DESIGN ANALYSIS OF A FINNED-TUBE CONDENSER FOR A RESIDENTIAL

AIR-CONDITIONER USING R-22

A Thesis

Presented to

The Academic Faculty

By

Emma May Sadler

In Partial Fulfillment

of the Requirements for the Degree

Master of Science in Mechanical Engineering

Georgia Institute of Technology

April 2000

ii

DESIGN ANALYSIS OF A FINNED-TUBE CONDENSER FOR A RESIDENTIAL

AIR-CONDITIONER USING R-22

Approved:

____________________________________

S. V. Shelton, Chairman

____________________________________

P. V. Kadaba

____________________________________

A. V. Larson

Date Approved________________________

iii

ACKNOWLEDGEMENTS

This work would not have been completed without the help and support of many

others. In particular, I would like to thank my advisor, Dr. Shelton, for his enthusiasm

for my scholastic, professional, and personal success. He has provided motivation and

insights that have been invaluable to this project and my sanity. I’d also like to thank

Monifa Wright and Shawn Klawunder for sharing their resources and discoveries.

I would never have made it this far without my parents who have unconditionally

supported any endeavor that would lead to my happiness, be it a Masters degree or a

career as a goat herder. This thesis is dedicated to my grandparents, Sol and Frieda

Gersen, who have been more concerned about my progress than anyone else.

iv

TABLE OF CONTENTS

Chapter I Introduction........................................................................................................ 1Background ..................................................................................................................... 1Considerations ................................................................................................................. 1Past Work ........................................................................................................................ 2Purpose............................................................................................................................ 4

Chapter II Residential Air Conditioning Systems.............................................................. 6Refrigeration Cycle ......................................................................................................... 6Air Conditioner Components .......................................................................................... 8

Compressor.................................................................................................................. 8Condenser.................................................................................................................. 11Condenser Fan........................................................................................................... 12Expansion Valve ....................................................................................................... 13Evaporator ................................................................................................................. 13Evaporator Fan.......................................................................................................... 15

Coefficient of Performance ........................................................................................... 16Seasonal COP................................................................................................................ 16

Chapter III Heat Exchangers............................................................................................ 20Geometry....................................................................................................................... 20NTU-Effectiveness Relations........................................................................................ 23Refrigerant Side Models................................................................................................ 30

Single Phase Heat Transfer Coefficient .................................................................... 30Condensation Heat Transfer Coefficient ................................................................... 33Evaporative Heat Transfer Coefficient ..................................................................... 35Pressure Drop in Straight Pipe .................................................................................. 36Pressure Drop in Bends............................................................................................. 39

Air Side Models ............................................................................................................ 44Heat Transfer Coefficient .......................................................................................... 44Pressure Drop ............................................................................................................ 46

Chapter IV Optimization of Operating Parameters.......................................................... 52Subcool and Seasonal Effects ....................................................................................... 54Effect of Varying Air Velocity...................................................................................... 58Effect on Cost Factor..................................................................................................... 60

Chapter V Effects of Geometry with Fixed Cost ............................................................. 62Number of Rows ........................................................................................................... 64Fin Pitch........................................................................................................................ 66Tube Diameter............................................................................................................... 71Tube Circuiting.............................................................................................................. 75

v

Operating Costs............................................................................................................. 79

Chapter VI Effects of Geometry with Fixed Frontal Area............................................... 85Number of Rows ........................................................................................................... 85Fin Pitch........................................................................................................................ 90Tube Diameter............................................................................................................... 92Comparing Fixed Area to Fixed Cost ......................................................................... 101

Chapter VII Conclusions and Recommendations .......................................................... 103

Appendix I Mass of Refrigerant in a Heat Exchanger Coil Undergoing Phase Change............................................................................................................................. 106

Appendix II EES Simulation Program........................................................................... 109

Appendix III Condenser Operating Conditions ............................................................. 136

References ....................................................................................................................... 146

vi

LIST OF TABLES

Table 1. Distribution of Cooling Load Hours ................................................................... 17Table 2. Euler number coefficients for inverse power series............................................ 49Table 3. Staggered Array Geometry Factor...................................................................... 50Table 4. Individual row correction factors........................................................................ 51Table 5. Air-Conditioner Design Conditions .................................................................... 52Table 6. Base Case Condenser and Evaporator Characteristics........................................ 53Table 7. Mass of Refrigerant in Air-Conditioner for Different Subcool Specifications... 54Table 8. Material Costs ..................................................................................................... 63Table 9. COP’s and Area Factors Based on Fin Pitch...................................................... 67Table 10. Data for Copper Tubes...................................................................................... 71Table 11. COP’s and Area Factors Based on Tube Diameter........................................... 72Table 12. Condenser Configurations for Circuiting Analysis........................................... 76Table 13. Maximum Seasonal COP’s for Different Tubes per Circuit with Fixed Cost .. 77Table 14. Pressure Drop Distributions at 83° F ................................................................ 78Table 15. COP and Flow Area for Different Circuiting Configurations........................... 80Table 16. Data for Varying Number of Rows at 83° F..................................................... 87Table 17. Overall UA and UA/ Length for Varying Rows at 83° F ................................. 89Table 18. Optimum Operating Conditions For Varying Number of Rows with Fixed Area

................................................................................................................................... 90Table 19. Optimum Operating Conditions For Varying Tube Diameter with Fixed Area94

vii

LIST OF FIGURES

Figure 1. Thermodynamic State of Refrigerant in Refrigeration Cycle.............................. 7Figure 2. Refrigeration Cycle Equipment ........................................................................... 8Figure 3. Typical Plate Finned-Tube Heat Exchanger...................................................... 11Figure 4. Effective Specific Heat ...................................................................................... 14Figure 5. General Heat Exchanger Dimensions................................................................ 22Figure 6. Layout of Heat Exchanger Geometry Parameters ............................................. 23Figure 7. Layout of Hexagonal Fins.................................................................................. 28Figure 8. Effects of Operating Conditions on Evaporator Frontal Area ........................... 54Figure 9. Condenser Subcool at Varying Ambient for Different Refrigerant Charges..... 56Figure 10. Effect of Ambient Temperature on Evaporator Capacity and Mass Flow Rate

................................................................................................................................... 57Figure 11. Trends in Seasonal COP vs. COP’s at Other Temperatures............................ 58Figure 12. Effect of Air Velocity on Seasonal COP for Different Subcool Conditions ... 59Figure 13. Effect of Air Velocity on Compressor and Condenser Fan Work................... 60Figure 14. Number of Rows vs. Seasonal COP with Fixed Cost...................................... 64Figure 15. Number of Rows vs. Compressor Power and Refrigerant Pressure Drop....... 65Figure 16. Rows vs. Air Side Pressure Drop and Fan Power for Fixed Cost at 83 F ....... 66Figure 17. Seasonal COP’s for Different Fin Pitches at Optimum Operating Conditions

with Fixed Cost ......................................................................................................... 67Figure 18. Effect of Fin Pitch on Seasonal COP at Different Air Velocities.................... 68Figure 19. Effect of Fin Pitch on Frontal Area ................................................................. 69Figure 20. Fin Pitch vs. Airside Pressure Drop at 83F...................................................... 70Figure 21. Effect of Fin Pitch on Power Requirements at 83F ......................................... 70Figure 22. Maximum Seasonal COP for Different Tube Diameters................................. 72Figure 23. Optimal Operating Conditions for Different Tube Diameters......................... 73Figure 24. Condenser Allocation for Different Tube Diameters at 83F ........................... 74Figure 25. Refrigerant Side Pressure Drop vs. Tube Diameter at 83F ............................. 75Figure 26. Maximum Seasonal COP for Different Circuiting .......................................... 77Figure 27. Pressure Drop vs. Circuiting at 83° F.............................................................. 78Figure 28. Operating Costs vs. Area Factor for Different Geometry Factors................... 82Figure 29. Operating Costs For Different Tube Diameters and Circuiting at 83° F with

Fixed Cost ................................................................................................................. 83Figure 30. Effect of Varying Fin Pitch for Base Case and Optimum Case at 83° F with

Fixed Cost ................................................................................................................. 84Figure 31. Seasonal COP for Varying Rows with Fixed Area.......................................... 86Figure 32. Tradeoffs Between Compressor and Fan Power for Varying Number of Rows

with Fixed Area at 83 F............................................................................................. 87Figure 33. Condenser Allocation for Varying Rows at 83° F........................................... 88

viii

Figure 34. Air Velocity vs. Seasonal COP for Different Row Configurations with FixedArea ........................................................................................................................... 90

Figure 35. Variance of Optimal Air Velocity with Fin Pitch for Fixed Frontal Area....... 91Figure 36. Condenser Allocation for Varying Fin Pitch at 83F........................................ 92Figure 37. Variance of Optimal Air Velocity with Tube Diameter at Optimum Subcool

for Fixed Frontal Area............................................................................................... 93Figure 38. Air Side Pressure Drop for Varying Tube Diameters at 83° F........................ 95Figure 39. Compressor and Fan Power Trends vs. Tube Diameter at 83° F .................... 96Figure 40. Operating Costs vs. Cost Factor for Different Geometry Factors ................... 98Figure 41. Operating Costs For Different Tube Diameters and Circuiting at 83° F with

Fixed Area................................................................................................................. 99Figure 42. Optimum Condenser Circuiting for Fixed Area at 83 F with Varying Rows100Figure 43. Comparison of Area Factor to Cost Factor Based on Number of Rows ....... 101Figure 44. Comparison of Area Factor to Cost Factor Based on Fin Pitch.................... 102Figure 45. Comparison of Area Factor to Cost Factor Based on Tube Diameter........... 102

ix

LIST OF SYMBOLS

Symbol Refers to

a Stanton number coefficient

a Ratio of transverse tube spacing to tube diameter

A Total heat transfer area

Ac Minimum free-flow cross sectional area

Af Total fin surface area

Afr Frontal area

Amin Minimum flow area

Ao Total airside heat transfer area, fins and tubes

AF Area Factor

b Stanton number coefficient

b Ratio of longitudinal tube spacing to tube diameter

Bθ Bend coefficient

BL Building Load

C Heat capacity

CF Cost Factor

CLF Cooling Load Factor

COP Coefficient of performance

cp Specific heat

cp,eff Effective specific heat

Cr Heat capacity ratio

Cz Average row correction factor

cz Individual row correction factor

D Tube Diameter

E& Electrical Power Demand

Eu Euler number

f Friction factor

x

FP Fin Pitch

Fr Froude number

G Mass flux

gc Gravitational constant

h Enthalpy

h Heat transfer coefficient

H Heat exchanger height

j Colburn factor

JP j-factor parameter

k Conductivity

k Bend pressure coefficient

k1 Staggered array geometry factor

L Length

m Fin parameter

m Mass

m& Mass flow rate

n Blasius coefficient

NTU Number of transfer units

Nu Nusselt number

pr Reduced pressure

Pr Pressure ratio

PD Piston displacement

PLF Part load factor

Pr Prandtl number

eQ& Evaporator capacity

r Outside tube radius

rb Radius of bend

re Equivalent radius

rr Relative radius

R Ratio of clearance volume to displacement

xi

Rw Wall Resistance

R” Fouling factor

Re Reynolds number

SF Size Factor

St Stanton number

t Fin thickness

Tr Temperature ratio

tpc Tubes per circuit

U Overall heat transfer coefficient

v Specific volume

Va Air face velocity

W Heat exchanger width

wa Actual specific compressor work

ws Isentropic specific compressor work

comW& Compressor power

fW& Fan power

x Quality

Xl Longitudinal tube spacing (parallel to air flow)

Xt Transverse tube spacing (normal to air flow)

z Number of rows

z/D Equivalent length

β Fin parameter

χtt Lockhart-Martinelli parameter

∆h Enthalpy change

∆hlat Enthalpy change due to condensation

∆hsens Enthalpy change due to temperature change

∆Pa Air-side pressure drop

∆Pf Refrigerant side two-phase friction pressure drop

∆Pm Refrigerant side two phase momentum pressure drop

xii

ε Heat exchanger effectiveness

ε Roughness

φ Fin parameter

Γ2 Bend physical property coefficient

ϕ2 Two phase bend multiplier

λ Friction factor

µ Viscosity

ρ Density

ηc Compressor thermal efficiency

ηf Fan efficiency

ηs Surface efficiency

ηv Volumetric efficiency

ψ Fin parameter

#circ Number of parallel circuits

xiii

SUMMARY

The purpose of this study was to develop an optimization methodology and

software for the detailed design of a finned-tube condenser heat exchanger coil in a

residential air-conditioning unit using the Engineering Equation Solver (EES) software.

The superheat, saturated, and subcool portions of the heat exchanger have been modeled

separately and in detail using appropriate pressure drop and heat transfer fundamental

equations for both the air-side and refrigerant-side of the heat exchangers. The study uses

accurate refrigerant property data for R-22, but can easily be modified to accommodate

other refrigerants. The cooling output and electrical input for the compressor and fans

have been calculated for various ambient temperature conditions. The compressor,

condenser fan, and evaporator components of the cycle are also modeled but in a more

global manner using thermal science laws. Ambient temperature weighting factors used

by the U.S. Department of Energy are used to determine the seasonal coefficient of

performance (COP) of the system.

A base condenser model was arbitrarily chosen and design conditions were

established at 95° F. The operating parameters of condenser subcool and air face velocity

were examined over a wide range of ambient conditions to determine their effects on the

seasonal COP. It was determined that there is a range of subcools and face velocities

where the effects on the seasonal COP were negligible. The COP the system at an

xiv

ambient temperature of 83° F was nearly identical to the seasonal COP and could be used

for quick comparisons.

The effects of changing the tube diameter, tube circuiting, number of rows, and

fin pitch have been investigated for both fixed cost and fixed frontal area. When the

parameters were varied from the base case individually, the changing the number of

circuits to 4 or changing the tube diameter to 1/2” gave the highest COP’s. It was

determined that tube diameter and tube circuiting should not be considered separately

because they both affect the refrigerant side pressure drop. When the cost or area was

fixed, the best tube diameter- circuiting configuration was 5 circuits of 5/16” tubing. In

both cases, 4 circuits of 3/8” tubing provided similar performance with better packaging.

In general, the COP will be the highest when the frontal area is maximized and

rows should only be added if there is a frontal area constraint. This is because of the

relationship between the air velocity, depth, and air-side pressure drop. When the cost is

fixed, fewer rows provide better performance. If the frontal area is constrained, adding

rows will increase the performance as long as the refrigerant side pressure drop does not

become too great.

Changing the fin pitch had a relatively negligible effect on the seasonal COP.

The fan power increases as the number of fins increases, but the compressor power

decreases by about the same amount. If cost is fixed, fewer fins provide better

performance. When the area is restricted, more fins provide better performance.

1

CHAPTER I

INTRODUCTION

Background

Refrigeration for personal comfort was first used in 1902. By 1997, 72% of all

American households had air-conditioning and 47% of all households were cooled with

central air i. According to the Air-Conditioning and Refrigeration Institute (ARI), 81% of

all new homes constructed were equipped with central air-conditioning in 1996.ii For a

single family, detached home, the amount of energy dedicated to air-conditioning can be

quite significant. In Atlanta, for example, air-conditioning accounts for approximately

19% of energy costs, which includes both gas and electricity, or 310 dollars per year. It

also accounts for 32% of the total peak power demand of electricity in these homes. iii

Obviously, improving the efficiency of residential air-conditioning units would decrease

utility bills and pollution produced by the power generation.

Considerations

Optimizing an air-conditioning system presents a complex problem for many

reasons. To start, there are many parameters that can be varied for each component. The

effect of varying most parameters is not independent on a component or system basis.

2

Even if a component is optimized for specific operating conditions, like inlet and outlet

conditions, it is necessary to optimize each component at its unique operating conditions

with all other system components. To get a fair comparison among different designs,

operating conditions such as air velocity and refrigerant charge need be optimized for

each design. However, optimizing these parameters will affect the cooling capacity of

the evaporator, skewing the comparison.

Past Work

Until recently, limited computing power and the complex relations for refrigerant

properties had restricted the system design process to experimental testing. In 1975,

James Propst performed a similar study on condenser performance. iv Because of the lack

of computing power, Propst used a simplified model that neglected the refrigerant

properties so the analysis is based on the performance of the air side only. Propst

developed his equations to be solved explicitly and did not depend on any refrigerant side

properties including the condensing temperature. He used a constant refrigerant side

convective heat transfer coefficient, neglected pressure drops in the system, ignored the

superheated and subcooled sections and assumed constant compressor performance.

With increased computing power, it is now possible to create detailed computer

models with accurate refrigerant properties. While manufacturers such as HeatCraft have

created proprietary models for their components, they are not available for general study

and the programs are limited to simulating the performance of the products they sell. The

analytical techniques and assumptions used to develop these models are not known.

3

Also, since most air-conditioner manufacturers outsource their components, the

components are not optimized in the context of the entire system. There have not been

very many recent developments in fundamental heat exchanger modeling. Recent studies

have focused on enhanced fin and wet coil modeling which are not pertinent to flat plate

condenser optimization. Most of the recent heat exchanger studies for air conditioning

applications have focused on the effects of enhanced fin and wet coils. These studies

have not integrated the heat exchanger models in a complete system. Several component

models were reviewed for this study and will be discussed in the chapters where the

component models are developed.

In the past ten years, there have been a few studies that have used modern

technology to evaluate cooling equipment on a system basis. Beans v developed a

computer simulation of a refrigeration cycle using R-12. The program requires the inlet

air properties, cooling load, heat exchanger working pressures and some compressor

characteristics to determine the heat exchanger UA and effectiveness, outlet air

properties, and COP, and the free compressor variables. Using the heat exchanger and

compressor characteristics, the program can also find the COP for off-design inlet air

conditions. Haselden and Chen created a simulation program for air-conditioning

systems focusing on the effects of different refrigerant mixtures.vi This program will

predict the system COP, compressor size, required heat exchanger areas, relevant

temperatures, pressures, and flows. Klein and Reindl have investigated the effects of heat

exchanger allocation between the evaporator and condenser on system performance.vii

The condenser and evaporator are modeled as counterflow heat exchangers, neglecting

4

the superheated and subcooled sections. They also assume the air-side heat transfer

coefficients and fan powers are equal for the condenser and evaporator. Chen et. al have

studied the effect of cooling load on COP using finite-time heat transfer analysis for

steady flow Carnot and Brayton refrigeration cycles.viii They later expanded this study to

include nonisentropic compression and expansion. ix

Purpose

This purpose of this study was to develop an optimization methodology and

software for the detailed design of a finned-tube condenser heat exchanger coil in a

residential air-conditioning unit using the Engineering Equation Solver (EES) software.

The superheat, saturated, and subcool portions of the heat exchanger have been modeled

separately and in detail using appropriate pressure drop and fundamental heat transfer

equations for both the air-side and refrigerant-side of the heat exchangers. The study uses

accurate refrigerant property data for R-22, but can easily be modified to accommodate

other refrigerants. The compressor, condenser fan, and evaporator components of the

cycle are also separately modeled. The cooling output and electrical input for the

compressor and fans have been calculated for various ambient temperature conditions.

Ambient temperature weighting factors used by the U.S. Department of Energy

are used to determine the seasonal coefficient of performance (COP) of the system. The

seasonal COP is the figure-of-merit used to optimize the condenser face velocity, tube

5

diameter, fin spacing, tube circuiting, number of rows and refrigerant charge. Because

there are tradeoffs between capital and operating costs that must be considered if the

system is to succeed on the consumer market, non-dimensional cost and area factors have

been used as constraints. Based on simulation results and considering monetary or

frontal area constraints, optimal condenser configuration recommendations have been

made.

6

CHAPTER II

RESIDENTIAL AIR CONDITIONING SYSTEMS

Before a detailed analysis of the operating conditions and geometry of the

condenser can be attempted, it is necessary to understand how the air conditioning system

works. In this chapter, the overall refrigeration cycle, system components and coefficient

of performance will be discussed.

Refrigeration Cycle

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. The refrigerant vapor is cooled to the saturation temperature (State 2a),

condensed to a liquid (State 2b), and cooled below the saturation point (State 3). The

high pressure liquid is forced through an expansion valve into the evaporator (State 4).

The pressure in the evaporator is much lower than the pressure in the condenser, so the

refrigerant enters the evaporator as a liquid-vapor mix at low temperature and pressure.

The refrigerant absorbs heat from warm indoor air that is blown over the evaporator coils.

The refrigerant is completely evaporated (State 4a) and heated above the saturation

7

temperature before entering the compressor. The indoor air is cooled and dehumidified

as it flows over the evaporator and returned to the living space. The refrigeration cycle is

shown in Figure 1 and the equipment setup is shown in

Figure 2.

s

T

4

3

2

1

4a

2b 2a

Figure 1. Thermodynamic State of Refrigerant in Refrigeration Cycle

8

3 Subcooled Saturated

Saturated

Superheated

Superheated 1

2 2a

4 4a

Compressor Expansion Valve

2b

Condens e r

Evaporator

Figure 2. Refrigeration Cycle Equipment

Air Conditioner Components

Compressor

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

Compressors fall into two general categories: positive displacement, which increase the

pressure of the vapor by reducing the volume, and dynamic, which convert angular

momentum into a pressure rise and transfer it to the vaporx. Scroll type, positive

displacement compressors which dominate the residential compressor market were

considered for this study. The amount of specific work done by an ideal compressor can

be found by the energy equation:

( )12, hhw scoms −=

9

where: h = refrigerant enthalpy

For a non-ideal compressor, the actual amount of work required depends on the

efficiency.

( )12,

, hhw

wc

comscoma −==

η

where: ηc = compressor thermal efficiency

For a scroll type compressor, Klein has determined the thermal efficiency is related to the

reduced pressure and reduced temperature with the following equation. xi

rrrrrrc TPTTPP 061.331.503.1110281.0814.325.60 22 +−+−−−=η

where: Pr = Pressure ratioevap

condr P

PP =

Tr = Temperature ratioevapsat

condsatr T

TT

,

,=

In his paper, Klein only considers the saturated sections of the heat exchangers.

Therefore, the coefficients in the compressor efficiency correlation are based on the

saturated temperatures rather than the actual inlet and outlet temperatures to the

10

compressor. Since pressure drops are included in the condenser model, the compressor

efficiency is based on the inlet saturation temperature and pressure in the condenser and

the outlet saturation temperature and pressure from the evaporator.

It is important to consider the volumetric efficiency in addition to the thermal

efficiency. The volumetric efficiency is the ratio of the mass of vapor that is compressed

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

the piston displacement and filled with evaporator exit state vapor. The volumetric

efficiency can be found by xii

−−= 1

vv

1out

inv Rη

Where:ηv = compressor volumetric efficiencyR = ratio piston/ cylinder of clearance volume to swept displacementv = specific volume

The volumetric efficiency is used to determine the mass flow rate of the refrigerant

through the compressor for a given compressor size.xiii

out

vmv

PDη=&

where: PD = piston displacement

11

Condenser

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

outside air. Heat exchangers come in many configurations, but finned-tube heat

exchangers are most common 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 will be the plate finned-tube type as shown in Figure 3.

Figure 3. Typical Plate Finned-Tube Heat Exchanger

When the refrigerant leaves the compressor, it enters the condenser as a

superheated vapor and leaves as a sub-cooled liquid. The condenser can be separated

into three sections: superheated, saturated, and sub-cooled. The specific heat rejected

from each section can be found by evaluating the refrigerant enthalpies at the inlets and

outlets.

12

32,

22,

22,

hhq

hhq

hhq

bsccon

basatcon

ashcon

−=

−=

−=

The heat transfer details on the air and refrigerant sides of the heat exchangers

will be discussed in Chapter 3.

Condenser Fan

Because natural convection will not produce sufficient airflow and heat transfer

over a reasonably sized condenser, a fan must be employed to keep the air moving.

Although the compressor uses the majority of the power consumed by the system, the fan

power must also be considered. The power required by the fan is directly related to the

air pressure drop across the condenser and the volume flow rate of the air.

conf

confrconaconaconf

APVW

,

,,,, η

∆=&

where: Va = air face velocity∆Pa = air-side pressure dropAfr = frontal areaηf = fan efficiency

The isentropic efficiency of the combined fan and motor is taken to be 65%. The air-side

pressure drop will be discussed in Chapter 3.

13

Expansion Valve

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

Under normal operating conditions, the thermo-static expansion valve opens and closes to

maintain a fixed superheat exiting the evaporator. In this study, that superheat will be

held at 10° F. Because the expansion valve is designed to pass a certain volume of

refrigerant, it cannot function properly if the refrigerant is not completely condensed.

The vapor refrigerant backs up behind the valve and the condenser pressure increases

until the refrigerant vapor is condensed. When this happens, the expansion valve cannot

regulate the refrigerant superheat exiting the evaporator. Under this condition, it converts

from maintaining superheat to maintaining a saturated liquid leaving the condenser. The

energy equation shows that the enthalpy is constant across the expansion valve.

43 hh =

Evaporator

The purpose of the evaporator is to transfer heat from the room air making the air

cooler and less humid. Because the refrigerant enters the evaporator in as a liquid-vapor

mix, it is only divided into saturated and superheated sections. The analysis for the

evaporator is nearly identical to that of the condenser, but some considerations must be

made for the dehumidification process. To keep the evaporator model simple, the coil is

assumed to be dry, so the air-side heat transfer coefficient is not affected, but the specific

heat is corrected to account for condensation. Because the air flowing over the

14

evaporator is cooled below the wet bulb temperature, some of the heat rejected by the air

results in condensing water out of the air rather than lowering the temperature. The total

enthalpy change of the air is the sum of the enthalpy change due to temperature drop, or

sensible heat, and the enthalpy change due to condensation, or latent heat.

latsenstot hhh ∆+∆=∆

As shown in Figure 4, using the specific heat for dry air will result in exit temperatures

that are too low. By using an effective specific heat, a more accurate exit temperature

can be obtained without the complications associated with using an air-water mixture.

Temperature

En

tha

lpy Effective

Dry AirMoist Air

∆hlat

∆hsens

Figure 4. Effective Specific Heat

15

Dividing the previous equation for enthalpy by the temperature change gives

Th

Th

Th latsenstot

∆∆

+∆

∆=

∆∆

By definition, the specific heat is the ratio of the sensible enthalpy change to the

temperature change. Substituting and rearranging results in the following:

Th

cc latpeffp ∆

∆+=,

where: cp = specific heat for dry aircp,eff = effective specific heat

The latent enthalpy accounts for about 25% of the total enthalpy change for air flowing

over an evaporator in residential applications. The effective specific heat can be

expressed in terms of the specific heat for dry air only.

ptot

senstotpeffp c

hh

Th

cc 33.175.0

25.0, =

∆

∆

∆

∆+=

Evaporator Fan

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

introduce unwelcome complications. In addition to affecting the heat transfer, wet coils

16

also affect the air-side pressure drop. Although there are correlations available to find the

pressure drop over wet coils, this is not the only issue. After the air flows over the

evaporator, it enters a series of ducts that return it to the inside living space. Because the

power required depends on the losses in the ducts which will change from case to case,

the default used by the Air-conditioning and Refrigeration Institute test standard of 365

W per 1000 cfm of airxiv will be used.

Coefficient of Performance

The coefficient of performance (COP) measures the efficiency of the entire

system. It is the ratio of the heat absorbed by the evaporator to the amount of electrical

energy used by the mechanical components, i.e. the compressor and two fans.

evapfconfcom

e

WWW

QCOP

,,&&&

&++

=

Seasonal COP

The American Refrigeration Institute has determined that the frequency

distribution of temperatures over the summer cooling season is roughly the same across

the country. However, in warmer, southern climates, there are more “cooling load

hours”, which are defined as the hours when the temperature is above 65 F, per year than

17

in cooler climates. In Atlanta, for example, the number of cooling load hours is

approximately 1300 hours per year, while it is only about 700 hours per year in

Cleveland, OH. Of these hours, the outside temperature will be between 80 F and 84 F

approximately 16.1% of the cooling season in either city. Table 1 shows the distribution

of the cooling load hours.

BinNumbe

r

Temperature

Range (F)

Representative

Temperature(F)

Fraction of TotalTemperature

Hours

1 65-69 67 0.2142 70-74 72 0.2313 75-79 77 0.2164 80-84 82 0.1615 85-89 87 0.1046 90-94 92 0.0527 95-99 97 0.0188 100-104 102 0.004

Table 1. Distribution of Cooling Load Hoursxv

The COP changes with the outside air temperature and the overall COP, or

seasonal COP, for an air conditioner depends on the temperatures at which the appliance

runs over an entire year. According to the ANSI/ASHRAE standard,xvi the seasonal COP

for a single speed, single compressor unit is found by:

18

( )

( )∑

∑= 8

jj

8

jje

seas

TE

TQCOP

&

&

where: Qe(Tj) = adjusted evaporator capacity at ambient temperature Tj

E(Tj) = adjusted electrical power demand at ambient temperature Tj

( )j = values corresponding to temperature bin j (from Table 1)

The adjusted evaporator capacity and adjusted electrical power demand are based on the

cooling load factor and the fraction of total temperature hours.

( ) ( ) jjssje nTQCLFTQ ⋅⋅= &

( ) ( )PLF

nTECLFTE jjss

j

⋅⋅=

&&

where: CLF = cooling load factorQss(Tj) = steady state evaporator capacity at Tj

nj = fraction of total temperature hours (from Table 1)Ess(Tj) = steady state electrical power demand at Tj

PLF = part load factor

The part load factor takes into account system cycling. For this study, the system

19

cycling is neglected so the part load factor is equal to 1. The cooling load factor is

defined:

( )( ) ( )

( ) ssj

ssjjss

j

QTBL1CLF

QTBLTQ

TBLCLF

&

&&

>=

≤=

where: BL = building load

The building load given by:

( ) ( )SF

TQ

65T35j

TBL ODss

ODj

&−−=

where: TOD = outdoor design temperature in Fahrenheit (in this case 95° F)

SF = size factor

The size factor determines the amount of over or undersizing of the system and is 1 for

this study because the system designed to meet the requirements at 95° F.

20

CHAPTER III

HEAT EXCHANGERS

Because this study focuses on optimizing the condenser geometry and operating

conditions, the characteristics of heat exchangers must be explored more thoroughly than

other components. In this chapter, the heat transfer and pressure drop models specifically

related to plate finned heat exchangers will be discussed. Plate finned heat exchangers

are made up of in-line or staggered tube bundles that are held in place by continuous,

rectangular fins. For this study, staggered, copper tubes are coupled with aluminum fins.

Geometry

It is important to understand the terminology used to describe the geometric

parameters of the heat exchangers used in this study. The term “tubes per circuit” is the

number of parallel passages the refrigerant mass flow rate is divided among. If the mass

flow rate is 100 lbm/hr and there is one tube per circuit, 100 lbm/ hr of refrigerant will

pass through that tube. If there are 2 tubes per circuit, then 50 lbm/hr of refrigerant will

flow through each tube. The number of parallel circuits is used to determine the number

of tubes in each row. The number of rows refers to the number of tube rows in the

direction normal to air flow. If the number of parallel circuits is set to 12, and the

number of tubes per circuit is 2, then there will be a total of 24 tubes in each row. The fin

21

pitch is the number of fins per unit length along the axial direction of the tubes. These

parameters and the overall dimensions of the heat exchanger are illustrated in Figure 5

and Figure 6. The model used to determine the air-side heat transfer coefficient depends

on the layout of the tubes, but not on the temperature of the refrigerant which would be

affected by circuiting. The only factors pertinent to the refrigerant side models affected

by the circuiting are the mass flow rate in each tube and the length associated with each

circuit. The layout in Figure 6 meets the requirements of the models and is easy to

conceptualize.

22

Figure 5. General Heat Exchanger Dimensions

23

Figure 6. Layout of Heat Exchanger Geometry Parameters

NTU-Effectiveness Relations

For any heat exchanger, the total heat rejected from the hot fluid, in this case,

refrigerant, to the cold fluid, air, is dependent on the heat exchanger effectiveness and the

heat capacity of each fluid.

( )icih TTCQ ,,min −= ε

24

where: ε = effectivenessCmin = smaller of heat capacities Ch and CcTh,i = inlet temperature of hot fluidTc,i = inlet temperature of cold fluid

The heat capacity, C, the extensive equivalent of the specific heat, determines the

amount of heat a substance absorbs or rejects per unit temperature change.

pcmC =

where: m = masscp = specific heat

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

proportional to the tube length associated with that section. For example:

tot

sat

tota

sata

LL

m

m=

,

,

The effectiveness is the ratio of the actual amount of heat transferred to the

maximum possible amount of heat transferred.

maxQQ

&&

=ε

25

The equations used to determine the effectiveness depend on the temperature

distribution within each fluid and on the paths of the fluids as heat transfer takes place, ie.

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

refrigerant mass flow is separated into a number of tubes and does not mix. As the air

flows through the fins, the plates prevent mixing and air at one end of the heat exchanger

will not necessarily be the same temperature as 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 equation:

( ) ( )[ ]{ }

−−

−= 1exp1exp1 78.022.0 NTUCNTUC r

r

ε

where: Cr = heat capacity ratio

max

min

CC

Cr =

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

approaches infinity and the heat capacity ratio goes to zero. When Cr=0, the

effectiveness for any heat exchanger configuration is:

26

( )NTU−−= exp1ε

The NTU is a function of the overall heat transfer coefficient.

minCUA

NTU =

The overall heat transfer coefficient, U, takes into consideration total thermal

resistance to heat transfer between two fluids. Even though the convective heat transfer

coefficients may be different on the air and refrigerant sides of the heat exchanger, the

UA product is the same on either side. This is because all of the heat taken from the

refrigerant must be transferred to the air.

aarr AUAUUA111 ==

where: A = total heat transfer area( )r = refrigerant side( )a = airside

Taking all of the thermal resistances into account produces the following

expression for the UA product:

27

rrrsrrs

rfw

aas

af

aaas AhA

RR

A

R

AhUA ,,

,

,

,

,

111ηηηη

+′′

++′′

+=

where: R”= fouling factorRw= wall resistanceηs = surface efficiencyh = heat transfer coefficient

Since there are no fins on the refrigerant side of the tubes, the refrigerant side surface

efficiency is 1. Neglecting the wall resistance, Rw, and the fouling factors, R”, the overall

heat transfer coefficient reduces to

1

,

11−

+=

rraaas AhAhUA

η

The methods for finding the heat transfer coefficients will be discussed later in

this chapter. To find the overall surface efficiency for a finned tube heat exchanger, it is

first necessary to determine the efficiency of the fins alone. The total air side surface

efficiency is given by:

( )fo

fs A

Aηη −−= 11

where: ηs = surface efficiencyAf = total fin surface areaAo = total air side surface area, tube and finsηf = fin efficiency

28

The fin efficiency, ηf, for a circular fin is a function of m, re and φ.

( )( )φ

φη

e

ef mr

mrtanh=

For a plate fin heat exchanger with multiple rows of staggered tubes, the plates

can be evenly divided into hexagonal shaped fins as shown in Figure 7.

Figure 7. Layout of Hexagonal Fins

29

Schmidtxvii analyzed hexagonal fins and determined that they could be treated like

circular fins by replacing the outer radius of the fin with an equivalent radius. The

empirical relation for the equivalent radius is given by

( ) 213.027.1 −= βψrre

where: re=equivalent radius of finsr = outside tube radius

The coefficients ψ and β are defined as:

rX t

2=ψ

2122

41

+= t

Lt

XX

Xβ

where: Xl = tube spacing in direction parallel to air flowXt = tube spacing normal to air flow

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

circular fins can be used. For the fins in this study, the length is much greater than the

thickness, so a parameter m can be expressed as:

30

212

=

kth

m a

where: ha = air side heat transfer coefficientk = conductivity of fin materialt = thickness of fins

For circular tubes, a parameter φ is defined as

+

−=

rr

rr ee ln35.011φ

Refrigerant Side Models

Single Phase Heat Transfer Coefficient

To find the single phase heat transfer coefficient, the standard heat transfer

equations and the experimental work of Kays and London were considered. For constant

surface heat flux in the laminar regime, the Nusselt number is a constant.

Nu=4.36

In the turbulent region, the Dittus-Boelter equation holds for fully developed flow in

circular tubes with moderate temperature differences. For refrigerant cooling in the

condenser, the Dittus-Boelter equation is:

31

NuD D= 0023 0 8 0 3. Re Pr. .

where: ReD = Reynolds number based on diameterPr = Prandtl number

This equation has been confirmed by experimental data for the range:

0.7 ≤Pr ≤160

ReD ≥ 10,000

L/D ≥ 10

where: L = tube length in single phase region

In the subcooled portion of the condenser, the temperature difference at the inlet

and exit is usually less than 20°F, but in the superheated portion, the inlet and exit

temperature can vary by as much as 90°F. The temperature differential between the air

flowing over the tubes and, as a result, the inner surface of the tubes and the refrigerant is

also much greater. Under these conditions, the Dittus-Boelter equation does not produce

an accurate value for the heat transfer coefficient. Sieder and Tatexviii have developed a

correlation equation for large property variations based on the mean fluid temperature

and the wall surface temperature.

32

NuD Dm

s

=

0027 0 8 1 3

0 14

. Re Pr.

.µµ

where: µ = viscosity( )m = evaluated at mean fluid temperature( )s = evaluated at surface

The viscosity µs is evaluated at the surface and all other properties are evaluated at the

mean fluid temperature.

Kays and London use empirical data taken from a variety of refrigerants in

circular tubes under different conditions. Unlike the other correlations, Kays and London

have established equations in the transition region. The heat transfer coefficient was

related to the Stanton number, St. The Stanton number is defined by the following:

pcGh

St =

St a bPr Re2 3 =

where: cp= specific heat

The coefficients a and b are based on the flow regime.

33

Laminar Re < 3,500 a=1.10647b=-0.78992

Transition 3,500 < Re < 6,000 a=3.5194 x 10-7b=1.03804

Turbulent 6,000 < Re a=0.2243b=-0.385

In the laminar and early transition regions, the Kays and London heat transfer

coefficient is lower than the others, but is it is higher in the turbulent region. The Dittus-

Boelter and Sieder and Tate equations assume that the pipe is smooth which would

explain this result. Because the Kays and London relation is based on data taken from

heat exchangers similar to those studied here and because transitional flow has been

addressed, this relation will be used in the simulation.

Condensation Heat Transfer Coefficient

Condensation heat transfer correlations by Shah and Traviss, Rohsenow and

Baronxix were considered for this study. Patexx showed that the results of Shah and the

results of Traviss et al. were not significantly different, however, Traviss’ model only

applies to annular flow regime while Shah’s relation is good in all flow regimes.

Traviss’ model also requires an iterative scheme while Shah’s method is very easy to use.

It is a simple dimensionless correlation which has been verified over a large variety of

experimental data. This model has a mean deviation of about 15% and has been verified

34

for many different condensing fluids, tube sizes and tube orientations. For any given

quality, the two-phase heat transfer coefficient is

( ) ( )

−+−=38.0

04.076.08.0 18.3

1r

LTP pxx

xhh

where: hTP= two phase heat transfer coefficientx= qualityhL= liquid only heat transfer coefficientpr= reduced pressure

By integrating the two-phase heat transfer coefficient over the length, the mean

two-phase heat transfer coefficient can be determined.

( ) ( ) ( )∫

−+−−

= 2

138.0

04.076.08.0

12

18.31

L

Lr

LTPM dL

pxx

xLL

hh

If the quality varies linearly with length which is consistent with constant heat

transfer per unit length, hTPM can be approximated by:

( )( ) 2

176.2

04.076.1

8.38.1

1 76.276.1

38.0

8.1

12

x

xr

LTPM

xxp

xxx

hh

−+

−−

−=

35

For complete condensation, that is x varies from 1 to 0, the mean two-phase heat

transfer coefficient reduces to:

+= 38.0

09.255.0

rLTPM p

hh

Evaporative Heat Transfer Coefficient

The expression for the average evaporative two-phase heat transfer coefficient is

taken from Tongxxi. This relationship assumes a constant temperature differential

between the wall and the fluid along the length of the pipe.

( )325.0325.0

075.0375.04.08.0

2.00186875.0

ie

ie

l

v

v

l

l

ll

l

levap xx

xx

k

CpGD

kh

−−

=

µµ

ρρµ

µ

where: D = tube diameter

G = mass flux

k = conductivity

( )l = properties evaluated at saturated liquid stage

( )v = properties evaluated at saturated vapor stage

( )e = properties evaluated at exit

( )i = properties evaluated at inlet

36

Pressure Drop in Straight Pipe

The pressure drop in the superheated and subcooled portions of the condenser can be

found easily by applying the standard pipe pressure drop equation.

∆pf G L

=2

ρ

where: f = friction factor

ρ = density

The friction factor, f, for circular pipe depends on the Reynolds number where the

turbulent expression is taken for the transition region.

000,2ReRe

51.27.3

log21

000,2ReRe64

211021 >

+−=

<=

fD

f

f

D

D

ε

For two-phase flow, the pressure drop calculation is substantially more complicated.

Hiller describes the method of Lockhart and Martinelli. The total two-phase pressure

drop is broken down into friction, gravitational, and momentum components.

37

dPdz

dPdz

dPdz

dPdzf g m

=

+

+

The frictional component is found using the following equation:

( ) [ ]dPdz

G

g D G Df

v

v

c

v

vtt

=

−

+

2

0.2

0.523 2009 1 2 85

ρ µχ. .

The momentum component is:

( ) ( ) ( )dPdz

Gg

dxdz

x x x xm c v

v

l

v

l

v

l

= −

+ −

+ −

− −

2 1 3 2 3

2 1 2 1 2 2 1ρ

ρρ

ρρ

ρρ

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

linear profile is assumed for simplicity, which is consistent with constant heat transfer per

unit length. The gravitational pressure drop for horizontal tubes is zero. Hillerxxii

integrates the pressure differential over the change in quality for the frictional and

momentum losses. The frictional pressure drop in the two-phase region is reduced to

38

( ) ( )[ ] e

i

x

xf xxCxxxCxCP 86.123

33.223

8.22 329.0538.00288.0141.0429.02357.0 −+−−+−=∆

where:

C l

v

v

l3

0 0523 0 262

285=

.

. .µµ

ρρ

CG

C g Dv

c v2

1 8

11 2

009=

. .

.

µρ

Lxx

C ie −=1

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

e

i

x

xl

v

l

v

l

v

l

v

l

v

l

v

cvm xx

gG

P

−

−

−

−

−

+=∆

3231

2

32312

21ρρ

ρρ

ρρ

ρρ

ρρ

ρρ

ρ

The total pressure drop is just the sum of the momentum and frictional pressure drops.

fmtot PPP ∆+∆=∆

39

Pressure Drop in Bends

The pressure drop in bends is found by assigning an equivalent length to each bend

based on the flow diameter and the bend radius. For two-phase flow, the method for

finding the pressure drop in bends based on Chisolmxxiii is used. The pressure drop is

calculated for liquid-only flow and correction factors are applied to determine the

approximate two-phase pressure drop. The method predicts the pressure drops for two-

phase flow in horizontal bends rather than the inclined bends found in a typical

condenser. However, the two-phase flow pattern in an inclined bend cannot be

accurately predicted and pressure gradients due to elevation changes are negligible

compared to friction pressure losses, so the horizontal bend model should be sufficient.

Since the bends are not finned and do not have air flowing over them, the heat transfer

and phase change in the bends is neglected.

The first step in computing the pressure drop is to determine the equivalent length of

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

rrDr

b

i

=

where: rb = radius of bendDi = inner diameter of pipe

40

Chisolm uses the correlation by Beij to determine the equivalent length, z/D. Typical

condensers will have a relative radius between 1 and 3 which corresponds to an

equivalent length between 12 and 15 for 90° bends. The equivalent length for a 180°

return bend is about twice that of a 90° bend. For this analysis, the equivalent length of

the return bend will be taken as 26. The single-phase pressure drop on a bend can be

evaluated by substituting the equivalent length for the straight pipe length in the standard

pressure drop equation.

eb D

zGp

=∆−

ρλ2

2

where: ∆pb = pressure drop in bendλ = friction factor

The friction factor can be determined with Haaland’s approximationxxiv:

211.1

7.3Re9.6

log8.1

−

+−= Dελ

where: ε = pipe roughness

For drawn copper pipes, the pipe roughness is taken to be 0.000005 ft. For two-phase

flow, the pressure drop in a bend is the product of the bend pressure drop for liquid only

and the two-phase multiplier.

41

2,,, loblobTPb pp ϕ∆=∆

where: ∆pb,lo = liquid oly bend pressure dropϕ2 = two-phase multiplier

The two-phase multiplier ϕ2 in a bend is:

( ) ( ) ( ) ( ) ( )[ ]ϕ θb lo bn n nB x x x,

2 2 2 2 2 2 21 1 1= + − − +− − −Γ

where: Γb2 = physical property coefficient

Bθ = bend coefficientn = Blasius coefficient

The physical property coefficient Γ2 for a bend is

Γbl

v

v

l

n

2 =

ρρ

µµ

The Blasius coefficient n used to determine ϕ2 and Γ2 is defined as

n

Lo

vo

l

v

=

ln

ln

λλ

µµ

42

The friction factors, λlo and λvo, are found using Haaland’s approximation. In these

cases, one assumes all of the mass is flowing as either a liquid or a vapor so the mass flux

G used to find the Reynolds number will be the same, but the viscosity will depend on the

refrigerant state.

n

Lo

vo

l

v

=

ln

ln

λλ

µµ

The B coefficient for bends other than 90° is

[ ]B Bk

kb

bθ

θ

= + −°°1 190

90,

The coefficient B90° is defined as

( )Bk R Db

9090

12 22°

°

= ++.

,

43

The recovery downstream of bends greater than 90° is assumed to be the same as 90°

bends. The pressure coefficient for a 90° bend, kb,90°, is used for convenience where

kzDb

e,90° =

λ

Assuming homogeneous two-phase flow, the friction factor for two-phase flow is found

using the same Haaland’s approximation, but the Reynolds number is based on the two-

phase viscosity.

Re =GD

TPµ

The two-phase viscosity is a function of quality.

( )µ µ µTP v lx x= + −1

In the case of 180° bends, the kb,180° is approximately twice kb,90° so B180° reduces to

[ ]B B180 90051° °= +.

44

Air Side Models

Heat Transfer Coefficient

The work of Rich and McQuiston were used to evaluate the air-side convective heat

transfer coefficient for a plate fin heat exchanger with multiple rows of staggered tubes.

The condenser coils are assumed to be dry. The heat transfer coefficient is based on the

Colburn j-factor which is defined as:

j St= Pr 2 3

Substituting the appropriate values for the Stanton number gives this relationship for the

convective heat transfer coefficient, h.

hj c G

a

p= max

Pr 2 3

where: Gmax = mass flux through minimum flow area

GmA

airmax

min

&=

For cases in this study, the minimum flow area is

( ) ( )( )( )DcirctpcHtFPWA #1min ⋅−=

45

where: W = width of heat exchanger

FP = fin pitch

H = height of heat exchanger

tpc = tubes per circuit

#circ = number of parallel circuits

McQuiston found the j-factor for a 4 row finned-tube heat exchanger to fit a linear model

based on the parameter JP.

j JP460 2675 1325 10= + × −. .

and

JPAAD

o

t

=

−

−

Re .

.

0 4

0 15

The Reynolds number is based on the outside diameter of the tubes, Do, and the

maximum mass flux Gmax. The heat transfer coefficient for heat exchangers with four or

less rows can be found using the following correlation:

( )( )jj

nn L

L4

1 2

1 2

1 1280

1 1280 4=

−−

−

−

Re

Re

.

.

46

ReL is based on the row spacing.

Re maxL

LG X=

µ

Pressure Drop

The work of Richxxv concludes that the air side pressure drop can be separated into

two components: the pressure drop due to the tubes and the pressure drop due to the fins.

fttot ppp ∆+∆=∆

where: ∆pt = pressure drop due to tubes∆pf = pressure drop due to fins

The pressure drop due to the fins can be expressed:

c

fmff A

AGvfp

2

2max=∆

where: ff = fin friction factorvm = mean specific volumeGmax = mass velocity through minimum areaAf = fin surface areaAc = minimum free-flow cross sectional area

47

In experimental tests, Rich found that the friction factor depends on the Reynolds

number, but is independent of fin spacing. For fin spacing between 3 and 14 fins per

inch, the fin friction factor is

5.0Re70.1 −= lff

where the Reynolds number is based on the transverse (in the direction of air flow) tube

spacing.

µl

l

GX=Re

To find the pressure drop over the tubes, the relationships developed by Zukauskas and

Ulinskasxxvi are used. The pressure drop over the banks of plain tubes is:

zG

Eup ct ρ2

2

=∆

where: Euc = corrected Euler numberz = number of rows

The corrected Euler number is:

48

EuCkEu zc 1=

where: Eu = Euler numberk1 = staggered array geometry factorCz = average row correction factor

The Euler number is related to the tube friction factor and depends on the

Reynolds number and the tube geometry. For staggered, equilateral triangle banks with

many rows, the Euler number is related to the Reynolds number by a fourth order inverse

power series.

432 ReReReReutsr

qEu ++++=

The coefficients, q, r, s, t, and u are dependent on the parameter a, the ratio of the

transverse tube spacing to tube diameter, and the Reynolds number. The coefficients for

distinct values of a determined by Zukauskas and Ulinskas from experimental data are

summarized in Table 2.

49

a Reynolds number q r s t u1.25 3< Re < 103 0.795 0.247 x

1030.335 x

103-0.155 x

1040.241 x 104

103< Re < 2 x 106 0.245 0.339 x104

-0.984 x107

0.132 x1011

-0.599 x1013

1.5 3< Re < 103 0.683 0.111 x 103 -0.973 x102

0.426 x 103 -0.574 x 103

103< Re < 106 0.203 0.248 x104

-0.758 x107

0.104 x 1011 -0.482 x1013

2.0 7< Re < 102 0.713 0.448 x102

-0.126 x103

-0.582 x103

0

102< Re < 104 0.343 0.303 x103

-0.717 x105

0.88 x 107 -0.38 x 109

104< Re < 2 x 106 0.162 0.181 x104

0.792 x108

-0.165 x1013

0.872 x1016

2.5 102< Re < 5 x 103 0.33 0.989 x102

-0.148 x105

0.192 x 107 0.862 x 108

5 x 103< Re < 2 x106

0.119 0.849 x104

-0.507 x108

0.251 x1012

-0.463 x1015

Table 2. Euler number coefficients for inverse power series

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

must be used as a correction. The staggered array geometry factor is dependent on the

Reynolds number, a and b, the ratio of tube spacing in the direction normal to the air flow

and the tube diameter. The equations for k1 are found in Table 3.

50

Re (a/b) k1

102 1.25 < a/b < 3.5 48.0

1 93.0

=

ba

k

103 0.5 < a/b <1.2 048.0

1

−

=

ba

k

1.25 < a/b < 3.5 284.0

1 951.0

=

ba

k

104 0.45 < a/b < 3.5

( ) ( ) ( )321

113.055.0708.028.1

bababak −+−=

105 0.45 < a/b < 3.5 432

1 021.0234.0948.0675.1016.2

+

−

+

−=

ba

ba

ba

ba

k

106 0.45 < a/b < 1.6 432

1 021.0234.0948.0675.1016.2

+

−

+

−=

ba

ba

ba

ba

k

Table 3. Staggered Array Geometry Factor

If the tube bank as 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 than the pressure drop over the rest of the rows. Cz is the average of the

individual row correction factors, cz.

∑=

=z

zzz c

zC

1

1

51

The equations for the individual row correction factors are given in Table 4.

Re z* cz

10 <3

297.018.0

065.1−

−=z

cz

102 <4

273.1497.3

798.1+

−=z

cz

103 <3

412.0411.0

149.1−

−=z

cz

104 <3

143.0269.0

924.0+

−=z

cz

>105 <4

667.0467.1

62.0+

−=z

cz

* For values greater than z, cz =1

Table 4. Individual row correction factors

Since the relations are given for discrete values of the a or the Reynolds number, linear

interpolation will be used to estimate the values of Eu, k1, and cz when the conditions are

outside of Zukauskas and Ulinskas’ scope.

52

CHAPTER IV

OPTIMIZATION OF OPERATING PARAMETERS

When comparing the performance of air conditioning systems, it is not valid to assert

that one condenser geometry is better than another if the operating conditions are not

optimized for each configuration. The operating parameters considered for this study are

refrigerant charge and air face velocity over the condenser. Because the performance of

an air-conditioner varies with ambient temperature, design conditions were established at

95° F to provide a fair basis for comparison. These conditions are summarized in Table

5.

Ambient Temperature 95° F

Evaporator Capacity 30,000 Btu/hr

Evaporator Saturation Temperature 45° F

Superheat in Evaporator 10° F

Table 5. Air-Conditioner Design Conditions

To see the effects the operating parameters have on the seasonal COP, a base case

condenser and evaporator coil pair typical for this application was selected. All of the

characteristics of the condenser and all but the width of the evaporator were specified.

These dimensions are given in Table 6.

53

Dimension Condenser EvaporatorTube spacing (in x in) 1.25 x 1.083 1.00 x 0.625Tube inner diameter (in) 0.349 0.349Tube outer diameter (in) 0.375 0.375Frontal area (ft2) 7.5 n/aFinned width (ft) 3 n/aFinned height (ft) 2.5 1.5Depth (in) 3.25 2.5Fin pitch (fin/ in) 12 12# rows 3 4# circuits 12 9Tubes per circuit 2 2

Table 6. Base Case Condenser and Evaporator Characteristics

The evaporator frontal area depends on the design conditions and is virtually

independent of operating conditions. In Figure 8, the evaporator frontal area remains

constant for different air velocities and refrigerant charges. The refrigerant charges are

specified by the number of degrees subcool, Tsc, in the condenser at the design

conditions.

54

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10 12 14 16 18

Air Velocity (ft/s)

Eva

po

rato

r F

ron

tal A

rea

(ft2

)

Tsc=5Tsc=10Tsc=15Tsc=20

Figure 8. Effects of Operating Conditions on Evaporator Frontal Area

Subcool and Seasonal Effects

The refrigerant charge is the mass of refrigerant in the system necessary to provide a

specified amount of subcool in the condenser at the design conditions. The relationship

between the specified subcool and refrigerant system mass is demonstrated in Table 7 for

air velocity of 8 ft/s.

DegreesSubcool@ 95° F

(°F)

Mass ofRefrigerantin System

(lbm)5 3.5010 4.3815 5.4920 6.45

Table 7. Mass of Refrigerant in Air-Conditioner for Different Subcool Specifications

55

The effects of a fixed refrigerant charge must be considered with varying ambient

temperature. As the outdoor air temperature drops, the condensing temperature also

drops and the enthalpy of the refrigerant entering the evaporator is lower. This means

that the inlet quality is lower and more of the refrigerant in the evaporator is in the liquid

state. Since the total mass of refrigerant in the system is held constant, the mass of the

refrigerant in the evaporator increases and the mass of refrigerant in the condenser

decreases as the ambient outdoor temperature decreases. When the mass of the

refrigerant in the condenser drops, the volume fraction of the condenser that is filled with

vapor must increase. If the mass of refrigerant in the condenser drops to the point where

the refrigerant is not completely condensed when it enters the valve, the valve goes wide

open and cannot maintain a fixed superheat in the condenser. Since a negligible amount

of vapor can pass through the expansion valve orifice, a saturated state is forced at the

valve entrance and the subcool in the condenser will be fixed at zero. The superheat in

the evaporator then varies from the specified 10° F. This condition occurs at higher and

higher ambient temperatures as the amount of subcool specified at 95° F decreases as

shown in Figure 9.

56

.

0

5

10

15

20

25

40 50 60 70 80 90 100 110

Ambient Temperature (F)

Co

nd

ense

r S

ub

coo

l (F

)

Tsc=5

Tsc=10

Tsc=15

Tsc=20

Figure 9. Condenser Subcool at Varying Ambient for Different Refrigerant Charges

Because the seasonal COP depends on the performance of the system over a range of

temperature, it is important that the refrigerant charge is high enough to ensure there be

subcool in the condenser at the lower temperatures. When the subcool disappears, the

superheat in the evaporator increases leading to lower density vapor at the compressor

inlet. This lower density vapor causes the mass flow rate to drop significantly, lowering

the evaporator capacity and the COP as shown in Figure 10.

57

385

390

395

400

405

410

415

420

425

50 60 70 80 90 100 110

Ambient Temperature (F)

Mas

s F

low

Rat

e (l

bm

/hr)

28500

2900029500

30000305003100031500320003250033000

Eva

po

rato

rCap

acity

(B

tu/h

r)

Mass Flow Rate Evaporator Capacity

Subcool = 0

Figure 10. Effect of Ambient Temperature on Evaporator Capacity and Mass Flow Rate

The optimum refrigerant charge will be different for each ambient temperature,

but the COP will remain relatively constant at every temperature as long as the subcool is

specified between 10° F and 15° F at 95° F ambient. In the range of 5-20° subcool, the

seasonal COP is within 0.5% of the COP at 83° F ambient. The trends in COP over the

season and at different ambient temperatures are plotted over a range of subcools in

Figure 11.

58

3.5

3.6

3.7

3.8

3.9

4

4.1

4.2

0 5 10 15 20 25

Subcool @ 95F

CO

PSeasonalTamb=77Tamb=82Tamb=83Tamb=87

Figure 11. Trends in Seasonal COP vs. COP’s at Other Temperatures

Effect of Varying Air Velocity

As expected, for a fixed amount of subcool at 95°, there is an air velocity that

produces the highest seasonal COP. The COP varies exhibits a maximum with the air

velocity for any subcool as shown in Figure 12. For subcools ranging from 5° to 20°, the

optimum air velocity is somewhere between 7 ft/s and 10 ft/s. In this range, the seasonal

COP is insensitive to the air velocity; for any refrigerant charge, it varies by less than 1%.

59

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

0 2 4 6 8 10 12 14 16 18

Air Velocity (ft/s)

Seasonal COP

Tsc=5Tsc=10Tsc=15Tsc=20

Figure 12. Effect of Air Velocity on Seasonal COP for Different Subcool Conditions

Because the seasonal COP varies so little with air velocity, it is difficult to

pinpoint the optimum air velocity for each subcool within more than ±0.1 ft/sec. In

practice, this is acceptable because the air speed cannot be specified to a such high

tolerance.

Since the fan work increases proportionally with the cube of the velocity, it does

not initially make sense that the COP would not be affected. However, in this range, as

the fan work is increasing, the compressor work is decreasing by roughly the same

amount, as demonstrated in Figure 13. As the air velocity increases, the condensing

temperature decreases, and the inlet enthalpy to the evaporator also decreases. When this

60

happens, the mass flow rate of refrigerant needed to maintain the design evaporator

capacity drops decreasing the compressor work. Since condensing temperature of the

refrigerant cannot be lower than the air inlet temperature, there is a minimum compressor

work. As the air velocity increases beyond the optimum range, the fan work will grow

exponentially and the decrease in compressor work does not compensate for it.

Air Velocity (ft/s)

Wo

rk (

BT

U/h

r)

CompressorCondenser FanTotal

Figure 13. Effect of Air Velocity on Compressor and Condenser Fan Work

Effect on Cost Factor

Changing the air velocity and refrigerant charge will slightly affect the cost of the

system because different compressors or fans should be used for different heat

exchangers. This would involve cost studies of compressors and fans which is outside

61

the scope of this study. They will be excluded from the cost factor calculation, but the

designer should be aware of the possible effects.

62

CHAPTER V

EFFECTS OF GEOMETRY WITH FIXED COST

When designing a heat exchanger for maximum system COP, the two most

important constraints are the cost of the exchanger and the amount of frontal area it takes

up. It is not possible to keep both the frontal area and cost constant while only varying

one geometry factor, but simultaneously changing more than one variable would make it

difficult to determine the effect each variable has on the system. To examine the tradeoffs

between frontal area and cost, cases with fixed cost and fixed frontal area were

considered.

To compare the relative frontal area of each condenser configuration, the area

factor parameter is defined as the ratio of the frontal area of the test configuration to the

frontal area of the base configuration.

baseAreaFrontalAreaFrontal

AF =

A similar factor, the cost factor, is used to compare the cost of condenser-

evaporator configurations:

63

base

CostCF

Cost=

The cost of the heat exchanger is largely determined by the cost of the materialsxxvii so the

cost factor of each configuration is taken as:

( ) ( ), , , ,Cucon Cu evap Cu Cu Al con Alevap Al AlCost Vol Vol Cost Vol Vol Costρ ρ= + + +

The costs of the materials are summarized in Table 8.

Material Cost ($/lbm)Copper 0.8

Aluminum 0.7

Table 8. Material Costsxxviii

The heat exchanger cost factor of the base configuration is $35.88. Although the piston

displacement will change slightly for each configuration, it varies from the base case by

no more than 3% under most conditions, so the cost variations of the compressor will be

ignored.

64

Number of Rows

Although altering any geometry factor will change the frontal area of the

condenser with the cost factor fixed, it is easiest to conceptualize this by changing the

number of rows. For these tests, the height of the condenser will remain fixed, but the

width is free to change. Intuitively, a heat exchanger with no bends and the largest

frontal area possible would provide the best performance.

Figure 14 verifies this notion.

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Number of Rows

Sea

son

al C

OP

Fixed Parameters

Fin Pitch =12 fpi

Tube Diameter = 3/8”

Tubes/ Circuit = 2

3.703.753.803.853.903.954.004.054.104.15

00.5 11.5 22.53 3.54 4.5Number of Rows

Seasonal COP

Fixed Parameters

Fin Pitch =12 fpi

Tube Diameter = 3/8”

Tubes/ Circuit = 2

Figure 14. Number of Rows vs. Seasonal COP with Fixed Cost

As the number of rows increases, the number of bends also increases. Obviously,

fewer bends in the tubing means less frictional losses and less compressor work. By

65

having the air only flow over one row of tubing, the temperature differential between the

air and the refrigerant is kept to a maximum, decreasing the refrigerant mass flow rate

and compressor work. The refrigerant side pressure drop and compressor power as

functions of the number of rows are plotted in Figure 15.

6100

6200

6300

6400

6500

6600

6700

0 1 2 3 4 5

Number of Rows

Co

mp

ress

or

Po

wer

(B

tu/h

r)

0

5

10

15

20

25

30

R22

Pre

ssu

re D

rop

(p

si)

CompressorPower

R22PressureDrop

Figure 15. Number of Rows vs. Compressor Power and Refrigerant Pressure Drop

While this is the main cause for the COP increase, the fan power also decreases as

with the number of rows. The pressure drop will go down as the depth of the air passage,

which is controlled by the number of rows, decreases. For larger number of rows, the

optimal air velocity is higher. This coupled with the increased pressure drop causes the

fan power to nearly double from 1-row to 4-rows as shown in Figure 16. However, if the

velocity remains constant, the fan power does not change.

66

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 1 2 3 4 5

Number of Rows

Air

-Sid

e P

ress

ure

Dro

p (

Psi

)

0

50

100

150

200

250

300

350

400

Fan

Po

wer

(B

tu/h

r)

Pressure DropFan Power

Figure 16. Rows vs. Air Side Pressure Drop and Fan Power for Fixed Cost at 83 F

Fin Pitch

Keeping the cost factor and all design parameters except the frontal area the same

as the base case, the model was run for fin pitches between 8 and 14 fins per inch (fpi).

The maximum seasonal COP’s and area factors based on fin spacing are summarized in

Table 9 and shown graphically in Figure 17. Based on these results, the fin spacing has

almost no effect on the seasonal COP or the optimal operating conditions. As seen in

Figure 18, the optimum velocity, for every fin pitch is between 8.5 and 9.5 ft/sec. This

figure is based on 10 F subcool at 95 F outdoor air temperature. Figure 18 also shows

that the seasonal COP varies shows an optimum with fin pitch, but the variation is

marginal.

67

Fin Pitch(fpi)

SeasonalCOP

AreaFactor

8 3.839 1.25810 3.856 1.11412 3.862 1.00014 3.860 0.906

Table 9. COP’s and Area Factors Based on Fin Pitch

Effect of Fin Pitch on Seasonal COP at Optimum Operating Conditions

3.835

3.840

3.845

3.850

3.855

3.860

3.865

6 8 10 12 14 16

Fin Pitch (fins/in)

Sea

son

al C

OP

Fixed Parameters

# Rows = 3

Tube Diameter = 3/8”

Tubes/ Circuit = 2

Effect of Fin Pitch on Seasonal COP at Optimum Operating Conditions

3.8353.8403.8453.8503.8553.8603.8656810121416Fin Pitch (fins/in)

Seasonal COP

Fixed Parameters

# Rows = 3

Tube Diameter = 3/8”

Tubes/ Circuit = 2

Figure 17. Seasonal COP’s for Different Fin Pitches at Optimum Operating Conditions with FixedCost

68

3.77

3.78

3.79

3.80

3.81

3.82

3.83

3.84

3.85

3.86

3.87

6 7 8 9 10 11 12

Air Velocity (ft/sec)

Sea

son

al C

OP

FPI=8FPI=10FPI=12FPI=14

Figure 18. Effect of Fin Pitch on Seasonal COP at Different Air Velocities

The maximum COP will occur when fin spacing is increased just before the point

where the airside pressure drop causes the fan work to increase faster than the compressor

work is decreasing, in this case, 12 fins per inch. As long as the operating conditions are

kept in the recommended range of 10-15 degrees subcool and 7-10 ft/sec air face

velocity, the maximum and minimum seasonal COP’s will only differ by about 1.6%.

The maximum occurs with 12 fins per inch, 8.8 ft/sec air face velocity and 10 F subcool.

The minimum occurs with 8 fins per inch, 10-ft/sec air face velocity, and 15 F subcool.

Although the fin spacing does not dramatically affect the COP, it does affect the

packaging size. If a more compact heat exchanger is desired, increasing the fin pitch will

decrease the frontal area as shown in Figure 19.

69

0

1

2

3

4

5

6

7

8

9

10

6 7 8 9 10 11 12 13 14 15

Fin Pitch (fins/in)

Figure 19. Effect of Fin Pitch on Frontal Area

As the fin pitch increases, the pressure drop across the fins also increases as seen

in Figure 20. This figure is based on operation at 77° F, but the trends are the same at

any temperature. As the fin pitch goes from 8 to 14, the pressure drop increases by

nearly 40%, and the fan power by about 13%. The compressor work decreases to offset

the fan power as shown in Figure 21. The optimum will occur when the increase in fan

work exceeds the decrease in compressor work.

70

0.0E+00

1.0E-03

2.0E-03

3.0E-03

4.0E-03

5.0E-03

6 7 8 9 10 11 12 13 14 15

Fin Pitch (fins/inch)

Figure 20. Fin Pitch vs. Airside Pressure Drop at 83F

6100

6150

6200

6250

6300

6350

6 8 10 12 14 16

Fin Pitch (fins/ inch)

100

150

200

250

300

350

CompressorFan

Figure 21. Effect of Fin Pitch on Power Requirements at 83F

71

Tube Diameter

For condenser circuiting, custom copper tubing is usually used.xxix The air side

heat transfer and pressure drop correlations are only valid for outer diameters between

5/16” and 5/8”, so only tubing in this range is considered. For this study, the tube sizes

were taken from AAON Heating and Refrigeration Products specifications. The smallest

wall thickness for a given outside diameter is used. The properties of the tubing tested

are summarized in Table 10. All other geometry factors will be the same as the base

case.

OutsideDiameter,

in

InsideDiameter,

in

WallThickness, in

0.3125 0.3005 0.01200.3750 0.3630 0.01200.5000 0.4840 0.01600.6250 0.6170 0.0180

Table 10. Data for Copper Tubesxxx

Compared to fin spacing, the seasonal COP varies considerably with the tube

diameter. As shown in Figure 22, 1/2” tubing produces the highest seasonal COP- 3.4%

higher than the base case. Although this is not terribly dramatic, using 5/16” or 5/8”

tubing will significantly hurt the COP. Seasonal COP’s and area factors for each tube

diameter at optimal conditions are given in Table 11.

72

3.00

3.10

3.20

3.30

3.40

3.50

3.60

3.70

3.80

3.90

4.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Outer Tube Diameter (in)

Sea

son

al C

OP

Figure 22. Maximum Seasonal COP for Different Tube Diameters

Tube Diameter MaximumSeasonal

COP

Area Factor

5/16” 3.494 1.0883/8” 3.870 1.0001/2” 3.931 0.8145/8” 3.520 0.601

Table 11. COP’s and Area Factors Based on Tube Diameter

Unlike the changing circuiting or fin spacing, changing the tube diameter has a

fairly significant effect on the optimal operating conditions. Both the optimum air

velocity and refrigerant charge show an optimum with respect to tube size, as illustrated

by Figure 23. As previously discussed, the seasonal COP is relatively insensitive to the

Fixed Parameters # Rows = 3 Fin Pitch =12 fpi Tubes / Circuit = 2

73

air velocity and refrigerant charge within about ± 25% of the optimum for 3/8” tubes.

The same result is expected for all tube diameters.

0

2

4

6

8

10

12

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Outer Tube Diameter (in)

Op

tim

um

Air

Vel

oci

ty (

ft/s

ec)

0

2

4

6

8

10

12

14

16

18

Op

tim

um

Su

bco

ol

(F)

VelocitySubcool

Figure 23. Optimal Operating Conditions for Different Tube Diameters

At the optimum operating conditions for each configuration, the amount of the

condenser allocated to the superheated region increases steadily as the tube size

increases. This is due to the lower velocity in the larger tubes providing a lower heat

transfer coefficient. The allocation for the saturated section is significantly lower and the

allocation for the subcooled section is significantly higher for the 5/16” tube than for the

other tubes, as shown in Figure 24. This is probably because the refrigerant side pressure

drop decreases exponentially as the tube size increases as seen in Figure 25.

Surprisingly, the pressure drop over the saturated section follows the same trends as the

74

total pressure drop even though the amount of tube dedicated to this region is

considerably smaller for the 5/16” tube.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8

Tube Diameter (in)

Con

dens

er A

lloca

tion

SuperheatedSaturatedSubcooled

Figure 24. Condenser Allocation for Different Tube Diameters at 83F

75

05

1015

2025

3035

4045

0 0.2 0.4 0.6 0.8

Tube Diameter (in)

Pre

ssur

e D

rop

(psi

)

SuperheatedSaturatedSubcooledTotal

Figure 25. Refrigerant Side Pressure Drop vs. Tube Diameter at 83F

Tube Circuiting

It is easy to get a fair comparison of how the tube circuiting affects the system

performance because changing the number of tubes per circuit does not affect the cost

factor or the frontal area of the condenser. The number of rows, tube diameter, tube

spacing, and fin spacing were held constant at the values for the base case. The number

of circuits was varied to keep the height to width ratio nearly constant as the circuiting

changed. The condenser configurations considered for this study are summarized in

Table 12. Each configuration was tested with air velocities between 7 and 11.5 ft/s and

for subcools of 10°, 15°, and 20° F at 95° F outdoor air.

76

Tubes/Circuit

#Circuits

Condenser

Width(ft)

2 12 3.03 8 3.04 6 3.05 5 2.9

Table 12. Condenser Configurations for Circuiting Analysis

As with air velocity and refrigerant charge, there is a range of circuiting where the

seasonal COP is relatively insensitive to the number of tubes per circuit. The maximum

seasonal COP, based on the optimum operating conditions for each configuration, is

shown in Figure 26. The COP is the highest when the refrigerant flow is divided among

four tubes. Although the COP for this configuration is 6% higher than the COP of the

base case, it is only about 0.5% higher than the one with three tubes per circuit and about

0.3% higher than the one with five tubes per circuit. The COP’s are listed in Table 13.

77

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

0 1 2 3 4 5 6

Tubes Per Circuit

Sea

son

al C

OP

Figure 26. Maximum Seasonal COP for Different Circuiting

Tubes perCircuit

MaximumSeasonal COP

2 3.8623 4.0854 4.1085 4.094

Table 13. Maximum Seasonal COP’s for Different Tubes per Circuit with Fixed Cost

The gains in COP with increased flow passages can be attributed to the reduction

in required compressor work due to the change in pressure drop. The refrigerant side

pressure drop decreases exponentially as the number of tubes per circuit increases, as

shown in Figure 27. However, as the tubes per circuit increases, the mass flow rate per

tube decreases, reducing the refrigerant side heat transfer coefficient.

Fixed Parameters# Rows = 3Fin Pitch =12 fpiDiameter = 3/8”

78

0.0

5.0

10.0

15.0

20.0

25.0

0 1 2 3 4 5 6

Tubes per Circuit

Pre

ssu

re D

rop

(p

si)

TotalBends

Straight Pipe

Figure 27. Pressure Drop vs. Circuiting at 83°° F

Although the total pressure drop decreases, the percentage of the pressure drop

attributable to bends increases significantly as the tubes per circuit increases. This is

summarized in Table 14.

Tubes/Circuit

TotalPressure

Drop(psi)

BendPressure

Drop(psi)

Straight PipePressure

Drop(psi)

% of TotalPressure

Dropfrom Bends

2 23.8 8.2 15.6 34.43 9.0 4.1 4.9 45.44 3.8 2.2 1.6 57.65 2.1 1.5 0.6 70.1

Table 14. Pressure Drop Distributions at 83°° F

79

Operating Costs

By looking at how the COP varies with each parameter, one can decide how best

to utilize the allotted area to produce the lowest operating costs. The operating cost is

inversely proportional to the COP. Changing the tube circuiting decreases the operating

costs most dramatically. Increasing the tube diameter to 1/2” would noticeably decrease

the operating costs and the area. There is a point where the COP begins to decrease as the

tube circuiting or tube diameter increases. The effects of varying each of the geometry

factors with respect to operating cost and frontal area are shown in Figure 28.

Since the variations in COP for both changing tube diameter and circuiting based

on altering the refrigerant mass velocity, different circuiting configurations for each tube

diameter were run at 83° F with optimum airflow and subcool to see if the optimum tube

diameter was affected. When the base case was varied with fixed circuiting, the 1/2”

diameter tube provided the best performance. However, when the tube diameter was

varied in conjunction with circuiting, the smaller, 5/16” tube performed the best. As

shown in Table 15, the mass flux has a significant effect on the COP. COP’s that are

markedly lower than average have flow areas outside of the 700-1350 lbm/in2-s range.

80

TubeDiameter

(in)

TubesPer

Circuit

Flow Area(in2)

Mass Flux(lbm/in2-

s)

COP at83 F

0.5 1 0.196 2091 3.5170.5 2 0.393 1060 3.8890.5 3 0.589 709 3.887

0.375 2 0.221 1853 3.8620.375 3 0.331 1244 4.0670.375 4 0.442 937 4.0880.375 5 0.552 753 4.0710.3125 2 0.154 2657 3.4870.3125 3 0.230 1782 3.9800.3125 4 0.307 1345 4.1150.3125 5 0.383 1077 4.1450.3125 6 0.460 899 4.1440.3125 7 0.537 772 4.131

Table 15. COP and Flow Area for Different Circuiting Configurations

The trade-offs between operating costs and frontal area for different circuiting is

shown in Figure 29. The optimum diameter-circuiting combination is a 5/16” tube with 5

tubes per circuit, but a 3/8” tube with 4 tubes per circuit provides similar performance

with better space management. The effects of fin spacing for the optimum diameter-

circuiting combination and for the base case are shown in Figure 30. For the base case,

the optimum fin pitch was 12 fpi, but for the 5/16” tube with 5 tubes per circuit, the trend

is different. In this case, reducing the fin pitch increases the performance because the

refrigerant side pressure drop is considerably lower and the reduction in compressor

power does not compensate for the increase in fan power. Various condenser operating

conditions for different condenser geometries can be found in Appendix III.

81

82

0.24

0.25

0.26

0.27

0.28

0.29

0.4 0.6 0.8 1 1.2 1.4 1.6

Area Factor

1/C

OP

FPITPCDiameterRows

5/8"

1/2"

5/16"

4

2

53

4

1410

8Base

FPI

Rows

DiameterBase Case: 12 Fins/in 2 Tubes/Circuit 3 Rows 3/8" Diameter

TP

C

Figure 28. Operating Costs vs. Area Factor for Different Geometry Factors

83

0.23

0.24

0.25

0.26

0.27

0.28

0.29

0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15

Area Factor

1/COP

4

5

6

74

2

53

11

3

2

1/2

" D

iam

ete

r

5/16

" Dia

met

er3/8"

Dia

met

er

3 Row CondenserFin Pitch = 12 fpiNumber next to data point denotes tubes per circuit

2

Figure 29. Operating Costs For Different Tube Diameters and Circuiting at 83°° F with Fixed Cost

84

0.230

0.235

0.240

0.245

0.250

0.255

0.260

0.265

0.270

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5Area Factor

1/C

OP

Tube Diameter = 5/16"Tubes/ Circuit = 6Rows = 3

Tube Diameter = 3/8"Tubes/ Circuit = 2Rows = 3

FPI=8

FPI=14

FPI=12 FPI=10FPI=14

FPI=12FPI=10

FPI=8

Figure 30. Effect of Varying Fin Pitch for Base Case and Optimum Case at 83°° F with Fixed Cost

85

CHAPTER VI

EFFECTS OF GEOMETRY WITH FIXED FRONTAL AREA

In the previous chapter, the effects of varying the number of rows, tube diameter,

circuiting, and fin pitch while keeping the total cost of the evaporator and condenser

fixed were examined. With the exception of circuiting, altering these geometry factors

affected the frontal area. In many cases, packaging constraints limit the frontal area. In

this chapter, the heat exchanger cost will be a free variable, but the frontal area will be

held constant.

Number of Rows

As seen in Figure 31, the seasonal COP decreases slightly as the number of rows

is increased beyond 3, even though the condenser heat transfer area is getting larger.

86

3.78

3.79

3.80

3.81

3.82

3.83

3.84

3.85

3.86

3.87

1 2 3 4 5

Rows

Sea

son

al C

OP

Fixed Parameters

Fin Pitch =12 fpi

Tube Diameter = 3/8”Tubes / Circuit = 2

Figure 31. Seasonal COP for Varying Rows with Fixed Area

There are several reasons for this. On the refrigerant side of the condenser, the

pressure drop increased as with the number of rows because of more bends and longer

tubes. At 83° F, the air-side pressure drop over the 2-row condenser is 15.1% lower than

the pressure drop over the 4-row condenser, so the fan power for the 2-row coil is only

20% greater even though the optimal velocity is 42% higher. Because the optimal air

velocity is greater, the air-side heat transfer coefficient is 26% higher for the 2 row

condenser compared to the 4 row condenser. These results are summarized in Table 16.

The tradeoffs between the fan and compressor power are shown in

Figure 32.

87

Number

OfRows

Evaporator

Capacity(Btu/hr)

Compressor

Power(Btu/hr)

FanPower

(Btu/hr)

Air-Side HeatTransfer

Coefficient(Btu/hr-ft2-R)

Air Side Pressure

Drop(psi)

MassFlowRate

(lbm/hr)2 30,982 6,487 332.8 12.55 3.972E-03 413.73 31,053 6,504 290.8 10.87 4.300E-03 409.64 31,073 6,674 276.8 9.94 4.676E-03 408.2

Table 16. Data for Varying Number of Rows at 83°° F

6450

6500

6550

6600

6650

6700

6750

0 1 2 3 4 5

Number of Rows

Co

mp

res

so

r P

ow

er

(Btu

/hr)

50

100

150

200

250

300

350

Fan

Po

wer

(B

tu/h

r)

CompressorFan

Figure 32. Tradeoffs Between Compressor and Fan Power for Varying Number of Rowswith Fixed Area at 83 F

Usually, increasing the heat transfer area will increase the COP of a system, but

the area added by increasing the number of rows performs inefficiently. As the number

88

of rows increases, the allocation of the subcooled section increases and the allocation of

the saturated section decreases (

Figure 33). This increased subcool allocation is due to the large refrigerant

pressure drop resulting in a lower saturation temperature at the exit. The total UA’s for

the 2, 3, and 4 row coils are given in Table 17. The 4 row coil has a UA 60% greater

than the 2 row coil. However, it does not provide as high a seasonal COP as the 2 row

due to the high refrigerant pressure drop and fan power. This demonstrates the

complexity of condenser design.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 1 2 3 4 5

Number of Rows

Co

nd

ense

r A

llo

cati

on

Superheated

Saturated

Subcooled

Figure 33. Condenser Allocation for Varying Rows at 83°° F

89

Rows Total UA(Btu/hr-

R)

UA/ Unit Length of Tube(Btu/hr-R-ft)

Superheated

Saturated Subcooled

Average

2 2504.5 15.8 40.7 22.3 35.43 3362.1 15.1 37.1 21.1 32.64 4097 14.7 34.8 20.4 29.9

Table 17. Overall UA and UA/ Length for Varying Rows at 83°° F

The optimum air velocity over the condenser coils is heavily dependent on the

number of rows. Although there is a velocity range for each coil where the seasonal COP

varies minimally from the optimum value, that range is different for each row

configuration. Figure 34 shows how the range of velocities varies for different numbers

of rows for optimum subcool at air inlet temperature of 95° F. As the number of rows

decreases, the optimum air velocity increases. The seasonal COP was relatively

insensitive to subcool in the range of 10° to 15° for 2, 3 and 4 row condensers. The

optimal conditions for each configuration are given in Table 18.

90

3.40

3.45

3.50

3.55

3.60

3.65

3.70

3.75

3.80

3.85

3.90

4 6 8 10 12 14

Air Velocity (ft/s)

Seasonal COPRows=2

Rows=3

Rows=4

Figure 34. Air Velocity vs. Seasonal COP for Different Row Configurations with Fixed Area

NumberOf

Rows

Seasonal

COP

CostFactor

AirVelocity

(ft/s)

Subcool@ 95°

F2 3.841 .7606 10.9 133 3.862 1.000 8.8 104 3.791 1.239 7.7 10

Table 18. Optimum Operating Conditions For Varying Number of Rows with Fixed Area

Fin Pitch

Holding the frontal area constant, like holding the cost constant, does not

appreciably impact the seasonal COP or operating conditions of the system when the fin

pitch changes. The range of recommended operating conditions remains the same, but

the variance of the optimal point is greater when the frontal area is fixed than when the

cost is fixed. When the cost is fixed, the optimum COP occurs when the air velocity is

between 8.5 and 9.5 ft/sec, but the optimum air velocity varies from about 8 to 10 ft/sec

91

when the frontal area is fixed, as seen in Figure 35. Although higher fin pitches give

better performance, the maximum difference in seasonal COP over the recommended

range is only about 4.0%, but the coil that produces the lowest COP costs 80% of the coil

that produces the highest.

3.7

3.72

3.74

3.76

3.78

3.8

3.82

3.84

3.86

3.88

3.9

6 7 8 9 10 11 12

Air Velocity (ft/sec)

Sea

son

al C

OP

FPI=8

FPI=10

FPR=12

FPI=14

Figure 35. Variance of Optimal Air Velocity with Fin Pitch for Fixed Frontal Area

When the cost is fixed, the fan power does not increase at the same rate as the

pressure drop because the area and the total air flow rate were decreasing. When the

frontal area is fixed, the increase in pressure drop due to increasing the fin pitch directly

affects the fan power. As always, at the optimum, the compressor work decreases by the

same amount as the fan power increases.

92

When the frontal area and number of rows are fixed, the tube length is also fixed.

When the tube length is fixed the allocation of condenser space is the opposite of when

the cost is fixed (Figure 36). As the fin pitch increases, the allocation of the subcooled

portion of the condenser increases and the allocation of the saturated portion decreases

while the percentage of tube length for the superheated section stays relatively constant.

This can be accounted for by the decrease in saturation temperature due to the higher UA

as the fin pitch increases and a longer, fixed tube.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

6 8 10 12 14 16

Fin Pitch (fins/in)

Co

nd

ense

r A

llo

cati

on

Superheated(Fixed Area)

Superheated(Fixed Cost)

Saturated(Fixed Area)

Saturated(Fixed Cost)

Subcooled(Fixed Area)

Subcooled(Fixed Cost)

Figure 36. Condenser Allocation for Varying Fin Pitch at 83F

Tube Diameter

As the tube diameter changes, the optimum operating conditions change, but the

seasonal COP varies little with air velocity or subcool. For 5/16” tubes, the maximum

93

variation in seasonal COP is about 3% with subcools ranging from 10 to 30° F and air

velocities ranging from 7 to 11.5 ft/sec. For 5/8” tubes, the maximum change in seasonal

COP is less than 3.5% for subcools between 10 and 20° F and air velocities between 7

and 10 ft/sec. Figure 37 shows that the optimum velocity does change, but the curve is

very flat. The optimum operating conditions are given in Table 19.

3.0

3.2

3.4

3.6

3.8

4.0

4.2

4 6 8 10 12

Air Velocity (ft/sec)

Sea

son

al C

OP

5/16"3/8"1/2"5/8"

Figure 37. Variance of Optimal Air Velocity with Tube Diameter at Optimum Subcool for FixedFrontal Area

94

TubeDiamete

r

Seasonal COP

CostFactor

AirVelocity

(ft/s)

Subcool@ 95°

F5/16” 3.491 0.942 9.5 183/8” 3.862 1.000 8.8 101/2” 4.074 1.160 7.6 105/8” 3.952 1.461 7.9 13

Table 19. Optimum Operating Conditions For Varying Tube Diameter with Fixed Area

Although the air velocity and subcool near the optimum do not significantly affect

the seasonal COP, it is interesting to note that the trends are nearly opposite the ones

when the cost is fixed. With a fixed cost condenser, the optimum subcool and air

velocity are both minimums when the tube diameter is 3/8”. When the area of the

condenser is fixed, the optimum velocity continues to decrease as the tube diameter

increases because the area is not decreasing to help compensate for the airside pressure

drop. Figure 38 shows how the airside pressure drop varies for fixed area compared to

fixed cost. In both cases, the minimum pressure drop occurs with a tube diameter of

3/8”, even though the air velocity trends are different at larger tube diameters, but the

increase in pressure drop is more marked for the fixed cost case.

95

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.2 0.3 0.4 0.5 0.6 0.7

Tube Diameter (in)

Air

Sid

e P

ress

ure

Dro

pFins (FixedArea)

Tubes (FixedArea)

Total (FixedArea)

Fins (FixedCost)

Tubes (FixedCost)

Total (FixedCost)

Figure 38. Air Side Pressure Drop for Varying Tube Diameters at 83°° F

The trends for the refrigerant side pressure drop are the same for fixed area as

they are for fixed cost. As the tube diameter increases, the refrigerant pressure drop

decreases leading to decreased compressor work. This pressure drop effect is larger than

the effect of the lowered heat transfer coefficient. However, for large tubes, the fan

power continues to increase and the decrease in compressor work becomes less

significant. The tradeoffs between compressor power and fan power are illustrated in

Figure 39.

96

6000

6200

6400

6600

6800

7000

7200

7400

7600

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Tube Diameter (in)

Co

mp

ress

or

Po

wer

(B

tu/h

r)

0

100

200

300

400

500

600

700

800

Fan

Po

wer

(B

tu/h

r)

Compressor(Fixed Area)

Compressor(Fixed Cost)

Fan (FixedArea)

Fan (FixedCost)

Figure 39. Compressor and Fan Power Trends vs. Tube Diameter at 83°° F

As previously discussed, the tube circuiting and tube diameter should not be

considered separately, but with fixed area, the number of rows must also be considered.

For single parameter variations of the base case, the effects of geometry factors on the

operating costs and cost factor are plotted in Figure 40. For a 3/8” tube with two tubes

per circuit, it is better to use two condenser rows instead of three because of the

refrigerant side pressure drop. For condensers with different numbers of rows, the 5/16”

and 3/8” tubes provide virtually the same performance, but the smaller tubes cost less.

The operating costs and cost factors for two and three row condensers with different tube

diameter- tube circuiting configurations at 83° F run at optimum air velocity and

refrigerant charge are shown in Figure 41. In most cases, the operating costs are

relatively insensitive to the number of circuits. The operating costs and cost factors for

97

different tube diameters with optimum circuiting for 2, 3, and 4 row condensers at 83° F

run at optimum air velocity and refrigerant charge are shown in Figure 42. This figure

illustrates that the operating costs will be lower with there are more rows when the

number of circuits is optimized for the tube diameter.

98

0.240

0.245

0.250

0.255

0.260

0.265

0.270

0.275

0.280

0.285

0.290

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Cost Factor

1/C

OP

FPITPCDiameterRows

5/8"

1/2"

5/16"

4

2

53

4

14

108

FPI

Rows

Diameter

Base Case: 12 Fins/in 2 Tubes/Circuit 3 Rows 3/8" Diameter

TPC

Base

Figure 40. Operating Costs vs. Cost Factor for Different Geometry Factors

99

Figure 41. Operating Costs For Different Tube Diameters and Circuiting at 83°° F with Fixed Area

100

0.235

0.240

0.245

0.250

0.255

0.260

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

Cost Factor

1/C

OP

Rows=2Rows=3Rows=4OD=5/16"OD=3/8"OD=1/2"

4*

3

2

4

3

5

75

3

* Denotes tubes per circuit for given case. All cases run with 12 fins per inch.

2 Rows

3 Rows

4 Rows

Figure 42. Optimum Condenser Circuiting for Fixed Area at 83 F with Varying Rows

101

Comparing Fixed Area to Fixed Cost

Figure 43, Figure 44, and Figure 45 show how the maximum seasonal COP’s vary

with rows, fin spacing and tube diameter for fixed cost and for fixed area. In these

figures, the values of the cost factor correspond to the cases where the frontal area is

fixed and the values of the area factor correspond to the cases where the cost is fixed.

The circuiting is optimized for each case and all other parameters are the same as the base

case unless otherwise stated, i.e. 3 rows, 12 fins per inch, and 3/8” tubing.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

2 3 4

Number of Rows

Sea

son

al C

OP

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6A

rea

Fac

tor

/ C

ost

Fac

tor

COP (FixedArea)

COP (FixedCost)

Cost Factor

Area Factor

Figure 43. Comparison of Area Factor to Cost Factor Based on Number of Rows

102

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

8 10 12 14Fin Pitch (fins/ inch)

Sea

son

al C

OP

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Are

a F

acto

r / C

ost

Fac

tor

COP, FixedCostCOP, FixedArea

Cost Factor

Area Factor

Figure 44. Comparison of Area Factor to Cost Factor Based on Fin Pitch

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5/16" 3/8" 1/2" 5/8"

Tube Diameter

Sea

son

al C

OP

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6C

ost

Fac

tor/

Are

a F

acto

r

COP, AreaFixedCOP, CostFixedCF

AF

Figure 45. Comparison of Area Factor to Cost Factor Based on Tube Diameter

103

CHAPTER VII

CONCLUSIONS AND RECOMMENDATIONS

In this study, an accurate condenser model was developed and integrated into an

air-conditioning system. A base condenser model was chosen and design conditions

were established at 95° F. The operating parameters of condenser subcool and air face

velocity were examined over a wide range of ambient conditions to determine their

effects on the seasonal COP. It was determined that there is a range of subcools and face

velocities where the effects on the seasonal COP were negligible. The COP of the system

at an ambient temperature of 83° F was nearly identical to the seasonal COP and could be

used for quick comparisons.

The effects of changing the tube diameter, tube circuiting, number of rows, and

fin pitch have been investigated for both fixed cost and fixed frontal area. When the

parameters were varied from the base case individually, the changing the number of

circuits to 4 or changing the tube diameter to 1/2” gave the highest COP’s. It was

determined that tube diameter and tube circuiting could not be considered separately

because they both affect the refrigerant side pressure drop. When the cost or area was

fixed, the best tube diameter- circuiting configuration was 5 circuits of 5/16” tubing. In

both cases, 4 circuits of 3/8” tubing provided similar performance with better packaging

in the fixed cost case.

104

In general, the COP will be the highest when the frontal area is maximized and

rows should only be added if there is a frontal area constraint. This is because of the

relationship between the air velocity, depth, and air-side pressure drop. When the cost is

fixed, fewer rows provide better performance. If the frontal area is constrained, adding

rows will increase the performance as long as the refrigerant side pressure drop does not

become too great.

Changing the fin pitch had a relatively negligible effect on the seasonal COP.

The fan power increases as the number of fins increases, but the compressor power

decreases by about the same amount. If cost is fixed, fewer fins provide better

performance. When the area is restricted, more fins provide better performance.

Improvements to the model might include the incorporation of moist air and

frosting. With these additions, modifications could be made to the evaporator with a high

degree of confidence that the results were accurate. An accumulator could also be added

to the condenser to ensure that the refrigerant always entered the valve as a liquid instead

of relying on the redistribution of refrigerant. Enhanced fins or tubes with interior fins

could also be included.

In the future, this computer model can be applied to many other studies. The

effects of modifying other condenser parameters such as longitudinal and transverse tube

spacing, frontal aspect ratio and materials, or running with different refrigerants could be

examined. In very hot areas like the Arizona desert, people often complain that their air-

conditioners do not supply sufficient cooling because the cooling capacity is rated for 95°

F and the air-conditioners are not designed to run at extremely high temperatures. The

105

model could be used to determine the design point and operating conditions for air-

conditioners used in these special circumstances.

106

APPENDIX I

MASS OF REFRIGERANT IN A HEAT EXCHANGER COIL UNDERGOING PHASECHANGE

This outlines the procedure for finding the refrigerant mass in the saturated

portion of the evaporator. The same process was used to find the mass of refrigerant in

the saturated portion of the condenser but with different boundary conditions. The mass

can be expressed:

∫=L

c

vdlA

m

Equation 1

Specific volume at saturated conditions is a function of quality.

gl vxvxv +−= )1()(

Equation 2

For the saturated portion of the evaporator, the boundary conditions are

107

( ) 10 xlx ==

Equation 3

( ) 1== Llx

Equation 4

Using the boundary conditions and assuming the quality varies linearly with length:

111

)( xlLx

lx +−

=

Equation 5

Substitute Equation 5 into Equation 2 to find the specific volume as a function of length.

( ) ( )lglgl vvL

xlvvxvlv −

−+−+= 1

1

1)(

Equation 6

For a uniform cross sectional area, substituting Equation 6 into Equation 1 yields:

( ) ( )∫

−

−+−+

=L

lglgl

c

vvLx

lvvxv

dlAm

01

1

1

Equation 7

108

Integrating gives:

( )( ) ( ) ( )L

lglgllg

c vvL

xlvvxv

vvxLA

m0

11

1

1ln

1

−

−+−+

−−=

Equation 8

Substituting for l gives the final mass in the saturated portion of the evaporator.

( )( ) ( )

+−−−=

llg

g

lg

cevapsat vvvx

v

vvxLA

m11

, ln1

Equation 9

109

APPENDIX II

EES SIMULATION PROGRAM

110

Inputs to Main Program

Name Stands for Type Range Units

Tsc Degrees subcool @ 95 °F Operating

>1 °F

Vac Condenser air face velocity Operating

4-25 ft/s

t_c Fin thickness Geometry

5e(-4) to 5e(-3)

ft

h_f_c Tube transverse spacing Geometry

0.5-2 in

d_f_c Tube longitudinal spacing Geometry

0.5-2 in

eta_c Fin pitch Geometry

96-168 1/ft

tpc_c Tubes per circuit Geometry

1-10 n/a

ncircuit_c Number of circuits Geometry

n/a n/a

nrow_c Number of tube rows Geometry

1-6 n/a

TubeType_c

Corresponds to tube diameter fromsubroutine “Tubing”

Geometry

1-4 n/a

111

{Refrigerant sidePressure Drop

singledptwophasedptpbenddrop

Heat transfer Coefficientsh_bar_singleh_bar_ch_bar_e

Air SideHeat Transfer coefficients

haPressure Drop

GetEulerHeat Exchangers

Surf_effExch_sizeExch_size_un_unsat_sizeTubing

CompressorCompeff

}

PROCEDURE singledp(m_r, nr,D,L,f,rho:delP)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 qualityVV- exit specific volume of vapor phase, ft^3/lbmnr- number of flow passagesL- length of tube

Output-DeltaP- pressure drop over two phase region}{Momentum component of 2 phase pressure drop}{if xi<xf then

xt=xfxf=xixi=xt

endif}Tav=(T1+T2)/2

112

If Tav>converttemp(K,F,339) then Tav=converttemp(K,F,339)G=(m_dot/(D^2*pi/4))/nrmu_v=viscosity(R22, T=Tav, x=1)mu_l=viscosity(R22, T=Tav, x=0)rhov=density(R22, T=Tav, x=1)rhol=density(R22, T=Tav, x=0)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)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+DPf)end

Procedure singlebenddrop(tpc, D_i, m_dot_r,P, T1, T2, L, Width, f:DP){Pressure Drop in single phase regions}T=(T1+T2)/2G=m_dot_r/(tpc*D_i^2*pi/4)equiv_L=13*2rho=density(R22, 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)*ncirc{DP=0}end

PROCEDURE tpbenddrop(nr,D_i_1,m_dot_r, h_f, T_c, L_c, L_22a, L_2a2b,width:DP)

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_22a=trunc(L_22a/width)num_circuit_2a2b=trunc((l_2a2b+L_22a)/Width)-num_circuit_22aL_o=L_22a-Width*num_circuit_22aL=width-L_omu_v=viscosity(R22, T=T_c, x=1)mu_l=viscosity(R22, T=T_c, x=0)grav=32.2*convert(1/s^2,1/hr^2)Rho_l=density(R22, T=T_c, x=0)rho_v=density(R22, T=T_c, x=1)Re_l=G*D_i_1/mu_lRe_v=G*D_i_1/mu_vlambda_l=(-1.8*log10(6.9/Re_l+((e/D_i_1)/3.7)^1.11))^(-2)lambda_v=(-1.8*log10(6.9/Re_v+((e/D_i_1)/3.7)^1.11))^(-2)n=ln(lambda_l/lambda_v)/ln(mu_l/mu_v)i=0repeat

i=i+1x=-L/L_2a2b+1

113

If x<=0 then goto 10mu_TP=mu_v*x+mu_l*(1-x)Re_tp=G*D_i_1/mu_tplambda_tp=(-1.8*log10(6.9/Re_tp+((e/D_i_1)/3.7)^1.11))^(-2)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/rho_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=Dp{10:DP=0}

end

Procedure h_bar_single(D, m_dot_r, T1, T2, P:Re,h_bar, rho)Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2IF Tav>converttemp(k,F,339) then Tav=converttemp(K,F,339)rho=density(R22, T=Tav,P=P)c_p=specheat(R22, T=Tav, P=P)mu=viscosity(R22, T=Tav, P=P)Re=m_dot_r*D/(Area*mu)Pr=prandtl(R22, T=Tav, P=P)If Re<3500 then

a=1.10647b=-.078992

endIFif (Re>3500) and (Re<6000) then

a=3.5194e-7b=1.03804

ENDIFif Re>6000 then

a=.2243b=-.385

endifSt=a*Re^b/(Pr^(2/3))h_bar=St*G*C_pend

FUNCTION h_bar_c(T, P,D, m_dot_r,nr)If T>converttemp(K,F,339) then T=converttemp(K,F,339)G=m_dot_r/(D^2*nr/4)mu_l=viscosity(R22, T=T, x=0)mu_g=viscosity(R22, T=T, x=1)rho_l=density(R22, T=T, x=0)rho_g=density(R22, T=T, x=1)Pr_l=prandtl(R22, T=T-1, P=P)k_l=conductivity(R22, T=T, x=0)P_r=P/p_crit(R22)Re_l=G*D/mu_lh_l=0.023*Re_l^.8*Pr_l^.4*k_l/Dh_bar_c=h_l*(.55+2.09/(P_r^.38))end

114

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 tubesDescription of parameters

Input De- Equivalent diameter of flow passage (ft) G- mass flow per unit area (lbm/hr-ft^2) xi- initial quality xe- exit quality PrL-Prandtl number of the liquid phase xkl-thermal conductivity of liq. phase (btu/hr-ft-F xmuv- viscosity of vapor phase (lbm/ hr-ft) xmul- viscosity of liquid phase (lbm/ hr-ft) rhol- density of liq. phase (lbm/ft^3) rhov- density of vapor phase (lbm/ ft^3)

Output h_bar_ave_e- evp. heat trans. coeff. (btu/hr-ft^2-F)}x_i:=x_inPr_L=prandtl(R22, T=Te-1, P=Pe) "Prandtl # of liquid phase in condenser"kl=conductivity(R22, T=Te, x=0) "conductivity of liq. phase"mu_v=viscosity(R22, T=Te, x=1) "viscosity of vap. phase"mu_l=viscosity(R22, T=Te, x=0)rho_l=density(R22, T=Te, x=0)rho_v=density(R22, 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 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/muRe_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}

{Modify Euler number to account for non- equilateral geometryfind correction factor k1 to account for a/b ratio, use k1 with other relationships to correct Euler # for rowspacing}a=dep_f/Db=h_f/DCheck1=1Check2=1Check3=1

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spacerat=a/bEu=0k1=0If (spacerat>.5) and (spacerat<1.2) and (re>=1000) and (Re<10000) then {this relationship is statedfor Re=1000, not the range 1000<Re<10000}

k1=spacerat^(-.048)k2=1.28-.708/spacerat+.55/(spacerat^2)-0.113/(spacerat^3)k1=(k2-k1)/(10000-1000)*(Re-1000)+k1

endIFif (spacerat>1.25) and (spacerat<3.5) and (Re>1000) and (Re<10000) then

k1=.951*spacerat^.284k2=1.28-.708/spacerat+.55/(spacerat̂ 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 for Re=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 for a=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

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)

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Eu=(Eu2-Eu1)/(2-1.5)*(a-1.5)+Eu1endif

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)endifIf (a>=2.5) and (Re>5000) and (Re<2000000) then

Eu:=(.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 thenrepeat

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

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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/nrowIf 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)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 pure Aluminum, 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 exch_size(Cmixed, Cunmixed, E:UA)if (Cunmixed>Cmixed) then

Cr:=Cmixed/CunmixedNTU=-ln(1+(1/Cr)*ln(1-E*Cr))

UA:=NTU*CmixedendIFif (Cmixed>Cunmixed) then

Cr:=Cunmixed/CmixedNTU:=-ln(1+(1/Cr)*ln(1-E*Cr)){NTU=1+(1/cr)*ln(1-E*Cr)}UA:=NTU*Cunmixed

ENDifend

Procedure sat_size(Cunmixed, E:UA)

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Cr:=0NTU:=-ln(1-E)UA:=NTU*Cunmixed

end

Procedure exch_size_un_un(Cair, Cfridge,UA:E)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 product specificationsType 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 evaporating Temperature and pressureFrom Klein paper}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 seasonalcop(Tac)seasonalcop=0If Tac=67 then

seasonalcop=.214endifIf Tac=72 then

seasonalcop=.231endif

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If Tac=77 thenseasonalcop=.216

endifIf Tac=82 then

seasonalcop=.161endifIf Tac=87 then

seasonalcop=.104endifIf Tac=92 then

seasonalcop=.052endifIf Tac=97 then

seasonalcop=.018endifIf Tac=102 then seasonalcop=.004END

Function clffunc(BL)clffunc=1If BL<30000 then clffunc=BL/30000end

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){System Constraints}

{variable refrigeration cycle parameters}{Design Conditions @ Tac1=95 F}Tac1=95 "[F]" {Air inlet T into Condenser}T4a=45 "[F]"Q_dot_e=30000 "[Btu/hr]"Tsh=10 "[F]" {refrigerant superheat in evaporator from states 4a-1,F}Tae1=80 "[F]" {Air inlet T into Evaporator}

{Design Constraints}A_c=7.5 "[ft2]"{CF=1}

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}mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) "[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "[lbm/ft^3]"c_p_air=specheat(AIR, T=Tac1) "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1)m_dot_ac=V_ac*A_c*rho_ac1 "[lbm/s]"m_ac=m_dot_ac*convert(1/s,1/hr) "[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)

"[Btu/hr-ft^2-R]"

{Condenser Fan Work}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]"

120

{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)

{Air Flow over Evaporator}mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec)rho_ae1=density(AIR, T=Tae1, P=14.7) "[lbm/ft^3]"V_dot_ae=30000*400/12000 "[cfm]" {air flow rate over evaporator in cfm assuming 400cfm/ton at design Q_e of 30,000 BTU/hr}m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) "[lbm/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)

"[Btu/hr-ft^2-R]"

{Evaporator Fan Work}W_dot_fe=365*V_dot_ae*convert(W, BTU/hr)/1000

{Compressor}{Compressor Inputs}Clearance=.05 "[%]" {Percent}R=.025 {ratio of clearance volume to displacement}

v1=volume(R22, P=P1,T=T1) "[ft^3/lbm]"v2=volume(R22, P=P2,T=T2) "[ft^3/lbm]"

nc=compeff(P2a,P4,tc_ave,T4) {compressor efficiency}nv=1-R*(v1/v2-1) {Klein}PD=m_dot_r*v1/nv "[ft^3/hr]" {piston displacement}

{condenser Characteristics}

Call tubing(TubeType_c:D_i_c,D_o_c)d_fft_c=d_f_c*convert(in,ft) "[ft]"Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}h_fft_c=h_f_c*convert(in,ft) "[ft]"H_c=h_fft_c*tpc_c*ncircuit_c "[ft]" {height of condenser, ft}L_c=Width_c*nrow_c*ncircuit_c "[ft]"V_c=Width_c*h_c*dep_c "[ft^3]" {Volume of Condenser}A_c=Width_c*H_c "[ft^2]" {area of condenser, ft^2}A_f_c=2*L_c*eta_c*tpc_c*(h_fft_c*d_fft_c-pi*(D_o_c/2)^2) "[ft^2]"A_i_c=L_c*D_i_c*pi*tpc_c "[ft^2]"

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A_t_c=D_o_c*pi*L_c*(1-t_c*eta_c)*tpc_c "[ft^2]"A_o_c=A_t_c+A_f_c "[ft^2]"A_flow_c=Width_c*(1-eta_c*t_c)*(H_c-D_o_c*ncircuit_c*tpc_c)"[ft^2]"A_i_c=A_i_22a+A_i_2a2b+A_i_2b3"[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)

{evaporator Characteristics}{Variable Evaporator charcteristics}TubeType_e=2eta_e=12*12 "[1/ft]" {condenser fin pitch, fins/ft}tpc_e=2 {number of rows per refrigerant parallel pass}ncircuit_e=9nrow_e=4 {number of columns of tubing}t_e=.006/12 "[ft]" {thickness of fins, ft}h_f_e=1 "[in]" {tube vertical spacing on centers, in}d_f_e=.625 "[in]" {condenser fin depth per tube, in}

Call tubing(TubeType_e:D_i_e,D_o_e)d_fft_e=d_f_e*convert(in,ft) "[ft]"h_fft_e=h_f_e*convert(in,ft) "[ft]"Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {condenser depth, ft}L_e=Width_e*nrow_e*ncircuit_e "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft) "[ft]" {height of condenser, ft}V_e=width_e*h_e*dep_e "[ft^3]" {Volume of Condenser}A_e=Width_e*H_e "[ft^2]" {area of condenser, ft^2}A_i_e=L_e*D_i_e*pi*tpc_e "[ft^2]"A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_e "[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 "[ft^2]"A_o_e=A_t_e+A_f_e "[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) "[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)

{***********************************************************Begin Cycle Analysis************************************************************}

{Compressor Equations}h1=enthalpy(R22, T=T1, P=P1) "[Btu/lbm]"s1=entropy(R22, T=T1, P=P1) "[Btu/lbm-R]"s1=s2s "[Btu/lbm-R]"h2s=enthalpy(R22, P=P2, s=s2s) "[btu/lbm]"h2=h1+wc "[btu/lbm]"T2=temperature(R22, P=P2, h=h2) "[F]"wcs= h2s-h1 "[btu/lbm]"wc=wcs/nc "[Btu/lbm]"

{Condenser Equations}

P3=P2b-DELTAP_2b3-DELTAP_b_2b3 "[psia]"

{Superheated portion of condenser}Q_22a=m_dot_r*(h2-h2a) "[Btu/hr]"

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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(R22, 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]"

P2a=P2-DELTAP_22a-DELTAP_b_22a "[psia]"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}x2a=1x2b=0Tc_ave=(T2a+T2b)/2 "[F]"T2a=temperature(R22, P=P2a, x=x2a) "[F]"h2a=enthalpy(R22, T=T2a, x=x2a) "[Btu/lbm]"T2b=temperature(R22, 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)P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b "[psia]"

h2b=enthalpy(R22, 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]"

{Subcooled portion of Condenser}h3=enthalpy(R22, 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]"

123

C_2b3=m_dot_r*specheat(R22, T=T3, P=P3) "[Btu/hr-R]"{assume Cp for R22constant over Tsc}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 refrigerant through 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))

{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]"T4=T4a "[F]"P4=pressure(R22, T=T4, h=h4) "[psia]"x4=quality(R22, T=T4, h=h4)

{saturated portion of evaporator}x4a=1Cp_44a_cor=specheat(AIR, T=Tae1)*1.33 "[Btu/lbm-F]"h4a=enthalpy(R22, 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=(A_i_e/(A_o_e*h_bar_ae)+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]"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(R22, T=T1, P=P1)call exch_size_un_un(C_4a1,C_a4a1, UA_4a1:E_4a1)A_i_4a1=L_4a1*tpc_e*pi*D_i_e "[ft^2]"UA_4a1=U_i_4a1*A_i_4a1 "[Btu/hr-R]"U_i_4a1=(A_i_e/(A_o_e*h_bar_ae)+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)1/f_4a1^0.5=-2*log10((e/(D_i_e*3.7))+2.51/(Re_4a1*f_4a1^0.5))

{COP}

124

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(R22, T=T2a, x=1)-volume(R22, T=T2a, x=0) "[ft^3/lbm]"m_2a2b=-(Vol_2a2b/vfg2a2b)*ln(volume(R22, T=T2a, x=0)/volume(R22, 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(R22, T=T4a, x=1)-volume(R22, T=T4a, x=0) "[ft^3/lbm]"m_44a=(Vol_44a/(x4*vfg44a))*ln(volume(R22, T=T4, x=1)/(volume(R22, 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}

{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 Metals Exchange}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_baseCF_base=35.88CF_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_baseCF_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_baseend

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: COP, Tsc, Q_dot_e, Qss, Ess){System Constraints}

{variable refrigeration cycle parameters}{Design Conditions @ Tac1=95 F}

{Tsc=1} "[F]" {refrigerant subcool in condenser from states 2b-3}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}

125

V_ac=V_dot_ac*convert(1/min,1/sec)/A_c "[ft/s]"mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) "[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "[lbm/ft^3]"m_dot_ac=m_ac*convert(1/hr,1/s) "[lbm/s]"m_ac=V_dot_ac*convert(1/min,1/hr)*rho_ac1 "[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)

"[Btu/hr-ft^2-R]"c_p_air=specheat(AIR, T=Tac1) "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1)

{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 cfm assuming 400cfm/ton at design Q_e of 30,000 BTU/hr}{V_ae=5}V_ae=V_dot_ae*convert(1/min,1/sec)/A_e "[ft/sec]"rho_ae1=density(AIR, T=Tae1, P=14.7) "[lbm/ft^3]"m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) "[lbm/s]"mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec)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)

"[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}{Volumetric efficiency from Threlkeld, p55- 56}gamma_R22=1.16 {ratio of Cp/Cv}Clearance=.05 "[%]" {Percent}v1=volume(R22, P=P1,T=T1) "[ft^3/lbm]"v2=volume(R22, P=P2,T=T2) "[ft^3/lbm]"{nv=v1/v2*(1+clearance-clearance*(P2/P1)^(1/gamma_R22))}nv=1-R*(v1/v2-1) {Klein}R=.025 {ratio of clearance volume to displacement}PD=m_dot_r*v1/nv "[ft^3/hr]" {piston displacement}

{condenser Characteristics}{Variable Condenser charcteristics}spac_rat=h_f_c/d_f_c

Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}

L_c=Width_c*nrow_c*ncircuit_c "[ft]"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]" {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)Call tubing(TubeType_c:D_i_c,D_o_c)A_i_c=L_c*D_i_c*pi*tpc_c "[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) "[ft^2]"A_o_c=A_t_c+A_f_c "[ft^2]"A_flow_c=Width_c*(1-eta_c*t_c)*(H_c-D_o_c*ncircuit_c*tpc_c)"[ft^2]"A_i_c=A_i_22a+A_i_2a2b+A_i_2b3"[ft^2]"

{evaporator Characteristics}{Variable Evaporator charcteristics}

126

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]" {condenser fin pitch, fins/ft}d_f_e=.625 "[in]" {condenser fin depth per tube, in}Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {condenser depth, ft}tpc_e=2 {number of rows per refrigerant parallel pass}nrow_e=4 {number of columns of tubing}ncircuit_e=9L_e=Width_e*nrow_e*ncircuit_e "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft) "[ft]" {height of condenser, ft}{V_c=3} "[ft^3]"TubeType_e=2V_e=width_e*h_e*dep_e "[ft^3]" {Volume of Condenser}A_e=Width_e*H_e "[ft^2]" {area of condenser, 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)Call tubing(TubeType_e:D_i_e,D_o_e)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]"A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_e "[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 "[ft^2]"A_o_e=A_t_e+A_f_e "[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) "[ft^2]"

{***********************************************************Begin Cycle Analysis************************************************************}

{Compressor Equations}h1=enthalpy(R22, T=T1, P=P1) "[Btu/lbm]"s1=entropy(R22, T=T1, P=P1) "[Btu/lbm-R]"s1=s2s "[Btu/lbm-R]"h2s=enthalpy(R22, P=P2, s=s2s) "[btu/lbm]"wcs= h2s-h1 "[btu/lbm]"wc=wcs/nc "[Btu/lbm]"h2=h1+wc "[btu/lbm]"T2=temperature(R22, P=P2, h=h2) "[F]"

{Condenser Equations}P2a=P2-DELTAP_22a-DELTAP_b_22a "[psia]"P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b "[psia]"P3=P2b-DELTAP_2b3-DELTAP_b_2b3 "[psia]"

{Superheated portion of condenser}T2a=temperature(R22, P=P2a, x=x2a) "[F]"h2a=enthalpy(R22, T=T2a, x=x2a) "[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(R22, 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]"

127

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(R22, 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(R22, 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]"

{Subcooled portion of Condenser}h3=enthalpy(R22, 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(R22, T=T3, P=P3) "[Btu/hr-R]"{assume Cp for R22constant 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 refrigerant through 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))

{Valve Equation}

128

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(R22, T=T4, h=h4) "[psia]"{m_ae=V_dot_ae*convert(1/min,1/hr)/volume(AIR, T=Tac1, P=14.7)}x4=quality(R22, T=T4, h=h4)

{saturated portion of evaporator}Cp_44a_cor=specheat(AIR, T=Tae1)*1.33 "[Btu/lbm-F]"h4a=enthalpy(R22, 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(R22, 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 for evaporator 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]"

129

Vol_4a1=A_i_4a1*D_i_c/4 "[ft^3]"

m_22a=rho_22a*Vol_22a "[lbm]"vfg2a2b=volume(R22, T=T2a, x=1)-volume(R22, T=T2a, x=0) "[ft^3/lbm]"m_2a2b=-(Vol_2a2b/vfg2a2b)*ln(volume(R22, T=T2a, x=0)/volume(R22, 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(R22, T=T4a, x=1)-volume(R22, T=T4a, x=0) "[ft^3/lbm]"m_44a=(Vol_44a/(x4*vfg44a))*ln(volume(R22, T=T4, x=1)/(volume(R22, 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)

{Seasonal COP section}BL=(Tac1-65)*30000/(30) "[Btu/hr]" {Building load}CLF=CLFfunc(BL)Qss=CLF*Q_dot_e*SeasonalCOP(Tac1)Ess=CLF*(W_dot_com+W_dot_fc+W_dot_fe)*SeasonalCOP(Tac1)end

Module WithoutSubcool(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:COP, Tsh, Q_dot_e, Qss, Ess){System Constraints}

{variable refrigeration cycle parameters}{Design Conditions @ Tac1=95 F}

Tsc=1 "[F]" {refrigerant subcool in condenser from states 2b-3}

130

x4a=1x2a=1Tc_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 "[ft/s]"mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) "[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "[lbm/ft^3]"m_dot_ac=m_ac*convert(1/hr,1/s) "[lbm/s]"m_ac=V_dot_ac*convert(1/min,1/hr)*rho_ac1 "[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)

"[Btu/hr-ft^2-R]"c_p_air=specheat(AIR, T=Tac1) "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1)

{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 cfm assuming 400cfm/ton at design Q_e of 30,000 BTU/hr}{V_ae=5}V_ae=V_dot_ae*convert(1/min,1/sec)/A_e "[ft/sec]"rho_ae1=density(AIR, T=Tae1, P=14.7) "[lbm/ft^3]"m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) "[lbm/s]"mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec)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)

"[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}{Volumetric efficiency from Threlkeld, p55- 56}gamma_R22=1.16 {ratio of Cp/Cv}Clearance=.05 "[%]" {Percent}v1=volume(R22, P=P1,T=T1) "[ft^3/lbm]"v2=volume(R22, P=P2,T=T2) "[ft^3/lbm]"{nv=v1/v2*(1+clearance-clearance*(P2/P1)^(1/gamma_R22))}nv=1-R*(v1/v2-1) {Klein}R=.025 {ratio of clearance volume to displacement}PD=m_dot_r*v1/nv "[ft^3/hr]" {piston displacement}

{condenser Characteristics}{Variable Condenser charcteristics}spac_rat=h_f_c/d_f_c

Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}

L_c=Width_c*nrow_c*ncircuit_c "[ft]"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]" {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)Call tubing(TubeType_c:D_i_c,D_o_c)A_i_c=L_c*D_i_c*pi*tpc_c "[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) "[ft^2]"

131

A_o_c=A_t_c+A_f_c "[ft^2]"A_flow_c=Width_c*(1-eta_c*t_c)*(H_c-D_o_c*ncircuit_c*tpc_c)"[ft^2]"A_i_c=A_i_22a+A_i_2a2b+A_i_2b3"[ft^2]"

{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]" {condenser fin pitch, fins/ft}d_f_e=.625 "[in]" {condenser fin depth per tube, in}Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {condenser depth, ft}tpc_e=2 {number of rows per refrigerant parallel pass}nrow_e=4 {number of columns of tubing}ncircuit_e=9L_e=Width_e*nrow_e*ncircuit_e "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft) "[ft]" {height of condenser, ft}{V_c=3} "[ft^3]"TubeType_e=2V_e=width_e*h_e*dep_e "[ft^3]" {Volume of Condenser}A_e=Width_e*H_e "[ft^2]" {area of condenser, 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)Call tubing(TubeType_e:D_i_e,D_o_e)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]"A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_e "[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 "[ft^2]"A_o_e=A_t_e+A_f_e "[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) "[ft^2]"

{***********************************************************Begin Cycle Analysis************************************************************}

{Compressor Equations}h1=enthalpy(R22, T=T1, P=P1) "[Btu/lbm]"s1=entropy(R22, T=T1, P=P1) "[Btu/lbm-R]"s1=s2s "[Btu/lbm-R]"h2s=enthalpy(R22, P=P2, s=s2s) "[btu/lbm]"wcs= h2s-h1 "[btu/lbm]"wc=wcs/nc "[Btu/lbm]"h2=h1+wc "[btu/lbm]"T2=temperature(R22, P=P2, h=h2) "[F]"

{Condenser Equations}P2a=P2-DELTAP_22a-DELTAP_b_22a "[psia]"P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b "[psia]"P3=P2b-DELTAP_2b3-DELTAP_b_2b3 "[psia]"

{Superheated portion of condenser}T2a=temperature(R22, P=P2a, x=x2a) "[F]"h2a=enthalpy(R22, T=T2a, x=x2a) "[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(R22, T=T2, P=P2) "[Btu/hr-R]"Call exch_size_un_un(C_a22a, C_22a,UA_22a:E_22a)

132

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)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(R22, 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(R22, 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]"

{Subcooled portion of Condenser}h3=enthalpy(R22, 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(R22, T=T3, P=P3) "[Btu/hr-R]"{assume Cp for R22constant 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]"

133

vel_2b3=m_r_t/((pi*D_i_c^2/4)*rho_2b3) "[ft/hr]" {velocity of refrigerant through 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))

{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(R22, T=T4, h=h4) "[psia]"{m_ae=V_dot_ae*convert(1/min,1/hr)/volume(AIR, T=Tac1, P=14.7)}x4=quality(R22, T=T4, h=h4)

{saturated portion of evaporator}Cp_44a_cor=specheat(AIR, T=Tae1)*1.33 "[Btu/lbm-F]"h4a=enthalpy(R22, 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(R22, 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 for evaporator 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]"

134

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(R22, T=T2a, x=1)-volume(R22, T=T2a, x=0) "[ft^3/lbm]"m_2a2b=-(Vol_2a2b/vfg2a2b)*ln(volume(R22, T=T2a, x=0)/volume(R22, 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(R22, T=T4a, x=1)-volume(R22, T=T4a, x=0) "[ft^3/lbm]"m_44a=(Vol_44a/(x4*vfg44a))*ln(volume(R22, T=T4, x=1)/(volume(R22, 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)

{Seasonal COP section}BL=(Tac1-65)*30000/(30) "[Btu/hr]" {Building load}CLF=CLFfunc(BL)Qss=CLF*Q_dot_e*SeasonalCOP(Tac1)Ess=CLF*(W_dot_com+W_dot_fc+W_dot_fe)*SeasonalCOP(Tac1)

end

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)

135

{CALL WithoutSubcool(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: COP67,Tsh[1],Q_dot_e[1], Qss67,E67)}{CALL WithoutSubcool(72,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: COP72, Tsh[2],Q_dot_e[2], Qss72, E72)CALL WithoutSubcool(77,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: COP77, Tsh[3],Q_dot_e[3], Qss77, E77)}{CALL WithoutSubcool(82,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: COP82, Tsh[4],Q_dot_e[4], Qss82, E82)}{CALL WithoutSubcool(87,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: COP87, Tsh[5],Q_dot_e[5], Qss87, E87)}{Call WithoutSubcool(92,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: COP92, Tsh[6],Q_dot_e[6], Qss92, E92)}

{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: COP67, Tsc[1], Q_dot_e[1], Qss67, E67)}{CALL WithSubcool(72,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: COP72,Tsc[2],Q_dot_e[2], Qss72, E72)CALL WithSubcool(77,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: COP77, Tsc[3],Q_dot_e[3], Qss77, E77)CALL WithSubcool(82,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: COP82, Tsc[4],Q_dot_e[4], Qss82, E82)CALL WithSubcool(87,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: COP87, Tsc[5],Q_dot_e[5], Qss87, E87)CALL WithSubcool(92,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: COP92, Tsc[6],Q_dot_e[6], Qss92, E92)CALL WithSubcool(97,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: COP97, Tsc[7],Q_dot_e[7], Qss97, E97)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: COP102, Tsc[8],Q_dot_e[8], Qss102, E102)}Call WithSubcool(83, 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:COP85, Tsc[9], Q_dot_e[9], Qss85, E85){COP_tot=(Qss67+Qss72+Qss77+Qss82+Qss87+Qss92+Qss97+Qss102)/(E67+E72+E77+E82+E87+E92+E97+E102)}

{Operating inputs}Tsc=13V_ac=8.9

{Condenser Geometry Inputs}h_f_c=1.25 "[in]" {tube vertical spacing on centers, in}d_f_c=1.083 "[in]" {condenser fin depth per tube, 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}tpc_c=2 {number of rows per refrigerant parallel pass}ncircuit_c=12 {number of parallel circuits}nrow_c=4 {number of columns of tubing}TubeType_c=2 {Indicates tube diameter for standard copper pipe}

136

APPENDIX III

CONDENSER OPERATING CONDITIONS

137

Operating Conditions for Different Fixed Cost Condenser Geometries at 83 F, English Units

TubeDiamet

er(in)

Tubes/

Circuit

#Circuit

s

FinPitch(fpi)

Rows AirFace

Velocity

(ft/s)

Subcool @95(F)

SaturationTemperatu

re(F)

Compressor Work(Btu/hr)

Condenser FanWork

(Btu/hr)

Evaporator

Capacity(Btu/hr)

IsentropicCompress

orEfficiency

Volumetric

Compressor

Efficiency

AreaFactor

COP

3/8” 2 12 12 3 8.8 10 94.9 6504 290.8 31053 0.590 0.976 1.000 3.8625/16" 6 4 8 3 8.9 10 96.24 5841 265.9 30998 0.633 0.976 1.408 4.2165/16" 6 4 10 3 8.8 13 97.63 5899 266.0 31009 0.638 0.976 1.227 4.1855/16" 5 5 12 3 8.9 13 97.53 5952 282.8 31002 0.635 0.976 1.088 4.1455/16" 5 5 14 3 9.1 13 98.05 5993 309.6 30981 0.637 0.975 0.977 4.1053/8" 4 6 8 3 9.0 13 97.95 5960 281.9 31023 0.637 0.975 1.259 4.1433/8" 4 6 10 3 8.8 10 97.75 6011 278.3 30991 0.637 0.975 1.115 4.1133/8" 4 6 12 3 9.2 13 98.54 6010 327.4 30997 0.640 0.975 1.000 4.0883/8" 4 6 14 3 9.3 13 99.05 6060 351.4 30983 0.641 0.975 0.907 4.0471/2" 2 12 8 3 10.0 10 99.48 6293 398.5 31014 0.636 0.974 0.969 3.9081/2" 2 12 10 3 9.8 13 100.1 6265 406.3 31006 0.638 0.974 0.885 3.9171/2" 2 12 12 3 9.7 13 100.3 6282 422.9 30999 0.639 0.974 0.815 3.8991/2" 2 12 14 3 9.6 15 101.3 6322 437.6 31001 0.642 0.973 0.755 3.873

138

Operating Conditions for Different Fixed Cost Condenser Geometries at 83 F, English Units (cont’d)

TubeDiameter (in)

Tubes/

Circuit

#Circuit

s

FinPitc

h(fpi)

Rows

Compressor Exit

Pressure(psi)

RefrigerantSide

PressureDrop(psi)

Air SidePressure

Drop(psi)

Air-Side h(Btu/hr-ft2-

R)

SuperheatedRefrigerant

Side h(Btu/hr-ft2-R)

SaturatedRefrigerant

Side h (Btu/hr-ft2-R)

SubcooledRefrigerant

Side h (Btu/hr-ft2-R)

3/8” 2 12 12 3 209 23.6 0.00430 10.9 127.2 1505 229.05/16" 6 4 8 3 202 3.0 0.00276 11.9 87.8 904 159.15/16" 6 4 10 3 205 2.4 0.00320 11.5 87.9 895 158.65/16" 5 5 12 3 206 4.1 0.00380 11.4 98.4 1035 177.45/16" 5 5 14 3 207 3.7 0.00453 11.3 98.7 1035 177.73/8" 4 6 8 3 207 3.4 0.00324 11.6 83.0 877 149.63/8" 4 6 10 3 206 3.4 0.00369 11.1 83.6 886 150.53/8" 4 6 12 3 208 2.9 0.00463 11.2 83.4 878 149.93/8" 4 6 14 3 209 2.7 0.00542 11.1 83.7 878 150.11/2" 2 12 8 3 213 6.4 0.00535 11.8 80.6 904 143.91/2" 2 12 10 3 214 5.6 0.00610 11.3 80.3 896 143.21/2" 2 12 12 3 215 5.4 0.00696 11.0 80.4 897 143.31/2" 2 12 14 3 217 5.0 0.00786 10.8 80.5 891 143.0

139

Operating Conditions for Different Fixed Cost Condenser Geometries at 28.3 C, SI Units

TubeDiamet

er(mm)

Tubes/

Circuit

#Circuit

s

FinPitch(1/cm

)

Rows

AirFace

Velocity (m/s)

Subcool @35(C)

SaturationTemperatu

re (C)

Compressor Work

(kW)

Condenser FanWork(kW)

Evaporator

Capacity(kW)

IsentropicCompress

orEfficiency

Volumetric

Compressor

Efficiency

AreaFactor

COP

9.53 2 12 4.72 3 2.7 5.6 36.0 1.91 0.0850 9.012 0.590 0.976 1.0003.86

2

7.94 6 4 3.15 3 2.7 5.6 35.7 1.71 0.0779 9.086 0.633 0.976 1.4084.21

6

7.94 6 4 3.94 3 2.7 7.2 36.5 1.73 0.0780 9.089 0.638 0.976 1.2274.18

5

7.94 5 5 4.72 3 2.7 7.2 36.4 1.74 0.0829 9.087 0.635 0.976 1.0884.14

5

7.94 5 5 5.51 3 2.8 7.2 36.7 1.76 0.0907 9.081 0.637 0.975 0.9774.10

5

9.53 4 6 3.15 3 2.7 7.2 36.6 1.75 0.0826 9.093 0.637 0.975 1.2594.14

3

9.53 4 6 3.94 3 2.7 5.6 36.5 1.76 0.0816 9.083 0.637 0.975 1.1154.11

3

9.53 4 6 4.72 3 2.8 7.2 37.0 1.76 0.0960 9.085 0.640 0.975 1.0004.08

8

9.53 4 6 5.51 3 2.8 7.2 37.3 1.78 0.1030 9.081 0.641 0.975 0.9074.04

7

12.70 2 12 3.15 3 3.0 5.6 37.5 1.84 0.1168 9.090 0.636 0.974 0.9693.90

8

12.70 2 12 3.94 3 3.0 7.2 37.8 1.84 0.1191 9.088 0.638 0.974 0.8853.91

7

140

12.70 2 12 4.72 3 3.0 7.2 37.9 1.84 0.1240 9.086 0.639 0.974 0.8153.89

9

12.70 2 12 5.51 3 2.9 8.3 38.5 1.85 0.1283 9.086 0.642 0.973 0.7553.87

3

Operating Conditions for Different Fixed Cost Condenser Geometries at 28.3 C, SI Units (cont’d)

TubeDiameter (mm)

Tubes/

Circuit

#Circuit

s

FinPitch

(1/cm)

Rows Compressor Exit

Pressure(kPa)

RefrigerantSide

PressureDrop(kPa)

Air SidePressure

Drop(kPa)

Air-Side h(W/m2-

K)

SuperheatedRefrigerant

Side h(W/m2-K)

SaturatedRefrigerant

Side h (W/m2-K)

SubcooledRefrigerant

Side h(W/m2-K)

9.53 2 12 4.72 3 1443 162.7 0.02965 61.7 722 8613 13007.94 6 4 3.15 3 1390 20.7 0.01903 67.7 499 5132 9037.94 6 4 3.94 3 1415 16.5 0.02209 65.4 499 5082 9017.94 5 5 4.72 3 1419 28.3 0.02620 64.4 559 5877 10077.94 5 5 5.51 3 1428 25.5 0.03124 64.2 560 5877 10099.53 4 6 3.15 3 1425 23.4 0.02233 65.8 472 4977 8499.53 4 6 3.94 3 1421 23.4 0.02544 63.1 475 5030 8559.53 4 6 4.72 3 1435 20.0 0.03191 63.6 473 4983 8519.53 4 6 5.51 3 1444 18.6 0.03735 62.9 475 4984 85212.70 2 12 3.15 3 1467 44.1 0.03691 66.9 457 5134 81712.70 2 12 3.94 3 1476 38.6 0.04203 64.3 456 5089 81312.70 2 12 4.72 3 1480 37.2 0.04800 62.6 457 5091 81412.70 2 12 5.51 3 1497 34.5 0.05417 61.0 457 5060 812

141

142

Operating Conditions for Different Fixed Area Condenser Geometries at 83 F, English Units

TubeDiamet

er(in)

Tubes /

Circuit

#Circui

ts

FinPitc

h(fpi)

Rows

AirFace

Velocity

(ft/s)

Subcool @95(F)

SaturationTemperatu

re(F)

Compressor Work(Btu/hr)

Condenser FanWork

(Btu/hr)

Evaporator

Capacity(Btu/hr)

IsentropicCompress

orEfficiency

VolumetricCompresso

rEfficiency

AreaFactor

COP

5/16" 4 6 12 2 11.7 15 101.1 6320 346.1 30939 0.642 0.973 0.720 3.9115/16" 5 5 12 3 9.5 13 98.22 6013 309 30982 0.637 0.975 0.942 4.0945/16" 6 4 12 4 8.3 13 97.36 5887 293.5 31020 0.637 0.976 1.163 4.1773/8" 3 8 12 2 11.2 15 101.2 6313 358 30961 0.643 0.973 0.760 3.9113/8" 4 6 12 3 9.2 13 98.55 6011 327.3 30997 0.640 0.975 1.000 4.0873/8" 5 5 12 4 8.0 13 97.83 5897 306.1 31025 0.640 0.976 1.239 4.1651/2" 2 12 12 2 10.4 15 101.9 6352 409.4 30986 0.645 0.973 0.872 3.8701/2" 3 8 12 3 8.6 13 99.56 6067 375.8 31015 0.644 0.974 1.160 4.0341/2" 3 8 12 4 7.5 13 98.17 5938 352.1 31035 0.640 0.975 1.449 4.119

143

TubeDiameter (in)

Tubes/

Circuit

#Circuit

s

FinPitc

h(fpi)

Rows

Compressor Exit

Pressure(psi)

RefrigerantSide

PressureDrop(psi)

Air SidePressure

Drop(psi)

Air-Side h(Btu/hr-ft2-

R)

SuperheatedRefrigerant

Side h(Btu/hr-ft2-R)

SaturatedRefrigerant

Side h (Btu/hr-ft2-R)

SubcooledRefrigerant

Side h (Btu/hr-ft2-R)

5/16” 4 6 12 2 217 4.8 0.00385 13.6 115.0 1228 204.55/16” 5 5 12 3 208 3.8 0.00423 11.9 98.8 1035 177.75/16” 6 4 12 4 205 2.8 0.00460 10.8 87.7 895 158.53/8” 3 8 12 2 217 4.5 0.00416 12.8 100.9 1096 179.33/8” 4 6 12 3 208 2.9 0.00463 11.2 83.4 878 149.93/8” 5 5 12 4 206 1.9 0.00498 10.2 72.3 734 130.41/2” 2 12 12 2 218 3.8 0.00542 11.6 80.8 892 143.31/2” 3 8 12 3 210 1.5 0.00568 10.2 62.2 651 111.51/2” 3 8 12 4 207 2.2 0.00611 9.3 61.7 651 111.2

144

Operating Conditions for Different Fixed Area Condenser Geometries at 28.3 C, SI Units

TubeDiamet

er(mm)

Tubes/

Circuit

#Circuit

s

FinPitch(1/cm

)

Rows

AirFace

Velocity (m/s)

Subcool @35(C)

SaturationTemperatu

re (C)

Compressor Work

(kW)

Condenser FanWork(kW)

Evaporator

Capacity(kW)

IsentropicCompress

orEfficiency

Volumetric

Compressor

Efficiency

CostFactor

COP

7.94 4 6 4.72 2 4.6 8.3 38.4 1.85 0.1014 9.068 0.642 0.973 0.7203.91

1

7.94 5 5 4.72 3 4.0 7.2 36.8 1.76 0.0906 9.081 0.637 0.975 0.9424.09

4

7.94 6 4 4.72 4 4.0 7.2 36.3 1.73 0.0860 9.092 0.637 0.976 1.1634.17

7

9.53 3 8 4.72 2 4.6 8.3 38.4 1.85 0.1049 9.075 0.643 0.973 0.7603.91

1

9.53 4 6 4.72 3 4.0 7.2 37.0 1.76 0.0959 9.085 0.640 0.975 1.0004.08

7

9.53 5 5 4.72 4 4.0 7.2 36.6 1.73 0.0897 9.093 0.640 0.976 1.2394.16

5

12.70 2 12 4.72 2 4.6 8.3 38.8 1.86 0.1200 9.082 0.645 0.973 0.8723.87

0

12.70 3 8 4.72 3 4.0 7.2 37.5 1.78 0.1101 9.090 0.644 0.974 1.1604.03

4

12.70 3 8 4.72 4 4.0 7.2 36.8 1.74 0.1032 9.096 0.640 0.975 1.4494.11

9

145

TubeDiameter (mm)

Tubes/

Circuit

#Circuit

s

FinPitch

(1/cm)

Rows Compressor Exit

Pressure(kPa)

RefrigerantSide

PressureDrop(kPa)

Air SidePressure

Drop(kPa)

Air-Side h

(W/m2-K)

SuperheatedRefrigerant

Side h(W/m2-K)

SaturatedRefrigerant

Side h (W/m2-K)

SubcooledRefrigerant

Side h(W/m2-K)

7.94 4 6 4.72 2 1493 33.1 0.02654 77.4 653 6973 11617.94 5 5 4.72 3 1432 26.2 0.02917 67.3 561 5877 10097.94 6 4 4.72 4 1411 19.3 0.03172 61.5 498 5079 9009.53 3 8 4.72 2 1494 31.0 0.02867 72.6 573 6223 10189.53 4 6 4.72 3 1435 20.0 0.03191 63.6 473 4983 8519.53 5 5 4.72 4 1417 13.1 0.03432 57.9 410 4170 74012.70 2 12 4.72 2 1505 26.2 0.03532 65.6 459 5066 81412.70 3 8 4.72 3 1449 10.3 0.03919 57.7 353 3695 63312.70 3 8 4.72 4 1425 15.2 0.04211 52.6 350 3694 631

146

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147

xv ARI Standard 210/240-89, p 3, sect. 5.1

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xxi Tong, L.S., Boiling, Heat Transfer and Two-Phase Flow. John Wiley & Sons, New York, 1965, CPT 5.Taken from Hiller, p372.

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xxvii Conversation with Chuck Kenwright, February 2000.

xxviii London Metals Exchange October, 1999

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