plate -fin-tube condenser performance

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PLATE-FIN-AND-TUBE CONDENSER PERFORMANCE AND DESIGN FOR

REFRIGERANT R-410A AIR-CONDITIONER

A Thesis

Presented to

The Academic Faculty

By

Monifa Fela Wright

In Partial Fulfillmenof the Requirements for the Degree

Master of Science in Mechanical Engineering

Georgia Institute of Technolog

May 2000


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PLATE-FIN-AND-TUBE CONDENSER PERFORMANCE AND DESIGN FOR

REFRIGERANT R-410A AIR-CONDITIONER

Approved:

________________________________

Samuel V. Shelton

________________________________

James G. Hartley

________________________________Prateen Desa

Date Approved____________________


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iii

TABLE OF CONTENTS

LIST OF TABLES vi

LIST OF ILLUSTRATIONS vii

NOMENCLATURE xii

List of Symbols xiiList of Symbols with Greek Letters

SUMMARY xxiii

CHAPTER I: INTRODUCTION 1

Research Objectives 4

CHAPTER II: LITERATURE SURVEY 5

Previous Studies on Variations of Heat Exchanger Geometric

Parameters 5

Previous Work in R-22 Replacement Refrigerants 8

Two-Phase Flow Regime considerations in Condenser and

Evaporator Design 13

Two-Phase Flow Heat Transfer Correlations 16

Two-Phase Flow Pressure Drop Correlations 19

CHAPTER III: AIR-CONDITIONING SYSTEM AND COMPONENT

MODELING 23

Refrigeration Cycle 23

System Component Models 25

Compressor 25

Condenser 28

Condenser Fan 40

Expansion Valve 40

Evaporator 41

Evaporator Fan 44


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Refrigerant Mass Inventory 45

CHAPTER IV: REFRIGERANT-SIDE HEAT TRANSFER COEFFIECIENT

AND PRESSURE DROP MODELS 51Single Phase Heat Transfer Coefficient 51

Condensation Heat Transfer Coefficient 56

Evaporative Heat Transfer Coefficient 61

Pressure Drop in the Straight Tubes 62

Pressure Drop In Tube Bends 70

CHAPTER V: AIR-SIDE HEAT TRANSFER COEFFICIENT AND PRESSURE

DROP MODELS 76Heat Transfer Coefficient 76

Pressure Drop 81

CHAPTER VI: DESIGN AND OPTIMIZATION METHODOLOGY 89

Figure of Merit (Coefficient of Performance) 89

System Design 94

Optimization Parameters 94

Operating Parameters 95

Geometric Parameters 96

Software Tools 97

CHAPTER VII: OPTIMIZATION OF OPERATING PARAMETERS 98

Effects of Air Velocity, Ambient Temperature, and Sub-Cool 100

Effects on the Seasonal COP 109

Range of Optimum Operating Parameter 111

Effect of Operating Parameters on System Cost 111

CHAPTER VIII: OPTIMIZATION OF GEOMETRIC DESIGN PARAMETERS

FOR FIXED CONDENSER COIL COST 112Area Factor and Cost Facto 136

Varying Number of Rows of Condenser Tubes 113

Varying Condenser Tube Circuiting 115

Varying Fin Pitch 124

Varying Tube Diameter 137


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Operating Costs 145

CHAPTER IX: OPTIMIZATION OF GEOMETRIC DESIGN PARAMETERS

FOR FIXED CONDENSER FRONTAL AREA 152Varying the Number of Rows of Condenser Tubes 153

Varying Fin Pitch 159

Varying Tube Diameter 163

Operating Costs 170

Varying the Base Configuration Frontal Area 179

CHAPTER X: CONCLUSIONS AND RECOMMENDATIONS 185

Conclusions 185

List of Conclusions 188

Recommendations 191

Optimization Parameters and Methodology 191

Computational Methods 193

Refrigerant-Side Heat Transfer and Pressure Drop Models 196

Economic Analysis 196

APPENDIX A: AIR-CONDITIONING SYSTEM: EES PROGRAM 197

REFERENCES 227


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LIST OF TABLES

Table 2-1: List of Refrigerant R-22 Alternative Refrigerant Mixtures 12

Table 5-1: Coefficients for the Euler Number Inverse Power Series 84

Table 5-2: Staggered Array Geometry Factor 85

Table 5-3: Correction Factors for Individual Rows of Tubes 87

Table 6-1: Distribution of Cooling Load Hours, i.e. Distribution of Fractional

Hours in Temperature Bins 91

Table 8-1: Material Costs (London Metals Exchange, 1999) 114

Table 8-2: Condenser Circuiting Configurations 124

Table 8-3: Refrigerant Pressure Drop Distributions at 82F Ambient Temperature128

Table 8-4: Seasonal COP and Area Factors for Varying Fin Pitch at Optimum Air

Velocity and Sub-Cool for Fixed Condenser Material Cost 130

Table 8-5: Condenser Tube Dimensions (www.aaon.com. AAOP Heating and Air-

Conditioning Products web site) 138

Table 8-6: Optimum Seasonal COPs and Area Factors for Varying Tube

Diameters 141

Table 9-1: Optimum Operating Conditions for Varying Number of Rows withFixed Condenser Frontal Area 154

Table 9-2: Optimum Operating Conditions and Cost Factor for Varying Fin Pitch

with Fixed Frontal Area 162

Table 9-3: Optimum Operating Conditions and Cost Factor For Varying Tube

Diameters with Fixed Frontal Area 166


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LIST OF ILLUSTRATIONS

Figure 2-1: Typical Plate Fin-and-Tube Cross Flow Heat Exchange 5

Figure 2-2: Horizontal Two-Phase Flow Regime Patterns 14

Figure 3-1: The Actual Vapor-Compression Refrigeration Cycle 24

Figure 3-2: Typical Cross Flow Heat Exchanger (fins not displayed) 30

Figure 3-3: Hexagonal Fin Layout and Tube Array 37

Figure 4-1: Refrigerant-Side Single Nusselt Number vs. Reynolds Numbe 55

Figure 4-2: Condensation Heat Transfer Coefficient vs. Total Mass Flux Fo

Refrigerant R-12 58

Figure 7-1: Effect of Operating Conditions on Evaporator Frontal Area 99

Figure 7-2: Effect of Air Velocity on COP for Various Ambient Temperatures and

Optimum Degrees Sub-Cool 101

Figure 7-3: Effect of Air Velocity on Compressor and Condenser Fan Power 13FSub-cool at 95F Ambient Temperature 103

Figure 7-4: Effect of Ambient Temperature on COP for Varying Degrees Sub-Cool

at 95F Ambient Temperature with an Air Velocity Over theCondenser of 8.5 ft/s 105

Figure 7-5: Effect of Ambient Temperature on the Evaporator Capacity forVarying Degrees Sub-Cool at 95F Ambient Temperature with atOptimum Air Velocity 106

Figure 7-6: Evaporator Capacity vs. Ambient Temperature for Various Sub-Cool

conditions at 95F Ambient Temperature and Optimum Air Velocity108


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Figure 7-7: Effect of Air Velocity on the Seasonal COP for Varying Sub-cool

Conditions 110

Figure 8-1: Effect of Number of Rows on the Seasonal COP at Optimum AirVelocity and Varying Sub-Cool for Fixed Cost of Condenser Materials

116

Figure 8-2: Effect of Number of Rows on Compressor Power and Refrigerant

Pressure Drop at Optimum Sub-Cool and Air Velocity for Fixed

Condenser Material Cost at 82F Ambient Temperature 118

Figure 8-3: Effect of Number of Rows of Tubes on Condenser Frontal Area fo

Fixed Condenser Material Cost at Optimum Sub-Cool and Air Velocity

119

Figure 8-4: Effect of Number of Rows of Tubes on Condenser Fan Power and

Airside Pressure Drop for Fixed Condenser Material Cost at 82FAmbient Temperature at Optimum Sub-Cool and Air Velocity 120

Figure 8-5: Effect of Air Velocity on Seasonal COP for Varying Number of Rows at

Optimum Sub-Cool for Fixed Condenser Material Cost 122

Figure 8-6: Effect of Number of Rows on the Optimum Air Velocity and

Volumetric Flow Rate of Air Over the Condenser at Optimum Sub-

Cool for Fixed Condenser Material Cost 123

Figure 8-7: Seasonal COP vs. Varying Condenser Tube Circuiting at Optimum

Sub-Cool and Air Velocity for Fixed Condenser Material Cost 126

Figure 8-8: Refrigerant-Side Pressure Drop for Various Circuiting at 82FAmbient Temperature and at Optimum Sub-Cool and Air Velocity fo

Fixed Condenser Material Cost 127

Figure 8-9: Seasonal COP vs. Air Velocity for Varying Fin Pitch at Fixed

Condenser Material Cost and Optimum Sub-Cool 130

Figure 8-10: Effect of Fin Pitch on the Seasonal COP at Optimum Sub-Cool and

Air Velocity Over the Condenser for Fixed Condenser Material Cost131

Figure 8-11: Air-side Pressure Drop vs. Fin Pitch for Fixed Condenser Material

Cost at Optimum Sub-Cool and Air Velocity at 95F AmbientTemperature 133


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Figure 8-12: Power Requirements vs. Fin Pitch for Fixed Cost at Optimum Sub-

Cool and Air Velocity and 95F Ambient Temperature 134

Figure 8-13: Effect of Fin Pitch on Condenser Frontal Area at Optimum Sub-Cooland Air Velocity for Fixed Condenser Material Cost 136

Figure 8-14: Optimum Seasonal COP for Varying Tube Diameter at Optimum Sub-

Cool and Air Velocity for Fixed Condenser Material Cost 138

Figure 8-15: Optimum Operating Parameters for Varying Tube Diameters at Fixed

Condenser Material Cost 140

Figure 8-16: Condenser Tube Length Allocation for Varying Tube Diameters at

Optimum Air Velocity and Sub-Cool and 82 F Ambient Temperature

for Fixed Condenser Material Cost 141

Figure 8-17: Effect of Tube Diameter on Pressure Drop at Optimum Sub-Cool and

Air Velocity at 82F Ambient Temperature for Fixed CondenserMaterial Cost 143

Figure 8-18: Power Requirements for the Condenser Fan and the Compressor vs.

Tube Diameter at Optimum Air Velocity and Sub-Cool for Fixed

Condenser Material Cost and 82F Ambient Temperature 144

Figure 8-19: Operating Costs vs. Area Factor For Various Geometric Parameter

at Optimum Sub-Cool and Air Velocity with Fixed Condenser

Material Cost 146

Figure 8-20: Seasonal COP at Optimum Sub-Cool and Air Velocity for Varying

Condenser Tube Circuiting with Fixed Condenser Material Cost and

5/16Tube Outer Diameter 149

Figure 8-21: Comparison of the Effect of the Number of Tubes per Circuit on

Seasonal COP for 5/16and 3/8Outer Tube Diameters at Optimum

Sub-Cool and Air Velocity with Fixed Condenser Material Cost 150

Figure 9-1: Effect of Air Velocity Over Condenser for Varying Numbers of Rows at

Optimum Sub-Cool with Fixed Condenser Frontal Area 154

Figure 9-2: Effect of the Number of Rows of Tubes on the Seasonal COP at

Optimum Sub-Cool and Air Velocity for Fixed Condenser Frontal Area

155


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Figure 9-3: Refrigerant-Side Pressure Drop vs. Number of Rows with Fixed

Condenser Frontal Area for Optimum Sub-Cool and Air Velocity at 82 F Ambient Temperatur 157

Figure 9-4: Compressor and Condenser Fan Power for Varying Number of Rows

with Optimum Sub-Cool and Air Velocity at 82F AmbientTemperature for Fixed Condenser Frontal Area 158

Figure 9-5: Effect of Air Velocity on Seasonal COP for Varying Fin Pitch with

Optimum Sub-Cool for Fixed Condenser Frontal Area 160

Figure 9-6: Effect of Fin Pitch on the Seasonal COP at Optimum Sub-Cool and Air

Velocity for Fixed Condenser Frontal Area 161

Figure 9-7: Effect of Air Velocity For Varying Tube Diameter at Optimum Sub-Cool for Fixed Condenser Frontal Area 164

Figure 9-8: Effect of Tube Diameter on the Seasonal COP for Fixed Condenser

Frontal Area at Optimum Sub-Cool and Air Velocity 165

Figure 9-9: Refrigerant-Side Pressure vs. Tube Diameter for Fixed Frontal Area at

82F Ambient Temperature, Optimum Sub-Cool and Air Velocity 168

Figure 9-10: Power Requirements for Varying Tube Diameters with Fixed

Condenser Frontal Area at 82F Ambient Temperature, OptimumSub-Cool and Air Velocity 169

Figure 9-11: Air-Side Pressure Drop vs. Tube Diameter for Fixed Condenser

Frontal Area at 82F Ambient Temperature, Optimum Air Velocityand Sub-Cool 171

Figure 9-12: Operating Cost Factor vs. Cost Factor of Condenser Materials for

Varying Geometric Parameters with Fixed Condenser Frontal Area

and Optimum Air Velocity and Sub-Cool 172

Figure 9-13: Seasonal COP for Varying Condenser Tube Circuiting with Fixed

Frontal Area and 5/16Tube Outer Diameter at Optimum Sub-Cool

and Air Velocity 175

Figure 9-14: Comparison of the Effect of the Number of Tubes per Circuit on th

Seasonal COP for 5/16and 3/8Outer Tube Diameters with Fixed

Frontal Area at Optimum Sub-Cool and Air Velocity 178


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Figure 9-15: Operating Cost Factor vs. Condenser Material Cost Factor for

Varying Tube Diameter and Tube circuiting at Optimum Air Velocity

and Sub-Cool 180

Figure 9-16: Operating Cost Factor vs. Condenser Material Cost Factor for

Varying Geometric Parameters and Various Fixed Frontal Areas at

Optimum Air Velocity and Sub-Cool 182


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NOMENCLATURE

List of Symbols

a = Ratio of the transverse tube spacing to the tube diameter

ast = Stanton Number coefficient in the Kays and London (1984)

Correlation

ax = Axial acceleration due to gravity

A = Total heat transfer area

Ac = Minimum free-flow cross sectional area

Aci = Cross sectional area of the refrigerant-side of the tube

Afin = Total fin surface area

Afr,con = Frontal area of condenser

Amin = Minimum free-flow area

Ao = Total air-side heat transfer area including the fin and tube areas

AF = Area Factor

B = Buoyancy Modulus

B = Two-phase flow refrigerant side pressure drop Coefficient for a tube bend odegrees

bst = Stanton Number coefficient in the Kays and London (1984)

Correlation

b = Ratio of the tube spacing normal to the air flow, to the tube diameter


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C = Heat capacity

C1 = Constant of the Hiller-Glicksman refrigerant-side pressure drop

Correlation


Correlation


Correlation

cp = Specific heat at constant pressure

cp,eff = Effective specific heat at constant pressure

cp,l = Specific heat of fluid in the liquid phase

Cmin = Minimum heat capacity between that of the air and the refrigeran

Cmax = Maximum heat capacity between that of the air and the refrigerant

Cr = Ratio of the minimum heat capacity to the maximum heat capacity

Cz = Average row correction factor

cz = Individual row correction factor

CF = Cost factor

COP = Coefficient of Performance

COPseas = Seasonal Coefficient of Perfor mance

Cost = Cost of materials for the heat exchangers

CostAl = Cost per pound of Aluminu

CostCu = Cost per pound of Copper

D = Tube diameter

Ddepc = Depth of condenser in the direction of air flow

Dh = Hydraulic diameter


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d( ) = Differential change in ( )

Eu = Euler number

Eucor = Corrected Euler number

f = Friction factor

fGO = Friction factor for fluid flowing as vapor onl

fLO = Friction factor for fluid flowing as liquid only

ffin = Fin friction factor

fri = Fraction of temperature bin hours

Fr = Froude number

G = Mass flux

Gmax = Mass flux of air through the minimum flow area

gcs = Units conversion constant

h = Specific enthalpy

h1 = Specific enthalpy of refrigerant entering the compressor

h2 = Actual specific enthalpy of refrigerant exiting the compressor

h2s = Ideal specific enthalpy of refrigerant exiting the compressor

h2a = Specific enthalpy of refrigerant exiting the superheated portion of the

condenser

h2b = Specific enthalpy of refrigerant entering the sub-cooled portion of the

condenser

h3 = Specific enthalpy of refrigerant entering the expansion valve

h4 = Specific enthalpy of refrigerant exiting the expansion valve

ha = Air-side heat transfer coefficien


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hevap = Two-phase refrigerant-side evaporative heat transfer coefficien

hL = Liquid phase refrigerant side heat transfer coefficien

hr = Refrigerant-side heat transfer coefficient

hr,SP = Single phase refrigerant-side heat transfer coefficient

hTP = Two-phase refrigerant-side heat transfer coefficient

i = Temperature bin number

j = Colburn factor

JP = Parameter for the Colburn factor calculation

k = Thermal conductivity

k1 = Geometry factor for staggered tube array for the air-side pressure drop

correlation

kl = Liquid phase thermal conductivity

kb, = Two-phase flow refrigerant side pressure drop Coefficient for a tube bend

odegrees

L = Length

l = Integral variable evaporating tube length

Lcon,sa = Tube length of the saturated portion of the condenser tubes

Lcon,sc = Tube length of the sub-cooled portion of the condenser tubes

Lcon,sh = Tube length of the superheated portion of the condenser tubes

Levap,sat = Tube length of the saturated portion of the evaporator tubes

Levap,sh = Tube length of the superheated portion of the evaporator tubes

Lsat = Tube length of the saturated portion of the heat exchanger tubes

Ltot = Total tube length of the heat exchanger tubes


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m = mass

m = mass flow rate

ma,sat = mass of flow rate of air f owing over the saturated portion of the

condenser

ma,tot = total mass flow rate of air flowing over the condenser

mair = mass flow rate of air flowing over heat exchanger

mcon,sat = mass of refrigerant in the saturated portion of the condenser

mcon,sc = mass of refrigerant in the sub-cooled portion of the condenser

mcon,sh = mass of refrigerant in the superheated portion of the condenser

mes = extended surface geometric parameter

mevap,sat = mass of refrigerant in the saturated portion of the evaporator

mevap,sh = mass of refrigerant in the superheated portion of the evaporator

n = Blausius coefficien

NTU = Number of transfer units

NuD = Nusselt number based on the tube diameter

P = Pressure

pr = Reduced pressure

Prat = Ratio of the condenser saturation pressure to the evaporator saturation

pressure

Pe = Perimeter

PD = Compressor piston displacemen

Pr = Prandtl number

Q = Rate of total heat trans erred between the refrigerant and the air

.

.

.

.

.


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q = Amount of heat per unit mass transferred between the air and the

refrigerant

Qave,seas = Average cooling load of the system over all cooling load hours

qcon,sat = Amount of heat per unit mass transferred between the air and the

refrigerant in the saturated portion of the condenser

qcon,sc = Amount of heat per unit mass transferred between the air and the

refrigerant in the sub-cooled portion of the condenser

qcon,sh = Amount of heat per unit mass transferred between the air and the

refrigerant in the superheated portion of the condenser

qcst = Empirical constant for the Euler number correlation

Qe = Cooling capacity of the syste

Qmax = Maximum possible amount of heat transferred between the refrigerant and

the air

r = Outer radius of tube

rb = Radius of tube bend

Rb = Tube bend recovery length

rcst = Empirical constant for the Euler number correlati

Rcv,PD = Ratio of clearance volume to the piston displacemen

Re = Equivalent radius for a hexagonal fin

Rf,r = Refrigerant-side heat exchanger fouling factor

Rf,a = Air-side heat exchanger fouling factor

rr = Relative radius of tube bend

Rw = Tube wall thermal resistance

Re = Reynolds number

ReD = Reynolds number based on diameter

.

.


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Vol,Al,cond = Volume of the aluminum components of the condenser (fins)

Vol,Al,eva = Volume of the aluminum components of the evaporator (fins)

Vol,Cu,cond = Volume of the copper co ponents of the condenser (tubes)

Vol,Cu,evap = Volume of the copper components of the evaporator (tubes)

wa,com = Actual compressor work per unit mass of refrigeran

Wave,seas = Average electricity required by the system over all cooling load hours

Wcom = Compressor power

Wf,con = Condenser fan power

Wf,evap = Evaporator fan power

ws,com = Isentropic compressor work per unit mass of refrigeran

x = Vapor quality

xe = Vapor quality at the exit of the heat exchanger

xi = Vapor quality at the inlet of the heat exchanger

Xl = Transverse tube spacing

Xt = Tube spacing normal to air flow

Xtt = Lockhart-Martinelli Parameter

y = Equivalent length of tube bend

z = Number of rows of tubes

.

.

.


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List of Symbols with Greek Letters

= Local void fraction.

= Coefficient of the empirical relation for determining the equivalen circular radius for hexagonal fins

hlat = Change in the latent enthalpy

hsens = Change in the sensible enthalpy

htot = Change in the total enthalpy

p = Pressure drop

p a,con = Pressure drop on the air-side of the condenser

p b = Refrigerant-side pressure drop inside a tube bend

p b,LO = Refrigerant-side pressure drop inside a tube bend with all fluid flowing as a liquid

p b,SP = Single phase refrigerant-side pressure drop inside a tube bend

p b,TP = Two-phase refrigerant-side pressure drop inside a tube bend

pf = Friction component of the two-phase refrigerant-side pressure drop inside a straight tube

pfins = Air-side pressure drop due to fins

pm = Momentum component of the two-phase refrigerant-side pressure drop inside a straight tube

p S,SP = Single phase refrigerant-side pressure drop inside a straight tube

p S,TP = Two-phase refrigerant-side pressure drop inside a straight tube

p tot,ac = Total air-side pressure drop

p tubes = Air-side pressure drop due to tubes


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x = Change in quality

= Fin effectiveness

pr = Pipe roughness

= Fin parameter that is a function of the equivalent circular radius of a hexagonal fin

b2 = Physical property coefficient for the refrigerant-side pressure drop determination inside a tube bend

c = Compressor thermal efficienc

f = Fin efficienc

fan,con = Condenser fan efficiency

s = Surface efficiency

s,a = Air-side surface efficienc

s,r = Refrigerant-side surface efficienc

v = Compressor volumetric efficiency

2b,LO = Two-phase multiplier for the refrigerant side pressure drop inside tube bends

= Viscosity

l = Viscosity of the fluid in the liquid phase

m = Viscosity of the fluid evaluated at the mean fluid temperature

s = Viscosity of the fluid evaluated at the temperature of the inner tube wall surface

TP = Two-phase fluid viscosity

v = Viscosity of the fluid in the vapor phase


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= 3.14159..

= Angle of tube bend

= Density

l = Density of the fluid in the liquid phase

v = Density of the fluid in the vapor phase

= Ratio of the minimum free-flow area to the frontal area of the hea exchanger

= Coefficient of the empirical relation for determining the equivalen circular radius for hexagonal fins


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SUMMARY

Current residential air-conditioners and heat pumps use the hydrochlorofluorocarbon

refrigerant, R-22, as the working fluid. In accordance with the Montreal Protocol, a

production ban of all equipment utilizing R-22 will begin in 2005, and a total ban on the

production of R-22 is also impending. A binary zeotropic mixture, R-410a, is a strong

candidate for R-22 replacement due to its many favorable performance characteristics;

e.g., non-flammability, high working pressures, and good cycle efficiency.

Since R-410a has significantly higher working pressure and vapor densities than R-

22, current air cooled finned tube condenser designs are not appropriate. The optimum

condenser and other high-pressure-side components are expected to employ smaller

diameter tubes, which will affect other design parameters. At this time, there is limited

information about condenser coil design and optimization using R-410a as the working

fluid. Furthermore, the heat transfer and friction data are also limited.

This work includes an examination of the available refrigerant-side two-phase flow

heat transfer and pressure drop models for refrigerants. A model based on first principles

is used to predict the performance of a unitary air-conditioning system with refrigerant R-

410a as the working fluid. The seasonal coefficient of performance of the air-

conditioning system is used as the figure of merit. The primary objective of this research

was to provide guidelines for the design and optimization of the condenser coil for tw


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distinct criteria: (1) fixed condenser frontal area (size constraint), and (2) fixed

condenser material cost (capital cost constraint).

This study concludes that for both design criteria, the velocity of air flow over the

condenser ranges between 7.5 ft/s and 8.5 ft/s while the optimum sub-cooling of the

refrigerant exiting the condenser is approximately 15F. It is also concluded that

condensers employing tubes of smaller diameters yield the best system performance.

Recommendations for further research into the modeling of the in-tube condensation o

refrigerant R-410a are outlined. An exhaustive search optimization study could not be

performed due to computational speed limitations, therefore more advanced optimization

search techniques are also recommended for further study.


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CHAPTER I

INTRODUCTION

The decade of the 1990s has been a challenging time for the Heating Ventilation Air

Conditioning and Refrigeration (HVAC&R) industry worldwide. Due to their role in the

destruction of the stratospheric ozone layer, provisions of the Montreal Protocol and its

various amendments required the complete phase-out of chlorine-containing refrigerant

such as chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs). These

compounds have been used extensively as refrigerants in heat pumps, air conditioners

and refrigeration systems (Ebisu and Torikoshi, 1998). CFCs, which are characterized by

a high ozone-depletion potential (ODP), underwent a complete production phase-out in

the United States in 1995. Because HCFC-22 (chlorodifluoromethane) has been readily

available, inexpensive, and less harmful to the environment than CFCs, HCFC-22 has

been widely used in the air-conditioning and heat pump industry, especially in residential

unitary and central air-conditioning systems, for many years (Bivens et al., 1995).

However, the 1992 revision of the Montreal Protocol stipulated the first producti

ceiling for HCFCs starting in 1996 (Domanski and Didion, 1993). In the United States,

regulations published by the Environmental Protection Agency (EPA) prohibit the


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production of HCFC-22 after 2010 except for servicing equipment produced prior to

2010. The deadline is much earlier in some European countries (Gopalnarayanan and

Rolotti, 1999).

In addition, another international agreement, the Kyoto Protocol, has been initiated to

reduce the emission of greenhouse gases (GHGs) in order to lower the potential risk o

increased global warming. Representatives of more than 150 countries met in Kyoto,

Japan in December of 1997. As a result of this agreement, the nations agreed to roll back

emissions of carbon dioxide (CO2) and five other GHGs, including HFCs, to about 5.2%

below 1990 levels by 2010. Individual emissions targets were adopted for most

developed countries (Baxter et al., 1998). With CO2emissions tied directly to energ

use, the pressures for further HVAC&R equipment efficiency improvements will increase

in the early decades of the next century. At the same time, pressures from internationa

competition have continued unabated.

The choices for short-term and long-term replacements for R-22 are being driven by

environmental regulations, energy standard requirements, and the cost of implementation.

The differences in R-22 phase-out dates for the different countries seem to significantl

influence the choice of replacement refrigerants (Gopalnarayanan and Rolotti, 1999).

However, several programs are underway for evaluating R-22 alternatives. One such

industry program is the Alternative Refrigerants Program (AREP) initiated by the Air

Conditioning & Refrigeration Institute (ARI). The objective of this program is to provide

performance data on replacement refrigerants in compressors, air-conditioning syste

components and/or systems by conducting tests with participating member companies.


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Throughout the evaluation process, equipment manufacturers have made requests that the

alternatives meet several requirements. In order to meet these customer needs, a family

of alternatives has been developed for replacing R-22 (Bivens et al., 1995).

Unfortunately, no single-component HFCs have been discovered that have

thermodynamic properties close to that of R-22. Consequently, this has led to the

introduction of binary or ternary refrigerant mixtures. Several alternatives, including

binary and ternary blends of HFCs, as well as propane, are being considered as potential

R-22 replacement fluids (Gopalnarayanan and Rolotti, 1999). One very promising

replacement, from the viewpoint of zero ODP and non-flammability, is the binary

mixture, R-410a (Ebisu and Torikoshi, 1998). Note that R-410a is a near azeotropi

mixture consisting of 50% (wt%) R-32 and 50% R-125.

Besides the basic characteristics such as thermal properties and flammability, very

little heat transfer and pressure drop data for R-410a is available; although Wijaya and

Spatz (1995)have shown limited experimental data for heat transfer coefficients and

pressure drops for R-410a inside a horizontal smooth tube. Yet, knowledge of the

performance characteristics of air-cooled refrigerant heat exchangers with alternative

refrigerants is of practical importance in designing air-cooled heat exchangers required in

air-conditioning equipment. Therefore, more knowledge of the two-phase flow heat

transfer and pressure drops that occur in refrigerant R-410a heat exchangers is needed.


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Research Objectives

The primary objective of this current work is to study the design and optimization o

the operating conditions and the geometric design parameters for the air-cooled

condenser coil of a vapor compression residential air-conditioning system wit

refrigerant R-410a as the working fluid. The condenser and total system operating

conditions are varied so that the systems coefficient of performance can be evaluated as

a function of the heat exchanger design. Subsequently, it is also the intent of this stud

that the optimization methodology detailed in this work provide guidelines to the coil

designer for future design optimizations of this type. A secondary objective of this study

is to investigate various two-phase flow heat transfer and pressure drop evaluation

methods for refrigerant R-410a.


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CHAPTER II

LITERATURE SURVEY

Previous Studies on Variations of Heat Exchanger Geometric Parameter

The heat exchanger of interest for this present study is of the plate-fin-and-tube

configuration. A schematic of a typical plate-fin-and-tube heat exchanger is shown in

Figure 2-1.

Figure 2-1: Typical Plate Fin-and-Tube Cross Flow Heat Exchange

AirCrossFlow

Air CrossFlow

T= f(x,y)

Refrigerant

Flow

Refrigerant

Flow


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There have been several studies on heat exchangers of this type. Wang et al. (1999)

conducted an experimental study on the air-side performance for two specific louver fin

patterns and their plain plate fin counterparts. This study investigated the effects of fin

pitch, longitudinal tube spacing and tube diameter on the air-side heat transfer

performance and friction characteristics. This study found that for plain plate fin

configurations ranging from 8 to 14 fins per inch, the effect of longitudinal tube pitch on

the air-side was negligible for both the air-side heat transfer and pressure drop. However,

the heat transfer performance increased with reduced fin pitch.

Chi et al. (1998) conducted an experimental investigation of the heat transfer and

friction characteristics of plate fin-and tube heat exchangers having 7 mm diameter tubes.

In this study, 8 samples of commercially available plate-fin-and-tube heat exchangers

were tested. It was found that the effect of varying fin pitch on the air-side heat transfer

performance and friction characteristics was negligible for 4-row coils. However for 2-

row coils, the heat transfer performance increased with a decrease in fin pitch. This stud

used a plate-fin-and tube heat exchanger configuration with louver fin surfaces, which are

widely used in both automotive and residential air-conditioning systems. The transverse

fin spacing ranged from 21 mm to 25.4 mm and longitudinal fin spacing ranged from

12.7 mm to 19.05 mm

Wang et al. (1998) also collected experimental data on a plate-fin-and tube hea

exchanger configuration. They examined the effect of the number of tube rows, fin pitch,

tube spacing, and tube diameter on heat transfer and friction characteristics. This stud

found that the effect of fin pitch on the air-side friction pressure drop was negligibly


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7

small for air-side Reynolds numbers greater than 1000. It was also found that the hea

transfer performance was independent of fin pitch for 4-row configurations.

Furthermore, the results indicated that reducing the tube spacing and the tube diameter

produced an increase in the air-side heat transfer coefficient. The fin surfaces utilized in

this study were of the louver type, with transverse fin spacing ranging from 21 mm to

25.4 mm, and longitudinal fin spacing ranging from 12.7 mm to 19.05 mm. The

longitudinal tube spacing investigated for this studied ranged from 15 mm to 19 mm and

the tube diameters ranged from 7.94 mm to 9.52 mm.

One of the earliest and most complete investigations of heat exchanger heat transfer

and pressure drop characteristics was performed by Kays and London (1984). An

extensive amount of experimental heat transfer and friction pressure drop data were

complied for several different plate-fin-and-tube heat exchanger configurations as part of

this study. However, no optimization of the heat transfer surfaces and geometry was

performed.

Shepherd (1956) experimentally tested the effect of various geometric variations on

1-row plate fin-and-tube coils. He investigated the effects of varying the fin spacing, fin

depth, tube spacing, and tube location on the heat transfer performance of the coil. The

results of Shepherds study showed that as the fin pitch increased, the air-side hea

transfer coefficient, for a given face velocity, increased only slightly. He also found tha

as the fin depth and tube spacing increased, with all other variables constant, the air-side

heat transfer coefficient decreased. Rich (1973) studied the effect of varying the fin

spacing on the heat transfer and friction performance of multi-row heat exchanger coils.


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8

Rich found that over the range from 3 to 14 fins per inch, the air-side heat transfer

coefficient was independent of fin pitch. Neither Richs nor Shepherds investigations

involved the optimization of the heat exchanger operating conditions and geometric

parameters.

All of the above studies provide valuable insight into the effects of varying different

geometric parameters on the heat transfer and friction performance of plate-fin-tube heat

exchangers. However none of the above works investigated the effects that varying these

geometric parameters has on the optimization of a complete air-conditioning system

Previous Work in R-22 Replacement Refrigerants

Again, a major focus of this work is the study of the effect of the condenser plate-fin-

and-tube heat exchanger design parameters on the performance of a refrigerant R-410a

unitary air-conditioning system. However, as discussed in Chapter I, due to the

impending ban of refrigerant R-22 production, there is a pressing need for studies on the

performance characteristics of alternative refrigerants in air-conditioning and heat pump

systems. Therefore a survey of the previous investigations on R-22 replacemen

refrigerants in these systems is a very important part of this present study.

There has been a substantial amount of work done in the area of air-conditioning and

heat pump R-22 replacement refrigerants. Only some of the relevant studies are

mentioned here. Radermacher and Jung (1991) conducted a simulation study of potential

R-22 replacements in residential equipment. The coefficient of performance (COP) and


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9

the seasonal performance factor (SPF) were calculated for binary and ternary substitutes

for R-22. They found that for a ternary mixture of R-32/R-152a/R-124 with a weight

concentration of 20 wt%/20 wt%/60 wt%, the COP was 13.7% larger and the compressor

volumetric capacity was 23% smaller than the respective values for R-22. This stud

found that in general, based on thermodynamic properties only, refrigerant mixtures have

the potential to replace R-22 without a loss in efficiency. Efficiency gains are possible

when counterflow heat exchangers are used and additional efficiency gains are possible

when capacity modification is employed.

Kondepudi (1993) performed experimental drop-in(unchanged system, same heat

exchangers) testing of R-32/R-134a and R-32/R-152a blends in a two-ton split-system air

conditioner. Five different refrigerant blends of R-32 with R-134a and R-152a were

tested as drop-inrefrigerants against a set of R-22 baseline tests for comparison. No

hardware changes were made except for the use of a hand-operated expansion device,

which allowed for a drop-incomparison of the refrigerant blends. Hence, other than

the use of a different lubricant and a hand-operated expansion valve, no form of

optimization was performed for the refrigerant blends. Parameters measured included

capacity, efficiency, and seasonal efficiency. The steady state energy efficiency ratio

(EER) and seasonal efficiency energy efficiency ratio (SEER) of all the R-32/R-134a and

R-32/R-152a blends tested were within 2% of those for a system using R-22. The 40

wt%/60 wt% blend of R-32/R-134a performed the best in a non-optimized system.

Fang and Nutter (1999) evaluated the effects of reversing valves on heat pump system

performance with R-410a as the working fluid. A traditional reversing valve enables a


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10

heat pump to operate in either the heating mode or cooling mode. It performs this

function by switching the refrigerant flow path through the indoor and out door coils,

thus changing the functions of the two heat exchangers. However, use of reversing

valves causes increased pressure drops, refrigerant leakage from the high pressure side to

the low pressure side, and undesired heat exchange. This study measured the overal

effects of a reversing valve on a 3-ton heat pump system using R-410a and made

comparisons to the same valves performance with R-22 as the working fluid. It was

found that changing from refrigerant R-22 to R-410a resulted in an increase in mass

leakage, but did not significantly change the effect that the reversing valve had on the

system COP.

Domanski and Didion (1993) evaluated the performance of nine R-22 alternatives.

The study was conducted using a semi-theoretical model of a residential heat pump with

a pure cross-flow representation of heat transfer in the evaporator and condenser

(Domanski and Mclinden, 1992). The models did not include transport properties since

they carried the implicit assumption that transport properties (and the overall heat transfer

coefficients) are the same for the fluids studied. Simulations were conducted for drop-

inperformance, for performance in a modified system to assess the fluidspotentials,

and for performance in a modified system equipped with a liquid line/suction-line hea

exchanger. The simulation results obtained from the drop-inevaluation predicted the

performance of candidate replacement refrigerants tested in a system designed for the

original refrigerant, with a possible modification of the expansion device. The drop-in

model evaluations revealed significant differences in performance for high-pressure


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11

fluids with respect to R-22 and indicated possible safety problems if those fluids were

used in unmodified R-22 equipment. The simulation results obtained from the constant-

heat-exchanger-loading evaluation corresponded to a test in a system modified

specifically for each refrigerant to obtain the same heat flux through the evaporator and

condenser at the design rating point. This simulation constraint ensures that the

evaporator pressures are not affected by the different volumetric capacities of the

refrigerants studied. The results for the modified system performance showed tha

capacity differences were larger for modified systems than for the drop-inevaluation.

However, none of the candidate replacement refrigerants exceeded the COP of R-22 at

any of the test conditions.

Bivens et al. (1995) compared experimental performance tests with ternary and binary

mixtures in a split system residential heat pump as well as a window air-conditioner.

This study investigated refrigerants R-407c, a ternary zeotropic mixture of 23 wt% R-32,

25 wt% R-125 and 52 wt% R-134a, and R-410b, a near azeotropic binary mixture

composed of 45 wt% R-32 and 55 wt% R-125 as working fluids. The heat pump used for

the evaluations was designed to operate with R-22 and was equipped with a fin-and-tube

evaporator with 4 refrigerant flow parallel circuits, and a spined fin condenser with 5

circuits and 1 sub-cooling circuit. It was found that R-407c provided essentially the same

cooling capacity as compared with R-22 with no equipment modification. R-410b

provided a close match in cooling capacity using modified compressor and expansion

devices. The energy efficiency ratio for R-407c versus R-22 during cooling ranged from

0.95 to 0.97. The energy efficiency ratio for R-410b versus R-22 during cooling ranged


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12

from 1.01 to 1.04. Window air-conditioner tests were conducted with R-407c in three

window air-conditioners ranging in size from 12,000 to 18,000 Btu/hr. The result

demonstrated equivalent capacity and energy efficiency ranging from 0.96 to 0.98

compared with R-22.

In summation, in the search for a replacement for refrigerant R-22 many refrigerants

have been studied. As discussed throughout this work, many of those studied are

refrigerant mixtures. A list of many of the refrigerant mixtures studied by the sources

sited in this literature survey is shown in Table 2-1.

Table 2-1: List of Refrigerant R-22 Alternative Refrigerant Mixtures

Refrigerant Weight Percent

R-410a R-32/50%, R-125/50%

R-407b R-32/45%, R-125/55%

R-407c R-32/23%, R-125/25%, R-134a/52%

Radermacher and Jung(1991)

R-132/20%, R-R-152a/20%, R-124/60%

Kondepudi (1993) R-32/40%, R-134a/60%


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13

As a result of many of the studies discussed in this literature survey, refrigerant R-410a

has emerged as the primary candidate to replace R-22 in many industrial and residential

applications. There is at least one commercially available air-conditioning system using

R-410a as the working fluid, which is made by Carrier. Therefore, as discussed in

Chapter I, R-410a is the refrigerant of interest for this current study.

Two-Phase Flow Regime Considerations in Condenser and Evaporator Design

The prediction of flow patterns is a central issue in two-phase gas-liquid flow in hea

exchangers. Design parameters such as pressure drop and heat and mass transfer are

strongly dependent on the flow pattern. Hence, in order to accomplish a reliable design

of gas-liquid systems such as pipelines, boilers and condensers, ana prioriknowledge of

the flow pattern is needed (Dvora et al., 1980).

Figure 2-2 shows one version of the commonly recognized flow patterns for two-

phase flow inside horizontal tubes. Description of these patterns is highly subjective, of

course, and there is some variation among researchers in the field concerning the

characterization of the various patterns. However, the essential situation is this: For

ordinary fluids under ordinary process conditions, two forces control the behavior and

distribution of the phases. These forces are gravity, always acting towards the center o

the earth, and vapor shear forces, acting on the vapor-liquid interface in the direction o

motion of the vapor. When gravity forces dominate (usually under conditions of low

vapor and liquid flow rates), one obtains the stratified and wavy flow patterns shown


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14

Figure 2-2: Horizontal Two-Phase Flow Regime Patterns


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15

in Figure 2-2. When vapor shear forces dominate (usually at high vapor flow rates), one

obtains the annular flow pattern (with or without entrained liquid in the core) shown on

the diagram. When the flow rates are very high and the liquid mass fraction dominates,

the dispersed bubble flow pattern is obtained, which is a shear-controlled flow of som

importance in boiler design but of very limited interest in condensers. Intermediate flow

rates correspond to patterns in which both gravitational and vapor shear forces are

important (Bell, 1988).

Although extensive research on flow patterns has been conducted, most of this

research has been concentrated on either horizontal or vertical flow. For horizontal flow

the earliest and perhaps the most durable, and best known of pattern maps for two-phase

gas-liquid flow was proposed by Baker (1954). Taitel and Dukler (1976) proposed a

physical model capable of predicting flow regime transition in horizontal and near

horizontal two-phase flow.

There are several points that need to be emphasized concerning the use of any flow

pattern map (Bell, 1988):

1. The definition of any two-phase flow pattern is highly subjective and differen

observers may disagree upon exactly what they are looking at. Adding to this

ambiguity are the various means of measuring two-phase flows and the resulting

different criteria that are used to characterize two-phase flows.

2. The boundaries drawn on a map as lines should be viewed as very broad

transition regions from one well defined flow pattern to another.


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17

assumed that the shear at the edge of the condensate film is directly proportional to the

pressure drop. This shear was expressed in terms of a constant friction factor and the

vapor velocity. Consequently, Nusselt succeeded in obtaining a correlation for the hea

transfer coefficient, which applies if the condensate is in laminar flow. However there

are significant discrepancies between Nusselts theory and the experimental data when

the condensate flow becomes turbulent or when the vapor velocity is very high (Soliman

et al., 1968).

Soliman et al. (1968) develop a model for two-phase flow heat transfer that includes

the contribution of the gravity, momentum and frictional terms to the wall shear stress.

In this work, a general correlation for the condensation heat transfer coefficient in the

annular flow regime was developed. The major assumption used in the development o

this correlation was that the major thermal resistance is in the laminar sublayer of the

turbulent condensate film. Experimental data for several fluids (including steam,

refrigerant R-22, and ethanol) was used to determine empirical coefficients and

exponents. This correlation predicts the experimental data within25%.

Yet another semi-empirical condensation heat transfer correlation for annular flow

was developed by Akers et al. (1959). Correlations for both the local and average values

of the condensation heat transfer coefficient were developed in the Akers study. The

Akers correlation predicts the experimental heat transfer coefficients generated b

Soliman et al. (1968), within 35%.

Traviss et al. (1973) applied the momentum and heat transfer analogy to an annular

flow model using the von Karman universal velocity distribution to describe the liquid


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18

film. Since the vapor core is very turbulent in this flow regime, radial temperature

gradients were neglected, and the temperatures in the vapor core and at the liquid-vapor

interface were assumed to be equal to the saturation temperature. Axial heat conduction

and sub-cooling of the liquid film were also neglected. An order of magnitude analysis

and non-dimensionalization of the heat transfer equations resulted in a simple

formulation for the local heat transfer coefficient. The analysis was compared to

experimental data for refrigerants R-12 and R-22 in a condenser tube, and the results

were used to substantiate a general equation for forced convection condensation. Since

the heat transfer analysis assumed the existence of annular flow, the sensitivity of this

analysis to deviations from the annular flow regime is important. When the mass flux of

the refrigerant vapor exceeded 500,000 lbm/hr-ft2, there is appreciable entrainment of

liquid in the upstream portion of the condenser tube. Since the analysis assumed tha

annular film condensation exists and that all of the liquid is on the tube wall, analytical

predictions are below the experimental data in the dispersed or misty flow regime.

However, the entrainment of liquid is not very large because the main resistance to hea

transfer occurs in the laminar sublayer, and liquid removed from the turbulent zone di

not increase the heat transfer coefficient in direct relation to the amount of liquid

removed. Yet, according to the experimental data collected and analyzed by Singh et al.

(1996), the mean deviation for the Traviss correlation deviates by -%40 from the data.

The above correlations were developed for one specific flow regime (annular flow).

However, in many instances a correlation that is applicable to more than one flow regime

is needed. Shah (1979) developed a very simple dimensionless correlation, which he


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20

considerable uncertainty. Simpler forms or firmer theoretical bases for predictive

methods can only be achieved with a narrowing of the ranges of applicability (Beattie and

Whalley, 1982).

Early two-phase flow studies emphasized the development of overall pressure drop

correlations encompassing all types of flow regimes. Furthermore, most of the

experimental data were obtained from relatively small and short pipes (Chen and

Spedding, 1981). Hence, no satisfactory general correlation exists. For several years,

experimental pressure drop data have been collected for horizontal gas-liquid systems,

and many attempts have been made to develop, from the data, general procedures for

predicting these quantities. Errors of about 20% to 40% can be expected in pressure-drop

prediction, and even this range is optimistic if one attempts to use the various predictive

schemes without applying a generous measure of experience and judgment. A major

difficulty in developing a general correlation based on statistical evaluation of data is

deciding on a method of properly weighing the fit in each flow regime. It is difficult to

decide, for instance, whether a correlation giving a good fit with annular flow and a poor

fit with stratified flow is a better correlation than one giving a fair fit for both kinds o

flow (Russell et al., 1974).

Lockhart and Martinelli (1949) developed one of the first general correlations.

Although various other general correlations have since been proposed the original

Lockhart-Martinelli approach is still in many respects the best. As discussed by Chen

and Spedding (1981), this method continues to be one of the simplest procedures for

calculating two-phase flow pressure drop. One of the biggest advantages of thi


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procedure is that it can be used for all flow regimes. For this flexibility, however,

relatively low accuracy must be accepted. Detailed checks with extensive data have

shown that the correlation overpredicts the pressure drop for the stratified flow regime

(Baker, 1954); it is quite reasonable for slug and plug flow (Dukler et al., 1964); and for

annular flow, it underpredicts for small diameter pipes (Perry, 1963), but overpredicts for

larger pipes (Baker, 1954).

Souza et al. (1993) developed a correlation for two-phase frictional pressure drop

inside smooth tubes for pure refrigerants using the Lockhart-Martinelli parameter,Xtt (the

square root of the ratio between the liquid only pressure drop and the vapor only pressure

drop), the Froude number, Fr, and experimental data. The pressure drop due to

acceleration was calculated using the Zivi (1964) equation for void fraction. A single

tube evaporator test facility capable of measuring pressure drop and heat transfer

coefficients inside horizontal tubes was utilized, and pressure drop data were collected.

During the tests, the predominant flow pattern observed was annular flow. For lower

mass fluxes and qualities, stratified-wavy, and semi-annular flow patterns were also

observed. The resulting correlation of experimental data for refrigerants R-134a and R-

12 for turbulent two-phase flow predicted the pressure drop within 10%.

Chisolm (1973,1983) has published important results on pressure drop and has

improved several correlations that predicted the frictional pressure drop during two-phase

flow for many different fluids. According to the data collected by Souza et al. (1993),

Chisolms two-phase flow multipliers overpredicted the experimental data for low

qualities and slightly underpredited those for high qualities. Overall, Chisolms


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correlation for friction pressure drop predicts the experimental values within 30% with a

mean deviation of 14.7%.

Jung and Radermacher (1989) developed a correlation for pressure drop during

horizontal annular flow boiling of pure and mixed refrigerants. For this correlation, a

two-phase multiplier based on total liquid flow was introduced for the total pressure drop

(frictional and acceleration pressure drop) and was correlated as a function of the

Lockhart and Martinelli parameter, Xtt. However, Jung and Radermachers correlation

overpredicts the experimental data by an average of 29%.

In summary, the general correlation procedures yield fair predictions of pressure drop

for all flow regimes because they are based on a large amount of correlatable data.

However, when these correlations are applied to systems other than those used in their

development, or to flow over extended distances (fully established flow), predicted

pressure drops can be in error by as much as a factor of 2. For more reliable predictions

of pressure drop, correlations based on specific models for individual flow regimes are

preferable, yet difficult to model analytically without concrete knowledge of the quality

distribution throughout the tubes (Greslpvoch & Shrier, 1971).


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24

Figure 3-1: The Actual Vapor-Compression Refrigeration Cycle

SaturatedSub-cooled Superheated

2b 2a3

ExpansionValve

Saturated Superheated

4 4a

Compressor

Condenser

Evaporator

1

2

S

T


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25

temperature (State 2b), and then cooled to below the saturation point until only sub-

cooled liquid is present (State 3). The high pressure liquid is then forced through the

expansion valve into the evaporator (State 4). The refrigerant then absorbs heat from

warm indoor air that is blown over the evaporator coils. The refrigerant is completel

evaporated (State 4a) and heated above the saturation temperature before entering the

compressor (State 1). The indoor air is cooled and dehumidified as it flows over the

evaporator and returned to the living space.

System Component Models

Compressor

The purpose of the compressor is to increase the working pressure of the refrigerant.

The compressor is the major energy-consuming component of the refrigeration system,

and its performance and reliability are significant to the overall performance of the

HVAC system. In general there are two categories of compressors: dynamic compressors

and displacement compressors. Dynamic compressors convert angular momentum into

pressure rise and transfer this pressure rise to the vapor (McQuiston and Parker, 1994).

Positive displacement compressors increase the pressure of the vapor by reducing the

volume. For this study scroll type positive displacement compressors, which dominate

the residential air-conditioning industry, are utilized.

The amount of specific work (work per unit mass of refrigerant) done by an ideal

compressor can be expressed with the following:


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27

where Pratis the pressure ratioand Tratis the temperature ratio, which are defined by

the following relationships,

The coefficients in this correlation are based on saturated temperatures and not on the

actual temperatures at the inlet and outlet of the compressor.

The volumetric efficiency is another important consideration in selecting and

modeling compressors. The volumetric efficiency is the ratio of the mass of vapor that is

compressed to the mass of vapor that could be compressed if the intake volume were

equal to the compressor piston displacement. The volumetric efficiency is expressed as:

evapsat

condsat

ratP

PP

,

,= (3-4)

evapsat

condsat

ratTTT

,

,= (3-5)


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where vis the compressor volumetric efficiency, Rcv,pdis the ratio of clearance volume

to the piston displacement, and v is the specific volume. The volumetric efficiency is

also used to determine the mass flow rate of the refrigerant though the compressor, m, for

a given compressor size by the following expression,

where PD is the Piston Displacement (Threlkeld, 1970).

Condenser

The condenser is a heat exchanger that rejects heat from the refrigerant to the outside

air. Although there are many configurations of heat exchangers, finned-tube hea

= 1

v

v1

2

1,v pdcvR (3-6)

2v

PDm v

= (3-7)

.


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29

exchangers are the type most commonly used for residential air conditioning applications.

Refrigerant flows through the tubes, and a fan forces air between the fins and over the

tubes. The heat exchangers used in this study are of the cross-flow, plate-fin-and-tube

type. A schematic of this heat exchanger is shown in Figure 3-2. The plate fins are

omitted from the schematic for simplicity.

When the refrigerant exits the compressor, it enters the condenser as a superheated

vapor and exits as a sub-cooled liquid. The condenser can be separated into three

sections: superheated, saturated, and sub-cooled. The amount of heat per unit mass o

refrigerant rejected from each section can be expressed as the difference between the

refrigerant enthalpy at the inlet and at the outlet of each section:

and

,22, ashcon hhq = (3-8)

,22, basatcon hhq = (3-9)

.32, hhq bsccon = (3-10)


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30

Figure 3-2: Typical Cross Flow Heat Exchanger (fins not displayed)

Horizontal

TubeSpacing

Air CrossFlow

Vertical TubeSpacing

Width

Depth

Height

row 1 row 2 row 3

1 Refrigerant FlowParallel Circuit

3 Tubes per Circuit


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31

The total heat rejected from the hot fluid, which in this case is the refrigerant, to the

cold fluid, which is the air, is dependent on the heat exchanger effectiveness and the hea

capacity of each fluid:

where is the heat exchanger effectiveness; Cminis the smaller of the heat capacities o

the hot and cold fluids, Chand Ccrespectively; Th,iis the inlet temperature of the hot

fluid; and Tc,iis the inlet temperature of the cold fluid. The heat capacity C, is expressed

as

where m is the mass flow rate of fluid and cpis the specific heat of the fluid. The hea

capacity, C, is the extensive equivalent to the specific heat, and it determines the amoun

of heat a substance absorbs or rejects when the temperature changes.

( )icih TTCQ ,,min = (3-11)

pcmC =(3-12)

.


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33

mass flow is separated into a number of discrete tubes and does not mix between fluids.

Furthermore, the plates of the heat exchanger prevent mixing of the air flowing over the

fins. Therefore, air at one end of the heat exchanger will not necessarily be the same

temperature as the air at the other end. For a cross flow heat exchanger with both fluids

unmixed, the effectiveness can be related to the number of transfer units (NTU) with the

following expression (Incropera & DeWitt, 1996):

where Cris the heat capacity ratio,

( ) ( )( )[ ] ,1exp1exp1 78.022.0

= NTUCNTU

Cr

r

(3-15)

.max

min

C

CCr= (3-16)


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34

In the saturated portion of the condenser, the heat capacity on the refrigerant side

approaches infinity and the heat capacity ratio, Crgoes to zero. When Cris zero, the

effectiveness for any heat exchanger configuration is expressed as

The NTU is a function of the overall heat transfer coefficient, U, and is defined as

where A is the heat transfer area upon which the overall heat transfer coefficient, U, is

based. The overall heat transfer coefficient accounts for the total thermal resistance

between the two fluids and is expressed as follows.

( ).exp1 NTU= (3-17)

,minC

UA

NTU=(3-18)


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35

where Rf,(a or r)is the fouling factor, Rwis the wall thermal resistance, s(a or r)is the

surface efficiency, andh is the heat transfer coefficient. There are no fins on the

refrigerant side of the condensing tubes; therefore, the refrigerant side surface efficiency

is 1. Neglecting the wall thermal resistance, Rw(this value is usually 3 orders o

magnitude lower than the other resistances), and the fouling factors, R f,(a or r), the overall

heat transfer coefficient reduces to:

The methodology for determining the refrigerant and air-side heat transfer coefficients

are discussed Chapter IV and Chapter V, respectively.

To determine the overall surface efficiency for a finned tube heat exchanger, it is firs

necessary to determine the efficiency of the fins as if they existed alone. For a plate-fin-

,111

,,

"

,

,

"

,

, rrrsrrs

rf

w

aas

af

aaas AhA

RR

A

R

AhUA ++++= (3-19)

.11

1

,

+=

rraaas AhAhUA

(3-20)


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36

and-tube heat exchanger with multiple rows of staggered tubes, the plates can be evenly

divided into hexagonal shaped fins as shown in Figure 3-3. Schmidt (1945) analyzed

hexagonal fins and determined that they can be treated as circular fins by replacing the

outer radius of the fin with an equivalent radius. The empirical relation for the equivalen

radius is given by

where r is the outside tube radius. The coefficients and are defined as

and

( ) ,3.027.1 2/1= rRe (3-21)

r

Xt

2=

(3-22)

,4

1

2/12

2

+= tl

t

XXX

(3-23)


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37

Figure 3-3: Hexagonal Fin Layout and Tube Array

Xt Tube Spacing

Normal to Air

Flo

Air Flow

Transverse Tube

Spacing

Xl


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38

where Xlis the tube spacing in the direction parallel to the direction of air flow, and X tis

the tube spacing normal to the direction of air flow.

Once the equivalent radius has been determined, the equations for standard circular

fins can be used. For this study, the length of the fins is much greater than the fin

thickness. Therefore, the standard extended surface parameter, escan be expressed as,

where hais the air-side heat transfer coefficient, k is the thermal conductivity of the fin

material, Pe is the fin perimeter, cis the fin cross sectional area, and t is the thickness o

the fin. For circular tubes, a parameter can be defined as

,2Pe

2/12/1

=

=

kt

h

kA

hm a

ces (3-24)

.ln35.011

+

=r

R

r

R ee (3-25)


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39

The fin efficiency, f, for a circular fin is a function of es, Re, and f, and can be

expressed as

The total surface efficiency of the fin, sis therefore expressed as

where Afinis the total fin surface area, Aois the total air-side surface area of the tube and

the fins.

( ).

tanh

ees

ees

fRm

Rm= (3-26)

( ),11 fo

fin

sA

A = (3-27)


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40

Condenser Fan

Natural convection is not sufficient to attain the heat transfer rate required on the air-

side of the condenser used in a reasonably sized residential air-conditioning system.

Therefore a fan must be employed to maintain the airflow at a sufficient rate of speed.

Although much of the power consumed by the total system is due to the compressor, the

condenser fan also requires a significant amount of power. The power required by the

fan is directly related to the air-side pressure drop across the condenser and to the

velocity of air across the condenser:

where Va,conis the air velocity over the face of the condenser, Pa,conis the air-side

pressure drop over the condenser, Afr,conis the frontal area of the condenser, and fan,conis

the condenser fan efficiency. Calculations for the air-side pressure drop are discussed in

Chapter V.

Expansion Valve

The expansion valve is used to control the refrigerant flow through the system

Under normal operating conditions, the expansion valve opens and closes in order to

confan

confrconacona

conf

APVW

,

,,,

,

= (3-28)


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maintain a fixed amount of superheat in the exit of the evaporator. In this study, the

superheat will be maintained at the typical 10F. Because the expansion valve can only

pass a limited volume of refrigerant, it cannot maintain the specified superheat at the

evaporator exit if the refrigerant is not completely condensed into liquid. If incomplete

condensation in the condenser occurs, the vapor refrigerant backs up behind the

expansion valve and the pressure increases until the refrigerant is fully condensed. As a

result, the expansion valve cannot regulate the refrigerant mass flow rate, and canno

maintain a fixed superheat at the evaporator exit. The energy equation shows that the

enthalpy is constant across the expansion valve.

Evaporator

The purpose of the evaporator is to transfer heat from the room air in order to lower

its temperature and humidity. Because the refrigerant enters the evaporator as a liquid-

vapor mixture, it is only divided into saturated and superheated sections. No sub-cooled

section is necessary. The analysis of the thermodynamic parameters of the evaporator is

43 hh =(3-29)


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where cpis the specific heat ratio for dry air and cp,effis the effective specific heat. To

maintain indoor humidity, the latent heat accounts for approximately 25% of the tota

enthalpy change of the air flowing over an evaporator. The effective specific heat can

thus be expressed in terms of the specific heat for dry air only,

Evaporator Fan

Because the evaporator is not the primary focus of this study, introducing wet coils

would present unwelcome complications in the overall analysis. In addition to affecting

the heat transfer, wet coils also have an effect on the air-side pressure drop. Although

there are correlations available for determining the pressure drop over wet coils, they are

cumbersome to use and again, the evaporator is not the primary focus of this

investigation.

After the air flows over the evaporator, it enters a series of ducts that then return the

air back inside the living space. The power required by the evaporator fan depends on

the losses in these ducts and can vary from configuration to configuration. Therefore, the

.33.1

75.0

25.0, p

tot

senslatpeffp c

h

h

T

hcc =

+= (3-33)


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default power requirement used by the Air-conditioning and Refrigeration Institute (ARI,

1989) of 365 Watts per 1000 ft3/minute of air will be used.

Refrigerant Mass Inventory

The degrees of sub-cooling at the condenser exit are controlled by the syste

operating conditions and the quantity of refrigerant mass in the system, as is discussed

further in Chapter VI. The mass of refrigerant in the tubes connecting the components is

neglected. Since the compressor contains only vapor, the mass of refrigerant in the

compressor is also neglected. Therefore the total mass of the system includes the mass o

refrigerant in the sub-cooled, saturated, and superheated portions of the condenser, and in

the saturated and superheated portions of the evaporator.

The following text outlines the procedure for finding the refrigerant mass in the

saturated portion of the evaporator. The same procedure is also used to determine the

mass of refrigerant in the saturated portion of the condenser, however the boundary

conditions are different

The mass of refrigerant can be expressed as

.v

=L

cidlAm (3-34)


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where, Aci is the cross sectional area of the refrigerant-side of the tube, and v is the

specific volume, which at saturated conditions is a function of quality expressed as

The boundary conditions for the saturated portion of the evaporator are

and

( ) ( ) .v1vv vl xx += (3-35)

( ) ixlx == 0(3-36)

1)( ==Llx (3-37)


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where lis integral variable evaporating tube length and L is the total evaporating tube

length. Using the boundary conditions and assuming the quality varies linearly with tube

length, the following expression results

Substituting (3-38) into (3-35) yields an expression for the specific volume as a functi

of length,

For a uniform cross sectional area, substituting (3-39) into (3-34) yields

( ) .1

ii xl

L

xlx +

= (3-38)

( ) ( ) ( ).vv1

vvvv lvi

lvilL

xlxl

++= (3-39)


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The mass of refrigerant in the superheated portions of the condenser and evaporator are

expressed simply as:

and

Finally, the mass of refrigerant in the sub-cooled section of the condenser is expressed as

shconcivshcon LAm ,, = (3-43)

.,, shevapcivshevap LAm = (3-44)

( )( ) ( )

.

vvv

vln

vv1

,,

+

=llvi

v

lvi

evapsatci

evapsat

xx

LAm

(3-42)


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.,, scconcivsccon LAm = (3-45)


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CHAPTER IV

REFRIGERANT SIDE HEAT TRANSFER COEFFICIENT AND PRESSURE

DROP MODELS

Single Phase Heat Transfer Coefficient

For a constant surface heat flux for single phase laminar flow, the Nusselt number can

be approximated by the following expression.

In the turbulent region, however, there are a number of expressions available for the

Nusselt number. One of the more commonly used correlations for turbulent flow is the

Dittus-Boelter equation. This correlation is valid for fully developed flow in circular

36.4=DNu (4-1)


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tubes with moderate temperature variations (Incropera & DeWitt, 1996). For refrigeran

cooling in a condenser, the Dittus-Boelter equation is expressed as

This mathematical relation has been confirmed by experimental data for the following

conditions:

0.7 Pr 160

ReD10,000

L/D 10

In the sub-cooled portion of the condenser in this study, the temperature difference at the

inlet and exit is usually less than 20F, and the moderate temperature variation

assumption is valid. However in the superheated portion of the condenser, the inlet and

exit temperatures can differ by as much as 90F. Therefore, the temperature difference

between the air flowing over the tubes and the refrigerant flowing inside the tubes is

large. This causes the temperature difference between the inner surface of the tubes and

the refrigerant to also be large in the superheated portion of the condenser. Thus, under

these conditions, the Dittus-Boelter equation is less accurate.

.PrRe023.0 3.08.0DDNu = (4-2)


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Yet another Nusselt number correlation for single phase turbulent flow has been

developed by Sieder and Tate(1936). This correlation was developed for a large range of

property variations based on the mean fluid temperature and the wall surface temperature,

and is expressed as

where all properties except for sare evaluated at the mean fluid temperature, and sis

evaluated at the temperature of the inner tube wall surface. Again, since this model is

developed for a large range of property variations, it is valid for larger temperature

differences within the fluid flowing inside the tube.

Kays and London (1984) have also developed a heat transfer correlation for single

phase turbulent flow. This correlation was developed using empirical data taken from a

variety of refrigerants in circular heat exchanger tubes under several thermodynamic

conditions. Unlike most heat transfer correlations, Kays and London have developed the

equations for the transition region between laminar and turbulent flow. The correlation is

expressed as:

,PrRe027.0

14.0

3/18.0

= sm

DDNu

(4-3)


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Figure 4-1: Refrigerant-Side Single Nusselt Number vs. Reynolds Numbe

0

20

40

60

80

100

120

140

0 5000 10000 15000 20000 25000

Reynolds Number

Nusse

ltNumb

er

Laminar, ConstantHeat Flux

Kays and Londo

Dittus Boelter

Sieder and Tate

TransitionLaminar

Turbulent

Dittus-Boelter

Sieder & Tate

Kays &

Londo

Kays &

Londo


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tube diameter of 0.2885 in, with refrigerant R-410a flowing as superheated vapor at a

mean temperature of 140 F and a pressure of 395 psia (conditions typically found in the

superheated portion of the condenser for this study). In the turbulent region, the value o

the Nusselt number calculated using the Kays and London correlation is on average about

70% higher than the Nusselt numbers calculated using both the Dittus-Boelter and the

Sieder and Tate correlations. This is due to the fact that both the Sieder and Tate and

Dittus-Boelter equations have assumed a smooth pipe. However the Kays and London

correlation was developed with experimental data taken from actual heat exchangers

which employ tubes with rougher surfaces. Because the Kays and London relation is

based on experimental data taken directly from heat exchangers similar to those

investigated in this work, and because the issue of the transition from laminar to turbulent

flow has been addressed, this correlation is used.

Condensation Heat Transfer

As discussed in Chapter II, the hea transfer coefficient in two-phase flow is

dependent on the flow regimes that are present. Annular flow is generally assumed to be

the dominant flow pattern existing over most of the condensing length during bot

horizontal and vertical condensing inside tubes (Soliman et al., 1968). Baker (1954) and

Gouse (1964) have derived flow pattern maps from numerous data, and have verified the

validity of this assumption. In most cases, annular flow is established soon after

condensation begins, and continues to very low quality. For horizontal condensing,


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gravity-induced stratification exists at low quality, but this usually occupies only a small

portion of the overall condensing length (Soliman et al., 1968). Annular flow is a

particularly important flow pattern since for a wide range of pressure and flow

conditions, and it occurs over a major part of the mass quality range, from 0.1 up to unity

(Collier & Thome, 1996). Therefore, heat transfer correlations developed for annular

flow, in addition to a correlation developed for all flow regimes, are considered for use in

this present study.

Two-phase flow heat transfer correlations developed by Traviss et al. (1973), Akers e

al. (1959), and Shah (1979) are evaluated for this current work. The correlations o

Akers et al. and Traviss et al. were developed for annular flow, while the Shah correlation

is proposed to be applicable to all flow regimes. Figure 4-2 shows the condensation hea

transfer coefficients for refrigerant R-12 calculated from the correlations of Shah, Traviss

et al., and Akers et al., versus the total mass flux. The figure also shows experimenta

condensation heat transfer coefficients for refrigerant R-12 taken from experimental data

collected by Eckels and Pate (1991). Using the parameters designated by the Baker

(1954) flow regime map, it is determined that for the experimental conditions of Eckels

and Pate, a slug flow pattern exists for mass fluxes between 100 and 250 kg/m2-s, and an

annular flow regime exists for mass fluxes greater than 250 kg/ 2-s. As Figure 4-2

shows, the Traviss correlation overpredicts the experimental data for the entire range o

mass fluxes shown. The Akers and Shah correlations slightly underpredict the

experimental values for relatively low mass fluxes and slightly overpredict the

experimental data at higher mass fluxes (annular flow).


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The fact that the Traviss correlation greatly overpredicts the experimental data for

when the flow regime is annular is surprising since this correlation was developed for

annular flow. The Akers correlation predicts the experimental data to within an average

14.3% while the Shah correlation predicts the experimental data to within an average o

14.7%. Therefore the Shah and Akers correlations are in good agreement with each

other, and are both more accurate than the Traviss correlation for the conditions

investigated.

Using the parameters of the Baker (1954) flow regime map, and the typical operating

conditions of the condenser studied in this present work (mass fluxes approximately

greater than or equal to 400 kg/ 2-s or 300,000 lbm/ft2-hr), it is determined that the

dominant flow regime is indeed annular. However, this study also finds that for low

qualities, stratified-wavy flow exists. As a result, the use of a general correlation that is

valid for more than one flow regime is advantageous for the work of this investigation.

Therefore, the correlations developed by Akers et al. and Traviss et al., are not used.

Hence, the two-phase flow heat transfer correlation developed by Shah is used for this

investigation.

The two-phase flow heat transfer model developed by Shah is a simple correlation

that has been verified over a large range of experimental data. In fact, experimental data

from over 20 different researchers has been used in its development. The model has a

mean deviation of about 15% and has been verified for many different fluids, tube sizes,

and tube orientations.


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For this model, at any given quality, the two-phase heat transfer coefficient is defined

as:

wherehTPis the two-phase flow heat transfer coefficient, x is the quality,hLis the liquid

only heat transfer coefficient, and p ris the reduced pressure. By integrating the

expression (4-6) over the length of the tube, the mean

plate -fin-tube condenser performance

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