-4: Comparison of For ster-Zuber and Stephan- Abdel sal am Methods.

6-5: Comparison of Complete Correl ation with Test Seotion Data.

6-6: Comparison of Complete Correlation with Selected Rig #1 Data

6-

7: Comparison of Complete Correlation with Others' Data.

7-

1: Isolated Bubble Growin.g in a Superheated Binary Liquid.

7-2: Pool Boiling Experiments of fiappel and Stephan with Binary

Mixture s.

7-3: Comparison of Mixture Correction Factors.

7-4: Comparison of Preheat Data to Pool Boiling Models.

7-5: Comparison of First Thermocouple Station Preheat Data to Pool

Boiling Models.

7-6: Comparison of Rig #1 Data to Thome's and Bell and Ghaly's

Me thods.

7-

7: Comparison of Measured Test Section Data to Evaporative Only

Me thods.

8-

1: Proposed New Test Rig.

4C-1: Visualization Methods.

7C-1: Microlayer Evaporation Models.

7E“1: Tbe Bell and Ghaly Method.

Xll
NOLIENCLATURE

Engl ish

T temperature

P pre ssnre M molcular weight

X concentration of liquid

Y concentration of vapor

R gas constant

Cp specific heat at constant pressure

q heat flux

X vapor quality

G mass flux

ID mass flow rate

V vel oc i ty

h enthalpy

latent heat of vaporization

s entropy

L length

E energy

(TD) as determined by a transducer

(GAUGE) as determined by a gauge

Ac cross sectional area

As surface area

V spe c if ic V ol ume

z di stance

F factor in Chen's method [Ch66]

S factor in Chen's method [Ch66]

d* break-off diameter [St80]

Greek

a heat transfer coefficient

a surface tension

viscosity

kinematic viscosity

Y conduct iv ity

A change in property

e eddy diffusivity or void fraction

P density

Ol two phase multiplier [Ma4 8]

5 thickness (length) of layer

Dimensionless Numb e r s

Re Reynolds Numbers GD/p

Pr Prandtl Number pC^/k

Co Convection Number

^tt Martinelli Parameter

L Lewis Number a^/ap

Sc Schmidt Number p/pa^

xiii
Superscripts

Subscripts

T

D

SL

SV

G

L

LO

A

B

DEW

BUB

LIN

O.TOT

C

BC

FC

TPF

i

jr

csat

in

out

fsc w

pr

anbc

enpool

e gb

id

V

act , mea s 20

m

molar value

vapor value in equilibrium with liquid

thermal

mass

sensible heat, liquid

sensible heat, vapor

ga s 1 iquid

liquid only

component A

component B

dew point

bubble point

as determined by a linear relation

overall, total

due to Chen

due to Bennett and Chen

forced convective

two phase, frictional component

component i component j

reduced

critical

saturation

inlet

outle t fluid

subcooled

wal 1 prehea t acceleration component

nucleate boiling contribution

evaporative contribution

nucleate boiling relation used in Chen'

pool boil ing

equilibrium value

ideal value (mole fraction weighted)

vapor

actual, measured value

two phase

mixture

me thod

XIV
PREAiBLE

This report is essentially the dissertation of Howard Ross which was submitted

to the University of Maryland in partial fulfillment of his Ph.D.

requirements. Ihe following are the acknowledgments from that document.

Special thanks must go first to my advisor, Marino di Marzo, for his spirited

and insightful advice in the preparation of this report. Also, deep gratitude

is expressed to Reinhard Radermacher for his generous and patient counsel in

the lab. Sponsors are usually noted in the cursory fashion. However, in this

case, David Didion provided support on both a technical and personal level for

which the author is grateful. Appreciation is given to Dave Ward for

accommodating my unusual schedule and demands in operating the brine cooling

system. Extra effort was required in typing this report. My special thanks

go to Laurie Watkins for enduring the several drafts, and Gail Crum and Mary

Baier for typing the final. I also thank everyone in the group at hCS,

especially Mark McLinden, Graham Morrison, and Brian Weber for many fruitful

technical discussions.

XV
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s‘V
CHAPTER 1 : BACKGROUND AND SCOPE

1 . 1 Introduction and Goals

The interest in two phase gas-liquid flow is increasing dramatically.

In 1966, less than 60 papers were published; in each of the last three

years (1982-84), more than 1000 papers have appeared in the technical

literature. Surprisingly, however, the study of flow boiling of mixtures, a commonly occurring process, has received relatively little

attention; a recent literature survey [St82] turned up only six papers.

While in fact there may be twice that number, the availability of

existing data and models is scarce. Of those studies many were with

aqueous solutions, which due to certain properties of water, may be

inapplicable for other fluids.

The boil ing/evapor ation of mixtures is a very common industrial application. In distilleries and in reboilers of which there are tens of

thousands in use, the evaporation of a mixture is inherent in the process. More recently, the use of refrigerant mixtures as the working

fluid in heat pumps and r ef r ige r at or/ f reez er s has shown theoretical

promise [St80, Sc85] which has been verified experimentally [Di84] . One

of the serious barriers to the use of these refrigerant mixtures is the

current lack of understanding of the heat transfer process in refrigeration equipment, specifically the impact of mixtures on the heat transfer

coefficient and therefore the heat exchanger size in evaporators and

condensers.
The principal goal of this study therefore is to experimentally

determine heat transfer

to assess and recommend

and to examine specific

coefficients under a wide range of conditions,

models and correlations for their predictions,

physical processes governing the heat transfer

The need for such work has been expressed widely in the literature:

"No other tests [of the Chen correlation for fluids

with Pr > 1] have been reported and this is a gap which

should be filled". — recent flow-boiling review keynote

paper at int'l Heat Transfer Conference [Bu82]

.

"It is clear that several possible methods are now available for convective vaporization. It is essential

in order for them to be tested, the pre*sent lack of data

for local convective heat transfer coefficients in

multicomponent systems should be remedied". [Sa82] .

"Further experiments with other mixtures are still necessary.

Some of the assumptions [in the models] seem to be very far

going and require further experimental scrutiny". — recent

boiling of mixtures review keynote paper at Int'l Heat

Transfer Conference [St82]

.

This study attempts to respond directly to these requests.

1 . 2 Text Organization

In the remainder of this chapter, background is given regarding the

boiling/evaporation process in flow boiling, especially annular flow.

The general complications introduced by the use of mixtures are also

discussed.

In Chapter

The use of

properties

fluids and

2, a review of the physical property determination is given,

a special equation of state for determining thermodynamic

is described. Transport property correlations for pure

rules for determining these properties for mixtures are

2
given; these rules take into account the non- ideal i tie s of mixing. Nonideal mixing properties are shown to reduce heat transfer coefficients,

both in single and evaporative two phase flow.

In Chapter 3, the experimental test rigs used in the heat transfer

coefficient investigation are discribed. Particular attention to

potential errors is included, as well as the testing protocol and

results of various quality assurance tests. A total of 1459 data

points are collected in this effort; about 15% are not in the

annular flow regime and are eliminated from further consideration.

Chapter 4 discusses a current controversy in the literature, the

suppression of nucleate boiling. For many years, increased heat

transfer at high vapor quality was attributed to the thinning of the

liquid film and the acceleration of the vapor core. Recently a much

different phenomena, an enhancement of nucleate boiling , has been suggested in this region. The literature is reviewed critically and new

experimental data are analyzed in favor of traditional theory. A suppression criterion is applied and validated for pure fluids. Extensions

to mixed fluids are hypothesized and partially validated.

In Chapter 5, the general results of the various experimental tests are

further discussed. A circumferential variation in heat transfer coefficient was observed in horizontal flow boiling of mixtures as compared to

pure fluids. A reason for the new variation is hypothesized. The

effect of quality on the mixtures' heat transfer coefficient is

3
discussed. Final ly« sudden departure from nucleate boiling (DNB) were

observed in some of the data. The implication of DNB events for heat

pumps are discussed.

Chapter 6 reviews the available models and correlations for predicting

heat transfer coefficients with pure fluids. In particular, the Oxen

correlation [Ch66] is reviewed and analyzed, as it is the most widely

recommended method in texts [Hs76, Co80] as well as within the nuclear

industry in general [Tr78] . The method has been dismissed historically within the refrigeration industry because of its poor predictive

ability with refrigerants. Recent modifications of the correlation

and the application of the method to refrigerants are examined. It

is shown that portions of the correlation may be used successfully

with refrigerants. A new procedure, more analytical, based on recent

correlations, is developed.

The modelling and correlations for pool and flow boiling of mixtures

is the subject of Chapter 7. Ihe available methods proposed for

estimating heat transfer coefficients are reviewed critically and

compared to the experimental data. None of the methods produced

agreement with the data as closely as was achieved for pure fluids,

however, closure was achieved to the same degree as is found currently in the mixtures' literature.

Conclusions and recommendations regarding flow boiling models for

pure and mixed refrigerants are discussed in Chapter 8. It is likely

4
that these first studies of mixtures will lead to further experimental

work. As such, several recommendations for test fluids, experimental

apparatus and testing protocol are also made in Chapter 8.

1.3 Nomenclature

There has been a recent attempt at standardized nomenclature in two

phase literature. As such, the author has used, wherever possible,

the latest international convention. In particular, the following

symbols should be noted:

a = heat transfer coefficient

Ahy = latent heat of vaporization

a<p = thermal diffusivity

ajj = mass diffusivity

X = molar concentration

X = vapor qual ity

X = thermal conductivity

The general nomenclature is ^iven in the foreward to this report. When

exceptions are made, the text will define the variable directly.

1 .4 Test Fluids

The test fluids used in this investigation are pure R152a (CH3CHF2),

pure R13B1 (CF3Br) and mixtures of various compositions of these fluids.

The two refrigerants are recommended as a mixture by their manufacturer

for heat pump use due to their relatively wide difference in boiling

point (35**C@4.7 bar). In addition, the mixture can be used in existing

machinery without major modification. Some tests have been performed

with pure R22 (CC1HF2), a much more widely utilized refrigerant. The R22

was used to ensure the experimental testing rig was operating correctly.

5
1 .5 General Description of Forced Convection Boiling (Flow Boiling) of

Pure Fluids

Figure 1-1 [La62] shews the typical flow pattern development of a moving

fluid being boiled and then evaporated. In most of the applications for

refrigerants, the annular flow pattern (sections E and F) is the one of

interest, as refrigerants commonly enter the evaporator at a vapor

quality of about twenty percent and quickly develop into annular flow.

For low heat flux, the heat transfer coefficient changes along the

length of the tube as follows; when the fluid is a single phase liquid

(section A on Figure 1-1), the heat transfer coefficient is approximately constant; it changes only as the thermodynamic and transport

properties of the liquid change with temperature. In Section B, subcooled boiling occurs, i.e., vapor forms at portions of the tube wall

despite the fact that the bulk fluid temperature remains below the

saturation temperature. In this flow section, the thermodynamic quality, X, defined as ^^^L 5 at)/Ah^ is still less than zero, and the heat

transfer coefficient owing to developing turbulence increases linearly.

When X equals zero (between Sections B and C) , saturated nucleate boiling begins, and the value ofais relatively constant. At a quality of

a few percent, an annular flow pattern forms (sections E and F) . In

annular flow with heat addition, the quality increases, stripping the

thickness of the liquid layer. Vapor generation in this region is

commonly considered to be by evaporation primarily at the liquid/ vapor

interface, rather than by nucleate boiling at the wall. If nucleate

boiling is completely absent, "suppression of nucleate boiling" is said

to have taken place. The suppression process is the subject of some

6
recent controversy discussed in a later chapter. Since the liquid film

becomes thinner and thinner with increasing quality and since the vapor

core velocity increases sharply, heat is conducted more readily through

the liquid, and the heat transfer coefficient increases. At some point,

the liquid film is entirely evaporated and dryout (also known as boiling

crisis) occurs: since vapor is a much poorer thermal conductor than

liquid, the heat transfer is suddenly and severely diminished. As the

quality approaches one, single phase vapor flow occurs, and the heat

transfer coefficient again is relatively constant, changing only as

fluid properties change.

The heat transfer coefficient depends not only on quality, but on mass

and heat flux. As in single phase flow, an increase in mass velocitycauses an increase in turbulence and may cause a consequent increase in

the heat transfer coefficient. It should also be noted that at higher

mass flux the dependence on quality becomes much stronger. ^ por the

case of increased heat flux, nucleate boiling at the wall may occur in

more locations, increasing the heat transfer coefficient. For very high

heat flux, no annular flow may be established and sudden reductions

in a values may occur at low quality or even in the subcooled boiling

regime. This phenomenon is known as a sudden departure from nucleate

boiling and is caused by sudden flashing of vapor all along the tube

wall (i.e., film boiling).

^If the vapor generation process is dominated by nucleate boiling, then

the heat transfer coefficients become nearly independent of mass flux.

This is one way among several to examine the physical process occurring

inside the tube.

7
As previously noted, this study concentrates on the annular flow region

prior to dryout. Some other comments are also appropriate: Figure 1-1

shows the flow patterns in a ver tical ly- oriented tube. In a horizontal

tube, the liquid film can be considerably asymmetric due to gravity.

The thick liquid film on the bottom of the tube tends to reduce the

local a values considerably; however the liquid film on the top and

sides is thinner in the horizontally-oriented tube, increasing the heat

transfer coefficient. To the author's knowledge only one group used the

same tube, fluid, and experimental appartus to measure the heat transfer

coefficient in both orientations: Lavin and Young showed that a horizontal was fifty percent larger typically than a vertical, when the heat

transfer coefficients at a location were averaged all around the tube

(a-avg equals [a-top plus a-bottom plus a-leftside plus a-r ight side ] /4) ,

[La66] . Actual average values are difficult to obtain in this

asymmetric case.

This simplistic explanation of the flow pattern and heat transfer

regimes masks many of the complicating features of real annular flow

boiling. First in any annular two phase flow, the vapor-liquid interface is wavy. Film thicknesses at a fixed spatial location may vary

over time by a factor of twenty due to wave passage. The wave changes

the turbulent structure of the film and may induce or retard nucleate

boiling at the wall. The presence of nucleate boiling may, in turn,

break-up the viscous sublayer in the liquid film. Information about the

turbulence structure at the vapor-liquid interface is unavailable,

though there are suggestions that the turbulence may be damped in this

8
region. Hie waves themselves are frequently sheared, and liquid droplets entrained in the vapor core. A large fraction of the total liquid

flow may be entrained in this manner. Rates of entrainment and droplet

deposition are, for the most part, poorly quantified. These rates in

fact control film thicknesses and are the key to any eventual analytical

model. Liquid film models derived from the momentum and energy equations have poorly predicted heat transfer rates [Co80]. The literature

suggests the problem is due to interfacial turbulence damping, but

recently it has been suggested that the root cause is poor understanding

of entrainment [He84] . In any case, these multiple problems have made

realistic analytical model development a rather distant hope.

1 . 6 The Differences Between Mixtures and Pure Fluids

In this section a review is presented of the additional characteristics

which must be considered when a fluid is a non-azeotropic mixture. The

review is not intended to be comprehensive, but stresses the most

important features of non-azeotropic refrigerant mixtures as applied to

flow boiling.

Figure 1-2 displays a temperature-composition phase diagram for the

R13B1/R152a mixture used in this report. It is typical of many nonazeotropic mixtures. Examination of the figure reveals immediately

the two most important mixture features:

1. The evaporation process in non- isothermal

.

9
2. As the fluid begins to evaporate, vapor is formed

preferentially of one component (the more volatile or "light” component).^

The non- isothermal nature of the mixture is advantageous in terms of use

in a counter-flow heat exchanger (a higher effectiveness is possible

since a constant temperature difference can be maintained throughout the

exchanger). On the other hand, the non^ isothermal nature also causes

only a portion of heat input to a flowing mixture to be used for vapor

generation; the remainder is required to heat sensibly the liquid and

vapor streams. Figure 1-3 shows a control volume for a flowing evaporating fluid (ignoring momentarily nucleate boiling). For vapor generation to occur, the vapor already formed must be further heated, and the

liquid heated as well to remain in near-equilibrium at their interface

(where the evaporation is taking place). From a heat balance on the

control volume, over a distance dz

:

^ ‘ISV (1-1)

or

dh = (1-x) Cpl dlL + (Ah^)dx + x Cp^dT^

where x is the mean quality over the interval. In the case of pure

fluids the first and third terms in the right side are equal to zero

(neglecting the superheating requirements for the liquid and other

^The term light component is a misnomer. In this study, R13B1 is more volatile but is the more dense of the two refrigerants.

10
non-equil ibrixun effects). In the case of mixtures, the sensible heating

may represent more than 20^ of the overall heating required.

The second feature shown on the previous page, the composition

difference between vapor and liquid, reveals that physical properties,

both thermodynamic and transport, vary substantially throughout the

evaporation process even in the absence of pressure drop. For example,

with pure fluids, one tends to think of liquid density as constant under

these conditions. With mixtures however, with one component stripped

preferentially away from the liquid layer during evaporation, the liquid

density may vary by 50% or more, even without pressure drop from inlet

to outlet of an evaporator tube. Other thermodynamic properties such as

latent heat of vaporization also possess this complicating feature.

Thus thermodynamic properties must be reevaluated continuously during

the evaporation process.

A great difficulty appears with mixtures in that the addition of a

second component into a pure fluid may have spectacular effects on

surface tension or viscosity. Precise prediction of these properties is

impossible in many cases. Surface tension directly affects the nature

of nucleate boiling, yet may be impossible to even estimate since

general mixing rules are unavailable.

In addition to the property compl ica tions, the vapor-liquid composition

difference introduces mass transfer resistance. The interfacial composition is different from the bulk liquid and vapor streams. In

11
condensation various calculation methods have been developed to account

for this problem, with rather extreme assumptions used in common practice. The addition of mass transfer resistance suggests that mass

dif fusiv ities should be known; yet these are rarely known for refrigerants. In turbulent flow one needs to estimate the eddy (mass)

diffusivity, a process which itself is uncertain, and made even more

complicated in the presence of nucleate boiling.

Given the above consideration along with those described earlier for

pure fluids, it is easy to understand the current futility of analytically modeling the the heat transfer process from first principles.

Instead, the literature has proceeded with correlations or simple models

which account for as many physical phenomena as their authors deemed

possible. 'To the author's knowledge, no published verification of their

proposed models has taken place prior to this report.

1.7 Literature Review of Experiments of Annular Flow Boiling of

Mixtures

A number of texts provide a general review of annular flow boiling

experiments for pure fluids [Co80, Hs76]. Table 1-1 lists experimental

investigations with refrigerants. Very few experiments however have

been conducted under similar conditions for mixtures. Some early

experiments used calorimetric methods to determine overall heat transfer

in reboilers [Bo51] or long steam heated evaporators [Mc42] . These

experiments did not provide sufficient information for evaluation of

local conditions or physical processes governing the heat transfer.
Shock investigated an ethanol-water mixture in a vertical tube [Sh73].

The inlet conditions were subcooled and the maximum outlet quality he

tested was 0.16. This quality is less than the inlet to most heat pump

evaporators. The flow patterns he investigated rarely included annular

flow. The ethanol-water mixture has a very non-ideal (see Qiapter 2)

property behavior. The tube used in his experiments was specially

plated with a thin nickel film, removing many cavity sizes and possible

nucleation sites. His experiments therefore are not particularly relevant to this report. However, Shock performed very substantial analytic

modelling in this effort, and several subsequent publications. These

efforts will be referred to frequently throughout this report.

Toral modified the test loop used by Shock [To79] . A copper tube was

vertically oriented, and the working fluid of e thonol-cy cl ohexa,ae was

selected due to its near-ideal property behavior. Wall thermocouples

were spaced very closely so that the position of the onset of nucleate

boiling could be located. They were however, mounted only on one side

of the tube and symmetry assxuned. He found a deterioration of heat

transfer due to mass transfer resistance and that nucleate boiling was

the dominant mechanism for his testing conditions. Maximum outlet

quality was 0.30. He compared his experimental results to the Chen

correlation; poor prediction was attributed to the poor prediction of

nucleate boiling. Surprisingly, the correlation unde rpr e di c ted the

experimental results. This result, as will be shown in Chapter 7, is

unusual since mass transfer resistance is not accounted by the

13
correlation. Like Shock, Toral performed substantial theoretical

studies and they will be quoted frequently.

Bennett recently tested mixtures of ethylene-glycol and water, again in

a vertical tube [Be80] . The test section was very short (L/D ~ 3) and

inlet flows were in the two phase region, provided by preheaters. Only

a single wall thermocouple was used in all the measurements, again with

symmetry assumed. Several hundred data points were taken over a wide

range of conditions. Bennett developed a modification to Chen's correlation to account for mixture effects. They predicted his data to a

mean deviation of + 15%.

Chaddock and Mathux investigated refrigerant-oil mixtures in a

serpentine horizontal copper tube [Ma7 9]. The full quality range was

covered. One potential complication with the study was the impact of

oil on properties such as surface tension. The authors noted a dependence of the heat transfer coefficient on heat flux, indicating a

nucleate boiling contribution (neglected in the authors' final correlation). Nucleate boiling behavior with refrigerant-oil mixtures defies

current understanding [Bu79]; pool boiling experiments with these mixtures show rather erratic results (see Figure 1-4). In the study of

Mathux and Chaddock, the addition of oil produced an increased heat

transfer at low qualities and a decrease at high qualities, the latter

due to the liquid composition being oil-rich.

14
Mishra, et al,, investigated mixtures of R12/R22 over a limited

composition range in a horizontal stainless steel tube [Mi81 , Va7 9] .

Two phase inlet conditions were maintained by a preheater. No tests of

pure R22 were conducted. The authors used pure fluid correlations and

revised the exponents of the correlations to fit most of their

experimental results to + 25%.

Singal, et al., experimented with an R13/R12 mixture, again with a

horizontal tube over a limited quality range [Si83]. The authors again

correlated their results with a different pure fluid correlation. They

concluded that the a was decreased for mixtures compared to pure R13

whenever the quality was less than 0.3, and that with a further increase

in vapor quality an increased heat transfer coefficient was observed

when mixtures were compared to pure R13

.

Radermacher, Ross and Didion investigated a mixture of R152a/R13B1

selected for its wide range of boiling points [Ra83]. This work has

been reanalyzed and is presented in detail as part of this report.

1 5
Table 1. Flow Boiling Experiments with Pure Refrigerants:

Literature Review

Anthors Refrigerant Ref

.

Bryan and Siegel

Bryan and Qnaint

Baker et al.

Pierre

Worsoe-Schmidt

Altman, Norris, and Stanb

Sacks and Long

Gonse and Conmon

Noerager and Chaddock

Gouse and Dickson

Lav in and Young

Staub and Zuber

Chawla

Bandel and S chi under

Anderson, Rich, and Geary

J allouck

Uchida and Yamaguchi

Thor sen et al.

Rhee and Young.

Purciple et al

.

Danilova

Al j aj arh and Duninil

Singal et al.

Mishra et al.

Radermacher et al.

Chaddock and Mathnr

Rll Br55

Rll Br51

R12 Ba53

R12 Pi56

R12 Wo60

R22 A160

Rll Sa61

R113 Go65

R12 Cb66

R113 , Rll Go66

R12, R22 La66

R22 St66

Rll Ch67

R12 Ba74

R22 An66

Rll Ja74

R12 Dc66

R113 Th7 0

R12, R22 Rh74

Rll, R12, -R113 Pu72

Rll Da69

R12, R22,R502, R13B1 A177

R13 Si83

R12 MiSl

R22, R152a,R13Bl Ra83

R22 Ch79

16
TEMP ouALirr

PEG^ES •'WC-g^A.SE ^LOW

A E P E ~ P 3562

PIG JPE I

igure 1-1: ReeiiTiGs Tvo ^ha?e ^lou’ (Reprinted fro:r. (La 62)

17
CONCENTRATION; wt. 152a

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

CONCENTRATION: wt. 13B1

Figure 1-2; Temperature-Concentration Diagrams for Test Fluids

in terms of Weight and Molar Fractions. Shown also

are the feed concentrations used in the experiments

CONCENTRATION: moles 152a

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

CONCENTRATION: moles 13B1

18
out

I

N

O

I

c

>”

I-

>-

i.

<

19

I’igure

l-<;

Ileal

lialanc('

on

Control

Volimu'
HEAT

TRANSFER

COEFFICIENT

(Wm«C)

o

MASS FRACTION OF THE OIL

WALL SUPERHEAT. AT*., ^/»C

Figure 1-A : Effect of Oil on Heat Transfer Coefficients of

Refrigerants. Small additions cause increase,

however further additions cause decrease.

20
CHAPTER 2: PROPERTY DETERMINATION

2 . 1 Introduction

Determination of transport and thermodynamic properties for mixtures is

much more difficult for mixtures than for pure fluids. This is due to

more complicated theoretical considerations of molecular interactions as

well as the very common lack of experimental data of the mixture's

properties.

The most frequent method for estimating many of the properties of

mixtures is to weight the mixture property by the mole fraction of the

individual components comprising the mixture:

•• - VPp

where

P = ary property

X = mole fraction

A = component A

B = component B

M == mixture

This approach has several deficiencies. First of all, spectacular

deviations from this presumed behavior have been observed. Examples

include surface tension (e.g. , ethanol water) and viscosity of liquids

(e.g., water-*N, N-dimithy lacetamide). Furthermore, a mixture may exist

of a liquid at a pressure which is at or above the critical point of one

of the components. In this region, specific heat and liquid viscosity

are either undefined or infinite. Most engineering work is done away

from the critical point; however, this point is exceeded with one of the

21
refrigerants of this report, R13B1, as it operates in a mixture in the

condenser of real heat pumps. ^ Thus, the problem is not simply an

academic one.

The refrigerant mixture of R152a and R13B1 presents a particular problem

in that both molecules are polar (R13B1 is weakly polar; R152a strongly

polar). Deviations from the ideal mixing rule of equation (2-1) can

therefore be expected. Extensive P, T, v, X measurements of the mixture

have been made by Morrison [Mo82] . However, no transport property

measurements of the mixture have been found in the literature.

2 .2 Thermodynamic Properties and the Equation of State

In order to determine the themodynamic properties of a mixture, an

equation of State (EOS) is required. The most commonly used one in

industry is the Redl ich-Kwong-Soave (R-K-S) equation:

Pv

RT V - b (v + b) RT

( 2 - 1 )

Mixing coefficients

molecular structure

equation is that it

a library of liquid

phase and vapor pha

empirical equations

used in de terming a and b can be estima ted f r om the

of the component s. The dif f icul ty w i th the R-K- S

is not appl icabl

e

to the 1 iquid phase

.

In pr act ice

proper 1ties is used in CO njunction with the R-K-S tw ^

se predictions. A1 terna t oly, curvef it or se m i

can be written for the 1 iquid phase and pie ced t 0

^Measurements in this report were conducted below the critical point of

either component.

22
the R-K-S model. Unfortunately, discontinuities appear in certain

properties (e.g. , with this approach. Extrapolation near the

critical point also produces significant error.

Morrison has applied the DeSantis equation of state to the R152a/R13B1

mixture. This EOS is continuous in both the liquid and vapor phases

[Mo82] :

Pv ^

1 ^ V + y2 - y3 a (2-2)

RT (1 _ y)3 (v + b)RT

where

The first term on the right hand side of equation (2-2) accounts for

molecular repulsive forces and the second term accounts for attractive

forces. As can be seen in the equation, the term b must have the

units of molecular volume. It is a means of adjusting the closest

approach distance between two molecules. As the temperature of a real

fluid is raised, this distance becomes smaller (since molecular kinetic

energy increases with increasing temperature). Thus, the variable b is

a function of temperature. The term a accounts for the non-spher ical

nature of the forces between molecules because the refrigerants are

polar. Again as temperature is raised, the directional attractions of

the molecules are reduced, as well as the average attractive force.

Thus, a has also a temperature dependence. Morrison determined

23
empirically tlie values of "a” and "b” from the pure R13B1 and R152a data

sets published in in ASHRAE Tables of Refrigerants after these data sets

checked with his own measurements.

In the case of mixtures, the terms ”a" and "b” become:

a E Z Xj- a^j

i j

b = E E Xi Xj bij

1 j

^ij = - fij) -j)

1/2

bij = [(bV^ + bj/3)/2]^

These account for molecular interaction between molecules of different

a components. The term,, f

i j

' an empirically determined mixing coefficient which might account for both the non- spherical nature of the

molecules and possible interactions such as hydrogen bonding.

The solution scheme, and actually the computer code, used in this

report, is taken directly from Morrison [Mo84] . It requires an inpat

pressure, temperature and overall composition and outputs enthalpy,

entropy, specific volume, and composition of each of the phases as well

as the overall mixture. Also output are molar qixal ity and liquid and

vapor specific heats.

The code requires several internal iterative loops. The form of

equation (2-2) is fifth order and does not have an analytic solution.

24
In general, given T and one determines bubble and dew point

pressures by iteration. If the given pressure is higher than Pgijg the

mixture state is subcooled; if P < Pg£^y» it is superheated vapor. In

the two phase region, given T and P, one guesses Xj^, and determines

by iteration Pguess. When the difference between P and Pg^ggg is sufficiently small, the solution is considered closed. P<,,„»cc i^ itself the

subject of certain conditions. For mixtures, the chemical potential of

each cemponent in each phase must be equal: this requirement determines

the final pressure guess.

The computer code for the equation of state is not arranged to handle

pure refrigerants easily. Furthermore, the data reduction time can be

reduced substantially by using curvefits to the property table data.

These curvefits are:

(13B1) 1/T = -.04 - .00046561n (P/21867.08454)

(152a) 1/T = .004039 - . 0003 8091n(P)

T[°K], P[bar]

T[0K], P[bar]

Most experimental tests with mixtures for this report were run at

pressures between 4.4 and 5.0 bar. Table 2-1 displays the calculated

densities for the liquid and vapor phases, as well as the latent heat of

vaporization at a pressure of 4.75 bar. Values of the thermodynamic

properties may vary by up to 15% from a mole fraction weighting of the

pure components' values at the same pressure.

25
2 .3 Transport Properties

Hie determination of various transport properties for mixtures is

complicated by the requirement of using proper mixing rules. The mixing

rules are taken inevitably from the widely referenced text by Reid,

Prausnitz and Sherwood [Re? 9]. The mixing rules which they recommend,

and which are used in this report, have not been verified experimentally

for the particular R13B1/R152a combination.

Transport property data for the pure refrigerants are available from two

sources: ASffRAE [As81] and RTFS [Ht83]

The ASHRAE tables are incomplete in their transport properties; the RTFS

data only was used in this report. All correlation coefficients (R^)

were greater than 0.99 for the pure fluid curvefits.

(a) Thermal Conductivity (Liquid Phase)

The curvefit equation for the pure refrigerants was:

Xl=A+BTj+(T^ + DT^ [10“^ w/M/k] X X X

A B C D Trmin T^rmax

(13B1) 150 .3 96 -77.341 -107.302 81.272 0.6 0.96

(152a) 244.93 2 -122.821 -177.969 133.061 0.6 0.88

^The former has an error in RlS2a specific heat [Ra83,Mo84a] and the

latter in latent heat [Mo84b]

.

26
Reference [Re79] recommends the following mixing rule, with a maximum

error of 4%:

= [(1 + C)W^ - + [(1 _ c)Wg + CW|]?.3

where

X = thermal conductivity

C = 0.72 (empirical constant)

W = weight fraction

Figure 2-1 shows the results of applying the mixing rule at various

compositions. It can be seen that there is a substantial deviation from

the ideal mixing rule of equation (2-1).

(b) Thermal Conductivity (Vapor Phase)

The vapor conductivity of each of the pure refrigerants was estimated

from the RTFS data as:

= A + BTj. + CT^ + DT^ [10 ^w/k]

A B C D Trmin Trmix

(13B1) -75 .295 305.035 -396.984

(152a) -27.900 130.237 -177.807

183 . 196

101.216 0.6 0.88

The mixing rule in [Re7 9] (maximum error = 5%) which was selected was:
where

[ 1 ~+

[8(1 + (M./Mj)]

M = molecxilar weight

Y = mole fraction of vapor

(c) Liquid Viscosity

The pure liquid viscosities were determined from:

P13B1 = 4935 .37126 - 43 .7022 T + 0. 13791^ “ 0.000152091^

T[»K], p[10“^Pa-sec] 220 < T < 300

I'l 52 a = A + BT^ * CT^ +

A = 387.5886 B = 1238.98 C = 2864.765 D = 13 13.244

0.6 < Tj. < 0.88

and the mixing rule used was (maximiun error at + 15%) described in terms

of the kinematic viscosity:
= Va'

K*

B B

4>b^

where

V r kinematic viscosity (liquid) = ji/e

(p = volume fraction

kJ = 0.27 In ^ + (1.3 In ^)0*5

A ^A

(d) Vapor Viscosity

The pure component vapor viscosities were estimated from:

= A + BTj. + (rr^ + OT^ [10"^Pa-sec]

A rmin Trmai

(13B1) -26.3 08

(152a) -10.320

132.34 -166.5 1 81.7 9 96 0.6

60.803 - 74.075 38.667 0.6

0.96

0.88

The same mixing rule as used for vapor conductivity was used to

determine vapor viscosity.

(e) Liquid Mass Diffusivitv (Diffusion Coefficient)

No measurements of the liquid mass diffusion coefficient have been taken

on any refrigerant pair. Furthermore, [Re7 9] makes no clear recommendation regarding this property, especially for polar mixtures.

Kandl ikar et al. [Ka75] attempted to predict the mass diffusion coefficient for an B22/R12 mixture, using a formula suggested in [Re79l. Ihe

29
method requires the mixture's liquid viscosity, an accurate equation of

state, and generous assumptions regarding activity coefficients, ideal

gas behavior, and interaction parameters. Their approach and result may

be viewed as an order of magnitude approximation. For their mixture at

0®C and 0.6 mole R22,

Up ~ aiji/ 60

In turbulent flow, the following assumption is sometimes made for the

eddy diffusivity:

Ep = e.p

Since the film flow is turbulent and since the presence of nucleate

boiling may destroy the viscous sublayer, the actual diffusivity may be

anywhere between these values (1 and 60).

In the models described in Chapter 7, a decision was made to assume

parametric values of a^ to try to bound the results.

( f) Surface Tension

Surface tension of the pure components was estimated via the following

rela tion

:

o = A+BT+Cr2 + DT3 T[»K] , T[mN-m]

30
A B C D

(13B1) 37.969 -.01575 -6.73E-4

(152a) 52.828 -.12150 -2.10E-4

1142E-9

4349E-10

For the surface tension of the mixture, [Re79] provides little guidance.

Mole fraction weighting was assumed, regarding equation (2-1). Since

the pure components are not particularly disparate, this assumption

should lead to little error.

2 .4 The Effect of Non-Ideal Property Behavior on the Heat Transfer

Coe f f ic ient

Transport properties of mixtures are rarely determined by ideal mixing,

i.e., simple mole weighting of the component properties. Mixtures tend

to have higher liquid viscosities and lower liquid thermal conductivities then would be suggested by ideal mixing. The impact of these

physical physical property tendencies are evaluated below.

In single phase heating, the following equation is widely accepted to be

of sufficient accuracy for predicting heat transfer coefficients:

Consider first, a as calculated from ideal mixing

(2-3)

31
and for a mixture using the appropriate mixing rules

a„ = SH c X ^ -0-“

“ jjO.2 PmL ®L

Dividing (2~3) into (2~4)

Q 0.4 0.4 0.6

^mL _ PmL aid Xm

a- . iim Xid id P ^ “L

Now, it is known

~ 1, < 1 < 1 from mixing rules

CPid ^^id

(2-4)

(2-5)

Theref ore Va . j id

< 1 always

Thus, the mixture's single phase heat transfer coefficient should be

less than that predicted by a mole fraction weighting of the pure fluid

properites. The analysis can now be extended to forced convection

evaporation flows.

For evaporating flows, the following correlation form appears often in

3 2

the literature.
“2(}) = “L A(X^^) ( 2 -6 ) -B

So, assuming ideal mising rules

^id2(+) “idL ^ -B (2-7)

and for actual mixing

A - A -B id2^ idr tt id ( 2- 8 )

Dividing (2-7) into (2-8)

^ cItt, X^. °2 V ^ ”L ^^id

“i'»L

(2-9)

Now,

Xtt

,0.9 , ,0.5 ,0.1 l-x\ /Pv\ P /^^L\

Pl

so.

Xtt id

Xttm

/r, \0-5 ,0.5 ,0.1 , ,0.1

/ ^Lm \ / P vid \ / PLid \ / Pvm \

vLid/ \Pym

/ y

^Lm / I, Py id /

( 2 - 10 )

Substituting (2-10) and (2-5) into (2-9)

33
a /C /ii \0 .4

°m2d) _/lPLm_\ /iiLid\

'id

2c{) 'PL id

,

id

0.4

/ PLm \

\PLidj

0.5B \0.5B 0.5B

P vid \ / PLid

vm PLm

Pym

Pvid,

v0.5B

Grouping terms:

*^m2cj) _ / ^PLm ^

/

PLid \

“id2(}) V^PLi^y Ulia /

/PVm

\PVid

O.IB

,0.5B , \0.5B '' PLm \ / Pyid \

^Lid / \ Pvm /

(2-11)

Away from the critical point the density ratios are ~ 1 and Pyaj/Pyid ~ 1

for R152a/R13B1 so, ®in2(})/®id24> ^ ^ always. The evaporative heat

transfer coefficient for the mixture is less than would be calculated

from ideal property behavior.

Now, near the critical point, PLn,/pLid > ^ PVm^PVid ^ these

tend to balance the other terms, so nothing definitive can be said.

Furthermore near the critical point, estimation of transport properties

is exceptionally difficult.

The exercise on the previous page, which to the author's knowledge, has

not appeared in the literature, simply shows that even in the absence of

the mass transfer resistance, assuming ideal mixing may lead to serious

overestimation of heat transfer in both single and two phase mixtures.

3 4
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• 06^ .278 a8 5.87 289 .65 .0010496 .0010567 .05**7 .35739 1.3935 1.42uS

.080 .345 28 4.40 289 .34 .0010369 .0010460 .05*36 .05*52 1.3710 1.4C56

.100 .403 28 ..97 28 9 .06 . 00 10245 .00103 53 .05359 .05204 1.3491 1.3907

.1^0 .453 28 1.59 288 .74 .0010122 .0010746 .05162 ,0*989 .1.3779 1.3758

.140 .496 i8C.2S 288.42 .0^10002 .0010139 .04989 .04*01 1.3073 1.3608

.160 .535 27t.96 288 .09 .0009883 .0010032 .04*37, .04636 1.2874 1.3*59

.160 .568 277.71 2*7 .74 .06 09767 .0009925 .04702 .04*9

1

1.2680 1.3310

, 2 q

'> 276.5’ 287 .39 ,06 09652 .00C9818 .0458? .04’62 1.2493 1.3161

.220 .625 275.37 287 .02 .C009539 .0009711 .0**7j .04748 1.2311 1.3011

.240 .6*9 27a. 2« 286 .64 . PO 09428 .000960* .04379 ,04146 1.2134 1.2*o2

.260 .670 273.23 286.24 .0609319 .0009497 .04292 .0*654 1.1962 1.2713

.280 .689 272.24 28 5 .fct • CO 09211 .0009389 .04714 .03972 1.1795 1.2564

.300 .706 271.29 t85 .41 .CP09104 .0009282 .0*14? ,03«98 1.1632 1.2415

.320 .722 27l.39 284 .97 ,00u8999 .0009175 .04077 .03831 1.1*74 1.2265

.340 .736 26 9.54 2*4 .5? .060»896 .0009068 .04017 .03770 1.l3c0 1.21 16 .360 .749 26 £.7? 284 .04 .0608794 .OOO806I .039o’ .03’1

5

1.1169 1.1967

.380 .760 26 7.95 283 .55 . 0008692 .0008854 .03916 .03664 1. 1022 1.1818

.*00 .771 467. 2» 293 .04 .060*592 .00087*7 .03863 .03618 1.05 78 1.1668

.420 .781 26c. S3 284 .51 •0008493 .00086*0 .03818 .03575 1.0737 1.1519

.440 .790 26 5.88 2*1 .94 . 0GuS395 .0008533 .03776 .03*36 1.0599 1.1370

.4 60 .799 265.26 281 .37 .ci008?97 .0008426 .03‘*36 .03*00 1.0*6* 1.1221

.460 .807 264.67 28 0 .76 , 000*701 .0008319 .0369* .03466 1.0331 . 1.1071

.SCO .814 264.11 280 .13 .000*105 .00C8212 .03661 .03*3* 1.02 CO 1.0922

.'-20 .821 26 .’.5* 279.46 .0008009 .0008105 .03626 .03404 1.0071 1.0773

.540 .827 263.07 29o .76 .0607914 .0007998 .03592 .03*76 .9944 1.0624

.560 .834 264.59 278 .03 .0007819 .0067*91 .03559 ,03»50 ,9819. 1.0475

.580 .839 26 4. 12 277 .26 .0607724 •0007784 .03526 .03’25 .96 95 1.0325

4800 .845 26 It 6.* .-^76 .44. .0007630 _,D007677 .0349* .03300 .95 73 l.ni 76 .da” .851 26 1.25 275 .59 •0007436 .00075^9 .03*61 .03’77 .9451 1.0027

.640 .856 26C.84 274 .68 . 0607441 .0007462 .03*29 .0325 * .9331 .9878

.660 .861 26C.44 273.73 .C"07346 .0007355 .0339u .03731 .9212 .9728

.680 .866 26l.U5_ 272 .71 .0007251 .0007248 •03362 ,03209 .909* ,95 79 .700 .871 25 S.66 271 .64 .06 071 5 5 .0007141 .0332‘* .03187 .8976 .9430

r72Q .677 25-.. 26 2-^0. 49 ,0007659 .000703* .0329? .03165 .83 5* .9281

.740 .8o2 25 4.92 269. 2« .000696? .0006927 .0325a .03142 .8741 .91 31

• 7 6 J .887 25 f.55 267 .V9 . 0006864 .0066*20 .03216 ,05119 .8625 .8982

.760 .893 256.19 266 .61 .0" 06 76 5 .0006713 .03175 .03094 .8508 .88 33 .800 .899 , 257.62 465 .16 . 0006664 .0j06*06 ,63133 .03069 .8391 .6684

.82u .905 25 7.46 263 .64 .0006562 •0006*99 .03088 .036*2 - .8 2 74 .85*5

»84ri .912 25 7.1'’, 262 .0“ ..uO 06458 .0066*92 .03041 .OaOl

3

.8156 ,8385

.660 .919 25 £.7t 26 0 .52 .0006352 .0006285 .0^992 .02982 • .8039 .8236

.8oO .9t7 25C.37 249 ,C^ . 0nQ6244 .00061 78 .0^9*3 .02948 .7920 .8P87

.90u .936 25c. 0? 25 7 .74 .0006 13

3

.0006071 .02*94 .02»1 1

• .7301 .7938

.920 .945 ?5 5.68 2*6. 6» . G00602C .006596* .02845 .02869 • .7681 -.7788 _

.940 .956 255.35 255 .85 . 0605904 .00058 57 .02’96 .Oc82? .7560 .7639

.960 . .969 ..25 5.05 _a55 ,25 ,C"'u5T8^ ,00057*9 ,64746 .02’6! _ '...ZOS .74 St .960 .933 25 0.8'' 254 .84 . 00 j5o61 .00656*2 .6e69? .02’36 .7315 .7*41

1 .OOT 1 .ouo 25 0,6? 254 .6? .0005535 .0005535 .02653 .02*3* • .7191 . .7J91 ,

Table 2-1: Comparison of EOS values and mole fraction weighting

of pure components.

35
Cb

4 0 20

Tt! T5 3^ 4^0 CCnFDSITIOtJ >*. 1 To T ?0 T t>v

t/'

COnPOSITIOrj ( \ \ Z2fi t>^ mol • s >

O'*

COnPOSlTlON f;i52fl bv

Figure 2-1: Comparison of Transport Properties as determined

by mole fraction weighting and mixing rules

36
CHAPTER 3 : EXPERIMENTS

3 . 1 Introduction and Historical Review

This chapter describes in detail the experimental apparatus,

instrumentation, and data reduction me thods used in this report. The

remainder of this section reviews the types of experimental test rigs

which have appeared in the literature. Sections 3.2 through 3.4

describe the detailed features of the test rigs. Section 3.5 displays

the tests done to provide some assurance of the quality of the data.

Problems which were encountered are discussed in Section 3.6. Finally a

summary of the data is provided in Section 3.7.

Host experimental rigs described in the literature have been designed as

shown in 'Figure 3-1. Fluid was circulated via a pump or compressor

through, a smooth heated circular tube where it was boiled/evaporated,

and then reliquified in a condenser. Preheaters and afterheaters and

sometimes pressurizers were employed to control entering or exiting

conditions. Pressure taps were installed along the test section, and

these pressure readings were used to determine the local saturation

temperature of the moving fluid. Wall temperatures were determined by a

series of thermocouples attached to the tube wall by solder [Ba53

,

A160], spot weld [Ch79, MiSl], braze [Sa61] or mechanical clip [Di66

,

Ra83 , Ab82] . The test section itself was electrically heated [Ch77,

Ch66a, St66, Go65, Di66, Mi81] or heated isothermally by fast flowing

water [A160, An66] or by a condensing fluid surrounding the tube [Ba53] .

In any case, the heat flux was considered well-known and the local heat

transfer coefficient was then experimentally determined by the equation:

37
a (3-1) q/As

The test section in some investigations was made of glass so that visnal

observation of flow patterns could be made [St66, Di66] . However, the

use of glass had a serious deficiency, forcing its eventual abandoument.

A plating process was used to provide a continuous metal film on the

inside of the glass test section. The metal film served as an excellent

electrical resistance heater, however nonunif ormi tie s in its surface

caused the surface roughness (despite attempts at milling smooth) to

cavitate and swirl the flcMr and augment the heat transfer. Ihe variable

surface thickness also caused nonuniform heat generation. Most studies

instead used thin wall metal tubes in which the temperature drop through

the wall is quite small. 'Flow visualization' with metal tubes can be

attempted through deduction, either from void fraction measur ement s, or

from the appearance of large differences between top and bottom wall

temperature measurements indicating stratified flow, [Ch66a] .

3 .2 General Description of Test Rigs Used In This Investigation

llirough the course of this investigation, two experimental rigs were

built and utilized.^ Both employed a horizontal stainless steel tube

(length 2.7 meters; inside diameter .9 cm; outside diameter .95 cm)

which was electrically heated.

^Preliminary results of tests conducted with Rig #1 have been published

in [Ra83] . Hie author wishes to stress that the construction and

original data collection described in [Ra83] was shared with his

advisor for the experimental portion of the report. Since then,

several improvements have been made independently in the data reduction

techniques as well as analysis, interpretation and presentation.

3 8
Rig #1 is described in Figure 3-2. A semi-hermetic, oil free pump

delivered subcooled liquid refrigerant to the test section. Heat was

generated in the tube wall by applying a DC voltage difference along the

tube. The test section itself was heavily insulated (approximately 15

cm radial thickness) to reduce heat gain from the surroundings; the

minimal heat gain was accounted by calibration (described later). The

vapor generated in the test section was reliquified in an oversized

conde nser/ rece iver. The pump then drew on the liquid reservoir in the

condenser and the cycle completed. Inlet subcooling and flow rate were

controlled by valves in the liquid line. Subcooling and pressure level

could also be modified by altering the condenser temperature (by changing

flowrate or supply temperature on the brine side of the condenser).

Thermocouple stations were located at axial positions shown in Figure 3-

2b. At each station, thermocouples were clamped at 90° intervals around

the outer tube circumference. Instream thermocouples were centered in

the flow, extended and pointed upstream for a distance of at least 2 cm,

at the single phase liquid inlet and two’ phase outlet. Pressures were

also measured at these locations but not in the heated section. Fluid

temperatures in the heated section were estimated from an assumed pressure drop distribution and thermodynamic equilibrium. Sight glasses

located at the test section inlet and outlet allowed visual verification

of the flow pattern. Flow rates were determined by means of a

calibrated turbine meter in the subcooied liquid line.

3 9
One of the features of Rig was the use of a uniform heat flux along a

fixed tube length. With a given heat and mass flux and degree of inlet

subcooling, the outlet quality is fixed at:

Ah ac t - Ah

"out

sc Ah.

(3-2)

where

Ah act

q DqL m

heat added to refrigerant by DC power supply

"^^sc = ^PT^^sc

= C (T^^^ - = heat needed to raise sub-

^ ^ cooled liquid to saturation

or bubble point

Generally, Ah >> Ah , i.e., the liquid is only slightly subcooled, so

V SC

that

:

^out DoL

mAh

V

(3-3)

At a specified heat and mass flux, the outlet quality is then determined

by the tube length. To reach high exit qualities with low heat flux a

tube length of more than 20 meters is required in some cases. This

length is impractical clearly for experimental purposes.

In order to obtain data over the full quality range at the required heat

and mass fluxes and without using a tube length greater than 5 meters

40
(available space), a second experimental rig was constructed. It is

displayed in Figure 3-3. The principal change is to employ two distinct

heating sections, the first of which serves as a preheater. The tube

itself was continuous, but heated separately by two independent DC power

supplies. The first serving as a preheater provides partially

evaporated fluid to the new shorter test section. The quality at the

test section inlet is:

^in = Ah^r - Ahse

Ah..

(3-4)

where

Ah

pr

_ ‘^nh ^o^T>h m

Lpj. = length of preheat section

Upon entering the test section, the fluid is further evaporated by heat

provided from a second power supply so that

X = X + out in ^ V

(3-5)

with

AhTS

qxs DqLxs

41
Lts “ length of test section

By using a large, at times unrealistic, preheat flux, qualities at the

test section inlet could be made greater than with Rig #1. In the test

section itself, lower more realistic heat fluxes were used to further

vaporize the fluid. The test section itself was .6 m in length, so that

quality changes across the test section were relatively small. To

'build up' the entire quality range of interest, 20% to 90% vapor,

several tests had to be run at a given mass flux. In each test, the

amount of preheat was selected to provide a different inlet quality to

the test section. While the use of a preheat section allowed the full

quality range to be investigated, the time for data collection was

increased greatly (factor 8) over that which would be necessary if a

long uniformly heated tube was used. It also requires much stricter

repr oducab il ity of flow rates, heat fluxes and composition. Recommendations regarding improved experimental design are made at the end of this

report.

While Rig ^2 differed conceptually only in its use of a preheater,

several changes were also made in the instrumentation and data reduction

techniques. The following sections describe both rigs in great detail

as such the discussion is somewhat fragmentary. A summary of their

differences is provided in Table 3-1.

The sections are organized as follows:
3.3 Testing Protocol

3.4 Measurement and Data Reduction Technique

(a) Wail temperature

(h) Mass flow rate

(c) Heat flux

(d) Pressure

(e) Instream temperature ( ini et- outl et)

(f) Data acquisition sysl:em

(g) Sampling for composiltion

(h) Calculated fluid temperature

( i) Overall logic: data reduct

i

on schem^

Qual ity Assurance Tests

(a) Single phase heating tests

(b) Energy balance

(c) Pressure drop: measured vs. predict

(d) Reproducabil ity

(e) Effect of Preheater

3 .3 Testing Protocol

With the uniformly heated test rig. Rig #1, a series of tests were

performed at the following conditions:

G =

( kg/m^/ sec) (kw/ m^)

P

COMPOSITION (bar)

R152a 200-700 10-40 1.2-2. 4 (a)

R13B1 400- 1200 20-40 5 .7-7

.833 wt R13B1 200-600 3 0-40 7-9

.750 wt R13B1 200-600 30-40 5. 7-6.

6

.706 wt R13B1 200-550 3 0-40 4-7

.662 wt R13B1 200-550 30-40 4-7

.454 wt R13B1 150-3 00 20-40 5-7

(a) isolated tests at higher pressure (5 bar)

The selected mixture compositions span those recommended by the

refrigerant supplier for use in heat pumps. Most of the mass fluxes

were typical of those which might be employed in heat pumps. The heat

43
fluxes were representative of those found in evaporators in today's heat

pumps. Rather th

trolled to be tho

boil ing phenomena

strict physical c

coefficients be tw

impossibl e.

an controlling pressure, outlet temperatures were conse typical in the desired application. Unfortunately,

is also a complicated functiLon of pre ssur e. so that a

ompari son and interpretation of the heat traiisf er

een pure fluids and mixtures is com pi icated. if not

With the second rig , the follow ing condition s were sel ec;ted:

COMPOSITION G ‘^•ph/ Ac ‘It s/ Ac Pts

(kg/m^/ sec) (kW/m^) (kW/m^) bar

R152a 100-300 10-95 10-20 4. 70-4. 80^

R13B1 200-500 10-50 10 4 . 70-4 . 80

.80 wt R13B1 200-500 10-70 10 4 . 70-4. 80

.5 8 wt R13B1 200-500 10-70 20-30 4 . 70-4 . 80®

.37 wt R13B1 100-400 10-80 10 4 . 70-4 . 80

.18 wt R13B1 100-300 10-90 10 4 . 70-4 . 80

a

:

isolated tests at other pre ssur e s

In all Rig #2 cases , pressure w as controlled a t a f ixe d level typ

that which might be found with mixtures in a heat pump. This eipi

tal pressure was se lected based on the range of condense r tern pera

which could be prov ided by the brine system.

3 .4. Measurement and Data Reduction Techni que s

Heat transfer coeff icients are calculated fr om

:

44
a (3-1)

The measurement of these and other critical variables are discussed in

detail below.

3. 4. a) Wall temperature, T^

Wall temperature measurements were made with 0.25 mm thermocouples (T/C)

which had been silver soldered and flattened to provide good thermal

contact. Silver soldering was selected so that the T/C junction would

survive dryout accidents. Ihe T/C leads were arranged as shown in

Figure 3-4 to reduce any 'fin' effect conduction gains. The T/C junction

and wires were isolated electrically from the tube by a very thin layer

of teflon tape (< .01 mm). Good thermal contact was maintained by

clamping the thermocouple to the tube (see Figure 3-5). Inside wall

temperatures were calculated from the measured outside temperatures by

use of the steady-state radial, one dimensional ( 1 - D) conduction

equation with uniform heat generation and assuming adiabatic conditions

on the outside of the tube.

With Rig #1, wall temperature difference s were in fact measured.

Specifically the difference between the instream outlet temperature and

the local wall temperature were used; this temperature difference itself

was referenced to a thermocouple submerged in a slush ice bath— see

Figure 3—6. The use of temperature differences is generally considered

more - accura te than absolute temperature measurements. However, the

45
potential stability of the measured outlet temperature may be questioned, Entrained droplets strike and depart this instream thermocouple

so that the T/C sees alternately vapor and droplet temperatures and may

read something in between depending on its response time. In the case

of pure fluids the measured outlet temperature was stable. This

stability results from the fact that saturation temperatures change

relatively little in the axial direction in the absence of pressure

drop, no change would occur. Droplets and vapor tend to be near this

saturation temperature. In the case of mixtures, however, entrained

droplets may have a much different temperature since the bubble point

temperature varies axially since evaporation is non- i sothe rmal even in

the absence of pressure drop. Thus, temperature fluctuations in outlet

T/C measurements were greater for mixtures than for pure fluids, and

wall temperature measurements which were referenced to the outlet T/C

reflect these fluctuations.

One other potential difficulty with the Rig #1 wall temperatures is the

analog-to-digital 'mV to °C' conversion. The usual industry technique

is to utilize the curvefit formulas of MBS monograph 125 [NB ]; the

published errors in these formulae is +.3°C. Near room temperature,

where most of the Rig #1 data was taken, the error is in fact much

smaller (<.1°C). However, at colder conditions (-20°C), the error can

in fact be 0.6°C.

Rig #2 employed a different measurement and data reduction technique for

wall temperatures. Each wall thermocouple was referenced strictly to an

electronic ice bath temperature (precision of electronic ice bath *.02®C

4 6
typically, +.05 maximum). In this way, the wall temperatures were freed

from instream fluctuations. Secondly, the use of an electronic ice bath

reduced uncertainties regarding the quality of the slush ice bath. The

use of more closely spaced test section thermocouple stations (see

Figure 3-3b) provided redundance to verify the goodness of the measured

data. Finally, data was reduced with a more accurate curvefit to the

'mV to °C' data of the NBS Monograph; the 4th order curvefit generated

by the author has a maximum error of +.01°C over the 100° C temperature

range of interest.

The higher precision of the data collected with Rig §2 was necessary

because of the lower heat fluxes employed in the test section of Rig #2.

The data of- Rig #1 is still of satisfactory quality.

Corrections for heat gain from the room and for the teflon tape

resistance and any contact resistances were made by the following procedure. Single phase liquid tests were run at high flow rate and zero

heat input. Under these conditions, the fluid inlet-outlet temperatures

rise was very small (.2°C). If there was no heat gain from the room and

if the T/C's were in perfect contact with the fluid, the wall T/C

readings would match exactly the local fluid temperature. These single

phase tests were run at various fluid temperatures covering the range

used in later tests. The AT between the fluid and room ranged frcm 0 to

50°C). At the maximum AT between fluid and room a heat gain of about

200 w/m^ was measured. This can be compared to the lowest heat flux

employed of 10,000 w/m^. Based on the measured AT of an actual boiling

47
test, this heat gain was subtracted away from the measured wall temperatures to give the value of used in equation (3-1).

b) Mass flow rate

Though mass flow rate is not necessary to determine local a, it is

required to calculate local equilibrium quality. In order to determine mass flow rate, a turbine meter was used in the subcooled liquid

line about 50 diameters upstream of the test section. With Rig #1 the

signal was sent to a pulse counter which took readings once per second.

With the second rig, the signal was sent additionally to a counter

integral to the data acquisition system. The two counters agreed to

within 1% over the range of interest.

The turbine meter/pulse counters were calibrated with water at near room

temperature (scale and electronic stopwatch technique). Temperature

corrections were not made, as they are very minor (<< IS)) [Ma83]. The

turbine meter response is also flat over a wide range of Reynolds numbers so that a viscosity correction was unnecessary. It was discovered

from energy balance tests that near the upper end of its rated flow rate

the spinning rate of the turbine meter was less than expected. Measurements in this flow rate range were avoided.

Calibration of the meter was made before the Rig #1 tests and before the

Rig #2 tests (approximately 1 year apart). The change in calibration

was less than 1%, the estimated accuracy of the measurement.
Finally with Rig #1, a rotameter was installed to provide visual confirmation of flow rate, as well as redundancy in measurement. It was

removed from Rig #2 after it developed an internal leak which was

difficult to repair.

c) Heat flux

Heat was generated by DC power supplies as noted previously:

o Rig #1 and Preheat Section of Rig #2: Dynapower Corporation

(0-60V, 0-300a)

o Rig #2 Test Section: Rapid Electric Company (O-lOv, 0-150a)

The DC power supplies were also checked for the addition of AC ripple

current. Though the Dynapower Corporation claimed the ripple to be <5%

at full load, its vhlue was found to be 50% at part load. A bank of

capacitors was used to reduce its ripple to the point that the AC

contribution to the total heat flux was less than 1% [Ra83]. The integrity of the capacitors was checked throughout the measurement program.

AC rippled with the Rapid Electric Company power supply was measured to

be less than 1%.

Heat flux measurements (i.e., electrical input) were made with digital

voltmeter integral to the data acquisition systems. Voltage drop across

the test section and preheat section was measured at the busbars.

Current was calculated by measuring the voltage drop across a calibrated

resistor in series with the test section. Early in the testing program,

the electrical resistance of the stainless steel tube was checked and

its resistance determined to be linear with distance suggesting the
absence of local hot spots. The variation of electrical resistivity

with temperature was calculated to be less than 1%, the estimated

accuracy of the heat flux measurement [Ra83]

.

d) Local pressure

Local pressure values are needed to estimate the local fluid temperature

of equation (3-1). In studies reported in the literature, it has been

common to place pressure taps near thermocouple stations so that in the

vicinity of the wall temperature measurements, one could calculate the

local fluid saturation temperature. A decision was made to avoid this

approach for the following reasons: (a) the stainless steel tube was

thin and pressure taps might have intruded into the flow stream; (b) the

only means to fix the pressure tap leads would be soldering;, the solder

would have provided a preferential electrical path (a local shunt)

creating a local irregularity in heat flux; (c) pressure drops were

relatively small, and errors would be small in estimating local pressure

from overall measured values of pressure.

To the author's knowledge, no determination of the effect of pressure

taps on measured heat transfer coefficients has appeared in the literature. As such, an experiment was devised to make such a determination.

A test was run with refrigerant R22 as the evaporating fluid. Pressure

was measured at the inlet and outlet, with boiling taking place very

near the inlet. A linear pressure drop was assumed to occur between the

location of x = 0 (saturation boiling point location) and the outlet.

The test was repeated twice with the local a varying about 1%.

50
Following these tests, holes were drilled and hypodermic needles silver

soldered in place about 5 cm downstream of each thermocouple station

(see Figure 3-7); the opening at the needle top was sealed with epoxy.

The needles served to simulate small pressure taps. The R22 test was

then repeated with identical conditions and data reduction. The results

of the comparison are shown in Table 3-2; in general the introduction of

the pressure taps reduced the a by 10%. No change in pressure or heat

flux was measured. The a result was surprising in that if any change

occurred it was anticipated that an increased a would be observed due

to increased nucleation at the tap locations or increased film

turbulence due to tap intrusion. Instead, the reduction might be

explained either by: the needles served as fins to add heat from the

room, causing the wall thermocouples to read somewhat higher than anticipated; or the pressure tap intrusion, if it extended into the flow,

increased the upstream film thickness slightly. The solder may also

offer lower electrical resistance, so that the heat flux in the other

parts of the tube might have been slightly raised. It is not clear

which, if any, of these mechanisms caused the observed change, but the

change is apparent. In any case, further tests were made without this

type of experimental arrangement.

Figure 3-2b shows the means by which pressure was measured for Rig #1.

At the outlet of the test section a tap was made through the busbar by

spark erosion so that the hole would be exceptionally smooth. A calibrated pressure transducer and gauge were connected. At the test section inlet, a similar tap was made and a pressure gauge installed.

5 1
Inlet and outlet differential pressure was also measured both with

a .139 bar (2 psi) pressure transducer [Sensotec] and a .6895 bar (10

psi) gauge. The absolute pressure devices were calibrated with a dead

load tester; the size of the pressure gauges however prevented readings

from being more precise than + .0689 bar (+ 1 psi). The outlet pressure which was used in the data reduction was that of the pressure

transducer accurate to .006895 bar (+ .1 psi).

The .139 bar (2 psi) differential pressure transducer unfortunately had

insufficient range. The .6895 bar (10 psi) differential pressure gauge

had sufficient range but could be read, to only .017 bar (+.25 psi) at AP

> .13 9 bar (2 psi). A decision was made in the original data reduction

[Ra83] to use the differential pressure gauge results in all cases. The

inlet pressure was then calculated as

Pin = Pout^TD) + AP( GAUGE) (3-6)

where the designations (TD) and (GAUGE) represent measurements by the

transducer and gauge, respectively.

For Rig #2, pressures were measured as shown in Figure 3-3b. Pressure

transducers were employed at the preheat inlet and test section outlet.

Differential pressure transducers were used across the test section with

a range = .139 bar (2 psi)) and across the whole tube with a range

= .345 bar (5 psi). While the pressure tap at the test section inlet may

be questioned due to the R22 test results described above, care was

52
taken to reduce its potential impact. First, the hole was made by spark

erosion so that there would be no intrusion into the flow. Secondly,

the tap was located in the busbar so that there was no problem with

electrical shunting. Thirdly, no thermocouple stations were placed in

the immediate area of the pressure tap. For Rig #2, pressures were then

obtained from

(Preheat) =

Pout^'^^^ +AP5 (TD) (3-?a)

(Test Section) P.^^ = Pq^^(TD) + AP2 (TD) (3-7b)

where APj(TD) and AP2 (TD) represent the measurements by the .345 bar (5

psi) and .139 bar (2 psi) differential pressure transducer.

The differential pressure transducers were calibrated in an upward and

downward traverse bellowmeter and a mercury manometer. Unfortunately,

this could only be done at atmospheric pressure. Any errors which might

develop by the use of the transducers at higher absolute pressure could

not be quantified. Estimated accuracy is +/- .005 bar.

Given these overall pressure drops, local pressure values, i.e., the

pressures at the thermocouple stations need still to be estimated. In

[Ra83] , the e st ima tion was done by: (a) neglecting the single phase

pressure drop in the region between the subcooled inlet and the

saturated boiling point location (BPL) , i.e., the position where i = 0;

and (b) assuming a linear pressure drop betwen the BPL and the outlet.

53
The implications of the latter, more critical assumption can be examined

by the following study.

Figure 3-8 displays the results of applying a widely recommended pressure drop correlation, that of Mar tinell i-Nel son modified by Chisholm

[Ma4 8 , Ch67 a] , to the typical flow conditions employed in Rig #2. The

correlation requires a numerical integration, and steps of Ax = 3% in

the preheat section and Ax < 1% in the test section were taken. The BPL

was determined by an energy balance, and is denoted in the Figure by an

arrow. The series of curves represent different levels of preheat flux,

i.e., different overall Ax's for a given flow rate. In all cases the

test section flux was fixed at 10 kW/m . It can be seen that as the

change in quality between inlet and outlet increases, the preheat section pressure drop becomes sharply non-linear. However, in the test

section, with the relatively small Ax, the pressure drop is nearly

linear. These results imply that the assumption of a linear pressure

drop in the test section for Rig #2 would be quite valid, but the same

assumption in the preheat section at large Ax is somewhat questionable.

The linear pressure drop assumption in [Ra83] then may be questionable

since (1) flow rates were high increasing the non-linearity and (2) the

distance between pressure taps was larger in Rig #1 than with Rig 02 .

These errors are balanced by the neglect of single phase pressure drop

and by the fact that at large flow rates x tended to be small with Rig

#1 .

54
In order to quantify these linear pressure drop errors a sensitivity

analysis was run with varying pressure drops. The linear pressure drop

assumption typically caused about a 5% error in a for Rig #1; errors

could be as high as 15%. The error in preheat a of Rig #2 would be

roughly 1/5 smaller, since the Rig #2 preheater is 20% shorter than the

Rig #1 test section.

A few alternatives are available to the linear pressure drop assumption.

The pressure drop correlation could be used to predict local pressure

values. This procedure however requires numerical integration,

increasing computation time dramatically in the case of mixtures where

an iterative scheme is required because of the nature of the EOS code.

It also requires normalization of the results to the measured pressure

drops. A more convenient approach, and the one used in the final data

reduction of Rig #1, was to weight the linear pressure drop assumption

depending on the overall x:

For ^out .4

.4 < ^out < 1

^^LIN 0 < X (3-8a)

' — P out xout/2 ^out/2 ^ ^ < ^out

^^LIN 0 < X (3-8b)

_ p out xout/2 ^out'^^ ^ ^ < ^out

where the pressure drop predicted by assuming a linear relation

between BPL and the outlet

^out

^o ut/2

the outlet quality

the outlet quality divided by 2.

5 5
The effect of this approach is to fit the curves on Figure 3-8 in a

piecewise linear fashion.

While not exact, the pressure drop is corrected in the proper direction

and reduces the overall error. The same approach was used in the preheat section of Rig #2; the direct linear pressure drop assumption was

retained in the test section of Rig #2, since errors were negligible.

e) Instream Temperature (Inlet-Outlet)

With Rig #1, unshielded thermocouples were installed in the flow stream

and supported by a brass collar (see Figure 3-6). The hole made by the

thermocouple was sealed with epoxy. This technique provided an accurate

measurement of the instream temperature however, the epoxy seal tended

to fail over time, causing leaks and refrigerant loss (the latter being

particularly critical with mixtures since one ' compone nt is lost preferentially) .

With Rig ^2, shielded thermocouples were sof t- sol de r ed in place (see

Figure 3-6b) . These thermocouples eliminated the leak problem but

provide poorer contact with the flow stream. They also tended to fail

inexplicably, therefore neither approach was particularly advantageous.

An attempt was made to insert an instream T/C at the test section inlet.

This thermocouple would have provided information about the true temperature rise across the test section. The thermocouple, unfortunately,

affected both the single phase and two phase wall thermocouple readings.

56
Figure 3-9a sicws the a calculated for single phase liquid heating R22

tests. The thermocouple was inserted into the flow stream near the tube

bottom. As can be seen, a wide circumferential scatter is observed.

Figure 3~9b shows a similar test with the thermocouple removed. A

series of tests were also conducted under flow boiling conditions.

Figure 3-10 shows the results of these tests with and without the

thermocouple in place. Again, data scatter is reduced without the

thermocouple. In order to preserve the purity of the wall temperature

measurements, the Rig #2 tests were run without the instream thermocouple at the test section inlet.

This finding of the effect of instream thermocouples may be signif

The literature abounds with test rigs employing instream T/C's; it

been assumed often that the' large turbulence in the flow is suffic

to overwhelm any disturbance introduced by the disturbance of the

mocouple. While this may be true with large tube diameters and sm

instream thermocouples, it was not the case here.

icant

ha s

ient

theral ler

f) Data acquisition system

Data collection for both rigs involved the use of a Hewlett-Packard (HP)

Series 80 computer connected to a data acquisition system (Rig ^1:

Fluke and Rig #2: HP 3497a). Automatic scanning of all thermocouples,

pressure transducers and flow meters was done. Data was saved when

steady-state was reached, i.e., when instream temperatures and pressures

variation dissipated. This requirements was satisfied typically one

hour after a change in mass or heat flux was made. With the second rig.

57
pressure control frequently added even more time between tests. With

Rig #1, the result of 10 scans which took place at 1 minute intervals

were stored. With Rig #2, seven to fifteen scans separated by 40 second

intervals were stored. These results were later averaged, their standard deviation determined, and used in further data reduction.

g) Sampling

Mixture composition was determined by withdrawing a liquid sample,

expanding it to a complete vapor state and analyzing the vapor sample by

gas chromatography. Sample bottles are shown in Figure 3-11. The addition of a pressure gauge to the sample bottle helped determine if the

sample had been completely vaporized in the expansion process (one could

check the measured pressure at room temperature to see if the sample was

well into the vapor region as predicted by the equation of state).

However, sampling techniques associated in Rig #2 introduced unnecessary

error. In what was thought an improvement, the sampling lines were

purged of air before taking a final sample. This was accomplished as

discussed in Figure 3-11; some vapor may have been trapped in the

process. This vapor, preferentially of the more volatile component, may

have caused variation in the results. Later sampling done without air

pxirging proved very reproducible. Sampling errors on the order of 0.5*5)

could have been avoided. On the other hand, the technique was able to

show that virtually no air had dissolved in the refrigerant based on the

5 8

GC analysis.
h) Calculated fluid temperatures

The only quantity missing

temperature. This had to

in the determination of the a is the

be estimated for reasons cited above

fluid

For pure refrigerants the saturation temperature of each thermocouple

station was calculated from property tables, given the local pressure

as found by the procedures previously used. Sometimes researchers

report their results based on Tf = Tgg^^CP)^ other times it is based on

T£ = Tjjjg^g = In this report, all values are reported on the

basis of

For mixture

s

, the standard approach in the literature is to base T£ in

equation (3-1) on Tgqt,' thermodynamic equilibrium temperature. The

equilibrium temperature was calculated from the equation of state since

at each thermocouple station, pressure, enth’alpy and original overall

composition are known.

i) Overall data reduction scheme

The above detailed discussion is necessarily fragmentary. Figure 3-12

is a flow chart of the data reduction scheme. As the figures are for

the most part self-explanatory, only a few comments are provided here,

principally on the mixtures' algorithms. All data reduction was

performed on HP series 80 computers. The Equation of State (EOS) necessary for the mixture work, is fifth order in nature with several internal iterative loops. The code was developed, by the EOS author [Mo82]

,

5 9
and used here without change. ^ It requires as input T, P and overall

molar composition (5^) and outputs overall h, v, s, X, Y, ^pj^ and Cp^

on a molar basis. Runtime for the equation of state alone is 1-2

minutes on the HP Series 80 computer. As seen in Figure 3-12, two

iterative loops involve the equation of state. The first is to determine the BFL; a bisection search method was used to determine a two

phase quality very close to zero. Qosure was reached typically in 6

iterations. The second iterative loop involved calculating the equilibrium temperature at each T/C station. There a secant method was used

to reduce the number of iterations to 3-5.

Overall the program took 30-45 minutes to reduce the data from a single

test, calculate the local a's, and print the results in tabular and

graphical form. By contrast, the data reduction for pure fluids took 5-

10 minutes on the Series 80 computer, most of which was for printing

t ime

.

Typical outputs of each run are shown in Figure 3-14; a complete set is

available upon request. Appendix 3A contains a summary of the measured

results which can be used by other researchers.

^The code results were compared by the author of this report with a separa.te code developed by [Mc85] with virtually identical results.

60
3 .5 Quality Assurance

3. 5. a) Single phase heating tests

In order to verify temperature measurements, several single phase

liquid heating tests were made. The results of those with Rig #1 are

shown on Figures 3~13a and 3-13b. The measured values have been

compared with the well-known equation:^

Ul = .023 ^(ReL)^-^(PrL) 0.4 (3-9)

as well as the more accurate equation [Pe70]:

(f/8)ReLPrL

ki + k2PrL(f/8) ^''^(Pr^/^ - 1

with f = ^1 "

ko =

(1.85 log^Q Re

1.64)

(3-10)

All tests show good agreement. These tests were for Rig #1; a few tests

with Rig #2 and R22 or R152a showed similar agreement.

b) Energy Balance

In order to assure that the instrumentation was behaving correctly, an

energy balance was made between fluid temperature rise and energy input.

Specifically, a comparison was made between

This equation has been credited variously in the literature to Dittus

and Boel ter, McAdams, Colburn, or Kraubold (F.R.G.). The author is not sure where credit belongs but will refer to it in this paper as DittusBoelter equation.

61
AEf = mC (T ^ - T. ) I out in' energy gained by the fluid

AE = qnDL = electrical heat input

The quantity | ^

I was less than 7% with single phase heating

zi£ R22 tests with Rig #1 and less than 5% with R22 and R152a tests with Rig

#2. Energy balances quoted in the literature by other researchers are:

REFERENCE

A160

An67

Ch66a

ENERGY BALANCE

+ 5%

+ 10%

+ 2%

1

In the process of these tests, the [As81] value for Cpj^ of R152a was

shown to be in error by 15%. Independent work by [Mo85] later confirmed

this finding.

c) Pressure drop

The most widely recommended two phase pressure drop correlation at low

pressures is that of Mar tinel 1 i-Nel son [Ma48], with various authors

suggesting modifications [Ch67a, Hs76] . In their original development,

Martinelli and coworkers used dimensional analysis and a large data base

to predict isothermal two-component (e.g. , air-water) pressure drop.

^In [Ch66a], measured outlet T and calculated outlet T based on pressure

measurements disagreed, however.

6 2
Later Martinelli and Nelson extended the approach to evaporating steam-

-water systems. Refrigerants were not included in the original

Martinelli efforts. A literature search of the application of the

technique to refrigerants revealed the following:

REFERENCE REF

An67 Rll

0^6a R12

Si83 R12

Ag82 R12

A16 0 R22

An67 R22

In horizontal evaporating flow, the

terms,

AP = A?£+ APj^

(AP - APexT>) /APexn

+ 10-3 0%

-30-50%

+50/

20%

+/-2 5%

0-20%

-20%

pressure drop is composed of two

(3-10)

where

AP£ = pressure drop due to friction

AP^ = pressure drop due to flow acceleration

Martinelli and coworkers developed an empirical procedure to predict the

frictional pressure drop.

63
APf = APl»2 (3-11)

where

(3-lla)

(3-llb)

APj^ = Pressure drop, as calculated for single phase liquid flow,

for that portion of the flow which is liquid.

^ f L G^(l - 2D Pl

L = length of tube

(3-llc)

and

Qiisholm [Ch65]^ (3-lld)

The pressure drop due to acceleration can be derived from momentum

considerations to yield

APa u_2_x^\

1 - e ;

(3-12)

An alternate procedure which has been suggested is to calculate a 'property index' ( ^ fluid of interest. Then

find the water pressure which gives the same value of the index and use the water/steam densities in (3-lld). For the refrigerants used here,

very nearly the same results occur.

64
assuming a quality of zero at the inlet.

To apply equations (3-10), (3-11) and (3-12) correctly, a stepwise

integration must be performed. This requirement derives from the fact

that X changes as the flow proceeds downstream. The frictional pressure

drop is a fairly strong function of quality (as was shown on Figure 3-

8). At each step, the inlet, mean, and outlet qualities were calculated. Void fractions were estimated from Mar tinell i-Nel son [Ma48] .

Equation (3-11) was applied at the mean quality equation (3-12) was

applied at the step's outlet and inlet qualities, and the results

subtracted:

APa APa

j out

- APaj in (3-13)

The total pressure drop was the sum of the individual steps. The

predicted results were compared with the pressure drop measurements of

Rig #2 for all pure fluid tests. Figure 3-16 shows the results of a

comparison between measurement and prediction. Results were considered

quite satisfactory.

d) Preheater effect

A preheat section is commonly used to help set a desired quality of the

fluid under investigation independent of the heat flux within the test

6 5

se ct ion.
Consequently, in most cases the fluid experiences an abrupt change in

heat flux upon leaving the preheater and entering the test section,

which may affect the entrainment and therefore the wall temperature

readings. The influence of sudden change in heat flux at wall

thermocouples was tested at high flow rates, high qualities and low test

section heat fluxes. For one set of experiments with pure R152a, no

heat was supplied to the test section, while the heat flux of the

preheater was changed between 30 kW/m^ and 90 kW/m^ . For a mass flow

rate of about 400 kg/ sqm/ s, no significant change was found in readings

of the test section wall temperatures. Nevertheless, all wall temperatures were an average of 0.25 K higher than the saturation temperature

of the fluid calculated from the pressure drop; the value was the same

for all thermocouples at a particular station. The data shown in figure

3-17 are for a thermocouple group which is 50 diameters downstream of

the preheater. The fa'ct that the wall temperatures are slightly higher'

than the saturation value, can be explained by the superheated liquid

leaving the preheater, which is significantly but not completely cooled

by further evaporation driven by both the existing superheat and the

pressure drop.

The test with 75 kW/m^ preheater heat flux was repeated with mass flow

rates lower and higher than the one previously chosen. The deviation of

the wall temperature readings becomes smaller with higher flow rates.

This behavior might be expected because with increasing flow rates

turbulence and the pressure drop increases causing higher evaporation

66
rates and a faster decrease of the superheat available in the liquid

phase

.

A second set of experiments was conducted with a 0.37 wt 13B1 mixture.

A fixed heat flux in the test section and a fixed mass flow rate was

maintained but heat flux was varied in the preheater. At the same time,

the degree of subcooling of the fluid entering the preheater was

changed. Therefore, when a large degree of subcooling was set, a large

amount of preheat flux was required in order to obtain a given quality

at the preheater outlet. Figure 3-18 shows the results of these tests.

The heat transfer coefficient measured with the test section is

obviously a function of the quality, but not of the amount of preheat

used. Lower case letters in Figure 3-18 refer to tests where the liquid

was subcooled by 5K, while the upper case letters refer to tests with a

considerably more subcooled liquid (25°K) entering the preheater. The

difference in preheat fluxes in order to obtain comparable qualities is

between 10 to 20 kW/m^ or 20 to 30 percent.

e) Reproducibility

Reproducibility of two phase flow results is rarely discussed in the

literature. In the case of refrigerants, only two values could be

found: +4% [Sa61] and +10% [A16 0] .

Some Rig #1 tests were repeated at various points in the day and sometimes from day to day. Agreement of Rig #1 heat transfer coefficients

was within +^2% for tests done one day apart and +^5% for tests done one

67
week apart. Eigliteeti tests with pure R152a were repeated approximately

3 weeks apart for Rig #2 , Preheat measured values were compared. In

the original tests, test section heat fluxes were lOkW/m ; iu the later

tests, the test section was set at 20kW/m^. Of the 54 data points, all

agreed within 8%; most agreed much closer (about 4-5%). Most of the

variation with Rig #2 was due to differences in mass flux. A few checks

were made with mixtures, with similar findings.

3 .6 Problems

Three problems occurred during the data collection with Rig §2 . First,

the measured and calculated temperatures at the outlet for one set of

tests with R13B1 disagreed by about 1°K (at high flow rate, high

quality). This set of data was not used in the further data analysis.^

0

Second, the electrical isolation failed during some of the mixture tests

at the top thermocouples in each of the preheat thermocouple stations.

At the time, the preheat data was considered superfluous and repairs

were not made in order to continue test section data collection. Later

it was realized that the preheat data was a substantial resource. This

data is included here by averaging only the side and bottom stations.

The estimated effect of excluding the top station from the average is to

increase the mixture's local a by 5%. The dependence of heat transfer

on circumferential location is discussed in Chapter 5. The third

problem was the failure of the electric icepoint reference for the last

^With R13B1, the higher the flow rate and the quality, the greater the error.
series of tests, those with 0.58 wt 13B1. To bypass this problem, the

data acquisition system was used directly with internal (software)

temperature compensation. For the tests the uncertainty in temperature

is + 0.1°K, according to Hewlett Packard specifications. As such, test

section heat fluxes were maintained at higher values for these tests to

reduce the overall uncertainty in the heat transfer coefficient.

3 .7 Summary of Experimental Data

A total of 1459 data points were collected with R152a/R13B1 in the

following proportions: R152a:409, R13B1:170, Mixture s ; 880 . The data

are tabulated with relevant variables in Appendix 3A.

Approximately 20% of the data is not in the annular flow regime and is

not included in further analysis.

The tested range of relevant variables includes:

Heat Flux: 10-95 kW/m^

Mass Flux: "150-1200 kg/m^/sec

Composition: 0. 0-1.0, several intermediate values

Pressure: 1. 7-9.0 bar

Quality: 0.0- 1.0

Martinelli Parameter (1/X^^): 0.3-35

Subcooled Liquid Reynolds Number: 3000-50000

Prandtl Number; " 3-4

All parameters, except Prandtl Number, varied by nearly an order of

magnitude. The data base then provides a strong basis for analysis of

physical phenomena as well as the heat transfer coefficient.

6 9
Table 3-la: Hardware Differences Between Rig #1 and Rig #2

Rig #1 Rig #2

Tw

o AT between T^ and T^ 0 individual T/C with

redundant stations

T

reference 0 slush ice bath 0 electronic ice point

^out 0 Ptd Pgauge 0 same

Pin o Pgauge o ?TD Pgauge

^Ptot o AP (2 psi) and Pg^uGE 0 AP (5 psi) AP (2 psi)

and APq^ugE

Heat Flux 0 uniform heat 0 preheater and test sec- tion heater

Tf 0 unshielded, inlet and

outl et

o shielded, inlet and

outl e t

D. A. S. 0 Fluke - HP85 o HP34 97 - HP86B

Sampling Technique 0 no air purge single

bottles

0 air purge, multiple

samples, pressiire gauge

Flow Metering 0 Rotameter Turbine

me ter

o Turbine meter

Condenser o Temp, controlled o Temp, and flow

controlled (via bypass)

to give improved

stability and pressure

control

7 0
Table 3~lb: Data Reduction Differences Between [Ra83] and This Thesis

(Rig #1

w

o NBS jMo no graph 0 same

1 ocal

Tf

o 1 ine ar

ba se d

pr e s sur e '^gaugedrop

o linear between T^^^

(measured) and ^BUB

o piecewise linear AP,

based on calibrated

APtd if within range,

else APq^q£

o equilibrium temperature based on improved

equation of state

7 1
Table 3-2: Effect of Pressure Taps on Heat Transfer Coefficient

Before (Af ter) Before ( Af ter) Before ( Af ter) Bef ore (After) Taps

4096 (3546) 4636 (43 46) 3665 (3069) 0.00 (0.00)

4494 (3830) 46 87 (4511) 3654 (3404) 0.10 (0.10)

4278 (3574) 43 80 (3915) 4233 (4062) 0.18 (0.18)

4221 (4068) 4448 (3393) 4096 (3620) 0.26 (0.26)

4488 (4040) 4352 (3393) 4091 (3416) 0.34 (0.34)

4584 (343 8) 4233 (3359) 3 807 (3126) 0.42 (0.42)

5402 (3801) 4454 (407 9) 3989 (3 93 8) 0.50 (0.50)

5504 (4698) 4749 (4516) 4153 (4034) 0.58 (0.57)

5379 (6656) 5612 (4182) 5033 (4925) 0.66 (0.65)

Refrigerant: R22

Mass flux: 228 kg/m^/sec

Heat flux: 2 93 18 W/m^
TYPICAL TEST RIG

T/C T/C

P P P

Figure 3-1: Typical Test Rig in the Literature: P=Pump;

C=Compressor ; p=pressure tap and gauge

73
RIG #1

TM-Turbine met*f

R-Rotam«tef

S-Sight glass

P-Pressure gaug*

F-Filter/drisr

Pu-Pump

AP-Differential pressura

TD-Tranaducer

TO

Flo>

FIGUP.E TEST SECTION RIG //I

Figure 3-2: Experimental Test Rig : Uniform Heating. No

Preheat Section,

74
RIG *2

Figure 3-3: Experimental Test Rig #2: Preheat and Test

Sections employed via separate DC power

supplies

.

75
76

conduction

losses

due

to

"fin"

effect.
Plain tube

Teflon tape

wrapped around

entire tube

Thermocouples

placed around top

and sides of tube

Second teflon tape

wrapped around tube,

covering thermocouples

Stiff teflon sleeve placed

over assembly and tied down to insure pressure.

Teflon tape under T/C

squeezed to 0.1mm thickness

Figure 3-5; THERMOCOUPLE MOUNTING SCHEME

INCLUDING ELECTRICAL ISOLATION

77
TEMPERATURE MEASUREMENT

1 - kMtrMin T /C

2 - Wall T/C

3 - lc«batt« roforanca T/C

Figure 3-6: Wall and Instream Temperature Measurement: D\'M=

Digital Volt Meter; DAS: Data Acquisition System

Unshielded Thermocouples were used v;ith Rig '/I. Shielded thermocouples were used with Rig ^/2

.

78
FIGURE SIMULATING PRESSURE TAPS

Figure 3-7: The Simulation of Pressure Taps: Taps mounted

about 5 cm downstream of wall thermocouple

measurement stations.

79
80

At

UNO

MMIK

(BL-tersI
Figure 3-9: EFFECT OF INSTREAM THERMOCOUPLE:

Single phase (liquid) heating test with and without instream

thermocouple at test section inlet

(T-Top, B-:Bottom, S-Sides)

DittusBoelter

equation

81
i m=135 Ib/hr

R-22 AVN066 AVN065

AVN067 s T uJ i s *

?

8

s

UJ0

O1

= 1

i 5 1

§

1 X

QUALITY: .47 , , ,.55 .55 I I I .62 .63 , 1 1 -7’

1

ul AVN186 AVN187 AVN188

LUo

o T

1 X

I i * 1

’ • 1 1

®

QUALITY: —.46 .54 .52 , , ,.60 .65 •T’3

L-j-i:LJL ii. -J 1 1

Figure 3-10: EFFECT OF INSTREAM THERMOCOUPLE ON EVAPORATIVE

HT. TRANSFER COEFF.

Top set of curves: with instream thermocouple

Bottom set of curves: without instream thermocouples

82
SAMPLING TECHNIQUE

Test rig Una (liquid)

S«mpt« bottle

Procedure:

1. Evacuate sample bottle lr>cludfng- vapor t liquid reservoirs: dose valves

2. Attach bottle to test rig (all valves closed)

3. Open valves PI & P2 to fill Hquid section

4. Close valves P1 &P2; remove bottle from test lig 5. Open valve P3 to expand liquid Into vapor

6. Bring bottle to gas chromatograph for analysis

Error: Between steps 2 and 3, valve P1 opened with bottle only loosely

attached. Purges air between valves P1 and P2, but Introduces

vapor rather than liquid Into this section.

Figure 3-11: Sampling Technique to determine mixture

composition

83
Figure 3-12a: Data Reduction Scheme for Pure Re<^r leerants

84
Figure 3— 12b: Data Reduction Scheme for Mixtures

85
300 — CDWENSATION ORVE: SO «t R13B1

aeo -i- _ 260 -I- I t

s »> t

S 200

CaWEhSiTlOH CURVE: 37 <rt R13B1

290 4-

Figure 3-13: Condensation Curves (T vs. H) for Various

Compositions. A poor guess of dH/dT may lead

to divergence.

86
REFRI6;HIXT. C0NCENT(«TI52a) .630 FLOM-.ANNULR 04;04:20:53:32_ —in preheat-

20.4 20.1 18.8 10.2 9.9 9.9 9.8 10.0 -14.2 17.5 18.3 18.2 9.5 9.7 9.6 9.6 9.6 8.1 7.7 ii

17.ti 17.9 17.8 9.5 9.6 9.5 9.5 9.4 17.9 17.8 18.3 9.6 9.7 9.5 9.6 9.5

1 preheat- —in 1 ——

AuxT: 22.1 -21.7 -13.9 12.3 8.0 -26.3 -7.9 deg C PRES; 4.77 .02 .05 4.70 5.08 4.84 .08 bars

HEAT; 124.08

n*r Q 45.2 2.60 51708 6800

FLOW; 67 144 80.4

4-++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++f++++++++++

HEAT TRANSFER COEFFICIENT (w/sqi/K) Ht. 152a TOP LSIDE BOTH RSIDE AVS KassQuaiity VapCoip LiqCoip Eqb.T

f++++++f+++++++++++++++++++++++++++++++++t+t++++++++<-+++++++++++++++++++++++++++

3119 3805 3784 3676 3596 .35 .41 .75 3.83

3474 3811 4117 4142 3886 .48 .46 .79 5.22

4231 4442 4607 4223 4376 .59 .50 .82 6.51 2777 3841 3981 3813 3603 .70 .54 .35 7.52

3074 3566 3869 3566 3519 .71 .54 .85 7.54

3254 3820 3980 3829 3721 .71 .54 .85 7.56

3522 3746 3937 3788 3748 .71 .54 .85 7.58 3129 3853 4223 4038 3811 .71 .54 .85 7.60 TESTSEC AV6; 3680 ENERGY BALANCE; I.IZ 7.66

Figure 3-14: Typical Output from Test Run Data Reduction.

T: Top; B: Bottom; S: Side average

87
ti- PREDICTED • Drttus t Boelter |W/m^/°K)

3000 3500 ^000

h PREDICTED Petukhov IW/m^ "K|

3000 3500 4000

Figure 3-15: Comparison of Predicted to Measured Data

for Single Phase Heating Tests

88

EXPtRIMtNTAL

IW

m^/"K|

h

EXPERIMENTAL

|W,fn^/

K|
PRESSURE

DROP

PREOICTION

PRESSURE

DROP

PREDICTION

89

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30 60 90

PREHEAT FLUX (kW/m^)

• Values shown are for T/C station 50 diameters

downstream of preheat. No heat in test station.

Top and bottom T/C agreed with each other

within 0.1 °C.

• Data at 15 kW/m2 (preheat) showed distinct

top/bottom difference even 50 diameters

downstream. This is due to thicker liquid film at bottom. (Continued evaporation occurs due to pressure drop.) Thus flow patterns persist

downstream.

^igure J-17: Effect of Preheat ^lux on Test Section

Ivall Temperature Measurements. The large

error bars are due to the use of the DAS

internal temperature compensator, rather than

the normal ice point reference.

QO
EFFECT

OF

PREHEAT

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91

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QUALITY*
?5aT.i
CHAPTER 4: ON THE SUPPRESSION OF NUCLEATE BOILING

4 . 1 Background

The most common explanation of the physical mechanism of heat transfer

in annular flow boiling is that of a superposition of a forced convection evaporative process and a nucleate boiling process. With

increasing vapor quality the liquid film thins and the core vapor

accelerates (as required by continuity). Heat transfer to the core is

improved by this acceleration and the thinning of the liquid film also

serves to lessen its conductive resistance. Heat transfer is thought to

improve sufficiently and to occur with such rapidity that bubble growth

disappears. At this point, the nucleate boiling process is said to be

suppressed, and vapor generation is due strictly to evaporation from the

vapor-liquid interface.

It is critical to know if nucleate boiling is suppressed. First, if the

process becomes purely convective/ evapora tive, then the heat transfer

coefficient should be independent of wall heat flux, and depend on flow

and fluid parameters (e.g., mass flow rate, eddy diffusivity, Prandtl

number), as in single phase shear-driven flow. In this case, the heat

transfer process might be modelled strictly from single phase considerations. Also, correlations for annular film condensation might be applicable to the evaporative case, in the absence of nucleate boiling. If,

on the other hand, nucleate boiling exists, from a sufficient number of

sites then the liquid film viscous sublayer may be destroyed, and the

fluid flow and heat transfer processes become more difficult to predict.

93
In the case of mixtures, chaotic concentration profiles may occur when

nucleate boiling is not suppressed.

For heat transfer purposes, it is the boiling site density which is

particularly important. The existence of an isolated, metastable bubble

is not significant. Throughout this chapter, the former is of interest.

However, as a starting point, the prediction of the existence of any

individual bubbles is required.

4.1.1 Conventional Theory of Onset and Suppression of Nucleate Boiling

The onset and suppression of nucleate boiling are effectively the same

problem, differing only in the direction from which the heat flux

required to sustain nucl ea tion/bubble growth is approached. Classical

theory for the growth of a bubble begins with a force balance.

The maintenance of a spherical bubble requires, from a force balance,

the liquid immediately surrounding the bubble to be superheated by an

amount

:

- Ty 2a

ap sat

3T

(4-1)

where r^ is the radius of the bubble. Upon applying the ClausiusClapeyron relation and assuming the inside bubble temperature to be

saturated, equation (4-1) becomes:

94
Tl - T* = (4-2) 2c

'*‘sa t j. TAv,

The same criterion can be applied to a heated surface with a vapor

bubble, assumed to be hemispherical, developing from a surface cavity of

mouth radius, r . In the case of a heated surface, however, the liquid

c temperature surrounding the bubble will not be uniform generally, but

instead diminish with distance from the heated surface. Also, the

bubble shape will be approximately that of a truncated sphere with

radius of curvature r^, rather than completely spherical. Both of these

effects were accounted by Hsu [Hs62] , followed by others. First from

pure geometrical considerations, the height, yg, and radius of

curvature, r^, of a spherical truncated bubble are related to the mouth

radius by: .

•

yg = ( 1 + COS0) r^ = c^r^ and rp = —^— r„ = ^ sine ^ ‘^2^c

so that equation (4-2) becomes:

Tl - 2o Ah,

sat (C2/Ci)yg TAv^

(4-3)

Secondly, Hsu assumed bubble growth to be possible only if the liquid

temperature at the bubble cap was superheated to satisfy (4-2). For a

linear temperature field as might be reasonably approximated across a

thin thermal boundary layer, the wall heat flux and temperature field

are represented by:

95
(4-4)

and

T(y) = \ y = \ — y o<.y<.6

At (4-5)

6

where y is the distance from the wall and 5 is the boundary layer

thickness, the temperature at the edge of which the condition is assumed

sa turate d.

Equations (4-3) and (4~5) may be plotted for a given heat flui and film

thickness, as shown on Figure 4-1, and most importantly the range of

cavity sizes which may be active ( i. e. , those from which ebullition is

possible) can be determined. At cavities outside the range shown on

Figure 4-1, the liquid is not sufficiently superheated for bubble growh

to occur. A large superheat is necessary to activate the more numerous

small cavities. The superheat may derive from either a large wall heat

flux or a 1 ow liquid thermal conductivity (see equation 4-5). For large

cavities the superheat requirement is small, but this superheat must be

maintained far from the heated surface for the bubble to grow to its

critical radius (hemispherical shape).

In the case of annular flow boiling, measured wall superheats have been

sufficient seemingly to initiate bubble growth even when none has been

observed [La62] . Collier and Pulling proposed to explain the apparent

96
contradiction by noting the sublayer thickness in turbulent films is

smaller than for stagnant pools [Co64] . They assumed that cwiug to

turbulence, the liquid outside the viscous sublayer was at or close to

saturation. The temperature drop occurs then across only the small

viscous sublayer, or:

Jw = ^ - Tsat)

VS

T(y) = X^-^y 0 <y< 6^3 (4-7)

where 6^^ is the thickness of the viscous sublayer.

Collier and Pulling recommended using a dimensionless viscous sublayer

thickness of y'*’ = 7, In the single phase turbulent flow literature, the

viscous sublayer thickness has been presented in values from y"*^ = 5 to

y"^ = 10. In fact turbulent eddies carrying cool fluid from the vaporliquid interface may penetrate the sublayer down to y"*^ = 1 [La62] . More

relevantly, Bej an has studied analytically buckling and rolling of

liquid layers in shear-driven flow (as occurs in annular flow boiling).

He determined the value of y^ = 7.62 as the viscous sublayer thickness

which persists regardless of possible buckling or rolling [Be82] .

Several years later. Collier suggested a modification to the viscous

sublayer approach, relating the point of suppression to the Martinelli

parameter, [C08O] . This parameter can be related however to the

97
viscous sublayer thickness, as both are subject to flow conditions The

viscous sublayer is a function of wall shear stress, which itself is a

function of frictional pressure drop. Finally, Martinelli et al

predicted frictional pressure drop for two phase flows through the

parameter

4.1.2 New Alternate Theory: Enhancement of Nucleate Boiling

Recently, the conventional explanation has been questioned initially by

Mesler [Me76,Me77] and subsequently by Beattie et al [Be79,Be84].

Mesler has suggested that the heat transfer process, rather than

becoming convective/evaporative at high quality, is due even in thin

turbulent films to nucleate boiling . He has suggested that the high

heat transfer rates experimentally measured with thin films (high

compared to pools or thick films) is due to an enhancement of nuc 1 ea te

boil ing with thin films. The high heat transfer rates seen with thin

films are hypothesized to be due to evaporation of the thin liquid

microlayer and rapid replenishment of the microlayer. The replenishment

process with thin films is improved over usual pool boiling. With thin

films, the bubble ruptures the film surface and vapor escapes through

the top of the broken bubble, causing the liquid film to be

reestablished quickly. An improved replenishment process which is

related to film thickness might account for the observed improvement is

heat transfer with increasing quality.

^Collier's recent suppression criterion is reviewed in Appendix 4-A, as are other proposed criterion.
4.1.3 Suppression of Boiling with Organic Fluids

A second issue was raised by Toral [To79] , who suggested that c

suppression of nucleate boiling will not occur under conunon con

in annixlar flow boiling of organic fluids . These fluids of whi

refrigerants are included, have a thermal conductivity much low

water, and as such will tend to yield high wall superheats, suf

for nucleation.

ompl e te

di tions

ch

er than

f icient

4.1.4 Problem Resolution Methods

The issues then are:

(1) can the physical process by which vapor is generated be

entirely evaporative, or is it best described by nucleate

boiling theory?

0

(2) is it possible for organic fluids, specifically refrigerants,

with their relatively low thermal conductivity, to be

vaporized by an entirely evaporative mechanism in annular

fl ow ?

(3) can conventional suppression theory or various other

suppression criteria be verified (and modified for mixtures)

to quantify the point at which nucleate boiling is absent?

(4) are there unique mechanisms which occur with nonazeotropic

mixture s?

99
The follcwing techniques might be employed to resolve the problem;

A. Visual Evidence (e.g., vapor generation without bubble

presence or bubble presence with thin films).

B. Experimental Evidence

1. Dependence of the heat transfer coefficient on heat

fluxes and mass flux.

2. Effect of pressure on heat transfer coefficient.

3. Presence of hysteresis.

4. Dependence of heat transfer coefficient on quality.

5. Predictive ability of evaporative or pool boiling

models to flow boiling data.

The following discussion critically analyzes the literature for pure and

mixed fluids. Detailed reviews are available in Appendix 4C through 4F.

New experimental evidence for single and binary refrigerants is

presented. The new criterion for determining the suppression point for

mixtures is hypothesized. The discussion will attempt to concentrate on

refrigerants, but will cite several studies from other literature in

response to the cautionary note and advice of Butterworth and Shock

[Bu82] . It also serves as an interaction to the data base developed for

this report, and as such several graphs are presented to display the

data.

4 .2 Summary of Visual Evidence

Several visualization studies of flow boiling of pure fluids have been

done to determine flow pattern and bubble existence", the major studies

100
are discussed in detail in Appendix 4C Host of tiie studies have been

with water, but some with refrigerants. The studies employed transparent metal coating, heater strips on one side, or glass tubes. Often

the surfaces had been milled smooth to ensure uniform heat generation,

however, this process removes potential nucleation sites, preventing

generalization of results. In one case an artificial nucleation site

was added to the surface in order to witness boiling in a thin film

flow. This study done by Hesler led him to formulate his alternate

theory.

Nearly all visualization studies show some isolated bubbl e s w ithin the

liquid film, the number of sited bubbles diminishes with increasing

quality. The authors attribute the continued vapor generation to

evaporation from the vapor-1 iquid interface. It is possible however that

ebullition continued in small cavities or that bubbles were so short . lived as to escape notice even with high speed films or still

photographs, thus visual evidence is not itself definitive.

Ihe study by Hewitt et al [He84] showed activation of a site whenever

heat transfer through the film was inhibited by wave passage, suggesting

film thickness was an important though not solely definitive criterion.

Ihe Hewitt et al study also observed that vapor velocity had a strong

influence on the observation of nucleation. Tbe study of boiling from

an artificial site did not have a higher vapor velocity and does not

correspond directly to the physical case of turbulent flow boiling in

tube s.

101
Many visualization studies used tubes which had been milled smooth or

which were of materials without large cavity sizes; this could inhibit

bubble growth. However, they suggest that vapor generation can take

place in the absence of such cavity size availability, suggesting that a

mechanism other than nucleate boiling is the cause of such vapor

generation.

4 .3 Summary and Analysis of Experimental Evidence: Dependence on Heat and Mass Flux

Appendix 4D describes in detail the studies which examined the

dependence of the heat transfer coefficient on heat and mass flux. When

no dependence on heat flux is observed (a a(q)), nucleate boiling is

considered suppressed, and a = a(G). On the other hand, when nucleate

boiling dominates , the heat transfer coefficient is a strong function of

heat flux and a weak funtion of mass flux. Thus, the dependence of a on

G or Q may define the dominant heat transfer mechanism, and if the heat

transfer coefficient is independent of heat flux (a ^ a ( q) ) , then the

sole mechanism is usually considered evaporative.

A recent study by Aounallah et al [Ao82] showed clearly a ^ u(q) for a

range of qualities, heat and mass flux values. Care was taken in their

experiment to ensure that measurements at the same spatial location were

ccmpared. In direct response, Beattie and Green [Be84] cited work by

Bertoletti et al [Be64] with a similar experimental apparatus and also

using water as the working fluid* the Bertoletti data showed a strong

dependence on heat flux and was correlated well by a pool boiling

correlation.

102
The results of Aounallah et al appear to contradict those cited by

Beattie and Green (the Bertoletti et al experiments). However, the

apparent discrepancy may be resolved by examining the test conditions

used by the two groups. Ihe latter, where nucleate boiling was observed

to be dominant, involved higher pressures and heat fluxes where conventional theory suggests a small superheat requirement. Ihe conventional

theory therefore allows both experimental observations to be valid. The

much higher heat fluxes employed by Bertoletti et al most likely

produced a vapor generation process dominated by nucleate boiling.

In a separate publication, Beattie and Lawther [Be?9] describe their own

successful work in predicting pressure drop, at high quality by

theorizing the existence of attached bubbles within a liquid film, Hiey

point to their success as a proof of bubble existence.

Ihe heat flux level of the Beattie and Lawther experiment was also very

high, since their observations were made in a critical heat flux

experiment. Here again, the existence of attached surface bubbles are

entirely possible, and explained by the conventional theory.

Me si er has examined many studies of nucleate boiling in thin films,

noting high heat transfer rates and a dependence on heat flux. However,

the boiling studies cited by Mesler involved slow mov ing films. For

example, the referenced Toda and Uchida study [To73] involved laminar or

near laminar flows. Ihe study by Fletcher et al (referenced by [Me77]) was

designed specifically to avoid high vapor velocities, which Hewitt et al

[He63] observed to be important in the suppression process. Thus the

103
referenced studies are not strictly comparable to the case of the turbulent

flows associated with annular flow boiling.

4 .4 Summary of Experimental Evidence: Dependence of Heat Transfer

Coefficient on Quality

The inverse Martinelli parameter (1/X^^) is sometimes referred to as a

surrogate for quality. Because of its successful employment in pressure

drop prediction, several authors have used it in heat transfer coefficient prediction. Ihe idea was first advanced by Dengler and Addoms

(Appendix 4D) based on their experimental observations [DeS6]. Mesler

has reviewed the [De56] data, and upon careful examination, showed that

the data is not closely correlated by the use of 1/X^^. He further

attempts to show on theoretical grounds that the general approach of

using a = inappropriate. However, these objections to

the use of X^^ as a correlating parameter do not seem warranted. As

shown in Appendix 4B, the Mesler analysis of a/a^ = f(l/X^^) inadvertently neglects the fact that some parameters he considered constant do

indeed vary.

The enhanced nucleate boiling theory cannot explain a phenomena observed

in several experiments, that of a gradual reduction in heat transfer

coefficient despite increasing quality. At times the measured reduction

disappears as quality is further increased. Such behavior, originally

attributed to an entrance length effect [Go66] has been seen at L/D

ratios greater than 100, with pure refrigerants, water and with refrigerant mixtures [Ch67, Ma76,Ra83 ] . The experiments show in the nucleate

104
boiling dominated region, a decreases with increasing quality, Such

observations are in sharp contradiction to the hypothesis of Mesler,

which requires a to increase with reduced film thickness, i.e., an

increased quality.

4 .5 Snmmarv of Experimental Evidence: Effect of Pressure

Pool boiling experimental heat transfer coefficients increase with

increasing pressure. This often seen observation is accounted in equation (4-1) since increases generally with pressure. Additionally, surface tension, at least for refrigerants, decreases with

increasing temperature (related directly to saturation pressure). Both

of these phenomena tend to reduce the superheat requirement so that more

sites are activated for a given superheat as pressure is increased.

Conversely, in the case of forced conve c tion/ evapora tion, the heat

transfer coefficient may decrease with increasing pressure [De56] . The

vapor density increases with pressxire, so that at a given core vapor

mass flux, the vapor velocity decreases. The reduced vapor velocity

diminishes the level of shear at the liquid-vapor interface, inhibiting

heat transfer through the liquid film. The correlating parameter,

1/X^^, decreases with increasing pressure so that again, the predicted a

would decrease.

The opposite behavior associated with boiling vs. convection/evaporation

might serve then as a line of demarcation between the two mechanisms.

The data of Toral with organic mixtures showed a proportional dependence

105
between a and pressure, even at 'bigh quality' (x = .3). This suggested

the dominance of nucleate boiling in his experiments.

4 .6 Siimmary of Experimental Evidence: Presence of Hysteresis

Hysteresis has been found sometimes in the pool boiling of pure fluids.

Different superheat requirements were needed to initiate boiling when an

experiment was conducted first with increasing and then with decreasing

heat fluxes. Murphy and Bergles [Mu72] suggested that in subcooled flow

boiling, high heat fluxes activated small cavities and bubbles from

these cavities then migrated and activated large cavities. These large

cavities remained active while the heat flux is reduced. On the upward

heat flux traverse, the large cavities were considered fully wetted. It

was noted that in subcooled flow boiling, a reduced hysteresis effect

should be expected due to the steeper temperature j5rofile; large cavities with trapped vapor may remain inac.tive due to the profile.

The presence of hysteresis then might confirm the presence of nucleate

boiling. No parallel process occurs with convective evaporative flows.

4.7 Summary of Literature Review: Mixtures

The introduction of a second component has several consequences in the

analysis of the onset and suppression of nucleate boiling, as described

in detail in Appendix 4E.

First, the terms of the applicable equation (4-1) are changed in value.

Surface tension may be drastically affected by even small additions of a

1 06
second component (e.g., figure 1-4 with refrigerant and oil). The

theoretical value of dP,_<./dT is less for mixtures than for an equivalent pure fluid, suggesting an increased superheat requirement*, however,

the actual superheat requirement may be less than for either pure component, due to the change in surface tension.

Toral [To79] has attempted a theoretical study of the effect of

turbulence damping near the liquid/vapor interface in thin film, sheaxdriven flow. He concludes that with organic fluids and organic fluid

mixtures sufficient superheat w il 1 be available to initiate nucleation

under common conditions of heat and mass flux. If turbulence damping

exists, nucl eation wil 1 be even more likely, as an additional resistance

exists to transfering the heat away from the wall region. However, the

boundary conditions used by Toral are flawed (see Appendix 4£). This

conclusion may then be questioned, though not necessarily rejected with

his problem being correctly reposed.

Thome and Shock recently reviewed the effect of composition on the ONE

point and boiling site density [Th82] . While fewer sites are active

with mixtures, the difference is not systematically related to |l - l| ,

though mass diffusion is a likely contributor to change in boiling site

density. In some onset of nucleate boiling studies, mass diffusion was

seen as an important factor and in others, the ONB point was unaffected

by composition.

107
To date, no one has analyzed, either theoretically or experimentally,

the nature of the concentration profile in flow boiling with the

presence of nucleate boiling, and the consequent mass transfer resistances in the liquid and vapor streams. With ebullition in flow boiling,

the liquid surrounding the bubbles in the wall region will be depleted

of the more volatile component. This will tend to increase the superheat requirement, i.e., make it easier to suppress bubble growth.

However, at the same time, any resistance near the film interface (turbulence damping, both mass and thermal diffusion) will inhibit surface

evaporation, so that more superheat might be available near the wall. A

further complication is that the conductivity of the two fluids might be

disparate, so that upon depletion of the more volatile component around

a bubble, heat might be conducted more readily or with more difficulty

through the viscous sublayer. The ultimate effect of these multiple

competing processes has not been studied analytically for flow boiling.

4 . 8 Comparison of Experimental Results to Theory

4.8.1 Application of Conventional Theory to Pure Refrigerants and

Refrigerant Mixtures

The Hsu/Collier and Pulling suppression criterion was applied to the two

pure refrigerants used in this report. The pressure gradient, needed to

determine the wall shear stress and subsequently the thickness of the

viscous sublayer, was estimated using the Mar tinel 1 i-Nel son/ (Th i shol n

correlation. Contact angle was assumed to be 35°, typical for

refrigerants [St82]. A flow chart of the calculation is given in Figure

4-2.

108
Measxired mass fluxes and pressures were used. Properties were estimated

using the equations of Qiapter 2. Assuming all cavities to be available, the criterion suggests a very small superheat requirement.

Instead, a heat flux needed to activate a critical cavity size of 1.0 um

was calculated. Both Polley [Po82] and Stephan [St80] have offered this

size as a rough guideline for refrigerants. Cavities of size greater

than 1.0 um were assumed to exist either in an insufficient number to

affect the heat transfer, or to be fully wetted by refrigerant . This

assumption then modifies the basic suppression criterion, so that a

greater wall superheat is needed to initiate boiling than if all sizes

were available in large numbers and were unwetted.

Three factors complicate the analysis, leading to substantial

uncertainty. First, the estimate of the critical viscous sublayer

thickness is not exact. It depends both on the determination of pressure drop and on a selected critical value (Collier and Pulling's y^ =

7). Secondly, the selection of a critical cavity size may be in error.

Collier has suggested 0.5 pm as a rough guideline for refrigerants

[Co80] . This leads to a larger estimate of the suppression heat flux.

Thirdly, vaporization may take place nearer the bubble base even in the

absence of vaporization at the bubble cap. The required heat flux in

this case would be less than as calculated. These complications lead to

an estimated uncertainty of about +/- 40%. Despite the large

uncertainty, it will be shown that the criterion can be used with

success.

109
Figure 4-3 displays sample results of the procedure, shoiring the effects

of changes in pressure and mass flux. As pressure is lovered or as mass

flux is raised, the criterion predicts a greater suppression heat flux.

If the experimental heat flux was below the calculated 'suppression heat

flux' value, the heat transfer coefficient should be independent of heat

flux and instead depend proportionately on mass flux and quality. Conversely, if the criterion predicts sufficient heat flux, a dependence on

heat flux should be observed.

A similar analysis can be applied to mixtures and was applied here to

the R13B1/R152a mixture. Ihe governing equation is effectively the same

for mixtures, except as noted in Section 4.7. Properties such as Av^

and A£^ were evaluated at different compositions, so

AE^ = - ^(ig)

and Av^ = v^(Y*) - Vj(Xg)

The suppression criterion was then applied, assxming the liquid layer

was well-mixed, i.e., without any mass transfer resistance. It was

therefore implicitly assumed that the turbulence in the liquid film

supplied a sxxfficient concentration of the more volatile ccnponent to

the bubble interface. This is a very conservative assmnption for predicting suppression, since boiling site density is likely to be reduced

by the mixture. The above treatment then considers the mixtures as an

equivalent pure fluid. *^0 possible approaches to correct for mixture

effects on boiling site density were also hypothesized. An exact solution is available in the literature for the growth rate of an iaolated

110
spherical bubble located in a quiescent, uniformly superheated liquid.

When the basic equations are solved, a reduction in bubble growth rate

for a mixture over that of an equivalent pure fluid can be calculated.

Chapter 7 discusses this problem in more detail*, the reduction due to

mass transfer resistance, is given in equation (7-0). When this factor,

is applied to the suppression criterion, the required heat flux to

sustain ebullition is raised, typically by about 25% with aj/aj^ = 5 or

40-80% with aj/a|j = 60 as shown in Figure 4-4. The concentrations shown

are 'feed concentrations', i.e., the initial concentration of a subcooled liquid being evaporated/boiled. At the larger value of a^/aj^,

the mixture effect may be sufficient to increase the suppression heat

flux above other pure components. The assixiption with this approach is

that mass diffusion is the sole reason for reducing boiling site density.

An alternate correction factor can be calculated from the literature on

pool boiling of mixtures. As described in Chapter 7, equation (7-0)

underpredicts the meausred reduction in heat transfer coefficient for

the pool boiling of mixtures. A variety of empirically based correction

factors are available for predicting the reduction (Table 7-1). None of

the methods of Table 7-1 has been tested for flow boiling of mixtures.

However, the method of Stephan and Korner [St69] has been used widely

with some success in pool boiling. When it is used, the increase in the

suppression heat flux, may be sufficiently substantial to raise

the suppression heat flux for mixtures above that of either pure

component (figure 4-5).

Ill
4.8.2 Experimental Results: Pure Refrigerants

The first experimental results to be examined are those for pure R152a

at low pressure*, the tests were conducted with Rig If measured data

taken at the same mass flux and pressure but different heat flux levels

yield identical heat transfer coefficients, then boiling is completely

suppressed. Unfortunately, pressure was not held strictly constant with

Rig #1; however in some cases, the pressure variation was small enough

to allow such comparisons. The suppression point can also be inferred

approximately by the dependence of da/dx on quality. When da/ di becomes

strongly positive, forced convection/evaporation is dominant. Complete

or near complete suppression should occur in this range. Figures 4-

6a,b,c plot the effect of heat flux at constant flow rate. A strong

heat flux dependence is observed at low qualities, but this effect is

reduced with increasing quality. Shown also is the prediction of the

suppression criterion for the heat flux level required to initiate

boiling as a function of quality and the given flow rate. When the

criterion states that boiling should be suppressed, the measured data

are shown in upper case^ lower case letters indicate the criterion

predicts sufficient heat flux to sustain boiling of a 1 pm cavity.

The criterion predicts quantitatively the quality at which complete

suppression occurs. Apparent discrepancies are seen in only two cases

(runs 0LDH201 and OLDH203) where the error is within the range of

uncertainty in the method.

112
Both the figures and the criterion show that as mass fluz is increased,

suppression occurs at lower quality. A strong dependence on mass flux

is observed suggesting a convective/evaporative process to be dominant.

Figure 4-7 shows the effect of pressure on the heat transfer coefficient. The experimental value is greater at high pressure initially,

but the difference is reduced or disappears at high quality. These

results indicate nucleate boiling, easier to achieve at high pressure,

to be dominant at low quality. The boiling process then diminishes in

favor of forced convection evaporation at high quality. The transition

point is a function of heat flux: the lower the heat flux, the lower

the quality at which nucleate boiling diminishes. The initial decrease

of the heat transfer coefficient despite increasing quality has been

observed by several other researchers [Ch67 , Ch66a] . Mesler's proposed

explanation of the heat transfer process cannot predict this observation*, it in fact suggests the opposite behavior.

These results are consistent with the traditional theory. They

that nucleate boiling can be suppressed even at significant heat

levels with relatively low conductive fluids such as refrigerant

however suppression becomes much more difficult as pressure is

increase d.

sugge St

flux

s;

Similar Rig

level since

The results

#1 tests were

the condenser

on Figure 4-9

done with pure R13B1 at

could not be made colder

show little quality depe

the high pressure

to reduce pressure,

ndence and suggests

113
nucleate boiling domination. These results are consistent with the

criterion.

All pure refrigerant tests with Rig #2 were done at a pressure around

4.75 bar (+.2/-.02 preheat, +/~ >05 test section). Measurements were

made in the preheat section where heat flux levels were varied over a

wider range (10-95 hi/ sqm Rl52a^ 10-55 kW/sqm R13B1). Representative

preheat data is shown on Figures 4-9 and 4-10. Here a clear dex>endence

on heat flux is observed, indicating a strong nucleate boiling contribution.^ The suppression criterion predicts that at this pressure level

the actual heat fluxes were sufficient to initiate nucleate boiling.

There is a very slight dependence on mass flux.

Hie test section data is for low heat flux but high vapor quality. The

data is shown on Figures 4-11 and 4~12. Tests were done with R152a and

10 and 20 kW/ sqm in the test section at three different mass fluxes.

Figure 4-lla shows that only a weak dependence on heat flux occurs. The

dependence on mass flux is seen clearly in Figure 4-12. The dependence

on quality increases with increasing mass flux as was observed with Rig

#1 and by others in the literature [An66]. These results suggest the

dominant vapor generation mechanism is by evaporation, but that complete

suppression may not be achieved. The criterion predicts sufficient heat

flux to prevent complete suppression.

^The only substantial contradiction to this trend is with heat flux

above 50,000 w/m^, which yielded lower heat transfer coefficient than

expected. The high heat flux initiated a departure from nucleate

boiling (DNB) , with film boiling being the probable heat transfer

regime. DNB events were observed with pure R13B1 in other tests around

the same heat flux.

114
The test section data for R13B1 shows a dependence on mass flnx at high

i quality, bnt not at low quality. Nucleate boiling dominates in the low

I

i quality region but the process is controlled by conve ction/evapora tion

I at high quality. This conclusion is made tentatively however. The

I outlet temperatxire and pressure measurements for R13B1 tended to dis-

!

I agree (Chapter 3). Shown here are the results based on pressure

measurements. The temperature based results show less mass flux depen—

A Q

dence. In either case the dependence on mass flux is less than H!r'°

which has been widely used in correlating a in pure evaporative flow.

I

I This suggests that some boiling is present, and is in agreement with the

I suppression criterion.

j Finally, Rig #2 also allows a unique examination of the effect of a step

change in heat flux, since preheat and test section heat fluxes were set

independently. If the process were completely independent of heat flux,

then one would expect the measured heat transfer coefficient in the test

section to be greater than that measured in the preheat section, due to

! a continued increase in vapor quality. If on the other hand, heat flux

I

! was dominant, then a large change in heat transfer coefficient should

I accompany a large step change in heat flux.

: One can compare the ratio

the last preheat measuring

of preheat to test section

I

I parison. Note that as the

\ section, the heat transfer

of measured heat transfer coeffici

station and the test section with

heat fluxes. Figure 4-13a plots

preheat flux is raised relative t

coefficient ratio increases also.

ent s

the

such

o the

but

be tw e e n

ra tio

a comte s t

to a

i

I 115
lesser degree. These comparisons suggest that both mechanisms, boiling

and evaporation, are contributing to the heat transfer (at this pressure

level), though evaporation is dominant. It thus serves as a further

verification of the suppression criterion.

4.8.3 Experimental Results; Mixtures

Four suppression methods were tried for mixtures. The first treats the

mixture as an EPF. The next three account for mass transfer resistance

in various ways. The 'exact' and SK methods were displayed on Figures

4-4 and 4~5 , respectively. The last way is empirical, based on a pool

boiling method of Thome. As will be shown in Chapter 7, this method

predicts the measured heat transfer coefficient best for a large number

of cases.

Figures 4-14 through 4-17 show the effect of heat and mass flux on the

heat transfer coefficient at fixed flow rate and initial composition for

Rig #1. A strong dependence on heat flux is clearly observed;^ a weaker

dependence on mass flux is also seen. The dependence on pressure

appears greater than the dependence on mass flux; this is an indication

that boiling is not only present, but dominant.

All criteria predict sufficient heat flux to sustain ebullition. The

only exception is Thome's method which predicts suppression at the lower

weight compositions of R13B1, and high quality and mass flux. The data

^The effect of heat flux is slightly exaggerated due to varying

pressure from test to test.

116
indicate the Thome prediction is in error in these cases. However, the

error is within the range of uncertainty of the method.

The Rig §1 tests were conducted with various pressure levels. In Rig

#2, pressure was maintained generally around 4.75 bar level. The preheat tests were conducted again with heat fluxes varied between 10 and

90 kW/ sqm. As before, a dependence on heat flux was observed indicating

nucleate boiling to be present (representative Figures 4~9 and 4-10).

All suppression criteria predicted sufficient superheat availability.

There is only a weak dependence on mass flux.

Some hysteresis tests were also performed with 0.80 wt R13B1.

Measurements were taken with preheat fluxes raised (to a maximum of

40kW/ sqm) and then lowered. No change in heat transfer coefficient was

observed in the preheat section or the test section (at lOkW/ sqm) .

Despite the lack of hysteresis, some effect of preheat flux can be

observed.

The preheat results suggest therefore that boiling is not suppressed.

For all concentrations, the suppression criteria are verified for the

case of nucleate boiling existence.

Representative test section data (low heat flux, high quality) is shown

on Figure 4-18. The EPF method predicts (boiling possible)

at all compositions and flow rates. The 'exact' method with a Lewis

number equal to 5 predicts complete suppression only at the highest mass

117
flow rates and low compositions of R13B1. The exact method with Lewis

equal to 60 and the empirical methods of Stephan and Korner and of Thome

predict suppression at all compositions at high flow rates. The measured data show a clear and strong dependence on mass flux. This indicates that convection/evaporation is strong in this region, but does not

necessarily imply that boiling is absent.

As was done for pure components, the new approach of the effect of a

step change in heat flux was examined. At low heat flux, the data shows

a positive da/dx so that evaporation is much more effective, and could

support the notion of complete suppression.

These resul ts show th at forced convection/evaporation e f f e cts dom

i

na te

in the te st section. but are incon elusive regarding comple te s u ppr e s s ion

of nuci ea te boil ing. If the fact that forced convecti on/ e vapor a 1 1 on is

dominan t is extrapola ted to sugges t complete suppress! on. the n the EPF

methods i s incorrect

.

The exact ( Lewis = 60) and the emp i r ica 1 me thods

would then be validat ed. Ev idence based on heat trans fer c or r e la t ions

sugge St com plete suppres sion does occur with mixtures at these con ditions. Thi s evidence is discus sed in Chapters 5 and 7 Measur erne nts at

lower heat flux could cl early conf irm this conjecture; how ever th e

acctiracy of such measurements would have been poor.

4 .9 Conclusions and Recommendations

1. Conventional suppression theory is supported by experimental te»t»

as well as a critical review of the literature. Con t ra d i c t or>-

118
findings in the literature can in fact be explained by conv

theory. The alternate hypothesis of enhanced nucleate boil

annular flow boiling is not supported analytically or

experimental ly

.

e nt ional

ing with

2 . At pressure, flow and heat flux

pump evaporators, complete suppr

commonly observed with pure refr

lowered, nucleate boiling may be

fluids such as refrigerants.

1 evel s

e s sion

iger ant

absent

of most

of nucl

s. How

even w

residential heat

eate boiling is not

ever, as pressure is

ith low conductive

3. The conventional suppression criterion is verified quantitatively

for pure refrigerants. For mixed refrigerants the criterion was

modified to include mass transfer resistance effects. The result

is to lower the heat flux at which complete suppression occurs.

Methods were hypothesized from 'exact' and pool boiling theory.

These methods were validated in a qualitative sense. It may be

possible to have complete suppression for mixtures and not for

either pure component.

4. The conclusions of Toral regarding suppression of flowing mixtures

may or may not be valid. The problem should be reposed with the

correct number of boundary conditions. Analytic development is

also needed which accounts for a revised liquid concentration

profile in the presence of nucleate boiling. Experimental data

119
should be taken at sufficiently low pressure that one

complete suppression.

5 . Incipient

for mixed

sparse in

and suppressed boiling experiments need

fluids in flow boiling. The literature

this critical area.

to

is

might expect

be conducted

par ticularly

120
I

Minimum

3dniva3d^^3±

121

Figure

4-1:

Criterion

for

the

Onset

of

Nucleate

Boiling

(reprinted

from

Hs76)
Figure 4-2: Flow Chart for Determining SuDDres>^ i Heat

122
CALCULATED

SUPPRESSION

HEAT

FLUX

CO sa

lO

cvi

CO CO CO n n

CO CO X) -o ^ ^ 2 CO CO

O)

t o

CO

o

d

cq

d

lO

o

d

CO

o

cvj

• o

<

O

(2 UJ/m>I) xmd 1V3H NOISSBdddnS

123

Figure

4-3:

Effect

of

Pressure

and

Mass

Flux

on

Suppression

Heat

Flux

(Rl52a)
(SUJ/MM)

xmj iV3H Noissaaddns

124

Calciil.ited

Suppression

Heat

Klux

for

Mixtures—

Isolated

Bubble

Theory
CALCULATED

SUPPRESSION

HEAT

FLUX O

a>o

00

o

o

CO

6 >

O <

o

D

o

CO

o

CNi o

o

o

(sUi/M>l)

xmj 1V3H NOissauddns

125

Figure

4-5:

Calculated

Suppression

Heat

Flux

for

Mixtures

—

Pool

Boiling

Theory
(X/sUU/M>l) -ddaOO-lH

COh-COUJ '^COCVIt-o

COd

(N

d

d

o

00d

t^d

COd

ind

d

COd

CMd

d

o

i)u

3

XX

lUu

3

Q

(U rjin

126

o

Complete

suppression

predicted

•

Sustained

nucleate

boiling

predicted
HT-COEF.

W.tuh/.,t/Fl

S

«T-C0EF.

(l<t.tut>/.q(/Fl

I &

Figure 4-7: Effect of Pressure on Pure R152a.

boiiing dominates at high pressure

at large quality.

Nucleate

, even

127
h€AT FLUX

• 42203 M/iqa (6.4 bar)

0UD02B5

b 29330 M/iqa (5.7 bar)

OLD0286

SUPPRESSION CfirTERION

3 ^®

4 ^^

Figure 4-8: Effect of Heat Flux on Pure R1331. Nu'"' i boiling uominaLes.

HEAT FLUX

a 42212 «</iqa (6.4 bar)

0LO02B4

b 29494 M/tqa (5 B bar)

OLD0283

128
F igure

c.m

llu.

LXJ o

0

1

EFFECT OF HEAT FLUX

4.75 (+0.2/-0.1) bar

- 10

CME$

ll

LLHIO

0

1

EQB. QUALITY

4-9: Effect of Heat Flux on Pure Rl52a and Pl52a/R13B1

Mixture: Preheat Data

SI3

LL

U.

LLI O0

1

EFFECT OF HEAT FLUX

4.75 (+0.2/-0.1) bar

10

$

LL

LUO

0

1 t-I

EQB. QUALITY

129
EFFECT OF HEAT FLUX

4.75 (+0.2/-0.1) bar

3

li. U-LUo

0

1 K

I

Figure 4-10: Effect of Heat Flux on Pure R13B1 and R152a/R13B1

Mixture: Preheat Data

130

HT-COEFF.

(kW/m^/K)
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CM< >

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(>i/ujbs/M>l) -d300-lH

lO

00

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d

CNJ d

>

h;

—I<

D

o

cd

O

ILI

CM

CO CD CM < !£

131

Figure

^i-ll:

Effect

of

Heat

Flux

on

Pure

Rl52a

—

Test

Section

Data
MASS FLUX

A 158 kg/sqa/sK

B 232 kg/sqa/sit C 281 kg/sqt/sic

D 339 kg/sqa/SK

E 419 kg/sqa/iK

Figure 4-12: Effect of Mass Flux: Test Section Data

R13B1

MASS FLUX

A 353 kg/sqa/w

B 433 kg/sqa/M

C 559 kg/tqa/Mt

132
Figure 4-13a: Effect of Step Change in Heat Flux: Pure Refrigerants

133
Figure 4-13b: Effect of Step Change in Heat Flux: Mixtures

134
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136

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137

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of

Heat

and

Maas

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on

0.76

weight

R13B1.

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boiling

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Heat Flux= 10 kW/m . Forced Convect ion/evaooration dominates.

139

CHAPTER 5: A FURTHER EXAMINATION OF THE DATA

5 . 1 Introduction

The last chapter revealed some of the features of the experimental data

base. They are summarized in Table 5-1. In this chapter, some additional features of the data base are discussed, including new physical

phenomena which were observed, and an analytical discussion of the use

of equilibrium temperature in the definition of the mixture heat

transfer coefficient.

5 .2 ri rcTLinf erent ial Variation in Heat Transfer in Horizontal Flow

Boil ing

In horizontal annular flow boiling the liquid film thickness is

asymmetric around the inner circumference of the tube. Due to gravity,

the film at the tube bottom is thicker than at the tube top. The effect

of this thick film for pure fluids is to produce a lower heat transfer

coefficient at the tube bottom due to increased resistance. This

behavior has been observed widely in the literature [Ch66a,Ra83] , and

was seen with both rigs.

In the case of horizontal flow boiling of mixtures, a new opposite

phenomena was observed, i.e., the heat transfer coefficient at the tube

bottom was higher than at the top by an amount far outside experimental

uncertainty. The observe tion wa s made consistently with both rigs; the

rigs utilized different tubes, thermocouples, and test section heaters,

and thus should not be a function of these apparatus. The wall temperature measurements deteirmine the circumferential variation and are not

dependent on the data analysis technique. The effect was observed with

141
and without a preheat section, with a variety of heat fluxes, flow

rates, and mixture compositions, and over a range of pressures (left

uncontrolled in the tests with the first rig).

Figure 5-1 displays a typical

The heat transfer coefficient

the tube top, except near x =

contrast. Figure 5-2 displays

is noted at qualities greater

with Rig #2 in both the prehea

data set (Rig #1) for the pure fluids,

at the bottom is seen to be lower than at

0.8, where dryout is beginning. In

similar plots for mixtures. Ihe reversal

than 0.2. Identical trends were observed

t and the test sections.

One might question why this finding has not been discussed before in the

literature. Section 1.7 discusses previous flow boiling of mixture

investigations. Three of the previous studies [Sh73 ,To79, Be80] involved

vertical flow with only one thermocouple mounted around the tube circumference. Both the lack of instrumentation and the flow orientation

preclude the possibility of observation.

Conjecture can be made regarding the reason for the reversal.

Possibilities include:

(a) Increased turbulence at bottom of tube

(b) Nucleate boiling at bottom of tube, and not at the

(c) Flow pattern differences between mixtures and pure

(d) Film boiling at tube top

(e) Different concentrations at tube bottom and top

top

fluids

142
The first two reasons may be dismissed in that they should appear for

the pure fluids as well. Further, in the case of mixtures, nucleate

boiling is more difficult to sustain, so it is unlikely that this is the

cause. If any trend should appear in the nucleate boiling dominated

region, it is that a greater disparity between top and bottom might

occur with mixtures, not a reversal. The third reason may be dismissed

in that flow patterns were observed at the outlet. Based on these

observations, a greater disparity again might have been expected at a

fixed quality. The effect of quality is discussed in the next section.

Film boiling is also a possibility since it will occur first at the tube

top. It is not likely since: (a) the wall temperatures were relatively

stable; (b) the wall temperatures at the top were not widely different

than at the bottom of the tube; (c) the wall temperatures were axially

consistent even at low quality. Still, film boiling is a possibility

which cannot be entirely dismissed.

The last possibility is believed to be the root cause of the reversal:

the higher heat transfer at the tube bottom is due to the relatively

greater amount of the more volatile component (R13B1) at the bottom of

the tube. Ihe gravity-driven drainage of bulk liquid to the tube bottom

provides a larger amount of fluid upon which to draw. Initially vaporization occurs at both tube top and bottom into the annular vapor core.

The top portion of the tube, with its thinner film (and initially higher

heat transfer rate) vaporizes most of the more volatile component. At

some point it becomes starved of this component and the vaporization

143
rate is diminished. In the bottcm portion of the tnbe, vaporization is

initially small then increases relative to the tube top; since it has a

greater bulk amount of fluid, it becomes depleted of the more volatile

component at a slower rate than the tube top.

There exists then a competition between the depletion of more volatile

component and film thickness. If this explanation is correct, one might

expect to see in the early portions of the vaporization process

greater than as both tube top and bottom have similar compositions. Then as the top becomes depleted of the more volatile component,

the two values should merge and then reverse. Figure 5-2 verifies this

conj ecture.

An attempt was made to correlate the top- to-bottom wall temperature

difference with local vapor-liquid composition difference. The latter

quantity is correlated with local mass transfer resistance. As seen on

Figure 5-3, no clear correlation was seen in the test section data. The

relatively small AT is due to the low heat flux in this region (constant

wall flux and pressure). A similar plot was made with initial composition as the independent variable. Here, there is a general trend that

the greater the initial composition of the more volatile R13B1, the

greater the observed AT. This suggests that the tube bottom has readily

available an amount of more volatile component at the higher initial

composition, while the top has been depleted.

14A
The finding of the circumferential variation is a further difficulty for

those interested in modelling the heat transfer process from first

principles. In addition to axial and radial gradients in composition,

there appears to exist a circumferential variation in composition. By

necessity then, a varying interfacial temperature exists. Furthermore,

circTunferential diffusion might exist due to the existence of the

exposition gradient. This latter effect is likely small*, if it were

large, then the gradient would disappear, as would the reversal in heat

transfer coefficient.

5 .3 Effect of Equilibrium Quality on Mixture Heat Transfer

When the thermodynamic equilibrium quality, is less than zero,

some vapor may be present due to subcooled flow boiling. The actual

quality then is higher than ^gqb ^eqb small. At values of

~ 0.7, dryout may occur with the remaining liquid entrained in the vapor

core. The liquid droplets may persist beyond the point where = 1,

due to relatively poor heat transfer through the vapor, so that at large

^gqb, ^ ^ ^eqb* values of Xg^^, up to 0.2, little vapor was seen for

some mixtures at the outlet sight glass. Also dryout was not often

measured until ^as near or exceeded 1. Inaccuracy of the EOS might

explain these observations. Alternatively, the above classic description of quality dependence may need to be altered for mixed fluids.

Mixtures have a hi^er onset of nucleate boiling point than do some

fluids. With less subcooled boiling, the actual x may lag Xgq^,* This

effect would explain both the lack of vapor at low Xg^^ and the lack of

dryout at high Xg^^. Also the addition of a second less volatile

145
component may simply delay dryout due to mass transfer resistance (see

Appendix 7C) . In either case, the quality dependence may be

structurally different for mixtures as compared to pure fluids.

In the last chapter the measured heat transfer coefficient of mixtures

was proportional to both heat flux and quality. This trend is also

opposite that commonly observed for pure fluids. The dependence on heat

flux requires the existence of nucleate boiling. In the nucleate

boiling regime, a weak inverse proportionality between quality and heat

transfer coefficient is usually observed for pure fluids [St82].

The quality dependence da/ dx varies with heat flux, composition and

quality itself. As seen in Figure 4-20, a larger da/ dx is observed at

higher heat flux and quality. Again, this is the opposite behavior as

that seen with pure fluids.

In this case, the reason might be the use of an equilibrium temperature

in the defining relation for the heat transfer coefficient:

a = q/(T, - (5-1)

If this equation is now partially differentiated by dx to determine the

rate of change with quality:

An ^ 3T„ 3T^„,

— Q W _ 6 QD

^

) 0X /rp nn \2dX dx

'*^w ‘^eqb^

1A6
The experimental values show 9a/9x > 0, so

9Teqb

9x

9T^

> —

9x

The quantity ^Tg^^/9x is a function of composition. It is largest when

the dew and bubble point temperature difference is largest (at AX = 1,

^^eqb ~ ^DEW ~ ^BDB^ “ Thus, it may be that the apparent dependence on

quality is largest in the regions where the dew-bubble temperature

difference is largest. In examining the data, a trend of this nature is

apparent. The quality dependence then may be an artifact of the

defining relation, rather than representative of the heat transfer

regime as it is in flow boiling of pure fluids.

5 .4 Departure from Nucleate Boiling (DNB) Events

In some of the data taken with Rig #1, DNB events were observed along

the tube top. The events occurred generally at large values of heat

flux, pressure and concentrations of R13B1. Some of the erratic

behavior of R13B1 can be attributed to this occurrence (Figure 5-4).

Surprisingly, in the case of mixtures, the bottom and side heat transfer

coefficients seem to be little affected by the behavior near the tube

top.

Seme available data in the literature were examined for the occurrence.

Ihe data of [Mi81] for pure R12 and a mixture of R12/R22 shows the same

behavior (Figure 5-5). The authors note the 'tube wall temepratures

exhibited large fluctuations which indicated the unstable behavior of

147
boiling . . . the scatter of the tube wall tempertnre is wider in the

case of mixtures than with pure R12.' They did not attribute the

scatter to DNB events, and analyzed their data as if it were in an

annular flow pattern with conventional nucleate boiling and evaporative

heat transfer contributions. Some data of [Ma76] also seems to exhibit

scatter at low flow rate and high heat flux, and is suspected of similar

events.

For standard heat pump applications with R13B1/R152a and with other

refrigerants, there is a possibility that the heat transfer x>rocess will

be diminished in the first row of coils (where q is largest). In this

case, the addition of a less volatile component may actually augment the

observed heat transfer. W® events were never observed with pure R152a,

the less volatile component of the tested mixture.

In the following chapters the tests suspected of featuring DNB events

are not included in the comparison to the predictive correlations.

5 .5 Comparison Between Pure and Mixed Refrigerants

In (3iapter 7 the measured heat transfer coefficients for mixtures are

compared to predicted values based on treating the mixture as an

equivalent pure fluid. In the process of that analysis, a comparison

will be made between pure fluids and mixtures when the heat transfer is

dominated by nucleate boiling. In that case, the comparison is made at

identical pressures and heat fluxes. In the case of flow boiling where

flow rate has a sizeable influence on the measured heat transfer

coefficient, the comparison is more difficult.

148
When there is an influence of flow rate, one can compare fluids on any

of the following basis:

(a) same mass flow rate

(b) same molar flow rate

(c) same volume flow rate

(d) same Reynolds/Prandtl number

The mass flow rate ccanparison is the one with which most engineers are

acquainted. On the other hand, chemists and physicists work in molar

quantities, and might claim that the weight of a molecule matters less

than the number of molecules which flow. The application to a heat pump

suggests the same volume flow rate: compressors are effectively

constant volume devices. In defense of the last item, single phase

scaling laws suggest Re and Pr should be used. These however are

derived from the single phase Dittus-Boel ter relation; on two phase

flow, other parameters affect the results.

Figure 5-6 displays the test section data for both the pure and mixed

refrigerants, at identical values of pressure, heat flux and the

Martinelli parameter. The measured heat transfer coefficient has been

normalized by so that mass flux effects are eliminated from the

comparison. The heat transfer coefficient for the mixtures are less

than for the pure refrigerants. This finding suggests that there is a

distinct mixture effect, possibly due to mass transfer resistance.

Shown also on the figure are two correlations to be discussed in

Qiapters 6 and 7. They are both for pure fluids. The Prandtl number

149
term is included whenever it is suspected that nucleate boiling has not

been suppressed. As can be seen, it appears that nucleate boiling is

suppressed for the mixtures, but not for the pure fluids. The presence

of nucleate boiling for the pure fluids might also explain their larger

heat transfer coefficients. This result is consistent with the

suppression criterion prediction of Chapter 4.

5 .6 Pressure Drop in Horizontal Flow Boiling of Pure and Mixed

Refrigerants

It has been suggested recently that conventional pressure drop

prediction methods must be modified to account for mixture effects

[Si83a]. Others claim that there is no physical reason for requiring

such a change. Arguments might be made for either case. All prediction

methods use the quantity in determining pressure drop. For pure

fluids at equilibrium qualities above zero, the vapor quality

difference, - Xgq^j, is usually small in the annular flow regime.

It is well established in nucleate boiling of nonazeotropic mixtures,

mass transfer resistance leads to degraded heat transfer. This

phenomena could change the vapor generation rate, such that the vapor

quality difference, ~ *eqb' dissimilar between pure fluids and

mixtures. The dissimilarity could lead to poor prediction using pure

fluid methods. On the other hand, it has been established analytically

that mass transfer resistance is of minor importance when nucleate

boiling has been suppressed and the vapor generation process becomes

evaporative only in turbulent annular flow [Sh77].

150
The Martinell i-Nel son method [Ma48] , as modified by Chisholm [Ch67] was

selected due to its simple application and success with the pure fluids.

The method requires stepwise integration as was described in Chapter 3.

For the tests conducted here, the inlet conditions were only slightly

subcooled, and single phase pressure drop was neglected. The entire

pressure drop was assumed to occur between the calculated position of

^eqb ~ ® outlet.

Figure 5~7 displays the comparison between prediction and measurement

for the mixtures' data. Agreement is satisfactory, and may be compared

to Figure 3-12. No correction for composition is required for this

refrigerant.

151
Table 5~ 1:

Simnnary

of

Experimental

Data

152

FC/E:

forced

convectlon/evapoxa

tion ;

nucleate

boll

lo|
it

CIRCUMFERENTIAL VARIATION

2.2 bar

2S020 M/sqa

Rl52a

140 kg/aqi/sec

T: TOP

S; SIDES

B: BOTTOM

10

3

V

1 --

"S

I i I

- . at

-- 5

u.

UJou

Rie# 1

.1 .2 .4 .5 .6 ’EQB. QUALITY’

t tOLOH211

Figure 5-1: Variation in Measured Keat Transfer

Coefficient. Heat transfer at tube bottom

lower than at top due to thicker film.

(a) R152a; (b) R13B1

u.m

3

g

V

1-1

CIRCUMFERENTIAL VARIATION

5.7 bar

29330 M/sqa

R13B1 ^ 819 kg/sqa/sec

T: TOP

S: SIDES

B: BOTTOM

* T

S S S

B B B

RI6# 1

.4 .5 .6 ’EQB. QUALITY’

-- 10

. . at

orB

-- 5

u.

OL002B6

153
\h0

u1

1 --

RI6# 1

CIRCUMFERENTIAL VARIATION

6.2 bar

41665 M/sqa

510

.75 wt.iaai

kg/sqa/sisec

T: TOP

S; SIDES

B: BOTTOM

i » f

’ ^

I

?

.4 .5 .6 •EQB. QUALITY*

-- 10

-- 5

0LDM251

Figure 5-2: Variation in Measured Heat Transfer

Coefficient. Heat transfer at tube bottom

higher than at top, presumably due to

greater availability of more volative componen t .

-- 10

-- 5 -

g

0L0M273

154
4 X

3 --

2 --

1 --

• V

\

* y ^jo i) ^ ^ ife l4o noun COMPOSITION OIFFECNCE

-1 --

-2 --

-3 --

Figure 5-3: Effect of Composition on Top-Bottom Wall Temnerature

Difference, (a) Effect of Local Molar Composition

Difference; (b) Effect of Feed Composition. Outlying

Points are due to stratified flow.

155
u.LUO

UI

1--

ni6# i

PROBABLE FILM BOILING

5.9 bar

16791 M/sqn

H13B1

413 kg/sq«/sec

T: TOP

S: SIDES

6: BOTTOM

-f f

,

B 9

i f

s

S c

B B B

-- 10

.1 .4 .'6 •EQB. OUALITT

.6 .9

-- 5

8

O'

u.uI

OLDOEBB Figure 5-4: Indications of probable film boiling

for pure R13B1 and a mixture.

jr3

JQ

&OCJ

I

1--

g

•fr

RIG# 1

PROBABLE FILM BOILING

6.5 bar 29214 M/sqra .B33 wt.l3Bl

269 kg/sqn/sec

T: TOP

S: SIDES

B: BOTTOM

f

»

-- 10

.4 .5 .6 'EQB. QUALITY'.9

-- 5 " s

0LDM256

156
(o) Purt refrigeront 12

(b) Binory miilure

Figure 5-5: Probable Film Boiling in the Data of (KiSl)

157
o

o

4-1 X

158

5-h:

Comparison

between

mixtures

and

pure

fluids

In

evaporative

flow
<N

<N

O

CM

00

(O

CM

OO

CO

CM

O

<

Q.

Q.

o

ccQ

LU

CCD

COCO

lU

cc

Q.

Q

lU

CCD

CO<

LU2

(VcjM) dOdO 3df1SS3dd a310ia3dd

cn(U3X

T-l

o

M-l

c.c

(3,

OJ

cncn

0)

!-i CU'O

0)

)-l 3

u:3

0)

T33

ra '3

a)

4Ju

T3

<U

i-i

3

3

3

s

•u3

333

O

cn •H3

3. E

O

CJ

I LPl3

3

3

&0

*H

13

159
Ill p

' '\i4

. iK n'flKt-,

5^1 '"' f

Si

11

8!?’.

rs

Til' 3i4H

j41

Mf.

' ,:o sIj-

:/

/ %

<M \

'P VV" °/ d

I f

y,' ')

n'-i

M L^’ /

O

0*1

A *

fdflirinH

^ % A

r

''* *c

D

&/

Vo/

'.;' I

' ii ;! M , A.

' \:tk

(«' 2

1^ 'HI MUi

I ..m 'Bn r

^''‘r * ot__x—i—.1^—iTS" - Ji "«r »

.' ', H?''-
CHAPTER 6: PREDICTION OF PURE REFRIGERANT HEAT TRANSFER

6.1 Introduction

In order to understand the effect of mixtures on flow boiling heat

transfer, one needs to be able to predict flow boiling behavior with

pure components. If such a prediction can be made accurately with a

single model/ correla tion, then the analysis of mixture behavior can

begin by treating the mixture as an 'Equivalent Pure Fluids (EPF)',

i.e,, one which has properties determined by appropriate mixing rules,

but which is modelled as if the properties belonged to a pure fluid. If

the EPF correlation underpredicts the measured heat transfer for mixtures, then some additional effect attributable to the mixture is augmenting the heat transfer. If, on the other hand, the EPF correlation

overpredicts, the mixture has some inhibiting feature, e.g., mass

transfer resistance.

The modelling of annular flow boiling heat transfer is not simple. As

discussed in Qiapter 1, there are many complicating features. Some

predictive estimation is needed, however, for design purposes. As such,

many correlations have been developed which attempt to consider some of

the physical aspects of the flow. In the remainder of this chapter,

these correlations are discussed (Section 6.2) and compared with the

experimental results of this report (Section 6.3). The best features of

variuos correlations are incorporated into an overall calculation procedure (Section 6.4) which yields excellent agreement with the data. It

is then compared favorably with data provided by other researchers.

Conclusions and recommendations are described in Section 6.5.

161
6 .2 Correlations for Annular Flow Boiling

In the earlier chapters, the mechanisms of vapor generation in annular

flow boiling were seen to be: (a) nucleate boiling at the wall

characterized experimentally by a strong dependence of a on heat flux,

or (b) evaporation from the vapor-liquid interface characterized by a

strong dependence on flow parameters and vapor quality, or (c) a

combination of (a) and (b) . In the case of refrigerants, both

mechanisms commonly contribute, with the more dominant contribution

switching from (a) at low quality to (b) at high quality for fixed heat

and mass flux.

Correlations have attempted to account for the simultaneous

of nucleate boiling and evaporation in an additive sense:

^1 C- = A^(—^—) + A

2 (X^^) , with Aj = 0 sometimes

iAh^

or, a multiplicative sense,

C3 C^ C5

a=A2mqd (6- lb)

or, a combination of the two approaches (^S(F)):

contirubtioD

(6-li)

a = UloF + <ipoolS (6- Ic)

Forms (6-la) and (6-lb) have been used widely in refrigeration induilrv';

form (6-lc) was developed originally by Chen [Ch66] and is commonly

162
advocated in the nuclear industry. All of the forms have the problem of

failing to predict accurately in all circumstances. All forms show

distinct contributions of nucleate boiling (seen in the inclusion of q

or Ujj) and forced convective evaporation (seen in either and/or •

Form (6“la) has the problem that it particularly has not proven general.

In some cases, although a dependence on heat flux could be seen from the

data, no improvement was achieved by including it as a correlating

parameter, i. e., setting Aj^ = 0 and defining A

2 and C

2 empirically

produced the same or better goodness of fit as including it [Ch79].

This result may merely demonstrate the inadequacy of the correlating

parameter or the ability to develop a false correlation. A second

difficulty arises in the use of ci^q, the single phase heat transfer, as

a normalizing parameter. The nucleate boiling contribution is then

aL()Ai( q/lliAh^) , which after inserting the usual correlations for Olq'

e.g., Dittus-Boel ter, indicates nucleate boiling heat transfer to depend

on the diameter for no apparent physical reason. Furthermore, the

specific fluid— surface combination has been proven important in nucleate

boiling heat transfer. The physical influence of the surface is lost in

the empirical constants Aj^ and Cj^. Still, agreement of form (6-la)

correlations with the data upon which they were developed is + 25

percent typically. This result is somewhat misleading since: (a) the

same correlation applied to a different ref rigerant/ surf ace yields poor

agreement; (b) the value of X^^’ developed to correlate pressure drop

with flow parameters, yielded agreement for that purpose of only + 30

percent; and (3) the Dittus-Boel ter equation correlated to measurement

163
data to + 13 percent [Sh73]. Despite these problems, the refrigeration

industry has typically applied form (6-1) correlations, and several

correlations of this type were examined. Table 6-1 lists the form (6-1)

correl ations.

Form (6-lb) is applicable only to average heat transfer coefficients.

Butterworth and Shock [Bu82] have published a summary table of values

for Cj , , and which is reproduced here as Table 6-2. The table

shows most of the experimental data to be characterized more often by

nucleate boiling, i.e., a fairly weak dependence on flow rate (0.1 to

0.25, excepting Danilov) and a dependence on heat flux of exponent 0.5

to 0.7, typical of pool boiling experiments. Form (6-lb) also has the

problem of a boiling dependence on tube diameter.

For annular flow, the most widely accepted correlations in the nuclear

industi^r was suggested by Chen [Ch66], It was developed originally from

a large set of data compiled from several authors' experiments; the data

are exclusively for vertical flows of water and various organic

compounds. The refrigeration industry has rejected its use principally

because it has proven inaccurate for refrigerants evaporating in

horizontal tubes, and perhaps because of the iterative nature of its

solution for the case of constant wall flux. Various researchers in

other fields have attempted to improve the methods as will be described.

164
6.2.1 Miscellaneous Forms

Some other correlations have appeared in the literature and have on

occasion predicted refrigerant HTC's with some accuracy. These are the

methods recently advanced by Shah [Sh76, Sh82] , Dembi et al [De78], and

Kandliker [Ka84] . Shah's method was checked with the results shown on

Figure 6-1. Due to its suppression criterion which does not include

mass flux effects, it selects the wrong heat transfer regime and

predicts poorly.

As shown in Appendix 6A, the approach recently has been to compile large

sets of data from various experiments and use regression analysis to fit

them. Extension of the methods to other data has been disappointing.

Furthermore, the regression analysis may lead to correlations which

ignore physical features in the data. The approach of this report is to

examine the older methods developed frcmi theory and analyze or extend

them.

6.2.2 The Original Chen Equation

Rosenhow originally suggested that in the case of flow boiling with

nucleation, that the forced convection/evapora tive and nucleate boiling

contributions might be additive. Following this line, Chen postulated:

= “e + “nbc (6-2)

= UloF + a^S (6-3)

165
The evaporative portion, a^, was related in the fashion similar to form

where Fg(X^^) is an empirical function of the Martinelli parameter;

It accounts for the increase in heat transfer which accompanies an

increase in quality when the flow is in a purely evaporative mode.

While Fg(X^^) was developed empirically, Qien also showed that, through

a Reynolds analogy.

so that one finds F related to the pressure drop ratio. This latter

ratio is itself correlated by X^^ as shown in the Mar tinel 1 i-Nel son

method. The empirical F^(X^^) of equation (6~7a) agrees closely with

equation (6-7b) over most of the probable range of X^

^ values when the

original Mar tinel 1 i-Nel son method is used [Be80] .

The nucleate boiling contribution of equation (6-4) was postulated as;

( 6- 1 ) :

(6-4)

Fp(X^^) = 2.35 + .213)*'^^^

X* 4. tt

for >0.1

ELSE Fg = 1 (6-5)

(6-5b)

166
“nbc

where is derived from a pool boiling correlation. The suppression

factor, S_, accounts for the general suppression of nucleate boiling as

flow rates and/or quality become large. It is derived from the

consideration that the temperature field in flow boiling differs from

that of pool boiling. The turbulent nature of the liquid film and the

excellent heat transfer to the fast moving vapor core tend to reduce the

temperature of the liquid near the wall, effectively preventing bubble

growth. The suppression factor, S^, was also determined empirically:

= 1/(1 + 2.53E-6 (RcloF^ 1.25n 1. 17 (6-6 a)

Chen selected the For ster-Zuber pool boiling relation for

Xl.79Cpl.45 PL. 49 0.24 0.75

an .00122 (6-6b)

(6-6c)

Since, by definition:

(6-7a)

(Ug + a^S) AT^^,. (6-7b)

one can substitute (6-6c) into (6~7b) to get:

167
( 6 - 8 )

The solution of the equation for q^ reuqires iteratively guessing values

of calculating the nucleate boiling contribution, and either

testing that the proper AT yields the given heat flux or interpolating

graphically toward it [Co80] .

6. 2. 2.1 Closed Form Solution for Chen's Method

Instead of iterating, a simple closed form solution can be found from

the following: for small AT/T as is common for evaporating refrigerant

applications, Clausius-Clapeyron can be used to eliminate the pressure

difference term:

(6-9)

Now if equation (6-9) is substituted into equation (6-8), then

0.99

q^ (ttg + K2 ) ATgg^ ( 6 - 10 )

where

Ah. 0.75

K2 = KjS (- V

) and AT = AT for convenience

Av, sa t sa t V

Approximately AT^*^^ by AT^ , equation (6-10) becomes a simple quadratic

for the unknown AT, the solution of which is

168
( 6- AT = 11 ) “O. ±4

2K.

Only the positive root is meaningful physically. Substituting this root

into (6-7a) gives

[ue + K2

-a. yfi 4^2

2K,

^) ] AT = [o^ + AT ( 6-12 )

or, since = oAT, the bracketed term is the overall heat transfer

coefficient; in simplified form:

2 2

(6-13)

All terms in this equation are knovn and a can be found directly,

eliminating the iterative process. Hiough the derivation seems obvious,

the author has never seen it in print.

6.2.3 Comparing Chen's Correlation to Experimental Data: Literature

Rev iew

When compared against the original data bank, Chen's formulation fit the

data to an absolute mean deviation of 11 percent. This excellent

agreement has been the principal source of the advocacy by the nuclear

industry of Chen's method. However, when compared to measured heat

transfer coefficients of flow boiling refrigerants, the method tends to

underpredict badly inmost cases [De78, (ni66a,Pu74] , or on occasion

169
overpredict [e.g., Cli67 data]. Fiir thermor e, the method tends to

nnderpredict the quality dependence. Lastly, though Chen compared his

method with five organic fluids, the maximum quality was 0.12. In this

range, nucleate boiling dominates. The method then was not really

tested in the range of interest to refrigerants. Ihe poor prediction

with refrigerants has been attributed by researchers for various

reasons

(a) the convective contribution is underpredicted due to a negligence of a Prandtl nonber effect [Be80];

(b) the nucleate boiling contribution is poorly predicted by the use of the Forster-Zuber correlation. Its contribution is

underpr edict ed [To79] or overpredicted [Ka84] with organic

1 iquids.

The two interpretations may then be directly opposed in trying to

understand the pl^sical heat transfer processes.

6.2.4 Modification to Nucleate Boiling Contribution in Chen's Method

Nearly all the terms in (hen's formulation have been suggested for

revision. Butterworth and Shock [Bu82] suggested that a different pool

boiling relation be used in equation (6~5). They reccnunended a recent

correlation by Stephan and Auracher [St81] which includes the fluid's

wetting characteristics and was specialized to various fluid

classifications (refrigerants, water, cyrogenic fluids, etc.). For the

pool boiling of refrigerants, Steihan and Abdel sal am recoonnended [St80]

^Eooll ^ 207 (Pv)-581

p

.533 (g_i4)

170
which Stephan and Anracher modified to include the effect of forced

convection:

29 1 - x)

j

|- ^ ( 1 - x) (6-15)

where the bracketed terms are Reynolds and Froude numbers, respectively.

The forced convection modification is actually based on Giawla'

s

supposition [Ch67].

Either (6-14) or (6-15) could replace the For ster-Zuber relation in

Qien's correlation. Alternately, another nucleate boiling correlation

could be used, such as that of Vaihinger [Va79] who correlated recently

various pool boiling refrigerant data for a wide range of reduced

pressures to within + 15 percent.

6.2.5 Modification of Forced Convection Contribution

Bennett and Chen recommended recently a modification of the F function

for fluids with Pr^^ > 1 (refrigerants have 2 < Pr^^ < 5) [Be80] .

Recalling equation (6-5), they noted the Reynolds analogy used in Chen's

original development was valid strictly for Pr^^ = 1. Bennett and Chen

proposed various Prandtl number corrections, the best fitting their data

with

UP/dz)j^

(dP/dz)Lo

171
~ Pr- (6-16) 0 .296

^ .445 ^ Ltt

Tlie frictional pressure drop ratio is to be predicted on a 'best

available' basis; commonly this selection is the JIartinelli method (and

referred by Bennett and Chen as a reasonable approach).

For Prj^ > 1, the recommended modification has the effect of increasing

the evaporative and decreasing the nucleate boiling contributions.

Development of the Prandtl number correction assumed that ebullition

destroys the viscous sublayer. nucleate boil ing i s snppre s sed

completely, Bennett and Chen recommend deletion of the Prandtl number

correction .

6.2.6 Modification of Suppression Factor

An alternative that has recently been proposed changes the suppression

factor. Bennett et al . derived a semi-analytical formulation for S,

given as [BeSOa] :

S« = > (1 - exp ( —i^^)) (6-18)

where z = 0.041 ( ) g(pL - Pv>

The only empirical value is 0.041.

172
6.2.7 Other Modifications to Chen's Method

Polley [Po82] has recently developed a modification to Chen's method

with the following characteristics:

(a) a simpler pool boiling relation

(b) a criterion to exclude the nucleate boiling contribution if

there is insufficient superheat

(c) a suppression factor based on the magnitude of the pool and

evaporative contributions, rather than the flow parameters

used in Chen's method

The suppression factor was optimized empirically from a large set of

water-steam data. The method produced improved agreement with this data

base. His equations are given in Appendix 6B.

6.2.8 Application of Modifications to Chen's Correlation

The previous sections have described several modifications to Chen's

original method; prior to this report, none has been applied

independently of the data base used by the authors of these

modifications. It is interesting to note that virtually every term

except the Dittus-Boel ter equation used in Chen's original method has

been recommended for change.

Considerable care must be taken in testing the changes suggested in the

previous sections, as will be shown. Chen's original superposition

employed the For ster-Zuber pool boiling relation where cipQQj = cip2 ~

f(AT) = f(T„ - This approach is different systematically than W Sow

®pooi - f(q) as suggested by equation (6-14). The pool boiling heat

transfer coefficient of Forster and Zuber is:

173
(6-19)

where Cp2

= Cp2 (properties), and which may be found by comparison to

equation (6-10). By examination of equation (6-10) or (6-11), it can be

seen that, for a fixed total heat flux, the calculated AT is lowered by

the presence of forced convection over that which would occur in pool

boiling alone. Consequently, because of the form of equation (6-11),

the nucleate boiling contribution is seen to be lower than for the pool

boiling beyond that accounted by the suppression factor. Put another

way.

so that = <1^ only in the case of no flow. In contrast, the

approach suggested by the use of equation (6-14) implies q^^jg = q^. In

Polley's development, this problem is resolved due to the reoptimization

of the suppression factor.

To use (6-14) in Chen's method, the equation must be reformulated in

terms of = f(AT) , as follows:

' Ifc + 1„b<. = + Cp2 AtI-S’s ( 6 - 20 )

“n

“

‘‘pool ®SA " ^A‘iw* ( 6 - 21 )

where Cg^ can be found by comparison to equation (6-14). For pool

boiling alone.

174
^pool ~

^^SA‘lpool

.745 )AT

upon eliminating ^pool

„ _ p 3.2916 . -2. 9216

®SA " ^SA ( 6-22 )

This result can now be substituted into equation (6-3) to get

a = aj^F + ^j2.9216 g ( 6-23

)

and

q = oAT = (apF + ^^2.9216 gj^j (6-24)

This equation must be solved iteratively for AT, and consequently a, in

the case of constant wall flux. Thus, the suggested modification of

Butterworth and Shock, which might yield more accuracy, pays the cost of

increased conputa tional difficulty.

i

!

j

6 .3 Experimental Results: Comparison to Measured Data

Recall Table 5-1 for the summary of the data base characteristics.

i

i Table 6-4 displays the many variations of Qien-styled methods which were

i

! considered in the analysis.

These characteristics must be considered in the analysis of the

predictive ability of correlations.

175
Table 6-3 displays the results of comparing many of the methods to the

experimental results. All methods are compared to the data according to

the mean fractional standard deviation:

meas^ ^®meas ^ ~N

The best two prediction methods are circled in Table 6-3.

6.3.1

All of

et al.

1 ikely

Comparison to Rig #1, R152a Data (Forced Convection/Evaporation

Dominant

the form (6-1) equations predict badly. The method of Traviss

is derived from condensation research. It underpredicts due most

to different entrainment rates in evaporation and condensation.

Of the many Chen-styled correlations, the evaporative portion of Chen's

original formul ation with being empirical and Chen's original

formulation with the reformulated Stephan- Abdel sal am method (based on

equation (6-24)) predict best. Figure 6-2 displays the variation of a

with quality for some of the Chen-styled correlations. Again, the two

methods mentioned above predict the slopes very well, though sometimes

the magnitude of o is in error. It is interesting to note that Chen's

original method overpredicts the measured values. Overprediction with

refrigerants has only occurred in one other instance [Ch67].

176
6.3.2 Ccanparison of Rig #2 Preheat Data (Nucleate Boiling Dominant)

This data base consisting of about 200 points, includes heat fluzes

ranging from 10 to 95 kW/m and mass fluxes of 100 to 500 kg/ sqm/ s.

Table 6~3 displays the predictive ability of various correlations

against both pure R152a and pure R13B1. None of the form (6-1)

correlations do well. Since nucleate boiling is the dominant feature,

one might expect pool boiling relations to perform well. The

correlation of Stephan and Abdelsalam (equation 6-14) predicts

exceptionally well with the data within + 20 percent and most

predictions within 5 to 10 percent. Since equation (6-14) was developed

from a large refrigerant data base, the results are pleasingly

consistent. Refrigerant R152a was not considered in the authors'

equation development, so the experimental data extends the verification

of the predictive ability of the method. The effects of mass flux and

quality are not accounted by equation (6-14). Equation (6-15) is the

attempt made by Stephan and Auracher to account for mass flux and

quality. It however overestimates their effect.

After eliminating the film boiling data for R13B1, the remaining data of

Rig #1 was seen to be dominated by nucleate boiling. As shown on Table

6-3, the measured values are predicted best by the same pool boiling

relations as R152a, adding further verification to the method.

177
6.3.3 Comparison of Rig #2 Test Section Data (Forced Convection

Dominant - Some Nucleate Boiling Contribution Possible)

Again, none of the Form (6-la) methods predict either the slope da/dx

nor the magnitude of a well. The best prediction techniques are those

when the Prandtl number correction suggested by Bennett and Chen is

combined with the empirical F function:

“e =

and the nucleate boiling contribution is that of Stephan and Abdel sal am

(equation 6-24). Figure 6-4 displays the results. There is a larger

error, but greater uncertainty with the R13B1 data (section 3.8). If

the measured values were based on measured outlet temperature, the R13B1

agreement with the above equation would be superior.

By using equation (6-24) and the Prandtl correction, the nucleate

boiling contribution is nearly negligible. Agreement is excellent even

when excluding the nucleate boiling contribution (methods (w) and (x) on

Table 6-3)

.

6 .4 Discussion of Findings

6.4.1 Nucleate Boiling Dominated Flow Situations

It was found that little or no mass flux correction was needed to fit

the data in this situation. Inclusion of the mass flux correction

suggested by Chawla and adopted by Stephan and Auercher degraded the

predictive ability of the pool boiling correlation of Stephan and

Abdelsalam (equation 6-14). In their original paper, Stephan and

178
Auracher examined eight refrigerant data bases (three with Rll, three

with R12, one with B22 and one with R1 14). Ihe R1 1 data was

provided by Chawla, so the forced convection modif ication, derived from

his data, should be expected to fit the data well, l^o of the remaining

five data bases are not as well predicted.

Further, Vaihinger noted no influence of mass flux in his results, nor

has Muller, has Brauer [Va79]. On the other hand, [Ma79] data clearly

has a mass flux effect.

The mass flux correction (equation 6~15) has a dependence on tube

diameter,: though the dependence is weak, there is no pl^sical reason for

any functional relation. Also, the heat transfer coefficient is

inversely proportional to quality. It agrees with various observations

in the literature [Ch67, Ma76, St82] of a heat transfer coefficient

reaching a minimum before convective/evaporative processes grow and

dominate. Such behavior is also observed with some of the Rig #1 data

when it is dominated by nucleate boiling.

Chen-styled correlations explicitly include a forced convection effect,

even with small flow rates. The influence of mass flux diminishes as

heat flux increases (i.e., as increases). It establishes a proper

trend, but never reduces the mass flux effect to zero. It suggests as

quality increases, mass flux effects increase in influence, the opposite

of (hawla's supposition.

179
The predictive ability of the ccanplete Chen-styled correlations

developed from the literature was not good for this heat transfer

regime. The best prediction came with using cip^Q^ ” ^sing

equation (6-14) in conj unction with equation (6-3). As previously

discussed, this is an incorrect application of the pool boiling relation

in Chen's method. Furthermore, use of the For ster-Zuber pool boiling

method instead of the Stephen- Abdel sal am method in Chen's formulation

revealed dramatic differences in the predicted a. In their original

pool bo il ing form, the methods are compared in Figure 6-3 a. Forster and

Zuber underpredicts a at large heat fluxes, e.g., However

when these formulas are used in Chen's method with cipQQi = “pool^*^^^'

their relationship is reversed (Figure 6-3b) . The Stephan and

Abdelsolam method predicts a larger nucleate boiling contribution. This

is due to the methods having a different functional dependence on AT.

It is clear that since the original Chen formulation of 1966, progress

has been made in predicting pool boiling heat transfer and that the

improved capability has as a prerequisite the specification of fluid

classifications (and surface characteristics). Given the pool boiling

progress, it may be useful to reformulate the suppression factor in

(Then's method to improve its overall predictive ability. Any

reformulation should allow the forced convection term to diminish in

influence to near zero, as shown in the experimental data.

The issue of the influence of mass flux is not settled. It has been

observed to be negligible in some cases and apparently not in others.

180
The predictive ability is not available to determine conditions when a

mass flnx correction term is needed.

6.4.2 Forced Convection Dominated Flow Situations

None of the form (6~la) equations fit the data well; this result is not

surprising since rarely bave they produced satisfactory agreement with

data sets other than the ones for which they were originally developed.

The original Chen correlation badly predicted da/dx slopes. This is

consistent with many other researchers' findings. The nucleate boiling

contribution is overestimated in this flow situation. It is interesting

to note that the method overpredicts the Rig #1 data and generally

underpredicts the Rig #2 data. Unde rpr edict ion of refrigerant heat

transfer coefficients is more common, although the method has

overpredicted in at least one instance [De78].

The use of the analytic form of the F-function (equation (6-5)) degraded

the predictive ability. The analytic form F = F^(AP) has a higher value

than the empirical F = F^(X^^) at values of 1/X^^ < 2 corresponding to

low quality. It overpredicts in this region. At high quality, the

methods nearly agree, and it makes little difference. In general the

empirical F was slightly more accurate.

Of the multiple Chenr-styled correlations, none fit both the Rig #1 and

Rig #2 results. Best agreement with Rig #1 data (R152a only) was

achieved including the Stephen-Abdel sal am relation with Chen's original

181
formulation (equation (6-24)). This approach requires iteration,

however, adding to the complexity. Further, it produced poor agreement

with both Rig #1 results and importantly the nucleate boiling dominated

reuslts previously discussed. In general the agreement with da/di is

good for the Chen predictions without the nucleate boiling contribution.

Best agreement with the Rig #2 data also used the Stephan- Abdel sal am

method, but included a Prandtl number correction suggested by Bennett

and Chen. The question then naturally arises as to how to predict the

need for the Prandtl number correction. An approach is discussed in the

next section.

6.4.3 A Complete Correlation

In the previous sections, it was seen that no single correlation fit all

the data. However, a particular correlation predicted well in certain

situations. In this section, a cr iter ion/procedure will be established

which determines when to use a particular correlation.

Following Chawla's suggestion [Ch6 7] , one can determine the heat

transfer regime and a by:

=

‘^pool “pool > 4c

= Up^, if Up^ >

182
The previous sections showed that, at low pressure, when nucleate

boiling was completely suppressed, the two best predictive methods

were;^

“FC = “LO^c^^tt^ AT^-^216 s [a = 0.07] (6-26 a)

and

“FC

“ “LO^c^^tt^ “ .212] (6-26b)

At higher pressures, where some nucleate boiling contribution was

observed (Chapter 4), the best predictions were with

ttpc = ^j2.9216 ^ [c = 0.055] (6-27 a)

and

Opc = aLoFj,(Xt^)Pr®*^^ [<r = 0.057] (6-27b)

The difference between the two methods is the Prandtl correction, which

is substantial. To determine when to include the correction, the

suppression criterion of Chapter 4 is recommended as the determinant.

If the given wall flux is greater than that predicted by the suppression

criterion, then equation (6-27a) or (6-27b) should be used. Alternate ly

^The pool boiling relation to be used is that of Stephen and Abdel sal am (equation (6-14)).

1 83
if the suppression criterion predicts insufficient heat flux, equation

(6-26 a) or (6-26b) should be used.

Although equation (6-26a) was superior to (6-26b), one might question on

theoretical grounds its use. If the data is in fact representative of a

completely suppressed nucleate boiling heat transfer regime, then there

is no reason to include the nucleate boiling term. In defense of its

inclusion, two reasons might be offered:

(a) The original Qien development/optimization presumed contributions from both regimes, so that F was not optimized for

complete suppression.

(b) The suppression criterion predicts ebullition from large

cavities even with very little superheat available. The large

cavities may then be 'active' but too few in number to destroy

the viscous sublayer (and require the Prandtl number correction) . The fact that some cavities are active may justify the

inclusion of the nucleate boiling term.

If the nucleate boiling term is included, however, there is an inherent

contradiction. With more substantial ebullition (e.g., higher q^) • the

Prandtl number correction is invoked, and the evapora t ive contribution

is increased at the expense of the nucleate boiling contribution. Thus

while one would expect to be greater at higher q^(q^ > ^sup^ '

in fact be reduced.

Because of this reason and others to be discussed below, the author

prefers the use of equation (6-26b) in the case when q^ < q^Qp* When

combined with the criterion of equation (6-25), a = 0.122 for Rig #1;

18 A
this value is superior to every other method, and yields better agreement

than appears in much of the literature for heat transfer correlations.^

Equation (6-27b) yields nearly as good agreement as (6-27a)

.

Elimination of the nucleate boiling contribution, though not correct

theoretically, offers the practical benefit of a non-iterative solution.

The prediction is also more conservative without the nucleate boiling

term. The use then of (6-26b) and (6~27b) with the criterion of (6-25)

is therefore recommended.

6.4.4 A Comparison with Other Data

As a further test of the approach, spot checks were done against other

refrigerant data in the literature.

Heat transfer coefficients for R22 were measured by at least three

different authors (Pr^^ ~ 2.5). Their data is shown on Figure 6-6, with

equation (6-27b). The need for the Prandtl correction for the Anderson

and Mathur/Chaddock data was supported by an examination of their raw

data. The Anderson data is predicted very well; it is known that it

excludes dryout data. The Mathur/Chaddock data is predicted very well

in the low and middle quality range. At high quality, the approach

slightly overpredicts: however this data is for dryout conditions. At

low quality, the data exhibits considerable scatter. The scatter is due

to the effect of heat flux, neglected by [Ch79]. The use of equation

1 Figure 6-5 show s the results of using the criteria.

185
(6-25) would have improved agrement in this region; however property

values were not available to perform the calculation.

Qiaddock and Noerager measured R12 (Pr = 3.1) and fit the average a to

+ 15% with

“ " “L0^3/X^^) 0.2 < < 0.5

Again, their data showed a fairly strong heat flux dependence, so

equation (6-27b) is appropriate. Agreement is fair: -30% for X^^ = 0.2

and -2% at X^^ = 0.5. The underestimates may be due to the effect of

heat flux.

Recall that only one data set from the literature [Ch67] was badly

overpredicted by the Qien correlation. However, the data of Chawla

exhibited heat flux dependence. In this case, equation (6-26b) is

the correct one for use, and reduces the prediction by more than 50%.

This will place the prediction in the appropriate range.

6 .5 Closing Remarks: Conclusions and Recommendations

A large data base was developed which included data from all possible

heat transfer regimes. A comparison was made between published

correlations and the data base. All form (6-1) correlations, widely

used in the refrigeration industry, predicted poorly. The result is not

surprising as they have tended in the past to suffer from a lack of

generality. The new Shah correlation also predicted badly.

186
In the nucleate boiling dominated regime, a recent pool boiling

correlation (equation (6-14)) predicted exceptionally well. A

correction for forced convection was unnecessary and its inclusion

degraded the agreement. Therefore, a criterion is needed for predicting

the onset and amount of a mass flux influence. The Chen correlation

implicitly includes one which is not correct. Forced convection should

be allowed to have little or no influence in certain cases.

The forced convection dominated regime was predicted best by Chen's

original method modified to include equation (6-14) for the Rig #1 data.

A Prandtl number correction was needed to achieve good agrement with the

Rig #2 data. The discrepancy between the results is believed due to

sustained ebullition. A criterion was developed to determine when to

apply the Prandtl number correction.

The complete Chen styled correlation is the most widely used method

outside the refrigerant industry for predicting heat transfer

coefficients. The literature has shown it to predict poorly for organic

fluids with blame placed and corrections suggested on various terms of

the original correlation. None of these corrections however had been

checked prior to this report. All changes suggested in the literature

were tested, alone and in combination. Certain forms of the correlation

predicted well. A procedure was developed to determine when to apply the

various forms. It was shown that the superposition principle could be

abandoned in favor of a single dominant mode ( e ither nucleate boiling .or

evaporation). In this respect, it draws upon the success of Shah,

187
Qiawla, and portions of Policy. It also eliminates the need for

iteration. It includes the recent suggestion by Bennett and Qien for a

Prandtl nimber correction.

If one chose to retain the complete Chen styled correlation, virtually

every term in the original formulation (equation (6-3)) could be changed

to imrpove agreement. As such each term will be discussed separately.

To date no one has suggested revising the term in equation (6-3).

Yet, the Dittus-Boel ter relation is accurate to + 13 percent, so that

agreement between two-phase (evaporative only) data and prediction may

be 1 imtied to this range of uncertainty. More accurate single-phase

relations are available, e.g., Petukhov's method [Pe70] which is

believed to be accurate to to 6 percent. This could be used without

adding much complexity since it is non-iterative.

In this chapter, a closed form solution was derived for Oien's original

method. Thus, iterative solutions, as suggested in recent texts, nay be

discarded for conditions away from the critical point. Ihe original

method employed the For ster-Zuber pool boiling correlation. However,

substantial progress has been made in pool boiling since the ForsterZuber developaent. It has been found that the best correlations for

pool boiling are fluid-specific, i.e., classes of fluid such as

refrigerants require their own empirical correlations. The pool boiling

predictive ability of Forster and Zuber's relation is poor when applied

to refrigerants.

188
The use of an analytic F-function, such as that found through Reynolds

analogy, suffers from the practical lack of predicting closely the

pressure drop. Available pressure drop correlations such as MartinelliNelson predict refrigerants to at best + 20%. This uncertainty combined

with the uncertainty of predicting single-phase heat transfer

coefficients yields an overall uncertainty of at leat + 25 percent in

predicting a in the simplest case of evaporation without nucleate

boiling. The use of the empirical F-function in Chen's original

supposition produced better agreement with the measured data. Future

work might concentrate on improving pressure drop correlations, perhaps

treating separately the cases of nucleate boiling and evaporation.

The semi-analytical S^function developed by Bennett et al. , aggravated

the overprediction of the nucleate boiling contribution. This

represented the first test of their approach. Since F and S were

developed empirically, and since it has been shown that pool boiling

predictions are specialized to classes of fluids, a reoptimization

of the F and S functions for refrigerants is recommended with:

a)

b)

®L0 from Petukhov

= QpQQ2 Stephan and Abdel salam, kept in its original

form to escape the need for iteration

c) a criterion included to eliminate forced convection effects

(F=0) in some cases

d) a criterion included to eliminate nucleate boiling effects

( S=0) in some cases, and

e) a large data base of similarly determined experimental data

( i. e. , all with subcooled inlet, or all with two-phase inlet)

over a wide pressure and heat flux range.

189
Finally the experimental data existent in the literature should be more

closely analyzed and stratified by experimental technique. If this is

done, improved predictive ability will likely be achieved. The author

also hopes that the complete correlation outlined in Section 6.4.3 will

be tested further.

190
Table 6-1

Some Simple Correlations for Flow Boiling of Pure Refrigerants

c c Form 6-la: Aj^(Bo) ^ + A

2 (l/X^^) ^ = a./ a^Q

Ai A2 C2 Authors — 3 1 Chaddock and Noeranger [Ch66]

6700 1 23.45 0.66 Collier and Pulling [Co64]

3.5 0.5 Dengler and Addoms [De56]

(English Units) 0.64q*^^ 0.74 Bennett et al [Be63]

Miscellaneous References and Relevant Refrigerants

0 Lavin and Young [La67] R12

0 Shah [Sh76,Sh82] many

0 Dembi et al [De7 8] many

0 Eandl ikar [Ea84] many

0 daddock and Mathur [Ch79,Ma79] R22

0 Stephan and Auracher [St81] many

0 Chawla [Ch67] Rll

0 Bendel and Schlander [Ba74] R12

0 Rhee and Young [Rh72] R12.R22

0 Pierre [Pi56] R12

0 Singal et al [Si83] RL3

191
Table 6-2: Simple Correlations for Average Heat Transfer of Flow

Boiling Refrigerants

Authors Cs ^4 C5 Ref r igerant s

Danilova [Da69] 0.5 0.5 -1 Rll

Aljarrah and Duminil [A177] 0.25 0.55 -.2 R12 ,R22,R5 02,R13B1

Riedle and Pur ci pie [Pu72] 0 0.7 -.6 Rll. R12 , R1 13

Slipevic [S170]

high m 1.4 0 -.54 many

low m 0.1 0.7 -.54 many

Bogdanov 0.2 0.6 -.6 R11,R12,R22,R113

[reprinted from [Bn82]]

192
193

Ctaplat*

Corralatlon
Table 6-4: Siaaary of Oien-Styled Methods

“ “

«L0*' “n®

o^o - 0.023 (Xl/D)(G( 1 - x)/nL)®*®PrL®*‘*

ICIHOD F “n S As Shown on Table 6-3

Qien Origiaal F«Ott>

(6-5a) (6-6a)

S (F)

(6-5c)

I

Bennett and Oien

Original

Fg(02)Prj^O*296

(6-15)

®P2(AT)

(6-6a)

S (F)

(6-5c) J

Bennett and Chen

Sapixioal F (6-26b) (6-6a)

Sg(F)

(6-5c)

E

Chen. Analytic F

(l-5a) (6-6a)

S_(F)

(6-5c) M

Chen vith Stephan's

Pool Boiling Method

«,a(«l)

(6-13)

S (F)

(6-5c) N

Chen Tith Sefoxanlated

Stephan Method w «sa(AT)

(6-21)

S (F)

(6-5c)

0

Benaett/Chen vith

Stephan's Method (6-15) a (n)

(6-13)

S (F)

(6-5c)

P

Bennett/Chen vith

Refoanlated Stephan

F (0?)°*^^

(^ih

« (AT)

(6-21)

S-(F)

(6-5c)

Q

Bennett/Chen vith

Stephan/ Chavia (l-lk)

“sa<«>*Ca,

(6-13)

S (F)

(6-5c) K

Same as Q, bnt vith

Bapxical F

F (LpPrL°-296

(6-21b) o (At)

(6-21)

S (F)

(6-5o)

S

Saae as S, bnt vith Fc(^t)PrL®*^®^‘' o (AT)

(6-21)

S.(F)

(6-5c)

T

Saae as E, bnt vith

Analytic S (6-21b)

«ra<^T)

(6-6a)

®B

.(6-16) D

Chen Original

<EvaporatiTe Contribntion

Only)

' y

Bennett and Chen

(Sraporative Only)

F (l^^)PrL®-^*'

(6-26b) — — f

194
CN CJLU

UJ <

UJX

UJ

CL

O. <

UJX

UJX

CL I

-t- cc

S-I C^ /- C '"cg

i+- o> I

0)

!-C\l

C_) UJ

cn

c/5 i-U

a

m

C- c

05 2 o

LO

cn o iH

J2 cc • •

S-i o r—1 O T 1 'w'

S-I }_, .. 05 W —i

J_l C

QJ • 05 E

CO 1—1 QJ

4-1 OJ ix

CO > a

p: Qj c

r—1•H

1—1CO CXJ p QJ C5 1—1

XJ

QJ U-i 05 S

•H XJ CJX

!-- CO 1—1 QJ QJ CO C- JO 35 X

tJ QJ }x XJ 0 C CO tx. XJ QJ •H QJ 'O s X. o c CO JO *iH XJ 05

QJ a^ ix X 3

-C

05 OC E - 3 3

j: o C

CO )- JO JO TO

(J5 XJ QJ

X- 0- 1—1 3O

05 05

C Sx Sx C QJ QJ

05 JO "3

•H E C

Li 3 3

to 3

C. QJ E OJ ,JO C JO

sJ E—1 I

ac

C9

t—t

(E

195
F FUNCTION: EMPIRICAL AND ANALYTICAL

Figure 6-2: Comparison of Empirical and Analytical Functions in

Chen's Method. Pressure= 4.75 bar.

S FUNCTION: EMPIRICAL AND ANALYTICAL

196
t

MASS FLUX

-- 10

a 140 Xg/sqB/S8c

b 234 kg/sQB/aec

c 461 kg/sqa/aec ^ d 710 kg/sqa/sec

oTca 1 'EOB. aUALITY’ 4-

.9

O'

RI6* 1

MASS FLUX

a 140 kg/sqa/sec

b 233 kg/sqa/sec

c 460 kg/sqa/sec

d 703 kg/sqa/sec

RIB#

MASS FLUX

a 231 kg/sqa/sec

b 453 kg/sqa/sec

c 699 kg/sqa/sec

Figure 6-3: Comparison of Chen-Styled Methods to Experiments. Overprediction is due to nucleate boiling contribution. Use of

analytic F-function aggravates overprediction at low x.

197
Figure 6-

O

Y£

ni5« 1

MASS FLUX

a lAO kg/sQi/aac

b 234 kg/sqa/tac

c 461 kg/aqa/aec

d 710 kg/aqa/aec

MASS FLUX

a 140 kg/aqa/aec

b 233 kg/aqa/tac

c 460 kg/aqa/aac

d 703 kg/aqa/aac

A

RI6« 1

MASS FLUX

a 231 kg/aqa/aac

b 463 kg/iqa/aac

c 699 kg/aqa/aac

3: Comparison of Chen-Styled Methods to ExnerlTTients .

198
Figure 6

HASS FLUX

a 140 kg/sQB/sec

b 234 kg/sQB/sec

c 461 kg/sqa/sec

0 710 kg/sqa/aec

MASS FLUX

a 140 kg/sqa/aec

b 233 kg/sqa/sec

c 460 kg/sqa/sec

d 703 kg/sqa/sec

MASS FLUX

a 231 kg/sqa/sec

b 453 kg/sqa/sec

3 (cont) Comparison of Chen-Styled Methods to Experiments.

199
Figure

POOL- BOILING COMPARISON

NUC. BOIL. CONTRIBUTION COMPARISON: CHEN

01234S6789 KTC F£2 [kW/sqa/K]

10 11

6-4: Comparison of SA and rz Methods. When put in

original pool boiling form, SA method predicts

than FZ. When used in Chen's correlation, the

trend occurs

.

t he i r re.i ter

opno s i t »•

200
[X/l**/MX} ‘iaCO-IH

U/*6«/V»n(Pfl -J303-1H [i/*b*/gtnq:g d305-iH

C-B

O

u

UJ

Ul

in

oc

55 *H

J-i toc.£

CJm

I vC

<D

OC —

(

Ci.

CJ

201

Number

correction

improves

agreement.
10 MASS flux

01 -

X

• 233 kg/sga/iit

b 460 kg/iqa/iic

c 703 kg/«qa/«t

Figure 6-6: Comparison of

Rig#l data.

Complete Correlation with selected

Chawla ' s criterion improves agreement.

3a

u.

UJ0

u1

RIG#

2 STEPHAN> CHFN EVAP ONLY 42257 M/sqn

R152a

•EQB. QUALITY'

-f- .7 .8

i

i

1

10

5

uI

MASS FLUX

• 231 kg/«qa/iK

b 453 kg/tqa/tK

202
o

o

o

in

_ o

- LO

CVJ

203

Figure

6-7:

Comparison

of

correlation

with

others'

data

CHAPTER 7: PREDICTION OF HEAT TRANSFER WITH MIXED REFRIGERANTS

7 .1 Introduction

As has been seen in the previous chapters, beat transfer may be

dominated by evaporation from the vapor-liquid interface or by nuclear

boiling at the wall surface. Thus, an understanding of each process,

and bow it is changed by the addition of a second component, is necessary. To date, relatively little work has been done in flow boiling of

mixtures. In contrast, a large experimental base exists for pool

boiling of mixtures. As with pure fluids no analytic model is available

for predicting beat transfer in pool boiling, and correlations have been

developed instead.

This chapter will review briefly the analytic modelling of individual

bubbles, discussing their implications on the real situation (section

7.2.1), pool boiling correlations for mixtures (7.2.2), analytic modelling of forced convection/ evaporation mixtxires and relation correlations

(7.3). Then complete correlations for flow boiling of mixtures are

described (7.4) and compared to experimental data (7.5). The findings

are discussed in section 7.6.

7 .2 Pool Boiling of Mixture

7.2.1 Modelling of Single Bubbles

As discussed in Chapter 1, mixtures differ from pure fluids in two

fundamental ways: (1) vapor is formed of a different composition than

liquid, and (2) the saturation or bubble point temperature is

205
non- iso thermal, being a function of local composition. The consequence

of these differences can be illustrated qualitatively:

Consider a liquid mixture of overall composition of Xg which is

superheated to temperature T^, i.e., the amount of superheat is Tg -

Tbub shown in Figure 7-1. As a spherical vapor bubble forms

and grows^, it is formed preferentially of the more volatile component.

Due to mass continuity, the liquid in the region near the bubble has a

lower composition than the bulk liquid. The liquid and vapor compositions at the bubble interface are considered to be in equilibrium. As

such the interfacial bubble point temperature is not T^^^(Xg) but

Tbub^^i^' and the appropriate driving force [the amount of superheat] is

not Tg-T^^^(Xg), but Tg-T^^ijd^) , the latter being the smaller quantity.

This loss of available superheat is commonly accepted as the principal

reason for reduced bubble growth rates, and lower nucleate boiling heat

transfer coefficients observed with mixtures as compared to an

equivalent pure fluid.

Several authors have analyzed the growth rate reduction [Sc59, Va67

,

Sh83] . The results of their analysis, all of which start with simple

heat and balances, is:

^Its initial growth rate is controlled by inertial forces, i.e., its

ability to push outwards the surrounding liquid fluid, the process is

simply that of an expanding sphere and governed by Rayleigh's equation.

Following the initial growth period, the growth of the bubble is

controlled by the rate at which heat can diffuse to the bubble

interface. In the case of mixtures, the growth rate is also influenced

by the rate at which the more volatile component can diffuse to the

interface.

206
R = ^EPF

1 - dT

%T® %PF

_iL (Y* - X ) Ally ap ® dX,

bub

where Rgpp is the growth rate of a bubble of an equivalent pure fluid

superheated by ^e~^bub (Xg) . The terms of this equation can be examined:

as might be expected by the previous discussion, the liquid-vapor composition difference (Y-X) and the ratio of thermal and mass diffusivitie

s

term dXg^g/dXg is the slope of the bubble point line.

It should be noted that this term and (Y-X) always have opposite sign,

so that the denominator is always greater than 1, and a reduced growth

rate is predicted. This relation has been verified experimentally [FI

74]. However, the above equation is valid only for the unrealistic

situation of an isolated spherical bubble in a uniformly superheated

liquid. Several efforts have been made to analyze microlayer evaporation under a binary bubble near a heated wall surface as described in

Appendix 7C.

7.2.2 Boiling of Mixtures versus Pure Fluid

All of the models described in Appendix 7C point to the vapor-liquid

composition difference as a principal factor in the degradation of heat

transfer observed in mixtures. This quantity is therefore a likely

candidate to be used as a correlating parameter. Before discussing

correlations however, a few other differences between mixtures and pure

fluids should be noted. As shown in section 4.4, a larger superheat

with a mixture is required to sustain bubble growth from a cavity of

207
fixed radius. In a similar fashion, for a fixed superheat, only larger

cavities will be activated for mixtures as compared to pure fluids.

Since the population of cavity sizes is

r

there will be fewer sites which will be active at a given superheat.

This finding suggests again a degradation in heat transfer occurs, due

to the reduced number of activated sites with mixtures.

When a site has been activated, observations have shown that the bubble

departure size and frequency is less for mixtures than for pure fluids.

This leads to less coalescence with neighboring bubbles. The

implication of the reduced frequency is again degraded heat transfer.

7.2.3 Mixture Correlations for Pool Boiling

None of these detailed points are considered in mixture correlations.

Virtually all correlations consist of correction factors to a pool

boiling heat transfer coefficient which would be predicted if the fluid

were considered to be pure or ideal. Table 7-1 lists the correction

factors. Note the parameter |Y-X| appears repeatedly. Experiments by

Happel and Stephan have shown that the maximum reduction in heat

transfer as compared to that predicted by ideal molar mixing occurs when

|Y-X| is maximum. They also found no degradation when the mixture it at

its azeotropic composition, as shown in Figure 7-2. These authors noted

208
a pressure dependence on the degradation, as in earlier experiments by

Stephan which led to equation (7-24). Shock recently reviewed some of

these correlations, and prioritized their application as:

(1) Use a correlation if it was developed from actual

experimental data for the fluid pair of interest.

(2) If one new experimental data point is available, use equation (7-14) with the constant A^determined from the

experimental value.

(3) Use equation (7-13)

(4) Use equation (7-14) with = 1.53

Section 6.3.2 showed that the pure refrigerant data was predicted to

+ 15% by the correlation of Stephan and Abdelsalam (equation 6-14).

Thus this equation might be used as the basis for analyzing the mixtures' methods shown in Table 7-1. The pure refrigerant data was calculated at the given system pressure and heat flux. An ideal heat

transfer coefficient, was then calculated using mole fraction

weighting of the pure refrigerant a's. This was then corrected for

mixture effects by the use of equations 7-13, 7-14, and 7-15. The

general curve shapes of these equations is shown on Figure 7-3. Note

that the methods produce a maximum degradation in heat transfer at

roughly the same molar composition. However the size of the maximxim

degradation differs considerably between methods. Also the general

shape of the method of Thome predicts a larger degradation over a wider

composition range.

209
A heat transfer coefficient based on treating the mixture as an

equivalent pure fluid was calculated with equation 6-14. Note that**EPF

is greater than ci^^. This result is in contrast to that for the

evaporative situation as described in Section 2.4. An analysis, similar

to that done in Section 2.4, was conducted with equation 6-14, with the

re sul t

:

.581

^vm

PVid

P-»Lid

P T.m

.454

P4Lm

.533

PLid

^•»PLm

^PLid

.533 ^Lid

^Lm

.278

The last three dimensionless groups have values greater than one. The

density ratios have values of about 0.9 or greater, and their opposing

effect is thus small. In this case, then, if it were not for other

mixture effects, an increased pool boiling coefficient (over an ideal

fluid) would be observed.

7 .3 Forced Convection/Evaporation of Mixtures

7.3.1 Analytic Modelling

Shock has examined in detail an ethanol water mixture in turbulent flow,

evaporating due to constant wall heat flux [Sh76]. This analysis

neglects entrainment phenomena and the presence of waves. Additional

assumptions included: a) negligible sensible heating of liquid; b)

equilibrium at the vapor-liquid interface; c) neglible axial density and

velocity gradients; d) constant shear. The liquid flow velocity profile

was approximated via mixing length theory, using eddy dif fusiv ities due

to Deissler (near the wall) and Von Karman. He then assumed the eddy

diffusivity for mass to have the same value, i.e.

210
Vapor side heat and mass transfer dif fnsiv ities were estimated via the

Chilton- Col burn analogy, which relates these coefficients to the

friction factor (calculated via Blasins equation):

in = Jd =

He then solved the basic continuity and energy equations to determine

the interfacial temperature and composition in a stepwise fashion along

the length of the tube. He examined changes in the magnitude of the

resistances, the heat flux, and the pressure gradient to determine their

relative importance. As a base case he assumed no mass transfer

resistance, and equilibrium flash vaporization, i.e. Xqjj^ = X^, =

He found:

(a) mass transfer resistance (MTR) on the liquid side has a negligible effect on the interfacial temperature and

composition.

(b) MTR on the vapor side controls what effects do appear;

(c)

(d)

however, the MTR effect is negligible, i.e. assuming

equilibrium vaporization leads to little error in estimating the temperature drop through the film.

the error introduced by (c) is lessened with reduced heat

flux

(e) the inclusion or exclusion of pressure gradient has no effect on the above conclusions, and

( f ) very little sensible heating of vapor occurs over the

range of tested variables (Tq - T^) .

I 211
Hie effect of finding (c) is that the mixture can be treated as an EPF

if the process is strictly evaporative. Any deviation in the heat

transfer coefficient from an ideal mole fraction weighting would be

caused by non-ideal property behavior, not mass transfer effects. This

finding then is in sharp contrast to the conclusion of the preceeding

section on pool boiling of mixtures. This is also in mild contrast to

condensation of vapors with noncondensible gases (NG); NG cause severe

degradation in condensing coefficient with stagnant vapor. A 20% - 30%

degradation can also be found when the vapor stream is in laminar flow.

There is unfortunately no literature on turbulent in-tube condensation

of vapor with NG.^ Recently Stoecker [St85] noted a condensing coefficient for an R-12/R-114 mixture which was lower than either pure

refrigerant. He attributed without analysis the degradation to slip,

and not mass transfer resistance.** Appendix 7D has additional comments

on Shock's analysis.

7.3.2 Predictive Modelling for Forced Convective/Evaporation of

Mixture (Bell and Ghaly Model)

Given the findings of the pr ev ious section, it is not surpr i sing

Shock has re commended the use of a s impl if ied equil i brium mode

[Sa82, Sh83] : the Bell and Ghaly method [Be72] . It wa s developed

originally for film condensation of a superheated vapor. It can however

be rederived for forced convection/evaporation, as is done in

Appendix 7E.

^Webb [We82] examined turbulent flow over a tube and fotind in

condensation of water vapor with 2% air (by volume) a 20% reduction in

condensing coefficient.

^It may be due to non— ideal property behavior, but this possibility was not analyzed.

212
i

^ A summary of the assumptions in the method is:

' (1) No sensible heating of the liquid.

(2) Over a small axial distance, the change in bulk vapor

I temperature is equal to the change in equilibrium

temperature.

(3) Mass transfer resistance is neglected. To balance the

j error of this assumption, single phase heat transfer

! coefficients are employed rather than the (higher) two

I phase values.

I The effective heat transfer coefficient is then given by:

_1 ^

<^Teqb/dh

“eff “LO

I Assumption (3) was later revised so that two phase heat transfer

coefficients are now reccanmended. For evaporation, the sensible heating

of vapor is small, so that the above equation reduces roughly to

= -1- 1 “off “L0|„ •‘“'5 (7-2)

I The term is identical to Qien' s evaporative term for pure component

I evaporation. Thus, with little sensible heating of the vapor stream the

I Bell and Ghaly model is actually a pure fluid liquid film correction.

j

I 7.4 Complete Mixtures* Correlations

! The previous sections have described each heat transfer regime, and

' methods to calculate a for mixtures. This section describes methods of

j calculation when both evaporation and nucleate boiling are present.

I

I 213
7.4.1 Modification to Bell and Ghaly to include Nucleate Boiling

Sardesai, Shock, and Butterworth suggested recently a modification to he

Bell and Ghaly method to include nucleate boiling [Sa82] . In this case,

equation (7E-1) of Appendix E becomes:

ItOT "

^i^ “n^^W " ^bub^^^^

where is found from the methods described in section 7.2.3. The

problem then is to estimate T^^|j(X). If one sets = T^, then,

equation (7-1) becomes

®eff

1

1 ^*^TOT

®L0 ®n ®G

(7-3)

If instead T^j^|j(X) = Tq, then equation (7-1) becomes

1 + gn/aLO

1 *^G^ *^TOT

“LO “G

(7-4)

The authors however do not suggest when to include the nucleate boiling

contribution, or if a suppression factor should be included. If in fact

one is included then equation (7-3) becomes very similar to Chen's

method described in the last chapter.

214
7.4.2 Modification to Bennett and Oien's Method to include Mixture

Effects

Bennett and Chen developed an extension of their method to include

mixture effects [Be80] . Their approach is dissimilar in its assumptions

to those advanced in all the previous sections. Specifically,

sensible heating of the vapor is neglected, but sensible heating of the

liquid is accounted. Additionally mass transfer resistance in the

liquid (and not in the vapor) is assumed and accounted semi-empirically.

Lastly, a much different approach is taken to account for reduced

nucleate boiling heat transfer.

In the case of mixtures, the nucleate boiling contribution is considered

reduced by the same factor as described in section 7.2.1 for single

bubbles (equation 7-0)

Sub

1 - PL

A\ ajj

(Y* - Xg)

dTBUB

dX,

(7-5)

so that the nucleate boiling part of equation (6-3) becomes

®n ~ “pool ^UB ^ (7 6)

The forced convection term is also modified to account for mass transfer

resistance in the liquid film. It is hypothesized that, due to this

resistance, the real interfacial temperature is higher than calculated

215
from equilibrium. In this manner, the driving potential, is less

for mixtures than for an equivalent pure fluid. Thus, for a pure fluid.

“ “LO ^eqb^

and for a binary mixture.

(Tm - TJ

“ ®L0 /T - T ) ^eqb^

~ ®L0 ^Con “^eqb^ ( 7 -7 )

The problem remains to eliminate the unknown interfacial temperature.

Appendix 7A shows how this elimination was achieved through the

introduction of a mass transfer coefficient:

dT

q y« BUB

con

= 1 +

dX,

Teqb>

( 7 - 8 )

where = mass transfer coefficient

The mass transfer coefficient was assumed to behave as

216
0.8sc0-4

where B was determined empirically to be 0.023. The authors note the

coincidental agreement with the Dittus - Boelter constant. The authors

next account for sensible heating of the liquid phase. A derivation of

this accounting is given in Appendix 7B; the equations (7-5) and (7-8)

should be replaced by an effective heat of vaporization:

and B = 0.015 gives better agreement with their dates when Ah^g££ is

used. The author noted little change in agreement resulted with the

inclusion or exclusion of equation (7-9) .

7.4.3 Other Modifications to Chen's Method to include Mixture Effects

Collier and Shock [Co80, Sh73] have suggested modifying the nucleate

boiling contribution when mixtures are used. They suggest treating the

components as separate resistances in series, and including a correction

factor for mixtures:

where C is found from Table 7-1. Tacitly they assume that sensible

heating of liquid and vapor are negligible. Consistent with Shock's

earlier findings, they assume the turbulent evaporation process to be

unaffected by mixtures so cilq. F, and S are unaffected.

^\eff = - CPl(Y* - (7-9)

®pool^

1 ^A ^

^ ~ ^A 1 ®pool^^ “poolg^ ^ (7-10)

217
7.4.4 Other Correlations for Flow Boiling of Mixtures

Varma et al. [Va79] studied a binary mixture of R12/R22, as discussed in

Chapter 1. They correlated their data to + 30% for low mass fractions of

R22 and + 15% for higher mass fractions, using the following form:

^— = 8.275 -i- 7-9— (1 - |Y| - x|

^tt mAhy

By its nature, the correlation does not consider

involved in the flow boiling of mixtures. It is

the only term which is explicit to mixtures:

(1 - lY* - XgI)"-9 (7-12)

(7-11)

the physical processes

interesting to examine

This term is always greater than unity, suggesting the use of a mixture

augments the heat transfer process over an EPF. Their experimental data

did show a higher heat transfer coefficient for the mixture than for

pure R12 . No tests were done with pure R22 . As previously noted, the

mixture degrades the heat transfer in nucleate boiling dominated situations. In forced convection dominated situations, the term (1/X^^)

generally appears to the exponent 2/3 to 3/4. Their correlation

suggests neither regime. The agreement between (7-11) and the data is

therefore not expected to be general. It however should not be

dismissed, since the heat and mass flux range they tested is qu^te

similar to that used in the test section of rig #2.

218
In the only other known study, Singal et al. measured R13/R12 mixtures

[Si83]. Their results produced erratic behavior with quality and

composition; there was a clear dependence on mass and heat flux. Average

heat transfer coefficient was compared with the Pierre correlation

for average heat transfer coefficient and agreement was poor (wide

scatter, both positive and negative).

7.4.5 Summary of Mixtures' Models

At this point, the literature may be summarized along the following

1 ine s

:

(1) Experiments with pool boiling of mixtures have shown severe degradation in heat transfer coefficient when compared to

ideal or equivalent pure fluid values. The degradation has

been accounted by various correction factors. Since pool

boiling methods have been extrapolated successfully in the

prediction of flow boiling of pure fluids, the same

extrapolation has been hypothesized as valid for mixtures.

(2) Shock's analytic treatment suggests that mass transfer resistance

(MIR) and sensible heating are negligible in turbulent flow

evaporation. His conclusions are generally supported by

condensation research. He concludes that non-mixture methods

are adequate for predicting the heat transfer. If MTR is

included. Shock suggests the dominant MTR is on the vapor side.

In sharp contrast, Bennett and Qien have advanced a true

mixtures' model which includes both MIR and sensible heat only on the liquid side; they correlated a large data set with

their model.

(3) Other authors in the literature have either attempted to use non-mixture relations in the presence of nucleate boiling, or have produced curvefits which are structurally flawed in their

interpretation of the physical phenomena.

Table 7-2 lists the complete mixture methods and their related assumptions.

219
7 .5 Comparison to Measured Data

Table 7~3 displays 46 variations of the models described in the previous

sections. Because the mass diffusion coefficient is unknown, parametric

runs were made, assuming a range of Lewis numbers. The best methods are

discussed in the following sections.

7.5.1 Comparison to Preheat Data of Rig §1

While the mixtures data of this section shows effects of mass flux and

quality, it is primarily affected by heat flux, suggesting that it might

be best represented by a pool boiling correlation corrected for

mixture effects, as discussed in Section 7.2.3.

Figure 7-4 displays some of the measured data superposed on the

predicted coefficients. In all cases, a severe degradation in heat

transfer is observed (about 40-50% as compared to and 70%

compared to Q^pp) . Hidden in these figures are the effects of mass

flux and quality. Also there is an uncertainty in the actual local

liquid composition, given that a mass transfer resistance and a nonequilibrium condition are part of the physical process. These complications can be mitigated by examining only that experimental data closest

to equilibrium, i.e. the first thermocouple group in the preheat section.

At this group, the vapor quality is lowest, so that the liquid composition will be close to the known subcooled inlet composition. At this

point also, the evaporative mode should contribute only weakly, so that

mass flux and vapor quality levels should not be significant. Figure

7-5 displays this data, along with the predictive methods. In this

220
figure, unlike the previous set, the Stephan and Korner method is

evaluated using = 2.64; this value was selected to predict exactly

one of the experimental data points. The vertical scatter is due to the

neglect of the mass flux effect. This approach was discussed in Section

7.2, and was in fact successful in evaluating Toral's subcooled flow

boiling data [To79].

Table 7~3 shows that the best correlations of the data are a pure

evaporative, non-mixture model (a = ®l(}Fq(X^^)) and two pool boiling

relations. The agreement between the evaporative model and the data may

be coincidental; the data itself does not exhibit the strong mass flux

dependence predicted by the model. Instead it exhibits a strong heat

flux dependence ignored by the evaporative model. Of the pool boiling

relations, the method of Thome and the specialized Stephan and Korner

methods predict the measured data fairly well. Thome's method is both

more conseirva tive and more accurate in the mixture concentrations at

which heat pumps are recommended for operation. It predicts the

observed level of degradation at points away from the maximum

degradation better than Stephan and Korner.

7.5.2 Comparison to Rig #1 Data

This data set consists of 184 points with equilibrium qualities

between .05 and 0.90. The data includes a wide range in molar composition (though not weight composition as shown in Table 3-1). A variety

of pressures were used so that a comparison between runs is difficult;

221
however the pressure variation provides an additional parameter upon

which to check the ability of the correlations.

The data shows a proportional dependence on heat flux, quality and

weakly mass flux. This suggests that nucleate boiling is principally

contributing to the vapor generation process; in this manner it is like

the previous data set.

All of the pure fluid correlations overpredict the measured values by an

amount exceeding their overprediction of the pure fluids. This is a

first indication of a degraded heat transfer with mixtures.

Of all the correlations, a few stand out for their predictive ability.

Since a is a strong function of heat flux, the pool boiling methods were

again examined. Here Thome's method is superior to Stephan and Korner

because much of the data has a greater molar composition of R13B1 than

was the case in Section 7.5.2. The Stephan and Korner method is only

superior at small molar compositions of R13B1. While Thome's method

yielded the lowest mean deviation, it did not represent well the data

trends. By its nature, Thome's method produces an inverse relationship

between vapor quality and heat transfer coefficient, opposite of the

measured observation. It tends to overpredict the measurements at low

quality and underpredict at high quality (Figure 7-6). Because of this

feature, it predicts the average heat transfer coefficient very well.

The two other methods which predict the data with any accuracy are

evaporative only , non-mixture modeling: Chen's original method

222
without Prandtl correction, and Bell and Ghaly' s method. They are

actually very similar, as is discussed shortly.

7.5.3 Comparison to Rig #2: Test Section Data

This data base consists of 141 points with equilibrium qualities between

0.05 and 0.90, and shows significant mass flux effects. It therefore is

likely dominated by forced convection/ evaporation. The poor predictive

ability of the pool boiling methods offers further verification of this

concl usion.

Several methods shown on Table 7~3 [(B), (J) , (CC), (FF) , (HH) (II)]

yielded mean deviations less than 0.20. The "evaporative only", nonmixture

correlation of (B) which is simply equation (6~26b)

:

1

I yielded one of the best agreements. This same equation predicted well for

I the pure R152A data when nucleate boiling was completely suppressed.

I However, unlike its underpredict ive tendency with the pure fluids it

overpredicts the mixtures' data (Figure 1 - 1 ). Slightly better prediction

i is achieved with methods (BB) and (FF) which do include a mass transfer

resistance effect. However the predictive ability of (BB) and (FF) is

I

I

! artificial. First the terms Pr^^, Ahg££ and AT/ATg tend to compensate

i

I each other and produce a value near 1. The Lewis number of 1 is unrealistic in any case. Finally the term AT/AT^ was calculated based

1

! on some nucleate boiling contribution, i.e. the complete Bennett and

223
Chen correlation was employed, and the nucleate boiling contribution

subtracted out. This is physically unrealistic. For these reasons,

methods (BE) and (FF) are not recommended.

Method (HH) is a Bell and Ghaly styled method, which reduces effectively

to the same method as (B) since the liquid film dominates. It therefore

is not really a new approach. It has all the same features as (B)

described above. He use of made little difference, since the

methods produced similar values in this pressure and quality range.

Method (J) yields the best agreement of the complete Bennett/ Chen- styled

correlations. It however tends to underpredict the dependence on vapor

quality and overpredict the nucleate boiling contribution. Agreement at

this stage of analysis can only be considered coincidental. The method

badly predicted the experimental data in the heat transfer regime dominated by nucleate boiling.

7 . 6 Discussion of Findings

The complete Chen-styled correlations predicted poorly. In general they

tended to overpredict the magnitude of a, and underpredict the dependence

on quality, da/dx. The overprediction is a principal result of the

treatment of the fluid as an equivalent pure fluid with the Forster and

Zuber correlation (i.e. calculating with EPF properties). This results

in a large nucleate boiling contribution, as was shown in Figure 7~3.

Secondly, the term reduces the nucleate boiling contribution to a

lesser extent than the methods in Table 7-1.

224
Furthermore a structural problem vas revealed in the mass transfer

resistance inclusion in the evaporative term (equation 1-1 ). At Lewis

nimbers of five or greater, as might be common for most organic fluids,

the term

” AT/ATg = equation (7~5)

could become negative at reasonable values of AT. (close to measured

values). A negative value of AT/AT^ has no physical meaning. As such

it was set to zero in these cases. This caused the method to reduce to a

pure nucleate boiling method, equal to a£ppCg^ S. Since the 0£pp is

too large, the method tends to overpredict.

Maiqr perturbations of the Qienrstyled correlation were tried, including a

few new approaches:

a) Collier and Shock's nucleate boiling contribution was changed so that and Up was determined via equation (6-17) corrected via

Thome' s me thod:

«nS = I ^A , (1 - Xa)

a^S UgS

b) Bennett and Chen's method without the Prandtl correction; this

was tried since pure R152a measured values were predicted well

without the correction (section 6.4) .

These modifications yielded improvements over the original approaches,

but did not give satisfactory agreement.

225
In the nucleate boiling regime,

mixture effects were seen to be

to predict the observed quality

simple to apply and is the most

re commended.

pool boiling methods corrected for

the most accurate. They failed however

dependence. Thome's method is very

accurate and conservative, and is thus

In the forced convection/ evaporative regime, a non-mixture method which

assumes nucleate boiling suppression predicted the data best. This result

is consistent with recent turbulent flow evaporation theory. The best

predictor for this data was also the best predictor for the completely

suppressed pure refrigerant data, lending further credibility to Qien'

s

evaporative correlation. Unlike pure fluids through it tended to overpredict the mass flux effect. It is tempting to attribute the overprediction to MTR, though no definitive statement can be made. MTR may

however account in a subtle way for the fact that the measured mixtures

data, ot/o^Q, was less than the pure fluid values at the same pressure,

heat flux and Martinelli parameter. This was shown on Figure 5-6.

It is known that MTR reduces bubble growth rates and decreases the heat

flux where complete suppression is predicted. The reduced a for

mixtures may be the result then of nucleate boiling having been

suppressed for the mixtures but not for the pure fluids. With ebullition, the viscous sublayer may be destroyed, thus increasing both the

evaporative and the nucleate boiling contributions. Such a theory would

explain the measured reduction and be consistent with turbulent flow

evaporation theory and the correlation results.

226
Tabic

7

- 1

:

Pool

Bolling

Correction

Factors

for

Binary

Mixtures

Z27
do• u m o 0 ** M O

01 Be« d

GO

GO

a*ddO (4 Da o

o« o «

•** <M

•*4

O «d

GO o o

>t

•§uM

«•d

•d

**m *0 o •*< D3 d o S

.O

•H (M

«•

O

do

09 «d0

•H 0

d« •M 8 a «• 0* .a 9 0 d d 40 0

«• CM •M

d •M

m

d 0 m CM •d ^ -d 0 d •*4 0 •M 0 M

CM 0 d•< 55 •d0 43 0 H d 0 0 M M d 0 z ^ 8 a d d M 0 0 ^ 0 u M 0 0 0 w d s 0« Ck d a* •M d

d 9 a

09 •MM

•M • • 0, <S1 M •M 0

r~

ad 0 0 0 CM •M

<M <M

M

.a 0 0 -H d d « Qi H 0 0 0 0 ** a u

on

d

d

d >* 91 •M

H

aB

SB «

«•do

.a

dd ^ o «

d>o

-a

g S o 4. oo

09

•oa

•d •M 0 d d 0 U

M

•dd

d cU CQ 0 M 0 0 S •W d 5

fH

fM

•dM

CQ • dd

B 0 d •w 0 0 d

a aa GO

W CiP ca >

228
§ou

as•u

CXi os o9

Ck cS39•MMOu

a0Io * w* 0 I o

** ^ao

Ot 00 ao M 00 ^ r- ^ 00 >0 » ^ 00 NO ® o o o

r- C4

M oo

•n cs f' €S • • • • O o o o ^ n 'o ^ 00 r* oj ^ ^ ® o o

c<

00

n

r*o

9s

cs

v»

cno

oo

00

M 0^ p* <n o p4 ir» p4 p** cs

A

O VO o C4 <s 00 P* o o «o o m <n 9i VO 'T ffi o VO <n 9s m • • o o o o o O o o O o o oo

esVO o

CO

•ooM

O^ d d o oO M 0 O z fiu S odH d d M ^ 0

01 o

cu

»4

flu

HH<H

<1I]

VI eu

(S -1 «o

Cb <H<

I] £o

Bb

H<5>

JO

li £ H<H

•<J «oa s >« IS a -a - "a ••o a o

VI 0i « fii O « -H • > IJ > a ea o cd a< a u Q

aad i3Mo

fid 01 oS ia S M 01 i 1 01 i i oz

229

1^1

F^jdjj.AhVjjj.AT/AT^)

0.736

“o“0

u«u*lly
Tabl«

7-3

(Contlnnsd)

o

>

oa

ao

58 - -H

m o

1

3

o

Mo

NO O

o

?: SJ cs flo o m o

So

«no

01

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o

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4-» a

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O M

d o Z fiU QQ 09 0 0 9

o

JO

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o o

« o u o

o>

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0« ^

• w

•Ol o

ua

•aoz

000 fiE« tta Cfa

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I)

(4 b

r< -io b

H>0H

•«s

£

o

CEi

^ m

a -2

230

(FH)

Ah^

•ffaotlv*

L-l

j.

Pr^.

AT/AT,.

0.387

0.402

0.393

0.163

BtliyGhtlr
Table

7-3

(Comtinuad)

a^ HtZJ «« a

>o

o a .4

flu

c«o

a •*« 9

m o

-4 Mo

S

>oo

e

esm

o m ^

<n «o

cs <n

<n

'O ^

o ^

•n esn

«oO d

<n c« o o

1-4 pH O >C ^ 00 o

O O pH

oU 9 9 Of O

pHo w

9 o z flu

6

J* am6GO I ?

<F

Eh

09 S

<F:C?

•9 •«

pH ^ 50 H H &

< <1 CJ2 w w d

9 5

Ck9 U

il) St

r'21

C4»J OHM-H *t

Ce«000Be> A

H

A

Vh- I I I

I a 3 3 ;

•• a 32 O ^

it z

5

H

99a 9 ^ ^

9 M

0 9 9 ^ pH a <s *

9 pHo

Ad 9

Oo _ _ _ ^ W W Ad W ^

9U pH O pH ^ s 2*

-1

9 9 Is0 pH

H» «

OQ Ad

231
I—Mass diffusion boundary layer, apt

[-^Thermal boundary layer /ajt

X,= X^. Tj

X|< X< Xe. Te

Xe* Tq (superheated

liquid)

Mass fraction of more volatile

component in vapor (Y)

Atact Y

Figure 7-1: Isolated Bubble Growing in a Superheated Binary Liquid.

232
q*10"W/m*

q=10°W/m

233

Figure

7-2:

Pool

Boiling

Experiments

of

Happel

and

Stephan

with

binary

mixtures

Reduction

in

heat

transfer

coefficient

correlated

with

vapor-liquid

composition

difference.
40000 W/sqm IDEM.

5>F

S/% noc

a

O'o

ae

u.UJ0

u1

2

3

1 S

--10

s -

Figure 7-3: Comparison of mixture correction factors. Note

the EPF model, which does not consider MTR suggest

a higher heat transfer coefficient than ideal.

234

KT-COEF.

CKW/iq«/Kl
(kbtu/h/aqf/FI

n>

HT-COEF.

Ocbtu/h/aqf/Fl

20000 W/sqm

PREHEAT: RIG#2

HEAL

p/s SA

THOME

10-

2 I

V

--10

z — &

ia>t. lai

* 196 241 ko/tqB/atc

a SO

• 346 473

a 37lrt. 13B1

• 206 ^ 262 kg/aqa/aac 6.909 ^S36

6 13Bi C 349 “ 466 kg/aqa/aac

a SOat. 13B1

® 266 ^ 372 kg/aqa/aac

0 459 664

7-4: Comparison of Preheat Data to Pool Boiling Models

i

30000 W/sqm rTTTTTPREHEAT: RIG#2 — ^

235
(kt)tu/h/M|f/Fl

i-i

HT-COEF.

Ucbtu/h/sqf/F]

40000 W/sqtn

PREHEAT: flIG#2

lOEAt. P/S

S/K THME

10-

2

X

i3Bi aos * 240 ko/tqii/atc

§ 297 • 349

472

h 971ft. taai 204 • 208 kg/iqa/uc

a 973 • 468

e Mt 13B1 » 484

d OQwt 13B1

" 271 984 kB/iqa/ddC

e 481 • 947 7-4 (cont) Comnarison of Preheat Data to Models

50000 W/sqm : . PREHEAT: RIG#2 T^T'r.r.

S--

2

-- £

--10

I<r

‘a

Ifllrt. 13B1

• 201 242 ko/dw/tac

t 299

473

a 37at 13B1 • 295

a 97S kg/iqa/dK • 469 535

a OQiit UBi

» 469 • 991 kf/doa/itc • 684

236
(kbtu/h/Mf/FI

“

HT-COCF.

Ocbtu/h/aqr/FI

20000 M/sqm

PREHEAT: RIG#2

IZEAL

P/S K/K»

T>OC

* ^41 kg/sqii/Mc

I 296 • 348 473

^ 282 kg/Mp/itc

369 >S3B

** 486 kg/aqa/tK " 372 kg/sqa/aac

684

30000 W/sqm

PREHEAT: RIG#2

IDEAL - - - P/S aSAa -noe

Figure 7-5: Comparison of 1st Station Preheat Data to Pool

Boiling Models

237
0(N/s4Ii/K)

HT-GOEF.

D(H/a90(l

10--

S--

40000 W/sqm

PREHEAT: RIG#2

DEAL

P/S

«S/Ka THONE

3s

2 I

•I

-- £

--10

Iftit. 13B1 203 • 240 kB/wv/aac

a 297 • 349

472

a 37wt. i3Bl

" 204 • 296 ko/aqa/aac a 373 v466

9s40

e Skit. 1391 a flout. UBl

“ 271 « 364 kg/aqa/a

a 461 • 547 692

10-

S--

50000 W/sqm

PREHEAT: RIG#2

DEAL

P/S

as/Ka T)OC

3

£

2

-- £

--10

a lart. 13B1

• 201 * 242 kg/aqa/aac

a 299 479

a 37at- 1361

•o as9

a 37S ko/aqa/aac • 469 S3S

a aoitt. 1391

p 469 • 591 kg/toa/aac

664

Figure 7-5 (cont) : Comparison of 1st Station Preheat Data to

Pool Boiling Models

238
(i/iln/WqJO i3K>-lH

[i/*6t/V>jq5fl i3D3-lH ^

n/lb*/H3Q 'i303-iM f

Ol-H (i/*bi/uo»qi(j ^

Cfi

il 0 2 > X iJ

CC > icc --

Zi X

E 0

9 ^ ^ 0

ij X

c:: X

j-i 0

-3

si: c.

u_ -:3 C C

cX ^

-H C3

CL= ~3

CJ 5

vC

I

0

SC

239
2

Figure 7-7: Comparison of Measured Test Section Data to

Evaporative Only Methods

240
CHAPTER 8: CONCLUSIONS AND RECOMJENDATIONS FOR FURTHER RESEARCH

8.1 Rnmtnarv of Findings and Contributions

The research described in this report involved determining experimental

heat transfer coefficients, (ETTC) examining the phenomena involved in

the physical process, and analyzing the predictive ability of available

models and correlations. This vork was done for both pnre and mixed

refrigerants. Over 1,000 data points were collected, covering a wide

range of pressure, composition, quality, and heat and mass flux.

Several data collection and reduction factors were shown to influence

the experimental heat transfer coefficients. The use of pressure taps

and instream thermocouples may affect the wall temperature measurements

(Chapter 3). The use of a preheater introduces concerns about entrainment and liquid film superheat, though the effect was seen to be minimal. The use of equilibrium temperature in the definition of the ETC

may itself cause a quality dependence to appear in the results (Chapter

5).

It is very important to be able to predict the dominant heat transfer

regime and the point of complete suppression of nucleate boiling

(Chapters 4 and 6). A controversy in the current literature regarding

suppression of nucleate boiling was resolved by critical analysis in

favor of traditional theory. It was seen that with pure refrigerants

complete suppression occurs only at lower pressures than would occur in

residential heat pump applications. A suppression criterion was appl ied

to pure refrigerants at a selected cavity size, and shown to predict

241
quantitatively the quality at which suppression occurs for a given

pressure, heat and mass flux. The method was extended to mixed refrigerants via several hypotheses, and illtoninated questions about predicting suppression with mixtures. The method predicted that ebul 1 ition

might be easier to achieve with mixtures than for pure R152a unless mass

transfer resistance was included. In contrast, inclusion of a mass

transfer resistance term suggests that suppression woul d be easier to

achieve. Various methods were suggested, and partially verified, for

including a mixture effect in the suppression criterion.

Many pure fluid correlations were examined critically (27 in total).

Older correlations proved to be inaccurate with data bases other than

the ones with which they were originally developed. The new method by

Shah was shown to be inaccurate due to its treatment of the suppression

point. The complete Chen correlation and its many variations were

tested. Ihe ccnplete correlation predicts badly, generally overestimating the nucleate boiling contribution. The use of the sem i- ana 1 y ti

c

suppression factor which has been suggested recently aggravated the

ov erpr edict ion. In the nucleate boiling regime, the new method of

Stephan and Abdel salam [St82] was validated. The inclusion of this

method [St82] into Chen's correlation required special reformulation,

and the method then predicted particularly well in the forced convection

dominated region. A Prandtl number correction suggested by Bennett and

Qien [Be80] was used in a new procedure to predict ETC s for pure

refrigerants. The new procedure incorporates a pool boiling method

[St82], the evaporative portion of the [Be80] method and uses the

242
suppression criterion verified in Qiapter 4. For these reasons it is

better grounded in theory than recent regression-based correlations. It

predicted the measured behavior better than calculations which have

appeared in the literature, and can be used in a non-iterative manner

with little loss in accuracy. Ihe method was also checked against other

independent data bases, and predicted the values well.

Sudden departure fran nucleate boiling (DNB) events were observed in

some of the pure fluid and mixtures' measurements. In examining other

data sets of refrigerants, similar events could be seen, though they

remained unattributed as such by their original authors. These events

may be the cause of some of the data scatter found in the literature;

the data in the literature should be critically reviewed for these

events. The occurrence of Dfffi events suggest reduced heat transfer in

the first row of coils in heat pump evaporators; methods could be

developed to prevent their occurrence (e.g. , addition of a second

component and/or modified).

I

I

I

I In the case of mixtures, previously unrecognized physical phenomena were

' noted: the circumferential variation in HTC may be opposite for mixI

i tures than observed for pure fluids. This observation suggests the

i

i

j existence of a circumferential gradient in concentration and interfacial

I temperature (Chapter 5). Modelling then of mixture heat transfer is

further complicated in that gradients exist in axial, radial and circumI lerential directions. In the flow boiling of mixtures when the onset of

nucleate boiling is more difficult to predict and when mass transfer

243
resistance occurs, the actual quality may lag the 'equilibrium' quality

in a different way than for pure fluids. This problem poses another

difficulty for the corr ela tions/model s suggested to date.

For mixtures it was shown that the measured ETC would be different from

ideal, even in the absence of mass transfer resistance, due to non-ideal

property behavior. In the nucleate boiling dominated regime, 0£pp is

greater than (Chapter 7) . In contrast, in the forced

convection/evaporation, regime, a^pp is less than (Chapter 2). The

measured values in each regime showed a degradation in heat transfer

over that predicted by equivalent pure fluid correlations, presumably

due to mass transfer resistance (Chapter 7). Ihe degradation compared

to either pure fluid was seen to be sometimes very severe (greater than

50%). In the nucleate boiling mode, this is due to mass transfer resistance restricting bubble growth. In the forced convection/evaporation

mode, it may be due to mass transfer resistance suppressing the nucleate

boiling for the mixture, but not for the pure components.

A total of 46 methods were examined for predicting heat transfer with

flow boiling of mixtures (Chapter 7). Many methods were simple variations of the few existing techniques or were designed originally for

pure fluids. Of the actual mixtures' models/correlations, some were

found to be flawed on physical grounds. The regression-based correlation of Varma et al suggests that heat transfer is enhanced by the use

of refrigerant mixtures over equivalent fluids; this has not been

observed to date. Ihe method of Bennett and Chen is also problematic at

244
large Lewis nimbers. Its correction term for mass transfer resistance

in evaporative flow becomes negative (not physically possible) in this

range. It should be excluded from further use.

None of the mixtures' calculation methods achieved closure with measured

values to the same degree as was achieved with pure fluids. Qosure,

however, was typical of that reported in the literature for mixtures.

In the nucleate boiling dominated regime, the method of Thome, suggested

for pool boiling of mixtures, achieved the best agreement with the

measured heat transfer coefficient. It however predicted the opposite

quality dependence than was observed in the data. It was able to predict the average heat transfer coefficient in this regime very well, and

is thus recommended. In the forced convection evaporative regime, none

of the methods predicted particularly well. Ihe best fit to the data

was achieved by the evaporative portion of Chen's original equation.

This method then neglects any mixture effect, i.e., MTR, and suggests

the absence of nucleate boiling. It does however tend to overpredict,

particularly at high mass flow rates. This tendency is opposite that

observed for pure fluids. Unlike the case of pure refrigerants, no

general complete correlation could be developed for mixtures. Chawla's

original supposition, which worked very well for pure fluids, sometimes

selected the less accurate predictive method. However, failing an

alternative, it is still recommended for use. This result, while disappointing, illustrates the difficulty with the prediction of mixture

behavior. It also suggests the wide need for more experiments in the

area.

2A5
8 .2 Further Research Needs

Several new efforts could be supported which would add to the

understanding of flow boiling of mixtures. First the experimental rig

could be redesigned in order to increase the speed with which data could

be collected. An example of such a rig is show in Figure 8-1. Ihe rig.

modular in orientation, could have removable tubes for special studies

(e.g.. enhanced surfaces, artificial nucleation sites, effect of pressure and temperature taps). It also could include one tube which is

designed for constant temperature operation and flow visualization.

Valving could be used to allow flow through the tubes in any order.

Thermocouples could be placed to determine the onset of nucleate boiling

point, film boiling occurrences, and instream temperatnres (microthermocouples could be tried). U-tubes with different radii of curvature

could be installed between passes to allow studies of the effect of

evaporator bends.

On a more fundamental basis, the principal efforts for pure flnidt could

be to understand and predict: (a) entrainment and deposition rates, and

(b) pressure drop. Data on the former is particularly scarce. For the

latter, pressure drop should be measured in an experiment with simple

evaporation (complete suppression) and again in an experiment with

nucleate boiling dominant. This might provide information to develop a

more accurate pressure drop correlation. An improved AP correlation

would assist both the heat transfer and suppression predictions.

2A6
For mixtiires, there is a fundamental need to know concentration on both

a bulk stream and local gradient basis. Because virtually no measure—

ments have been taken to date, even instrusive measurements would help.

To this end, isokinetic sampling probles or hot wire techniques could be

used in principle. In the immediate future, measurements of other

mixtures should be done. If possible, an ideal mixture should be used.

Ihe measurement program should vary parametrically, pressure, concentration, mass and heat flux, and cover the full quality range. The pressure levels should cover a range which suggests complete suppression.

This would provide information about possible mass transfer resistance

and nonr equilibrium in the pure evaporative mode.

The issue of onset and suppression of nucleate boiling for mixtures

needs to be resolved. The literature offers few papers on experimentally determined ONB values and boiling site densities for mixtures.

Ihe new experimental rig could be designed to include boiling from

artificial nucleation sites in a glass section (visualization studies

would then be possible). If in this section, constant temperature,

rather than constant heat flux, could be maintained, then excellent

I

' resolution of the OhB point should be possible. Hysteresis studies

I

' would also be assisted in the use of such a section.

I

lu all cases, any future studies occur in parallel with measurements of

i transport properties of the mixed fluids. Precise knowledge of these

I

I properties would allow the separate determination of the contribution of

I Bass transfer resistance to each heat transfer regime.

'

1
Even without further measurements, the existing data base and correlations can be examined further. There are near endless combination of

portions of existing correlations which could be tested against the

data. Data in the literature should be examined critically for experimental technique and data interpretation. In particular, inlet conditions (subcooled liquid versus two phase) may have an effect on results.

DNB events for mixed refrigerants also needs to be studied further.

Some of the scatter in the predictive ability in correlations may in

fact be due to poor experimental technique or interpretation rather than

a problem with the correlations.

248
1

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tube

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249

Figure

8-1:

Proposed

New

Test

Rig.
ci W*4H^rt *'.U ,, vf M

. A xj4«l4 kaAmjti

.m -^^^

t, j»

1 ^** !>*»<: u f

^ ^ *«ijfll

l3fl^J ¥«r*«^ •»? *• • '*')i ^ k.

"

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>'|i iv'^U I . • i» -»t>rr* «

• • I

‘S'" j'f*

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• • • • .

.*4|
appendix 3 A: EXPERIMENTAL DATA SUMBIARY

Bie following lists the data collected for this report. It is arranged

so that other researchers may use it most easily.

These items should be noted:

(a) The tests where film boiling occurred at the tube top are:

225, 236, 237, 252, 253 , 256, 265, 274, 275. Though the

average heat transfer coefficient is only partially affected,

this data should not be used for comparison to annular flow

boiling correlations.

(b) The heat transfer coefficients, ETC, for values of x = 0.00

may be incorrect. The actual thermodynamic quality was less

than 0.00, however in many cases, ETC was mistakenly calculated with the Tf = Tg^^, instead of Tf = Tg^. These values

should not be used.

(c) 'Feed Comp' refers to the measured composition at the

subcooled inlet. 'Mass Qual it/ refers to the calculated

quality based on weight, not moles. 'Liquid Comp' and 'Vapor

Comp' refer to calculated compositions at the local pressure,

enthalpy and given feed composition. 'Teqb' refers to the

calculated fluid temperature assuming equilibriom conditions.

251
TEST SECTION DATA: RISfl R1

Rlifi nH:: FLUX HEAT FLUI QUALITY HTC Tsit

U'iQiiiys tf/sci M/sqa/K deCK

194 69° 420c£ 0.00 1750 257.5

i99 42063 0.00 1782 262.7

699 4206S .00 31 17 264.5

699 42068 264.0

6^>9 4206S .05 3120 263.4

kOQ

W ’ ' 42069 .08 3459 262.3

699 42063 .11 3813 IcZ.O 699 42v'ao AZ 4197 261.2

699 42D6B «

• • iZ 4670 260.4

I?5 703 29c36 0.00 1861 256.6

1

j

29636 0.00 1392 260. j 703 29636 0.00 2538 261.1

/VO 29636 .02 2501 260.6

1 03 * 29636 .04 2oOA

/ VO .05 259.6

t Vo 29636 .07 3119 259.0

703 29636 .09 3433 ^co *• ^jy« u 703 29636 .11 3969 / 4 y

19fi 711 1 3 / O.CC 1759 •c #

*>

711 1S725 0.00 1776 256.3

711 1B725 0.00 2063 257.5

711 18725 .01 2009 257.2

711 i 3/ ^ J

.*,A .Oi ;049 258.=

711 l3'25 • v«> 2112 CJ 711 13725 .04 ::39 256.

1

711 18725 .05- 2765 255.6

711 1=725 .06 vT37 rtr '' • *

4i7/ / lo 10350 0.00 1763 * 713 IC350 0.00 i:’60 254.0

713 10350 0.00 1-61 254.8

713 10350 .00 1643 254.5

713 10350 .01 loAO 254.3

713 10350 .02 Ic31 254.0

713 10350 .02 1833 253.7

713 10350 .03 2121 253.4

713 10350 .03 2603 252.0

4l7C *tCw 1103S 0.00 1153 257.4

4oS I103B 0.00 1109 255.8

465 11038 .01 915 253.7

465 11033 A';• V* 1126 258.6 465 11038 .03 1507 258.5

465 11038 .04 17=6 256.4 465 11033 .05 1929 258.2 465 1 1038 .06 2033 253.1 465 11038 .07 AC* a

il i M

252
\Z3. sECTJON i/ATr! *12*1 RI52i

RUN’ f!A=£ FLUI HEAT FLuX flunLlIV HTC TSaw

kg/'sqs/s U/SSi M/e;8.K ieqt:

11 1 4c2 1S592 0. 00 1192

f>cr t ^iJO« i 442 1E592 0. 00 1571 • 6 442 125": .01 2044 242.: 4o2 1S592 .03 2197 241.9

4o2 125?2 .04 2291 241.8

442 1S592 .06 2417 241.4

442 135=2 .08 2414 241.4

442 IS592 .10 ^CCO 261.1

4fi2 13592 .12 3195 240.9

200 •fllf *^7710 0. 00 1443 '’Am ^ ^OV* A 4oO « e ^771

J

0.00 2470 245.4

440 29415 eOI 7Q*r

^4/ . w 440 29415 .04 2945 2o7.1 440 29415 .07 3027 244.0

440 29415 .10 3184 244.4

440 29415 .13 3544 244.

3

440 29415 .14 3942 24a. 0 440 29415 .13 443= 245.4

201 453 41920 0.00 2043

7*7 crJ 453 •17-.V 0. 00 3402 270.3

• *. C7A 7i 7^y .02 3993 272.1 4S3 41920 .07 3914 271.9

453 41920 .11 3703 271.7 41920 .15 .39^= 271.5

453 ^1920 .1? 4432 77^ 7 a; 453 41920 .24 4997 270.=

41920 .^0 5675 270.0

202 18750 .02 1649 7CC 7

t * w J IB 750 .05 1955

7CQ e

i.UO« J 235 18750 .09 2120 258.4

235 13750 .12 2148 258.2

n^c

^ Jw 1S750 . 14 2474 258.0

13750 .19 2743 7C7 7

12750

77 2950 7e^ •

• 7 18750

n ' .za 3253

7C7 « tl 4VJ 18750 .29 3417 254.=

203 0?- 10414 .01 1413 257.3

237 10414 .03 1498 7r7 ^

• 0 10414 .05 1703

7C7 7 LJf • ^ 237 10414 .07 1742 *w/ • ^

*«// 10414 .09 1748 257.1 10414 .11 1372 257.1

10414 .13 2007 7C7 A ^j/

237 10414 .15 2215 257.0

10414

4 7

• if 2341 254.9

20A 229 4471 0.00 982 7C3 e ^WWt J

253
TEST SECTION DATA; Ric*l S I52i

RUN FLU

I

HEiiT ?L3i JUALJTY HTC Tsat ^g/sqa/s y/sqa M/sqa/K degK

4i7l .00 1267 259.0

4671 ,L1 .1527 252.9

nnp

4671 .02 I55c 253.3

2.7 4671 .03 17S4 258.7

4671 .04 1928 258.6

4671 .05 1937

AT A e ^40* 4 4671 .06 1839

•

4671 .07 1572 ''PQ ^ A*^W • w 205 2*r73l .02 2697 261.7

4.^' J 29761 .07 2491 261.5

233 29761 .13 2439 261.2 2io 29761 .19 2750 ^dl • 0 29761 .24 3142 260.3 233 2‘’7oi .30 3514 260.5

*wC 29761 .35 3776 260.

1

233 29761 .41 4133 ^cz 7 233 29761 .47 4336

APA A *04 206 42257 .01 3947 265.4

•'?'> 42257 . .09 J/ 265.1

.13 3453 264.8

42257 .26 3306 264.5

232 .34 4«icJ 264.2

A^n

j / .42 4622 263.7

.50 i375 263.2

*W^

IAAC7

.59 526- 262.6

^U4>

• *ncT

.66 55=2 262.0

210 140 19265 .03

A? • r 262.3

140 192S5 .0? 2433 4.6^. / 140 19285 .15 2264 262.6

140 19235 .21 2238 2o2.5

140 19285 .27 2415 262.4

140 19285 .33 2471 262.3

140 19285 .40 2852 262.1

140 19285 .46 3124 261.=

140 19235 .52 261.=

211 141 29021 .02 :025 2;5.5

141 29021 .11 3223 265.4

141 29021 .21 3027 268.3

141 29021 .30

» 1 -*x 4 144 268.

1

141 29021 .39 3204 268.0

141 29021 .4? v5o6 267.8

141 29021 .53 4095 267.0

141 29021 .67 4245 267.4

141 2=021 .77 4591

A . A A

4.0/ • A 212 2i>6 41722 .02 o43j 263.9 230 41722 .10 3449

254
TEST SziriJDN iXATAs eisti Ri C*>-

MSS Flax HEAT Flax sImLITV HTC TSat kq'sqa/s iy'sqa a/'5c.«/K degK

2Zb 41722 .13 34a: w 2Zb .25 3764 263.0

2Z6 41722 4045 262.7

ZZb 41722 .41 4391 262.1

^wO

1 • 41/6:^ .49 4732 261.5

i LJO 41722 C7

• w r 4914 261.0

236 41722 .64 UvJ/ 260.4

i^4 ^ 27BS1 0.00 1/ 230.6

• f* zxc .01 4525 239.5

213 27881 .07 445? 235.5

213 27SS1 .13

f ^

-tC-97 239.4

218 27831 4275 259.4

215 27S31 .26 4210 239.3

218 27351 4022 aSTi A 218 27981 .32 4194 289.2

218 27881 .44 4675 239.1 427 27314 0.00 1601 230.

7

427 27S14 0.00 2313 235.9

427 27314 0.00 4129 291.2

427 27814 .03 C'^C’C JaJ7 292.3

^27 j .06 47'^* A 427 27S14 .00 4537 A / M 427 27314 .12 4211 292.1

427 27314 .15 4234 A Aa i

f 27SI4 .13 4747 292.0

415 39971 0.00 2007 235.0

415 37971 0.00 3192 292.6

415 37971 .01 > j6/ 299.4

415 39971 .05 7103 2»9.4

415 39971 .10 6511 299.3

415 39971 c 599? 299.3

415 39971 .20 5441 7QO 7

A • ' a A 415 39971 .25 5233 299.1 415 39971 .29 5746 299.0

fcic 22191 0.00 189: Avtif J 646 2E191 0.00 1940 233.3

646 23191 0.00 1959 646 28191 0.00 3342 295.7

646 23191 .01 4049 297.2

646 23191 .03

J<77-T 7a/. 297.2

646 2S191 .06 4v< ^ 297.1 646 23191 .08 41°9 2=7.0

646 23191 .10 4014 296.= 645 40539 0.00 1362 233.4

645 40539 o.co 2524 233.4

645 40539 0.00 3751 293.4

255
TEST SECTION DATA: RIS41 Rl52i

«AS3 FLUX

fcg/sqa/s

KEAT FLUX U/sqifiUALITY HTC

l(/sqs/K

Tsat degK

4053S f t'O 5636 2'?7.6 645 4&5S? 561= 297.5

645 4059'? .(*7 5407 297.4

645 405=5 .10 5370 2=7.4

645 40585 .13 51 :: 297.3

645 40539 • i W 5137 297.2

256
TEST SECTION DATA; RISIl R13B1

BASS FLL'X HEAT FLOl CUAlITV HTl Tsat

Irc/ sQa/s ii/sqi «/£h5/K degK

7b4 10649 C.OO ,1497 ^J7^J

764 10649 .00 2601 261.8

764 10649 .02 2662 261.3

764 10649 .04 2900 261.3

764 10649 .06 3125 261.3

764 10649 .06 3401 261.7

764 10649 .10 3619 '^Lt 7 764 10649 .12 3489 261.6

764 10649 . 13 AC vXvJ 261.6

121 ? 29494 0.00 4216 261.4

! 21 ? 29494 .02 5428 262.4

1219 29494 .06 4788 262.2

1219 29494 .09 4451 262.0

1219 29494 .12 4162 261.9

1219 29494 .15 3990 261.7

1219 29494 .19 4103 261.4

1219 294<54 • XX 4213 261.2

1219 29494 • Xti 4416 261.0

1210 nxxlx 0.00 5127 26v . 7 1210 4 ''’?p .03 7780 265.9

1210 42212 • Os 6923 XSj* / 1210 42212 .13 6319

A/C c J* J 1210 42212 5359 Xwk^a w' 1210

f A 4 A

• X* 265.0

1210 • */ rc • 7

/ 264.7

1210 42212 T7

• wX 5320 264.5

1210 42212 • v / 5913 264.2

902 42204 .01 7436 802 42204 .08 7789

802 42204 - .IS 7093 265.1 802 42204 .23 6900 264.9

802 42204 .30 6383 2 c4.3 802 42204 .37 6172 264.6

802 42204 .44 6300 264.4

802 42204 « JX 6111 264.1

802 42204 .59 4752 263.9

s:o nOTTA

^ J wwv .01 5397 261.6

820 47WWV .06 559C 261.5

820 29330 .11 5033 261.4

320 29330 .16 4923 261.3

320 29330 .21 460 v 261.2

B20 29330 • 25 4511 261.0

320 29330 .30 4655 260.8

CD O 29330 .35 4664 260.6

320 29330 .40 4644 260.4

257
TEST SECTION DATA; RIGIl R13B1

HASS FLUX

k^/SGa- 5

HEAT FLUX

W'/aqs

QUALITY HTC

U/s(;i/K

Tsot degK

tU- 29l8S .05 sin”' "t *> e

413 29138 .15 ..’433 262.4

413 291S3 • 3331 413 29139 • 34 3271 i>6^. w 413 29 IBB .44 3592 262.3

413 29188 .54 4S9a 262.2

413 29193 . 5211 262.1

413 291 S3 . / 1) 5917 262.0

413 29 133 .93 6534 261.9

414 1B792 .03 4279 261.8

414 1B792 .09 4396 261.7 414 18792 .15 3845 2cl.7

414 18792 261.7

414 •13792 .29 «;*/ 7 261.6

414 18792 .34 3.^49 261.5

414 18792 .40 4854 261.4

414 18792 .46 5539 261.3 414 18792 CT C" • • 261.2

403 10522 0.00 1775 262.9 403 10522 .02 376? 265.3 403 10522 .05 3823 265.

7

4C3 10522 .09 4321 265.7

403 10522 t

'< 4ifi9 265.6

4C3 i AC?’’

• la 3646 265.0 403 10522 .20 3492 265.5 403 1G522 ‘ 4170 265.4

403 10522 .27 4100 265.3

W v% 13753 0.00 1709 260.

4

803 18753 0.00 2795 264.5

803 18758 .01 4787 267.4 803 1S753 .04 5279 267.4

SC3 13758 .02 ei-ra 2s7.3

303 13758 .11 5249 267.3

303 13758 .14 5520 267.2

303 13758 17• 4 t 6065 267.1 303 18759 .21 5909 267.1

1220 18814 0.00 1306

'^CQ t

1220 1S314 0.00 2517 261.2

1220 18814 0. 00 3310 264.0

1220 1SS14 .01 5313 265.

0

1220 IS314 .04 2o4.?

1220 13914 .06 5263 264.3

1220 13914 .08

ec *c 264.7

1220 18814 .10 tlZZ 264.6

1220 18914 .12 5632 264.5

258
TEr =e:ti:n data: aieii

HEAT ?LL'7. “A S3 HTC Teqb LIOOIS VAFCF; FEED PP.EcSus. I-S 2L'al:tv W/sqa/K degK COITF. CjI^F. CD.’l.-. hcTl

436 29309 • «*w 1103 260.2 .C3 .36 .662 4.6:

4Si 29309 .10 . 1:23 260.4 .64 .06 4.67

4c6 :?309 .17 i VWA 260.7

• r .C^ .85 4.65 nCD 29309 1374 261.0 .61 .35 4.63

4S6 2?30? .30 1467 261.3 .59 .84 4.62 4S6 29309 • v6 1529 261.7 .56 .84 4.59

486 293C9 .42 1577 262.1 .54 4.5c

486 2930? .48 1661 262.5 .51 .S3 4.53

486 a7 wv 7 .54 176? 263.1 < 43 .32 4.50

48’ 41309 .03 16P 262.3 . 66

Qc:

• 0w4l c i'.Q w • .'W 427 41308 .12 1724 263.1 .64 C5

• b«^ 5.06

437 t ** 1309 263.6 .61 .84 5.04

487 41303 .31 1920 264.0 .58

r» 4

• on 5.02

437 4iwv8 .40 2033 264.7 re .33 4.9?

427 41308 .43 2216 265.4 e f .82

J wi

n • y 487 41308 €[7 2336 266.3 .47 .31

4 rr

n# 487 41303 .63 2502 267.1 .43 .7? 4.33

487 41308 .70 ?7i t 263.1

r

• •9V .73 4.33

* .08 112c 260.1 .65 .96 • wS^ 4.64

23671 .20 1045 260.7 .61 .35 4.63

2S671 1122 261.5 .34 4.c2

23671 .44 1337 2*2.5 e 53 .83 4.61 22t71 .54 1494 2:3.9 .48 .31 4.c0

23671 .64 1640 2:5.3 .43 .7? • .55 ^CM 22671 • / V 1/66 266.9 .37 4 • 1 4.57

22671 .50 192 c ;63.2 • wv .74

4 CS

22671 .97 2068 2e9.5 •i• W V i

C'T «ro 41190 .09 1570

r • « r

/ ^

4 .35 .o62 5 . 0 : 258 41190 1434

r * ^ r Xdv.' .60 . 34 5.01 res ^JT 41190 .43 1731 265.0 • S4 5.00

SCO 41190 .58 2084 266.9 • 47 .30 4.39

259 41190 .70 2395 263.9 .40 .77 4.97 25? 41190 .31 2651 271.0 .34 .74 4.96

rep 41190 .91 2348 272.3 .29 .70 4.94

41190 1.00 ?1T- 274.4 re .66 4.92

259 41190 11 . V w .er i a ^ V « 7 rr

• .62 4,=0

73? 29154 0. 30 1037 «ea

V .CO 1. 00 .co2 4.CV

735 29154 .03 1129 259.5 . 66 .36 4.59

73? 29154 .08 1227 25=.6 .65 .36 4.57 73? 29154 .12 1301 259.7 .64 .36 4.55 739 29154 .17 1336 259.8 .62 .35 4.52

73?

ro« e« • TA.n .21 1431 25^.9 .61 .35 4.50

739 29154 .26 1474 260.0 .60 .85 4.47

739

rn • e • i*7* jn .30 1523 260.1 .58 .85 4.44

739 29154 .34 1602 260.2 .57 .34 4.41

259
TEST 3ECTIGN DATA: RI54I

MSS rLUi HEAT FLUK HASS HTC T-qD LlSiJID VAFGF 12 rr* PFEcSOF

kg.''£;;a/5 i'&qz QOALITV H/33i/F dear; CORF. CORF. CCf*.F. Cere

;• 42115 0.00 1461 261.0 .00 1 . 00 .c62 5.03

72? 42115 AC• VU 1710 262. S .65 .35 5.06 7?3 42115 .12 1780 263.0 .64 .95 5.04

729 42115 , .10 1920 263.2 .62 Of

4 5.v2

729 42115 .25 2023 263.4 .60 .34 4.25 72® 42115 • W A M « A m

. t n 263.7 .53 .24 4.96

72? 42115 .37 2191 263.9 .56 . 53 4.92 42115 .43 2305 264.2 .54 .33 4.97 729 42115 .49 2463 264.6 .51 • 32 4. S3 4=7 29340 .01 1110 258.9 .70 .37 .70c 4.65 497 29340 .08 126c 259.

1

.c9 .37 4.c3 497 •29340 .15 1326 »'ro .63 • cc 4.62

497 29340 •V7

t ** L'C/ 259.5 .66 • s-Wm 4.oI 4®7 29340 .29 1 iT • 14 , *f '>eo 4j? • 4 .65 . 3c 4.5® 497 29340 .34 1533 260.0 .63 .35

• C"

4®7 29340 .41 159S 260.3 .61 . 95 4.54 497

• 29340 .47 1625 260.6 .59 .94 4.52 497 29340 .53 1224 261.1 .56 .34 4.49 507 41411 .01 1620 262.1 .70 .37 .706 5.14 507 41411 .10 1761 262.4 .69 . 8 c r • n

W V

' 41411 .20 1 0

1

262.6 .67 .36 5.10

jV / 41411 .23 1920 263.0 . 65

• C

• M ^ 5. '3

C,''^ JV: 41411 « 2074 263.4 .c. .35 5... 6 5C7 41411 .46 2l?9 26:.9 .59

C

•

5>'.7 41411 .54 2320 264.5 .56 .33 4.95 507 41411 .62 ;493 ^4

e

• * .32

« ^ «

507 41411 .69 2742 266.1 .47 .21 4.®0 247 * < i .09 115: . 6 ? .3' . ':6 4.55 247 • 1032 259.1 .6c .3c 4.54 247 29231 • Ww 1159 259.9 .63 • «4 W

•i • ww 247 .47 1339 260.7 .59 .84 4 , 5; 247 '^9*^31 .58 15..0 261.9 . j3 .93 4.52

247 29231 .69 lo6? 263.4 .47 .81 4.50 247 29231 .78 1221 265.1 .41 .79 4.4S 247 29231 .83 • 1952 2s6.6 t .7c % ,

«• 1

• ••/ 29231 .°4 2120 263.2

*1

• V 4 • . J 4.4:

^17 3301® .10 1323 25®. 3

i.5

• W ' . 3c

*»* 4.': 247 3i019 .26 1229 260.5 .65 . 36

• - • ^ • * 247 3i019 .41 i 261.5 .61 .65 4.'1

247 36019 .56

fk j 262.9 .54 .83 4.'j

247 36019 .69 1961 264.7 .47 .81 4 . c’ 247 36019 .SO 2179 26o.7 .40 .78 4.0/ 247 36019 .90 2417 268.7 .34 .75 4.65 247 36019 1.00 270.7 .29 .71 4.c3

247 36019 1.00 272.6 .24 . c6 4. cl 753 29391 0.00 1216

C

4.W/ • J .71 l.uO . '')c 4.

260
TEST SECTION DATA: RISIl

RUN Nh== Fi.UI HEAT FLUX flASS HTC Teqs LIQUID VAPOR FEED PRESSURE

3 * -Wf* ^ ^ H/sqs SUalITY M.'sqs/l;. deol'' C2HP. COXP. r-KC

ww**r 4 bars

T3S 2”:9i

• ^

i 1541 ntf e ^04 4 J .o'O .S5 4.71 733 29391 .07 1433 259.4 .69 .37 4.63

755 29391 .12 1428 . 259.4 .88 .38 4.00

758 29391 .18 1479 259.5 .83 .36 4.84

758 29391 .21 1520 nc3 ^

• ^ / 4 y .87 .38 4.82

753 29391 IcOl 259.5 • wy .33 4.59

75S 29391 .30 1723 259.8 .84 .S8 4.5o

753 29351 .34 1782 259.7 .83 .S5 4.53

23? 754 41485 0.00 15cl 259.9 74

4 / • I.OO .708 c tc y4 • . 754 41485 .04 1 262.4 .70 3i

4 wy

C 1 y • * / 754 41485 .11 1378 2e2.5 .8? .Sc y t i y 754 41485 .17 1916 262.7 .67 .Sc

r 1-5 w • i 754 414E5 2029 282.3 .88 .38 5.10

754 41485 .29 2120 262.9 .65 JC

4 Wy 5.08

. 754 41435 . V J 2s3.1 .83 .55 5.02. 754 41485 .41 263.2 .61 .95 4. rS 754 41485 .47 2556 283. A 4 V 7 .34 4. "3 502 41732 .01 1830 283.4 .70 .38 .70e ^ '*1 y • Jv* 41732 .10 1797 2c3.8 .89 .88 ff TT

«• 4 y%

5r>'' W V* 41732 .19 132? 263.9 .87 .38 5.31

* CA? wV^ 41732

M m

» 2 1927 2o4.3 .s5 5.29

502. 41732 .37 2108 2s4.

9

.82 .35 5.27 41732 .48 2215 « w y 4 V .59 .34

c "r

41732 « wlw 2:8.0 .58 .33

ffy • 502 41732 25a-3 288.3 .52 • 5. IS 502 41732 Tu

. } V 2344 287.7 .45 .31

r < c

y4 4 w ^v 501 w0v5B .01 1315 2&0.5 .70

• ^

• 2 / 7.*; A 4.39

30! 30053 .08 1408 280.7 .89 .88 4.37

50^ 30053 .14 260.9 .83 .38 4,3c

501 vv05S

^4 1427 261.1 .88 .06 4.35

501 30053 .28 1512 261.4 .85 .86 4,54

501 30058 .34 15a9 281.8 . 83 .35 4.32

501 30053 .41 1643 282.0 .81 .85 4.79

501 30055 .47 1731

4 4S^4^ .59 .34 4.77

501 • 53 lEel :82.9 .58 .34 4.75

214 247 iC; f Z .07 1132 259.8 .89 .57 .708 4, '2 247 237'6 .2v 1206 280.1 .o7 .88 4.7! 247 2S77o 4 WJ 1158

n # A «

4.3V. 0 . o3 . 85 4.70 247 23778 .45 4 75c 281.7 .59 .84 4.a9 247 28778 .57 1541 282.9 .54 .33 4.o9 2S778 .87 1879

A • • A 4 ^

4 -to

4

• •

-t. Oi 247 23778 .77 iOOt 285.9

4^

4 TO 4 « . 4. C5 247 23778 4 34 2083 2:7.4 .37 .77

• • • m , 247 23778 .92 2347 269.0 4 y J .74 4. d j 245 779 23943 0.00 1049 25s. 3 4 / J l.CO .750 6.75 779 28943 0.00 1259 284.6 .75 1.00 0.75

261
TEST SECTIDJi DATA: RIoll

HAS5 FLLi^ HEAT FLUJl HTC Teqt LICUID '* AF'CR FEED FREiSuPE

kg/5i;a/£ eUALITY degK COHP. E0«F. CDfIP. bars

779 2S943 .05 1553 270.4 .74 .87 0 . 75 779 23943 .04 •1570 270.3 • / w .37 6.74

779 2S943 .08 1648 270.4 .74 .37 6 . 7; 779 2B943 .13 1735 270.4 .73 .86 0.71 779 28943 .17 1734 270.5 • i 0 .36 0.67

779 25543 1835 270.

6

.72 .86 6.53

779 2B°43 .26 2044 270.6 .71 .=0 0. 6: 7&7 41793 0.00 1425 261.0 .75 LOO .750 6. 4o 7e7 41793 0.00 1909 2&6.8 .85 .91 6.J5 767 41793 .07 2161 265.8 .74 .37 6.44 76? 41793 .13

n« 2e3.9 .73 .87 6. •• 767 41793 .20 2133 269.1 • /X .06 6.40 767 41793 .26 xe^.x 4 . i .86 6.35 767 41793 Xi>/X 269.3 .70 .36 6 . 35 767 41793 .33 24S5 269.4 .o9 .35 w* 767 41793 .44 2729 269.5 .67 .85 0.29

511 30125 o.oc 1206 261.9

nc

• J td 1.00 .750 5.31 511 30125 .04 1523 265.3 .74 .37 5.31 511 30125 .11 15ol "ft®' 5 . 7: .37 5.3'.' 511 30125 .13 1j3c 265.6 .72 .37 5.79

511 30125 1573 265.0 • 1 i .56 j. . 5 511

y • • W * 1634 26o.O .70 .Soc

511 30125 .33 266.2 . 6

^ 5.75

511 wv * ^5 .44 ISOS 266.5 .67 .35 5.73

511 30125 .51 1972 2o6.9 .65 cc4 W M 5 . 7 ;

51v' 41666 0.00 1630 265.0 .75 l.OC .75j 6.40 510 4l6c6 .07 2094 266.6 .74 . c7 W4 3? 510 416oo .16 2007 263.3 4 t W .36 6.33 510 41655 .26 2046 269.1 .71 .36 6.3 = 510 41666 • 35 2142 269.4 .59 .so 6.35 510 41666 .44 2281 269.3 • C/ .35 6.33

510 41666 2436 270.3 .65 .84 64 >f\f 510 41666 .61 2614 270.9 .62

» 4 • on 0* .9 510 41s66 .69 X7WJ 271.6 .53 6.25

251 .05 1269 2=4.6

^ •

• f *9 .57

•c ' 5. OS 251 29222 .13 1180 265. V .72 .97 5.0*

251

^ 4 • V 1 1226 265.5 .70 .36 5 . 0

'

net

•.Ji *^9122 .44 1303 2c6.1

-•

• 0/ .85 5.06 251 nQ222

.57 1521 267.0 .o3 .84 5.o5

251 .63 1675 263.1 .59 .33 5.64

251 29222 .73 1824 2o9.5

en

4 .81 5. o3 251 .87 2032 271.2 .4o .73 5. o3 251 .95 2373 272 .

7

.40 .77 5.ol •

254 34447 .05 1463 2=6.2 .74 .87 .’50 5.96 254 34447 .21 1354 266.6 .72 .36 5.95 254 34447 • 1384

^ ^ .07 .86 5. '5

262
TEST SEETISfl DATA: P.ISIl

flhSS FLUX KE.47 FLijl «ASS HTC Te-:5 LISL'ID VAPOR FEED FRE53-JRE

li§’s£;il/5 it'-SqA SuALlTY U.r’sqa.' ffeCK ccap. CuNF. COHP. tlif 3

2S-? 34447 .51

itrsr

i 2aS. 1 .85 5,«4

254 34447 .64 1S65 269.

3

.60 • 5w 5.93

254 34447 » f

• 2109 270.9 .53 .32 S C"

254 34447 .87 2513 272.8 .47 .79 5.91 254 34447 .97 2953 274.3 .40 .76 «: cr,

254 34447 1.00 2616 276.3 .34 « / J 5. 55 269 29215 .02 1489 ibi .

' . 90 .833 6.59 269 29215 .15 1462 267.9 .22 .90 6.55 269 29215 .23 1424 263.1 .51 .59 0.57

269 29215 .42 1335 263.3 .30 .39 6.56

269 29215 .54 1415 268.7 .78 .38 6* 269 C .66 1632 269.1 .76 .87 6.55

269 29215 • /I 1311 269.6 .73 .Ss 6.53

269 29215 .39 2039 270.5 .69 fic

• Ww 2* 5^

• 3 C .93 2319 271.3 .63 .34 6.51

C'^c; Wa«« 41410 0.00 1533 261.3 .S3 1.00 . 3j./ 7.26 41410 0.00 2447 269.7 .23 l.OC 7.26

S25 41410 .05 *0 / w 271.0 .23 .90 / *^J S25 41410 .11 Jw 271.1 .33 .90 S25 41410 .17

Ai'-. 271.1 .82 .39 / • 3<*c 41410 .24 2370 271.1 .32 .29 7.20

325 41410 .29 2434 271.1 .31 .c? 7.17

825 41410 .36 2573 271.1 .50 .69 7. 14 325 41410 .42 2762 271.0 .90 .58

^ X

4 • * « 326 26642 0.00 1147 • ww • C .83 1.00 .333 6.61 326 28642 0.00 1540 2s4.4 .33 1.00 6. ol 826 23642 .01 193? 267.8 .23 .90 o.oO

326 2So42 .06 1347 267.3 .33 .90 6.59

32s 29642 .10 1796 267.9 • 3 j .90 6.57

326 23642 .14 1759 267.3 .32 .90 w« 2d 326 23642 .19 1777 4^2 / • / .32 .39 0.54

326 28642 • ^ j 1316 id/*/ .32 .39 6.52

326 23642 1921 267.7 .31 .59 C.50

C^Q JIQ 22463 0.00 1094 260.7 .93 i.OO / *i7 523 22463 0. 00 1644 267.9 .23 1.00

- -0 c-e 22463 .02 2241 271.1 .53 .90

• •• C^n 22463 .03 2031 TT1 0 .33 .90 / • 523 22463 .13 2037 271.2 .32 .39 7.25

eno 22463 .18 1951 271.2 .82 .89 7.24 529 224o3 .24 1912 271.2 .32 .39

523 22463

''0

• ^4 2002 ^4 i .81 .59 7.20 523 22463 .34 2096 271.2 .31 .3? MS

cir 37301 0.00 1469 265.2 .33 1.00 .333 3.25 . 543 37301 0.00 2237 O’?- 1 *4 w* * .97 .98 3.:< 543 r:oi .09 2373 275.6 .33 .89 8.23

543 57301 .13 2700 275.7 .32 .89 3.::

263
TEST SECTICN CATA; RlStl

rhSS flux HEAT fLL'i «AS= HTC Teqs l:5L'I2 VAF2R FEED FSEESuFi

fcg/Ei^B/S li/sga SWLITV H/sga/K oecK CC!*P. C3f*P. C2.TP. bars

37301 .26 ^ J w ^ u • s .81 .3? 3.21 37301 .35 275.9 .SI .S3 3.2(1 -»3 37301 «C« L 276.0 .so .33 3.15

553 37301 cn 2710 ^/O. I . 79 20 3.15 543 37301 .59 2966

*• 0 • V ^5 .87 3.13 54o 23655 O.OC lls2 263.2 .S3 1. 00 7.5’ 346 23655 0.00 1853 (I 4 V .33 1 . vv

• c z

4 • 546 23655 .06 2162

• .33 .90 7.53 546 23655 .12 20o4 272.0 .32 .39 • 57 546 .19 2045 272.7 .52

»• .ST 7.56 346 23655 1C84 272.3 .31 .89 7.54 546 23655 .31 2005 Q

0 .81 .39 • «4 V 546 28653 .38 2093 272.3 .80 .83 7.51 54s 2Ss55 .44 272.9 .79 .35 7. <9 266 18598 .01 1110 265.7 .33 . TV .333 0«

Hi. • «.30 18598 .09 1246 265. S .33 .90 6.20 266 1259S .18 1243 265.9 .32 .90 0. ;9 266 13593 .26 1125 266.1 .31 .39 6.15 lih 13599

T M

i 1067 2o6.2 .30 .39 6.19 266 1359S .42 1066 2o6.4 .79 .39 6.13 266 1S59S .51 1136

^ t t 1 »00* 0 .73 .oc C.12 2s6 13593 CO

• ww 1235 26i).9 • / » .03 5.17 266 1S593 .66 1350 267.1 • 4 J .37 6. Is

c*.c 41457 0.00 ic=5 266.5 . S3 1 . 00 .523 7.5* e"c A* *c-y .05 297i 272.6 .33 .90 7.59 C^C

J*J ^inj/ .15

'*1'— 172.7 .3° 7.57

entr 41457 '^C 272.3 .81

• cc

• r'^tr 41457 t 0J 2s71 272.9 .80 .39

• C •

1 • 41437 .44 2650 273.1 .79 .38 7.52

T^-C 41457 j3 ''7Cf

4»/ 273.2 .73 .53 7.50

e»^c 41457 .62 3014 273.4 / f .37 7.-3 525 41457 .71 v4v i 273.7 .75 .37 ^45

423 13539 0.00 745 259.4 .45 1.00 .454 c

W* w4 423 13539 0.00 939 264.9 .45 l.OC 5.2* 423 13539 .03 1039 2^0.2 .44 'C

• / . Z -T

423 13539 .04 ic:: 270.2 .44 .79

c ?r

423 18539 .09 1035 270.6 .42 • 4 0 5.24 423 IS539

« ^ 1131 271.0 .M .77 5.;: 18539 .17 1144 271.5 .39 .76 5.21 13539 .21 1217 271.9 • w

‘ . 7e 5.29 423 13539 «C 1329 ''7? i .36 ?e

• ^ w

C

428 29731 0.00 A«2 263.6

• r

t l.Oo .454 e.:4 428 2373

1

0.00 1264 271.7 .45 l.OO d.M , 423 2S7S1 .04 1467 .44 .78 6.:; 425 28781 .11 1543 275.7 .42 .77 0. 1 3 428 28781 .17 1619 276.5 .39 • 4 J 0. l2

264
TEST SECTI2.M E-ATAj R:5#l

i<;sS nux HEAT FLU?. MAS: hi: Teqt] LIGUIO VAFOF FEE2 9'F;£2EL;r*

ka. £S3/i U>'sqt SiiALITV il/sqa/K teSK COKF. CuMr. c:*ip. tars

428 2S73I i23 1749 .37

^ i

• 6.12 423 2873

1

.25 134? 273.1 .72 6. 12 42S 25701 .34 200? 279.0 .71 6. i i 42B 287S1 .3? 22®5 279.3 .30 i.a

f w 6 • 1

V

432 ^1167 0.00 1253 T

t .45 1.00 .454 o.Ol ^ZZ 41 li? 0.00 1662 270.7 .56 .32 C.Ol 4ZZ 4:ioT • 0^ 2037 274.7 .77 o.OC 4Uf.7 .13 21 SB 275.3 .39 .75 5.99

4ila7 2345 277.0 . 35 .73 W. 7C 411a7 .34 2500 273.

2

• / * 5.97

433 41167 .41 2795 279.4 .29 .63 5

0*' w • ' w 433 411i7 .40

n .• 290.4 « * i .06 5. ?4 433 41167 .54 3539 231.4 J

• 63 5.92

274 213 4045? 0.00 1671 277.2 .45 l.OO

JC i

• nu-* 6.2? 4045? .17 1945 230.7 .4(1 .74 6. 82 2!3 4045? .33 2142 233.0 .33 .70 d«CO

213 4045? .47 257? 2S5.4 .22 .65 6.32

213 4045? .59 237.4 .24 .60 6. 37 213 4045? .70 3737 239.0 .56 6.2s

213 4045? .32 4233 290.4 .13 t 6.56

213 40459 5o22 291.6 .16

4 • ‘•C 0.25

213 40459 1.00 6654 292.7 « 14

1 J 6.34

'T'TC 215 23745 0.00 1013 263.1 .45 I.OC .454 5.33

215 23745 .11 1215 '71.2 .41 .78 5.3= 215 23745 .24 1353 272.9 rr 5.33

215 4C/

• » 147! L

« .71 Z ^W« lA/ 215 23745 .44 1751 276.4 .23 .63 ff w/ 215 23745 t ^ V 2043 27Si 0 .24 .64 C

w« %•/ 215 2S745 .61 2236 279.3 • .61 w .* n « c 28745 .69 2497 «.ov«o .19 .57 w'O 23745 . 76 2707 231.6 .17 .54 5.36

265
Preheat secticm data; ris*: Risia

RUN BASE FLUX kc/s^/s

H£iT PlUX auALin HTC

b/ s^/ K 1

S-I1 z:^ 15E 10026 .06 3254 2=0.0

15E '•>026 .09 3317 290.6

;5H lv02i .12 •3:ii 2?0.6

:eb 157 20002 .14 3561 290.4

157 20002 « A A 3027 290.4

157 20002 .23 zz-n 290.4

')or 154 25024 .19 3436 I’O.O

154 25024 .23 3619 290.0

154 25024 .36 399- 2=0.0

157 30697 .24 3249 290.4

157 30697 r• WM 4273 290.3

157 30697 .45 4e64 290.3 :si 164 y ^ 9 .26 46/5 290.4

164 35079 .33 4338 290.3

164 35079 .49 521? 290.3

234 15? 39996 5209 290.2

15? 39996 .45 5279 290. 1

•

15? 39996 .59 5534 290.1

*i^W 153 45020 .37 5709 290.3

15B 45020 .52 5707 290.3

158 45020 .67 5921 290.2

««* A wiV 20036 .08 3o76 290.6

.12 3764 290.6

232 20036 .17 w « 290.5

295 23S 30240 t 1

J

4593

AM A « -TU.O 23S 30240 .20 4465 290.5

jS 30240 .26 4734 290.5

'^r n iTd . 40442 .1? 5:19 2=0.4

238 40442 .25 5458 290.3

233 40442 .37 5751 290.2

302 240 49890 .24 6391 290.3

240 49390 .35 6291 290.2 240 49390 .46 Of 4.^ 290.1

304 246 59991 .29 7396 290.9 246 59991 .42 7249 290.9 246 59991 .54 76/0 290.3

310 246 69992 .35 8215 290.3 246 69993 .50 3011 290.7

246 69999 .65 c6j^ 290.

0

282 20003 .05 3607 290.2

'>Q'> 20009 .09 3745 2?0.2

2S2 2 0003 .13 3990 290.1

•’04 ^SJ 30250 .10 4615 290.8

IEj 30250 .15 4511 290.5

285 30250 .21 4766 290.5

266
PREHEAT SECTION BATA; RJSi: R152-

RUN HAS: FLUX

kg/sqft/5

HEAT FLUX N/sqi

SUALITY HTC N/sqi/KTsoi

deoK

2S9 -»cc ^0o?4 .14 55T5 290.6

2S9 A0a94 • 44. '5470 290.5

2S9 406?4 .29 5771. 290.4 290 4??S6 .19 6534 291.0

* 233 4?9Sa .28 6512 290.9

tkmm 43 J

jCCOi. •t T . ww .33

< nc • 07jH 290.3

2»1 293 599=2 .24 7535 290.7

2S3 59??2 7413 290.5

293 59?92 .46 79C4 290.3

292 271 70003 .30 3310 290.7

/' 7CCG3 .43 8143 290.6

X . < 70C03 r*?

• w

;

S646 250.4

2?3 281 ?4?5T 8782 290.9

2S1 74967 .46 5653

nQA n 470 tC 28

1

74967 .60 8932 290.5

324 sons • 33 7i^l 291.1 237 30118 .47 290.9

49 i 80113 .62 9193 290.7

321 340 20033 .04 3657 290.6 340 20033 .07 w/ 290.5

340 20033 .10 4074 290.5

29: 3S4 30225 .02 4711

nn’i / * . « « 0 TT ? TA»^ne

WV*4»W .11 4655 250.6 30225 .15 4=22 2=0.5

297 -Ci. WWW 40447 » iSJ 5535 250.5

jIq 40447 .16 5419 250.4

?c;, WwW 40447 An 5715 290.4

•W 4 35? 49930 .13 6539 290.9

359 49930 .21 6.:'2j 290.3

35? 49930 .23 6657 ''C.I 0

4 / w • 0 356 CDOO?

W i 7 w4 .17 7338 2=0.5

356 59981 .26 7120 290.4

356 59991 •C

• ww

77'’’’ 290.2

30? 367 69993 .20 8324 290.7

w6> 69993 .30 8068 290.5

ww/ 69993 .40 3301 2=0.4

311 366 80C36 • 9173 2=0.9

366 30036 • wU 8833 290.7

366 80036 .47 9070 290.5

316 363 39907 .23 10063 250.9

363 89907 .41 5718 290.7

8==07 .54 9712 250.4 41? 20020 .02 3E67 290. B 41? 20020 .04 3791 290.7

41? 20020 .07 4143 290.7

267
PREHEAT SECTION DATA; RIo»2 R152a

RUN, flASS FLUX kg/sqs/5HEAT FLUX M.sqa

8UALITV HTC H'sga/KTsat degK

::s 418 30342 • 05 4913 290.7

413 30342 .09 4735 290.6

413 30342 .13 4817 290.5

2?5 425 40416 .07 5821 290.9

425 40416 .12 5702 2«0.8

4?*^' 40416 .17 5988 290.7

300 427 49945 .10 6594 2=0.9 427 49945 .16 6349 290.3

427 4”45 .22 6o5S 290.7

305 430 60275 774e 291.3

430 60275 .20 7392 2=1.1 430 60275 .23 7403 290.9

3G3 430 70011 .16 3389 290.9 430 70011 .24 8127 290.7

43<3 70011 8242 290.5 312 42? 30101 .19 9254 290.9

42? 30101 .29 8995 2=0.3

42? SClOl .38 J 290.6

351 143 lOOSc .09 333'J 290.3

14B 10086 .12 3306 290.3

148 lOOBS .16 3007 29C.3

340 153 20421

A A

• 4»V 3341 290.4

ijZ 20421 .21 3431 290.4

153 20421 • 3653 290.4 350 14= 2534a 3497 290.2

149 25346 .31 3839 290.

1

149 25346 .40 4080 290.1

150 30731 .30 4390 290.4

150 30731 • .41 4611 290.4

150 30731 .52 4332 29C.3

w*t7 150 35105 .36 4992

150 35105 .49 5023 290.1

150 35105 .61 5224 290.1

156 39937 ?c.-, r

• V • w 156 39937 .46 53"~ 290.3

156 39937 .5° CTCC wwwJ 290.2

339 2S6 20404 .05

A » A • 290.4

^ n ' 4.Z0 20404 .09 3712 290.4

AM 20404 .12 3733 290.3

Ww« 233 30700 .09 4367 290.8 283 30700 .15 493? 290.3

238 30700 .20 5157 290.7

wwl :S6 39391 .14 5697 290.2

236 39891 .21 55o9 2=0.1 286 39S91 .29 5672 290.0

268
PREHEAT SECTION 3ATA: RIG«2 Rl52a

RiifT f»A£3 FLU I HEAT FLUX CuALITY HTC TSat kg/sqi/5 H/aqt M/sqs/k degk;

334 50004 .19 6^7 290.7

235 50004 .23 oa46 290.6

285 50004 .37 •6716 290.5

342 287 60003 .26 776a nzi'i p 237 6000S .37 7736 290.8

297 60008 .48 7927 290.7

344 295 70761 .32 5673 291.0

285 70761 .45 2CO 290.9

70761 .58 9812 290.7

346 293 80452 .36 9737 290.9

293 30452 .50 9773 290.7

293 80452 .65 10139 290.4

33c 423 30684 .02 5092 290.3

423 30684 # Oo 5050 290.8

423 30634 .10 T" 1? 290.7

423 39BS7 .07 5S/ y 290.3

42S 39837 § 5669 290.2

429 393B7 .17 5737 290.1 42? 50004 .09 6935 291.1 429 50004 .16 6751 291.0

429 50004 6623 290.9

34! 426 59966 .13 7519 290.9

426 59966 .20 774o 290. S 426 59966 nr

• 7933 290.7

343 »2a 70721 . la 3799 291.4 42a 7M 7 C

2

'•C 5o04 291.3

42o 707SI .34 8745 291.0

3^5 424 79772 .20 =506 291.1 424 79772 .30 9219 290.9

424 79772 .40 9122 290.6

347 424 89915 10315 291.4

424 39915 .35 10034 291.2

424 89915 .46 9934 290.9

269
PREHEAT SECTIOH DATA; RI5S2 R13B1

RL'N «AS3 FLUl HEAT flu; CUALITY HTC Tsat

i;q/:qa<'5 H/sqa £q:/K degK

5v6 353 10029 .10 2276 254.4

10029 .14 •2246 254.4

10029 .18 1755 254.4

532 360 15173 .16 2293 254.4

360 1517B J 254.3

360 15175 .23 2231 254.3

S03 359 19955 .21 2353 254.3

359 19955 .2? 2743 254.3

359 19955 .37 3189

-? .bJ**. i, 504 359 25015 J 255.0

359 25015 .37 3551 255.0

359 25015 .47 4174 254.9

505 356 30766 .34 3201 254.7

30766 .46 4619 254.6

/5o 30766 .59 47=0 r

J 491 4 vw 10C06 .08 2601 254.3

10006 .11 2541 254.3

4wj 10006 .14 2413 254.2

439 434 15C26 .12 2952 254.2

434 15026 .17 2796 254.2

434 15026 « 2720 254.1

490 441 19973 .17 2750 254.5

441 19973 • ^ J 2952 254.5

441 19973 • «^V / / 254.4

4c7 451 .21 3168 254.5

451 25216 .29 3991 254.8

451 • w'

/

3969 254.7

433 432 3Q736 .29 4273 255.1 432 30786 .3? 4713 255.0

432 li^oyss .50 4615 25i.9

483 445 rcn«eJ .31 45;3 A

445 35215 .42 C* ''T 254.9

445 35215 .54 5149 254.8

473 451 41013 .34 4705 254.9

451 41013 .47 jS/v # J^ J* • y 451 41013 .60 C7T 1 W A «CJ ^

/ 492 CC5 14947 .08

71''^' 254.6

559 14947 • 6* w 1 wC 254.5

559 14947 .16 At/ 254.5

4Ss 555 20278 « ^

• i W 3534 254.5

55B 2C273 .13 3630 254.5

55S 20273 .24 3653 254.4 493 5=4 24949 .15 ^243 254.8

564 24949 .21 41S0 254.3

564 24949 .28 4223 254.7

270
PREHEAT 3ECTI3N DATA: RI3I2 RITE!

RiJN HAE= FLl/r HEAT FL'jJ QUALITY ht: !£ot kg/i;3,

s

«i/sqi y/sga/K degK

4S2 30613 .19 4596 255.0

rr * 30613 -T 4/55 254.9

554 30613 .35 4643 254.8

562 34900 5'^3 W « w W 255.0

5o2 34900 .31 254.9

562 34=00 .40 5232 254.3

472 560 40206 .26 4544 254.9

560 40206 .36 5467 '!Ci 5 560 40206 .47 5405 254.6

495 WWw 4496c .30 5609 255.4

rrr 4496S .41 6256 255.2

rcff wwW 44968 .53 6211 255.0

477 5:36 Cl T'OT W A 4» f V • 3l 3691 ?

W 5s6 51-70 .44 5301 255.1

C*

w i* 7^ « y / 5081 254.9

271
PREHEAT SEETICH DATA: RISI2 .60 at R1 :si

RL'N RfiSS FLiJJ he;: FLiiX NSs KTC Teqb LiauiD VArOR kg/SqirS M< sqa CUALITY «/sca/K deqK CCHP. CCf..'.

wvw 2*3 lOOOF .10 1133 255.0 70 .99 2Ls lOCO? .15 1154 252.1 .79 .39 2-3 10009 .19 1442 253.2 .78 .69 535 2cS 15020 .17 1429 258.3 .75 .39 2o0 15020 .24 152a 256.4 .73 .29 26S 15020 .31 179= 3^0 i XjWa 5 .77 .39 2c6 20041 .24 167" 7

^Wk»a V .75 .39 2oc 20041 .34 15=1 253. s .7= .33 2Co 20041 .43 2111 259. S .75 .23 533 2iB 2500S .31 1822 255.3 . 77 .55 2=8 * M V V W .42 259.2 .75 .3: 2iS J V W .53 2445 259.6 77

a / ^

C7

a y

;

W V V w « .37 1997 258.9 .76 .23 30059 .50 255S 259.4 a / W 37

a y 4 30059 • Ow 2B15 2=0.0 .=9 . 27 531 35062 .44 2245 259.1

^ •

a / 7 .£5

nr'y

i. 35062 .59 2840 259.3 .71 .37

'^7? 35062 a y J 3215 2=0.' .o5 .56 530 271 40041 .50 246" 259.5 a / •/ .37

271 4C-041 .C7

'^37^

i ^ 2=0.4 .63 .36

271 4004

1

.33 3674 262.1 . oO .94 53c *7i't W 4 k 10021 .04 1127 257.0 .90 .29 370 10021 .07 1216 257.6 .79 .39 370 10021 • 1 1 1246 257.7 .79 .3' c^e

V j V iC.r-T .09

« a ifOi 253.1 70

a ( . .59

*>7T V } w 15027 .14 1479 ^<i#9a ^ ^5 .3=

^ / w 15027 .19 1561 ^cz “• ^«awa J a « 2 . 29 cn - W i W 20028 .14 1733 255.0 .79 .39

w.' *> 2002S a^i 1759 255.

1

.75 .39

^/ w 20028 .27 1871 253.: . 77 ao

a y 523 3oo 25057 .20 1971 253.1 . 0 .59 363 25057 .23 2C06 255.3 •

' / .35 366 25057 .36 ;:o0 253.5 .76 .35 362 30044 .25

*^1 7^1 * A

’ •'cj e ^ • w a / / .99 362 30044 ““a- 153.7 .76 .38

• • ^ 3004- a 4 J 2577 259. r .7- .SB 321 vwO 34959 .30 234" 255.3

“7 .53 3u6 34959 .42 2535 259.1 a .23 366 34959 .53 2045 259.5 7^ .57 527 364 39750 2431 259.0 . 7o .33 364 39750 .47 2772 259.4 .74 .39 364 39750 .59 3v07 259.9 .71 .37 529 362 45B9C .41 25'.

5

-r

a * W .29 362 45B90 • tJf 31=4 260.0 .71 .87 362 45390 .7! :6B0 260.9 .CO

4k • .00 547 372 55110 .48 3289 259.

a

• / V .67

272
Fr.EHEAT SECTION DATA: RIES: .30 Nt 11

<

11

s

1

RWi KASrpLui HEAr?IIil iA== HT? Yftir‘*'112^0' VApOR

kg.'sos.s «/sgs QUALITY H/sqc/K c’egK CQf^P. COftF.

t 55110 . iZ 3694 260.4 .69 .36 372 55110 .31 4504 261.9 .61 .35 C37 447 99S4 .02 1143 257.6 .80 .89 447 9934 .05 1374 257.6 .80 .89 447 9984 .08 1611 257.6 .79 .39 532 459 19946 .10 1712 257.? .79 .89 453 19946 .15 lSo5 253.0 .7? .89 459 19946 .21 253.1 .78 .29 53? 449 29950 .18 2036 258.6 .78 .89 449 29950 • * / 2357 *nc2 ^

/ .77 .29 449 29950 2777 oco q .7b .83 543 4cl 40909 • *J 2489 253.9 .77 .89

461 40909 . ^6 2301 259.1 .76 .88

461 40=09 .46 j.^43 259,4 • .83 544 465 49331 2964 •U * • V .76 .38 465 49S3I .45 *Tcr

259.3 .74 .53 4o5 49S31 .58 394c 259.7 .71 .37

545 467 57963 .33 3380 259.5 .75 .83 467 57963 .53 3795 260.0 .72 .57 467 57963 .o7 440? ^3V.q .63 .86

CC.-, W WV *a0 67675 .4o 3992 259.6 .74 .38 460 67675 .63 4403 260.3 .69 .87 460 • 67675 .79 5102 261.6 .62 .35

W*.V 5‘tc 250aC .06 1913 258.0 .80 .89 546 1979 25E.1 .79 .3? 54o .18 *jC« 1 .73 oa

f W / 5IF ^rc; 35031 .13 2259 . 7® .89 JJJ 3Suol . 2412 'SCS P

4«fS* U .78 .39 e*c 33031 .30 2753 7 .77 .36 540 534 29951 .17 2233 .78 .39 534 29951

«

»

2399 '*ra c4.«ir3« »i .73 .89 534 29951 •M • W • 2771 253.6 .77 .33 51c 547 39946 .16 2435 253.3 .79 .3? 547 39946 .2b 2661 253.9 .77 .89 547 39946 .34 310= 259.0 .'6 .33 54S ^w* 50017 • *J V A d

'* 253.9 • / 1 CO

t w « 551 50017 .36 ^“11 **co 1

i • * .76 .33

551 50017 .48 4342 259.3 .73 .88 546 550 55035 .29 3320 259.0 .77 .88 550 55035 .41 3646 ^CQ ^ «wTt^ rc

• .' J .83 550 55035 .53 4307 259.5 .37

551 540 649S3 • JJ 3=69 25=.4 .76 .38 540 c4953 .50 4208 259.3 • / w .37 540 64953 .o4 c?rr 260.4 .65 .36

511 635 20055 .02 1802 257.6 .so .89 6S5 20055 .06 1747 257. a .80 .89

273
PREHEAT SECTION DATA; Riet2 .80 «t R13B1

RLiN *A3S FLUX HEAT FLUX HAS8 HTC Teqb LIQUID VAPOR

kg' sqa/s • i/sqi QUALITY' degk CDHP. CC.-.P.

co5 20055 .10 1341 ^J * * ; .79 .39 S« dc4 20134 .04 1861 258.1 .30 .39 684 20184 .03 1330 253.1 .79 .89 634 20IS4 .12 1966 253.2 .79 .8« 510 6E3 • 30190 .07 2164 253.1 .90 .99 653 30 ISO .13 2191 253.

1

.79 .89 6SB 30180 .13 2423 253.1 .73 .39 541 67? 29911 .10 22S5 253.

1

.79 .99 679 29911 .16 253.1 .79 .69 67? 29911 .21 2692 .78 .59 513 6®1 350S5 .09 2390 ncs c *JS. J .79 .39 691 35085 .15 2377 255.5 .79 .8? 691 35085 2733 255.6 .79 .39 509 682 40729 .13 2445 ^CQ y .79 oc

• w < 632 40/29 .20 2651 253.4 • t 0 .39 632 40729 .28 3240 253.4

yy

• t 1 .29 512 693 447S3 .14 258.4 .7= .89 693 44758 .23 2939 258.4 .73 .39 693 4i75B .31 TCnc

253.

5

.77 .88 50? 65^ 49S14 .17 2379 253. S .73 .39 i24 49314 .27 ::43 252.9 • t t .3£ 634 49814 .36 3345 259.0 .76 .33 54? 653 49973 .13 3210 253.'= .73 .89 683 49973 • 1/ 33 BO 259.0 • / f .33 683 49973 .3c 4354 259.1 .76 .39 523 6 93 3<tC.i6 • X* 4021 259.0 .73 .35 693 64S26 .34 AI12 259.1 .76 . 33 6?3 64826 .46 5339 259.3 .74 .33

cr-^ 651 64923 40j5 259.7 .39 cSl 64923 .36 4140 259.9 .76 .53 681 64923 .49 5396 260.0 .73 .87 554 700 74948 0 * « 4375 •

' / .38 700 74943 .41 4719 c

A.W7* J .75 .S3 700 74948 .54 5940 259.7 « / X 2

274
PREHEAT SECTION DATA: RIslI .38 HI R13B1

RUrt «45£ FLUX HEAT FLUX aAS3 HTC Teqo LICUID VAFuR

ku/ 3^2/

%

H/scs SL'AIITY K.sqs/K aegK COHr. COHP.

4:?' :o£ 25102 1416 . 6 • .73 :os 25102 • 1553 272.4

M V .c9 :os 25102 • Ote I7S0 274.1

n «

• o5 410 20a 2C0B1 1674 272.1 .23 .a9 206 20021 .30 1205 6 .25 .00 20a 20031 • w ^ 2342 274.9 .63 200 20392 .27 1343 273.1 / A

« .67 200 20392 • 34 IcIO 274.5 • * W .64 200 20392 # 7i 1335 275.9 .20 .oO

411 2CB 29584 .32 1957 274.0 .24 .65 208 29224 .42 2192 275.3 • * J .oO 202 2==34 .51 2459 277.4 .17 .56 415 205 «wO 27? I •'TC ? JfJ .o2 205 TC 4 .4? 3127 277.3 .12 .57 205 351’’*’ .59 3812 273. S .16 S'?

4i; 2uS THCTO w7CvW .42 2303 276.0 .20 .60 205 39S33 .54 3129 278.0 .17 .54 205 3"33B .66 3471 279.6 .14

« M .•T 416 ''A* 44834 .47 3402 277.1 .19 .53 204 44884 .60 3751 279.1 .15 .51 204 44884 • / V 442? 230.6 .13 .46 445 230 15015 . 13 1220 270.2 .73 230 15015 .17 1233 271.0 .30 .71 230 15015 « 1356 271.9 .22 .69 442 2S3 20496 .18 1446 271.5 .30 .71

-'OT

*U<»' 20496 .24 1553 272.5 .27 .69 283 20496 .29 1732

' Q • ^ai' .66 43S ^30

* 24387

^ « 1917 272.0 .23 .70 239 24827 .23 1987 4>/ W .26 .'67 22? 24537 t34 2126 274.5 .64 453 2?2 30041 2367 273.1 .26 .67 292 30041 .34 2565 274.5 .23 .64 2?2 30041 .42 2B42 275.8 .20 .60 237 40262 .35 2973 274.9 • •»«** .64 237 40262 .45 3313 276.6 .19 .59 40262 C7

t ww 3657 277.9 .17 ce

• 445 295 CAAOC

J .41 3531 276.1 .61 295 J 3962 277.9 .17

SC

295 5-)2S5 .62 4341 279.3 .15 .51 447 22? 60539 .48 415a 277.3 .12 .57 229 6C589 .61 4540 279.1 .15 .51 229 6058? . 73 4902 280.

5

tT

• *. w

• « .^0

441 369 1 w .11 1356 269.9 .32 • ; J 369 J .16 1429 270.3 .30 • /X 369 20375 .21 1600 271.6 .23 .70 43? 363 24S3B .14 1B55 "?A A

* / V « * .31 • / w

275
®®frf£A: ffr^'ON DATA; ^lEi:

1

* 1

•: !

9! 331

:iA5= fll; HtAT Flijl .'.AiS h~,L JiZt LI22ID y-=;R

vC/s:i/5 K'ECS SCALiTY *<‘'=54/1^' legK C3^f,

363 :4b:3 .20 1952 i • V .2? .70

»' a a 24S33 .25 2027 272.

3

.26

m .so

W V* 30944 .16 1341 271.0 .30

I. J »/ aW''H-r 19o6 a .6®

%W V 30944 .30- e 273.4 .6s TOT

w / .* 374 :9s='; .21 2336 272.0 .23 .70

4 39539 .30 ; a 273.5

n 5 .66 3T4 39539 TT

» • f 3039 274.9 .62

CXJ ^ / c 49660 .27 2B97 273.4 .2c .67 376 4®660 .37 3263 275.1 .22 .63 376 49660 .i6 TB61 276.7 .19 .58 3? 9 372 .59445 rr

« ov 3560 274.7 .24 .65 59445 .44 4007 276.6 .20 .59

V ^ 5t445 .54 4609 Wt i .17 .54 400 374 69055 4 wS 4159 a 4/a«a .62 374 69055 .50 4733 277.8 .13 .56 374 69055 .61 5276 279.3 .15 .51 401 372 79304 .43 4853 277.0 .20 .59 TTn

V / ^ 79304 .57 5471 279.1 .16 • Wa

- 372 79804 .69 3540 230.5 .14 4^i 440 4o0 24312 .09 1905 269.7 • 34

^ « • / 460 248 1

5

.14 1937 270.5 .31 •

«' W 460 24313 .13 19S0 271.3 .29

"•1

• A 454 467 29981 .15 2350 270.8 .31 .71 467 29=91 • 4.V n •cff JW

-.-1. 3

w . i • w . '0 467 29031 nr

t wa

a ^

.

• — n ^

w / .26 .CO 451 4o7 40110 .20 *.£74 A

• w T .:o 467 i/.l

*^V 4 4 V

»• •• 30S0 27a« 4 .26 .67

4fi7 40:10 • aw Wv6a

mm 4 C m 4 .65 aw 46? 4979c .24 jOlS ^ / a* * .27 .o8 46® ir?9b 3643 2’4.5 .24 .65 46® 4?7<?6 .40 4142 275.9 .21 .61 447 60525 .32 3548 274.3 .24 .65 447 60525 .41 4111 27c. 0 .21 .61 447 60525 .50 4345 w . / • w .13 r ^ 456 453 69S5C nr

• aw 4106

'' ^ a • w • *a . ,T 453 o9S50 .46 4752 2’7.0 . 19 .59 453 69850 CC

• JW 5448 273.3 .17 .54 45S 467 79S56 .33 4dwa 275.^

mm • m

• a* 467 79856 .50 C* « wan« 277.6 .19 .56 467 79856 .60 60*:-

3

27=.4 .15 .51 460 446 90060 .42 52o4 277.0 .20 .60 446 90060 .55 wOSa 273.3 .17 .54 44o 90060 .67 6735 230.2 .14 .48 463 522 10052 .02 1118 266.7 ' ^ .76 10052 .04 1144 269.0 i oW • 4 a

276
PREHEAT SECTI3N DATA: RIB42 .3£ «.t RiDBl

RLIfi nA3£ FLl/r Ig/aqs/s

HEAT FLU2 ftAsE COALlTr

HTC

«(./3q*/K

Teqt

fi£ 0

.--

l: 2-ic

C 2HP.

VAF2!

CDltf

523 loos: .06 H5C 269.3 .35 .75 467 i 20033 .36 .1720 269.2 • vS

?C !3‘ ;oo:g . 0 ? 1746 269.3 • ww .74 20032 .13 1337 270.3

^ m

• 4=£

C-- 3007C .10

^p, 1 270,0 • «/v . ; ^ C-T 30070 .15 234c 270.3 .31 • * * e'* ww* 3007C .20 25.C :?i .6 .29 .70 465 541 4o:si .14 2726 270.7 .31 5-: 40221 .20 2'«3 271.3 . 70 541 1022

1

.26 --C W*Ww 272.3 .It .62 4c4 535 4P957 .12 3171 271.2

• 3 , • * 535 4P957 ,2a 3530 273. i • •• .sc 5v5 44957 3926 27-. 5 t .cf 4c 3 543 601c3 36o2 7 .5' 543 501c5 • wV 411: . :c c*r 6vlc5 .33 4591 2*5.6 • . s2

*e^ 5i5 cPTa: • 4016 274.0 . c: 545 5 PT 33 .33 4:31 ::3.5

P .s2 5-5 c"T:3 ,4c 5299 276.9 . i? C*

• to «. -cl :4i 30304 .30 4524 I'-.

6

.25 • M to 54o W1 - ^ ^ f 5203 276.3 .21 . s: 54c . .50 5344 277.2 .13 .56 3’Phc . 34 :c=. 235.3 t 4k* • w*

5 35 39 -“6 .ii e*^cr

J: .1 =

ff*.

VWte c ? .5g s334 • . Wf **

. 16

277
?'£K»|i7 EE-713'N’ ?:E42 .1: -t R;”F1

«-•: ?LiiV w£AT i^Af: hi: 7sC2 •i 4 » VAr'OF. '? j;!

A. U*wn«»« ' 1 ::rr. WW> •( •

j ZZ’Z~^ ,0c 922 275.“ .13

1 'v 9=93 .10 1074

• « - 1 . i . 1 - .50 IrO 95=3 • !• 1207 2'=.’ .1' .4' c-r 20140 .13

' 1935

••.A • i T ,

•»

1 •• • 4 • ^ • 20140 .20 202“ 951 < a 4

4 ^

• ;• . 43

l9i .26 2055 252.0 • Iv .35

f^L •rc;?-* •• ^93 « .11

« *4 « — - * • A ^•• • V 1t2 29=31 T.-'l 2925 23:. 2 .0= .37

i?6 nacsf 3153

"r • « ^01. i .03 » w J w '.’ ••• 1'J .• • t .29 3865 232.6 .10

• *4 ..'S

•i J

(** T2

® .41 3940 3 .03

• •

t W* 2C3 40729 .51 4089 284.7 .07 .28 cat ‘49992 • W/ 4779 284.0 .04 499P2 .50 4SS6 285.2 .07 .29

A « 49992 .64 5006 236.0 .06 S90 205 60132 .44 5643 2S4.3 .08 .31 205 60132 .60 5705 285.3 .06 .26 6ulw« .75 6093 236.0 « VW a 5=S 10C23 .04 854 273.4 .16 .53 242 1002S .07 1022 279.1 .15 .51 2^2 10023 .09 1115 279.7 .15 .50 577 241 20118 .09 1390 ’’72.9 4 C

• 4 J .50 2011S t 1913 230.0 . 1 : a 4C

'^1 * 20113

M A

' V 2C04 230.9 .12 a 43 5SC 29939 .Is 2309 • 0^* /

4 ^

• 4V .45

241 29939 .24 2=51 232.0 ' 1 • 4 4 .41 241 29539 .31 3087 232.= .09

oi Cl 240 40744 .24 36=6 ?3? *5 .11 .41 240 4C744 .34 . / / • 283.5 .0= •c

a 2A0 40744 .42 3‘?33 234.3 .08 .31

ffmt 1 aQO 242 49S13 .29 46s0 “C-l 7 .10 .37 242 49813 .41 4809 234.0 .03 a 242 49313 .52 4955 284.3 .0' ?P a eCO

<«w * 249 59915 .35 5464 253.7 .09 ••r

a w J 24? 59915 .43 5604 284.9 .07 .2= 249 59915 .61 J / V'J 235.7 .Os

"*C

a eO" ^9 • •13 70750 .42

. •• .C :S4.5 .05 a 24t 70750 .53 3384 255.6 .06 .2s 246 70750 .73 i}8ww 286.3 .05 597 295 10003 .02 856 278.

0

.17 .55

A : J 10003 1055 273.5 .16 .53 295 10003 .07 1133 279.0 .15 .51 576 29s 20109 .06 1905 273.9 .16

Cl

a 296 20109 .11 1796 279.9 .14 .4? 29s 20109 .15 1929 230.7 . 1 : .46 5S1 :oo 29960 .11 2727 279.9 .14 .43

278
PFEHE.AT SECTION .IB Mt Pi 331

F.liN FLUi HEAT HASS HTC icqs lIEuIO VA^Sr. koi'ca.'s 4/ £qa SWLITj U/sqa/K degK CQilP. COHP.

Tc'.w :?=av « i / to.» w 121.0 .12 .44 300 :mo 1 24 . 298i 282.0 .11 .41 5b: :?s 3991! .17 3517 280.9 .12 .45

i-'C :-r;i •'C

• 3694 tA .10 .40

"'C3 3’9n « to-W 3920

4 ^OWA A .0? .36

* 2^5 «?S5 rn

« 4517 291.9 .11 .41 299 49785 t WA 4703 '^er n ^UWf * .05 .36 299 49785 .41 4B93 234.0 .08 .32 5S3 293 5??n .23 52E3 282.9 .10 .33 298 59873 .39 5499 234.

2

.08 .33 293 59873 .5y 5708 2S5.0 .07 .29 593 300 79923 .38 6758 284.2 .08 .33 300 79923 t 6534 235.4 .07 .23 300 79923 .63 7934 286.1 .05 .24 594 ^oS S9372 .43 7549 234.6 .05 .31 305 39372 .55 7740 295.6 .06 .26 305 99372 .75 8597 236.2 .05 eai

w

j

• .tc 1006? .01 353 277.3 I "r 9 i / • w J 345 10C69 .03 706 0. ^ .17 .54 345 1006? l(M

• « to 763 278.7 . 16 9 err

w< a 349 20C95 .04 1955 ^iO.O . 16

er-^ 34? 20055 .03 17=6 / Tt * .15 . 51 34? 200<55 1 ^

9 1376 230.0 .14 .48 555

• w*.** 30743 .03 2450 279.3 . 15 .51

•*r» v-n 30743 .14 2711 280.4 .13 .47

•c J w**"t vU74^ Li JJ 231.4

4 09

. U .43 55? 350 35S55 .13 TT * vwXO 230.

0

.13

4 ^ 9^f

?r/‘, 39335 .20 3484 281.2 .12

35C 39SS5 3573 .10 .3? 560 351 51196 .13 4265 281.5 .12 .44

35! 51196 4459 232. S .10 9 W > 351 51196 • Ou 4630 233.

7

.09 • ^3 562 354 59907 4968 •^C*^ r .11 .41 354 55907 .32 5160 233.7 .09 .36 T 9 59907

f • 5364 294.0 .08 yn

9 W0W c9S47 5717

r to3^. 7 . 10 TS 351 69347 .38 5364 234.2 .03 t 351 65647 .49 6136 235.0 .07 .29 564 348 79720 • w4 6464 293.6 .09 .36 348 79720 .45 6587 234.3 .07 .31 348 79720 .57 6914 295.5 .06 .26 565 351 50237 .36 71=6 294.4 .09 .34

351 90237 .51 7308 -'GC c

toOJ. J .07 .28

351 90237 s'; t uw 7699 256.2 .06 .24 566 349 95147 .39 7545 234.6 .08 .33 349 95147 .54 7648 285.7 .07 .27

279
PREHEAT SECTION DATA: RI3I2 .18 «t RI 331

RijN BASi FLUX kg/sqa/s

HEAT FLUX

il/sqa

BASS QUALITY

HTC U/sqc/KTeqS

deoK

LICUID

CGBP.

VArQP. CGBP.

345 55147 .69 8207 236.3 .05 .23

595 46S 10032 .00 •1206 277.4 .18 .56 46S IC'032 .02 5S2 277.7 .17 .55 4^a 1W32 .03 273.1 .17 .54 574 473 20065 ,01 2101 .17 .55 473 20065 .04 1374 •'”»0 ? .16 • mJmJ 473 20065 .07 1376 27B.3 ir

« 4 «.» .51 C7^

mi 47: 3C052 .04 2i:i 273.

1

.16 .54 472 30C82 ,03 2434 275.0 1C

• • ari .50 472 30032 . 13 2al8 279.9 .14 .48

» 4m 473 35535 .07 3233 275.2 4 C

t 4 w .51 473 3553B .13 280.3 • 14 .47 473 39538 .18 3382 ^ .12 .44 475 50064 .10 3556 275.3 .14 .45 475 50064 1 1

• A i 3550 231.0 .12 . 44 475 50064 .24 419<5 232.0 .11 .40 570 473 60044 .14 4660 291.3 .13 . 46 473 60044 « 4610 .11 .41 473 6C044 .30 4955 n .10 • a// 53? 479 70723 .18 5274 231.6 .12 .44 475 70723 • mi C* .10 .3^ 47? 70723 • 00 565o 233.7 .09 .34 5cb 4SC SO 154 .21 6253 .11 .42 4S0 30154 .31 6545 223.4 .05 • v/ 4S0 30154 .40 7132 264.2 .08 53? . 473 50336 3?40 .11

a A

473 9C336 t36 7205 .<j9 . 34 473 50336 .46 7330 224.5 .07 .30

280
PREHEAT SECTION DATA; RISI2 .58 Nt R13B1

R'JN MSS FLUX HEAT FLUX HASS HTC Teol! LiauiD VAPOi kg/sqa/s W/SOI DUALITY H/’sqt/Y. degK CQHP. CQHF,

640 350 20042 .20 1574 264.7 cn.82 350 20042 .2a 1702 265.3 .49 .82 330 20042 7”?

« ww 1933 265.9 .47 .81 637 "*CC ww 30305 .28 2147 265.7 .49 .81 TPC 30305 266.7 .45 .80 VMW 30305 .45 2799 267.3 .41 .79 639 351 20048 .20 1578 264.7 .52 .32

351 20C43 t 1697 265.3 .49 .62

351 20043 • 1924 265.9 .47 .81 635 349 30311 • wO 2153 265.3 .48 .81 349 30311 .39 2428 266.8 .44 .80 349 30311 .47 2256 263.0 .40 .78 635 'tyS 10002 .01 987 262.5 .58 .34

1“^®^ 10002 0.00 904 261.3 .62 .35 475 10002 0.00 862 260.2 .67 .36 630 486 20404 .14 1532 263.6 .54 .83 486 20404 .18 1801 263.9 • .33 436 20404 .23 2012 264.3 Cl

• Wi .82

o34 481 10006 .07 1040 2a3.0 • jO .84

481 10006 .09 1077 263.1 .55 .83

481 10006 .12 1174 263.3 .54 .83

631 476 20406 .15 1564 2a3.7 • Jw .S3 h7g 20406 1811 264.1 .52 .82 476 20406 .25 2029 264.5 .50 .32 47a 3004a .21 2104 264.7 .51 .82 476 30046 .28 2407 w .49 .81 47a 30046 .34 2779 266.0 .46 .30 434 4*0429 7'^

• X/ 2640 ^Lt ? ^0 V .49 .31 484 40429 . w6 3131 26o.2 .45 .60 484 4042? .44 3709 .41 .79

fiv* 479 20407 .14 1561 43w • i .54 .83 479 20407 .19 1788 264.1 • «j4 .82 479 20407 .24 2008 264.5 .50 .32

629 479 30046 .21 2134 264.3 .51 .32 479 30046 .27 2429 265.0 .49 .32 479 30046 .34 265.7 .46 .81 624 479 40436 .28 2a50 265.3 .49 .31 47? 40436 »C 266.2 .45 .30 479 40436 .45 3720 267.3 .41 .73 616 476 1999S .12 1774 T .55 .81 476 19993 .17 1779

• 4/ 0 .53 .81 476 19998 1844 2/6.1 .52 .30

611 478 30104 .19 '>1 276.1 .52 .30 473 30104 .26 2136 276.7 .50 .79 478 30104 TT

• vw 2406 277.4 .48 .73 617 478 70452 .43 3598 273.

9

.44 .77

281
PREHEAT SECTION DATA; RIGI2 .58 Hi R13BI

RON RA33 FLUX

l:g/sqB/5

HEAT FLUX H/sqi

NASS SUALITY

HTC U/sqi/KTeqb

deoK

LIQUID

CQfIF.

VAFQR

CONF.

478 70452 .57 4157 2B0.B .38 .73 478 70452 .68 4694 232.7 .70 olS 475 20C11 .12

' .1776 4m d J B W er

.91 475 20011 .16 176S • w J .91 475 20011 .21 1832 276.1 • .80 ai: 475 30 1 38 .19 2148 276.

1

• .30 475 «>01 j3 .26 2204 276.9 • uU .79 475 30133 2436 277.5 .48 .79 a09 476 40672 .27 2400 277.0 .50 .79 476 40672 .35 2619 277.9 • *9/ .79 476 40672 .44 3002 279.0 .43 .76 613 482 70453 .42 3714 279.2 .44 T7

• t • 482 70453 .55 4245 281.1 .39 / w 482 70458 .67 4305 233.0 • vw .70 614 479 •20037 .11 1776 275.5 .55 .81 479 20037 .16 1754 g

^4 J* 9 « Jw .3! 479 20037 .21 1823 276.3 .52 .80 613 474 w0136 .19 2150 276.1 • S3 .80 474 30136 .26 2217 276.9 .50 .79 474 30136 .32 2452 277.5 .49 .78 60S 471 40714 .27 22S7 277.1 .50 .79 471 40-14 .36 278.1 .4o .73 471 40714 .45 2398 279.2 .43 .76 620 517 49540 .30 3193 267.4 .48 .31 517 4=540 .40 •CQO 26S.5 .44 .7=

^ * 4 49540 .49 4123 269.9 .29 .77 621 475 49502 266.3 .4q .91 475 49502 .43 3694 26/ . 5 .42 --c

• • • 475 49502 429= 269.= • 0 / .76 607 432 6'jv42 • 3476 ^/C.4 .46 .79 432 60042 .48 3945 279.7 .41 •r

• « J 482 60042 .59 46o3 281.4 .36

7''

619 477 70430 .42 278.3 .44 .77 477 70430 .56 4346 230.7 .33 .74 477 70430 .67 4942 292.6 .70

282
TEST SECTION DATA; RIGS2 R152a

RUN (IAS: rLUI HEAT FLUl GUA’lITY HTC Tsat

k5/£q*..'3 U/sca H/sqa/K iegK

32? 158 96/5 .19 2872 i7V.6

:se 157 10103 • w• ww 3544

'‘ cr* - ^ « -k « •50- 154 10095 .49 3760 259,9

233 157 9954 50

t w < P0 W

• » . "Ct'i *7

2Bd li4 10036 .64 4400 2=0.2

284 159 icon • 6 4oI 0 290.0

285 153 lOv^l .06 4903 290.1

320 975 ? .24 3217 290.5

?OP 238 10125 • w6 4310 290.4

• TS 233 10:21 .43 4419 290.1

302

^ J ,**•, • *^v 10116 .60 5650 289.9

304 245 10102 .70 6420 -7CA P

V- 246 9976 .33 6433 290.3

2s: 9675 .19 0 290.1

« ncp ^WW 102C3 .29 4tfs5 290.4

-55 2S9 1015S .39 ^,p\rn 290.3

250 -3T *wW 10163 .49 P2P0

JSJ7 290.6

2?1 223 10159 .60 6686 290.0

292 *4 « 10199 .72 7302 290.1

293 281 10125 .76 71a5 290.2

324 237 9315 .79 7625 •^5^ 7 ^ / V a W

4 340 9730 .15 J -«-w 290.4

2=5 354 1C132 4wij 290.4

'*C‘* 35: 10121 .30 5017 250.2

^ 4 V..U rca ww7 10101 a W « • 5995 290.5

vvw 35a 10093 .45 c302 290.0

“.15 WWr IC017 • w^ 7374 290.0

311 3dc 9975 .60 8413 2Crt t ^ « w a 4 w 4 3 3dw 10074 .6? 8575 -’PO 9 .•c 419 969S .11 338? 290.6

32S 412 9569 .13 4010 290.4

299 425 1C1C4 .24 5123 250.5

wOO 427 I009B .30 5955 290.5

305 430 9954 .36 7035 290.6

303 430 9933 .43 7459 290.0

T • n 429 9975 .50 S590 290.1

^c1-:S 19067 .27 3453 290.2

340 153 20214 .4? 401? 290.3

350 14? 19660 .57 3909 290.0

338 150 20248 .71 4640 290.2

349 150 19428 .31 5105 290.0

332 156 20037 .81 5120 290.

1

286 20221 .20 3321 2=0.2

337 233 20202 .30 4277 290.6

Owl 2B6 20057 .40 5191 289.9

vi<4 235 20033 .51 6560 290.3

283
TEST SECTION DATA: RI6#2 Rl52a

RL’N NASS FLSl

t'C/ Suif S

HEAT FLUX

• /'£yl

DUALITY HTC

M/sqi/fl

Tsat aegK

3A2 297 19563 .63 .7!';'3 290.4

344 2S5 IS930 .75 7832 290.4

346 293 19191 .83 3159 290.0

423 20163 .17 4104 290.6

%• W 428 19909 2

^ 5350 239.9 333 429 20042 .31 o?27 2C0.O

341 426 19597 t «>3 7204 290.4

42a 1SS05 .45 7936 290.6

345 424 19143 .52 8B57 2'?0.1 3^7 424 19353 .60 10560 290.5

TEST SECTION SATA: RI6I2 R13B1

RUN flAES FLU)( kg/s:;3/s

HEAT FLUX

iii/5;a

QUALITY HTC'P)

N/=qt/K

HTC(T)

W/sqi/K

Tsat!F

degK

506 10043 .27 2735 252' 254.3

502 360 10048 .39 3503 :C'57

•'Cl a

503 359 10C53 .50 •7C0

t 3275 254.1 504 359 10042 .32 4093 3497 254.5

505 356 10057 .76 4593 373? 254.3

491 10115 305» ac • ^

489 434 10107 .31 2931 2333 254.0

49C 441 10113 .40 3719 Wto* t aci T

4S7 451 10104 .49 39s5 3370 254.5

483 432 10005 .64 4735 3888 254.7

483 445 10107 .69 5262 4113 254.6 473 451 9988 .TJ C077

w 4632 254.4

492 559 10117 .23 3410 3005 254.4 48s 353 9992 • •*re7 :o?i

493 5y4 10107 • w / •136 34Ec «c • r

482 554 9987 .46 4819 3909

c

494 562 10105 536S 41=2 254.5

•91 A 560 1C031 .60 5934 4632 7

495 555 10100 .66 6799 4745 254.7

477 566 9983 77

t 4 W 7283 5134 254.5

284
TEST SECTICN DATA: 21642 .53 wt R13rl

!!;££ FLUX HEAT rlUi i‘tA:5 Hie Teqi LISLID VAFOR

kQ/sqii/9 (4/ sea QUALITY U/sqa/L degK CGKr, CQ?1F.

330 19:73 .45 2434 2c7.5 .41 .72- Trr WWW 2G252 .59 • wwwJ 269.9 .34 .74

351 30274 .43 2307 2o7.9 .40 .73

<j02v0 .62 U/.Z1 270.5 • ww .73 475 999s .17 137s 263.6 • So .83 426 10067 .30 1810 265.0 .43 .91 481 20019 .20 1793 WWW* 7 9 ww .32 476 20019 .34 2479 265.5 .46 .91 4?a 20013 .45 WiWW 267.5 .41 .78 484 20013 .56 3930 269.0 Tr

• Ww .75 479 30217 • wd •JCIT Xut'J 265.8 .45 .30 479 30011 3604 t • «i .4(1 .78 479 30609 .59 4509 269.5 .34 .75 476 9997 ; ,29 1?49 276.7 .49 .79 473 10000 • 2297 278.5 .44 .77 473 10034 .30 32«0 284.6 .28 .65 475 20015 W i 2329 277.0 .48 .7? 475 20040 .44 2977 278.9 .43 .76 476 20048 r

• uO j»i>4 220.8 • ww .73 4S2 19937 .31 4644 WWW* w .23 .65 47? 30109 .33 2537 i.n.1 .48 ,73 474 30008 .46 77c 7 w/7 t w .76

0^4 rOCiO

4» V V W f .59 3421 231.3 .36 *• / ^

J 1

1

rASHf WVW*4 .&3 50=1 771 0 wi a « 7 • WW • / w

^ : W .67 5246 ^7 ' 7

Wi i • w .30 .71 4S2 30024 *^C 4 M « Oi7H 2S3.3 .30 .67 477 30276 Ww !l9a wSO*

!

.27 .64

285
7EBT SECT I Oil 2h7h: R16I2 .18 Mt nl oBi

RASE FLLiX

a^fi/ 3

HEATH/sqiflAS£ EUALJ^f

HTC

M/sqa/K

Teat

de^' C05F

.

VhFOs

COffF.

190 9971 .20 1436 281.

1

.11 .43 196 9972 • 35 •1923 233.2 .09 • zz 19S 9961 .51 285.1 .07 .2S 203 9891 .65 31S5 285.4 .Oo .24 2C2 9885 .80 3646 286.3 .05 205 9910 .93 34c4 •'Ci, c

W .04 .19 242 9972 .15 1339 230.8 .13 .4c 241 9983 .28 1810 292.1 .10 241 9974 .41 2517 2B3.9 .08 240 9852 re

w’4*V 285.1 .06 .27

n 9892 .66 3610 ''OP P .06 .24 249 9891 .76 4142 '•-i ^ .05 246 991a .90 4147 286.7 .04 .19 2=5 997? .12 1288 2SG.0 .14 .43

^ 1 w 9935 • 1705 2B1.9 .11 .42 9931 .32 2341 283.0 .09 .36 293 9972 .43 2986 284,0 .08 .31 299 9900 e:? 3491 284.8 .07 .22 298 9897 .63 4011 235.6 .06 •r

300 9923 .83 4535 286.4 .05 .20 305 9910 .92 3o41 286.5 .04 .1? w4j 9962 .10 1155 279.6 .14 .4? 349 9986 .13 1628 281.

0

.12 .44 354 9887 « 2250 282.

4

.10 .39 9839 .35 2770 283.1 .3? TC

• Vm

?ct 9855 .45 3443 rcj' P

• w .07 .31 •Cf Vm)*t 9345 3876 2B5.2 .07 .23 351 9849 .61 4415 285.5 .06 .25 34S 9641 .71 4794 -oc g .05 351 9934 .79 5032 296.5 .05 .21 349 9835 .84 4925 286.0 .05 .20 469 9973 .06 1184 278.8 .15 .52 473 9995 • 4^ 1530 279.7 .14 .i8 472 9P<?5 .18 1969 280.3 .12 .44 473 9977 .25 2473 232.1 .11 .40 475 9<?62 .31 3043 282.3 .0= .3o 473 9957 .33 3583 '!or 3

• ' .05 479 9944 .45 4046 .07 .31 480 9S63 .50 4439 294.7 .07 .29 473 9844 .53 4959 235.3 .06 .26

286
] 2ST sElTION DATA: Riui:- .30 Ht S 13B1

ffnct ri.i;Z fiSAT FLO n'TC tecz LiCuIl VfiFCi^

tZj'iSiill M.'3uS CchLiiy 4/ s(;s< K iegf CCf.f

.

CaflF.

2ts 10073 .29 1757 258.4 .77 .88 2iB 1C V 1 •* .43 •1848 258.9 .74 .88

^uZk IC-C7J • tit 2006 259.4 .71 .37

2si 10065 .0? 2202 260.6 .67 .36

if ^ 10045 .30 2530 261.6 .al .85

4^i i 10060 vVm 2:3.4 .54 . 83

271 10054 .93 3457 165.4 . 4a .31 370 10210 .15 1464 257.8

•73

• t w .59 ^/v 10201 .28 1635 255.4 .77 so • y « 3/ j 10211 .38 1930 .75 cs 2o6 10159 .49 2193 258.9 t * V .25

vOil 10160 .59 259.5 .71 .37 Zhb 10174 .63 2639 i^60t j .63 .86 364 10170 .75 2870 261.1 .64 .55 3s2 10062 .87 3407 262.9 .57 .54 372 10094 .97 3994 264.9 .43 .31 447 10102 .14 2086 257.7 .79 .39 459 100B6 .29 2200 253.2 .77 .38 449 10032 .46 2505 255.1 .74 .58 461 10127 .60 259.9 .70 .37 445 10134 ,1Z 3061 260.6 9 Qy .36 4c7 10123 .83 3414 .59 .34 440 10050 .94 vww4 264,3 .50 cn

^ *1

mint 9991 2099 ^ra a

• / / .89 c-r

Jw J 100 IS .40 '•ca z w« 3 T«

• i y .33 534 10244 .41 2651 '^='3 *yy • qw •r

• / y .33 547 10029 .46 2719 7CC •* .74 .33 551 10143 .60 3052 255.7 .70 .37 550 10140 .67 3127 260.0 .68 • w3 540 10075 .79 3295 261.5 .62 OC

• wy 435 10145 *w 1997 257.7 .79 .89

684- 10265 .18 2165 ^CO a ^ye* ^ .78 .39 433 1012? .26 2504 occ ^

• « i .89 679 10291 .29 2728

ac5 a *ywt tm .77 .33

691 10136 .30 2694 253.6 .77 .35 632 10097 .37 2568 258.4 ^ J 00

• y y 653 10146 .40 29=8 rcz c yyy • y .75 .88 634 10114 .46 3102 259.0 .74 .38 633 10154 .47 3132 259.1 .74 .33

W t V 10113 .59 3451 259.5 .71 .37 681 10096 .61 TTJ« 260.3 .70 .37 7C0 10099 .65 260.2 .68 .96

287
TEST SECTION DATA: RISIC .3S nt R13E1

RASs FLwI HEAT FLL'K NASS HTC Teqt LIQUID VArCE

kg/ sea/

3

H/sqa CUALITY H/saa/K' dEor;: CO.-.P. CQRP.

COS 9922 .45 1407 27o.4 .19 .59 COi t2?1

CW4M * .46 tCTT

, i VI ^

:V*0 .19 .58

200 9934 COOS 277.6 .17

rr

• vv COB 10113 .64 2404 279.1 .13 .50 10105 .11 2652 2S0.5 .13 .4a CC5 10106 .80 2SB6 2S1.1 f • .43 204 10091 .BB 3072 232.0 .11 .40

'>0(^ 4WV 10192 .30 1430 T

4 « V • V rc

• ^v .aa 2S3 10032 t vB 1612 .62 CS9 9933 .43 2051 276.1 .20 . cO 292 10036 .51 2573 211.

Z

.13 .5a 2B7 10015 .64 3131 279.4 .14 .30 10013 .74 3557 2S0.5 .13 .4c 239 9995 .87 3924 231.7 .11 .41 3a9 99SS .23 Ida 2

^*^ 0

• *v .67 363 9969 • vv iBal 273.7 TT

• *v . o5

VI V 9801 .35 2159 275.0 .62 374 9S00 .47 2770 276.5 .19 c;

37a 9771 .56 3239 273.1 . la p372 973o .65 36ca 279.

5

.14 .49 374 9746 .73 1m''

1

^WV • J .13 .46 TT^

VI ^ 9731 .S3 ;ai.a .11 .42 460 9967 rt

• * V 1696 272.4 • • * .oc 467 10064 t ^v "163 0

^1 v« .24 1 ww 4g7 - 10043 .41 **s73 273.3

''1 .61 ic9 10043 .49

* 9 Z r**

447 10039 .60 3504 273.5 1 c• *v • vl 43a 10001 .6o 42ol

^ • • •

. 1** .4? 467 10023 .71 4337 230.0 .13 .47 44d =?B6 .30 3747 221.3 .43 aqv^y 1002? .10 Ills 2o9.3 • JV .74 eri VVl 10C41 .IB 14a4 ^ / 1 • ^ • vO • 1 * mVA 10034 %4,t IS79 .26 .63

341 10031 .34 2307

''-4 1 .23 .64 333 10029 .41 ..1 lO ^ f v« 0 .20 • dl w“w 10010 .47 ;i:s 3"c. ’ .19 c-

• V • P «C VHw 10039 .3o 393: 273. 0 . la c34o 9990 .60 wvw 273.9 .13 .51 336 loci: .hi 429S 279.6 .14 .4S

288
APPENDIX 4A: ALTERNATE SUPHIESSION (SITERION

llree alternate suppression criterion were found in the literature. All

are based somewhat on Chawla's original suggestion: to decide on the

paper heat transfer regime one should calculate the heat transfer coefficient based on an accurate pool boiling relation, and again on an

accurate forced conve ction/ evapora tive relation (e. g., one based solely

on n or X^^, but not heat flux). The larger a determines the correct

heat transfer regime.

Collier has used Dengler and Addoms relation:

= A(l/Xtt)® = <3/ at a = 3.5, B = 0.5

and combined it with an 'onset of nucleate boiling' criterion of Davis

and Anderson similar to that derived by Hsu:

AT =

0.5

^^v>^LPv

(4Arl)

to yield

(4A-2)

Policy employed a similar approach; however, he used Chen's equation

ccnbined with (4A-1) to yield:

289
AT, = 2aTsat (V^ - Vi>

Ted - Fa LO

If the given AT < AT^, the flow is considered to be absent of nucleate

boiling.

Shah has recently correlated a large amount of refrigerant data with a

new correlation described in Chapter 6. He utilizes Chavla's suggestion

exactly and employs the dimensionless ntmber

Co (4A-4)

and relates Co to an evaporative heat transfer coefficient. By a

separate relation, he calculates a nucleate boiling a. The larger of

the two determines the flow regime. His method therefore equates

dominant evaporative heat transfer regime with the complete suppression

regime. This may not be true. As shown in Chapter 6, the criterion

frequently selected the wrong flow regime and badly predicted the

experimental data.

290
APffiNDIX 4B; REVIEW OF CORRFLATIONS a/a.^ WIIH

A ccBDinon. f oim of a correlation of the heat transfer coefficient with

flnid flow parameters is

s- vs f(-^) (4B-1)

“L

Hesler (9) has examined snch a form noting:

Xt jp 0,8 Pj 0,4

= 0.023 (~)

D nOpL Xl

(4&-2)

(-:L) = Xtt 1 - X V

(4B-3)

L

o =

<l/A,

AT

He then approximates

=- ^

and

xGAh^ = / ^nDdz

or

(4B-4)

(4B-5)

291
X (4B-6)

zf (q/A)nD dz = o G Ali^

where z is the distance from the point of interest and the saturated

BPL.

Equation 4B-6 assumes saturation conditions at z = 0. Substituting

equations 4B-2 and 4B-4 into the left side of 4B-1, and 4B-6 into 4B-5

and 4B-5 into 4B-3, one gets:

q/

A

AT

0.023

^ 4G

D ttDu

0.8 CT)t^L 0.4

vs.

/(q/A)nDdi

^ (,_j gi

GAh^

_v (4B-7)

If one now assumes slowly varying properties, the equation reduces to:

z q/

A

f (q/A)dz

AT ~ o

Cl (4B-8)

qO.8 G

^

where = a constant made up of fluid properties. Mesler then

approximates G®*® as G to get

1 5ZA ^ c, i / ^ dz (4B-9)

G AT ^ G A

The right side must remain in integral form since in the Dengler and

Addoms experiment with which Mesler is concerned, there was an axial

292
variation of heat flnx.^ If the integral does not vary sharply in the

axial direction, one should get a strong correlation between the two

sides of eqtiation 4B-9.

This is as far as Hesler took the derivation. If one has a constant

axial heat flux, then the last equation reduces to:

AT ~ ct = C2 (4B-10)

where the constant includes the presupposed slowly varying fluid

properties. Yet, temperature differences do not remain constant in

evaporating flows. This derivation leads then to an apparent contradiction: on the one hand, o/a^^ = f(l/X^^) yields good agreement since maiy

of the same parameters appear on both sides of the equation. On the

other hand, when the derivation is extended to constant heat flux,

resulting in equation 4 B- 10, disagreement appears between experimental

data and the form of the equation.

Ihe contradiction in fact results, not from the extension to constant

heat flux, but from the overabundance of rounding and approximation.

The assumption put forth in equation 4B-5 is valid only at relatively

low qualities. At a quality of .5, the error in the assumption is 100%,

at large qualities the error is even greater. Thus, the (x/(l - x))®*^

parameter should not be approximated as stated in (4B-S) except at

qualities less than 0.2. This accounts for the variation one sees in

^In protesting Mesler's analysis, Standiford points out that (q/A)

varied axially, and that liesler did not consider this fact. Actually,

Mesler is very careful in this regard, as seen above.

293
^ P ^ 5a heat transfer coefficient in evaporating flow, and helps explain the^ .

^ Illegitimacy of using (1/X^^) as a correlating parameter.

h

I*-' !'?,' .w?UtlK9p« W

m ttt. ^

' j at *i « ( i' It# yk* adk b rWh4»r«

•^" :, v.

.':o'j ' • iwo'ft'O't •*'M-t #a-'«

n

~''W

.. . ‘-.,1^ '*-v.

'

s(£ 4r a»« l} ^

”^ f»trlUA.

Tia'\

KS#' “A

fcijli »»*r-*»

*» t J>»i'-«i » •'•*v

^ o«a . J 7 ^ . w

««i iftViaiMii* ^<^1 afcUii; ^

kds ffO ^ • ah II •'* taaqa*

MN^^tikDc *4 iar-T >V «*|E 1|UiAN^ •' W •-.<'4 %•

.«rii mi lAfrinw tiW»r«f tTmrf ^rmri • 1

siill'lt'iailttijfaa

^ fci iiifJ

,/ Ci/i‘ir

«i

4<l • n

xJM«;

1

iR

J.M& »l •*» •>'» ••• .•»*»••* '••>

Hilt «Hi* m Tf llv- ‘

i Yt«N2*|

...til

ttlmaiTa* * j| <y CO iwt

»i ttao Wtaf #* t**«> utl'

^ ,^0t »i' hoia^«*ii •<* * 19 »f* «i» •%» H ; '**^*‘*J^'

jjj V - «4t«* ‘)\»» •“> «*<’" ‘•‘••*» •’* •* •»»»• *^» » *^i!

19 ana* hH*^* ** 9i

’"It; ai • I #• »<» •olialxat **^*^*f ^ atf la f«wr» alt^ »'• «»tvaiv«’ st^LiiSS

' -t..t .»« ""J?" rY^.*^rU ;Ui .1 wj taal aiiJ

.avudi Bwha t* *haf<|ti •*’

! *

, 1.

294
APPENDIX 4C: VISUAL EVIDENCE: REVIEW OF LITERATURE

Hewitt et al [He63] built an experimental rig designed specifically to

observe nncleation on a steam core-water film vertical flow, as shown in

Figure 4C-1. A double annulus was formed with an inner metal rod and

two glass tubes. Water could be introduced as a film attached around

the rod and steam introduced in parallel with the water in the remainder

of the inner annulus. The glass tube wall was kept clear and free of

condensation by forcing hot air through the outer annulus. Both steam

and water were introduced near saturation conditions, and heat applied

directly through the inner metal rod. The experimental arrangement

allowed film thickness, flow rate and heat flux to be varied. High

speed films were used to observe rapid processes. The authors observed

qualitatively that bubble nucleation depended on the flow rates

involved. At high steam velocity, as occur in flow boiling processes,

no bubbles were seen; this study therefore supports the notion of a

complete suppression of nucleate boiling. The authors also noted that,

for lower steam velocities, when nucleate boiling was observed, that the

heat flux determined the number of sites and activity level of nuclea—

tion. The high speed film was shown recently [He84] and one could

observe nucleation at a particular site whenever a liquid wave passed

over it. When the wave passed and the film thickness receded, the

nucleation disappeared.

Tippets [Ti62] attempted to observe flow patterns of vertical upward

flow of high pressure boiling water at various heat fluxes. A rectangular channel was built with heater strips on two sides. High speed

2S5
films (4300 frames/sec) were taken throngk the anheated sides (Figure

4C-lb) . In the annular flow regime and qualities of 45-60% (i. e., very

thin films), the author noted less but clear agitation of the liquid

film on the unheated surfaces as compared to the heated surfaces. He

considered this agitation the result of bubble growth within the liquid

film; calculations revealed there to be sufficient wall superheat for

bubble formation.

Hosier [Eo63] noted that the Tippetts study suffered from a lack of

depth perception. He constructed a horizontal rectangular channel with

the bottom surface being electrically heated. The two sides were made

of quartz prisms, allowing the sides as well as the top to be viewed

simultaneously (see Figure 4C-lc). He filmed medium pressure boiling

water at 4000 frames/sec as well as took still photographs of 0.5 ^-sec

exposure duration. His still photographs were much clearer than those

of Tippets. An annular flow pattern was observed at a 10% calculated

quality. Very few bubbles were observed, and he concludes, 'when the

vapor column nearly fills the channel, the mechanism of heat transfer

apparently changes from bubble generation to surface evaporation.'

There may, however, be a bias in Hosier's study: he mentions, in passing, that the heater strip was 'machined' to ensure uniform heat generation. The machining process may have eliminated many nucleation sites,

restricting potential bubble growth.

Ihe study of Berensen and Stone [Be63] differs from those previously

mentioned in several interesting ways. They observed the vaporization

296
of R113 in a horizontal tube using constant temperature air as the heat

source. It therefore differs frcxn the studies in terms of fluid type,

flow orientation, and boundary condition (constant temperature, rather

than constant heat flux) . The refrigerant flowed inside a pyrex tube

which was surrounded by a rectangular quartz duct (Figure 4C-ld) .

Inside the annulus, 800^F air passed in counterflow to the refrigerant.

Subcooled refrigerant entered the heated chamber and exited at moderate

to high quality, depending on the amount of subcooling. Initially high

speed films (7000 frames/sec) had poor resolution between the liquid and

vapor; the authors then added a refrigerant-coloring agent (used in leak

detection) in a concentration of about 1% wt. Hiey considered resolution to be excellent. Berenson and Stone observed a few bubbles in the

film but considered the effect on the rate of vapor generation to be

negligible. The authors conclude:

'[Although] nucleation of bubbles on the wall

was observed whenever the wall was wet, in all flow

regimes, (...) the dominant heat transfer

mechanism in annular flow is conduction and convection through the liquid film on the wall. The

vapor formation process occurs primarily at the

interface between the liquid annulus and the vapor

I core, and not by the formation of bubbles within

I the liquid annulus.'

I

I

297
Unfortunately this study, like that of Hosier, suffers frooi the

potential lack of nucleation sites in that a pyrex tube was used. Also

R113 has a very small contact angle (4^) [Be84] , so that very few

cavities were unwetted in all likelihood.

Staub and Zuber [St66] also observed flow patterns with R22 flowing

vertically in a glass tube (quality range 0.14 to 0.22). An electrically conducting transparent coating was bonded to the inside of the

tube. Observations and photographs were made with the conclusion about

the annular flow regime: 'this well-defined mechanism consists of a

vapor core with or without entrained droplets and a liquid annulus on

the wall that is often quite thick and wavy and sometimes still contains

very small vapor bubbles.'

Gouse and Coumou [Go65] used a similar arrangement as [St66] with R113

except that the coating was placed on the outside of the tube. They

observed suppression of nucleation whenever an annular flow was

observed. Again, their glass tubes did not contain the full range of

activation sites, and R113 has a very small contact angle.

Uesler [Me77] reviews several studies of nucleate boiling in stat ionary

and moving thin liquid films. In his own study, high speed movies were

taken of boiling of stationary water on a metal surface. An artificial

nucleation site was created in the surface; very near the site, a rapid

response small thermocouple was installed and polished flush with the

surface. Films were taken which photographed simultaneously the bubbles

298
growing and departing the surface and the thermocouple reading on an

oscilloscope face. With this arrangement he was able to monitor local

cooling ( i. e. , heat transfer) rates and bubble position. He observed

high heat transfer rates

periods. It is the high

boiling as the principal

in the small area under the bubble for short

heat transfer rate which led him to consider

mechanism with all thin films.
Observation

(b) Tippets

Figure 4C-1: Visualization Methods

300
APPENDIX 4D: DEPENIKNCE ON HEAT AND MASS FLUX

Nucleate boiling suppression was first proposed by Dengler and Addons

[De56] based on an experiment with vaporizing water which flawed inside

1 in. OD copper tubes. Steam was used as a heat source in five separate

sections of a 20 foot copper tube. Wall thermocouples were embedded in

the tube wall, and pressure taps were installed at the entrance and exit

I of each section. Of note, the void fraction was measured to within 10%

I

I

j using a radioactive tracer. Hie idea of suppression was advanced on the

i

I following experimental and theoretical observations:

i

, (1) Heat flux increased sharply along the tube; the quality

I increased as well but the wall-steam temperature difference

: remained constant, i. e. , heat transfer coefficient increased

sharply with quality.

(2) Both liquid and vapor velocities could be obtained from the

measured void fraction and mass flow rates. An average velocity of the two phase mixture was calculated and used in a

single phase convection heat transfer correlation to predict

the heat transfer rate. Good agreement was achieved over much

of the tube, excepting the low quality portion.

(3) The use of a flow parameter, l/X^^, correlated the data fairly

well, except at low quality.

(4) Previous studies showed that forced convection raised the

value of the wall superheat necessary to initiate nucleate

I

I boiling. Thus, if one raised the velocity sufficiently.

nucleation should cease.
At low quality, Dengler and Addons considered both convection and

nucleate boiling to be important, and their effects to be superposed.

This conclusion is derived frcm the underprediction of heat transfer at

low quality by the correlation techniques described in observations (2)

and (3) above.

Mesler [He77] examined in detail the data of Dengler and Addams.

Dengler and Addons claimed no correlation between measured heat flux and

wall superheat (observation (1) above). Mesler reviewed the raw data

from Dangler's report, and rejects for various reasons (dryout,

highly fluctuating wall temperatures, erratic thermocouples) over 100 of

Dengler' s original 185 data points. The original Dengler and Addons

plot of a/uj^ versus l/X^^ showed a few points at low quality to have

relatively high values of a/a^, and the authors attributed these points

to have been caused by the presence/addition of nucleate boiling.

Mesler replots their data with only his 'acceptable' points, and shows

that nucleate boiling, if it is the proper explanation, contributes at

all qualities. Using only the acceptable data, Mesler also plots heat

flux versus the slope of which represents the heat transfer

coefficient. He then plots in the same fashion the data of five pool

boil ing experiments and shows them to have a similar, general shape as

the flow boiling data of Dengler and Addams. He thus establishes a

general relation between heat flux and wall superheat and draws from the

data precisely opposite conclusions of the physical process than the

authors who first collected and explained the data. In a brief letter

of response, Standiford (15) points out an error in one of the five pool

302
boiling experiments, which Mesler accepts but points to the remaining

experiments.

Mesler also considers observation (3) of Dengler and Addoms, the correlation of a/uj^ with (1/X^^) on a log-log basis. He argues about two

potential pitfalls of such an approach. First the use of log-log plots

tends to reduce the appearance of variation. Secondly, he points out

that there are several common variables in o/uj^ and that with

slowly varying fluid properties, one should automatically expect a

strong correlation, as Dengler and Addams achieved. His analysis is

reviewed in more detail in Appendix 4B.

Mesler goes on to note that as convection of the vapor increases,

(l/X^^) must increase. At the same time, with stronger convection one

would expect a smaller AT. Mesler then states 'This, in turn, predicts

that when a/a^^, which tends to increase with 1/X^^, is multiplied by AT,

which tends to decrease with 1/X^^, the quantity obtained should vary

less with than did a/a^^. The actual data . . . contradict this

prediction.' Since convection does not explain the data trends sufficiently, Mesler argues that nucleate boiling may be the phenomena, and

compares the Dengler and Addams data to pool boiling data as previously

discussed.

In further arguing for nucleate boiling as the dominant mechanism for

all flow boiling situations, Mesler cites several studies of boiling

with thin moving films.

303
Beattie and Lawther have presented briefly evidence to support the

notion of bubble existence in thin turbulent flowing films [Be79]. They

maintain that attached bubbles exist and serve to enhance surface roughness. The bubble contribution to surface roughness is dependent on

surface tension and shear forces. They then find agreement between a

flow model which includes these forces (rather than say, a model

including Reynolds Number) to experimental data of velocity profile and

friction factor in annular flows with thin films. This agreement, they

conclude is 'consistent with the existence of attached wall bubbles in

the film . . . [and] that the nucleate boiling mechanism can contribute

to heat transfer in thin film annular flows.' Ihe notion of attached

bubbles is not new: Lacey et al discuss the possibility, suggesting

that bubbles might remain fixed within the viscous sublayer [La62].

Turning to refrigerants, Qiawla [Ch67] noted that vaporization data

taken with many flowing refrigerants indicated two separate regimes for

heat transfer. The first regime showed near independence of the heat

transfer coefficient from mass flow rate but a strong dependence on heat

flux. This regime in behaving similarly to pool boiling experiments was

considered to be dominated by nucleation. A second regime showed complete independence from heat flux but a strong dependence on mass flow.

This second regime was characterized as being convection-dominated. A

small region between these two general regimes is considered to be of

transiti«re nature, with nucleation and evaporative mechamisms

suppressed. Chawla' s correlation of his data actually suggests a sni>-

pression criterion (see Appendix 4A) . Additionally, an independence of

304
the heat transfer coefficient from heat flux has been observed with

benzene, toluene and in at least one case R12 [Da65,St65]. These

studies suggest then an absence of nucleate boiling phenomena. Others

have previously observed similar behavior with vertical flow of water;

several studies are cited in Lacey, Hewitt, and Collier [La62] .

In the most definitive study to date, Aounallah et al [Ao82] have

recently built an apparatus to determine if two phase heat transfer

coefficients can be indeed completely independent of heat flux for a

given flow rate, film thickness and quality. Ihe comparison is potentially difficult since the amount of droplet entrainment is a weak

function of heat flux; entrainment affects the thickness of the liquid

film. All previous experiments cited above used a uniform heat flux.

For a given inlet condition and mass flow rate, the point at which a

certain quality is reached is related directly to this heat flux (as

shown in Chapter 3); with a larger heat flux, the same vapor quality

i will be achieved at a different location in the flow. A comparison of

1 the effect of heat flux would require then a comparison of heat transfer

I

! coefficients at different positions along the tube and is complicated by

I the fact that boiling is a function of local surface conditions. To

' avoid this problem, Aotmallah et al built an apparatus similar in mai^

I

I

I ways to the second test rig used in this report. They used a vertical

t

t

j tube comprised of three sections: a preheat section, a 'calming' adiaI batic section, and a test section. The preheat section was used to

I bring the flow to the desired quality. The calming section was included

I to bring the flow to estimated 'hydrodynamic equilibrium' at the inlet
of the test section. ^drodynamic eqnilihrinin is achieved when the rate

of entrainment exactly equals the rate of droplet deposition under

adiabatic conditions. In this manner, not only the quality but the film

thickness could be controlled at the test section inlet. The test

section was outfitted with several closely spaced wall thermocouple

stations; at each station, four thermocouples were mounted circumferentially. Fluid temperature was assumed as saturated and calculated from

pressure measurements along the test section.

Ihe authors then determined heat transfer coefficients for water at a

fixed flow rate and quality for five heat flux values. The heat transfer coefficients were found to be constant, i. e,, independent of heat

flux. These results were reported for four different qualities (.05

to .42), showing that as quality increased, so did the heat transfer.

Their results therefore support the notion of the complete suppression

of nucleate boiling. It should be noted that their measured values were

not predicted well by a detailed film flow model but were predicted to

about + 20% by the forced convective portion of the Chen correlation

[Ch66]

.

Beattie and Green [Be84] responded to the publication of Aounallah et al

by examining in detail an old experiment by Bertolleti et al whose

experimental apparatus closely resembled that of Aounallah. The

Bertoletti data is at much higher pressure, flow rates, and heat fluxes

though also with flowing water. Ihe data of Bertoletti did not show a

constant heat transfer coefficient, but instead one which 'varied

306
significantly with heat flux, having negligible dependent on mass flux,

quality, tube diameter, and distance from the inlet of the heated section'. Beattie and Green also compared the Bertoletti data to the pool

boiling correlation of Aladiev et al . Agreement, as shown on a log-log

plot is excellent.
» X

i'Mi- .w

Sf«|

**** "'^

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fvvilif -."'k w «tf>««u..itl«, i,«*« l*4>ii*»^|yi ^ kttgj

iti^y t«4' let *4it«ci«4 t'

i# 4iA tt- v>‘»*

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' / li.’^"‘H 4liN)m44ll b* *pt«#, »iut u*if ••»» li M*f

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Sib 4 • ip* «i«fk

.'1^ 4^ 4 «i:|HrTi»«*x i>/ Mtfilt-f^l il «il "*•4^1 fe

^1**4

.f <*l*4y r* iMIBJbj •t (%ml

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i* *« bip ptah I|I|M^ *iM 1 »*

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:;.BltA' > ''“S'

It JO*

\
APPENDIX 4E: MIXTDRES - LITERAITJRE REVIEW

Little work has been done specifically addressing suppression or

incipience of nucleate boiling of mixtures. However, the general study

of nucleate boiling of nonazeotropic mixtures is itself a large and

growing field major portions of tests have been devoted to this subject. As such a ccmpr ehensive review of all features of nucleate

boiling of mixtures is beyond the scope of this report. In this appendix certain critical features of bubble growth as applied to the

suppression question are introduced.

Equation (4-1) for the superheat requirement for a vapor nucleas of

radius r^ to exist in pure fluids is also applicable for mixtures.

However there are important differences in the values of the terms of

equation (4-1). First the term dP^^^/dT for a mixture differs from that

of a pure fluid or an ideal mixture as given by Collier:

(K - 1)1

ax/p T

where K is the equilibrium constant (Y/X) and g is the Gibbs free

energy. The term dP/dX)^ is identical to what would appear for a pure

fluid. Ihe second term on the right side is always negative so that

dP^at/dT for a mixture is always less than that for an ideal mixed

fluid. On applying this finding to equation (4-1), the incipient superheat requirements for mixtures is increased over that of an ideal mixed

fluid.

^sat ^ ^ ^ ^ dT 3T 1 _ RT dT ) / X /p

309
His change, however, has been shown by Shock (Sh77) to be less

important than the behavior of the mixture's surface tension. Small

additions of a second component may have drastic consequences on surface

tension, such that the superheat requirement may decrease substantially

over that of one of the pure fluids or that presupposed of an ideal

mixture.

Three studies of the onset of nucleate boiling (onb) with binary

mixtures were found in the literature. Thome, Shakir, and Mercier

[Th82] performed a careful study of the activation of a single first

boiling site on a polished heated surface with mixtures of liquid

nitrogen-argon and ethanol-water. The composition of the cyrogenic

mixture had no effect on the activation of the single site. However,

composition yielded a strong effect on their results with ethanol water.

The results in both cases are due to the wetting characteristics of the

mixtures. The cryogenic mixture components have similar contact angles,

whereas the addition of slight amounts of ethanol to water has a drastic

effect on surface tension and therefore the contact angle. The authors

did not consider the effect of mass transfer resistance (mtr) in their

results. In fact, the cryogenic mixture results suggest no effect of

mtr. However, the onb point for ethanol water is underpredicted by

treating the analysis as an equivalent pure fluid.

Shock evaluated binary mixtures of ethanol-water and ethanol-benzene,

with similar conclusions regarding the influence of wetting

characteristics [Sh77]. The onb point was found by wall temperature

310
measurement in his flow boiling experiments. He suggests that

suppression of boiling of mixtures might not be strictly treated as the

same as the onb problem, due to the possible existence of local

concentration gradients around established nuclei. He leaves open the

possibility of mtr effects.

Toral studied ethanol-cyclohexane, which behaves in a more ideal fashion

than the previous ethanol mixtures, in a flow boiling apparatus similar

to Shock's [To79]. He differentiates between activation of an isolated

cavity and the sudden transition to multiple cavity activation. Ihe

latter mechanism, more relevant to the work of this report, is called

the onb by Toral. He concludes that composition has a considerable

influence on mul tipi e cavity activation, 'indicating the presence of mtr

effect and suggesting that onb is governed by bubble growth

dynamics . . .

' If Toral's conclusions are correct, then mtr should be

considered in subsequent prediction methods for mixtures.

Toral [To79] also attempted a basic theoretical stucfy of the potential

for nucleate boiling in thin film flow of two non-azeotropic mixtures:

an aqueous solution of methanol and one of ethanol-cyclohexane. He

posed the following problem:

'A thin liquid film flows in upward direction on a flat plate of

infinite depth by the action of shear stress imposed upon it by

vapor flowing concurrently. Thermodynamic equilibrium is assumed

between liquid and vapor phases with uniform temperature

311
distribution dne to the adiabatic condition at the bonndary with

the flat plate. At time t = o heat flux is applied at this

bonndary over the axial length x = o to x = L. The temperature

profile begins to develop. A net rate of evaporation begins when

the heat flux reaches the interface. It is assumed that for t > 0

heat flux at the wall remains constant at '

As time goes on, the thickness of the layer decreases due to evaporation, the

film thickness also decreases with downstream distance.

The basic equations governing the problem are:

Momentum

p®m

a^u =

3y2

pg + 7® = Ct

dx

F.tiergy or Mass Transfer

^ + u e. 2

^

at dx ^ dy2

0 = T in energy equation

0 = C in mass equation

The boundary conditions he used are discussed later.

Toral investigates the effect of assuming various thermal and mass

dif fusiv ities (e^) in the above expression. Most researchers have

assumed a single phase eddy diffusivity throughout the layer, i.e., a

312
growing turbulence as one proceeds toward the interface. Sene research

has shown that the turbulence may be damped in the vicinity of the

interface, providing an increase of thermal and mass transfer

resistance.^ The damped and undamped diffusivity models produced widely

different results. Using an undamped profile, a small wall superheat

developed for the non- az eotropic mixture, one which would be insufficient for nucleation. Using a damped profile, the calculated wall

superheat increased by a factor of 6, to the point that nucl eation was

likely. For the aqueous mixture, wall superheat was too 1 ow to initiate

bubble growth in either case. He concludes that only with high conductivity fluids, such as with aqueous mixtures, can one anticipate the

suppression of nucleate boiling, if in fact turbulence damping occurs at

the interface. It is important to note that the conductivity of water

or aqueous mixtures is roughly 100 times that of maz^ other fluids,

including most common refrigerants.

Toral's work is most relevant to this report since it is concerned with

non- azeotropic mixtures. A detailed review of his posed problem reveals

some potential difficulties with his analysis.

1

! Ihe parabolic form of the energy and mass transfer equations requires

i

I

I the use of only one boundary condition on x. Toral however uses:

' 1

I In the vicinity of the

equation reduced to the

interface, the eddy diffusivity

thermal diffusivity, X/ pC^.

in the energy

313

I

i
T(0, y, t) -

dT(L. y, t)/dx = 0

c(0, y, t) —

dc(L, y, t)/dx = 0

Hie use of two x boundary conditions converts tbe solution technique

from a 'forward marching' one to a closed form type. The effect of

specifying the downstream condition propogates upstream in the solution

technique. Toral even notes 0T/3x = 0 shortly after the inlet. Thus,

the use of two boundary conditions is mathematically incorrect.

The physical meaning of dT/dx = 0 can be interpreted simply with the use

of a control volume heat is transferred into the control volume by

diffusion away from the wall and by convection. It is transferred out

by convection and by diffusion toward the interface. The difference

must be the amount of heat stored. If dT/dx = 0, there is no sensible

heating of the liquid, and net flow of heat must either be to storage or

toward the interface. A similar explanation is valid for the mass

transfer equation.

The mathematical error might not have serious conseque nee r, a marching

type solution could produce the same result, since the specification of

'no sensible heating' may or may not be valid. Many condensation

researchers consider the term to be small, and that, at steady^ state,

all wall heat flux is transferred to the interface (e.g., [Co37]).

Bennett and Chen in their flow boiling study of an e tl^lene-glycol/water

mixture considered sensible heating of the liquid layer, and achieved

only a slightly improved agreement with data [Be80]. On the other hand.

314
Toral called the stored heat 'sensible heat', and noted it represented

40~50% of the total heat flux in the damped cases.

Despite its potential difficulties, Toral's posed problem is of

substantial interest. An alternate means of sol ution woul d be to assnme

steady-state and approximate an initial film thickness 5(x = 0) = 5q,

and march downstream until the film is depleted. In the case of refrigeration cycles, the initial condition in the x-direction can be simply

equilibrium vapor and liquid compositions, since a two phase mixture in

fact enters an evaporator from an isenthalpic expansion device. At the

entering vapor quality of about 20% the phases separate into an annular

flow pattern very near the evaporator inlet. At each Ax step, the film

thickness must be calculated from energy and species balances. Such a

solution requires as input the same y-boundary conditions and x initial

condition as Toral assumes.

315
'fua}\ i,

,

rira

^V:!'

tri:' ^;‘; ,„ ,,

t£ • (r

- v^> lUiwTiiE: ^. . i

'^4

mt

*^»iS<« owl - *o»iit ,«itftifU«i»i>* %tt« J *t**

'C

:.., - i'K-^ “

«tfp|wr'«.,«.i'i«w*« ^UHtma uamn*

t4ipltt4« a44 t *•i

. . t M t4. '•« •« * “•*' **' tlm |4 |Jli» % itiftift, fc#t fl«w I>f %M%% mt

«ayt*i«tiftB itvftlUfnr t%*»4«»

W' 3P

3' ‘s.

.ISmi 4«*^ Biruiiigii ii#r« .^-i-'Wt «-vft#«%M»<Mi|'»

Ui4 t««e t4i«il^ in* *Hi

ri«4* «t ‘‘'K »»t b# •tT S*4f

% 4M^’ tvpi V0 <41^ t-k^r, *1 •i«4 4r*4'

f4iW V*'^ ?i«|t~>i to f>< ^•l•rl^•• (4*|»«

slEI^.!'.'5SB»’

‘ '" ' “ii,, ' *' i*; ' «

* ’*’*

' ;iS?iS»t'i 4w4.,^a^^ tu^ U| miy of «b *t%l4##-*«ini4

ftf itB'llt*!* lty*r 4*^ •«4»|rf

-- '

« r f*lO 4*l« ri 4M|< fN^iUt

• t.^- •

' TSs, ^iy%. • ,yi K'ii ii f

' i*iK 4%’-^
APPENDIX 6A: MISCELLANEOUS HEAT TRANSFER FORMS

The graphical method of Shah, like Chen's method, attempts to predict a

in either heat transfer regime. Hass flnr and quality effects are

considered in the nucleate boiling regime through the single phase heat

transfer coefficient where

® “ ®nbc = aLo(f(Bo) (6A-1)

Like form 6-la equations, the nucleate boiling has a dependence on tube

diameter (explicit in Olo^* forced convection dominated regime,

called by Shah the 'fully suppressed nucleate boiling regime,' yields

® “ ®FC " ^LO^(Co) (6A-2)

where

Co (iz)

Pl

0.5

(6A-3)

and Co is called the convection number. Co is similar to X^^ without

the dimensionless viscosity term.

The correlation was compared to 810 data points from Rll, R12, and R22

experiments with a mean fractional deviation of 23% and a tendency to

underpredict [De78]. Shah recently computerized the method [Sh82] , and

the algorithm was compared to the experimental data of this report. In

general^ the method predicted poorly (figure 6-1). Hie suppression

317
criterion was incorrect, so that the algorithm selected a heat transfer

coefficient calculated from equation (6~2b) instead of the more

appropriate equation (6~2a). All of the Rig #2 data tended to be

unde rpr edict ed, less severely for the forced convection regime. The Rig

#1 data was also poorly predicted (figure 6-1), though the mean

deviation is reduced.

After analyzing Shah’s correlation and others; Dembi et al. introduced a

new correlation for the forced convective/evaporative regime of the form

[De7 8] :

a = 0.115

- 0.11 G2Ah„0.44

x2) ) ( 1) gPlC

(Pr^)®-'^ (6A-4)

It correlated the same 810 point data base to a mean deviation of 0.15.

However, the coefficients were determined by regression analysis of the

data base, so good agreement might be expected. It is interesting to

note that heat flux does not appear in the equation though a weak

dependence on heat flux was observed in the experimental data. No

attempt was made to apply this correlation. It is also interesting to

note that the Prandtl number dependence is to the 0.7 power, similar to

Bennett and Chen's correlation.

Most recently, Kandilihar [Ea84] has developed, via regression analysis,

a correlation which yields good agreement with a large body of

experimental data on refrigerants, water, and organic fluids in both

318
'horizontal and vertical orientations. Hie method involves the classic

superposition of convective/evaporation and nucleate boiling. It

contains seven empirically determined constants, one of which is

dependent on fluid type (and therefore fitted to the individual

experiment with that fluid). Test with R152a and R1361 are not included

in this data base, and therefore the correlation could not be checked.

I

'i

I

I

I

I

tj

319
*®^^^** f*l?ctii4 • M«t um«*f*r

JlA^ ifc|Ji^it»«ft i»«* «0

rc<a^iwite4>trl'^^ ^ Af U*^r# _ - •

Kfit ‘‘*vt MMd4j tu i#

bi#n .c 1..^.

" '*»*» ’••'^ **" '

•'’‘'^i''* ;i»;t _ITS^ u>*' -ttk^ ...53 ^ no4i*l#5*o^»

S'^.WP

"Vr

iim. Tt' t, vo»je#4liiUon othtri; |><f«ihi tt tl.'iiita t&t^4 •"

ik« fQr^*<t '0*Mrr»4% w«y9«f^otnij<r* &«r|iit« «4 ttaid^

I' tTM ' ir,

.

1^

J m O.lo 0 .4<4 - « (x*fl • *") ) I Jty ;JT )Q.

•>15

* -I

PlO fr«>4llf Attt b«M to * »» 4 it» 4 r«’iitir*

•'''p , . n

^ ^1^ ' A

* * 1 A ^a#«f','40 ii»M vithi M oxiM^Ctt* i% it UI«»«#lUt

^Ij' ' . B1 " tfcii 4«tt ii4t U li*4 tkttfl < %*•% ^ 4VCW 4ife^t«t fits «»« '>b4«rf«ll Ia U-* « i;.»tLM«tA4 At««. Hi

ff.

'tpm--

’'•id* c» »yi4y _lk«« U torrti4tiu«i It t> *1 lo i«tur*filA|t4lMlf/

i^- ^>«.. .;

' '',JB9|HI

?r«a4tl c«i^£ <UHt»w«Av* i * if Ut 0«T Ifft W Oif

f

worffXttioau

Iff pi#«At.tf, ffff4UU»r OCiiiil d*»»lo)p«>4e fU 1

1

-m.

44|f fi> It ••«;•. fiftt. *m; 4Mrft«4« |lt.<« i» i#tii

Ul

•M
APPENDIX 6B: POLLEY' S METHOD

Pol ley has recently modified Chen's method and suggested a different

pool boiling relation due to Cooper [Po82] :

“n ' “pool = Cl (|-)-12«(l

* (6B-1)

jwhere Cj^ varying between 3 and 4.1 for refrigerants, and other values

for different fluids. Also, he modified the suppression factor:

S = 1.0 if — < 0.15 (6D-2)

“pool

I

I

= -.5271 in ( ) if 0.15 < — < 1.0 (6B-3)

“pool “pool

= 0 if > 1.0

“pool

The justification for the changes were given as:

(6B-3)

(a)

(b)

(c)

The pool boiling relation is simpler to apply, as it requires

fewer proi>erties;

The suppression factor is based on heat transfer contributions

directly; and most importantly.

The revised form fit a very large data bank of steam-water

data to a higher degree of accuracy than Chen's equation.

I

I

i

I

I

321
Polley included an additional criterion to determine if a nucleate

boiling contribution should be included. He suggested that the Davis

and Anderson incipient superheat, be calculated (see Appendix 4A)

.

If the given AT is less than that calchlated, then no nucleate boiling

should be included. It is, however, not clear how to apply it in the

case of constant wall flux where AT is not known a priori.

322
APPENDIX 7: DEVELOPMENT OF COON (MASS lEANSFER EFFECT ON LIQUID SIDE)

IN BENNETT AND CHEN'S METHOD

Bennett and Chen postulated mass transfer does not affect a, but does

effect the driving force.

For a pure fluid

^evap “

“LO'-'W (Tm ^eqb^ 'eqb = equilibrium temp, for pure

fluid Tgqij = Tgj^iFor a binary

^BIN " “L0^% "

^i^ Ti = interfacial temp.

Tw “ T. = a 1 S- (T* -

‘LO

"^eqb

®L0 ^CON “

^eqb^ (7A-1)

Since T^ is unknown, Bennett derived a way of eliminating it from

(7A-1), as follows (steps not shown in Bennett's report):

Define a mass transfer coefficient,

^v PL^^^eqb ^i^ (7A-2)

mv = more volatile

323
Now, assume all heat input results in evaporation

^evap = ^ Ah^ (7A-3)

and assume Y = Y*, i.e., Y* = Y* , not Yj^ (this is not strictly

correct) and since

TW- Tj

_

(Ij)

Tw ^bub <^eqb*

equations (7A-2), (7A-3) and (7A-4) can be combined to give as

f oil ows

:

From (7A-2) and (7A-3)

.

^eqb ~ ^i

= = q^*

PlPl Ah^PL

A1 so

^eqb ^i

dX^

(Tfi - T^)

bub

combining (7A-5) and (7A-6)

dX

dX

(T

bub

eqb

* Y*

- T.) =

" aVlPl

(7A-5)

(7A-6)

32A
or

^eqb

*^bub

qY* ~ir~

Add and subtract and multiply by -1

(Tw - Teqb) - - Ti)

qY* dTbiib^^^eqb

Divide by (T^ -

1 Tw - Tj _ -qY* dXb^b/dX

^eqb ~ ^eqb^

or

Tw - Tj

_ ^ ^ qY* dTbub/dXeob

% “ Tgqb PL^^H<T^ - Tgqb>

Note that (+) sign« In Bennett and Chen's paper they have a (-) sign.

The difference is due to definition. In the development here, X is

defined in terms of the more volatile component. Bennett and Chen used

X as the less volatile component. If defined in that manner, a (-) is

corre ct.

325
I li 'Bp ' ,’ ^ ||*l^^^ <til» It «vt «»ri€.fi« 7^

I'' X^ ^t'y

1OAU<10* ^S0 j

r Tt

'“ *» * * -

-

I afe, Ji->U^ • - ,t, .

,

n.&i. ljk*4} ‘iPt to* •0«toil>*a to ti”*0

i>\^,jn n>- tLiilf

^ , !<».? - ‘ 4,,t - iT ^ ^

ITlM)

d..H>W.<T» U, , .uLlC

'f i »T0 i !»«• 1 »•<*•* «t '*!*•

•'

:j

i*> * ... i. 'C.’' too* ia«ui»a 4oMo^W’^ tUtolot UM ii«tf «l l***^

• ,:i««ut«ji a*»ia «l towaiok U •Ua#Ms
APPENDIX 7B: BENNETT AND CHEN'S INaUSION OF SENSIBLE HEATINS OF LIQUID

® “ ®evap ^sens^ + '-sens.

Qevap jiA\

^sensL ~ Jd

^ 'PL dz

so

Q - ^ i^CpL

dTbttb

jtD ^ dz

Mass balances give

total mass: -d(^) = mnD dz

component mass: -d(MXL) ~ mY*nD dz

-XgdMj^ - M^ 3^ = mY*nD dz

Rearranging (7B-3)

= -mY* D ^B ^^L

dz \ «L

dz

7-a?f- D + JlD“ Xg from (7B-2)

\ Ml

(7B-la)

(7B-lb)

(7B-lc)

(7B-2)

(7B-3)

327
so, rearranging the last equation

Ml

= m(X« - Y*)

jiD ®

dz

dXg

Substituting (7B-4) into (7B-lb)

®sensL

~ dTbub

dXB

and (7B-lc) beccanes

Q = mdh^ + mCpL (Xb - !•)

dT

= ndh

dXfi

eff

or

dTbnb

dXB

where again XB and y are in terms of more volatile component,

and Chen used less volatile so for their equation:

^^^eff ~ ^PL^^LV Ylv>

dT

dl

bub

LV

(7B-4)

Benne 1

1

328
APPENDIX 7C: MKUCLAYER EVAPORATION MODELS

Van Oinrerkerk [Va72] analyzed a hemispherical bubble with a thin

nicrolayer of liquid under it (see Figure 7C-1). The assumed physical

properties were independent of both composition and temperature. The

transient analysis of bubble grcwth showed that bubble growth rates were

greatly reduced over an EPF fluid due to the depletion of the more volatile component in the microlayer. Ih.e depletion caused the usual rise

in bubble point temperature reducing the evaporation rate. He noted

I that the Harangoni effect (i. e., surface tension gradient around a bubble

influencing the growth rate) could theoretically assist evaporation by

drawing the more volatile component from the bubble cap region to the

i microlayer. Upon calculation, he noted the effect is negligible for

realistic bubble sizes.

1

i Toral [To79] examined microlayer evaportion, but allowed thermal

I properties to vary with composition. His numerical analysis treated the

inicrolayer as a 1-D transport problem (see Figure 7C-1) . His conclusions

1

I

I are similar to Van Ouwerkerk. He further noted that all evaporation may

i cease, so that a dryout condition might never be reached. In this situaI tion, much higher critical heat fluxes would be possible with a mixture.

i Recently, Stephan and Preuber [St82] developed a model which suggests

I that, while microlayer evaporation occurs, condensation might occur

simultaneously at the bubble cap. They assume the microlayer has a

1 lower liquid composition then the bulk liquid (see figure 7C-2) . However,

vapor is produced in this region due to its proximity to the heated wal 1

surface. The vapor produced in microlayer evaporation is in equilibrium

I

329
with the liquid in this region, and once produced mixes completely

with the vapor in the bubble (assumed). The vapor therefore has a composition no longer in equilibrium with the liquid at the bubble cap. To

move toward equilibrium, the less volatile component condenses out at

the same time the more volatile component evaporates. Ihey note that,

if this modelled process indeed is accurate, the mass transfer resistance

between the bulk and microlayer increases, i. e., the boundary layer has

more difficulty in finding available more volatile component.

330
Vapor Tq

See below—^-"1 |qQ

Liquid

'V^7777yT7777~/

‘^TOT = ^w "^TOT

j^/wall '/A

^TOT

AZ

01(3 out

Figure 7E-1: The Bell and Ghaly Method
0 m .'T*>kT

aT.lSS^f

. , „ „

’*J *>11©' - - '

. ,.^v:- ,/^, ^

. «. t)i«.t«f i* •air' ‘f

^ t/ ‘ tJb t tielbu »*p. 'to

p»&'

p aSit JtfJijJgj^*^ fyJkir *®*-=

.• > * » f ^ uJlIjLI^

|^4it<S artti? w«l|W''iJR«tJnni r*»^ A il <*

. ," gS^P^'L}*^*

'

’--iPio^ufK w?»tx»i<rrrr'

5' ii»w^

«rTOtP wP*TofP

'>»A # .« 1 « *.l

SL

SjoP*^ * »uo®^“

|T

-it;-. 0P OfflA

oTOaqO£)fn»<o^ - |T)e>n*oP

V IW .'!>> .'

f:m

' V

p* ^cC

M(3#K *»*»
APPENDIX 7D: FUR3HER COMMENTS ON SHOCK'S ANALYSIS

There are some concerns regarding the analysis. Turbulence damping near

the interface was neglected (this might affect finding (a) in

particular); eddy mass dif f usivitie s are generally related to thermal

diffusivities by

not Eq = Eq as assimed in the analysis. However, finding (a) is

supported by analytic modelling of multicomponent condensation by Webb

and Sardesai [We82] . They examined two limiting cases: one in which

the rate of mass transfer in the condensate film was assumed to be infinitely slow, and the other infinitely fast. Condensation rates of

individual components agreed to within 15% of each other and within 10%

of experimental results.

Shock's initial condition, selected to maximize the vapor-liquid

composition difference, was only 7*C from the boiling point of water.

This suggests that with the maximum mass transfer resistance, the

j interfacial temperature could differ from equilibrium by 7**C. Since

i

I the total temperature drop across the liquid film was calculated 40-70*’C,

I the largest possible reduction in heat transfer coefficient was 10-15%.

I Shock does note that the findings may vary for mixtures with a wider

boiling range than the considered 20*’C of ethanol-water (R152a/S13B1 at

|4.75 have about a 30'*C boiling range). In a related problem Price and

Bell [Pr74] compared a simplified condensation model which neglects mass

I

I

333
transfer resistance to a more exact model. Agreement was

mixture of methanol-water (small boiling range), but not

n-octane mixture (wide boiling range) .

good for a

for an n-butane

334
APPENDIX 7E: IHE BELL GHALY MODEL

Figure 7E-1 shows simple heat transfer across a film and to a vapor core.

Neglecting aj^ sensible heating of the liquid (Q_ = 0 in equation 1-1),

®L

*1tOT = ‘IL " “L^% "

"^i) (7&-1)

Similarly on the vapor side.

“ ®G^^i

“ (7E-2)

Combining the previous equations, and eliminating yields

^TOT "

“L^'^V “ ^G

®G

and dividing both sides by

1 = (T, - Tg) -

‘^TOT ®G ^TOT

or

•^TOT

«L

®L *1T0T

(7E-3a)

so that defining an effective heat transfer coefficient.

335
1 i_ ^ V*^TOT

“l “g

(7E-3b)

Hie ratio represents the ratio of the heat gained by the vapor

to the total heat. Over a length AZ,

«G ' (7B-4.)

where the mass flow rate of vapor is a mean qnantity over the interval.

The total heat snpplied is over this same length.

*1tot “ “tot^ (7E-4b)

so that

—— . G n AT — ! '

^TOT ®TOT

(7E-4c)

over an infinitesmal length (AZ^O) ,

<1G qTOT

dT

^ 'PG 4h

G (7^4d)

To this point, the derivation is exact. The quantity dTg is now

approximated as

dTg = dTi *^^eqb

(7E-5)

336
so that eqxiation (7-4) becomes

-i§- = I Cp

^TOT ®

(7E-6)

The term dT^^^/dh is referred to commonly as the 'condensation cnrve'.

Typical curves for R13Bl/RlS2a mixtures are shown on Figure 3-13. The

effective heat transfer coefficient of equation (7£-3b) is then

1

^ ^ xCp^ (dXeqb/dh)

«G “G

(7E-7)

The problem remains to evaluate the heat transfer coefficients

and Uq. Bell and Ghaly recommended the classic single phase relations:

(7E-8)

and

(7E-9)

The stated philosophy behind their approach was to underestimate the

heat transfer coefficients to compensate for the error of ignoring mass

transfer resistance. There is however no assurance that the two errors

(neglecting both two phase flow effects and most transfer resistance)

are of the same magnitude.

337
In a later paper. Price and Bell [Pr74] suggest modifying equation

(7“8) to include a two phase flow effect via the Martinelli parameter,

tacitly assuming a Reynolds analogy;

(7E-10)

In a separate paper, Qiisholm [ChSl] suggests using the two phase

multiplier on the liquid phase as well:^

(7E-11)

At this point, one can analyze the method in light of the previous

section's discussion. First, Shock found little difference between

and Tq, and even less difference between dT^ and dT^. Thus the assumption

of (7-5) is minor for evaporation, though for condensation of a highly

superheated vapor flow one might suspect problems.

Finding (c) of section 7.3 suggested that mass transfer resistance might

be neglected without serious error. The basic philosphy of compensating

errors with the original method is then undermined; it is not surprising

that the modification suggested in equations (7E-10) and (7E-11) were

required.

^Chisholm credits Price and Bell, but no reference to this step could be

found in their paper.

338
In still another paper, McNanght [Mc79] attempted to modify the whole

approach to include a mass transfer effect on the vapor side. If,

however, the finding (c) of section 7.3 is valid, this final change is

unnecessary except for laminar flow.

Finding ( f } of section 7.3 suggested that the sensible heating required

on the vapor side is small when compared to the total heat (7-46) .

Taking this to an extreme, equation (7~4d) yields

<1G qiDT

:: 0 (7E-12)

or, on examining the condensation curves dX/dh is small. Equation (7-3b)

becomes then

'eff = a

.445

tt

(7E-13)

or, the heat transfer coefficient is descibed completely by the liquid

1

i

' filml Ihe suggestion by Chisholm to include a two phase effect is then

I

II well-placed. Equation (7-12) is only valid in the case of turbulent

i|

: vapor flow. If the vapor heat transfer coefficient becomes small, as in

i

' stagemant or small laminar flow, then

i

1

I ^TOT 1

I

\

i

339
and the vapor side heat transfer must not be neglected. It is

interesting to note that Price and Bell found the liquid side to control

the process in several test cases. The implication of (7E-13) and in

fact the findings of the previous section is that forced convection/

evaporation of mixtures may be treated exactly as for pure fluids,

requiring a good estimate, however, of the liquid properties.

340
MICROLAYER EVAPORATION MODELS

Vapor

b) Toral

c) Stephan and Preuber

Figure 7C-1: Microlayer Evaporation Models

341
Ff .i

4t j is''' t.» ouTir r tfi.

.-.bii.«Minn»>-*- . • -~7-—-7>'—

i'i{*m thti*.

naV (»

tpqsV

T

i , i.ivK',';'- btuplj - eVBbM-

>-m

o—

?r^

IbkiT (d

35.

iJ ^noO

o

i;— 'jrjragy j I

4

<jm.T jX

wdufli'l bn* n*rtq»j3 (j - -

0 yr .-Sr vv . -uji'.

.

mxtJiF*xo^*T:i » 1*3^ ’»M>1|

SV' ’s "i' I

' ^'

t*’"' ^M'J'kiiyj®
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Slii!l5i'3>ite>n«>a luta ii«IHB l»slif»» T>*J«

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U.s, DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET fSee instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-86/3450

2. Performing Organ. Report No. 3. Pu bl icacion Date

nOVEMBER 1986 4.

TITLE AND SUBTITLE

An Investigation of Horizontal Flow Boiling of Pure and Mixed Refrigerants

5. AUTHOR(S)

Howard D. Ross

6. PERFORMING ORGANIZATION (If joint or other than NBS. see /n struct/on s; 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

National Bureau of Standards U.S. Department of Energy

Building Equipment Division, CBT (via Oak Ridge National Laboratory)

Thermal Machinery Group Washington, D.C. 20585

Gaithersburg, MD 20899

10. SUPPLEMENTARY NOTES

I

I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

The research involved determining experimental heat transfer coefficients (HTC)

examining the phenomena involved in the physical process, and analyzing the predictive

ability of available models and correlations. This work was done for pure Rl52a and

R13B1 and for mixtures of these refrigerants. The mixtures yielded sharply lower heat

transfer coefficients than either pure refrigerant.

With pure refrigerants full suppression of nucleate boiling (FSNB) occurs only at

rather low pressures. Correlative evidence suggests that suppression is easier to

achieve with mixtures than pure fluids.

1^ The evaporation—dominated heat transfer regime, Chengs correlation was successfully

applied to our refrigerants with and without the occurrence of FSNB conditions. A

Prandtl number correction is needed when some nucleation occurs. For mixtures, mass

diffusion may not complicate the problem substantially under FSNB conditions, and the

same correlation may be used with success.

1^ The nucleate boiling dominated regime, the Stephan and Abdelsalam method was validated for pure fluids, and used successfully with Thome *s method for mixtures.

Pressure drop correlations for pure fluids were also extended to mixtures without

modif ication.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s/ evaporative flow; flow boiling; nonazeotropic mixtures; refrigerants heat transfer;

two phase flow

13.

AVAILABILITY

|X I Unlimited

I I For Official Distribution. Do Not Release to NTIS

I i Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

14. NO. OF

PRINTED PAGES

358

15. Price

jy I Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $28.95

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