plate-fin-and-tube condenser performance...

PLATE-FIN-AND-TUBE CONDENSER PERFORMANCE AND DESIGN FOR REFRIGERANT R-410A AIR-CONDITIONER

A ThesisPresented 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 TechnologMay 2000

ii

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____________________

iii

TABLE OF CONTENTS

LIST OF TABLES vi

LIST OF ILLUSTRATIONS vii

NOMENCLATURE xiiList of Symbols xii

List of Symbols with Greek Letters

SUMMARY xxiii

CHAPTER I: INTRODUCTION 1Research Objectives 4

CHAPTER II: LITERATURE SURVEY 5Previous 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 COMPONENTMODELING 23

Refrigeration Cycle 23

System Component Models 25Compressor 25Condenser 28Condenser Fan 40Expansion Valve 40Evaporator 41Evaporator Fan 44

iv

Refrigerant Mass Inventory 45

CHAPTER IV: REFRIGERANT-SIDE HEAT TRANSFER COEFFIECIENTAND PRESSURE DROP MODELS 51

Single 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 PRESSUREDROP MODELS 76

Heat Transfer Coefficient 76

Pressure Drop 81

CHAPTER VI: DESIGN AND OPTIMIZATION METHODOLOGY 89Figure of Merit (Coefficient of Performance) 89

System Design 94

Optimization Parameters 94Operating Parameters 95Geometric Parameters 96

Software Tools 97

CHAPTER VII: OPTIMIZATION OF OPERATING PARAMETERS 98Effects 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 PARAMETERSFOR FIXED CONDENSER COIL COST 112

Area 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 PARAMETERSFOR FIXED CONDENSER FRONTAL AREA 152

Varying 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 185Conclusions 185

List of Conclusions 188

Recommendations 191Optimization Parameters and Methodology 191Computational Methods 193Refrigerant-Side Heat Transfer and Pressure Drop Models 196Economic 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 FractionalHours 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 82° F Ambient Temperature128

Table 8-4: Seasonal COP and Area Factors for Varying Fin Pitch at Optimum AirVelocity 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 COP’s and Area Factors for Varying TubeDiameters 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 Pitchwith Fixed Frontal Area 162

Table 9-3: Optimum Operating Conditions and Cost Factor For Varying TubeDiameters 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 FoRefrigerant 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 andOptimum Degrees Sub-Cool 101

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

Figure 7-4: Effect of Ambient Temperature on COP for Varying Degrees Sub-Coolat 95°°°° F 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 95°°°° F Ambient Temperature with atOptimum Air Velocity 106

Figure 7-6: Evaporator Capacity vs. Ambient Temperature for Various Sub-Coolconditions at 95°°°° F Ambient Temperature and Optimum Air Velocity

108

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Figure 7-7: Effect of Air Velocity on the Seasonal COP for Varying Sub-coolConditions 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 RefrigerantPressure Drop at Optimum Sub-Cool and Air Velocity for FixedCondenser Material Cost at 82°°°° F Ambient Temperature 118

Figure 8-3: Effect of Number of Rows of Tubes on Condenser Frontal Area foFixed 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 andAirside Pressure Drop for Fixed Condenser Material Cost at 82°°°° FAmbient Temperature at Optimum Sub-Cool and Air Velocity 120

Figure 8-5: Effect of Air Velocity on Seasonal COP for Varying Number of Rows atOptimum Sub-Cool for Fixed Condenser Material Cost 122

Figure 8-6: Effect of Number of Rows on the Optimum Air Velocity andVolumetric 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 OptimumSub-Cool and Air Velocity for Fixed Condenser Material Cost 126

Figure 8-8: Refrigerant-Side Pressure Drop for Various Circuiting at 82 °°°° FAmbient Temperature and at Optimum Sub-Cool and Air Velocity foFixed Condenser Material Cost 127

Figure 8-9: Seasonal COP vs. Air Velocity for Varying Fin Pitch at FixedCondenser Material Cost and Optimum Sub-Cool 130

Figure 8-10: Effect of Fin Pitch on the Seasonal COP at Optimum Sub-Cool andAir Velocity Over the Condenser for Fixed Condenser Material Cost

131

Figure 8-11: Air-side Pressure Drop vs. Fin Pitch for Fixed Condenser MaterialCost at Optimum Sub-Cool and Air Velocity at 95°°°° F 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 95°°°° F 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 FixedCondenser Material Cost 140

Figure 8-16: Condenser Tube Length Allocation for Varying Tube Diameters atOptimum Air Velocity and Sub-Cool and 82 °°°° F Ambient Temperaturefor Fixed Condenser Material Cost 141

Figure 8-17: Effect of Tube Diameter on Pressure Drop at Optimum Sub-Cool andAir Velocity at 82°°°° F 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 FixedCondenser Material Cost and 82°°°° F Ambient Temperature 144

Figure 8-19: Operating Costs vs. Area Factor For Various Geometric Parameterat Optimum Sub-Cool and Air Velocity with Fixed CondenserMaterial Cost 146

Figure 8-20: Seasonal COP at Optimum Sub-Cool and Air Velocity for VaryingCondenser Tube Circuiting with Fixed Condenser Material Cost and5/16” Tube Outer Diameter 149

Figure 8-21: Comparison of the Effect of the Number of Tubes per Circuit onSeasonal COP for 5/16” and 3/8” Outer Tube Diameters at OptimumSub-Cool and Air Velocity with Fixed Condenser Material Cost 150

Figure 9-1: Effect of Air Velocity Over Condenser for Varying Numbers of Rows atOptimum Sub-Cool with Fixed Condenser Frontal Area 154

Figure 9-2: Effect of the Number of Rows of Tubes on the Seasonal COP atOptimum 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 FixedCondenser 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 Rowswith Optimum Sub-Cool and Air Velocity at 82°°°° F AmbientTemperature for Fixed Condenser Frontal Area 158

Figure 9-5: Effect of Air Velocity on Seasonal COP for Varying Fin Pitch withOptimum Sub-Cool for Fixed Condenser Frontal Area 160

Figure 9-6: Effect of Fin Pitch on the Seasonal COP at Optimum Sub-Cool and AirVelocity 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 CondenserFrontal Area at Optimum Sub-Cool and Air Velocity 165

Figure 9-9: Refrigerant-Side Pressure vs. Tube Diameter for Fixed Frontal Area at82°°°° F Ambient Temperature, Optimum Sub-Cool and Air Velocity 168

Figure 9-10: Power Requirements for Varying Tube Diameters with FixedCondenser Frontal Area at 82°°°° F Ambient Temperature, OptimumSub-Cool and Air Velocity 169

Figure 9-11: Air-Side Pressure Drop vs. Tube Diameter for Fixed CondenserFrontal Area at 82°°°° F Ambient Temperature, Optimum Air Velocityand Sub-Cool 171

Figure 9-12: Operating Cost Factor vs. Cost Factor of Condenser Materials forVarying Geometric Parameters with Fixed Condenser Frontal Areaand Optimum Air Velocity and Sub-Cool 172

Figure 9-13: Seasonal COP for Varying Condenser Tube Circuiting with FixedFrontal Area and 5/16” Tube Outer Diameter at Optimum Sub-Cooland Air Velocity 175

Figure 9-14: Comparison of the Effect of the Number of Tubes per Circuit on thSeasonal COP for 5/16” and 3/8” Outer Tube Diameters with FixedFrontal Area at Optimum Sub-Cool and Air Velocity 178

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Figure 9-15: Operating Cost Factor vs. Condenser Material Cost Factor forVarying Tube Diameter and Tube circuiting at Optimum Air Velocityand Sub-Cool 180

Figure 9-16: Operating Cost Factor vs. Condenser Material Cost Factor forVarying Geometric Parameters and Various Fixed Frontal Areas atOptimum 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

Bθ = Two-phase flow refrigerant side pressure drop Coefficient for a tube bend o θ degrees

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



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

xv

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,θ = Two-phase flow refrigerant side pressure drop Coefficient for a tube bend o θ degrees

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

.

.

.

.

.

xvii

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

R”f,r = Refrigerant-side heat exchanger fouling factor

R”f,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

.

.

xviii

Rel = Reynolds number based on transverse tube spacing

Rers = Reynolds number based on row spacing

S = Entropy

scst = Empirical constant for the Euler number correlati

St = Stanton Number

T = Temperature

Tc,i = Temperature of cold fluid entering the heat exchanger

tcst = Empirical constant for the Euler number correlation

Th,i = Temperature of hot fluid entering the heat exchanger

Ti = Representative bin temperature

Trat = Ratio of the condenser saturation temperature to the evaporator saturation Temperature

U = Overall heat transfer coefficient per unit area

u = Empirical constant for the Euler number correlati

UA = Overall heat transfer coefficien

UAhouse = Overall “house” heat transfer coefficien

v = Specific volume

v1 = Specific volume of refrigerant entering the compressor

v2 = Specific volume of refrigerant exiting the compressor

Va,con = Velocity of the air flowing over the condenser

vl = Specific volume of the fluid in the liquid phase

vm = Mean specific volume of air flowing over the heat exchanger

vv = Specific volume of the fluid in the vapor phase

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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

.

.

.

xx

List of Symbols with Greek Letters

α = Local void fraction.

β = 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

xxi

∆x = Change in quality

ε = Fin effectiveness

εpr = Pipe roughness

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

Γb2 = Physical property coefficient for the refrigerant-side pressure drop

determination inside a tube bend

ηc = Compressor thermal efficienc

ηf = Fin efficienc

ηfan,con = Condenser fan efficiency

ηs = Surface efficiency

ηs,a = Air-side surface efficienc

ηs,r = Refrigerant-side surface efficienc

ηv = Compressor volumetric efficiency

ϕ2b,LO = Two-phase multiplier for the refrigerant side pressure drop inside tube

bends

µ = Viscosity

µl = Viscosity of the fluid in the liquid phase

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

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

µTP = Two-phase fluid viscosity

µv = Viscosity of the fluid in the vapor phase

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π = 3.14159…..

θ = Angle of tube bend

ρ = Density

ρl = Density of the fluid in the liquid phase

ρv = Density of the fluid in the vapor phase

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

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

xxiii

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

xxiv

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 15° F. 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.

1

CHAPTER I

INTRODUCTION

The decade of the 1990’s 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

2

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 CO2 emissions 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.

3

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.

4

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 system’s 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.

5

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)

RefrigerantFlow

RefrigerantFlow

6

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

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 Shepherd’s 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.

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 Rich’s nor Shepherd’s 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

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-in” refrigerants 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-in” comparison 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

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 valve’s 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-

in” performance, for performance in a modified system to assess the fluids’ potentials,

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

exchanger. The simulation results obtained from the “drop-in” evaluation 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

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-in” evaluation.

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

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%

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, an a priori knowledge 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

14

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

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.

16

3. Few flow pattern maps are represented in non-dimensional form.

4. Most flow pattern maps are based on air-water flows. Hence it is assumed tha

the ratio of the vapor to liquid mass flow does not change from one part of the

conduit to another. Yet condensing and vaporizing flows are in a state of

perpetual change form one quality to another.

Even considering all of the above warnings, it is still better to use whatever limited

information one can find and to use it with full recognition of its limitations than to

totally ignore these considerations in the design of equipment (Bell, 1988).

Two-Phase Flow Heat Transfer Correlations

A very large number of techniques for predicting the heat-transfer coefficients during

condensation and evaporation inside pipes have been proposed over the last 50 years or

so. These range from very arbitrary correlations to highly sophisticated treatments of the

mechanics of flow. While many of these have been valuable as practical design tools and

have added to our understanding of the phenomena involved, there does not appear to be

any general predictive technique which has been verified over a wide range of parameters

(Shah, 1979).

Nusselt (1916) extended his vertical plate analysis to laminar film condensation

inside a vertical tube with forced vapor flow. He assumed a constant condensate fil

thickness, and that the condensing process in no way affected the vapor flow. He further

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 Nusselt’s 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 within ±25%.

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

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-ft 2, 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

19

then verified by comparison with a wide variety of experimental data. Data analyzed

included refrigerants, water, ethanol, and benzene, condensing in horizontal, vertical and

inclined pipes and included diameters ranging from about 7 to 40mm. Very wide ranges

of heat flux, mass flux, vapor velocities and pressures were covered. The 473 data points

from 21 independent experimental studies were correlated with a mean deviation of abou

15%. From this study, Shah asserts that this semi-empirical correlation is recommended

for use in all flow patterns and flow orientations. However, according to the

experimental data collected and analyzed by Singh et al. (1996) the values for

condensation heat transfer coefficients computed using the Shah correlation deviate by

mean of –30% from the data.

Again, a substantial amount of research has been performed in the development o

two-phase flow heat transfer models. The models most applicable to this current stud

are from the works of Akers et al. (1959), Traviss et al. (1976) and Shah (1979). A more

detailed evaluation of these models and their relevance to this current study is contained

in Chapter IV.

Two-Phase-Flow Pressure Drop Correlations

Despite the importance of pressure drop in two-phase flow processes, and the

consequent extensive research on the topic, there is still no satisfactory method for

calculating two-phase pressure drop. The best current methods are cumbersome in

structure, heavily dependent on empirically determined coefficients, and have

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

21

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),

Chisolm’s two-phase flow multipliers overpredicted the experimental data for low

qualities and slightly underpredited those for high qualities. Overall, Chisolm’s

22

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 Radermacher’s 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).

23

CHAPTER III

AIR-CONDITIONING SYSTEM AND COMPONENT MODELING

Refrigeration Cycle

Heating, Ventilating, and Air-Conditioning (HVAC) systems that provide a cooling

effect depend on a refrigeration cycle. Both the control and performance of HVAC

systems are significantly affected by the performance of the refrigeration cycle.

Therefore a basic understanding of the refrigeration cycle is needed in the design and

optimization of HVAC systems. Of the three basic refrigeration cycles (vapor

compression, absorption, and thermo-electric), the cycle typically used in the HVAC

industry is the vapor compression cycle. Vapor compression refrigeration has many

complex variations, but only the basic compression cycle will be discussed here. The

working fluid for the system in this study is refrigerant R-410a.

The vapor compression refrigeration cycle modeled for this study is shown in Figure

3-1. As the figure shows, low pressure, superheated refrigerant vapor from the

evaporator enters the compressor (State 1) and leaves as high pressure, superheated vapor

(State 2). This vapor enters the condenser where heat is rejected to outdoor air that is

forced over the condenser coils. Next the refrigerant vapor is cooled to the saturation

24

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

SaturatedSub-cooled Superheated2b 2a

3

ExpansionValve

Saturated Superheated

4 4a

Compressor

Condenser

Evaporator

1

2

S

T

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:

26

where h is the refrigerant enthalpy. For a non-ideal compressor, the actual amount o

work done depends on the efficiency,

where ηc is the compressor thermal efficiency. For a scroll type compressor, Klein and

Reindl (1997) have determined that the thermal efficiency is related to a “pressure ratio”

and a “temperature ratio” by the following relationship,

( )12, hhw scoms −= (3-1)

( )12,

, hhw

wc

comscoma −==

η(3-2)

ratratratratratratc TPTTPP 061.331.503.111281.0814.325.60 22 +−+−−−=η (3-3)

27

where Prat is the “pressure ratio” and Trat is 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

condsatrat

P

PP

,

,= (3-4)

evapsat

condsatrat

T

TT

,

,= (3-5)

28

where ηv is the compressor volumetric efficiency, Rcv,pd is 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 pdcvRη (3-6)

2v

PDm vη

=� (3-7)

.

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)

30

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

HorizontalTube

Spacing

Air CrossFlow

Vertical TubeSpacing

Width

Depth

Height

row 1 row 2 row 3

1 Refrigerant FlowParallel Circuit

3 Tubes per Circuit

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 ε is the heat exchanger effectiveness; Cmin is the smaller of the heat capacities o

the hot and cold fluids, Ch and Cc respectively; Th,i is the inlet temperature of the hot

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

as

where m is the mass flow rate of fluid and cp is 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 −= ε�

(3-11)

pcmC �= (3-12)

.

32

The amount of air flowing over each section of the condenser is proportional to the

tube length, L, corresponding to each specific section. For example, the mass of air

flowing over the saturated section of the condenser can be found by the following

relation,

The heat exchanger effectiveness discussed earlier in this chapter is the ratio of the actua

amount of heat transferred to the maximum possible amount of heat transferred,

The heat exchanger effectiveness is dependent on the temperature distribution within

each fluid and on the paths of the fluids as the heat transfer takes place, i.e. parallel-flow,

counter-flow, or cross-flow. In most typical condensers and evaporators, the refrigeran

tot

sat

tota

sata

L

L

m

m=

,

,

�

�

(3-13)

maxQ

Q�

�

=ε (3-14)

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 Cr is the heat capacity ratio,

( ) ( )( )[ ] ,1exp1

exp1 78.022.0

−−

−= NTUCNTU

C rr

ε (3-15)

.max

min

C

CCr = (3-16)

34

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

approaches infinity and the heat capacity ratio, Cr goes to zero. When Cr is 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−−=ε (3-17)

,minC

UANTU = (3-18)

35

where R”f,(a or r) is the fouling factor, Rw is the wall thermal resistance, ηs(a or r) is the

surface efficiency, and h 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

rfw

aas

af

aaas AhA

RR

A

R

AhUA ηηηη++++= (3-19)

.11

1

,

−

+=

rraaas AhAhUA

η(3-20)

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 ψ and β are defined as

and

( ) ,3.027.1 2/1−= βψr

Re(3-21)

r

Xt

2=ψ (3-22)

,4

12/12

2

+= t

lt

XX

Xβ (3-23)

37

Figure 3-3: Hexagonal Fin Layout and Tube Array

Xt

Tube Spacing Normal to Air Flo

Air Flow

��

��

��

��

��

��

��

��

��

��

Transverse TubeSpacing

Xl

38

where Xl is the tube spacing in the direction parallel to the direction of air flow, and X t is

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, es can be expressed as,

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

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

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

,2Pe

2/12/1

=

=

kt

h

kA

hm a

ces (3-24)

.ln35.011

+

−=

r

R

r

R eeφ (3-25)

39

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

expressed as

The total surface efficiency of the fin, ηs is therefore expressed as

where Afin is the total fin surface area, Ao is the total air-side surface area of the tube and

the fins.

( ).

tanh

φφη

ees

eesf

Rm

Rm= (3-26)

( ),11 fo

fins A

Aηη −−= (3-27)

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,con is the air velocity over the face of the condenser, ∆Pa,con is the air-side

pressure drop over the condenser, Afr,con is the frontal area of the condenser, and ηfan,con is

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

Chapter V.

Expansion ValveThe 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

confrconaconaconf

APVW

,

,,,, η

∆=� (3-28)

41

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

superheat will be maintained at the typical 10° F. 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)

42

nearly identical to that of the condenser. However, the dehumidification process

involving the evaporator results in some modifications of the analysis. To maintain the

simplicity of the evaporator model, the evaporator coil is assumed to be dry, thus the air-

side heat transfer coefficient is not affected. However, because the air flowing over the

evaporator is cooled to a temperature below the wet bulb temperature, some of the heat

rejected by the air causes water to condense out of the air rather than simply lowering the

temperature of the air. Therefore, the specific heat must be modified to account for this

condensation. The total enthalpy change of the air is thus the sum of the enthalpy change

due to the decrease in temperature (sensible heat), and the enthalpy change due to

condensation (latent heat).

If the specific heat for dry air is utilized in the model for the evaporator, the resulting

exit temperatures will be too low for complete vaporization. Therefore, an effective

specific heat that takes into account both the latent heat and the sensible heat must be

utilized. Using an effective specific heat will result in a more accurate determination o

latsenstot hhh ∆+∆=∆ (3-30)

43

the evaporator exit temperature without the complications associated with using the

standard equations for air-water mixtures. Since the evaporator is not the focus of this

study, this approximation should not effect the condenser optimization methodology.

Dividing (3-30) by the temperature change gives the following.

The ratio of the sensible heat enthalpy change to the temperature change is by definition,

the specific heat, cp. Therefore, after substituting cp into (3-31) and rearranging, the

following expression is obtained:

T

h

T

h

T

h latsenstot

∆∆+

∆∆=

∆∆ (3-31)

T

hcc lat

peffp ∆∆+=, (3-32)

44

where cp is the specific heat ratio for dry air and cp,eff is 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

.33.175.0

25.0, p

tot

senslatpeffp c

h

h

T

hcc =

∆

∆

∆∆

+= (3-33)

45

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)

46

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)

47

where l is 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

lvil L

xlxl −

−

+−+= (3-39)

48

Integrating (3-40) yields the following expressi

Substituting for l, the expression for the final mass in the saturated portion of the

evaporator is expressed as:

( ) ( ).

vv1

vvv

1

0, ∫

=

=

−

−

+−+=

Ll

llv

ilvil

cievapsat dl

L

xlx

Am (3-40)

( )( ) ( ) ( ) .vv1

vvvlnvv1

0v,

Ll

llv

ilvil

li

cievapsat

L

xlx

x

LAm

=

=

−

−

+−+−−

= (3-41)

49

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 ,, ρ= (3-43)

.,, shevapcivshevap LAm ρ= (3-44)

( )( ) ( ) .vvv

vln

vv1,

,

+−−−

=llvi

v

lvi

evapsatcievapsat xx

LAm

(3-42)

50

.,, scconcivsccon LAm ρ= (3-45)

51

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)

52

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

ReD ≥ 10,000

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 20° F, 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 90° F. 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)

53

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 µs are evaluated at the mean fluid temperature, and µs is

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:

,PrRe027.014.0

3/18.0

=

s

mDDNu

µµ (4-3)

54

where the coefficients ast and bst are as follows:

Laminar Re < 3,500 ast = 1.10647, bst = -0.78992

Transition 3,500 ≤ Re ≤ 6,000 ast = 3.5194 x 10-7, bst = 1.03804

Turbulent 6,000 < Re ast = 0.2243, bst = -0.385

and the Stanton number, St is expressed as:

where cp is the specific heat at constant pressure, and G is the total mass flux.

The Nusselt numbers calculated using each of the correlations discussed above are

plotted versus the Reynolds number in Figure 4-1. The difference between the wall

temperature and the refrigerant is taken as 40° F. The calculations are performed using a

p

SPrD

Gc

hNuSt ,

PrRe== (4-5)

stbstaSt RePr 3/2 = (4-4)

55

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

Nu

ssel

t N

um

ber

Laminar, ConstantHeat Flux��Kays and Londo

Dittus Boelter

Sieder and Tate

TransitionLaminar

Turbulent

Dittus-Boelter

Sieder & Tate

Kays & Londo

Kays & Londo

56

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,

57

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).

58

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

Refrigerant R-12

��

��

��

��

��

��

��

��

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 400 500 600 700

Total Mass Flux (kg/m2-s)

Co

nd

ensa

tio

n H

eat

Tra

nsf

er

Co

effi

cien

t (W

/m2 -s

)

Eckels&Pate-experimental data

Traviss, et al., -correlation

Shah-correlation��Akers et al.,-correlation

experimental data

Traviss, et al., correlation

Shah correlation

Akers-correlation

59

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.

60

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

as:

where hTP is the two-phase flow heat transfer coefficient, x is the quality, hL is the liquid

only heat transfer coefficient, and pr is the reduced pressure. By integrating the

expression (4-6) over the length of the tube, the mean two-phase flow heat transfer

coefficient can be determined.

If one assumes that the quality varies linearly with length, the mean two-phase flow hea

transfer coefficient can be approximated b

( ) ( )

−+−=38.0

04.076.08.0 18.3

1r

LTPp

xxxhh (4-6)

( ) ( ) ( )∫

−+−−

=e

i

L

L rie

LTPM dL

p

xxx

LL

hh

38.0

04.076.08.0 18.3

1(4-7)

61

This assumption of linearly varying quality typifies fixed heat transfer per unit length.

For complete condensation, (x varying from 1 to 0), the mean two-phase heat transfer

coefficient reduces to the following expression.

Evaporative Heat Transfer Coefficient

As discussed in Chapter III, the modeling of the evaporator is not the primary focus

of this study. To this end, the correlations investigated to determine the evaporator hea

transfer coefficient were limited. The expression for the average evaporative two-phase

heat transfer coefficient is taken from Tong (1965). This relationship assumes a constan

temperature difference between the wall and the fluid along the length of the pipe and is

expressed as:

+=

38.0

09.255.0

r

LTPMp

hh (4-9)

( )( )

.76.2

04.076.1

8.38.1

1 76.276.1

37.0

8.0 e

i

x

xrie

LTPM

xx

p

xxx

hh

−+−−

−= (4-8)

62

Pressure Drop in the Straight Tubes

The pressure drop in the straight-tube portions of the superheated and sub-cooled

sections of the condenser (single phase vapor and liquid respectively) can be determined

by applying the standard pressure drop relationship for pipe flow.

The friction factor, f, for circular pipes depends on the Reynolds number as shown in the

following expressions:

ρLfG

p SPS

2

, =∆ (4-11)

( )

−

−

=

325.0325.0

075.0375.04.0,

8.0

2.00186875.0

ixex

ixex

l

v

v

l

lk

lpCl

l

G

D

lkevaph

µ

µ

ρ

ρµ

µ(4-10)

63

and

where εpr is the pipe roughness, which for the drawn copper tubes utilized in this study, is

assumed to be 0.000005 ft.

For two-phase flow, determining the pressure drop is not as simple. As discussed in

Chapter II, there is still no satisfactory, universal method for calculating the two-phase

pressure drop, while taking into account flow regime considerations. Again using the

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

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 for low qualities, stratified-wavy flow also exists.

Therefore, only semi-empirical, general pressure drop correlations are considered for use

in this study. Although, various other general correlations have since been proposed, as

discussed in Chapter II, the original Lockhart-Martinelli approach is still one of the

.Re

51.2

7.3

/log2

12/1

pr102/1

+−=

f

D

f D

ε (4-13)Turbulent(Colebrook, 1938)

D

fRe

64= (4-12)Laminar(Incropera &Dewitt, 1996)

64

simplest, as discussed by Chen and Spedding (1981). Again, one of the bigges

advantages of this procedure is that it can be used for all flow regimes. While the cost o

this flexibility is decreased accuracy, as indicated in Chapter II, subsequent genera

correlations do not appear to be substantially more accurate than the Lockhart-Martinell

model. Therefore, the method of Lockhart and Martinelli is used to determine the two-

phase flow refrigerant-side pressure drop for the heat exchangers investigated in this

study.

The Lockhart-Martinelli method, or L and M method, is derived from the separated

flow model of two-phase flow. This model considers the phases to be artificiall

segregated into two streams; one of liquid and one of vapor (Collier and Thome, 1996).

The separated flow model is based on the following assumptions:

1) constant but not necessarily equal velocities for the vapor and liquid phases, and

2) the attainment of thermodynamic equilibrium between the phases

Hiller and Glicksman (1976) detail the procedures for calculating the frictional

momentum, and gravitational components of the two-phase flow pressure drop using the

Lockhart-Martinelli model. Hiller and Glicksman expound on the method of Lockhart-

Martinelli in the following manner.

The total two-phase pressure drop is divided into frictional, gravitational, and

momentum components as follows:

65

Hiller and Glicksman then derive the following expression for the frictional component,

where gcs is a units conversion constant, and Xtt is the Lockhart-Martinelli parameter

which is expressed as:

,mgf dz

dP

dz

dP

dz

dP

dz

dP

+

+

= (4-14)

( ) ( )2523.0

2.0

2

85.2109.0 ttv

v

cs

v

v

f

XDGDg

G

dz

dP +

−

=

µρ (4-15)

125.05.0875.01

−=

v

l

l

vtt x

xX

µµ

ρρ

(4-16)

66

The gravitational component is then expressed as:

where Fr is the Froude number based on the total flow (Traviss, 1973),

with ax defined as the axial acceleration due to gravity; B is the Buoyancy modulus;

D

G

Frx

v

a

2

2

=ρ

(4-18)

,v

vlBρ

ρρ −= (4-19)

−

=

α

ρρρ

BFrDg

G

dz

dP

v

l

cs

v

v

g2

2

1 (4-17)

67

and α is the local void fraction

Finally, Hiller and Glicksman give the momentum pressure drop component as:

Unfortunately, it is difficult to predict the variation of the quality with length, dx/dz.

However, as is the case with the condensation heat transfer coefficient, a linear profile is

assumed for the work of this study. If the quality variation is divided in to small

increments of ∆x, the resulting pressure drops over each small increment can be summed

to yield the total pressure drop over the entire length. For horizontal tube flow, the

gravitational pressure drop term is neglected. The pressure drop per unit length as a

.1

1

13/2

−+

=

l

v

x

x

ρρ

α (4-20)

( ) ( ) ( ) .12212123/23/12

−−

−+

−+

−=

l

v

l

v

l

v

vcsm

xxxxdz

dx

g

G

dz

dP

ρρ

ρρ

ρρ

ρ(4-21)

68

function of the variation in quality for the frictional and momentum components are then

integrated over the length of the tube, utilizing the aforementioned incremental

procedure. The frictional pressure drop in the two-phase region then reduces to the

following expression:

where the constants C3, C2, and C1 are determined by:

( )[( ) ] e

i

xx

f

xxC

xxxCxCp

86.123

33.223

8.22

329.0538.0

288.0141.0429.02357.0

−+

−−+−=∆ (4-22)

262.00523.0

3 85.2

=

l

v

v

lCρρ

µµ (4-23)

2.11

8.1

2

09.0

DgC

GC

vc

v

ρµ= (4-24)

.1ie

ie

zz

xxC

−−

= (4-25)

69

The momentum pressure drop in the two-phase region then reduces to:

Hence, the total two-phase refrigerant pressure drop in the straight tube section is simply

the sum of the momentum and frictional pressure drop components.

.2

1

3/23/1

3/23/12

e

i

x

xl

v

l

v

l

v

l

v

l

v

l

v

cvm

x

xg

Gp

−

−

−

−

−

+=∆

ρρ

ρρ

ρρ

ρρ

ρρ

ρρ

ρ (4-26)

fmTPS ppp ∆+∆=∆ , (4-27)

70

Pressure Drop In Tube Bends

The work of Chisolm (1983) is used to determine the pressure drop inside tube bends.

For single phase flow, the pressure drop in tube bends is calculated simply by assigning

an equivalent length to each bend based on the flow diameter and the bend radius. For

two-phase flow in tube bends, the pressure drop is calculated for liquid-only flow, and

correction factors are applied to determine the approximate two-phase flow pressure

drop. Instead of predicting the two-phase pressure drop in inclined bends that are found

in most heat exchangers, this method predicts the pressure drops for two-phase flow in

horizontal bends. However, no accurate correlations are available for predicting the two-

phase flow pattern in an inclined bend. Furthermore, the pressure gradients due to

elevation changes caused by the incline are negligible compared to friction pressure

losses. Hence, the horizontal bend model developed by Chisolm is sufficient for this

study. Since the bends are not finned and do not come into contact with air flow, the hea

transfer in the bends is neglected.

The first step in computing the pressure drop in tube a tube bend is to determine the

equivalent length of the bend. The equivalent length, y, is a function of the relative

radius, rr:

D

rr b

r = (4-28)

71

where rb is the radius of the bend, and D is the inner diameter of the tube. Most

condensers utilize tubes with a relative radius between 1 and 3, which according to

Chisolm’s model corresponds to an equivalent length of between 12 to 15 diameters for

90° bends. The equivalent length for a 180° return bend is approximately twice the

equivalent length of a 90° bend. For this study, 180° return bends are assumed to have an

equivalent length of 26 diameters.

Chisolm approximates the single-phase pressure drop in a bend by simply substituting

the equivalent length of the bend, y, for the straight pipe length in the standard pressure

drop equation,

where ∆pb,SP is the single phase pressure drop in the bend.

eSPb

D

fGp

=∆ y

2

2

, ρ(4-29)

72

For the two-phase flow pressure drop in bends, the calculations are more involved.

Assuming homogeneous two-phase flow, the friction factor is determined by the same

expressions that are used for single phase flow as shown in (4-12). However, Chisolm’s

development uses a Reynolds number based on the two-phase flow viscosity.

The two-phase viscosity is a function of the quality and is determined by the following

expression:

Chisolm defines a two-phase flow bend pressure drop coefficient for a 90° bend, kb,90°,

which is expressed as:

TP

GD

µ=Re (4-30)

( ) .1 lvTP xx µµµ −+= (4-31)

73

Another coefficient for 90° bends, B90° is also defined, and is expressed by:

where Rb is the bend recovery length. The B coefficient for bends that are not 90° is

expressed as:

In the case of 180° bends, the bend pressure coefficient kb,180°, is approximately twice the

value of kb,90°, so B180° can be calculated by the following expression.

eb D

fk o

= y

90, (4-32)

( )DRk bb o

o

/2

2.21B

90,90 +

+= (4-33)

[ ]θ

θ,

90,

901B1B

b

b

k

k o

o −+= (4-34)

74

Chisolm defines a two-phase multiplier, ϕ2, for the pressure drop in a tube bend as:

where Γb2 is the physical property coefficient for a tube bend and is determined by,

and n is the Blausius coefficient, which is calculated by the following expression.

( )oo BB90180

15.0 += (4-35)

( ) ( ) ( ) ( )( )nnnblob xxxB −−− +−−Γ+= 22/)2(2/222

, 111 θϕ (4-36)

,2

n

l

v

v

lb

=Γ

µµ

ρρ (4-37)

75

The friction factors fLO and fGO are determined using (4-12) by assuming all of the mass is

flowing alone as either a liquid or a vapor.

The two-phase pressure drop is then calculated as the product of the liquid-onl

single-phase pressure drop and the two-phase multiplier, ϕ2b,LO:

The liquid-only bend pressure drop, ∆pb,LO is then determined by (4-28).

=

l

v

GO

LO

f

f

n

µµ

ln(4-38)

2,,, LObLObTPb pp ϕ∆=∆ (4-39)

76

CHAPTER V

AIR-SIDE SIDE HEAT TRANSFER COEFFICIENT AND PRESSURE DROP

MODELS

The works of McQuiston (McQuiston and Parker, 1994), Rich (1973), and Zukauskas

and Ulinskas (1998), are used to evaluate the air-side heat transfer and pressure drop over

finned tubes in air cross-flow. The following development of the work of McQuiston,

Rich, and Zukauskas is taken from a thesis entitled “Optimization of a Finned-Tube

Condenser for a Residential Air-Conditioner Using R-22” by Emma Saddler (2000).

This development is detailed here in this study for completeness.

Heat Transfer Coefficient

The work of McQuiston (McQuiston and Parker, 1994) is used to evaluate the air-side

convective heat transfer coefficient for a plate finned heat exchanger with multiple rows

of staggered tubes. The model is developed for dry coils. The heat transfer coefficient is

based on the Colburn j-factor, which is defined as:

77

Substituting the appropriate values for the Stanton number, St, gives the following

relationship for the air-side convective heat transfer coefficient, ha,

where cp is the specific heat, and Gmax is the mass flux of air through the minimum flow

area which is expressed as:

.Pr 3/2Stj = (5-1)

,Pr 3/2

maxGjch p

a = (5-2)

,min

max A

mG air�

= (5-3)

78

where Amin is the minimum air flow area.

McQuiston (McQuiston and Parker, 1994) use a 4-row finned tube heat exchanger as the

baseline model, and define the Colburn j-factor for a 4-row finned-tube heat exchanger

as:

and the parameter JP is defined as:

where, Ao is the total air side heat transfer surface area (fin area plus tube area), and t is

the tube outside surface area. The Reynolds number, ReD in the above expression is

based on the outside diameter of the tubes, Do, and the maximum mass flux, Gmax. The

area ratio can be expressed as:

,10325.12675.0 64

−×+= JPj (5-4)

,Re15.0

4.0

−−

=

t

oD

A

AJP (5-5)

79

where Xl is the tube spacing parallel to the air flow (transverse), Xt is the tube spacing

normal to the air flow, D depc is the depth of the condenser in the direction of the air flow,

Dh is the hydraulic diameter defined as:

and σ is the ratio of the minimum free-flow area to the frontal area,

,4 σπ depc

t

h

l

t

o

D

X

D

X

A

A = (5-6)

.min

frA

A=σ (5-8)

,4 min

o

depch

A

DAD = (5-7)

80

The j-factor for heat exchangers with four or fewer rows can then be found using the

following correlation:

where z is the number of rows of tubes, and Re rs is the Reynolds number based on the

row spacing, Xrs,

( )( ) ,Re412801

Re128012.1

2.1

4−

−

−−

=rs

rsz z

j

j (5-9)

.Re max

µrs

rs

XG= (5-10)

81

Pressure Drop

According to Rich (1973), the air-side pressure drop can be divided into two

components, the pressure drop due to the tubes, ∆ptubes, and the pressure drop due to the

fins, ∆pfin. The work of Rich is used to evaluate the air-side pressure drop due to the fins,

which is expressed as

where, ffin is the fin friction factor, vm is the mean specific volume, fin is the fin surface

area, and Ac is the minimum free-flow cross sectional area. In experimental tests, Rich

found that the friction factor is dependent on the Reynolds number, but it is independent

of the fin spacing for fin spacing between 3 and 14 fins per inch. In this range of fin

spacing, Rich expresses the fin friction factor as:

,2

v fin2max

finfinc

mA

AGfp =∆ (5-11)

,Re7.1 5.0fin

−= lf (5-12)

82

where the Reynolds number is based on the tube spacing parallel to the direction of the

air flow (transverse tube spacing), Xl,

To determine the pressure drop over the tubes, the relationships developed by

Zukauskas and Ulinskas (1998) are used. The pressure drop over the banks of plain tubes

is expressed as:

where z is the number of rows, and Eu is the Euler number. Rich expresses the Euler

number as a function of the Reynolds number and the tube geometry. For staggered,

equilateral triangle tube banks with several rows, Rich expresses the Euler number by a

fourth order inverse power series by the following:

,2

2

tubes zG

Eupρ

=∆ (5-14)

.Reµ

ll

GX= (5-13)

83

where ReD is the Reynolds number based on the outer tube diameter. The coefficients

qcst, rcst, scon, tcst, and u are dependent on the Reynolds number and the parameter “a”,

which is defined as the ratio of the transverse tube spacing to the tube diameter. The

coefficients for a range of Reynolds numbers and spacing to diameter ratios have been

determined from experimental data by Zukauskas and Ulinskas (1998) and are expressed

in Table 5-1.

For non-equilateral triangle tube bank arrays, the staggered array geometry factor k1

must be used as a correction factor to the coefficients in Table 5-1. The staggered arra

geometry factor is dependent on the Reynolds number based on: the outer tube diameter;

the parameter “a”, which again is defined as the ratio of the transverse tube spacing to the

tube diameter; and the parameter “b”, which is defined as the ratio of the tube spacing in

the direction normal to the air flow and the tube diameter. The equations for k 1 are found

in Table 5-2.

432 ReReReRe DD

cst

D

cst

D

cstcst

utsrqEu ++++= (5-15)

84

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

a Reynolds Number qcst rcst scst tcst u

3 < ReD < 103 0.795 0.247 x 103 0.335 x 103 -0.155 x 104 0.241 x 104

1.25

103 < ReD < 2 x 106 0.245 0.339 x 104 -0.984 x 107 0.132 x 1011 -0.599 x 1013

3 < ReD < 103 0.683 0.111 x 103 -0.973 x 102 0.426 x 103 -0.574 x 103

1.5

103 < ReD < 2 x 106 0.203 0.248 x 104 -0.758 x 107 0.104 x 1011 -0.482 x 1013

7 < ReD < 102 0.713 0.448 x 102 -0.126 x 103 -0.582 x 103 0.000

102 < ReD < 104 0.343 0.303 x 103 -0.717 x 105 0.880 x 107 -0.380 x 1092.0

104 < ReD < 2 x 106 0.162 0.181 x 104 -0.792 x 108 -0.165 x 1013 0.872 x 1016

102 < ReD < 5 x 103 0.330 0.989 x 102 -0.148 x 105 0.192 x 107 0.862 x 108

2.5

5 x 103 < ReD< 2 x 106 0.119 0.848 x 104 -0.507 x 108 0.251 x 1012 -0.463 x 1015

85

Table 5-2: Staggered Array Geometry Factor

ReD a/b k1

102 1.25 < a/b < 3.5

0.5 < a/b < 3.5

103

1.25 < a/b < 3.5

104 0.45 < a/b < 3.5

105 0.45 < a/b < 3.5

106 0.45 < a/b < 1.6

( ) ( ) ( )321/

113.0

/

55.0

/

708.028.1

bababak −+−= (5-19)

43

2

1

021.0234.0

948.0675.1016.2

+

−

+

−=

b

a

b

a

b

a

b

ak (5-20)

48.0

1 93.0

=

b

ak

(5-16)

048.0

1

−

=

b

ak (5-17)

284.0

1 951.0

=

b

ak (5-18)

86

If the tube bank has a small number of transverse rows, the average row correction

factor, Cz, must be applied because the pressure drop over the first few rows will be

different from the pressure drop over the subsequent rows. Cz is the average of the

individual row correction factors, cz.

The equations for the individual row correction factors are given in Table 5-3. Once

the average row correction factor is found, the corrected Euler number can be determined

as

∑=

=z

zzz c

zC

1

1(5-21)

.1 EuCkEu zcor = (5-22)

87

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

ReD z cz

10 < 3

102 < 4

103 < 3

104 < 3

> 105 < 4

For values of z greater than 4, cz = 1

297.0

18.0065.1

−−=

zcz (5-23)

273.1

497.3798.1

+−=

zcz (5-24)

412.0

411.0149.1

−−=

zcz (5-25)

143.0

269.0924.0

+−=

zcz (5-26)

667.0

467.162.0

+−=

zcz (5-27)

88

The corrected Euler factor, Eucor can then be used in equation (5-14) to determine the

pressure drop over the tubes. Since the relations in Table 5-1, Table 5-2, and Table 5-3,

are given for discrete values of the “a” parameter and the Reynolds number, a linear

interpolation is used to estimate the values of Eu, k1, and cz. The total pressure drop over

the heat exchanger is then simply the sum of the pressure drop over the tubes and the

pressure drop over the fins:

.fintubes, ppp actot ∆+∆=∆ (5-28)

89

CHAPTER VI

DESIGN AND OPTIMIZATION METHODOLOGY

Figure of Merit (Coefficient of Performance)

In order to quantitatively evaluate the performance of any air-conditioning system, a

figure of merit must be established. For an air-conditioning system utilizing a vapor

compression refrigeration cycle, the efficiency is expressed in terms of the cooling

coefficient of performance or the COP. The coefficient of performance is a

dimensionless quantity. It is the ratio of the rate of cooling or refrigeration capacity (hea

absorbed by the evaporator), to the electrical or mechanical power used to drive the

system (compressor power, condenser fan power, and evaporator fan power). The COP

is expressed as:

.,, evapfconfcom

e

WWW

QCOP

��

�

++= (6-1)

90

In the United States, the performance of residential air-conditioning equipment is

often given in dimensional terms, Btu/(W-hr), as an energy efficiency ratio or EER.

Since 3.412 Btu = 1.0 W-hr, an EER rating of 10.0 would be equivalent to a COP o

10/3.412 or 2.93. The performance of an air-conditioning device over a summer is

referred to as the seasonal COP, or COPseas, in dimensionless terms. The seasonal COP

takes into account the effect of varying outside temperatures on the performance of the

system. It is the ratio of the average cooling load for the system during its normal usage

or “cooling load hours” to the average electricity required by the system over all cooling

load hours. Cooling load hours are defined as hours when the temperature is above 65 °

F, which is when air-conditioning systems are typically operated. In warmer climates,

there are more cooling load hours, per year than in cooler climates. In Atlanta, for

example, the total cooling load hours are approximately 1300 hours per year, while in

Detroit, MI the cooling hours are about 700 per year. The air-conditioning syste

actually runs fewer hours than the cooling load hours since at ambient temperatures

below 95° F, the system usually cycles on and off, as regulated by a thermostat. (The

cycling inefficiencies that result from the system cycling on and off are neglected in this

study.) The distribution of temperature during these cooling hours is approximately the

same for all major cities in the United States. Therefore, the Air-Conditioning

Refrigeration Institute, ARI, has developed a temperature distribution model based on

cooling load hours which is used throughout the United States. This is shown in Table 6-

1 as the distribution of fractional hours in temperature “bins” (ARI, 1989). Table 6-1

shows for example that the outside temperature will be between 80° F and 84° F

91

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

Hours in Temperature Bins

Bin #

i

Bin Temperature

Range (°F)

Ti, Representative

Temperature for Bin (°F)

fri, Fraction of Total

Temperature Bin Hours

1 65-69 67 0.214

2 70-74 72 0.231

3 75-79 77 0.261

4 80-84 82 0.161

5 85-89 87 0.104

6 90-94 92 0.052

7 95-99 97 0.018

8 100-104 102 0.004

(temperature bin # 4) approximately 16.1% of the time that the ambient temperature is

above 65° F.

Again, the seasonal COP is therefore the ratio of the average cooling load for the

system over all cooling load hours to the average electricity required by the system over

all cooling load hours, and is expressed as:

.,

,

seasave

seasaveseas W

QCOP = (6-2)

92

The average cooling over all cooling load hours is calculated by summing the hourly

“house” cooling load over all cooling load hours, and is expressed as:

where UAhouse is the overall “house” heat transfer coefficient, i is the temperature bin

number, Ti is the representative temperature bin, and fri is the fraction of total

temperature bin hours (as shown in Table 6-1). The average electricity required by the

system over all cooling load hours is expressed as:

where COPi is the COP at each representative temperature bin.

( ) ,frF65T i

8

1i

oi, ∑

=−= houseseasave UAQ (6-3)

( ),

frF65T8

1i i

io

i, ∑

=

−=

COP

UAW house

seasave (6-4)

93

Since the overall “house” heat transfer coefficient, U house, is common to both

expressions, dividing (6-3) by (6-4) yields the following expression for the seasonal

COP:

The numerator of the above expression is a constant. Since the air-conditioning syste

of this study is sized to deliver a specified amount of cooling at 95 °F ambient

temperature, the indoor temperature will rise when the ambient temperature is greater

than 95 °F. As a result, the temperature difference of (Ti - 65°F) is limited to a maximu

of 30 °F for this study.

In dimensional terms, the seasonal COP can be given as the seasonal energ

efficiency ratio, or SEER, and is expressed in Btu/W-hr. This is the efficiency rating tha

is required by the United States Department of Energy to be placed on a yellow sticker on

all air-conditioning systems sold in the United States.

( )( ) .

frF65T

frF65T

8

1i i

io

i

8

1ii

oi

∑

∑

=

=

−

−=

COP

COPseas

(6-5)

94

System Design

The primary focus of this study is the optimization of the condenser configuration.

However, some assumptions about the parameters of the complete air-conditioning

system must be made. Air-conditioning systems are characterized by their cooling

capacity at 95° F ambient temperature. The most common residential air-conditioning

systems sold in the United States have a cooling capacity rating of 30,000 Btu/hr (2 1/2

tons). Hence, for the air-conditioning system modeled in this study, the cooling capacity

at 95° F is fixed to 30,000 Btu/hr. It is also customary in most residential air-

conditioning applications to employ an evaporator that has a 45 ° F saturation

temperature. At this temperature, humidity control is maintained by removing sufficient

water vapor from the cooled air. Therefore the evaporator saturation temperature is fixed

at 45° F in this study. As discussed in Chapter III, the evaporator fan power and the

volume flow rate of air over the evaporator, are fixed to 365 Watts per 1000 ft 3/minute o

air flow respectively (equates to a constant fan power of 1245 Btu/hr).

Optimization Parameters

When designing and optimizing the condenser to yield the maximum seasonal COP

of the air conditioning system there are a large number of parameters that can be varied.

For this investigation, these optimization parameters have been divided into two

categories: operating parameters for the system, and geometric design parameters specific

to the condenser coil.

95

As part of the optimization process, comparisons are made between the seasona

performances of air-conditioning systems with condensers of various geometric

configurations (tube diameters, fin spacing, etc.). However, it is not possible to make

valid comparisons between different heat exchanger configurations without first

optimizing the operating parameters at each configuration to yield the maximum seasonal

COP. For example, it is erroneous to compare the performance of a system with a 3-row

condenser coil configuration in which the operating parameters have been optimized to

system with a 2-row condenser coil configuration in which the operating parameters have

not been optimized. No valid conclusions can be made about which configuration yields

the best performance unless the operating parameters are re-optimized for each new

geometric configuration tested. Therefore, in this study, the performance of each

configuration at its optimum operating conditions will be determined and compared.

Operating Parameters

The operating parameters of the system studied are the refrigerant charge, the ambien

temperature, the level of superheat exiting the evaporator, the amount of sub-cool exiting

the condenser, and the velocity of the air flowing over the condenser. For this study, the

level of superheat exiting the evaporator is fixed at a constant value of 10° F, which is

typically used in most residential air-conditioning systems, and required by the

compressor manufacturers to prevent liquid from returning to the compressor.

For this study, the air velocity over the condenser and the sub-cool in the condenser

are specified at 95° F. The resultant compressor piston displacement and mass o

96

refrigerant in the system (refrigerant charge) that yield 30,000 Btu/hr of cooling capacity

at 95° F are determined. The mass inventory at 95° F dictates the sub-cool at other

ambient temperatures. Hence, the air velocity over the condenser and the sub-cool in the

condenser at 95° F are the two operating parameters that are optimized for each

condenser geometric configuration investigated during this study. The method for

calculating the mass of refrigerant in the system (mass inventory) is detailed in Chapter

III.

Geometric Parameters

There are a large number of condenser coil geometric design parameters that can be

varied in order to optimize the seasonal performance of an air-conditioning system.

These parameters include the tube diameter, the tube spacing, the number of refrigerant

parallel flow circuits, the number of tubes per refrigerant parallel flow circuit, and the fin

spacing or pitch. For this study, the tube diameter, the number of refrigerant parallel flow

circuits, the number of tubes per refrigerant flow circuit, and the fin spacing will be

optimized. In all cases, the vertical and horizontal tube spacing are specified as 1 in. and

0.625 in., respectively. These values are typical of those found in condenser coils for

unitary air-conditioning systems. In Chapter III, Figure 3-2 shows a schematic of a

typical finned-tube condenser coil. In this figure, geometric parameters such as the tube

spacing, number of tube refrigerant flow circuits, number of tubes per refrigerant flow

circuit, and the number of rows of tubes are detailed.

97

Software Tools

For this study, all modeling and simulations are performed using Engineering

Equation Solver (EES). EES is a software package developed by Dr. Sanford Klein of

the University of Wisconsin. EES incorporates the programming structures of C and

FORTRAN with a built-in iterator, thermodynamic and transport property relations,

graphical capabilities, numerical integration, and many other useful mathematica

functions. By grouping equations that are to be solved simultaneously, EES is able to

rapidly solve large numbers of transcendental equations. EES can also be used to

perform parametric studies. Most important for this study, EES has the ability to

seamlessly incorporate fluid property calls. Thermodynamic transport properties for

steam, air, and many different refrigerants are built into EES.

98

CHAPTER VII

OPTIMIZATION OF OPERATING PARAMETERS

The performance of air conditioning systems is highly dependent on specific

operating conditions and parameters. As detailed in Chapter VI, without optimizing the

operating conditions, it is not possible to determine the condenser configuration that

yields the optimum seasonal COP. Again, the operating parameters investigated for this

study are the air velocity over the condenser and the refrigerant charge measured by the

sub-cool in the condenser at 95° F ambient temperature. To determine the effects of the

various operating parameters on the seasonal COP, a typical evaporator and condenser

coil pair is arbitrarily selected for the “base configuration”. All of the characteristics o

the condenser are specified, and all but the frontal area of the evaporator are specified.

The dimensions of the heat exchangers are shown in Table 7-1.

Figure 7-1 shows the effect that the operating parameters of refrigerant charge (given

here in terms of the degrees of sub-cool at 95°F ambient temperature) has on the frontal

area of the evaporator for the given design conditions and a fixed condenser geometry.

99

Table 7-1: Base Case Condenser and Evaporator Characteristics

Dimension Condenser Evaporator

Tube Spacing (in x in) 1.25 x 1.083 1.00 x 0.625

Tube inner diameter (in) 0.349 0.349

Tube outer diameter (in) 0.375 0.375

Height (ft 2.5 1.5

Finned width (ft) 3 N/A

Fin pitch (fin/in) 12 12

Number of rows 3 4

Number of circuits 12 9

Number of tubes per circuit 2 2

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

2

2.2

2.4

2.6

2.8

3

3.2

3.4

5 6 7 8 9 10 11 12 13 14 15

Air Velocity Over Condenser (ft/s)

Eva

po

rato

r F

ron

tal A

rea

(ft2 )

Tsubcool=5 F

Tsubcool=10 F

Tsubcool=15 F

Tsubcool = 20 F

100

As the figure shows, the necessary finned frontal area of the evaporator is virtually

independent of this operating parameter. The compressor piston displacement is

calculated such that at each design condition, the system will deliver an evaporator

capacity of 30,000 Btu/hr at 95° F ambient temperature. The mass inventory at 95° F

ambient temperature dictates the sub-cool at other ambient temperatures. Therefore, the

air velocity over the condenser and the sub-cool (refrigerant charge) are the operating

parameters optimized for each condenser geometric configuration investigated in this

study.

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

For a fixed amount of sub-cool at 95° F ambient temperature, there is an air velocity

that yields the maximum COP. Figure 7-2 shows the effect of air velocity on the COP for

various ambient temperatures at optimum degrees sub-cool. As the figure shows, the

COP has an optimum with respect to the air velocity for any ambient temperature. For

ambient temperatures ranging from ° F to 97° F, the maximum seasonal COP occurs at

an air velocity between 8.0 ft/s and 9.0 ft/s for this sub-cool condition (15 ° F). For each

ambient temperature, in this range of velocities the COP is relatively insensitive to the air

velocity and varies by less than 1%. For example, at 77 ° F sub-cool, the maximum COP

is 4.31 and it occurs at an air velocity of 8.5 ft/s. Because the COP varies so little with

air velocity in the optimum range, it is difficult to determine the exact optimum velocity

for each sub-cool within an accuracy of more than ± 0.1 ft/s. However in actual practice,

101

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

Optimum Degrees Sub-Cool

2.90

3.40

3.90

4.40

4.90

4 6 8 10 12 14 16


CO

P

Tambient = 67 F

Tambient = 77 F

Tambient = 97 F

Locus of Optimums

102

the air speed cannot be specified to such high tolerances. Hence, the accuracy which is

indicated in this investigation is sufficient.

The above observations of the insensitivity of the COP to air velocity near the

optimum range may initially be counter intuitive. Since the condenser fan power

increases proportionally with the cube of the velocity, one does not expect the COP to

become insensitive to changes in the velocity. However, in this range of velocities, as the

condenser fan power requirement is increasing, the required compressor power is

decreasing by approximately the same amount. This phenomenon is demonstrated in

Figure 7-3, which shows the effect of the air velocity on the compressor power and the

condenser fan power at 95° F ambient temperatures and optimum sub-cool. As the air

velocity over the condenser increases, the condensing temperature decreases, and the

inlet enthalpy to the evaporator also increases. This causes a reduction of the mass flow

rate of refrigerant required to maintain the evaporator cooling capacity. Hence, the

amount of compressor work is decreased. The condensing temperature of the refrigeran

can never be lower than the inlet air temperature. Thus, there is a minimum power

requirement for the compressor. As the air velocity increases beyond the optimal

recommended range, the power required for the condenser fan begins to grow rapidly. At

this point, the decrease in the compressor power requirement will not compensate for this

increase in the condenser fan requirement, thus resulting in lower values of the seasonal

COP.

103

Figure 7-3: Effect of Air Velocity on Compressor and Condenser Fan Power 13°°°° F

Sub-cool at 95°°°° F Ambient Temperature

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

5 6 7 8 9 10 11 12 13 14 15Air Velocity Over Condenser (ft/s)

Po

wer

(B

tu/h

r)

Total Power

Compressor Power

Condenser Fan Power

104

Figure 7-2 also shows that as the ambient temperature decreases, the COP increases.

This phenomenon is also displayed in Figure 7-4. This figure shows how the COP varies

with the ambient temperature for various sub-cool conditions. This phenomenon can be

explained by an analysis of the effects of ambient temperature on the condensing

temperature and pressure, the compressor power, and the evaporator cooling capacity.

As the ambient temperature decreases, the saturation pressure in the condenser also

decreases. Therefore, the pressure rise in the compressor decreases. As a result, the

compressor requires less power, and hence, the COP increases. Furthermore, as the

ambient temperature decreases, the condensing temperature decreases. Thus, the

enthalpy of the refrigerant entering the evaporator is reduced. The decrease in the

enthalpy of the refrigerant entering the evaporator that is produced by the decrease in the

ambient temperature causes the evaporator cooling capacity to increase. This decrease in

the enthalpy of the refrigerant entering the evaporator also causes a reduction of the mass

flow rate of refrigerant required to maintain the evaporator cooling capacity. Hence, the

amount of compressor work is decreased. Therefore, the ultimate result of decreasing the

ambient temperature is an increase in the COP of the system.

Figure 7-5 shows how evaporator capacity varies with ambient temperature. For the

reasons mentioned above, the figure shows that as the ambient temperature decreases, the

evaporator capacity increases. Unfortunately, this trend is the opposite of the trend in the

residential cooling requirements, which increase with ambient temperature.

105

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

at 95°°°° F Ambient Temperature with an Air Velocity Over the Condenser of 8.5 ft/s

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

0 5 10 15 20 25

Degrees of Sub-Cool at 95 F Ambient Temperature (F)

CO

P

Tambient=67 F

Tambient=82 F

Seasonal

Tambient=97 F

Tambient=102 F

Locus of Optimums

106

Figure 7-5: Effect of Ambient Temperature on the Evaporator Capacity for

Varying Degrees Sub-Cool at 95°°°° F Ambient Temperature with at Optimum Air

Velocity

2.00

2.50

3.00

3.50

4.00

4.50

5.00

60 65 70 75 80 85 90 95 100 105

Ambient Temperature (F)

CO

P

Tsubcool at 95 F =10

Tsubcool at 95 F =15

Tsubcool at 95 F =5

Tsubcool at 95 F = 20

107

Figure 7-6 shows the effect that the refrigerant charge (sub-cool at 95° F ambient

temperature) has on the COP at various ambient temperatures at optimum air velocity

over the condenser. According to the figure, as the ambient temperature decreases the

optimum sub-cool at 95° F increases. As discussed in Chapter VI, the sub-cool is

specified at 95° F. The resultant mass of refrigerant in the system (refrigerant charge)

that yields 30,000 Btu/hr of cooling capacity at 95° F is determined, and the mass

inventory at 95° F dictates the sub-cool at other ambient temperatures. As noted earlier,

as the ambient temperature decreases, the condensing temperature also decreases, and the

enthalpy of the refrigerant entering the evaporator is reduced. As a result, the inle

quality is also lower and more of the refrigerant in the evaporator exists in the liquid

state. The total mass of refrigerant in the entire system is constant. Hence, as the

ambient temperature decreases, the mass of refrigerant in the evaporator increases and the

mass of refrigerant in the condenser decreases. When the mass of refrigerant in the

condenser decreases, the volume of the condenser that contains low density refrigerant

vapor increases and the volume of refrigerant in the condenser that contains higher

density sub-cooled liquid decreases, causing an overall decrease in the mass of the syste

(refrigerant charge). Thus it is possible for the mass of refrigerant in the condenser to

drop to very low levels such that complete condensation does not occur. In these

instances where the refrigerant is not completely condensed when it exits the condenser

108

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

conditions at 95°°°° F Ambient Temperature and Optimum Air Velocity

28500

29000

29500

30000

30500

31000

31500

32000

32500

33000

33500

65 70 75 80 85 90 95 10 10

Ambient Temperature (F)

Eva

po

rato

r C

apac

ity

(Btu

/hr)




109

and enters the expansion valve, the valve goes to its wide open position, and a fixed

superheat cannot be maintained. This reduces the COP of the system. As a result, more

sub-cool at 95 °F is needed to maintain some sub-cool at the lower ambient temperatures

(i.e. as the ambient temperature decreases, the degrees of sub-cool also decrease).

Effects on the Seasonal COP

Figure 7-4 also shows that the seasonal COP is nearly identical to the COP that exist

at 82° F ambient temperature for a vast range of sub-cool conditions. This is due to the

relatively large seasonal weighting assigned to the 82° F ambient temperature. Ambien

temperatures at 82° F and below constitute more than 82% of the seasonal COP

weightings. Thus the performance of the system at these ambient temperatures greatly

influence the seasonal performance of the system.

Figure 7-7 shows the effect of air velocity on the seasonal COP at varying sub-cool

conditions. As the figure shows, the COP varies quadratically with the air velocity for

any sub-cool condition. For sub-cools ranging from 5 ° F to 30° F, the maximum seasonal

COP occurs at an air velocity between 7.5 ft/s and 10.0 ft/s. This figure also shows that

the maximum seasonal COP occurs at a sub-cool between 10° F and 15° F, while the

minimum seasonal COP occurs at a sub-cool of 20° F.

110

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

Conditions

3.50

3.55

3.60

3.65

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4 6 8 10 12 14 16


Sea

son

al C

OP

Tsub-cool at 95 F = 15




111

Range of Optimum Operating Parameter

Based on the results discussed in this chapter, it is clear that there is a range of

operating parameters that yield the optimum performance for the base configuration

system. It is determined that systems with between 10 ° F and 16° F degrees sub-cool in

the condenser and air flowing over the condenser with velocities ranging from 6 ft/s and

12 ft/s will yield the optimum seasonal COP for the base configuration investigated in

this study.

Effect of Operating Parameters on System Cost

As the sub-cool and the air velocity over the condenser are varied for a fixed

condenser geometric configuration, the cost of the entire system is affected. This is

because the size and cost of the condenser fan are also assumed to vary with changes in

the operating conditions. This varying condenser fan and compressor equipment cos

analysis is beyond the scope of this study, however the variation of these costs is not

expected to be large. Therefore, only the condenser cost of materials is considered in this

study. However, the designer should be aware of the effects of these factors on syste

costs.

112

CHAPTER VIII

OPTIMIZATION OF GEOMETRIC DESIGN PARAMETERS FOR FIXED

CONDENSER COIL COST

The two most pertinent constraints on condenser design are its costs and space

requirements (frontal area). It is not possible to maintain a fixed condenser frontal area

and a fixed condenser cost while varying only one geometric design parameter. Yet, it i

very difficult to isolate the effects of individual geometric design parameters while

simultaneously varying more than one. The condenser frontal area is the dominant

geometric design variable, since it determines the volume of the entire system. Hence,

for this study, two distinct investigations of the condenser geometric design effects are

considered: (1) effects of geometric design changes with fixed condenser cost, and (2)

effects of geometric design changes with fixed condenser frontal area. Each, geometric

design parameter is isolated and varied while the others are maintained at the values of

the base configuration. After an analysis of these results, the geometric parameters

having the greatest effect on the COP are varied simultaneously in the appropriate

combinations to yield a more nearly absolute optimum configuration. In this chapter, the

113

cost of the condenser is fixed while the condenser frontal area is allowed to vary for each

of the configurations investigated.

Area Factor and Cost Facto

In order to compare the frontal area of each condenser configuration investigated, an

area factor, defined as the ratio of the frontal area of the test configuration to that of the

base configuration (detailed in Chapter VII) is given by the following.

.

To compare the relative cost of each condenser and evaporator configuration a cost

factor, defined as the ratio of the cost of the test configuration to that of the base

configuration (detailed in Chapter VII) is given by the following.

baseAreaFrontal

AreaFrontalAF = (8-1)

baseCost

CostCF = (8-2)

114

The cost of the heat exchanger is determined primarily by the cost of materials. Hence

the cost of each heat exchanger configuration is defined as:

where Vol is the volume of the component, ρx is the density of the x material, and Cost x

is the cost per lbm of the x material. The costs of the heat exchanger materials per lbm

are summarized in Table 8-1.

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

Material Cost ($/lbm)

Copper 0.8

Aluminum 0.7

The material cost of the base condenser configuration is $26.00. The optimum

compressor piston displacement, and thus the compressor size, will change with each

condenser configuration. For the vast majority of reasonable operating conditions, the

AlAlevapAlcondAlCuCuevapCucondCu CostVolVolCostVolVolCost ρρ )()( ,,,, +++= (8-3)

115

compressor piston displacement varies 3% from the optimum configuration to the base

case configuration. Therefore, the cost of the compressor will not be considered for this

investigation.

Varying Number of Rows of Condenser Tubes

The number of rows of condenser tubing, which dictates the condenser coil depth, is

the first geometric design parameter studied. For this investigation, the height of the

condenser remained constant while the width of the condenser was free to vary. The

number of tubes per circuit, the fin spacing, the tube diameter, and the tube spacing were

fixed to the values of the base configuration. Figure 8-1 shows the effect of the number

of rows of condenser tubing on the optimum seasonal COP at the optimum air velocity

over the condenser and varying degrees sub-cool at ° F ambient temperature.

One would expect that a heat exchanger with only one long row of tubes and no tube

bends, providing the largest heat exchanger frontal area possible, would yield the best

performance. This prediction is verified by Figure 8-1, which shows that as the number

of rows of tubes decreases, the seasonal COP increases. This is because decreasing the

number of rows of tubing also decreases the number of tube bends. Hence the frictional

losses in the tubes and the required compressor work are also reduced, increasing the

seasonal COP. The difference between the temperature of the refrigerant flowing inside

the condenser tubes and the temperature of the air flowing over the condenser tubes is

116

Figure 8-1: Effect of Number of Rows on the Seasonal COP at Optimum Air

Velocity and Varying Sub-Cool for Fixed Cost of Condenser Materials

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

4.30

0 1 2 3 4 5

Number of Rows of Condenser Tubes

Sea

son

al C

OP

15 degreees sub-cool at 95 F



117

also maximized by using only one row of tubes. This also results in a decrease in

compressor power, further contributing to increasing the COP. This reduction in

compressor power and refrigerant-side pressure drop is shown in Figure 8-2.

While decreasing the number of rows produces an increase in the seasonal COP, it

also causes an increase in the frontal area of the condenser. Figure 8-3 shows the effec

of the number of rows of tubes on the frontal area. As the number of rows is decreased

from 4 to 1, where the seasonal COP is the maximum, the frontal area of the condenser

nearly quadruples from approximately 5.9 ft2 to 23.2 ft2. A condenser that has a frontal

area of 23.2 ft2 is generally not feasible in most residential air-conditioning applications.

Therefore, when determining the number of rows of tubes, one must make a tradeoff

between space constraints and optimum performance when the cost of the configuration

is fixed.

Although the main cause of the increased seasonal COP with decreased number of

tube rows (decreased coil depth) is the decrease in compressor power, there is also a

decrease in condenser fan power with a decreased number of tube rows. Figure 8-4

shows the effect of the number of tube rows on the condenser fan power and the air-side

pressure drop. The figure shows that the air-side pressure drop also decreases as the

number of tube rows decreases. In fact, the decrease in the condenser fan power is due to

the reduction in air-side pressure drop, which results from a decrease in the depth of the

air passage produced by using fewer tube rows.

118

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

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

Material Cost at 82°°°° F Ambient Temperature

5700

5800

5900

6000

6100

6200

6300

6400

6500

6600

0 1 2 3 4 5


Co

mp

ress

or

Po

wer

(B

tu/h

r)

11

12

13

14

15

16

17

18

19

20

Refrig

erant S

ide P

ressure D

rop

(psia)

Compressor Power

Refrigerant Side Pressure Drop

119

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

0

5

10

15

20

25

0 1 2 3 4 5


Co

nd

ense

r F

ron

tal A

rea

(ft2 )

120

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

Airside Pressure Drop for Fixed Condenser Material Cost at 82°°°° F Ambient

Temperature at Optimum Sub-Cool and Air Velocity

0

50

100

150

200

250

300

350

0 1 2 3 4 5


Co

nd

ense

r F

an P

ow

er (

Btu

/hr)

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

Air S

ide P

ressure D

rop

(psia)

Condenser Fan Power

Air Side Pressure Drop

121

The number of rows of condenser tubes also effects the optimum operating

parameters such as the air velocity over the condenser. Figure 8-5 displays the effect o

air velocity over the condenser on the optimum seasonal COP for varying number o

rows. The figure shows that as the number of rows increases, the optimum air velocit

increases. For example, for a condenser configuration utilizing only 1 row of tubes, the

optimum seasonal COP occurs at an air velocity of approximately 7.0 ft/s. However for a

deeper condenser configuration utilizing 4 rows of tubes, the optimum seasonal COP

occurs at an air velocity of approximately 9.0 ft/s. The increase in optimal air velocity

coupled with the increase in air-side pressure drop shown in Figure 8-4 causes the fan

power to more than double as the number of rows is increased from 1 to 4.

Figure 8-6 shows the effect of the number of rows on the optimum air velocity and

optimum volumetric flow rate of air over the condenser. This figure shows that while the

optimum air velocity increases as the number of rows increases, the optimum volumetric

flow rate of air over the condenser decreases.

122

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

Optimum Sub-Cool for Fixed Condenser Material Cost

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

4.30

4.35

5 6 7 8 9 10 11 12 13 14


Sea

son

al C

OP

1 row

2 rows

3 rows

4 rows

Locus of Optimums

123

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

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 1 2 3 4 5


Op

tim

um

Air

Flo

w R

ate

Ove

r C

on

den

ser

(ft3 /m

in)

0

1

2

3

4

5

6

7

8

9

10

Op

timu

m A

ir Velo

city Over C

on

den

ser(ft/s)

Optimum Air Flow Rate

Optimum Air Velocity Over Condenser

124

Varying Condenser Tube Circuiting

Another condenser geometric design parameter that has an effect on system

performance is the tube circuiting. Varying the number of condenser tubes per circui

does not affect either the cost factor or the configuration or the frontal area of the

condenser. For this investigation, the number of rows, the tube diameter, the tube

spacing, and fin spacing were fixed to the values used for the base configuration. While

varying the number of tubes per circuit, the number of circuits was also varied in order to

maintain a nearly constant height to width ratio of approximately 0.83. The refrigeran

flow circuit configurations investigated for this study are summarized in Table 8-2. Each

configuration was tested for air velocities ranging from 6 ft/s to 13 ft/s and sub-cools

ranging from ° F to 20° F at 95° F ambient temperature. The maximum seasonal COP

for every configuration tested occurs within this selected range of operating conditions.

Table 8-2: Condenser Circuiting Configurations

Tubes/CircuitNumber of

Circuits

Condenser Width

(ft)

2 12 3.0

3 8 3.0

4 6 3.0

5 5 2.9

125

Figure 8-7 shows the effect of the number of tubes per circuit on the optimum

seasonal COP based on the optimum operating conditions for each configuration. The

figure shows that the maximum seasonal COP occurs when the refrigerant flow is divided

among 3 tubes. However, the seasonal COP for the optimal configuration is only

approximately 2.0 % greater than that of the base configuration (2 tubes per circuit), 0.2

% greater than a configuration utilizing 4 tubes per circuit, and 0.6 % greater than a

configuration with five tubes per circuit. Hence, in the range of optimum operating

conditions, the seasonal COP is relatively insensitive to variations in the number of tubes

per circuit.

The improved seasonal COP that occurs when the tubes per circuit increases from 2

to 3 results from the decrease in refrigerant pressure drop which tends to reduce the

required compressor power. The decrease in pressure drop occurs because as the number

of tubes per circuit increases, the mass flow of refrigerant through each individual tube

decreases. This decrease in the amount of mass flowing in each tube leads to a decrease

in the pressure drop through each tube. Figure 8-8 shows how the refrigerant-side

pressure drop varies with changes in the number of tubes per circuit at an ambient

temperature of 82° F for the optimum operating conditions for each configuration. As the

figure shows, the refrigerant-side pressure drop does indeed decrease with an increased

number of tubes per circuit. However, increasing the number of tubes per circuit also

causes the refrigerant-side heat transfer coefficient to decrease, which has a negative

effect on the seasonal COP. Therefore, two competing effects are at work. At a certain

point, the decrease in the refrigerant-side heat transfer coefficient that results fro

126

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

Sub-Cool and Air Velocity for Fixed Condenser Material Cost

4.08

4.09

4.10

4.11

4.12

4.13

4.14

4.15

4.16

1 2 3 4 5 6

Number of Condenser Tubes per Circuit

Sea

son

al C

OP

127

Figure 8-8: Refrigerant-Side Pressure Drop for Various Circuiting at 82 °°°° F

Ambient Temperature and at Optimum Sub-Cool and Air Velocity for Fixed


��

��

��0

2

4

6

8

10

12

14

16

18

1 2 3 4 5 6


Ref

rige

ran

t-S

ide

Pre

ssur

e D

rop

(psi

a)

Total

Straight Pipe�� Bends

128

increasing the number of tubes per circuit has a larger effect than the resulting decrease in

the refrigerant-side pressure drop. As a result, the seasonal COP begins to decrease as

the number of tubes per circuit increases. According to Figure 8-7, this point occurs

when the number of tubes per circuit is increased from 3 to 4.

While the total refrigerant-side pressure drop decreases with an increase in the

number of tubes per circuit, the percentage of the total pressure drop due to tube bends

actually increases considerably. This is because the actual number of bends is increased

by increasing the number of parallel flow passages. The refrigerant-side pressure drop

distribution between the straight tube and the tube bends at an ambient temperature of

82° F for various condenser tube circuit configurations is shown in Table 8-3.

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

Tubesper

Circuit

BendPressure

Drop(psia)

Straight PipePressure Drop

(psia)

Total PressureDrop(psia)

% of TotalPressure DropDue To Bends

2 5.40 11.2 16.6 32.5 %

3 1.70 3.32 5.02 33.9 %

4 0.77 1.31 2.08 37.0 %

5 0.41 0.44 0.85 48.2 %

129

Varying Fin Pitch

The condenser fin pitch is another geometric design parameter considered for this

study. To investigate the effect of condenser tube fin pitch on system performance for a

fixed heat exchanger cost factor, the tube size, tube spacing, circuiting, and number o

rows were fixed to the values of the base configuration. For this study, the syste

performance was calculated for fin pitches ranging from 8 fins per inch to 14 fins per

inch (fpi). With the cost of the condenser materials fixed, varying the fin pitch involves a

compromise between purchasing more aluminum fins versus purchasing more copper

tubing.

Figure 8-9 shows the variation of seasonal COP with air velocity for various fin pitch

values at optimal sub-cool conditions for each configuration (15° sub-cool at 95° F for

every case). As the figure shows, the optimum velocity for every fin pitch configuration

occurs between 8 ft/s and 9 ft/s. Thus, according to these results, the fin spacing has very

little affect on the seasonal COP or the optimal operating conditions. The optimu

seasonal COPs and area factors for varying fin pitch at fixed heat exchanger cost ar

shown in Table 8-4. Figure 8-10 shows a graphical demonstration of the effect of the fin

pitch on the optimum seasonal COP that is documented in Table 8-4.

Table 8-4 and Figure 8-10 also show that as the number of fins per inch increases

from 8 fins per inch to 10 fins per inch, the seasonal COP increases slightly from 4.10 to

4.11. However, as the fin pitch increases from 10 fins per inch to 14 fins per inch, the

seasonal COP decreases steadily from 4.11 to 4.08. It might be expected that increasing

130

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

Condenser Material Cost and Optimum Sub-Cool

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

Velocity and Sub-Cool for Fixed Condenser Material Cost

Fin Pitch (fpi) Optimum Seasonal COP Area Factor

8 4.10 1.30

10 4.11 1.15

12 4.09 1.00

14 4.08 0.93

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4 5 6 7 8 9 10 11 12 13 14 15 16


Sea

son

al C

OP

8 fins per inch

10 fins per inch

12 fins per inch

14 fins per inch

131

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 Cost

4.06

4.07

4.08

4.09

4.10

4.11

4.12

6 8 10 12 14 16

Fin Pitch (fins/inch)

Sea

son

al C

OP

132

the fins per inch should decrease the power requirements of the compressor and thus

increase the seasonal COP. However, as the fin spacing becomes smaller, the air-side

pressure drop also increases thus increasing the required power for the condenser fan.

This phenomenon is displayed in Figure 8-11, which shows the air-side pressure drop

versus the fin pitch at optimal operating conditions. At a certain plateau, the fin spacing

becomes too small and produces a pressure drop so large that the resultant increase in

condenser fan power is more than the decrease in the compressor power requirement.

Hence, the seasonal COP is lower.

Figure 8-12 shows how the power requirements of the condenser fan and the

compressor vary with the fin pitch at the maximum seasonal COP. The figure shows

that, as expected, the condenser fan power requirement increases with increasing fin

pitch. Figure 8-12 also shows that as the fin pitch increases from eight fins per inch to

ten fins per inch, the compressor power decreases from 7440 Btu/hr to approximatel

7400 Btu/hr at the maximum seasonal COP of each configuration. However, this figure

appears to contradict the theoretical prediction of decreased compressor power with

increased fin pitch since as the fin pitch increases from ten fins per inch to fourteen fins

per inch, the compressor power increases from approximately 7400 Btu/hr to 7420

Btu/hr. While this increase is a very small percentage of the total power requirement, it is

still surprising given the theoretical prediction. One possible explanation for this result

can be found in an analysis of the optimal operating conditions yielding the maximu

seasonal COP. The optimum seasonal COP occurs at a slightly different air velocity for

each configuration. The compressor power requirement steadily decreases with increased

133

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

Cost at Optimum Sub-Cool and Air Velocity at 95°°°° F Ambient Temperature

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0050

7 8 9 10 11 12 13 14 15


Air

sid

e P

ress

ure

Dro

p (

psi

a)

134

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

Cool and Air Velocity and 95°°°° F Ambient Temperature

7200

7250

7300

7350

7400

7450

7500

7 8 9 10 11 12 13 14 15


Co

mp

ress

or

Po

wer

(B

tu/h

r)

50

100

150

200

250

300

350

Co

nd

enser F

an P

ow

er (Btu

/hr)

Compressor Power

Condenser Fan Power

135

air velocity over the condenser while conversely the condenser fan work steadily

increases with increased air velocity. The maximum COP for each fin pitch

configuration occurs where the combined power requirement for the condenser fan and

the compressor is at a minimum. For fixed cost of condenser materials, as the number o

fins per inch increases, the air-side heat transfer area increases thus causing a decrease in

the compressor power and an increase in the seasonal COP. However increasing the fin

pitch also reduces the refrigerant-side heat transfer area, since for fixed cost, the fronta

area decreases with increasing fin pitch. Therefore, two competing effects are at work.

When the fin pitch is increased from 8 to 10, the effect of the increase in the air-side hea

transfer area is larger than the effect of the decrease in the refrigerant-side heat transfer

area. Therefore, the compressor power is decreased, producing an increase in the

seasonal COP. However when the fin pitch is further increased from 10 to 12, the effec

of the reduction in the refrigerant-side heat transfer area is larger than the effect of the

increase in the air-side heat transfer area. Hence, the compressor power begins to

increase, thus causing the seasonal COP to decrease.

While the fin pitch has very little effect on the seasonal COP it does affect another

important aspect of heat exchanger design, the frontal area. Figure 8-13 shows the effec

of the fin pitch on the condenser frontal area. The figure shows that as the fin pitch is

increased, the frontal area decreases. This is due to the fixed material cost constrain

requiring less tubing with increasing fin pitch. This trend can also be seen in Table 8-4,

which shows that increasing the fin pitch causes a decrease in the area factor. Thus, if the

136

Figure 8-13: Effect of Fin Pitch on Condenser Frontal Area at Optimum Sub-Cool

and Air Velocity for Fixed Condenser Material Cost

6.00

6.50

7.00

7.50

8.00

8.50

9.00

9.50

10.00

6 8 10 12 14 16


Co

nd

ense

r F

ron

tal A

rea

(ft2 )

137

designer’s primary goal is for a more compact heat exchanger, a larger fin pitch should be

utilized. Again, the fin pitch has very little effect on the optimal operating conditions and

the seasonal COP; thus using the maximum fin pitch would create a compact hea

exchanger without significantly sacrificing performance.

Varying Tube Diameter

Yet another geometric design parameter studied in this work is the condenser tube

diameter. The tube sizes considered for this study are taken from the AAON Heating and

Refrigeration Products specifications (www.aaon.co . AAON Heating and Air-

Conditioning Products web site). The dimensions of the tubes investigated are

summarized in Table 8-5. For this investigation, the number of rows, number of tubes

per circuit and number of fins per inch were all maintained at the values used in the base

configuration.

Figure 8-14 shows how the optimum seasonal COP is affected by the tube diameter.

For all sub-cool conditions in the recommended range of 10° F to 20° F at 95° F ambient

temperature, utilizing tubes of 5/8” outer diameter yields unreasonably low condensing

temperatures inside the tubes for the resultant frontal area at the given fixed hea

exchanger cost.

138

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

Conditioning Products web site)

OutsideDiameter (in.)

InsideDiameter (in.)

Wall Thickness(in.)

0.3125 0.3005 0.0120

0.3750 0.3630 0.0120

0.5000 0.4840 0.0160

0.6250 0.6170 0.0180

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

Cool and Air Velocity for Fixed Condenser Material Cost

3.88

3.92

3.96

4.00

4.04

4.08

4.12

1/4 5/16 3/8 7/16 1/2 9/16

Outer Tube Diameter (in)

Sea

son

al C

OP

139

Tubes of this size also greatly deteriorate the system performance, and thus are not

considered in this discussion of the effect of tube size at fixed heat exchanger cost. As

Figure 8-14 shows, the optimum seasonal COP occurs with a tube diameter of 3/8”. The

optimum seasonal COP of 4.09 is exactly equal to the optimum value for the base

configuration.

While varying the tube circuiting and the fin spacing has very little effect on the

optimal operating conditions, varying the tube diameter does indeed have a significan

effect. Figure 8-15 shows the effect of the tube diameter on the optimum air velocity

over the condenser and the optimum sub-cool conditions. As the figure shows, the

optimum air velocity increases continuously with tube diameter. However the optimu

sub-cool has a distinct minimum which exists at a tube size of 3/8”. The optimu

seasonal COP, area factor, and operating conditions for each tube size investigated are

shown in Table 8-6. The decreasing frontal area with increasing tube diameter is a result

of the fixed condenser material cost constraint. As both Table 8-6 and Figure 8-15

demonstrate, the optimum air velocity varies with changes in tube diameter.

The length of condenser tubing allocated to the superheated, saturated, and sub-

cooled portions of the condenser is also affected by the tube diameter, as shown in Figure

8-16. The figure shows that as the tube diameter increases from 5/16” to 5/8”, the

condenser allocation for the superheated and the saturated portions of the condenser tube

increases steadily while that of the sub-cooled portion decreases steadily. The portion o

140

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


11

12

13

14

15

16

1/4 5/16 3/8 7/16 1/2 9/16


Op

tim

um

Su

b-C

oo

l (F

)

6

7

8

9

10

11

Op

timu

m A

ir Velo

city (ft/s)

Subcool

Air Velocity

141

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

Outer TubeDiameter (in)

OptimumSeasonal COP

Optimum AirVelocity (ft/s)

Optimum DegreesSub-cool (F)

AreaFactor

5/16” 3.91 8.0 15 1.13

3/8” 4.09 8.5 15 1.00

1/2” 3.99 10.0 15 0.82

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


��

��

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

1/4 5/16 3/8 7/16 1/2 9/16

Tube Outer Diameter (in)

Con

dens

er A

lloca

tion

Saturated

��Subcooled

Superheated

142

the condenser allocated to the sub-cooled and superheated portions is nearly identical a

the optimum tube diameter of 3/8”. The amount of tube length allocated to each portion

of the condenser will have an effect on the refrigerant pressure drop, which in turn affects

the compressor power required. Figure 8-17 shows the effect of the tube diameter on the

refrigerant-side pressure drop at optimum operating conditions and 82° F ambient

temperature. As the figure shows, the refrigerant-side pressure drop decreases as the tube

diameter increases.

Figure 8-18 shows the effect of the tube diameter on the power required for the

condenser fan and the compressor for the optimum seasonal COP at each tube diameter.

As the figure shows, the compressor power required is a minimum at the optimum tube

diameter 3/8”. Again, the optimum seasonal COP occurs where the total power required

by the condenser fan and the compressor is at a minimum. Just as with the fin spacing,

the minimum power required varies as the tube diameter varies. While the total power

required at the optimum steadily decreases with increased tube diameter, the required

compressor power reaches a minimum at a tube diameter of 3/8” and then increases when

the tube diameter increases to 1/2”.

143

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

Air Velocity at 82°°°° F Ambient Temperature for Fixed Condenser Material Cost

0

5

10

15

20

25

30

35

40

45

1/4 5/16 3/8 7/16 1/2 9/16


Ref

rig

eran

t-S

ide

Pre

ssu

re D

rop

(p

sia

Total

saturated

superheated

subcooled

144

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 82°°°° F Ambient Temperature

7200

7300

7400

7500

7600

7700

7800

7900

8000

1/4 5/16 3/8 7/16 1/2 9/16


To

tal P

ow

er &

Co

mp

ress

or

Po

wer

(B

tu/h

r)

0

100

200

300

400

500

600

700

800

Co

nd

enser F

an P

ow

er (Btu

/hr)

Total Power

Compressor Power

Condenser Fan Power

145

Operating Costs

The operating costs for the air-conditioning system are inversely proportional to the

seasonal COP (1/COP ∝ operating cost). In this study, an operating cost factor is defined

as: 1/COP = operating cost factor. Figure 8-19 shows how the operating cost factor

varies with the area factor for all of the geometric parameters investigated for this study.

According to the figure, decreasing the number of rows from the base configuration value

of 3 rows to 1 row produces the largest decrease in operating costs. In fact, the lowes

operating cost occurs when 1 row of tubing is used. However, the frontal area for this

configuration is more than 3 times that of the base configuration. The frontal area for the

2-row configuration is 50% greater than that of the base configuration. Hence

configurations utilizing 2 and 3 rows of tubing generally may not be feasible at a fixed

condenser material cost factor when space constraints are of concern. In this space

constrained situation, the configuration using 3 rows of tubing will yield the best

performance and lowest operating cost with the most reasonable frontal area.

Once configurations of 1, 2, and 4 rows of tubes are eliminated, Figure 8-19 shows

that the two geometric parameters having the most significant effect on the operating cos

of the complete air-conditioning system are the tube diameter and the number of tubes

per circuit. The figure shows that when only 2 tubes per circuit are used, as in the base

configuration, the optimum tube diameter is 3/8” with fixed heat exchanger cost.

However, the figure also shows that for a tube diameter of 3/8”, and 3 rows of tubing, the

lowest operating cost occurs for a condenser configuration utilizing 3 tubes per circuit.

The initial investigations outlined throughout this chapter did not test the effect of tube

146

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

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

0.230

0.234

0.238

0.242

0.246

0.250

0.254

0.258

0 0.5 1 1.5 2 2.5 3 3.5

Area Factor

1/C

OP

(O

per

atin

g C

ost

Fac

tor)

Tube Diameter

Fin Pitch

Number of Rows

Tubes per Circui

Base configuration:12 Fins Per Inch (FPI)

2 Tubes per Circuit (TPC)

3 Rows

3/8" Diameter

TubeDiameter

5/16"

1/2"

4 rows

2 rows

1 row

10 FPI 8 FPI14 FPI

5 TPC

4 TPC

3 TPC

Base Case

147

diameter on the system performance when tube circuiting other than the base

configuration of 2 tubes per circuit is utilized. From an analysis of the figure, it is

obvious that an examination of this effect is warranted.

While Figure 8-19 shows that for fixed heat exchanger cost, a configuration with a

5/16” tube diameter yields the highest operating cost and the worst performance, this tube

diameter was only investigated for the base case configuration of 2 tubes per circuit.

When the number of tubes per circuit is increased, the amount of mass of refrigerant

flowing through each individual tube is decreased. Therefore, tubes of smaller diameter

can be utilized without degrading system performance. Employing a smaller diameter

tube does not greatly increase the frontal area with fixed condenser material cost since the

resultant area factor is only 1.13. Furthermore, increasing the number of tubes per circuit

has no affect on the frontal area.

As a result of the above analysis, the effect of the number of tubes per circuit on the

system performance was investigated, for a configuration utilizing a tube diameter of

5/16”, 3 rows of tubes, and 12 fins per inch. Although Figure 8-10 shows that the

optimum fin pitch is 10 fins per inch for the base case configuration, Figure 8-19 shows

that the fin pitch has virtually no effect on the optimum system operating cost and system

performance. In fact, both Figure 8-10 and Figure 8-19 show that there is very littl

difference in the optimum seasonal COP (minimum operating cost) for a range of 8 fins

per inch to 12 fins per inch. Therefore since there is very little difference in the operating

cost for the varying fin pitch, a configuration employing 12 fins per inch was used in this

supplemental investigation of the effect of tubes circuiting with tubes of 3/8” and 5/16”

148

diameter. A configuration of 12 fins per inch will yield an area factor of unity while stil

providing a near optimum seasonal COP (lowest operating cost).

Figure 8-20 shows the effect of the number of tubes per circuit on the optimum

seasonal COP for a condenser configuration with a tube diameter of 5/16” with a fixed

cost factor. The figure shows that for a tube diameter of 5/16”, as the number of tubes

per circuit increases from 2 to 4, the optimum seasonal COP increases by approximately

8% from approximately 3.91 to 4.22. As the number of tubes per circuit increases from 4

to 5, the optimum seasonal COP increases from 4.22 to a maximum of 4.23. The

optimum seasonal COP then decreases to 4.21 when the number of tubes per circuit

increases from 5 to 6. The explanations for this trend are the same as for the trends

discussed earlier in this chapter under the section entitled “Varying Condenser Tube

Circuiting”. As discussed in that section, the improved seasonal COP that occurs when

the tubes per circuit increases from 2 to 5 results from the decrease in the refrigeran

pressure drop having a larger effect on increasing the COP than the decrease in the

refrigerant-side heat transfer has on decreasing the COP.

Figure 8-21 shows the optimum seasonal COP versus the number of tubes per circuit

for the both 3/8” tube diameter configuration (base configuration) and the 5/16” tube

diameter configuration. As the figure shows, the optimum seasonal COPs achieved for

condensers using a 5/16” diameter tube are higher than those with a 3/8” diameter tube.

For a condenser with a tube diameter of 3/8”, the optimum seasonal COP occurs when 3

tubes per circuit is used. However, when the diameter is decreased to 5/16”, the optimu

149

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

Condenser Tube Circuiting with Fixed Condenser Material Cost and 5/16” Tube

Outer Diameter

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

1 2 3 4 5 6 7


Sea

son

al C

OP

5/16" Tube Diameter

3 rows of tubes12 fins per inch

150

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

Seasonal COP for 5/16” and 3/8” Outer Tube Diameters at Optimum Sub-Cool and

Air Velocity with Fixed Condenser Material Cost

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

1 2 3 4 5 6 7


Sea

son

al C

OP

5/16" Outer Tube Diameter


Fixed Material Cost


151

seasonal COP occurs when 5 tubes per circuit are used. When the number of tubes per

circuit is the value used for the base configuration (2 tubes per circuit), a tube diameter of

3/8” yields a slightly higher optimum seasonal COP than a 5/16” diameter tube.

Conversely, when the tubes per circuit are increased, configurations with a tube diameter

of 5/16” yield the highest seasonal COP. The optimum seasonal COP for the 5/16” tube

diameter configuration is 4.23, which is approximately 2% greater than the optimum

seasonal COP for the 3/8” diameter tube configuration that has a value of 4.15.

Therefore, when the cost factor of the heat exchanger configuration is fixed, a condenser

with an outer tube diameter of 5/16”, 5 tubes per circuit, 3 rows of tubes, and 12 fins per

inch yields the highest seasonal COP (lowest operating cost) with the most reasonable

frontal area.

152

CHAPTER IX

OPTIMIZATION OF GEOMETRIC DESIGN PARAMETERS FOR FIXED

CONDENSER FRONTAL AREA

The effects of varying the number of rows, the number of tubes per circuit, the tube

diameter, and the fin pitch while keeping the heat exchanger costs constant wer

presented in the previous chapter. While producing changes in performance, varying

these parameters (with the exception of the tubes per circuit) also produces changes in the

frontal area of the condenser since it is allowed to vary freely. However, as discussed

earlier, the residential air-conditioning system designer encounters space constraints tha

prevent the use of a heat exchanger with a large frontal area. In this chapter, the effects

of varying the number of rows, the tube diameter, and the fin pitch for fixed frontal area

with variable cost will be investigated.

153

Varying the Number of Rows of Condenser Tubes

Varying the depth of the coil by changing the number of rows of condenser tubing

with fixed frontal area is the first geometric design parameter investigation considered for

this part of the study. The number of tubes per circuit, fin spacing, tube diameter, frontal

area, and tube spacing are all fixed to the values of the base configuration. Figure 9-1

shows the effect of the air velocity on the seasonal COP for varying numbers of rows

with optimum sub-cool at 95° F ambient temperature. According to the figure, for much

of the range of air velocities shown, the optimum seasonal COP occurs for configurations

utilizing 3 rows of tubes. The figure also shows that as the number of rows decreases, the

optimum air velocity increases. This trend is summarized in Table 9-1, which shows the

optimum operating conditions for each row configuration. Figure 9-2 shows the effect o

the number of rows on the seasonal COP at optimum operating conditions. This figure

reinforces the trends observed in Figure 9-1, and again shows that the maximum seasonal

COP occurs when 3 rows of tubes are employed.

As shown in the Table 9-1, the maximum seasonal COP occurs when 3 rows of tubes

are utilized with 15° F sub-cool at ° F ambient temperature and an air velocity of 8.5

ft/s. The seasonal COP while showing a major increase when the number of rows i

increased from 2 rows to 3 rows, actually shows a slight decrease when the number o

rows is further increased from 3 to 4. Continuing to increase the number of rows of tubes

also further increases the heat transfer area. Hence, intuitively one might assume that the

seasonal COP would also continue to increase. However as both Figure 9-1 and Table 9-

1 have shown this is not the case.

154

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

Optimum Sub-Cool with Fixed Condenser Frontal Area

Table 9-1: Optimum Operating Conditions for Varying Number of Rows with

Fixed Condenser Frontal Area

Number ofRows

SeasonalCOP

Cost FactorAir Velocity

(ft/s)Degrees Sub-coo

at 95° F (° F)

2 3.98 0.75 11.0 13

3 4.09 1.00 8.5 15

4 4.07 1.32 7.0 13

��

��

��

��

��

��

��

��

��

��

3.65

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

5 6 7 8 9 10 11 12 13 14


Sea

son

al C

OP

��3 rows

4 rows

2 rows

Locusof

Optimums

155

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

3.96

3.98

4.00

4.02

4.04

4.06

4.08

4.10

1 2 3 4 5

Number of Rows of Tubes

Sea

son

al C

OP

156

As the number of rows of tubes increases, the depth of the condenser increases and

both the refrigerant-side and air-side heat transfer areas increase. However, increasing

the number of rows also increases the refrigerant flow path, as well as the air flow path

(deeper coil), thus increasing both the refrigerant-side and air-side pressure drops. The

increase in the refrigerant-side pressure drop with increasing number of rows is shown in

Figure 9-3. Therefore, two competing effects are at work. As the number of rows is

increased from 2 to 3, the increase in the overall heat transfer area has a larger effect on

the seasonal COP than the resultant increase in the in the pressure drop, hence the

seasonal COP increases. Figure 9-4 displays the compressor and condenser fan power

versus the number of rows, and shows that the compressor power decreases when the

number of rows is increased from 2 to 3. Again, this is because the increase in the overall

heat transfer area has a larger effect on the seasonal COP than the increase in pressure

drop. However, when the number of rows is increased from 3 to 4, the resultant increase

in the pressure drop has a larger effect on the seasonal COP than the increase in the

overall heat transfer area, thus the seasonal COP decreases. Figure 9-4 shows that as the

number of rows is increased from 3 to 4, the compressor power actually increases, thus

confirming the aforementioned trend.

157

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

Temperature

0

5

10

15

20

25

1 2 3 4 5

Number of Rows of Tubes

Ref

rig

eran

t S

ide

Pre

ssu

re D

rop

(p

sia)

Total

Straight Tube

Bends

158

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

with Optimum Sub-Cool and Air Velocity at 82°°°° F Ambient Temperature for Fixed

Condenser Frontal Area

5825

5850

5875

5900

5925

5950

5975

6000

1 2 3 4 5


Co

mp

ress

or

Po

wer

(B

tu/h

r)

175

200

225

250

275

300

325

350

Co

nd

enser F

an P

ow

er (Btu

/hr)

Compressor Power

Condenser Fan Power

159

Varying Fin Pitch

The next geometric design parameter varied while fixing the condenser frontal area is

the fin pitch. The frontal area, tube diameter, number of rows, number of tubes per

circuit and the tube spacing are all fixed to the values of the base configuration. Figure 9-

5 shows the effect of air velocity on the seasonal COP for varying fin pitch with optimu

sub-cool at 95° F ambient temperature. As the figure shows, varying the fin pitch has a

small affect on the optimum seasonal COP when keeping the frontal area of the

condenser fixed (optimums range from 4.00 to 4.10). According to the figure, the

recommended range of operation is between air velocities of 8.0 ft/s and 11.0 ft/s. The

optimum air velocity increases from 8.0 ft/s to 10.5 ft/s as the fin pitch decreases from 14

fins per inch to 8 fins per inch.

Figure 9-6 shows the effect of the fin pitch on the seasonal COP at optimum air

velocity and sub-cool. The figure shows that the optimum seasonal COP increases as the

number of fins per inch increases. However, the increase in the optimum seasonal COP

is only approximately 2.5 % when the number of fins per inch increases form 8 to 14.

Thus the fin pitch has only a small on the optimum seasonal COP when the frontal area

of the condenser is fixed. Varying the fin pitch also has very little affect on the optimum

sub-cool conditions. However, unlike the case in the previous chapter where the hea

exchanger cost is fixed, varying the fin pitch does have a significant affect on the

optimum air velocity over the condenser when the frontal area of the condenser is fixed.

160

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

Optimum Sub-Cool for Fixed Condenser Frontal Area

3.50

3.60

3.70

3.80

3.90

4.00

4.10

4.20

4 6 8 10 12 14 16


Sea

son

al C

OP

14 fins per inch

12 fins per inch

10 fins per inch

8 fins per inch

Locus ofOptimums

161

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

Velocity for Fixed Condenser Frontal Area

3.98

4.00

4.02

4.04

4.06

4.08

4.10

4.12

6 8 10 12 14 16


Sea

son

al C

OP

162

As is demonstrated in Figure 9-5, at a fin pitch of 8 fins per inch the optimum air velocity

is approximately 10.5 ft/s. Yet when the fin itch increases to 14 fins per inch, the

optimum air velocity decreases to 8.0 ft/s.

Using condenser designs with more fins per inch yields better performance. The

maximum variation in the optimum seasonal COP as the fin pitch is varied from 8 fins

per inch to 14 fins per inch is approximately 2.0 %. For this improvement in the seasona

COP, the cost of this configuration increases by approximately 41% as shown in Table 9-

2. This table shows the cost factor, optimum operating conditions, and the optimum

seasonal COP for varying fin pitch with fixed condenser frontal area.

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

with Fixed Frontal Area

FinPitch

Optimum Sub-cool a95° F ambient

Temperature (95° F)

Optimum AirVelocity (ft/s)

OptimumSeasonal COP

CostFactor

8 15 10.5 4.00 0.78

10 15 9.5 4.05 0.89

12 15 8.5 4.09 1.00

14 15 8.0 4.10 1.10

163

As the fin pitch increases, the airside pressure drop over the fins also increases. When

the frontal area of the condenser is fixed, the increased pressure drop due to increasing fin

pitch is transferred directly to the fan power, causing it to increase as well. However, the

compressor fan power required decreases by approximately the same amount as the fan

power increases. Thus, the phenomenon of increased airside pressure drop resulting fro

increased fin pitch does not cause the seasonal COP to decrease.

Varying Tube Diameter

The final geometric parameter varied with fixed condenser frontal area is the tube

diameter. The frontal area, the number of rows, the fin pitch, the tube spacing and the

number of tubes per circuit are all maintained at the values utilized for the base

configuration. Figure 9-7 shows the effect of the air velocity on the seasonal COP for

various tube diameters at optimum sub-cool. According to the figure, the absolute

maximum seasonal COP is 4.11 and occurs at a tube diameter of 1/2”. Conversely, in the

previous chapter is was found that for fixed heat exchanger cost and variable frontal area,

the maximum seasonal COP is 4.09 and occurs for a tube diameter of 3/8”. Figure 9-8

shows how the seasonal COP varies with the tube diameter at optimum operating

conditions. Figure 9-8 only reinforces the trends displayed in Figure 9-7. The seasonal

COP increases by approximately 5.4 % from 3.88 to 4.09 as the tube diameter is

increased from 5/16” to 3/8”. The seasonal COP then increases by only 0.5% from 4.09

164

Figure 9-7: Effect of Air Velocity For Varying Tube Diameter at Optimum Sub-

Cool for Fixed Condenser Frontal Area

3.60

3.70

3.80

3.90

4.00

4.10

4.20

5 6 7 8 9 10 11 12 13 14


Sea

son

al C

OP

1/2" tube diameter

3/8" tube diameter

5/8" tube diameter

5/16" tube diameter

Locus ofOptimums

165

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

Frontal Area at Optimum Sub-Cool and Air Velocity

3.85

3.90

3.95

4.00

4.05

4.10

4.15

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16


Sea

son

al C

OP

166

to 4.11 when the tube diameter increases from 3/8” to 1/2”. When the diameter is further

increased from 1/2” to 5/8”, the optimum seasonal COP decreases by only 2.8 % fro

4.11 to 4.00. These results, along with the optimum operating conditions and cost factors

for varying tube diameters, are shown in Table 9-3.

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

Diameters with Fixed Frontal Area

TubeDiameter

(in)

Optimum Sub-cooat 95° F ambient

Temperature (95° F)

OptimumAir Velocity

(ft/s)

OptimumSeasonal COP

CostFactor

5/16” 15 8.5 3.88 0.92

3/8” 15 8.5 4.09 1.00

1/2” 15 8.5 4.11 1.20

5/8” 15 8.0 4.00 1.59

Increasing the tube diameter has a large impact on many physical phenomena in the

system. Increasing the tube diameter causes a decrease in the refrigerant-side pressure

drop and an increase in the refrigerant-side heat transfer area. Both of these phenomena

have a positive impact on the seasonal COP. However, increasing the tube diameter also

reduces the minimum air flow area, producing an increase in the air drag. As a result, the

167

air-side pressure drop increases, and the condenser fan power also steadily increases.

These phenomena have a negative impact on the COP. Hence, there are competing

negative phenomena and positive phenomena at work. According to Figure 9-8, when

the tube diameter is increased from 5/16” to 1/2”, the increase in the COP that results

from the reduction in the refrigerant-side pressure drop and the increase in the

refrigerant-side heat transfer area is larger than the reduction in the COP that results from

the increased air-side pressure drop and increased condenser fan power. Thus, as Figure

9-8 shows, the seasonal COP increases when the diameter is increased from 5/16” to

1/2”. Figure 9-9 shows the refrigerant-side pressure drop versus tube diameter at

optimum sub-cool and air velocity. According to Figure 9-9, when the tube diameter is

increased from 5/16” to 1/2”, the refrigerant-side pressure drop decreases significantly.

Figure 9-10 shows the power requirements of the compressor and the condenser fan

versus the tube diameter at optimum sub-cool and air velocity. The figure shows that the

reduction in the refrigerant-side pressure drop is indeed large enough to produce a

decrease in the compressor power as the tube diameter is increased from 5/16” to 1/2”,

while the condenser fan power increases steadily.

Conversely, when the tube diameter is further increased from 1/2” to 5/8”, the

reduction in the COP that results from the increased air-side pressure drop and increased

condenser fan power is larger than the increase in the COP that results from the decrease

in the refrigerant-side pressure drop and the increase in the refrigerant-side heat transfer

area. Therefore, when the diameter is increased from 1/2” to 5/8”, the seasonal COP

168

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

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

0

5

10

15

20

25

30

35

40

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16


Ref

rig

eran

t S

ide

Pre

ssu

re D

rop

(p

sia)

Total

Straight Tube

Bends

169

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

Condenser Frontal Area at 82°°°° F Ambient Temperature, Optimum Sub-Cool and

Air Velocity

5700

5800

5900

6000

6100

6200

6300

6400

6500

6600

6700

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16


To

tal &

Co

mp

ress

or

Po

wer

(B

tu/h

r)

0

100

200

300

400

500

600

700

800

900

1000

Co

nd

enser F

an P

ow

er (Btu

/hr)

Total Power (Fixed Area)

Compressor Power (Fixed Area)

Condenser Fan Power (Fixed Area)

170

decreases, as shown in Figure 9-8. The increase in the air-side pressure drop tha

accompanies an increase in the tube diameter is displayed in Figure 9-11. Figure 9-10

shows that when the tube diameter is increased from 1/2” to 5/8”, the compressor power

actually increases. Moreover, Table 9-3 shows that when the tube diameter is increased

from 1/2” to 5//8”, the optimum air velocity decreases in an effort to reduce the increase

in the fan power that results from the increased drag. The reduction in the optimum air-

velocity results in a decrease in the effective temperature difference between the

refrigerant and the air. Therefore, the reduction in the minimum air flow area coupled

with the decrease in the effective refrigerant-to-air temperature difference produces a

decrease in the air-side heat transfer coefficient. Hence, the negative effects on the

seasonal COP become even larger.

Operating Costs

As discussed in the previous chapter, the operating cost of the air-conditioning system

is inversely proportional to the seasonal COP (1/COP ∝ operating cost). In this study, an

operating cost factor is defined as: 1/COP = operating cost factor. Figure 9-12 shows

how the operating cost factor, varies with the condenser material cost factor with fixed

frontal area for all of the geometric parameters investigated for this study. According to

the figure, when the frontal area of the condenser is fixed, the lowest operating cost i

achieved when a configuration utilizing 3 rows of tubes, with tube of diameter 3/8”, a fin

171

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

Frontal Area at 82°°°° F Ambient Temperature, Optimum Air Velocity and Sub-Cool

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16


Air

-Sid

e P

ress

ure

Dro

p (

psi

a)

Total (Fixed Area)

Fins (Fixed Area)

Tubes (Fixed Area)

172

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

��

��

��

0.240

0.242

0.244

0.246

0.248

0.250

0.252

0.254

0.256

0.258

0.260

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Condenser Material Cost Factor

1/C

OP

(O

per

atin

g C

ost

Fac

tor)

��Tube Diameter

Number of Rows

Fin Pitch

Tubes per Circuit

TubeDiameter

1/2"

4 rows

2 rows

10 FPI

8 FPI

14 FPI

5/16"

5/8"

3 TPC

5 TPC

4 TPC

Base Configuration

Base Configuration12 Fins Per Inch (FPI)


3 Rows

3/8" Diameter Tube

173

pitch of 12 fins per inch, and employing 3 tubes per circuit. This configuration has a cost

factor of unity, and thus cost the same as that of the base configuration.

Figure 9-12 also shows that, unlike in Chapter VIII where the cost factor of the hea

exchangers is fixed, when the frontal area is fixed the lowest operating cost occurs when

3 rows of tubes are used. Increasing the number of rows to 4 actually increases both the

coil material cost and the operating cost factor. Although there is a relatively significant

2.3% decrease in operating cost when the fin pitch decreases from 8 fins per inch to 12

fins per inch, there is only a 0.2% decrease in the operating cost when the fin pitch is

further decreased to 14 fins per inch. A configuration using 14 fins per inch yields lower

operating costs than do those employing fewer fins per inch. However, the material cos

factor of this configuration is 1.1, which is 10% greater than the base case configuration

(12 fins per inch). Therefore, when the frontal area of the condenser is fixed, it is

recommended that a fin pitch of 12 fins per inch be employed.

It can also be discerned from Figure 9-12 that the tube diameter and the number o

tubes per circuit have a significant effect on the operating cost of the complete air-

conditioning system. Figure 9-12 shows that when only 2 tubes per circuit are used, as in

the base configuration, the optimum tube diameter is 1/2” with fixed heat exchanger cost.

However, the figure also shows that for a tube diameter of 3/8” and 3 rows of tubes, the

lowest operating cost occurs for a condenser configuration utilizing 3 tubes per circuit.

The initial investigations outlined throughout this chapter did not examine the effect of

tube diameter on the system performance when tube circuiting other than the base

174

configuration of 2 tubes per circuit is utilized. From an analysis of Figure 9-12, it is

obvious that an examination of this effect is warranted.

While Figure 9-12 shows that for fixed heat exchanger cost, a configuration with a

5/16” tube diameter yields the highest operating cost, and the worst performance.

However, this tube diameter was only tested for the base case configuration of 2 tubes per

circuit. This low performance is related to the higher refrigerant-side pressure drop tha

results when a tube diameter this small is employed with only 2 tubes per refrigerant flow

circuits. Increasing the number of tubes per circuit should relieve the detrimental effec

of the higher refrigerant-side pressure drop. When the number of tubes per circuit is

increased, the amount of mass of refrigerant flowing through each individual tube is

decreased. Therefore, tubes of smaller diameter can be utilized without degrading syste

performance. Employing a 5/16” diameter tube with the frontal area of the condenser

fixed actually reduces the cost factor to 0.92. Furthermore, increasing the number o

tubes per circuit has no effect on the frontal area. Therefore, configurations with smaller

diameter tubes and a greater number of tubes per circuit do not increase the cost o

materials for the total system when the frontal area of the heat exchangers is fixed. As a

result of the above analysis, the effect of the number of tubes per circuit on the system

performance will be investigated, for a configuration utilizing a tube diameter of 5/16”, 3

rows of tubes, and 12 fins per inch.

Figure 9-13 shows the effect of the number of tubes per circuit on the seasonal COP

at optimum operating conditions for a heat exchanger configuration with a tube diameter

175

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

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

Velocity

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

1 2 3 4 5 6 7


Sea

son

al C

OP

5/16" Tube Diameter


176

of 5/16” with a fixed cost factor. The figure shows that for a tube diameter of 5/16”, as

the number of tubes per circuit increases from 2 to 4, the seasonal COP increases by

approximately 7.2% from approximately 3.88 to 4.16. As the number of tubes per circuit

increases from 4 to 5, the optimum seasonal COP increases from 4.16 to a maximum o

4.17. The optimum seasonal COP then decreases to 4.14 when the number of tubes per

circuit increases from 5 to 6.

The explanations for the aforementioned trends in the optimum seasonal COP with

varying number of tubes per circuit are the same as for the trends discussed earlier in

Chapter VIII under the section entitled “Varying Condenser Tube Circuiting”. As

discussed in that section, the improved seasonal COP that occurs when the tubes per

circuit increases from 2 to 5 results from the decrease in refrigerant pressure drop which

reduces the required compressor power. The decrease in pressure drop occurs because,

as the number of tubes per circuit increases, the amount of mass of refrigerant through

each individual tube decreases. This decrease in the amount of mass flowing in each tube

leads to a decrease in the refrigerant-side pressure drop through each tube, which has a

positive effect on the seasonal COP. However increasing the number of tubes per circuit

also decreases the refrigerant-side heat transfer coefficient, which has a negative effect on

the seasonal COP. For the 5/16” diameter tube configuration, when the number of tubes

per circuit is increased from 2 to 5, the positive effect of the reduced refrigerant-side

pressure drop has a larger impact on the seasonal COP than the negative effect of the

decreased refrigerant-side heat transfer coefficient. Thus the seasonal COP increases.

However, when the tubes per circuit is increased from 5 to 6 for the 5/16” tube

177

configuration, the decreased refrigerant-side heat transfer coefficient has a larger effec

on the seasonal COP than the decreased refrigerant-side pressure drop, and the seasonal

COP decreases. Hence, there is a certain plateau at which the number of tubes per circuit

cannot increase without causing a decrease in system performance. For a condenser with

a tube diameter of 3/8”, this occurs when 3 tubes per circuit are used. However when the

tube diameter is decreased to 5/16”, this plateau occurs at a configuration utilizing 5

tubes per circuit.

Figure 9-14 shows the optimum seasonal COP versus the number of tubes per circui

for the both 3/8” tube diameter configuration (base configuration) and the 5/16” tube

diameter configuration with fixed condenser frontal area. As the figure shows, the values

of the optimum seasonal COP achieved for condensers using a 5/16” diameter tube are

slightly higher than those with a 3/8” diameter tube. For a condenser with a tube

diameter of 3/8”, the optimum seasonal COP is 4.15 and occurs when 3 tubes per circuit

is used. However, when the diameter is decreased to 5/16”, the optimum seasonal COP is

4.17 and occurs when 5 tubes per circuit are used. Thus, the optimum seasonal COP

obtained when using tubes of 5/16” diameter is 0.5 % higher than the optimum obtained

using tubes of 3/8” diameter.

When the number of tubes per circuit is the value used for the base configuration (2

tubes per circuit), a condenser using tubes of diameter of 3/8” yields a much higher

optimum seasonal COP, COP = 4.09, than a condenser using tubes of diameter 5/16”,

COP = 3.88. Conversely, when the number of tubes per circuit is increased,

178

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

Seasonal COP for 5/16” and 3/8” Outer Tube Diameters with Fixed Frontal Area at

Optimum Sub-Cool and Air Velocity

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

1 2 3 4 5 6 7


Sea

son

al C

OP



Fixed Frontal Area


179

configurations utilizing tubes of 5/16” diameter yield the highest seasonal COP.

Furthermore, the cost factor of a configuration utilizing tubes of diameter 5/16” and 5

tubes per circuit, 0.92, is 8.0% lower than the 1.0 cost factor obtained when condenser

tubes of 3/8” diameter are employed. Figure 9-15 shows the operating cost versus the

material cost factor for varying tube circuiting and tube diameter. Only the tube

circuiting of the base configuration, 2 tubes per circuit, is utilized for tube diameters o

1/2” and 5/8”. As shown in Figure 9-15, condensers with tube diameters of 1/2” and 5/8”

have not only significantly higher material cost factors but also higher operating cost than

condensers employing tubes of 5/16” and 1/2” diameter. Therefore, when the frontal area

of the heat exchanger is fixed to the area of the base configuration (7.5 ft2), a condenser

with an outer tube diameter of 5/16”, 5 tubes per circuit, 3 rows of tubes, and 12 fins per

inch yields the highest seasonal COP (lowest operating cost) of all configurations

investigated in this study, and has the most reasonable heat exchanger material cost (cost

factor lower than the base configuration).

Varying the Base Configuration Frontal Area

As discussed in Chapter VIII, the frontal area of the base heat condenser

configuration, 7.5 f 2, has been selected as a value typically found in most residential air-

conditioning systems rated at 30,000 Btu/hr. In many instances, there are space

constraints and/or material cost constraints imposed on the heat exchanger designer that

180

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

0.236

0.240

0.244

0.248

0.252

0.256

0.260

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Material Cost Factor

1/C

OP

(O

per

atin

g C

ost

Fac

tor

3/8" Tube Diameter

5/16" Tube Diameter

1/2" Tube Diameter

5/8" Tube Diameter

4 tpc6 tpc

2 tpc

4 tpc

2 tpc

2 tpc

5 tpc

3 tpc

5 tpc

2 tpc

181

restrict the size of the condenser and consequently sacrificing performance. In these

situations, the frontal area of the condenser may have to be even smaller and/or cheaper

than that of the base configuration used in this study. However, there are also examples

in which space and material cost constraints are not stringent, and a larger and/or more

expensive condenser can be employed to produce a lower operating cost (or higher

seasonal COP). Yet, as shown in Figure 9-13, the cost of materials can be increased or

decreased in a number of ways including: increasing the number of rows, increasing the

fin pitch, increasing the tube diameter, or by simply increasing the frontal area. Hence,

two hypothetical questions arise from this: (1) If the material cost of the condenser must

be reduced by a specified amount, what geometric parameter or dimension should be

reduced to ensure that only a minimum increase in the operating cost results? (2) If the

cost of materials is allowed to increase by a specified amount, what geometric parameter

or dimension should be increased in order to produce the maximum decrease in the

operating cost?

As discussed earlier, Figure 9-15 shows that condenser configurations employing

tube diameters of 1/2” and 5/16” do not yield the best system performance. Therefore in

addressing the two hypothetical questions posed above, tube diameters of this size are not

studied. Figure 9-16 shows the operating cost factor versus the material cost factor for

varying fin pitch and varying numbers of rows for the base configuration. This figure

also shows the operating cost of the condenser configuration utilizing 5/16” diameter

tubes, 5 tubes per circuit, 3 rows of tubes, and 12 fins per inch for 3 condenser frontal

areas: (1) frontal area equal to the base configuration, (2) frontal area 20% lower than the

182

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

0.228

0.232

0.236

0.240

0.244

0.248

0.252

0.256

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Material Cost Factor

1/C

OP

(O

per

atin

g C

ost

Fac

tor)

Fin Pitch

Number of Rows

5/16" diameter, 5 tubes per circuit

4 rows

2 rows

10 FPI

8 FPI

14 FP5/16" diameter Base

Configuration

20% smaller frontal area

Base case frontal area

20% greater frontal area

Base Configuration12 Fins Per Inch (FPI)


3 Rows

3/8" Diameter Tube

183

base configuration, and frontal area 20% greater than the base configuration. An

investigation of the slopes of the curves in this figure is needed to discern the best

methods to vary the frontal area in order to achieve reductions in the material cost or the

operating cost.

In question (1), the material cost of the condenser is to be reduced by a specified

amount. The three methods considered for reducing the material cost are: reducing the

number of rows, reducing the fin pitch, and reducing the frontal area. According to

Figure 9-16, decreasing the fin pitch from the base configuration value of 12 fins per inch

to 8 fins per inch produces a smaller increase in operating cost than decreasing either the

number of rows or decreasing the frontal area. The slope of the line of row variation is

smaller than the slopes for frontal area variation and fin pitch variation in the direction of

decreasing material cost.

In question (2), the material cost of the condenser is allowed to increase by a

specified amount in order to reduce the operating cost. Again, the three methods

considered for increasing the material cost are: increasing the number of rows, increasing

the fin pitch, and increasing the frontal area. According to Figure 9-16, increasing the

frontal area, produces the largest reduction in the operating cost. The slope of the line o

frontal area variation is negative in the direction of increased material cost. The slope of

the line of fin pitch variation is also negative in the direction of increased material cost.

However, increasing the fin pitch produces only a slight decrease in the operating cost.

Conversely, increasing the number of rows actually increases the operating cost for the

184

base configuration detailed in the figure. Therefore, increasing the material cost in this

manner is a “lose-lose” proposition in that no reduction in the operating cost results.

While the above analysis attempts to address the two hypothetical questions posed in

regards to methods of increasing and decreasing material cost, the questions have not

been universally answered by the work of this study. As indicated in the figure, the

frontal area was varied only for the configuration optimized with fixed frontal area

configuration (5/16” diameter tubes, 5 tubes per circuit, 3 rows of tubes, and 12 fins per

inch). For the reasons detailed in the section of this chapter entitled “Operating Costs”,

the number of rows and the fin pitch were varied only for the base configuration (3/8”

diameter tubes, 2 tubes per circuit, 3 rows of tubes, and 12 fins per inch). Therefore in

the above discussion it is assumed that the slopes of the lines of varying fin pitch and

varying number of rows will be the same regardless of tube diameter and tube circuiting

in order to address the hypothetical questions posed in this study.

185

CHAPTER X

CONCLUSIONS AND RECOMMENDATIONS

Conclusions

Refrigerant R-410a is one of the primary candidates to replace refrigerant R-22 in

residential heat pump and air-conditioning applications. As a result of this current study,

many conclusions can be drawn regarding the design of a fin-and-tube condenser coil for

a unitary air-conditioning system with refrigerant R-410a as the working fluid. A

computational model that determines the seasonal COP of an air-conditioning system for

various operating conditions and geometric configurations of the condenser is also used.

In addition, a methodology is detailed for optimizing the condenser design using the

seasonal COP of the system as the figure of merit. While the primary objectives of this

work are not to perform detailed economic analyses, the system operating cost factor and

the capital cost factor for the heat exchanger materials are both considered when detailing

the selection of the best design. Design guidelines taking into account space constraints

have also been given. It is concluded that selecting the final optimum configuration

depends on the constraints imposed upon the heat exchanger designer. If the space

constraints are stringent, then the base condenser configuration for the system

186

investigated with the frontal area of the condenser fixed is the optimum (5/16” tube

diameter, 5 tubes per circuit, 3 rows of tubes, 12 fins per inch, 7.5 ft2 frontal area).

However, if the space constraints are not stringent, and a higher seasonal COP is the

primary goal, then the condenser configuration for the system optimized with the cost o

heat exchanger materials fixed may be preferred (5/16” tube diameter, 5 tubes per circuit,

3 rows of tubes, 12 fins per inch, 8.5 ft2 frontal area). Hence, more information about the

space and economic constraints imposed on the designer is required before the bes

condenser configuration of those investigated in this study can be selected.

As discussed in previous chapters, due to the impending ban of refrigerant R-22

production there is a pressing need for studies on air-conditioning systems that utilize

alternative refrigerants. Therefore, in this current study comparisons are made between

the condenser configurations and seasonal performance of air-conditioning systems

designed using refrigerant R-410a as the working fluid (this current study) to systems

designed using refrigerant R-22 as the working fluid. A thesis entitled “Optimization of

Finned-Tube Condenser for a Residential Air-Conditioner Using R-22” by Emma Saddler

(Saddler, 2000), details the design methodology for an air-conditioning system with

refrigerant R-22 as the working fluid. The base configuration condenser, as well as the

component and property models used in Saddler’s study are similar to those used in this

current work. Likewise, the geometric and operating parameters varied in Saddler’s

optimization are also similar to those of this current study.

According to Saddler’s results, the R-22 air-conditioning system designed with the

frontal area of the condenser fixed has a maximum seasonal COP of 4.18, 13 degrees of

187

sub-cool in the condenser, and an air velocity of 8.3 ft/s over the condenser with the

following geometric parameters: a frontal area of 7.5 ft2, 4 rows of tubes, 6 tubes per

circuit, tubes that are 5/16” in diameter, and 12 fins per inch. The major differences

between the geometric and operating parameters of this system and those of the R-410a

system designed with the fixed condenser frontal area constraint are the number of rows,

and the tube circuiting. The maximum seasonal COP for the R-22 system designed with

the fixed condenser frontal area constraint is approximately 0.2% greater than the

maximum seasonal COP for the comparable R-410a system.

With a fixed heat exchanger cost constraint identical to that used in this current study,

Saddler’s results show that the R-22 air-conditioning system has a maximum seasonal

COP of 4.22. For this maximum seasonal COP design, the R-22 system has 10 degrees

of sub-cool in the condenser, and an air velocity of 8.3 ft/s over the condenser with the

following geometric parameters: a frontal area of 10.6 ft2, 3 rows of tubes, 6 tubes per

circuit, 5/16” tube diameter, and 8 fins per inch. The major differences between the

geometric and operating parameters of this system and those of the R-410a system

optimized with the fixed heat exchanger cost constraint are the tube circuiting, and the fin

pitch. The maximum seasonal COP for the R-22 system designed with the fixed cost

constraint is approximately 0.2% lower than the maximum seasonal COP for the

comparable R-410a system.

Because the seasonal COP of the R-22 systems and the R-410a systems optimized

with both the fixed material cost and fixed frontal area constraints are nearly identical

(vary within ± 0.3%), the estimated operating costs of both systems are also roughl

188

equivalent. In addition, for both the R-22 and R-410a air-conditioning systems, the best

performing condenser configurations investigated utilize the smallest tube diameter

examined in both studies (tube diameter = 5/16”).

It is expected that the best performing condenser configurations investigated for the

R-410a air-conditioning system would require fewer tubes per circuit than the best

condenser configurations investigated for the R-22 air-conditioning system. This is

because the working pressure and the vapor phase density for R-410a are much higher

than for R-22. Based on the results of both this current work and Saddler’s thesis, this

expected trend has been confirmed.

The results of this study confirm the viability of refrigerant R-410a as a replacemen

for refrigerant R-22 in vapor compression air-conditioning systems similar to those

investigated in this work. The R-410a systems have seasonal performance and operating

costs equivalent to those of the R-22 systems designed with the same frontal area and

material cost constraints. Therefore environmental safety is achieved without sacrificing

cost and performance.

List of Conclusions

The specific conclusions drawn from this study are as follows:

• Condenser design for air-conditioning systems must be based on seasonal

performance. The United States Department of Energy regulations require a seasonal

189

performance rating, which incorporates the system’s performance at ambien

temperatures ranging from °F to 102 °F, weighted with the cooling load

distribution factors. Whether this rating is consistent with actual practice is

questionable. However, the United States Department of Energy regulations require

all residential air-conditioning systems to be labeled with this rating.

• The seasonal performance of an air-conditioning system can be closely approximated

by calculating the system’s performance at 82 °F ambient temperature.

• Condenser tubes of smaller diameter enhance performance.

• When packaging and space constraints are not present, the condenser configuration

with the largest frontal area possible yields the best system performance.

• When typical volume and space constraints are imposed, condensers employing 3

rows of tubes yield the best performance. Contrary to intuition, increasing the

number of rows to 4 actually increases the material cost of the coil and decreases the

system performance when space constraints are imposed.

• For all geometric configurations investigated, a refrigerant charge producing between

10 and 15 degrees sub-cool at 95 °F ambient temperature produces the optimu

performance.

190

• For all geometric configurations investigated, the optimum velocity of air flow over

the condenser coil ranges from roughly 6 ft/s and 12 ft/s.

• As the ambient temperature decreases, the sub-cool at 95 °F ambient temperature that

is needed to produce the highest COP increases.

• If the material cost of the condenser must be reduced, decreasing the fin pitch from

the base configuration value of 12 fins per inch to 8 fins per inch produces a smaller

increase in operating cost than decreasing either the number of rows or the frontal

area.

• If the cost of materials is allowed to increase by a specified amount, increasing the

frontal area produces the largest reduction in the operating cost. However, increasing

the number of rows or the fin pitch actually increases the operating cost for the base

configuration detailed in the figure. Therefore, increasing the material cost in this

manner is a “lose-lose” proposition, in that no reduction in the operating cost results.

• All parameters that do not affect material cost of the condenser, such as the operating

parameters and the tube circuiting, should be optimized for every geometric

configuration investigated before the performance of different systems is compared.

191

Recommendations

Optimization Parameters and Methodology

Again, a principal goal of this study was to provide heat exchanger designers with

guidelines for optimizing a condenser with the alternative refrigerant R-410a as the

working fluid using the seasonal COP of the air-conditioning system as the figure of

merit. Perhaps the most salient lesson learned during this study is the significant effec

that the operating conditions have on the system performance, and subsequently the

optimization process. The operating parameters examined in this study include the sub-

cool in the condenser and the velocity of airflow over the condenser. It is of the utmost

importance that heat exchanger designers be aware that it is not possible to make valid

comparisons between heat exchangers of different geometric configurations without first

optimizing the operating parameters at each configuration to yield the maximum seasonal

COP. Therefore, in all future studies of this kind, it is recommended that the operating

parameters continue to be optimized at each geometric configuration in a manner similar

to the method detailed in this study.

Varying the sub-cool in the condenser and the air velocity over the condenser does

not significantly alter the frontal area or the material cost of the heat exchanger. During

this study, it has also been determined that varying the number of tubes per refrigeran

flow parallel circuits also does not alter the cost of materials or the frontal area of the hea

exchanger. However, as discussed in Chapter VIII and Chapter IX, the refrigerant flow

tube circuiting does have a major effect on the optimum seasonal COP, and hence, the

optimum design. Therefore, for future optimization studies of this kind, it is

192

recommended that in addition to the operating conditions, the condenser tube circuiting

should also be optimized at each geometric configuration investigated. For example, in

order make a valid comparison between a system using a condenser with 2 rows of tubes

to one using 3 rows of tubes, the optimum air velocity, the optimum degrees sub-cool in

the condenser, and the optimum tube circuiting arrangement should be determined for

both systems.

The spacing of the tubes in the condenser during this investigation is the standard

recommended for condensers by most heat exchanger manufacturers. However, it is

possible that this spacing is not the optimum spacing. The tube spacing affects the

efficiency of the fins. The closer the tube spacing, the higher the fin efficiency, and

hence a higher air-side heat transfer coefficient is produced. As a result, it is

recommended that the tube spacing be varied and optimized for future studies of this

kind.

Due to the limitations of the air-side pressure drop and heat transfer models,

condensers utilizing tubes of diameter smaller than 5/16” have not been investigated in

this study. As stated previously, for the air-conditioning systems investigated in this

study, the optimum condenser configurations utilize the smallest tube diameter

investigated, 5/16”. It is therefore recommended that condensers with tubes of 1/4” outer

diameter be included in future optimization studies, since it is possible that even better

performance can be achieved. As a result, air-side pressure drop and heat transfer models

that are valid for tubes of smaller outer diameter must be used.

193

Computational Methods

For this study, all modeling computations were performed using Engineering

Equation Solver (EES) operating on a 250 MHz Intel Pentium II processor. The

optimization parameters analyzed in this study included the sub-cool in the condenser,

the air velocity over the condenser, the number of rows of tubes, the refrigerant tube

circuiting, the fin pitch, and the tube diameter. A breakdown of the computational time

involved to determine the effects of these various parameters on the system performance

is as follows:

• For this study, in order to calculate the seasonal COP at one condenser geometri

configuration and with the operating parameters specified (1 “run”), 5 minutes o

computational time was needed: 5 minutes/”run”

• Determining the optimum air velocity at one sub-cool condition at one geometric

configuration required a minimum of 12 “runs”: 12 “runs”/ velocity

• Determining the optimum sub-cool at one condenser geometric configurati

required 12 “runs”: 12 “runs”/ sub-coo

Therefore calculating the seasonal COP for one condenser geometric configuration

required:

194

(12 “runs”/velocity) x (12 “runs”/sub-cool) x (5 minutes/“run”) = 720 minutes (12 hours)

of run time to determine the optimum sub-cool and air velocity for one geometric

configuration of the condenser.

An exhaustive search over the range of geometric design parameters requires:

• Investigating fin pitch varying from 8 to 14 fins/inch: 4 “runs”/fin pitch

• Investigating tube diameter varying from 5/16” to 5/8”: 4 “runs”/tube diameter

• Investigating tube circuiting varying from 2 to 6 tubes per circuit: 5 “runs”/tube

circuiting

• Investigating the number of tube rows varying from 1 to 4: 4 “runs”/number of rows

• Design constraints of fixed frontal area and fixed material cost: 2 “runs”/design

constraint

Therefore the total computational time required for an exhaustive optimization search

scheme is:

195

(5 minutes/ “run”) x (12 “runs”/velocity) x (12 “runs”/sub-cool) x (4 “runs”/fin pitch) x

(4 “runs”/tube diameter) x (5 “runs”/tube circuiting) x (4 “runs”/number of rows) x (2

“runs”/design constraints) = 460,800 minutes or 7,680 hours of computational time.

Hence, the total computational time involved is 7,680 hours, or more than 10 and 1/2

months. The EES model developed to calculate the system performance for this stud

involves more than 2000 equations. Of these 2000 equations, 1000 must be solved

through iteration. The solution of these 100 simultaneous equations is heavily dependen

on the “guess values” for each variable. For varying geometric configurations and

operating conditions, the guess values must be continuously adjusted in order to ensure

the convergence of the solution. Therefore, the researcher is required to be in attendance

for all computations, since in nearly all instances, the guess values must be adjusted for

every “run”. Therefore, the actual total time for this exhaustive search is considerably

longer than the 7,680 hours that have been calculated. Hence, for future studies of this

kind, a more powerful and concise method for finding the optimum values of each

parameter should be developed. For example, entropy minimization techniques tha

quantify the tradeoff between pressure drop irreversibilities and heat transfer

irreversiblilities might be useful in finding a universal optimization relation for the tube

circuiting. More advanced search techniques will allow further investigation into the

coupling and interactions of the geometric parameters for a larger number of

configurations.

196

Refrigerant Side Heat Transfer and Pressure Drop Models

Several echniques for predicting the heat transfer coefficients and pressure drops

during condensation and evaporation inside tubes have been evaluated during this study

Many of the current methods are cumbersome in structure, heavily dependent on

empirically determined coefficients, and have considerable uncertainty. In this work,

general correlations based on statistical evaluation of data, and proposed to be valid for

all flow regimes, were used to calculate the condensing heat transfer coefficients and

pressure drop. While it was determined that the dominant flow regime for the conditions

of this present study is the annular flow regime, at low qualities, stratified-wavy flow also

exists. Furthermore it was assumed that the quality varies linearly with length. It is

recommended that this assumption be studied further, and that correlations based on

specific models for individual flow regimes should be used.

Economic Analysis

Again, the goal of this study is not to conduct a detailed economic analysis for

residential air-conditioning systems. Moreover, the cost of the compressor and condenser

fan units are excluded from the cost analysis (material cost factor) for this investigation.

However, in determining the optimum heat exchanger configuration, a tradeoff must be

made between the capital cost and the operating cost (using the reciprocal of the seasonal

COP as an operating cost factor). It is recommended that a detailed economic analysis be

performed that includes both the capital cost and the operating cost of each component o

the system.

197

APPENDIX A

AIR-CONDITIONING SYSTEM: EES PROGRAM

{I. Refrigerant-Side Procedures and FunctionsA. Pressure Drop

1. singledp2. twophasedp3. tpbenddrop

B. Heat transfer Coefficients1. h_bar_single2. h_bar_c

3. h_bar_e

II. Air -Side A. Heat Transfer coefficients

1. ha B. Pressure Drop

1. GetEuler

III. Heat Exchanger Procedures and Functions A. Surf_eff B. Exch_size C. Exch_size_un_un D. sat_size E. Tubing

IV. Compressor Procedure A. Compeff}

198

PROCEDURE singledp(m_r, nr,D,L,f,rho:delP){Purpose-to determine the single phase pressure drop for flow in tubes}vel=m_r/((pi*D^2/4)*rho*nr) "[ft/hr]" {velocity of refrigerant through tube, ft/hr}delP=(f*(L/D)*(rho*Vel^2)/2)*convert(lbm/ft-hr2,psi)end

PROCEDURE twophasedp(xi,xf,T1, T2, D, m_dot, nr,L:DP){Purpose- to determine the two phase pressure drop for flow in tubes

InputsD- equivalent diameter of flow passage, ftE- surface roughness, ftG- mass flow per unit area lbm/hr-ft^2mu_v- viscosity of vapor phase, lbm/hr-ftmu_l- viscosity of liquid phase, lbm/hr-ftrhov- density of liquid phaserhol- density of vapor phaseReV- Reynold's number of vapor phaseReL- Reynold's number of liquid phaseDztp- length of two phase regionxf- final qualityxi- initial qualityv- exit specific volume of vapor phase, ft^3/lbnr- number of flow passagesL- length of tube

Output-DeltaP- pressure drop over two phase region}

Tav=(T1+T2)/2G=(m_dot/(D^2*pi/4))/nrmu_v=viscosity(R410A, T=Tav, x=1)mu_l=viscosity(R410A, T=Tav, x=0)rhov=density(R410A, T=Tav, x=1)rhol=density(R410A, T=Tav, x=0){Momentum component of 2 phase pressure drop}DpM=((xf^2-xi^2)*(1+rhov/rhol-(rhov/rhol)^.333-(rhov/rhol)^(2/3))-(xf-xi)*(2*rhov/rhol-(rhov/rhol)^(1/3)-(rhov/rhoL)^(2/3))*G^2/(rhov)*convert(lbm/hr^2-ft,psi))

C1=(xf-xi)/L "[1/ft]"C2=.09*mu_v^.2*G^1.8/(C1*rhov*D^1.2*32.2*convert(ft/s^2,ft/hr^2))*convert(lbf/ft^2, psia)

199

C3=2.85*(mu_l/mu_v)^(.0523)*(rhov/rhoL)^.262

{Friction component of 2 phase pressure drop}DPf2=2*c3*(.429*(xf^2.33-xi^2.33)-.141*(xf^3.33-xi^3.33)-.0287*(xf^4.33-xi^4.33))DPf3=C3^2*(.538*(xf^1.86-xi^1.86)-.329*(xf^2.86-xi^2.86))DPf=c2*(.357*(xf^2.8-xi^.28)+DPf2+DPf3)

DP=(DpM+DPfend

Procedure singlebenddrop(tpc, D_i, m_dot_r,P, T1, T2, L, Width, f:DP){Pressure Drop in bends for single phase regions}T=(T1+T2)/2G=m_dot_r/(tpc*D_i^2*pi/4)equiv_L=13*2rho=density(R410A, T=T, P=P)grav=32.2*convert(1/s^2,1/hr^2)ncirc=trunc(L/width)DP=f*G^2*equiv_L/(2*grav*rho)*convert(lbf/ft^2, psia)*ncircend

PROCEDURE tpbenddrop(nr,D_i_1,m_dot_r, h_f, T_c, L_c, L_22a, L_2a2b,width:DP){Pressure Drop In bends for two-phase regions}equiv_L=13*2 {for 180 degree bends}R_b=h_f/2 "[ft]"z=R_b/D_i_1G=m_dot_r/(nr*D_i_1^2*pi/4)e=.000005DP=0num_circuit_2a2b=trunc(l_2a2b/Width)num_circuit_22a=trunc(L_22a/width)L_o=L_22a-Width*num_circuit_22a

L=width-L_omu_v=viscosity(R410A, T=T_c, x=1)mu_l=viscosity(R410A, T=T_c, x=0)grav=32.2*convert(1/s^2,1/hr^2)Rho_l=density(R410A, T=T_c, x=0)rho_v=density(R410A, T=T_c, x=1)

Re_l=G*D_i_1/mu_lA_l=(2.457*ln(1/((7/Re_l)^0.9+.27*e/d_i_1)))^16B_l=(37530/Re_l)^16lambda_l=8*((8/Re_l)^12+(1/((A_l+B_l)^(3/2))))^(1/12)

200

Re_v=G*D_i_1/mu_vA_v=(2.457*ln(1/((7/Re_v)^0.9+.27*e/d_i_1)))^16B_v=(37530/Re_v)^16lambda_v=8*((8/Re_v)^12+(1/((A_v+B_v)^(3/2))))^(1/12)n=ln(lambda_l/lambda_v)/ln(mu_l/mu_v)i=0repea

i=i+1x=-L/L_2a2b+1If x<=0 then goto 10mu_TP=mu_v*x+mu_l*(1-x)Re_tp=G*D_i_1/mu_tpA_tp=(2.457*ln(1/((7/Re_tp)^0.9+.27*e/d_i_1)))^16B_tp=(37530/Re_tp)^16lambda_tp=8*((8/Re_tp)^12+(1/((A_tp+B_tp)^(3/2))))^(1/12)DELTAp_b_lo=lambda_l*G^2*equiv_L/(2*grav*rho_l)*convert(lbf/ft^2, psia)k_b=lambda_tp*equiv_L/2 {k_b for 90 degree bend}GAMMA_B=rho_l/ ho_v*(mu_v/mu_l)^nB=1+2.2/(k_b*(2+R_b/D_i_1)) {B for 90 degree bend}B=.5*(1+B) {B for 180 degree bend}phi_b_lo=1+(GAMMA_b-1)*(B*x^((2-n)/2)*(1-x)^((2-n)/2)+x^(2-n))DELTAp_b=DELTAp_b_lo*phi_b_loDP=DP+DELTAp_bL=L+width

until i>=num_circuit_2a2b-110:DP=Dpend

Procedure h_bar_single22ash(D, m_dot_r, T1, T2, P:Re,h_bar, rho){single phase heat transfer coefficient in the superheated portion of the condenser}Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2rho=density(R410A, T=Tav,P=P)c_p=specheat(R410A, T=Tav, P=P)mu=viscosity(R410A, T=Tav, P=P)Pr=prandtl(R410A, T=Tav, P=P)If Re<3500 then

a=1.10647b=-.078992

endIFif (Re>3500) and (Re<6000) then

a=3.5194e-7

201

b=1.03804ENDIFif Re>6000 then

a=.2243b=-.385

endifSt=a*Re^b/(Pr^(2/3))h_bar=St*G*C_pend

Procedure h_bar_single4a1sh(D, m_dot_r, T1, T2, P:Re,h_bar, rho){Single phase refrigerant heat transfer coefficient for the superheated portion of thevaporator}Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2rho=density(R410A, T=Tav,P=P)c_p=specheat(R410A, T=Tav, P=P)mu=viscosity(R410A, T=Tav, P=P)Re=m_dot_r*D/(Area*mu)Pr=prandtl(R410A, T=Tav, P=P)If Re<3500 then

a=1.10647b=-.078992


a=3.5194e-7b=1.03804

ENDIFif Re>6000 then

a=.2243b=-.385


Procedure h_bar_single2b3sc(D, m_dot_r, T1, T2, P:Re,h_bar, rho){Single refrigerant heat transfer coefficient for the sub-cooled portion of the condenser}Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2rho=density(R410A, T=Tav,P=P)

202

c_p=specheat(R410A, T=Tav, P=P)mu=viscosity(R410A, T=Tav, P=P)Re=m_dot_r*D/(Area*mu)Pr=prandtl(R410A, T=Tav, P=P)If Re<3500 then

a=1.10647b=-.078992


a=3.5194e-7b=1.03804

ENDIFif Re>6000 then

a=.2243b=-.385


FUNCTION h_bar_c(T, P,D, m_dot_r,nr){Shah-Correlation: Two-phase refrigerant heat transfer coefficient in the condenser}G=m_dot_r/(D^2*nr/4)mu_l=viscosity(R410A, T=T, x=0)mu_g=viscosity(R410A, T=T, x=1)rho_l=density(R410A, T=T, x=0)rho_g=density(R410A, T=T, x=1)Pr_l=prandtl(R410A, T=T-1, P=P)k_l=conductivity(R410A, T=T, x=0)P_r=P/p_crit(R410A)Re_l=G*D/mu_lh_l=0.023*Re_l^.8*Pr_l^.4*k_lh_bar_c=h_l*(.55+2.09/(P_r^.38))end

Function h_bar_e(Te, Pe,De, m_r, x_in){Purpose to evaluate the evaporation two phase heattransfer coefficient for forced convection flow inside tubes}x_i:=x_in

Pr_L=prandtl(R410A, T=Te-1, P=Pe) "Prandtl # of liquid phase in evaporator"kl=conductivity(R410A, T=Te, x=0) "conductivity of liq. phase"mu_v=viscosity(R410A, T=Te, x=1) "viscosity of vap. phase"

203

mu_l=viscosity(R410A, T=Te, x=0)rho_l=density(R410A, T=Te, x=0)rho_v=density(R410A, T=Te, x=1)x_e:=1g:=m_r/(pi*De^2/4)h_bar_ave_e1 := 0.023 * 0.325 * 2.5 * kl * (g / mu_l) ^ 0.8 * De ^ (-0.2) * Pr_L ^ 1.4h_bar_ave_e2 := (rho_L / rho_V) ^ 0.375 * (mu_v / mu_l) ^ 0.075 * (x_e - x_i) / (x_e^.325 - (x_i ^ 0.325))h_bar_e := h_bar_ave_e1 * h_bar_ave_e2End

FUNCTION ha(hf, eta,t,L, ma, mu, D_o, Ao,At, Cp, Pr, n){Returns air-side heat transfer coefficient based on McQuiston Method}{h_bar_a- external heat transfer coefficient (btu/hr-ft^2-R)}A_min=(hf/2)*(1/eta-t) "[ft^2]"Gmax=ma*(1/eta-t)/(A_min*L) "[lbm/hr-ft^2]"Re_D=Gmax*D_o/mRe_L=Gmax*hf/mudum1=(Ao/(At))JP=Re_D^(-.4)*(Ao/(At/(1-t*eta)))^(-.15)j4=.2675*JP+1.325*10^(-3)jn=(1-n*1280*Re_L^(-1.2))*j4/(1-4*1280*Re_L^(-1.2))ha=jn*Cp*Gmax/(Pr^(2/3))*convert(1/s,1/hr)end

FUNCTION geteuler(Re, h_f, dep_f, D, nrow){finds Euler number for staggered banks of tubes for a fin-and-tube cross flow heaexchanger}

{Modify Euler number to account for non- equilateral geometryfind correction factor k1 to account for a/b ratio, use k1 with other relationships tocorrect Euler # for row spacing}a=dep_f/Db=h_f/DCheck1=1Check2=1Check3=1spacerat=a/bEu=0k1=0If (spacerat>.5) and (spacerat<1.2) and (re>=1000) and (Re<10000) then {thisrelationship is stated for Re=1000, not the range 1000<Re<10000}

k1=spacerat^(-.048)k2=1.28-.708/spacerat+.55/(spacerat^2)-0.113/(spacerat^3)

204

k1=(k2-k1)/(10000-1000)*(Re-1000)+k1endIFif (spacerat>1.25) and (spacerat<3.5) and (Re>1000) and (Re<10000) then

k1=.951*spacerat^.284k2=1.28-.708/spacerat+.55/(spacerat^2)-0.113/(spacerat^3)k1=(k2-k1)/(10000-1000)*(Re-1000)+k1

endIFIf (spacerat>.45) and (spacerat<3.5) and (Re>=10000) and (Re<100000) then {stated forRe=10000}

k1=1.28-.708/spacerat+.55/(spacerat^2)-0.113/(spacerat^3)k2=2.016-1.675*spacerat+.948*spacerat^2-.234*spacerat^3+.021*spacerat^4k1=(k2-k1)/(100000-10000)*(Re-10000)+k1

endifIf ((spacerat>.45) and (spacerat<3.5) and (Re>=100000)) or ((spacerat>.45) and(spacerat<1.6) and (Re>=1000000)) then {stated for Re=100000}

k1=2.016-1.675*spacerat+.948*spacerat^2-.234*spacerat^3+.021*spacerat^4endIFif (spacerat>1.25) and (spacerat<3.5) and (Re>100) and (Re<1000) then

k1=.93*spacerat^.48k2=spacerat^(-.048)k1=(k2-k1)/(1000-100)*(Re-100)+k1

endIF

if (spacerat=1.155) thenk1=1

endifIf k1=0 then check1=0

If (a>=1.25) and (a<1.5) and (Re>3) and (re<1000) then {Stated fora=1.25}

Eu1:=(.795+247/re+335/(re^2)-1550/Re^3+2410/Re^4)eu2:=(.683+1.11e2/re-97.3/Re^2+426/re^3-574/re^4)Eu=(Eu2-Eu1)/(1.5-1.25)*(a-1.25)+Eu1

endifIf (a>=1.25) and (a<1.5) and (Re>1000) and (Re<2e6) then

Eu1:=(.245+3390/Re-9.84e6/Re^2+1.32e10/re^3-5.99e12/Re^4)Eu2:=(.203+2480/re-7.58e6/re^2+1.04e10/re^3-4.82e12/re^4)Eu=(Eu2-Eu1)/(1.5-1.25)*(a-1.25)+Eu1

endif

If (a>=1.5) and (a<2) and (Re>3) and (Re<100) theneu1:=(.683+1.11e2/re-97.3/Re^2+426/re^3-574/re^4)Eu2:=(.713+44.8/Re-126/Re^2-582/Re^3)Eu=(Eu2-Eu1)/(2-1.5)*(a-1.5)+Eu1

205

endifIf (a>=1.5) and (a<2) and (Re>100) and (Re<1000) then

eu1:=(.683+1.11e2/re-97.3/Re^2+426/re^3-574/re^4)Eu2:=(.343+303/re-7.17e4/re^2+8.8e6/re^3-3.8e8/Re^4)Eu=(Eu2-Eu1)/(2-1.5)*(a-1.5)+Eu1

endifIf (a>=1.5) and (a<2) and (Re>1000) and (Re<10000) then

Eu1:=(.203+2480/re-7.58e6/re^2+1.04e10/re^3-4.82e12/re^4)Eu2:=(.343+303/re-7.17e4/re^2+8.8e6/re^3-3.8e8/Re^4)Eu=(Eu2-Eu1)/(2-1.5)*(a-1.5)+Eu1

endif

If (a>=1.5) and (a<2) and (Re>10000) and (Re<200000) thenEu1:=(.203+2480/re-7.58e6/re^2+1.04e10/re^3-4.82e12/re^4)Eu2=(.162+1810/Re+7.92e7/re^2-1.65e12/Re^3+8.72e15/re^4)Eu=(Eu2-Eu1)/(2-1.5)*(a-1.5)+Eu1

endif

If (a>=2) and (a<2.5) and (Re>7) and (Re<100) thenEu1:=(.713+44.8/Re-126/Re^2-582/Re^3)Eu2:=(.33+98.9/re-1.48e4/Re^2+1.92e6/re^3-8.62e7/re^4)Eu=(Eu2-Eu1)/(2.5-2)*(a-2)+Eu1

endif

If (a>=2) and (a<2.5) and (Re>100) and (Re<5000) thenEu1:=(.343+303/re-7.17e4/re^2+8.8e6/re^3-3.8e8/Re^4)Eu2:=(.33+98.9/re-1.48e4/Re^2+1.92e6/re^3-8.62e7/re^4)Eu=(Eu2-Eu1)/(2.5-2)*(a-2)+Eu1

endif

If (a>=2) and (a<2.5) and (Re>5000) and (Re<10000) thenEu1:=(.343+303/re-7.17e4/re^2+8.8e6/re^3-3.8e8/Re^4)Eu2:=(.119+498/Re-5.07e8/Re^2+2.51e11/Re^3-4.62e14/re^4)Eu=(Eu2-Eu1)/(2.5-2)*(a-2)+Eu1

endif

If (a>=2) and (a<2.5) and (Re>10000) and (Re<2000000) thenEu1:=(.162+1810/Re+7.92e7/re^2-1.65e12/Re^3+8.72e15/re^4)Eu2:=(.119+4980/Re-5.07e7/Re^2+2.51e11/Re^3-4.62e14/re^4)Eu=(Eu2-Eu1)/(2.5-2)*(a-2)+Eu1

endifIf (a>=2.5) and (Re>100) and (Re<5000) then

Eu:=(.33+98.9/re-1.48e4/Re^2+1.92e6/re^3-8.62e7/re^4)endif

206

If (a>=2.5) and (Re>5000) and (Re<2000000) thenEu:=(.119+4980/Re-5.07e7/Re^2+2.51e11/Re^3-4.63e14/re^4)

endifIf Eu=0 then Check2=0

{Modify for less than 4 rows}z=1C=0c_z=0if nrow<10 thenrepea

If z>=3 thenc_z=1

elseIF Re>=10 THEN

c_z1=1.065-(.180/(z-.297))c_z2=1.798-(3.497/(z+1.273))c_z=(c_z2-c_z1)/(100-10)*(Re-10)+c_z1

endifIF Re>=100 THEN

c_z1=1.798-(3.497/(z+1.273))c_z2=1.149-(.411/(z-.412))c_z=(c_z2-c_z1)/(1000-100)*(Re-100)+c_z1

endif

IF Re>=1000 THENc_z1=1.149-(.411/(z-.412))c_z2=.924+(.269/(z+.143))c_z=(c_z2-c_z1)/(10000-1000)*(Re-1000)+c_z1

endif

IF Re>=10000 THENc_z1=.924+(.269/(z+.143))c_z2=.62+(1.467/(z+.667))c_z=(c_z2-c_z1)/(100000-10000)*(Re-10000)+c_z1

endifIF Re>=100000 THEN

c_z=.62+(1.467/(z+.667))endif

endifz=z+1C=C+c_z

until z>nrowC=C/nrow

207

If C=0 then Check3=0endifEu=Eu*C*k1geteuler=Euend

Procedure surf_eff(D_o_1, h_bar_a,h_f, d_f,t, Af,Ao:fin_eff,surfeff){finds the tube surface efficiencey and fin efficiency }h_f=h_f*convert(in,ft)d_f=d_f*convert(in,ft)r_t=D_o_1/2 "[ft]" {outside radius of tube}M=h_f/2 "[ft]"L=.5*sqrt(d_f^2+M^2) "[ft]"psi=M/r_tBETA=L/MR_e=R_t*1.27*psi*(BETA-.3)^.5 "[ft]"k=237*convert(W/m-K, BTU/hr-ft-R) "[BTU/hr-ft-R]" {conductivity for pureAluminum, Incropera & Dewitt}m_eff=sqrt(2*h_bar_a/(k*t))"[1/ft]"phi=(R_e/R_t-1)*(1+.35*ln(R_e/r_t))fin_eff=tanh(m_eff*r_t*phi)/(m_eff*r_t*phi)surfeff = 1 - Af/Ao*(1-fin_eff)end

Procedure sat_size(Cunmixed, E:UA){Finds the UA of the saturated portions of the heat exchangers}

Cr:=0NTU:=-ln(1-E)UA:=NTU*Cunmixed

end

Procedure exch_size_un_un(Cair, Cfridge,UA:E){Finds the UA of the sub-cooled and/or superheated sections of the heat exchangers}Cmin=min(Cair, Cfridge)Cmax=max(Cair, Cfridge)Cr=Cmin/CmaxNTU=UA/CminE=1-exp((1/Cr)*NTU^.22*(exp(-Cr*(NTU^.78))-1))end

Procedure tubing(Type:D_i,D_o){Returns the inner and outer diameter of copper tubes based on AAON productspecifications

208

Type Standard size(in)1 5/162 3/83 1/24 5/8}if type=1 then

D_i=.2885D_o=.3125

endIFif type=2 then

D_i=.3490D_o=.375

endIFif type=3 then

D_i=.4680D_o=.5000

endIFif type=4 then

D_i=.5810D_o=.6250

endIFD_i=D_i/12D_o=D_o/12

end

Function compeff(P_o, P_i, T_o, T_i){computes efficiency of scroll compressor based on condensing and evaporatingTemperature and pressure}Pr=P_o/P_iTr=(T_o+459)/(T_i+459)compeff=-60.25-3.614*Pr-.0281*Pr^2+111.3*Tr-50.31*Tr^2+3.061*Tr*Prend

Function fri(Tac){Sets the ambient temperature weight fractions in order to compute the seasonal COP}fri=0If (Tac>65) and (Tac<69) then

fri =.214endifIf Tac=72 then

fri =.231endif

209

If Tac =77 thenfri =.216

endifIf Tac = 82 then




fri =.018endifIf Tac=102 thenfri =.004END

Module At95(Tsc, V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c, nrow_c, Tubetype_c,ncircuit_c:PD, m_sys, A_e, A_c,Tc_ave,width_e,width_c,W_dot_fc,W_dot_com,DELTAP_tot_ac,CF_e,CF_c,DELTAP_ResideBEND_total,DELTAP_Residecondnser_total,L_22a,L_2a2b,L_2b3){This model returns the compressor piston displacement, amount of sub-cool, evaporatorfrontal area,condenser frontal area and mass of refrigerant in the system in order to provide anevaporator capacityof 30,000 Btu/hr at 95 F ambient temperature}

{System Constraints}

{variable refrigeration cycle parameters}{Design Conditions @ Tac1=95 F}T4a=45 "[F]"Q_dot_e=30000 "[Btu/hr]"

x4a=1x2a=1Tsh=10 "[F]" {refrigerant superheat in evaporator from states 4a-1, F}Tc_ave=(T2a+T2b)/2 "[F]"e=.000005 "[ft]" {roughness for drawn tubing (White), ft}m_r_t=m_dot_r/tpc_c "[lbm/hr]" {mass flow rate per tube}

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{Air flow over Condenser}Tac1=95 "[F]" {Air inlet T into Condenser}V_ac=V_dot_ac*convert(1/min,1/sec)/A_c {Air velocity over condenser} "[ft/s]"mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) {viscosity of air flowing over thecondenser} “[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "{density of air flowing over the condenser}[lbm/ft^3]"m_dot_ac=m_ac*convert(1/hr,1/s) "{mass flow rate of air flowing over the condenser}[bm/s]"m_ac=V_dot_ac*convert(1/min,1/hr)*rho_ac1 "{mass of air flowing over thecondenser} [lbm/hr]"h_bar_ac=ha(h_c, eta_c,t_c, width_c,m_dot_ac, mu_ac, D_o_c, A_o_c,A_t_c, C_p_air,Pr_ac, nrow_c) {air-side heat transfer coefficient over the condenser} "[Btu/hr-ft^2-R]"c_p_air=specheat(AIR, T=Tac1) {specific heat at constant pressure of air flowing overthe condenser} "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1) {Prandtl number of air flowing over the condenser}

{Air Flow over Evaporator}Tae1=80 "[F]" {Air inlet T into Evaporator}V_dot_ae=30000*400/12000 "[cfm]" {air flow rate over evaporator in cfmassuming 400 cfm/ton at design Q_e of 30,000 BTU/hr}V_ae=V_dot_ae*convert(1/min,1/sec)/A_e "{Velocity of air flow over evaporator}[ft/sec]"rho_ae1=density(AIR, T=Tae1, P=14.7) {Density of air flow over the evaporator}

"[lbm/ft^3]"m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 {mass of air flowing over theevaporator} "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) {mass flow rate of air flowing over theevaporator} "[lbm/s]"mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec) {Viscosity of are flowing over theevaporatr} "[lbm/ft-s]"h_bar_ae=ha(h_e, eta_e,t_e, width_e,m_dot_ae, mu_ae, D_o_e, A_o_e, A_t_e, C_p_air,Pr_ac, nrow_e) {heat transfer coefficient of air flowing over the evaporator} "[Btu/hr-ft^2-R]"W_dot_fe=365*V_dot_ae*convert(W, BTU/hr)/1000

{Compressor}nc=compeff(P2a,P4,tc_ave,T4) {compressor efficiency thermal efficiency}

gamma_R410A=1.16 {specific heat ratio of Cp/Cv}Clearance=.05 "[%]" {Percent}v1=volume(R410A, P=P1,T=T1)"[ft^3/lbm]"

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v2=volume(R410A, P=P2,T=T2)"[ft^3/lbm]"nv=1-R*(v1/v2-1) {Compressor volumetric efficiency, Klein}R=.025 {ratio of clearance volume to displacement}PD=m_dot_r*v1/nv "[ft^3/hr]" {compressor piston displacement}

{condenser Characteristics}{Variable Condenser characteristics}spac_rat=h_f_c/d_f_c {tube spacing ratio-horizontal to vertical tube spacing}Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}width_c=3 {base configuration width} "[ft]"L_c=Width_c*nrow_c*ncircuit_c "[ft]" {Total length of condenser}H_c=h_fft_c*tpc_c*ncircuit_c "[ft]" {height of condenser, ft}V_c=Width_c*h_c*dep_c "[ft^3]" {Volume of Condenser}A_c=Width_c*H_c "[ft^2]" {frontal area of condenser, ft^2}CALL Surf_eff(D_o_c, h_bar_ac,h_f_c, d_f_c,t_c, A_f_c,A_o_c:phi_f,phi_c) {calls thefin efficiency and tube surface efficiency for the condenser}Call tubing(TubeType_c:D_i_c,D_o_c) {calls the tube diameter based on the 4 tubetypes for the condenser}A_i_c=L_c*D_i_c*pi*tpc_c {the condenser refrigerant-side inner tube heat transferarea} "[ft^2]"A_t_c=D_o_c*pi*L_c*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_c=2*L_c*eta_c*tpc_c*(h_fft_c*d_fft_c-pi*(D_o_c/2)^2) {the total fin heat transferarea} "[ft^2]"A_o_c=A_t_c+A_f_c {the total heat transfer area -air-side and refrigerant}

"[ft^2]"A_flow_c=Width_c*(1-eta_c*t_c)*(H_c-D_o_c*ncircuit_c*tpc_c) "{the total refrigerantflow area} [ft^2]"A_i_c=A_i_22a+A_i_2a2b+A_i_2b3 {the condenser refrigerant-side inner tube heattransfer area} "[ft^2]"

{evaporator Characteristics}{Variable Evaporator characteristics}h_f_e=1 "[in]" {tube vertical spacing on centers, in}t_e=.006/12 "[ft]" {thickness of fins, ft}eta_e=12*12 "[1/ft]" {evaporator fin pitch, fins/ft}d_f_e=.625 "[in]" {evaporator fin depth per tube, in}Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {evaporator depth, ft}tpc_e=2 {number of tubes per refrigerant flow parallel circuit}nrow_e=4 {number of rows of tubing}ncircuit_e=9L_e=Width_e*nrow_e*ncircuit_e {evaporator tube length} "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft "[ft]" {height of evaporator ft}TubeType_e=2

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V_e=width_e*h_e*dep_e "[ft^3]" {Volume of evaporator}A_e=Width_e*H_e "[ft^2]" {frontal area of evaporator ft^2}CALL Surf_eff(D_o_e, h_bar_ae,h_f_e, d_f_e,t_e, A_f_e,A_o_e:phi_f_e,phi_e) {callsthe fin efficiency and tube surface efficiency for the evaporator}Call tubing(TubeType_e:D_i_e,D_o_e) {calls the tube diameter based on the 4 tubtypes for the evaporator}d_fft_e=d_f_e*convert(in,ft) "[ft]"h_fft_e=h_f_e*convert(in,ft "[ft]"A_i_e=L_e*D_i_e*pi*tpc_e "[ft^2]" {the evaporator refrigerant-side inner tubeheat transfer area}A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_ {the total refrigerant side tube heat transferarea for the evaporator} "[ft^2]"A_f_e=2*h_fft_e*tpc_e*d_fft_e*eta_e*L_e-2*pi*(D_o_e/2)^2*eta_e*L_e*tpc_e {thetotal fin heat transfer area for the evaporator} "[ft^2]"A_o_e=A_t_e+A_f_e {the total heat transfer area -air-side and refrigerant}

"[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) {the total refrigerantflow area for the evaporator}"[ft^2]"

{***********************************************************Begin Cycle Analysis -analyzes the vapor-compression refrigeration cycle************************************************************}

{Compressor Equations}h1=enthalpy(R410A, T=T1, P=P1) "[Btu/lbm]"s1=entropy(R410A, T=T1, P=P1) "[Btu/lbm-R]"s1=s2s "[Btu/lbm-R]"h2s=enthalpy(R410A, P=P2, s=s2s) "[btu/lbm]"wcs= h2s-h1 "[btu/lbm]"wc=wcs/nc "[Btu/lbm]"h2=h1+wc "[btu/lbm]"T2=temperature(R410A, P=P2, h=h2) "[F]"

{Condenser Equations}P2a=P2-DELTAP_22a-DELTAP_b_22a {pressure of refrigerant exiting thesuperheated portion of the condenser} "[psia]"P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b {pressure of refrigerant exiting thesaturated portion of the condenser}"[psia]"P3=P2b-DELTAP_2b3-DELTAP_b_2b3 {pressure of refrigerant exiting the sub-cooled portion of the condenser} "[psia]"

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{Superheated portion of condenser}T2a=temperature(R410A, P=P2a, x=x2a) {Temperature of refrigerant exiting thesuperheated portion of the condenser} "[F]"h2a=enthalpy(R410A, T=T2a, x=x2a) {Enthalpy of refrigerant exiting thsuperheated portion of the condenser} "[Btu/lbm]"Q_22a=m_dot_r*(h2-h2a) "[Btu/hr]"Q_22a=E_22a*min(C_22a,C_a22a)*(T2-Tac1) "[Btu/hr]"C_a22a=m_ac*specheat(AIR, T=Tac1)*L_22a/L_c "[Btu/hr-R]"C_22a=m_dot_r*specheat(R410A, T=T2, P=P2) "[Btu/hr-R]"Call exch_size_un_un(C_a22a, C_22a,UA_22a:E_22a)

UA_22a=U_o_22a*A_o_22a {Superheated UA} "[Btu/hr-R]"U_o_22a=(1/(phi_c*h_bar_ac)+A_o_22a/(h_bar_22a*A_i_22a))^(-1) "[Btu/hr-ft^2-R]"Call h_bar_single(D_i_c, m_r_t, T2, T2a, P2:Re_22a, h_bar_22a, rho_22a)A_t_22a=D_o_c*pi*L_22a*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_22a=2*h_f_c*tpc_c*convert(in, ft)*d_f_c*convert(in,ft)*eta_c*L_22a-2*pi*(D_o_c/2)^2*eta_c*L_22a*tpc_c "[ft^2]"A_o_22a=A_t_22a+A_f_22a "[ft^2]"A_i_22a=L_22a*tpc_c*pi*D_i_c "[ft^2]"

Q_22a=(A_i_22a/A_i_c)*m_ac*(hac22a-hac1) "[Btu/hr]"Q_2a2b=(A_i_2a2b/A_i_c)*m_ac*(hac2a2b-hac1) "[Btu/hr]"Q_2b3=(A_i_2b3/A_i_c)*m_ac*(hac2b3-hac1) "[Btu/hr]"Tac22a=temperature(AIR, h=hac22a) "[F]"Tac2a2b=temperature(AIR,h=hac2a2b) "[F]"Tac2b3=temperature(AIR,h=hac2b3) "[F]"hac1=enthalpy(AIR, T=Tac1) "[Btu/lbm]"

Call SingleDP(m_dot_r, tpc_c,D_i_c,L_22a,f_22a,rho_22a:DELTAP_22a)call singlebenddrop(tpc_c, D_i_c, m_dot_r,P1, T2, T2a, L_22a, Width_c,f_22a:DELTAP_b_22a)1/f_22a^0.5=-2*log10((e/(D_i_c*3.7))+2.51/(Re_22a*f_22a^0.5))

{Saturated portion of condenser}T2b=temperature(R410A, P=P2b, x=.1) "[F]"CALL TwophaseDp(x2a, x2b,T2a, T2b, D_i_c, m_dot_r, tpc_c,L_2a2b:DELTAP_2a2b)CALL tpbenddrop(tpc_c,D_i_c,m_dot_r, h_f_c, T_c, L_c, L_22a, L_2a2b,Width_c:DELTAP_b_2a2b)x2b=0h2b=enthalpy(R410A, T=T2b, x=x2b) "[Btu/lbm]"Q_2a2b=m_dot_r*(h2a-h2b)"[Btu/hr]"Q_2a2b=E_2a2b*C_a2a2b*(T2a-Tac1)C_a2a2b=m_ac*specheat(AIR, T=Tac1)*L_2a2b/L_c "[Btu/hr-R]"

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Call sat_size(C_a2a2b, E_2a2b:UA_2a2b)U_o_2a2b=(1/(phi_c*h_bar_ac)+A_o_2a2b/(h_bar_2a2b*A_i_2a2b))^(-1) "[Btu/hr-ft^2-R]"UA_2a2b=U_o_2a2b*A_o_2a2b "[Btu/hr-R]"h_bar_2a2b= h_bar_c(T2a, P2a,D_i_c, m_dot_r,tpc_c) "[Btu/hr-ft^2-R]"A_t_2a2b=D_o_c*pi*L_2a2b*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_2a2b=2*tpc_c*L_2a2b*eta_c*(h_fft_c*D_fft_c-pi*(D_o_c/2)^2) "[ft^2]"A_o_2a2b=A_t_2a2b+A_f_2a2b"[ft^2]"A_i_2a2b=L_2a2b*tpc_c*pi*D_i_c "[ft^2]"

{Sub-cooled portion of Condenser}h3=enthalpy(R410A, T=T3, P=P3) "[Btu/lbm]"T3=T2b-Tsc "[F]"Q_2b3=m_dot_r*(h2b-h3) "[Btu/hr]"Q_2b3=E_2b3*min(C_2b3, C_a2b3)*(T2b-Tac1) "[Btu/hr]"C_a2b3=m_ac*specheat(AIR, T=Tac1)*L_2b3/L_c "[Btu/hr-R]"C_2b3=m_dot_r*specheat(R410A, T=T3, P=P3) "[Btu/hr-R]"{assume Cp forR410A constant over Tsc}{CALL Exch_size(C_2b3, C_a2b3, E_2b3:UA_2b3)}Call exch_size_un_un(C_a2b3, C_2b3,UA_2b3:E_2b3)

UA_2b3=U_o_2b3*A_o_2b3 "[Btu/hr-R]"U_o_2b3=(1/(phi_c*h_bar_ac)+A_o_2b3/(h_bar_2b3*A_i_2b3))^(-1) "[Btu/hr-ft^2-R]"Call h_bar_single(D_i_c, m_r_t, T2b, T3, P2b:Re_2b3,h_bar_2b3, rho_2b3)A_t_2b3=D_o_c*pi*L_2b3*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_2b3=2*h_f_c*tpc_c*convert(in, ft)*d_f_c*convert(in,ft)*eta_c*L_2b3-2*pi*(D_o_c/2)^2*eta_c*L_2b3*tpc_c "[ft^2]"A_o_2b3=A_t_2b3+A_f_2b3 "[ft^2]"A_i_2b3=L_2b3*tpc_c*pi*D_i_c "[ft^2]"

vel_2b3=m_r_t/((pi*D_i_c^2/4)*rho_2b3) "[ft/hr]" {velocity of refrigerantthrough tube, ft/hr}Call SingleDP(m_dot_r, tpc_c,D_i_c,L_2b3,f_2b3,rho_2b3:DELTAP_2b3)call singlebenddrop(tpc_c, D_i_c, m_dot_r,P2b, T2b, T3, L_2b3, Width_c,f_2b3:DELTAP_b_2b3)1/f_2b3^0.5=-2*log10((e/(D_i_c*3.7))+2.51/(Re_2b3*f_2b3^0.5))

{Total Refrigerant Side Pressure Drop for condenser}DELTAP_Residecondnser_total= DELTAP_22a+DELTAP_b_22a+DELTAP_2a2b+DELTAP_b_2a2b+DELTAP_2b3+DELTAP_b_2b3 "[psia]"

{Total Refrigerant Side Pressure Drop Due To Bends in the Condenser}

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DELTAP_ResideBEND_total=DELTAP_b_22a+DELTAP_b_2a2b+DELTAP_b_2b3"[psia]"

{Valve Equation}h4=h3 "[Btu/lbm]"

{Evaporator Equations}P4=P4a "[psia]"P4=P1 "[psia]"Q_dot_e=Q_44a+Q_4a1"[Btu/hr]"A_i_e=A_i_44a+A_i_4a1 "[ft^2]"{A_o_e=A_i_e*D_o_1/D_i_c}T4=T4a"[F]"P4=pressure(R410A, T=T4, h=h4) "[psia]"{m_ae=V_dot_ae*convert(1/min,1/hr)/volume(AIR, T=Tac1, P=14.7)}x4=quality(R410A, T=T4, h=h4)

{saturated portion of evaporator}Cp_44a_cor=specheat(AIR, T=Tae1)*1.33 "[Btu/lbm-F]"h4a=enthalpy(R410A, T=T4a, x=x4a) "[Btu/lbm]"Q_44a=m_dot_r*(h4a-h4) "[Btu/hr]"Q_44a=E_44a*C_a44a*(Tae1-T4)Q_44a=(A_i_44a/A_i_e)*C_a44a*(-Tae44a+Tae1) "[Btu/hr]"C_a44a=m_ae*Cp_44a_cor*A_i_44a/A_i_ecall sat_size(C_a44a,E_44a:UA_44a)UA_44a=U_i_44a*A_i_44a "[Btu/hr-R]"U_i_44a=(C1+1/h_bar_44a)^(-1) "[Btu/hr-ft^2-R]"h_bar_44a=h_bar_e(T4, P4,D_i_c, m_dot_r, x4) "[Btu/hr-ft^2-R]"{CALL TwophaseDp(x4a,x4, T4, T4a, D_i_e, m_dot_r, tpc_e,L_44a:DELTAP_44a)CALL tpbenddrop(tpc_c,D_i_c,m_dot_r, h_f_c, T_c, L_c, L_22a, L_2a2b,Width_c:DELTAP_b_2a2b)}A_i_44a=L_44a*tpc_e*pi*D_i_e "[ft^2]"

{superheated portion of evaporator}T1=T4a+Tsh "[F]"Q_4a1=m_dot_r*(h1-h4a) "[btu/hr]"Q_4a1=E_4a1*min(C_4a1, C_a4a1)*(Tae1-T4a)C_a4a1=m_ae*specheat(AIR, T=Tae1)*A_i_4a1/A_i_eC_4a1=m_dot_r*specheat(R410A, T=T1, P=P1)call exch_size_un_un(C_4a1,C_a4a1, UA_4a1:E_4a1)UA_4a1=U_i_4a1*A_i_4a1 "[Btu/hr-R]"U_i_4a1=(C1+1/h_bar_4a1)^(-1) "[Btu/hr-ft^2-R]"Call h_bar_single(D_i_e, m_dot_r, T4a, T1, P4a:Re_4a1,h_bar_4a1, rho_4a1)

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{C1=D_i_c/(D_o_1*h_bar_ae)} {constant represents air side term forevaporator U}C1=1/(Area_rat*h_bar_ae) "[hr-ft^2-R/BTU]"

Area_rat=A_o_e/A_i_e

{Call SingleDP(m_dot_r, tpc_e,D_i_e,L_4a1,f_4a1,rho_4a1:DELTAP_4a1)call singlebenddrop(tpc_e, D_i_e, m_dot_r,P4a, T4a, T1, L_4a1, Width_e,f_4a1:DELTAP_b_4a1)}1/f_4a1^0.5=-2*log10((e/(D_i_e*3.7))+2.51/(Re_4a1*f_4a1^0.5))A_i_4a1=L_4a1*tpc_e*pi*D_i_e "[ft^2]"

{COP}W_dot_com=wc*m_dot_r "[Btu/hr]"Q_c=Q_22a+Q_2a2b+Q_2b3 "[Btu/hr]"COP=Q_dot_e/(W_dot_com+W_dot_fc+W_dot_fe)

{Mass balances}Vol_22a=L_22a*D_i_c^2*pi*tpc_c/4 "[ft^3]"Vol_2a2b=L_2a2b*D_i_c^2*pi*tpc_c/4 "[ft^3]"Vol_2b3=L_2b3*D_i_c^2*pi*tpc_c/4 "[ft^3]"Vol_44a=A_i_44a*D_i_c/4 "[ft^3]"Vol_4a1=A_i_4a1*D_i_c/4 "[ft^3]"

m_22a=rho_22a*Vol_22a "[lbm]"vfg2a2b=volume(R410A, T=T2a, x=1)-volume(R410A, T=T2a, x=0) "[ft^3/lbm]"m_2a2b=-(Vol_2a2b/vfg2a2b)*ln(volume(R410A, T=T2a, x=0)/volume(R410A, T=T2a,x=1)) "[lbm]"m_2b3=rho_2b3*Vol_2b3 "[lbm]"m_c=m_22a+M_2a2b+m_2b3 "[lbm]"

m_4a1=rho_4a1*Vol_4a1 "[lbm]"vfg44a=volume(R410A, T=T4a, x=1)-volume(R410A, T=T4a, x=0) "[ft^3/lbm]"m_44a=(Vol_44a/(x4*vfg44a))*ln(volume(R410A, T=T4, x=1)/(volume(R410A, T=T4,x=0)+x4*vfg44a)) "[lbm] check this equation"m_sys=m_4a1+m_44a+m_c "[lbm]"m_e=m_4a1+m_44a

{Air Side Pressure Drop}E_fc=.65 "fan efficiency"W_dot_fc=V_ac*DELTAP_tot_ac*convert(psia,lbf/ft^2)*A_c/E_fc*convert(ft-lbf/s,btu/hr) "[Btu/hr]"d_fft_c=d_f_c*convert(in,ft) "[ft]"h_fft_c=h_f_c*convert(in,ft "[ft]"

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{Flow rate}G_max_ac=m_ac/A_flow_c "[lbm/ft^2 hr]"Pac2=P_atm "[psia]"P_atm=14.7 "[psia]"grav=32.2*convert(1/s^2,1/hr^2) "[lbm-ft/hr^2-lbf]"Re_D_c=G_max_ac*D_o_c/(mu_ac*convert(1/s,1/hr))

{Pressure Drop Calculation}DELTAP_tot_ac=Pac1-Pac2 "[psia]"

Eu_c=GetEuler(Re_d_c, d_f_c, h_f_c, D_o_c, nrow_c)DELTAP_tubes=Eu_c*G_max_ac^2*nrow_c/(2*rho_ac1)*convert(lbm-ft/ft2-hr2, psia)

"[psia]"DELTAP_tubes_inH2O=DELTAP_tubes*convert(psia, inH2O) "[inH2O]"DELTAP_tot_ac=DELTAP_tubes+DELTAP_fin

DELTAP_fin=(f_f*G_max_ac^2*A_f_c/(2*A_flow_c*grav*rho_ac1))*convert(1/ft^2,1/in^2) "[psia]"DELTAP_fin_inH2O=DELTAP_fin*convert(psia,inh2o) "[inh2O]"f_f=1.7*Re_L_ac^(-.5)Re_L_ac=G_max_ac*h_fft_c/mu_ac*convert(1/hr, 1/s)

{Cost Factors for metalsFins made from pure aluminumTubes made from pure copper}Cf_cu=.8 "[1/lbm]" {copper is about $0.8/lb on the London MetalsExchange}Cf_al=.7 "[1/lbm]" {aluminum is about $0.7/lb}rho_al=2702*convert(kg/m^3,lbm/ft^3) "[lbm/ft^3]"{Incropera and DeWitt}rho_cu=8933*convert(kg/m^3, lbm/ft^3) "[lbm/ft^3]"V_cu=L_c*pi*(D_o_c^2/4-D_i_c^2/4)*tpc_c+L_e*pi*(D_o_e^2/4-D_i_e^2/4)*tpc_e

"[ft^3]"V_al=A_f_c*t_c/2+A_f_e*t_e/2 "[ft^3]"CF=(rho_al*V_al*Cf_al+rho_cu*V_cu*Cf_cu)/CF_base_totalCF_base_total=35.88{CF=1}CF_e=(rho_al*A_f_e*t_e/2*Cf_al+rho_cu*L_e*pi*(D_o_e^2/4-D_i_e^2/4)*tpc_e*Cf_cu)/CF_base_eCF_c=(rho_al*A_f_c*t_c/2*Cf_al+rho_cu*L_c*pi*(D_o_c^2/4-D_i_c^2/4)*tpc_c*Cf_cu)/CF_base_c

End

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Module WithSubcool(Tac1, PD, A_e, A_c, m_sys, V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c,nrow_c, Tubetype_c, ncircuit_c: Den_COPseas_i, Tsc){This module returns the seasonal COP of the system and the sub-cool in the condenserfor the various ambient temperatures for a system whose compressor has been sized for asystem capacity of 30,000 Btu/hr at 95 F ambient temperature}

x4a=1x2a=1Tsh=10 "[F]" {refrigerant superheat in evaporator from states 4a-1, F}Tc_ave=(T2a+T2b)/2 "[F]"e=.000005 "[ft]" {roughness for drawn tubing (White), ft}m_r_t=m_dot_r/tpc_c "[lbm/hr]" {mass flow rate per tube}

{Air flow over Condenser}V_ac=V_dot_ac*convert(1/min,1/sec)/A_c {Air velocity over condenser} "[ft/s]"mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) {viscosity of air flowing over thecondenser} “[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "{density of air flowing over the condenser}[lbm/ft^3]"m_dot_ac=m_ac*convert(1/hr,1/s) "{mass flow rate of air flowing over the condenser}[bm/s]"m_ac=V_dot_ac*convert(1/min,1/hr)*rho_ac1 "{mass of air flowing over thecondenser} [lbm/hr]"h_bar_ac=ha(h_c, eta_c,t_c, width_c,m_dot_ac, mu_ac, D_o_c, A_o_c,A_t_c, C_p_air,Pr_ac, nrow_c) {air-side heat transfer coefficient over the condenser} "[Btu/hr-ft^2-R]"c_p_air=specheat(AIR, T=Tac1) {specific heat at constant pressure of air flowing overthe condenser} "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1) {Prandtl number of air flowing over the condenser}

{Air Flow over Evaporator}Tae1=80 "[F]" {Air inlet T into Evaporator}V_dot_ae=30000*400/12000 "[cfm]" {air flow rate over evaporator in cfmassuming 400 cfm/ton at design Q_e of 30,000 BTU/hr}V_ae=V_dot_ae*convert(1/min,1/sec)/A_e "{Velocity of air flow over evaporator}[ft/sec]"rho_ae1=density(AIR, T=Tae1, P=14.7) {Density of air flow over the evaporator}

"[lbm/ft^3]"m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 {mass of air flowing over theevaporator} "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) {mass flow rate of air flowing over theevaporator} "[lbm/s]"

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mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec) {Viscosity of are flowing over theevaporatr} "[lbm/ft-s]"h_bar_ae=ha(h_e, eta_e,t_e, width_e,m_dot_ae, mu_ae, D_o_e, A_o_e, A_t_e, C_p_air,Pr_ac, nrow_e) {heat transfer coefficient of air flowing over the evaporator} "[Btu/hr-ft^2-R]"W_dot_fe=365*V_dot_ae*convert(W, BTU/hr)/1000

{Compressor}nc=compeff(P2a,P4,tc_ave,T4) {compressor efficiency thermal efficiency}

gamma_R410A=1.16 {specific heat ratio of Cp/Cv}Clearance=.05 "[%]" {Percent}v1=volume(R410A, P=P1,T=T1)"[ft^3/lbm]"v2=volume(R410A, P=P2,T=T2)"[ft^3/lbm]"nv=1-R*(v1/v2-1) {Compressor volumetric efficiency, Klein}R=.025 {ratio of clearance volume to displacement}PD=m_dot_r*v1/nv "[ft^3/hr]" {compressor piston displacement}

{condenser Characteristics}{Variable Condenser characteristics}spac_rat=h_f_c/d_f_c {tube spacing ratio-horizontal to vertical tube spacing}Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}L_c=Width_c*nrow_c*ncircuit_c "[ft]" {Total length of condenser}H_c=h_fft_c*tpc_c*ncircuit_c "[ft]" {height of condenser, ft}V_c=Width_c*h_c*dep_c "[ft^3]" {Volume of Condenser}A_c=Width_c*H_c "[ft^2]" {frontal area of condenser, ft^2}CALL Surf_eff(D_o_c, h_bar_ac,h_f_c, d_f_c,t_c, A_f_c,A_o_c:phi_f,phi_c) {calls thefin efficiency and tube surface efficiency for the condenser}Call tubing(TubeType_c:D_i_c,D_o_c) {calls the tube diameter based on the 4 tubetypes for the condenser}A_i_c=L_c*D_i_c*pi*tpc_c {the condenser refrigerant-side inner tube heat transferarea} "[ft^2]"A_t_c=D_o_c*pi*L_c*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_c=2*L_c*eta_c*tpc_c*(h_fft_c*d_fft_c-pi*(D_o_c/2)^2) {the total fin heattransfer area} "[ft^2]"A_o_c=A_t_c+A_f_c {the total heat transfer area -air-side and refrigerant}

"[ft^2]"A_flow_c=Width_c*(1-eta_c*t_c)*(H_c-D_o_c*ncircuit_c*tpc_c) "{the total refrigerantflow area} [ft^2]"A_i_c=A_i_22a+A_i_2a2b+A_i_2b3 {the condenser refrigerant-side inner tube heattransfer area} "[ft^2]"

220

{evaporator Characteristics}{Variable Evaporator charcteristics}h_f_e=1 "[in]" {tube vertical spacing on centers, in}t_e=.006/12 "[ft]" {thickness of fins, ft}eta_e=12*12 "[1/ft]" {evaporator fin pitch, fins/ft}d_f_e=.625 "[in]" {evaporator fin depth per tube, in}Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {evaporator depth, ft}tpc_e=2 {number of tubes per refrigerant flow parallel circuit}nrow_e=4 {number of rows of tubing}ncircuit_e=9L_e=Width_e*nrow_e*ncircuit_e {evaporator tube length} "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft "[ft]" {height of evaporator ft}TubeType_e=2V_e=width_e*h_e*dep_e "[ft^3]" {Volume of evaporator}A_e=Width_e*H_e "[ft^2]" {frontal area of evaporator ft^2}CALL Surf_eff(D_o_e, h_bar_ae,h_f_e, d_f_e,t_e, A_f_e,A_o_e:phi_f_e,phi_e) {callsthe fin efficiency and tube surface efficiency for the evaporator}Call tubing(TubeType_e:D_i_e,D_o_e) {calls the tube diameter based on the 4 tubtypes for the evaporator}d_fft_e=d_f_e*convert(in,ft) "[ft]"h_fft_e=h_f_e*convert(in,ft "[ft]"A_i_e=L_e*D_i_e*pi*tpc_e "[ft^2]" {the evaporator refrigerant-side inner tubeheat transfer area}A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_ {the total refrigerant side tube heat transferarea for the evaporator} "[ft^2]"A_f_e=2*h_fft_e*tpc_e*d_fft_e*eta_e*L_e-2*pi*(D_o_e/2)^2*eta_e*L_e*tpc_e {thetotal fin heat transfer area for the evaporator} "[ft^2]"A_o_e=A_t_e+A_f_e {the total heat transfer area -air-side and refrigerant}

"[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) {the total refrigerantflow area for the evaporator}"[ft^2]"

{***********************************************************Begin Cycle Analysis -analyzes the vapor-compression refrigeration cycle************************************************************}

{Compressor Equations}h1=enthalpy(R410A, T=T1, P=P1) "[Btu/lbm]"s1=entropy(R410A, T=T1, P=P1) "[Btu/lbm-R]"s1=s2s "[Btu/lbm-R]"

221

h2s=enthalpy(R410A, P=P2, s=s2s) "[btu/lbm]"wcs= h2s-h1 "[btu/lbm]"wc=wcs/nc "[Btu/lbm]"h2=h1+wc "[btu/lbm]"T2=temperature(R410A, P=P2, h=h2) "[F]"

{Condenser Equations}P2a=P2-DELTAP_22a-DELTAP_b_22a {pressure of refrigerant exiting thesuperheated portion of the condenser} "[psia]"P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b {pressure of refrigerant exiting thesaturated portion of the condenser}"[psia]"P3=P2b-DELTAP_2b3-DELTAP_b_2b3 {pressure of refrigerant exiting the sub-cooled portion of the condenser} "[psia]"

{Superheated portion of condenser}T2a=temperature(R410A, P=P2a, x=x2a) {Temperature of refrigerant exiting thesuperheated portion of the condenser} "[F]"h2a=enthalpy(R410A, T=T2a, x=x2a) {Enthalpy of refrigerant exiting thsuperheated portion of the condenser} "[Btu/lbm]"Q_22a=m_dot_r*(h2-h2a) "[Btu/hr]"Q_22a=E_22a*min(C_22a,C_a22a)*(T2-Tac1) "[Btu/hr]"C_a22a=m_ac*specheat(AIR, T=Tac1)*L_22a/L_c "[Btu/hr-R]"C_22a=m_dot_r*specheat(R410A, T=T2, P=P2) "[Btu/hr-R]"Call exch_size_un_un(C_a22a, C_22a,UA_22a:E_22a)

UA_22a=U_o_22a*A_o_22a "[Btu/hr-R]"U_o_22a=(1/(phi_c*h_bar_ac)+A_o_22a/(h_bar_22a*A_i_22a))^(-1) "[Btu/hr-ft^2-R]"Call h_bar_single(D_i_c, m_r_t, T2, T2a, P2:Re_22a, h_bar_22a, rho_22a)A_t_22a=D_o_c*pi*L_22a*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_22a=2*h_f_c*tpc_c*convert(in, ft)*d_f_c*convert(in,ft)*eta_c*L_22a-2*pi*(D_o_c/2)^2*eta_c*L_22a*tpc_c "[ft^2]"A_o_22a=A_t_22a+A_f_22a "[ft^2]"A_i_22a=L_22a*tpc_c*pi*D_i_c "[ft^2]"

Q_22a=(A_i_22a/A_i_c)*m_ac*(hac22a-hac1) "[Btu/hr]"Q_2a2b=(A_i_2a2b/A_i_c)*m_ac*(hac2a2b-hac1) "[Btu/hr]"Q_2b3=(A_i_2b3/A_i_c)*m_ac*(hac2b3-hac1) "[Btu/hr]"Tac22a=temperature(AIR, h=hac22a) "[F]"Tac2a2b=temperature(AIR,h=hac2a2b) "[F]"Tac2b3=temperature(AIR,h=hac2b3) "[F]"hac1=enthalpy(AIR, T=Tac1) "[Btu/lbm]"

Call SingleDP(m_dot_r, tpc_c,D_i_c,L_22a,f_22a,rho_22a:DELTAP_22a)

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call singlebenddrop(tpc_c, D_i_c, m_dot_r,P1, T2, T2a, L_22a, Width_c,f_22a:DELTAP_b_22a)1/f_22a^0.5=-2*log10((e/(D_i_c*3.7))+2.51/(Re_22a*f_22a^0.5))

{Saturated portion of condenser}T2b=temperature(R410A, P=P2b, x=.1) "[F]"CALL TwophaseDp(x2a, x2b,T2a, T2b, D_i_c, m_dot_r, tpc_c,L_2a2b:DELTAP_2a2b)CALL tpbenddrop(tpc_c,D_i_c,m_dot_r, h_f_c, T_c, L_c, L_22a, L_2a2b,Width_c:DELTAP_b_2a2b)x2b=0h2b=enthalpy(R410A, T=T2b, x=x2b) "[Btu/lbm]"Q_2a2b=m_dot_r*(h2a-h2b)"[Btu/hr]"Q_2a2b=E_2a2b*C_a2a2b*(T2a-Tac1)C_a2a2b=m_ac*specheat(AIR, T=Tac1)*L_2a2b/L_c "[Btu/hr-R]"Call sat_size(C_a2a2b, E_2a2b:UA_2a2b)U_o_2a2b=(1/(phi_c*h_bar_ac)+A_o_2a2b/(h_bar_2a2b*A_i_2a2b))^(-1) "[Btu/hr-ft^2-R]"UA_2a2b=U_o_2a2b*A_o_2a2b "[Btu/hr-R]"h_bar_2a2b= h_bar_c(T2a, P2a,D_i_c, m_dot_r,tpc_c) "[Btu/hr-ft^2-R]"A_t_2a2b=D_o_c*pi*L_2a2b*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_2a2b=2*tpc_c*L_2a2b*eta_c*(h_fft_c*D_fft_c-pi*(D_o_c/2)^2) "[ft^2]"A_o_2a2b=A_t_2a2b+A_f_2a2b"[ft^2]"A_i_2a2b=L_2a2b*tpc_c*pi*D_i_c "[ft^2]"

{Sub-cooled portion of Condenser}h3=enthalpy(R410A, T=T3, P=P3) "[Btu/lbm]"T3=T2b-Tsc "[F]"Q_2b3=m_dot_r*(h2b-h3) "[Btu/hr]"Q_2b3=E_2b3*min(C_2b3, C_a2b3)*(T2b-Tac1) "[Btu/hr]"C_a2b3=m_ac*specheat(AIR, T=Tac1)*L_2b3/L_c "[Btu/hr-R]"C_2b3=m_dot_r*specheat(R410A, T=T3, P=P3) "[Btu/hr-R]"{assume Cp forR410A constant over Tsc}{CALL Exch_size(C_2b3, C_a2b3, E_2b3:UA_2b3)}Call exch_size_un_un(C_a2b3, C_2b3,UA_2b3:E_2b3)

UA_2b3=U_o_2b3*A_o_2b3 "[Btu/hr-R]"U_o_2b3=(1/(phi_c*h_bar_ac)+A_o_2b3/(h_bar_2b3*A_i_2b3))^(-1) "[Btu/hr-ft^2-R]"Call h_bar_single(D_i_c, m_r_t, T2b, T3, P2b:Re_2b3,h_bar_2b3, rho_2b3)A_t_2b3=D_o_c*pi*L_2b3*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_2b3=2*h_f_c*tpc_c*convert(in, ft)*d_f_c*convert(in,ft)*eta_c*L_2b3-2*pi*(D_o_c/2)^2*eta_c*L_2b3*tpc_c "[ft^2]"A_o_2b3=A_t_2b3+A_f_2b3 "[ft^2]"A_i_2b3=L_2b3*tpc_c*pi*D_i_c "[ft^2]"

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vel_2b3=m_r_t/((pi*D_i_c^2/4)*rho_2b3) "[ft/hr]" {velocity of refrigerantthrough tube, ft/hr}Call SingleDP(m_dot_r, tpc_c,D_i_c,L_2b3,f_2b3,rho_2b3:DELTAP_2b3)call singlebenddrop(tpc_c, D_i_c, m_dot_r,P2b, T2b, T3, L_2b3, Width_c,f_2b3:DELTAP_b_2b3)1/f_2b3^0.5=-2*log10((e/(D_i_c*3.7))+2.51/(Re_2b3*f_2b3^0.5))

{Total Refrigerant Side Pressure Drop for condenser}DELTAP_Residecondnser_total= DELTAP_22a+DELTAP_b_22a+DELTAP_2a2b+DELTAP_b_2a2b+DELTAP_2b3+DELTAP_b_2b3 "[psia]"

{Total Refrigerant Side Pressure Drop Due To Bends in the Condenser}DELTAP_ResideBEND_total=DELTAP_b_22a+DELTAP_b_2a2b+DELTAP_b_2b3

"[psia]"

{Valve Equation}h4=h3 "[Btu/lbm]"

{Evaporator Equations}{Neglect Pressure drop across evaporator}P4=P4a "[psia]"P4=P1 "[psia]"Q_dot_e=Q_44a+Q_4a1"[Btu/hr]"A_i_e=A_i_44a+A_i_4a1 "[ft^2]"{A_o_e=A_i_e*D_o_1/D_i_c}T4=T4a"[F]"P4=pressure(R410A, T=T4, h=h4) "[psia]"{m_ae=V_dot_ae*convert(1/min,1/hr)/volume(AIR, T=Tac1, P=14.7)}x4=quality(R410A, T=T4, h=h4)

{saturated portion of evaporator}Cp_44a_cor=specheat(AIR, T=Tae1)*1.33 "[Btu/lbm-F]"h4a=enthalpy(R410A, T=T4a, x=x4a) "[Btu/lbm]"Q_44a=m_dot_r*(h4a-h4) "[Btu/hr]"Q_44a=E_44a*C_a44a*(Tae1-T4)Q_44a=(A_i_44a/A_i_e)*C_a44a*(-Tae44a+Tae1) "[Btu/hr]"C_a44a=m_ae*Cp_44a_cor*A_i_44a/A_i_ecall sat_size(C_a44a,E_44a:UA_44a)UA_44a=U_i_44a*A_i_44a "[Btu/hr-R]"U_i_44a=(C1+1/h_bar_44a)^(-1) "[Btu/hr-ft^2-R]"h_bar_44a=h_bar_e(T4, P4,D_i_c, m_dot_r, x4) "[Btu/hr-ft^2-R]"{CALL TwophaseDp(x4a,x4, T4, T4a, D_i_e, m_dot_r, tpc_e,L_44a:DELTAP_44a)

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CALL tpbenddrop(tpc_c,D_i_c,m_dot_r, h_f_c, T_c, L_c, L_22a, L_2a2b,Width_c:DELTAP_b_2a2b)}A_i_44a=L_44a*tpc_e*pi*D_i_e "[ft^2]"

{superheated portion of evaporator}T1=T4a+Tsh "[F]"Q_4a1=m_dot_r*(h1-h4a) "[btu/hr]"Q_4a1=E_4a1*min(C_4a1, C_a4a1)*(Tae1-T4a)C_a4a1=m_ae*specheat(AIR, T=Tae1)*A_i_4a1/A_i_eC_4a1=m_dot_r*specheat(R410A, T=T1, P=P1)call exch_size_un_un(C_4a1,C_a4a1, UA_4a1:E_4a1)UA_4a1=U_i_4a1*A_i_4a1 "[Btu/hr-R]"U_i_4a1=(C1+1/h_bar_4a1)^(-1) "[Btu/hr-ft^2-R]"Call h_bar_single(D_i_e, m_dot_r, T4a, T1, P4a:Re_4a1,h_bar_4a1, rho_4a1){C1=D_i_c/(D_o_1*h_bar_ae)} {constant represents air side term forevaporator U}C1=1/(Area_rat*h_bar_ae) "[hr-ft^2-R/BTU]"

Area_rat=A_o_e/A_i_e

{Call SingleDP(m_dot_r, tpc_e,D_i_e,L_4a1,f_4a1,rho_4a1:DELTAP_4a1)call singlebenddrop(tpc_e, D_i_e, m_dot_r,P4a, T4a, T1, L_4a1, Width_e,f_4a1:DELTAP_b_4a1)}1/f_4a1^0.5=-2*log10((e/(D_i_e*3.7))+2.51/(Re_4a1*f_4a1^0.5))A_i_4a1=L_4a1*tpc_e*pi*D_i_e "[ft^2]"

{COP}W_dot_com=wc*m_dot_r "[Btu/hr]"Q_c=Q_22a+Q_2a2b+Q_2b3 "[Btu/hr]"COP=Q_dot_e/(W_dot_com+W_dot_fc+W_dot_fe)

{Mass balances}Vol_22a=L_22a*D_i_c^2*pi*tpc_c/4 "[ft^3]"Vol_2a2b=L_2a2b*D_i_c^2*pi*tpc_c/4 "[ft^3]"Vol_2b3=L_2b3*D_i_c^2*pi*tpc_c/4 "[ft^3]"Vol_44a=A_i_44a*D_i_c/4 "[ft^3]"Vol_4a1=A_i_4a1*D_i_c/4 "[ft^3]"

m_22a=rho_22a*Vol_22a "[lbm]"vfg2a2b=volume(R410A, T=T2a, x=1)-volume(R410A, T=T2a, x=0) "[ft^3/lbm]"m_2a2b=-(Vol_2a2b/vfg2a2b)*ln(volume(R410A, T=T2a, x=0)/volume(R410A, T=T2a,x=1)) "[lbm]"m_2b3=rho_2b3*Vol_2b3 "[lbm]"m_c=m_22a+M_2a2b+m_2b3 "[lbm]"

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m_4a1=rho_4a1*Vol_4a1 "[lbm]"vfg44a=volume(R410A, T=T4a, x=1)-volume(R410A, T=T4a, x=0) "[ft^3/lbm]"m_44a=(Vol_44a/(x4*vfg44a))*ln(volume(R410A, T=T4, x=1)/(volume(R410A, T=T4,x=0)+x4*vfg44a)) "[lbm] check this equation"m_sys=m_4a1+m_44a+m_c "[lbm]"m_e=m_4a1+m_44a

{Air Side Pressure Drop}E_fc=.65 "fan efficiency"W_dot_fc=V_ac*DELTAP_tot_ac*convert(psia,lbf/ft^2)*A_c/E_fc*convert(ft-lbf/s,btu/hr) "[Btu/hr]"d_fft_c=d_f_c*convert(in,ft) "[ft]"h_fft_c=h_f_c*convert(in,ft "[ft]"

{Flow rate}G_max_ac=m_ac/A_flow_c "[lbm/ft^2 hr]"Pac2=P_atm "[psia]"P_atm=14.7 "[psia]"grav=32.2*convert(1/s^2,1/hr^2) "[lbm-ft/hr^2-lbf]"Re_D_c=G_max_ac*D_o_c/(mu_ac*convert(1/s,1/hr))

{Pressure Drop Calculation}DELTAP_tot_ac=Pac1-Pac2 "[psia]"

Eu_c=GetEuler(Re_d_c, d_f_c, h_f_c, D_o_c, nrow_c)DELTAP_tubes=Eu_c*G_max_ac^2*nrow_c/(2*rho_ac1)*convert(lbm-ft/ft2-hr2, psia)

"[psia]"DELTAP_tubes_inH2O=DELTAP_tubes*convert(psia, inH2O) "[inH2O]"DELTAP_tot_ac=DELTAP_tubes+DELTAP_fin

DELTAP_fin=(f_f*G_max_ac^2*A_f_c/(2*A_flow_c*grav*rho_ac1))*convert(1/ft^2,1/in^2) "[psia]"DELTAP_fin_inH2O=DELTAP_fin*convert(psia,inh2o) "[inh2O]"f_f=1.7*Re_L_ac^(-.5)Re_L_ac=G_max_ac*h_fft_c/mu_ac*convert(1/hr, 1/s)Den_COPseas_i = (Tac1-67)*fri(Tac1)/COPEnd

226

Call At95(Tsc, V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c, nrow_c, Tubetype_c,ncircuit_c:PD, m_sys, A_e, A_c, Tc_95, width_e, width_c, W_dot_fc, W_dot_com,DELTAP_tot_ac95,CF_e,CF_c,DP_Rbend_95,DP_Rtotal_95,L_22a95,L_2a2b_95,L_2b3_95)

Call WithSubcool(67,PD,A_e,A_c, m_sys,V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c, nrow_c,Tubetype_c, ncircuit_c: Den_COPseas_67,Tsc[1])







Call WithSubcool(102,PD,A_e,A_c, m_sys,V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c,nrow_c, Tubetype_c, ncircuit_c: Den_COPseas_102,Tsc[1])

COPseas = 11.27/(Den_COPseas_67 + Den_COPseas_72 + Den_COPseas_77 +Den_COPseas_82 + Den_COPseas_87 + Den_COPseas_92 + Den_COPseas_97 +Den_COPseas_102)

Tsc=15 “[F]” {Sub-cool in the condenser}V_ac=8 “[ft/s]” {Air velocity over condenser, ft/s}h_f_c=1.25 "[in]" {tube vertical spacing on centers, in}t_c=.006/12 "[ft]" {thickness of fins, ft}eta_c=12*convert(1/in,1/ft) "[1/ft]" {condenser fin pitch, fins/ft}d_f_c=1.083 "[in]" {condenser fin depth per tube, in}tpc_c=2 {number of rows per refrigerant flow parallel circuit}nrow_c=3 {number of columns of tubing}TubeType_c=2 {Indicates tube diameter for standard copper pipe}ncircuit_c=12 {indicates number of refrigerant flow parallel circuits}

227

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