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
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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
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
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
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
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
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))
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)
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
115
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}
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
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
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
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
119
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
{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}
{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]"
{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
{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}
{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
ii Hayter, Richard B., Ph.D., P.E. The Future of HVAC: The Perspective of One American. Presented at the40th anniversary of the Netherlands Technical Association for Building Services (TVVL), June11, 1999, Amsterdam, The Netherlands. http://www.engg.ksu.edu/people/rhayter/tvvlpapr.htm
iii Home Energy Saver Web page. http://homenergysaver.lbl.gov
iv Propst, James L. “Air Conditioner Condenser Optimization”. Georgia Institute of Technology Thesis.August, 1975.
v Beans, E. William. “Computer program for refrigeration cycle analysis”. Thermodynamics and theDesign, Analysis, and Improvement of Energy Systems. ASME Adv Energy Syst Div Publ, AES v27, 1992, ASME, New York, NY, p 153-159.
vi Haselden, Geoffrey. Chen, J. “Computer simulation program for mixed-refrigerant air conditioning.” IntJ Refrig, v 17, n 5, Jun 1994, p 343-350.
vii Klein, S. A. Reindl, D. T. “The relationship of optimum heat exchanger allocation and minimum entropy-generation for refrigeration cycles.” Advanced Energy Systems Division, ASME Adv Energy SystDiv Pupl AES v 37 1997 ASME, Fairfield, NJ, p 87-94.
viii Chen, Lingen. Wu, Chih. Sun, Fengui. “Optimisation of steady flow refrigeration cycles .”International Journal of Ambient Energy, v 17, n 4, Oct. 1996, Ambient Press Ltd, Lutterworth,England, p 199-206.
ix Chen, Lingen. Wu, Chih. Sun, Fengui. “Cooling load versus COP characteristics for an irreversible airrefrigeration cycle.” Energy Conversion and Management, v 39, n 1-2, Jan 1998, Elsevier SciLtd, Exeter, England, p 117-125.
x McQuiston, Faye. Parker, Jerald. Heating, Ventilating, and Air Conditioning Analysis and Design, 4thEd. John Wiley & Sons, Inc. New York, 1994 p636
xi Klein, S.A. and Reindl, D.T. “The Relationship of Optimum Heat Exchanger Allocation and MinimumEntropy Generation for Refrigeration Cycles.” AES-Vol. 37, Proceedings of the ASME AdvancedEnergy Systems Division, p 87-94
xii Klein, S.A.
xiii Threlkeld, James R. Thermal Environmental Engineering , 2nd Ed. Prentice Hall International, NY, 1970,p55.
xiv ARI Standard 210/240-89, p 3, sect. 5.1
147
xv ARI Standard 210/240-89, p 3, sect. 5.1
xvi ANSI/ASHRAE Standard 116-1983 “Methods of Testing for Seasonal Efficiency of Unitary Air-Conditioners and Heat Pumps.: American Society of Heating, Refrigerating, and Air-Conditioning Engineers, Inc. Atlanta, GA, 1983 p22.
xvii McQuiston, Faye. Parker, Jerald. p579
xviii Sieder, E.N., and Tate, G. E. Ind. Eng. Chem., 28 1429, 1936 as referenced in Incropera, F., DeWitt, D.Fundamentals of Heat and Mass Transfer, 4th Ed. John Wiley & Sons, New York, 1996, p445.
xix Traviss, D. P., Rohsenow, W. M., Baron, A.B. Forced-Convection Condensation Inside Tubes: A HeatTransfer Equation for Condenser Design. ASHRAE Transactions 1972.
xx Pate, M.B. “Design considerations for air-conditioning evaporator and condenser coils.” Two-PhaseFlow Heat Exchangers: Thermal-Hydraulic Fundamentals and Design. Kakac et. al. Ed. KluwerAcademic Publishers, Boston, 1987, p 849- 884.
xxi Tong, L.S., Boiling, Heat Transfer and Two-Phase Flow. John Wiley & Sons, New York, 1965, CPT 5.Taken from Hiller, p372.
xxii Hiller, Carl. Improving Heat Pump Performance Via Compressor Capacity Control: Analysis and Test.PhD Thesis. Massachusetts Institute of Technology, 1976, p 381-387
xxiii Chisolm, D. Two-Phase Flow in Pipelines and Heat Exchangers. George Godwin, New York, 1983.Pp. 154-163.
xxiv Haaland, S.E. “Simple and explicit formulas for the friction factor in turbulent pipe flow,” Fluids Eng.,March 1983, p89-90. as referenced in White, Frank. Fluid Mechanics, 3rd ed. McGraw Hill, Inc.New York, 1994, p317
xxv Rich, D. G. “The effect of fin spacing on the heat transfer and friction performance of multi-row,smooth plate fin-and-tube heat exchangers”. ASHRAE Transactions Vol. 79, Part 2, 1973
xxvi Zukauskas, A., Ulinskas, R. “Banks of plain and finned tubes”. Heat Exchanger Design Handbook .G.F. Hewitt, ed. Begell House, In. NY 1998, p 2.2.4-1- 2.2.4-17.
xxvii Conversation with Chuck Kenwright, February 2000.
xxviii London Metals Exchange October, 1999
xxix 1996 ASHRAE Handbook- HVAC Systems and Equipment. American Society of Heating, Refrigeratingand Air-Conditioning Engineers, Inc. Atlanta, 1996, p 40.1.
xxx AAON Heating and Air-Conditioning Products web site. http:// www.aaon.com.