PLATE-FIN-AND-TUBE CONDENSER PERFORMANCE AND DESIGN FOR REFRIGERANT R-410A AIR-CONDITIONER A Thesis Presented to The Academic Faculty By Monifa Fela Wright In Partial Fulfillmen of the Requirements for the Degree Master of Science in Mechanical Engineering Georgia Institute of Technolog May 2000
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PLATE-FIN-AND-TUBE CONDENSER PERFORMANCE AND DESIGN FOR REFRIGERANT R-410A AIR-CONDITIONER
A ThesisPresented to
The Academic Faculty
By
Monifa Fela Wright
In Partial Fulfillmenof the Requirements for the Degree
Master of Science in Mechanical Engineering
Georgia Institute of TechnologMay 2000
ii
PLATE-FIN-AND-TUBE CONDENSER PERFORMANCE AND DESIGN FOR REFRIGERANT R-410A AIR-CONDITIONER
Approved:
________________________________Samuel V. Shelton
________________________________James G. Hartley
________________________________Prateen Desa
Date Approved____________________
iii
TABLE OF CONTENTS
LIST OF TABLES vi
LIST OF ILLUSTRATIONS vii
NOMENCLATURE xiiList of Symbols xii
List of Symbols with Greek Letters
SUMMARY xxiii
CHAPTER I: INTRODUCTION 1Research Objectives 4
CHAPTER II: LITERATURE SURVEY 5Previous Studies on Variations of Heat Exchanger Geometric
Parameters 5
Previous Work in R-22 Replacement Refrigerants 8
Two-Phase Flow Regime considerations in Condenser and Evaporator Design 13
Two-Phase Flow Heat Transfer Correlations 16
Two-Phase Flow Pressure Drop Correlations 19
CHAPTER III: AIR-CONDITIONING SYSTEM AND COMPONENTMODELING 23
Refrigeration Cycle 23
System Component Models 25Compressor 25Condenser 28Condenser Fan 40Expansion Valve 40Evaporator 41Evaporator Fan 44
iv
Refrigerant Mass Inventory 45
CHAPTER IV: REFRIGERANT-SIDE HEAT TRANSFER COEFFIECIENTAND PRESSURE DROP MODELS 51
Single Phase Heat Transfer Coefficient 51
Condensation Heat Transfer Coefficient 56
Evaporative Heat Transfer Coefficient 61
Pressure Drop in the Straight Tubes 62
Pressure Drop In Tube Bends 70
CHAPTER V: AIR-SIDE HEAT TRANSFER COEFFICIENT AND PRESSUREDROP MODELS 76
Heat Transfer Coefficient 76
Pressure Drop 81
CHAPTER VI: DESIGN AND OPTIMIZATION METHODOLOGY 89Figure of Merit (Coefficient of Performance) 89
CHAPTER IX: OPTIMIZATION OF GEOMETRIC DESIGN PARAMETERSFOR FIXED CONDENSER FRONTAL AREA 152
Varying the Number of Rows of Condenser Tubes 153
Varying Fin Pitch 159
Varying Tube Diameter 163
Operating Costs 170
Varying the Base Configuration Frontal Area 179
CHAPTER X: CONCLUSIONS AND RECOMMENDATIONS 185Conclusions 185
List of Conclusions 188
Recommendations 191Optimization Parameters and Methodology 191Computational Methods 193Refrigerant-Side Heat Transfer and Pressure Drop Models 196Economic Analysis 196
APPENDIX A: AIR-CONDITIONING SYSTEM: EES PROGRAM 197
REFERENCES 227
vi
LIST OF TABLES
Table 2-1: List of Refrigerant R-22 Alternative Refrigerant Mixtures 12
Table 5-1: Coefficients for the Euler Number Inverse Power Series 84
Table 5-2: Staggered Array Geometry Factor 85
Table 5-3: Correction Factors for Individual Rows of Tubes 87
Table 6-1: Distribution of Cooling Load Hours, i.e. Distribution of FractionalHours in Temperature Bins 91
Table 8-1: Material Costs (London Metals Exchange, 1999) 114
Figure 3-3: Hexagonal Fin Layout and Tube Array 37
Figure 4-1: Refrigerant-Side Single Nusselt Number vs. Reynolds Numbe 55
Figure 4-2: Condensation Heat Transfer Coefficient vs. Total Mass Flux FoRefrigerant R-12 58
Figure 7-1: Effect of Operating Conditions on Evaporator Frontal Area 99
Figure 7-2: Effect of Air Velocity on COP for Various Ambient Temperatures andOptimum Degrees Sub-Cool 101
Figure 7-3: Effect of Air Velocity on Compressor and Condenser Fan Power 13°°°° FSub-cool at 95°°°° F Ambient Temperature 103
Figure 7-4: Effect of Ambient Temperature on COP for Varying Degrees Sub-Coolat 95°°°° F Ambient Temperature with an Air Velocity Over theCondenser of 8.5 ft/s 105
Figure 7-5: Effect of Ambient Temperature on the Evaporator Capacity forVarying Degrees Sub-Cool at 95°°°° F Ambient Temperature with atOptimum Air Velocity 106
Figure 7-6: Evaporator Capacity vs. Ambient Temperature for Various Sub-Coolconditions at 95°°°° F Ambient Temperature and Optimum Air Velocity
108
viii
Figure 7-7: Effect of Air Velocity on the Seasonal COP for Varying Sub-coolConditions 110
Figure 8-1: Effect of Number of Rows on the Seasonal COP at Optimum AirVelocity and Varying Sub-Cool for Fixed Cost of Condenser Materials
116
Figure 8-2: Effect of Number of Rows on Compressor Power and RefrigerantPressure Drop at Optimum Sub-Cool and Air Velocity for FixedCondenser Material Cost at 82°°°° F Ambient Temperature 118
Figure 8-3: Effect of Number of Rows of Tubes on Condenser Frontal Area foFixed Condenser Material Cost at Optimum Sub-Cool and Air Velocity
119
Figure 8-4: Effect of Number of Rows of Tubes on Condenser Fan Power andAirside Pressure Drop for Fixed Condenser Material Cost at 82°°°° FAmbient Temperature at Optimum Sub-Cool and Air Velocity 120
Figure 8-5: Effect of Air Velocity on Seasonal COP for Varying Number of Rows atOptimum Sub-Cool for Fixed Condenser Material Cost 122
Figure 8-6: Effect of Number of Rows on the Optimum Air Velocity andVolumetric Flow Rate of Air Over the Condenser at Optimum Sub-Cool for Fixed Condenser Material Cost 123
Figure 8-7: Seasonal COP vs. Varying Condenser Tube Circuiting at OptimumSub-Cool and Air Velocity for Fixed Condenser Material Cost 126
Figure 8-8: Refrigerant-Side Pressure Drop for Various Circuiting at 82 °°°° FAmbient Temperature and at Optimum Sub-Cool and Air Velocity foFixed Condenser Material Cost 127
Figure 8-9: Seasonal COP vs. Air Velocity for Varying Fin Pitch at FixedCondenser Material Cost and Optimum Sub-Cool 130
Figure 8-10: Effect of Fin Pitch on the Seasonal COP at Optimum Sub-Cool andAir Velocity Over the Condenser for Fixed Condenser Material Cost
131
Figure 8-11: Air-side Pressure Drop vs. Fin Pitch for Fixed Condenser MaterialCost at Optimum Sub-Cool and Air Velocity at 95°°°° F AmbientTemperature 133
ix
Figure 8-12: Power Requirements vs. Fin Pitch for Fixed Cost at Optimum Sub-Cool and Air Velocity and 95°°°° F Ambient Temperature 134
Figure 8-13: Effect of Fin Pitch on Condenser Frontal Area at Optimum Sub-Cooland Air Velocity for Fixed Condenser Material Cost 136
Figure 8-14: Optimum Seasonal COP for Varying Tube Diameter at Optimum Sub-Cool and Air Velocity for Fixed Condenser Material Cost 138
Figure 8-15: Optimum Operating Parameters for Varying Tube Diameters at FixedCondenser Material Cost 140
Figure 8-16: Condenser Tube Length Allocation for Varying Tube Diameters atOptimum Air Velocity and Sub-Cool and 82 °°°° F Ambient Temperaturefor Fixed Condenser Material Cost 141
Figure 8-17: Effect of Tube Diameter on Pressure Drop at Optimum Sub-Cool andAir Velocity at 82°°°° F Ambient Temperature for Fixed CondenserMaterial Cost 143
Figure 8-18: Power Requirements for the Condenser Fan and the Compressor vs.Tube Diameter at Optimum Air Velocity and Sub-Cool for FixedCondenser Material Cost and 82°°°° F Ambient Temperature 144
Figure 8-19: Operating Costs vs. Area Factor For Various Geometric Parameterat Optimum Sub-Cool and Air Velocity with Fixed CondenserMaterial Cost 146
Figure 8-20: Seasonal COP at Optimum Sub-Cool and Air Velocity for VaryingCondenser Tube Circuiting with Fixed Condenser Material Cost and5/16” Tube Outer Diameter 149
Figure 8-21: Comparison of the Effect of the Number of Tubes per Circuit onSeasonal COP for 5/16” and 3/8” Outer Tube Diameters at OptimumSub-Cool and Air Velocity with Fixed Condenser Material Cost 150
Figure 9-1: Effect of Air Velocity Over Condenser for Varying Numbers of Rows atOptimum Sub-Cool with Fixed Condenser Frontal Area 154
Figure 9-2: Effect of the Number of Rows of Tubes on the Seasonal COP atOptimum Sub-Cool and Air Velocity for Fixed Condenser Frontal Area
155
x
Figure 9-3: Refrigerant-Side Pressure Drop vs. Number of Rows with FixedCondenser Frontal Area for Optimum Sub-Cool and Air Velocity at 82°°°°F Ambient Temperatur 157
Figure 9-4: Compressor and Condenser Fan Power for Varying Number of Rowswith Optimum Sub-Cool and Air Velocity at 82°°°° F AmbientTemperature for Fixed Condenser Frontal Area 158
Figure 9-5: Effect of Air Velocity on Seasonal COP for Varying Fin Pitch withOptimum Sub-Cool for Fixed Condenser Frontal Area 160
Figure 9-6: Effect of Fin Pitch on the Seasonal COP at Optimum Sub-Cool and AirVelocity for Fixed Condenser Frontal Area 161
Figure 9-7: Effect of Air Velocity For Varying Tube Diameter at Optimum Sub-Cool for Fixed Condenser Frontal Area 164
Figure 9-8: Effect of Tube Diameter on the Seasonal COP for Fixed CondenserFrontal Area at Optimum Sub-Cool and Air Velocity 165
Figure 9-9: Refrigerant-Side Pressure vs. Tube Diameter for Fixed Frontal Area at82°°°° F Ambient Temperature, Optimum Sub-Cool and Air Velocity 168
Figure 9-10: Power Requirements for Varying Tube Diameters with FixedCondenser Frontal Area at 82°°°° F Ambient Temperature, OptimumSub-Cool and Air Velocity 169
Figure 9-11: Air-Side Pressure Drop vs. Tube Diameter for Fixed CondenserFrontal Area at 82°°°° F Ambient Temperature, Optimum Air Velocityand Sub-Cool 171
Figure 9-12: Operating Cost Factor vs. Cost Factor of Condenser Materials forVarying Geometric Parameters with Fixed Condenser Frontal Areaand Optimum Air Velocity and Sub-Cool 172
Figure 9-13: Seasonal COP for Varying Condenser Tube Circuiting with FixedFrontal Area and 5/16” Tube Outer Diameter at Optimum Sub-Cooland Air Velocity 175
Figure 9-14: Comparison of the Effect of the Number of Tubes per Circuit on thSeasonal COP for 5/16” and 3/8” Outer Tube Diameters with FixedFrontal Area at Optimum Sub-Cool and Air Velocity 178
xi
Figure 9-15: Operating Cost Factor vs. Condenser Material Cost Factor forVarying Tube Diameter and Tube circuiting at Optimum Air Velocityand Sub-Cool 180
Figure 9-16: Operating Cost Factor vs. Condenser Material Cost Factor forVarying Geometric Parameters and Various Fixed Frontal Areas atOptimum Air Velocity and Sub-Cool 182
xii
NOMENCLATURE
List of Symbols
a = Ratio of the transverse tube spacing to the tube diameter
ast = Stanton Number coefficient in the Kays and London (1984) Correlation
ax = Axial acceleration due to gravity
A = Total heat transfer area
Ac = Minimum free-flow cross sectional area
Aci = Cross sectional area of the refrigerant-side of the tube
Afin = Total fin surface area
Afr,con = Frontal area of condenser
Amin = Minimum free-flow area
Ao = Total air-side heat transfer area including the fin and tube areas
AF = Area Factor
B = Buoyancy Modulus
Bθ = Two-phase flow refrigerant side pressure drop Coefficient for a tube bend o θ degrees
bst = Stanton Number coefficient in the Kays and London (1984) Correlation
b = Ratio of the tube spacing normal to the air flow, to the tube diameter
xiii
C = Heat capacity
C1 = Constant of the Hiller-Glicksman refrigerant-side pressure drop Correlation
C2 = Constant of the Hiller-Glicksman refrigerant-side pressure drop Correlation
C3 = Constant of the Hiller-Glicksman refrigerant-side pressure drop Correlation
cp = Specific heat at constant pressure
cp,eff = Effective specific heat at constant pressure
cp,l = Specific heat of fluid in the liquid phase
Cmin = Minimum heat capacity between that of the air and the refrigeran
Cmax = Maximum heat capacity between that of the air and the refrigerant
Cr = Ratio of the minimum heat capacity to the maximum heat capacity
Cz = Average row correction factor
cz = Individual row correction factor
CF = Cost factor
COP = Coefficient of Performance
COPseas = Seasonal Coefficient of Perfor mance
Cost = Cost of materials for the heat exchangers
CostAl = Cost per pound of Aluminu
CostCu = Cost per pound of Copper
D = Tube diameter
Ddepc = Depth of condenser in the direction of air flow
Dh = Hydraulic diameter
xiv
d( ) = Differential change in ( )
Eu = Euler number
Eucor = Corrected Euler number
f = Friction factor
fGO = Friction factor for fluid flowing as vapor onl
fLO = Friction factor for fluid flowing as liquid only
ffin = Fin friction factor
fri = Fraction of temperature bin hours
Fr = Froude number
G = Mass flux
Gmax = Mass flux of air through the minimum flow area
gcs = Units conversion constant
h = Specific enthalpy
h1 = Specific enthalpy of refrigerant entering the compressor
h2 = Actual specific enthalpy of refrigerant exiting the compressor
h2s = Ideal specific enthalpy of refrigerant exiting the compressor
h2a = Specific enthalpy of refrigerant exiting the superheated portion of the condenser
h2b = Specific enthalpy of refrigerant entering the sub-cooled portion of the condenser
h3 = Specific enthalpy of refrigerant entering the expansion valve
h4 = Specific enthalpy of refrigerant exiting the expansion valve
ha = Air-side heat transfer coefficien
xv
hevap = Two-phase refrigerant-side evaporative heat transfer coefficien
hL = Liquid phase refrigerant side heat transfer coefficien
hr = Refrigerant-side heat transfer coefficient
hr,SP = Single phase refrigerant-side heat transfer coefficient
hTP = Two-phase refrigerant-side heat transfer coefficient
i = Temperature bin number
j = Colburn factor
JP = Parameter for the Colburn factor calculation
k = Thermal conductivity
k1 = Geometry factor for staggered tube array for the air-side pressure drop correlation
kl = Liquid phase thermal conductivity
kb,θ = Two-phase flow refrigerant side pressure drop Coefficient for a tube bend o θ degrees
L = Length
l = Integral variable evaporating tube length
Lcon,sa = Tube length of the saturated portion of the condenser tubes
Lcon,sc = Tube length of the sub-cooled portion of the condenser tubes
Lcon,sh = Tube length of the superheated portion of the condenser tubes
Levap,sat = Tube length of the saturated portion of the evaporator tubes
Levap,sh = Tube length of the superheated portion of the evaporator tubes
Lsat = Tube length of the saturated portion of the heat exchanger tubes
Ltot = Total tube length of the heat exchanger tubes
xvi
m = mass
m = mass flow rate
ma,sat = mass of flow rate of air f owing over the saturated portion of the condenser
ma,tot = total mass flow rate of air flowing over the condenser
mair = mass flow rate of air flowing over heat exchanger
mcon,sat = mass of refrigerant in the saturated portion of the condenser
mcon,sc = mass of refrigerant in the sub-cooled portion of the condenser
mcon,sh = mass of refrigerant in the superheated portion of the condenser
mes = extended surface geometric parameter
mevap,sat = mass of refrigerant in the saturated portion of the evaporator
mevap,sh = mass of refrigerant in the superheated portion of the evaporator
n = Blausius coefficien
NTU = Number of transfer units
NuD = Nusselt number based on the tube diameter
P = Pressure
pr = Reduced pressure
Prat = Ratio of the condenser saturation pressure to the evaporator saturation pressure
Pe = Perimeter
PD = Compressor piston displacemen
Pr = Prandtl number
Q = Rate of total heat trans erred between the refrigerant and the air
.
.
.
.
.
xvii
q = Amount of heat per unit mass transferred between the air and the refrigerant
Qave,seas = Average cooling load of the system over all cooling load hours
qcon,sat = Amount of heat per unit mass transferred between the air and the refrigerant in the saturated portion of the condenser
qcon,sc = Amount of heat per unit mass transferred between the air and the refrigerant in the sub-cooled portion of the condenser
qcon,sh = Amount of heat per unit mass transferred between the air and the refrigerant in the superheated portion of the condenser
qcst = Empirical constant for the Euler number correlation
Qe = Cooling capacity of the syste
Qmax = Maximum possible amount of heat transferred between the refrigerant and the air
r = Outer radius of tube
rb = Radius of tube bend
Rb = Tube bend recovery length
rcst = Empirical constant for the Euler number correlati
Rcv,PD = Ratio of clearance volume to the piston displacemen
pitch of 12 fins per inch, and employing 3 tubes per circuit. This configuration has a cost
factor of unity, and thus cost the same as that of the base configuration.
Figure 9-12 also shows that, unlike in Chapter VIII where the cost factor of the hea
exchangers is fixed, when the frontal area is fixed the lowest operating cost occurs when
3 rows of tubes are used. Increasing the number of rows to 4 actually increases both the
coil material cost and the operating cost factor. Although there is a relatively significant
2.3% decrease in operating cost when the fin pitch decreases from 8 fins per inch to 12
fins per inch, there is only a 0.2% decrease in the operating cost when the fin pitch is
further decreased to 14 fins per inch. A configuration using 14 fins per inch yields lower
operating costs than do those employing fewer fins per inch. However, the material cos
factor of this configuration is 1.1, which is 10% greater than the base case configuration
(12 fins per inch). Therefore, when the frontal area of the condenser is fixed, it is
recommended that a fin pitch of 12 fins per inch be employed.
It can also be discerned from Figure 9-12 that the tube diameter and the number o
tubes per circuit have a significant effect on the operating cost of the complete air-
conditioning system. Figure 9-12 shows that when only 2 tubes per circuit are used, as in
the base configuration, the optimum tube diameter is 1/2” with fixed heat exchanger cost.
However, the figure also shows that for a tube diameter of 3/8” and 3 rows of tubes, the
lowest operating cost occurs for a condenser configuration utilizing 3 tubes per circuit.
The initial investigations outlined throughout this chapter did not examine the effect of
tube diameter on the system performance when tube circuiting other than the base
174
configuration of 2 tubes per circuit is utilized. From an analysis of Figure 9-12, it is
obvious that an examination of this effect is warranted.
While Figure 9-12 shows that for fixed heat exchanger cost, a configuration with a
5/16” tube diameter yields the highest operating cost, and the worst performance.
However, this tube diameter was only tested for the base case configuration of 2 tubes per
circuit. This low performance is related to the higher refrigerant-side pressure drop tha
results when a tube diameter this small is employed with only 2 tubes per refrigerant flow
circuits. Increasing the number of tubes per circuit should relieve the detrimental effec
of the higher refrigerant-side pressure drop. When the number of tubes per circuit is
increased, the amount of mass of refrigerant flowing through each individual tube is
decreased. Therefore, tubes of smaller diameter can be utilized without degrading syste
performance. Employing a 5/16” diameter tube with the frontal area of the condenser
fixed actually reduces the cost factor to 0.92. Furthermore, increasing the number o
tubes per circuit has no effect on the frontal area. Therefore, configurations with smaller
diameter tubes and a greater number of tubes per circuit do not increase the cost o
materials for the total system when the frontal area of the heat exchangers is fixed. As a
result of the above analysis, the effect of the number of tubes per circuit on the system
performance will be investigated, for a configuration utilizing a tube diameter of 5/16”, 3
rows of tubes, and 12 fins per inch.
Figure 9-13 shows the effect of the number of tubes per circuit on the seasonal COP
at optimum operating conditions for a heat exchanger configuration with a tube diameter
175
Figure 9-13: Seasonal COP for Varying Condenser Tube Circuiting with Fixed
Frontal Area and 5/16” Tube Outer Diameter at Optimum Sub-Cool and Ai
Velocity
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
1 2 3 4 5 6 7
Number of Condenser Tubes per Circuit
Sea
son
al C
OP
5/16" Tube Diameter
3 rows of tubes12 fins per inch
176
of 5/16” with a fixed cost factor. The figure shows that for a tube diameter of 5/16”, as
the number of tubes per circuit increases from 2 to 4, the seasonal COP increases by
approximately 7.2% from approximately 3.88 to 4.16. As the number of tubes per circuit
increases from 4 to 5, the optimum seasonal COP increases from 4.16 to a maximum o
4.17. The optimum seasonal COP then decreases to 4.14 when the number of tubes per
circuit increases from 5 to 6.
The explanations for the aforementioned trends in the optimum seasonal COP with
varying number of tubes per circuit are the same as for the trends discussed earlier in
Chapter VIII under the section entitled “Varying Condenser Tube Circuiting”. As
discussed in that section, the improved seasonal COP that occurs when the tubes per
circuit increases from 2 to 5 results from the decrease in refrigerant pressure drop which
reduces the required compressor power. The decrease in pressure drop occurs because,
as the number of tubes per circuit increases, the amount of mass of refrigerant through
each individual tube decreases. This decrease in the amount of mass flowing in each tube
leads to a decrease in the refrigerant-side pressure drop through each tube, which has a
positive effect on the seasonal COP. However increasing the number of tubes per circuit
also decreases the refrigerant-side heat transfer coefficient, which has a negative effect on
the seasonal COP. For the 5/16” diameter tube configuration, when the number of tubes
per circuit is increased from 2 to 5, the positive effect of the reduced refrigerant-side
pressure drop has a larger impact on the seasonal COP than the negative effect of the
decreased refrigerant-side heat transfer coefficient. Thus the seasonal COP increases.
However, when the tubes per circuit is increased from 5 to 6 for the 5/16” tube
177
configuration, the decreased refrigerant-side heat transfer coefficient has a larger effec
on the seasonal COP than the decreased refrigerant-side pressure drop, and the seasonal
COP decreases. Hence, there is a certain plateau at which the number of tubes per circuit
cannot increase without causing a decrease in system performance. For a condenser with
a tube diameter of 3/8”, this occurs when 3 tubes per circuit are used. However when the
tube diameter is decreased to 5/16”, this plateau occurs at a configuration utilizing 5
tubes per circuit.
Figure 9-14 shows the optimum seasonal COP versus the number of tubes per circui
for the both 3/8” tube diameter configuration (base configuration) and the 5/16” tube
diameter configuration with fixed condenser frontal area. As the figure shows, the values
of the optimum seasonal COP achieved for condensers using a 5/16” diameter tube are
slightly higher than those with a 3/8” diameter tube. For a condenser with a tube
diameter of 3/8”, the optimum seasonal COP is 4.15 and occurs when 3 tubes per circuit
is used. However, when the diameter is decreased to 5/16”, the optimum seasonal COP is
4.17 and occurs when 5 tubes per circuit are used. Thus, the optimum seasonal COP
obtained when using tubes of 5/16” diameter is 0.5 % higher than the optimum obtained
using tubes of 3/8” diameter.
When the number of tubes per circuit is the value used for the base configuration (2
tubes per circuit), a condenser using tubes of diameter of 3/8” yields a much higher
optimum seasonal COP, COP = 4.09, than a condenser using tubes of diameter 5/16”,
COP = 3.88. Conversely, when the number of tubes per circuit is increased,
178
Figure 9-14: Comparison of the Effect of the Number of Tubes per Circuit on th
Seasonal COP for 5/16” and 3/8” Outer Tube Diameters with Fixed Frontal Area at
Optimum Sub-Cool and Air Velocity
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
1 2 3 4 5 6 7
Number of Condenser Tubes per Circuit
Sea
son
al C
OP
5/16" Outer Tube Diameter
3/8" Outer Tube Diameter
Fixed Frontal Area
3 rows of tubes12 fins per inch
179
configurations utilizing tubes of 5/16” diameter yield the highest seasonal COP.
Furthermore, the cost factor of a configuration utilizing tubes of diameter 5/16” and 5
tubes per circuit, 0.92, is 8.0% lower than the 1.0 cost factor obtained when condenser
tubes of 3/8” diameter are employed. Figure 9-15 shows the operating cost versus the
material cost factor for varying tube circuiting and tube diameter. Only the tube
circuiting of the base configuration, 2 tubes per circuit, is utilized for tube diameters o
1/2” and 5/8”. As shown in Figure 9-15, condensers with tube diameters of 1/2” and 5/8”
have not only significantly higher material cost factors but also higher operating cost than
condensers employing tubes of 5/16” and 1/2” diameter. Therefore, when the frontal area
of the heat exchanger is fixed to the area of the base configuration (7.5 ft2), a condenser
with an outer tube diameter of 5/16”, 5 tubes per circuit, 3 rows of tubes, and 12 fins per
inch yields the highest seasonal COP (lowest operating cost) of all configurations
investigated in this study, and has the most reasonable heat exchanger material cost (cost
factor lower than the base configuration).
Varying the Base Configuration Frontal Area
As discussed in Chapter VIII, the frontal area of the base heat condenser
configuration, 7.5 f 2, has been selected as a value typically found in most residential air-
conditioning systems rated at 30,000 Btu/hr. In many instances, there are space
constraints and/or material cost constraints imposed on the heat exchanger designer that
180
Figure 9-15: Operating Cost Factor vs. Condenser Material Cost Factor for
Varying Tube Diameter and Tube circuiting at Optimum Air Velocity and Sub-Cool
0.236
0.240
0.244
0.248
0.252
0.256
0.260
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Material Cost Factor
1/C
OP
(O
per
atin
g C
ost
Fac
tor
3/8" Tube Diameter
5/16" Tube Diameter
1/2" Tube Diameter
5/8" Tube Diameter
4 tpc6 tpc
2 tpc
4 tpc
2 tpc
2 tpc
5 tpc
3 tpc
5 tpc
2 tpc
181
restrict the size of the condenser and consequently sacrificing performance. In these
situations, the frontal area of the condenser may have to be even smaller and/or cheaper
than that of the base configuration used in this study. However, there are also examples
in which space and material cost constraints are not stringent, and a larger and/or more
expensive condenser can be employed to produce a lower operating cost (or higher
seasonal COP). Yet, as shown in Figure 9-13, the cost of materials can be increased or
decreased in a number of ways including: increasing the number of rows, increasing the
fin pitch, increasing the tube diameter, or by simply increasing the frontal area. Hence,
two hypothetical questions arise from this: (1) If the material cost of the condenser must
be reduced by a specified amount, what geometric parameter or dimension should be
reduced to ensure that only a minimum increase in the operating cost results? (2) If the
cost of materials is allowed to increase by a specified amount, what geometric parameter
or dimension should be increased in order to produce the maximum decrease in the
operating cost?
As discussed earlier, Figure 9-15 shows that condenser configurations employing
tube diameters of 1/2” and 5/16” do not yield the best system performance. Therefore in
addressing the two hypothetical questions posed above, tube diameters of this size are not
studied. Figure 9-16 shows the operating cost factor versus the material cost factor for
varying fin pitch and varying numbers of rows for the base configuration. This figure
also shows the operating cost of the condenser configuration utilizing 5/16” diameter
tubes, 5 tubes per circuit, 3 rows of tubes, and 12 fins per inch for 3 condenser frontal
areas: (1) frontal area equal to the base configuration, (2) frontal area 20% lower than the
182
Figure 9-16: Operating Cost Factor vs. Condenser Material Cost Factor for
Varying Geometric Parameters and Various Fixed Frontal Areas at Optimum Air
Velocity and Sub-Cool
0.228
0.232
0.236
0.240
0.244
0.248
0.252
0.256
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Material Cost Factor
1/C
OP
(O
per
atin
g C
ost
Fac
tor)
Fin Pitch
Number of Rows
5/16" diameter, 5 tubes per circuit
4 rows
2 rows
10 FPI
8 FPI
14 FP5/16" diameter Base
Configuration
20% smaller frontal area
Base case frontal area
20% greater frontal area
Base Configuration12 Fins Per Inch (FPI)
2 Tubes per Circuit (TPC)
3 Rows
3/8" Diameter Tube
183
base configuration, and frontal area 20% greater than the base configuration. An
investigation of the slopes of the curves in this figure is needed to discern the best
methods to vary the frontal area in order to achieve reductions in the material cost or the
operating cost.
In question (1), the material cost of the condenser is to be reduced by a specified
amount. The three methods considered for reducing the material cost are: reducing the
number of rows, reducing the fin pitch, and reducing the frontal area. According to
Figure 9-16, decreasing the fin pitch from the base configuration value of 12 fins per inch
to 8 fins per inch produces a smaller increase in operating cost than decreasing either the
number of rows or decreasing the frontal area. The slope of the line of row variation is
smaller than the slopes for frontal area variation and fin pitch variation in the direction of
decreasing material cost.
In question (2), the material cost of the condenser is allowed to increase by a
specified amount in order to reduce the operating cost. Again, the three methods
considered for increasing the material cost are: increasing the number of rows, increasing
the fin pitch, and increasing the frontal area. According to Figure 9-16, increasing the
frontal area, produces the largest reduction in the operating cost. The slope of the line o
frontal area variation is negative in the direction of increased material cost. The slope of
the line of fin pitch variation is also negative in the direction of increased material cost.
However, increasing the fin pitch produces only a slight decrease in the operating cost.
Conversely, increasing the number of rows actually increases the operating cost for the
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base configuration detailed in the figure. Therefore, increasing the material cost in this
manner is a “lose-lose” proposition in that no reduction in the operating cost results.
While the above analysis attempts to address the two hypothetical questions posed in
regards to methods of increasing and decreasing material cost, the questions have not
been universally answered by the work of this study. As indicated in the figure, the
frontal area was varied only for the configuration optimized with fixed frontal area
configuration (5/16” diameter tubes, 5 tubes per circuit, 3 rows of tubes, and 12 fins per
inch). For the reasons detailed in the section of this chapter entitled “Operating Costs”,
the number of rows and the fin pitch were varied only for the base configuration (3/8”
diameter tubes, 2 tubes per circuit, 3 rows of tubes, and 12 fins per inch). Therefore in
the above discussion it is assumed that the slopes of the lines of varying fin pitch and
varying number of rows will be the same regardless of tube diameter and tube circuiting
in order to address the hypothetical questions posed in this study.
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CHAPTER X
CONCLUSIONS AND RECOMMENDATIONS
Conclusions
Refrigerant R-410a is one of the primary candidates to replace refrigerant R-22 in
residential heat pump and air-conditioning applications. As a result of this current study,
many conclusions can be drawn regarding the design of a fin-and-tube condenser coil for
a unitary air-conditioning system with refrigerant R-410a as the working fluid. A
computational model that determines the seasonal COP of an air-conditioning system for
various operating conditions and geometric configurations of the condenser is also used.
In addition, a methodology is detailed for optimizing the condenser design using the
seasonal COP of the system as the figure of merit. While the primary objectives of this
work are not to perform detailed economic analyses, the system operating cost factor and
the capital cost factor for the heat exchanger materials are both considered when detailing
the selection of the best design. Design guidelines taking into account space constraints
have also been given. It is concluded that selecting the final optimum configuration
depends on the constraints imposed upon the heat exchanger designer. If the space
constraints are stringent, then the base condenser configuration for the system
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investigated with the frontal area of the condenser fixed is the optimum (5/16” tube
diameter, 5 tubes per circuit, 3 rows of tubes, 12 fins per inch, 7.5 ft2 frontal area).
However, if the space constraints are not stringent, and a higher seasonal COP is the
primary goal, then the condenser configuration for the system optimized with the cost o
heat exchanger materials fixed may be preferred (5/16” tube diameter, 5 tubes per circuit,
3 rows of tubes, 12 fins per inch, 8.5 ft2 frontal area). Hence, more information about the
space and economic constraints imposed on the designer is required before the bes
condenser configuration of those investigated in this study can be selected.
As discussed in previous chapters, due to the impending ban of refrigerant R-22
production there is a pressing need for studies on air-conditioning systems that utilize
alternative refrigerants. Therefore, in this current study comparisons are made between
the condenser configurations and seasonal performance of air-conditioning systems
designed using refrigerant R-410a as the working fluid (this current study) to systems
designed using refrigerant R-22 as the working fluid. A thesis entitled “Optimization of
Finned-Tube Condenser for a Residential Air-Conditioner Using R-22” by Emma Saddler
(Saddler, 2000), details the design methodology for an air-conditioning system with
refrigerant R-22 as the working fluid. The base configuration condenser, as well as the
component and property models used in Saddler’s study are similar to those used in this
current work. Likewise, the geometric and operating parameters varied in Saddler’s
optimization are also similar to those of this current study.
According to Saddler’s results, the R-22 air-conditioning system designed with the
frontal area of the condenser fixed has a maximum seasonal COP of 4.18, 13 degrees of
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sub-cool in the condenser, and an air velocity of 8.3 ft/s over the condenser with the
following geometric parameters: a frontal area of 7.5 ft2, 4 rows of tubes, 6 tubes per
circuit, tubes that are 5/16” in diameter, and 12 fins per inch. The major differences
between the geometric and operating parameters of this system and those of the R-410a
system designed with the fixed condenser frontal area constraint are the number of rows,
and the tube circuiting. The maximum seasonal COP for the R-22 system designed with
the fixed condenser frontal area constraint is approximately 0.2% greater than the
maximum seasonal COP for the comparable R-410a system.
With a fixed heat exchanger cost constraint identical to that used in this current study,
Saddler’s results show that the R-22 air-conditioning system has a maximum seasonal
COP of 4.22. For this maximum seasonal COP design, the R-22 system has 10 degrees
of sub-cool in the condenser, and an air velocity of 8.3 ft/s over the condenser with the
following geometric parameters: a frontal area of 10.6 ft2, 3 rows of tubes, 6 tubes per
circuit, 5/16” tube diameter, and 8 fins per inch. The major differences between the
geometric and operating parameters of this system and those of the R-410a system
optimized with the fixed heat exchanger cost constraint are the tube circuiting, and the fin
pitch. The maximum seasonal COP for the R-22 system designed with the fixed cost
constraint is approximately 0.2% lower than the maximum seasonal COP for the
comparable R-410a system.
Because the seasonal COP of the R-22 systems and the R-410a systems optimized
with both the fixed material cost and fixed frontal area constraints are nearly identical
(vary within ± 0.3%), the estimated operating costs of both systems are also roughl
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equivalent. In addition, for both the R-22 and R-410a air-conditioning systems, the best
performing condenser configurations investigated utilize the smallest tube diameter
examined in both studies (tube diameter = 5/16”).
It is expected that the best performing condenser configurations investigated for the
R-410a air-conditioning system would require fewer tubes per circuit than the best
condenser configurations investigated for the R-22 air-conditioning system. This is
because the working pressure and the vapor phase density for R-410a are much higher
than for R-22. Based on the results of both this current work and Saddler’s thesis, this
expected trend has been confirmed.
The results of this study confirm the viability of refrigerant R-410a as a replacemen
for refrigerant R-22 in vapor compression air-conditioning systems similar to those
investigated in this work. The R-410a systems have seasonal performance and operating
costs equivalent to those of the R-22 systems designed with the same frontal area and
material cost constraints. Therefore environmental safety is achieved without sacrificing
cost and performance.
List of Conclusions
The specific conclusions drawn from this study are as follows:
• Condenser design for air-conditioning systems must be based on seasonal
performance. The United States Department of Energy regulations require a seasonal
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performance rating, which incorporates the system’s performance at ambien
temperatures ranging from °F to 102 °F, weighted with the cooling load
distribution factors. Whether this rating is consistent with actual practice is
questionable. However, the United States Department of Energy regulations require
all residential air-conditioning systems to be labeled with this rating.
• The seasonal performance of an air-conditioning system can be closely approximated
by calculating the system’s performance at 82 °F ambient temperature.
• Condenser tubes of smaller diameter enhance performance.
• When packaging and space constraints are not present, the condenser configuration
with the largest frontal area possible yields the best system performance.
• When typical volume and space constraints are imposed, condensers employing 3
rows of tubes yield the best performance. Contrary to intuition, increasing the
number of rows to 4 actually increases the material cost of the coil and decreases the
system performance when space constraints are imposed.
• For all geometric configurations investigated, a refrigerant charge producing between
10 and 15 degrees sub-cool at 95 °F ambient temperature produces the optimu
performance.
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• For all geometric configurations investigated, the optimum velocity of air flow over
the condenser coil ranges from roughly 6 ft/s and 12 ft/s.
• As the ambient temperature decreases, the sub-cool at 95 °F ambient temperature that
is needed to produce the highest COP increases.
• If the material cost of the condenser must be reduced, decreasing the fin pitch from
the base configuration value of 12 fins per inch to 8 fins per inch produces a smaller
increase in operating cost than decreasing either the number of rows or the frontal
area.
• If the cost of materials is allowed to increase by a specified amount, increasing the
frontal area produces the largest reduction in the operating cost. However, increasing
the number of rows or the fin pitch actually increases the operating cost for the base
configuration detailed in the figure. Therefore, increasing the material cost in this
manner is a “lose-lose” proposition, in that no reduction in the operating cost results.
• All parameters that do not affect material cost of the condenser, such as the operating
parameters and the tube circuiting, should be optimized for every geometric
configuration investigated before the performance of different systems is compared.
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Recommendations
Optimization Parameters and Methodology
Again, a principal goal of this study was to provide heat exchanger designers with
guidelines for optimizing a condenser with the alternative refrigerant R-410a as the
working fluid using the seasonal COP of the air-conditioning system as the figure of
merit. Perhaps the most salient lesson learned during this study is the significant effec
that the operating conditions have on the system performance, and subsequently the
optimization process. The operating parameters examined in this study include the sub-
cool in the condenser and the velocity of airflow over the condenser. It is of the utmost
importance that heat exchanger designers be aware that it is not possible to make valid
comparisons between heat exchangers of different geometric configurations without first
optimizing the operating parameters at each configuration to yield the maximum seasonal
COP. Therefore, in all future studies of this kind, it is recommended that the operating
parameters continue to be optimized at each geometric configuration in a manner similar
to the method detailed in this study.
Varying the sub-cool in the condenser and the air velocity over the condenser does
not significantly alter the frontal area or the material cost of the heat exchanger. During
this study, it has also been determined that varying the number of tubes per refrigeran
flow parallel circuits also does not alter the cost of materials or the frontal area of the hea
exchanger. However, as discussed in Chapter VIII and Chapter IX, the refrigerant flow
tube circuiting does have a major effect on the optimum seasonal COP, and hence, the
optimum design. Therefore, for future optimization studies of this kind, it is
192
recommended that in addition to the operating conditions, the condenser tube circuiting
should also be optimized at each geometric configuration investigated. For example, in
order make a valid comparison between a system using a condenser with 2 rows of tubes
to one using 3 rows of tubes, the optimum air velocity, the optimum degrees sub-cool in
the condenser, and the optimum tube circuiting arrangement should be determined for
both systems.
The spacing of the tubes in the condenser during this investigation is the standard
recommended for condensers by most heat exchanger manufacturers. However, it is
possible that this spacing is not the optimum spacing. The tube spacing affects the
efficiency of the fins. The closer the tube spacing, the higher the fin efficiency, and
hence a higher air-side heat transfer coefficient is produced. As a result, it is
recommended that the tube spacing be varied and optimized for future studies of this
kind.
Due to the limitations of the air-side pressure drop and heat transfer models,
condensers utilizing tubes of diameter smaller than 5/16” have not been investigated in
this study. As stated previously, for the air-conditioning systems investigated in this
study, the optimum condenser configurations utilize the smallest tube diameter
investigated, 5/16”. It is therefore recommended that condensers with tubes of 1/4” outer
diameter be included in future optimization studies, since it is possible that even better
performance can be achieved. As a result, air-side pressure drop and heat transfer models
that are valid for tubes of smaller outer diameter must be used.
193
Computational Methods
For this study, all modeling computations were performed using Engineering
Equation Solver (EES) operating on a 250 MHz Intel Pentium II processor. The
optimization parameters analyzed in this study included the sub-cool in the condenser,
the air velocity over the condenser, the number of rows of tubes, the refrigerant tube
circuiting, the fin pitch, and the tube diameter. A breakdown of the computational time
involved to determine the effects of these various parameters on the system performance
is as follows:
• For this study, in order to calculate the seasonal COP at one condenser geometri
configuration and with the operating parameters specified (1 “run”), 5 minutes o
computational time was needed: 5 minutes/”run”
• Determining the optimum air velocity at one sub-cool condition at one geometric
configuration required a minimum of 12 “runs”: 12 “runs”/ velocity
• Determining the optimum sub-cool at one condenser geometric configurati
required 12 “runs”: 12 “runs”/ sub-coo
Therefore calculating the seasonal COP for one condenser geometric configuration
required:
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(12 “runs”/velocity) x (12 “runs”/sub-cool) x (5 minutes/“run”) = 720 minutes (12 hours)
of run time to determine the optimum sub-cool and air velocity for one geometric
configuration of the condenser.
An exhaustive search over the range of geometric design parameters requires:
• Investigating fin pitch varying from 8 to 14 fins/inch: 4 “runs”/fin pitch
• Investigating tube diameter varying from 5/16” to 5/8”: 4 “runs”/tube diameter
• Investigating tube circuiting varying from 2 to 6 tubes per circuit: 5 “runs”/tube
circuiting
• Investigating the number of tube rows varying from 1 to 4: 4 “runs”/number of rows
• Design constraints of fixed frontal area and fixed material cost: 2 “runs”/design
constraint
Therefore the total computational time required for an exhaustive optimization search
scheme is:
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(5 minutes/ “run”) x (12 “runs”/velocity) x (12 “runs”/sub-cool) x (4 “runs”/fin pitch) x
(4 “runs”/tube diameter) x (5 “runs”/tube circuiting) x (4 “runs”/number of rows) x (2
“runs”/design constraints) = 460,800 minutes or 7,680 hours of computational time.
Hence, the total computational time involved is 7,680 hours, or more than 10 and 1/2
months. The EES model developed to calculate the system performance for this stud
involves more than 2000 equations. Of these 2000 equations, 1000 must be solved
through iteration. The solution of these 100 simultaneous equations is heavily dependen
on the “guess values” for each variable. For varying geometric configurations and
operating conditions, the guess values must be continuously adjusted in order to ensure
the convergence of the solution. Therefore, the researcher is required to be in attendance
for all computations, since in nearly all instances, the guess values must be adjusted for
every “run”. Therefore, the actual total time for this exhaustive search is considerably
longer than the 7,680 hours that have been calculated. Hence, for future studies of this
kind, a more powerful and concise method for finding the optimum values of each
parameter should be developed. For example, entropy minimization techniques tha
quantify the tradeoff between pressure drop irreversibilities and heat transfer
irreversiblilities might be useful in finding a universal optimization relation for the tube
circuiting. More advanced search techniques will allow further investigation into the
coupling and interactions of the geometric parameters for a larger number of
configurations.
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Refrigerant Side Heat Transfer and Pressure Drop Models
Several echniques for predicting the heat transfer coefficients and pressure drops
during condensation and evaporation inside tubes have been evaluated during this study
Many of the current methods are cumbersome in structure, heavily dependent on
empirically determined coefficients, and have considerable uncertainty. In this work,
general correlations based on statistical evaluation of data, and proposed to be valid for
all flow regimes, were used to calculate the condensing heat transfer coefficients and
pressure drop. While it was determined that the dominant flow regime for the conditions
of this present study is the annular flow regime, at low qualities, stratified-wavy flow also
exists. Furthermore it was assumed that the quality varies linearly with length. It is
recommended that this assumption be studied further, and that correlations based on
specific models for individual flow regimes should be used.
Economic Analysis
Again, the goal of this study is not to conduct a detailed economic analysis for
residential air-conditioning systems. Moreover, the cost of the compressor and condenser
fan units are excluded from the cost analysis (material cost factor) for this investigation.
However, in determining the optimum heat exchanger configuration, a tradeoff must be
made between the capital cost and the operating cost (using the reciprocal of the seasonal
COP as an operating cost factor). It is recommended that a detailed economic analysis be
performed that includes both the capital cost and the operating cost of each component o
the system.
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APPENDIX A
AIR-CONDITIONING SYSTEM: EES PROGRAM
{I. Refrigerant-Side Procedures and FunctionsA. Pressure Drop
1. singledp2. twophasedp3. tpbenddrop
B. Heat transfer Coefficients1. h_bar_single2. h_bar_c
3. h_bar_e
II. Air -Side A. Heat Transfer coefficients
1. ha B. Pressure Drop
1. GetEuler
III. Heat Exchanger Procedures and Functions A. Surf_eff B. Exch_size C. Exch_size_un_un D. sat_size E. Tubing
IV. Compressor Procedure A. Compeff}
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PROCEDURE singledp(m_r, nr,D,L,f,rho:delP){Purpose-to determine the single phase pressure drop for flow in tubes}vel=m_r/((pi*D^2/4)*rho*nr) "[ft/hr]" {velocity of refrigerant through tube, ft/hr}delP=(f*(L/D)*(rho*Vel^2)/2)*convert(lbm/ft-hr2,psi)end
PROCEDURE twophasedp(xi,xf,T1, T2, D, m_dot, nr,L:DP){Purpose- to determine the two phase pressure drop for flow in tubes
InputsD- equivalent diameter of flow passage, ftE- surface roughness, ftG- mass flow per unit area lbm/hr-ft^2mu_v- viscosity of vapor phase, lbm/hr-ftmu_l- viscosity of liquid phase, lbm/hr-ftrhov- density of liquid phaserhol- density of vapor phaseReV- Reynold's number of vapor phaseReL- Reynold's number of liquid phaseDztp- length of two phase regionxf- final qualityxi- initial qualityv- exit specific volume of vapor phase, ft^3/lbnr- number of flow passagesL- length of tube
Output-DeltaP- pressure drop over two phase region}
{Friction component of 2 phase pressure drop}DPf2=2*c3*(.429*(xf^2.33-xi^2.33)-.141*(xf^3.33-xi^3.33)-.0287*(xf^4.33-xi^4.33))DPf3=C3^2*(.538*(xf^1.86-xi^1.86)-.329*(xf^2.86-xi^2.86))DPf=c2*(.357*(xf^2.8-xi^.28)+DPf2+DPf3)
DP=(DpM+DPfend
Procedure singlebenddrop(tpc, D_i, m_dot_r,P, T1, T2, L, Width, f:DP){Pressure Drop in bends for single phase regions}T=(T1+T2)/2G=m_dot_r/(tpc*D_i^2*pi/4)equiv_L=13*2rho=density(R410A, T=T, P=P)grav=32.2*convert(1/s^2,1/hr^2)ncirc=trunc(L/width)DP=f*G^2*equiv_L/(2*grav*rho)*convert(lbf/ft^2, psia)*ncircend
PROCEDURE tpbenddrop(nr,D_i_1,m_dot_r, h_f, T_c, L_c, L_22a, L_2a2b,width:DP){Pressure Drop In bends for two-phase regions}equiv_L=13*2 {for 180 degree bends}R_b=h_f/2 "[ft]"z=R_b/D_i_1G=m_dot_r/(nr*D_i_1^2*pi/4)e=.000005DP=0num_circuit_2a2b=trunc(l_2a2b/Width)num_circuit_22a=trunc(L_22a/width)L_o=L_22a-Width*num_circuit_22a
i=i+1x=-L/L_2a2b+1If x<=0 then goto 10mu_TP=mu_v*x+mu_l*(1-x)Re_tp=G*D_i_1/mu_tpA_tp=(2.457*ln(1/((7/Re_tp)^0.9+.27*e/d_i_1)))^16B_tp=(37530/Re_tp)^16lambda_tp=8*((8/Re_tp)^12+(1/((A_tp+B_tp)^(3/2))))^(1/12)DELTAp_b_lo=lambda_l*G^2*equiv_L/(2*grav*rho_l)*convert(lbf/ft^2, psia)k_b=lambda_tp*equiv_L/2 {k_b for 90 degree bend}GAMMA_B=rho_l/ ho_v*(mu_v/mu_l)^nB=1+2.2/(k_b*(2+R_b/D_i_1)) {B for 90 degree bend}B=.5*(1+B) {B for 180 degree bend}phi_b_lo=1+(GAMMA_b-1)*(B*x^((2-n)/2)*(1-x)^((2-n)/2)+x^(2-n))DELTAp_b=DELTAp_b_lo*phi_b_loDP=DP+DELTAp_bL=L+width
until i>=num_circuit_2a2b-110:DP=Dpend
Procedure h_bar_single22ash(D, m_dot_r, T1, T2, P:Re,h_bar, rho){single phase heat transfer coefficient in the superheated portion of the condenser}Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2rho=density(R410A, T=Tav,P=P)c_p=specheat(R410A, T=Tav, P=P)mu=viscosity(R410A, T=Tav, P=P)Pr=prandtl(R410A, T=Tav, P=P)If Re<3500 then
a=1.10647b=-.078992
endIFif (Re>3500) and (Re<6000) then
a=3.5194e-7
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b=1.03804ENDIFif Re>6000 then
a=.2243b=-.385
endifSt=a*Re^b/(Pr^(2/3))h_bar=St*G*C_pend
Procedure h_bar_single4a1sh(D, m_dot_r, T1, T2, P:Re,h_bar, rho){Single phase refrigerant heat transfer coefficient for the superheated portion of thevaporator}Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2rho=density(R410A, T=Tav,P=P)c_p=specheat(R410A, T=Tav, P=P)mu=viscosity(R410A, T=Tav, P=P)Re=m_dot_r*D/(Area*mu)Pr=prandtl(R410A, T=Tav, P=P)If Re<3500 then
a=1.10647b=-.078992
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
Procedure h_bar_single2b3sc(D, m_dot_r, T1, T2, P:Re,h_bar, rho){Single refrigerant heat transfer coefficient for the sub-cooled portion of the condenser}Area=(D/2)^2*piG=m_dot_r/AreaTav=(T1+T2)/2rho=density(R410A, T=Tav,P=P)
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c_p=specheat(R410A, T=Tav, P=P)mu=viscosity(R410A, T=Tav, P=P)Re=m_dot_r*D/(Area*mu)Pr=prandtl(R410A, T=Tav, P=P)If Re<3500 then
a=1.10647b=-.078992
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){Shah-Correlation: Two-phase refrigerant heat transfer coefficient in the condenser}G=m_dot_r/(D^2*nr/4)mu_l=viscosity(R410A, T=T, x=0)mu_g=viscosity(R410A, T=T, x=1)rho_l=density(R410A, T=T, x=0)rho_g=density(R410A, T=T, x=1)Pr_l=prandtl(R410A, T=T-1, P=P)k_l=conductivity(R410A, T=T, x=0)P_r=P/p_crit(R410A)Re_l=G*D/mu_lh_l=0.023*Re_l^.8*Pr_l^.4*k_lh_bar_c=h_l*(.55+2.09/(P_r^.38))end
Function h_bar_e(Te, Pe,De, m_r, x_in){Purpose to evaluate the evaporation two phase heattransfer coefficient for forced convection flow inside tubes}x_i:=x_in
Pr_L=prandtl(R410A, T=Te-1, P=Pe) "Prandtl # of liquid phase in evaporator"kl=conductivity(R410A, T=Te, x=0) "conductivity of liq. phase"mu_v=viscosity(R410A, T=Te, x=1) "viscosity of vap. phase"
FUNCTION ha(hf, eta,t,L, ma, mu, D_o, Ao,At, Cp, Pr, n){Returns air-side heat transfer coefficient based on McQuiston Method}{h_bar_a- external heat transfer coefficient (btu/hr-ft^2-R)}A_min=(hf/2)*(1/eta-t) "[ft^2]"Gmax=ma*(1/eta-t)/(A_min*L) "[lbm/hr-ft^2]"Re_D=Gmax*D_o/mRe_L=Gmax*hf/mudum1=(Ao/(At))JP=Re_D^(-.4)*(Ao/(At/(1-t*eta)))^(-.15)j4=.2675*JP+1.325*10^(-3)jn=(1-n*1280*Re_L^(-1.2))*j4/(1-4*1280*Re_L^(-1.2))ha=jn*Cp*Gmax/(Pr^(2/3))*convert(1/s,1/hr)end
FUNCTION geteuler(Re, h_f, dep_f, D, nrow){finds Euler number for staggered banks of tubes for a fin-and-tube cross flow heaexchanger}
{Modify Euler number to account for non- equilateral geometryfind correction factor k1 to account for a/b ratio, use k1 with other relationships tocorrect Euler # for row spacing}a=dep_f/Db=h_f/DCheck1=1Check2=1Check3=1spacerat=a/bEu=0k1=0If (spacerat>.5) and (spacerat<1.2) and (re>=1000) and (Re<10000) then {thisrelationship is stated for Re=1000, not the range 1000<Re<10000}
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
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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
IF Re>=1000 THENc_z1=1.149-(.411/(z-.412))c_z2=.924+(.269/(z+.143))c_z=(c_z2-c_z1)/(10000-1000)*(Re-1000)+c_z1
endif
IF Re>=10000 THENc_z1=.924+(.269/(z+.143))c_z2=.62+(1.467/(z+.667))c_z=(c_z2-c_z1)/(100000-10000)*(Re-10000)+c_z1
endifIF Re>=100000 THEN
c_z=.62+(1.467/(z+.667))endif
endifz=z+1C=C+c_z
until z>nrowC=C/nrow
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If C=0 then Check3=0endifEu=Eu*C*k1geteuler=Euend
Procedure surf_eff(D_o_1, h_bar_a,h_f, d_f,t, Af,Ao:fin_eff,surfeff){finds the tube surface efficiencey and fin efficiency }h_f=h_f*convert(in,ft)d_f=d_f*convert(in,ft)r_t=D_o_1/2 "[ft]" {outside radius of tube}M=h_f/2 "[ft]"L=.5*sqrt(d_f^2+M^2) "[ft]"psi=M/r_tBETA=L/MR_e=R_t*1.27*psi*(BETA-.3)^.5 "[ft]"k=237*convert(W/m-K, BTU/hr-ft-R) "[BTU/hr-ft-R]" {conductivity for pureAluminum, Incropera & Dewitt}m_eff=sqrt(2*h_bar_a/(k*t))"[1/ft]"phi=(R_e/R_t-1)*(1+.35*ln(R_e/r_t))fin_eff=tanh(m_eff*r_t*phi)/(m_eff*r_t*phi)surfeff = 1 - Af/Ao*(1-fin_eff)end
Procedure sat_size(Cunmixed, E:UA){Finds the UA of the saturated portions of the heat exchangers}
Cr:=0NTU:=-ln(1-E)UA:=NTU*Cunmixed
end
Procedure exch_size_un_un(Cair, Cfridge,UA:E){Finds the UA of the sub-cooled and/or superheated sections of the heat exchangers}Cmin=min(Cair, Cfridge)Cmax=max(Cair, Cfridge)Cr=Cmin/CmaxNTU=UA/CminE=1-exp((1/Cr)*NTU^.22*(exp(-Cr*(NTU^.78))-1))end
Procedure tubing(Type:D_i,D_o){Returns the inner and outer diameter of copper tubes based on AAON productspecifications
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Type Standard size(in)1 5/162 3/83 1/24 5/8}if type=1 then
D_i=.2885D_o=.3125
endIFif type=2 then
D_i=.3490D_o=.375
endIFif type=3 then
D_i=.4680D_o=.5000
endIFif type=4 then
D_i=.5810D_o=.6250
endIFD_i=D_i/12D_o=D_o/12
end
Function compeff(P_o, P_i, T_o, T_i){computes efficiency of scroll compressor based on condensing and evaporatingTemperature and pressure}Pr=P_o/P_iTr=(T_o+459)/(T_i+459)compeff=-60.25-3.614*Pr-.0281*Pr^2+111.3*Tr-50.31*Tr^2+3.061*Tr*Prend
Function fri(Tac){Sets the ambient temperature weight fractions in order to compute the seasonal COP}fri=0If (Tac>65) and (Tac<69) then
fri =.214endifIf Tac=72 then
fri =.231endif
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If Tac =77 thenfri =.216
endifIf Tac = 82 then
fri =.161endifIf Tac=87 then
fri =.104endifIf Tac=92 then
fri =.052endifIf Tac=97 then
fri =.018endifIf Tac=102 thenfri =.004END
Module At95(Tsc, V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c, nrow_c, Tubetype_c,ncircuit_c:PD, m_sys, A_e, A_c,Tc_ave,width_e,width_c,W_dot_fc,W_dot_com,DELTAP_tot_ac,CF_e,CF_c,DELTAP_ResideBEND_total,DELTAP_Residecondnser_total,L_22a,L_2a2b,L_2b3){This model returns the compressor piston displacement, amount of sub-cool, evaporatorfrontal area,condenser frontal area and mass of refrigerant in the system in order to provide anevaporator capacityof 30,000 Btu/hr at 95 F ambient temperature}
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}
210
{Air flow over Condenser}Tac1=95 "[F]" {Air inlet T into Condenser}V_ac=V_dot_ac*convert(1/min,1/sec)/A_c {Air velocity over condenser} "[ft/s]"mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) {viscosity of air flowing over thecondenser} “[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "{density of air flowing over the condenser}[lbm/ft^3]"m_dot_ac=m_ac*convert(1/hr,1/s) "{mass flow rate of air flowing over the condenser}[bm/s]"m_ac=V_dot_ac*convert(1/min,1/hr)*rho_ac1 "{mass of air flowing over thecondenser} [lbm/hr]"h_bar_ac=ha(h_c, eta_c,t_c, width_c,m_dot_ac, mu_ac, D_o_c, A_o_c,A_t_c, C_p_air,Pr_ac, nrow_c) {air-side heat transfer coefficient over the condenser} "[Btu/hr-ft^2-R]"c_p_air=specheat(AIR, T=Tac1) {specific heat at constant pressure of air flowing overthe condenser} "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1) {Prandtl number of air flowing over the condenser}
{Air Flow over Evaporator}Tae1=80 "[F]" {Air inlet T into Evaporator}V_dot_ae=30000*400/12000 "[cfm]" {air flow rate over evaporator in cfmassuming 400 cfm/ton at design Q_e of 30,000 BTU/hr}V_ae=V_dot_ae*convert(1/min,1/sec)/A_e "{Velocity of air flow over evaporator}[ft/sec]"rho_ae1=density(AIR, T=Tae1, P=14.7) {Density of air flow over the evaporator}
"[lbm/ft^3]"m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 {mass of air flowing over theevaporator} "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) {mass flow rate of air flowing over theevaporator} "[lbm/s]"mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec) {Viscosity of are flowing over theevaporatr} "[lbm/ft-s]"h_bar_ae=ha(h_e, eta_e,t_e, width_e,m_dot_ae, mu_ae, D_o_e, A_o_e, A_t_e, C_p_air,Pr_ac, nrow_e) {heat transfer coefficient of air flowing over the evaporator} "[Btu/hr-ft^2-R]"W_dot_fe=365*V_dot_ae*convert(W, BTU/hr)/1000
gamma_R410A=1.16 {specific heat ratio of Cp/Cv}Clearance=.05 "[%]" {Percent}v1=volume(R410A, P=P1,T=T1)"[ft^3/lbm]"
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v2=volume(R410A, P=P2,T=T2)"[ft^3/lbm]"nv=1-R*(v1/v2-1) {Compressor volumetric efficiency, Klein}R=.025 {ratio of clearance volume to displacement}PD=m_dot_r*v1/nv "[ft^3/hr]" {compressor piston displacement}
{condenser Characteristics}{Variable Condenser characteristics}spac_rat=h_f_c/d_f_c {tube spacing ratio-horizontal to vertical tube spacing}Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}width_c=3 {base configuration width} "[ft]"L_c=Width_c*nrow_c*ncircuit_c "[ft]" {Total length of condenser}H_c=h_fft_c*tpc_c*ncircuit_c "[ft]" {height of condenser, ft}V_c=Width_c*h_c*dep_c "[ft^3]" {Volume of Condenser}A_c=Width_c*H_c "[ft^2]" {frontal area of condenser, ft^2}CALL Surf_eff(D_o_c, h_bar_ac,h_f_c, d_f_c,t_c, A_f_c,A_o_c:phi_f,phi_c) {calls thefin efficiency and tube surface efficiency for the condenser}Call tubing(TubeType_c:D_i_c,D_o_c) {calls the tube diameter based on the 4 tubetypes for the condenser}A_i_c=L_c*D_i_c*pi*tpc_c {the condenser refrigerant-side inner tube heat transferarea} "[ft^2]"A_t_c=D_o_c*pi*L_c*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_c=2*L_c*eta_c*tpc_c*(h_fft_c*d_fft_c-pi*(D_o_c/2)^2) {the total fin heat transferarea} "[ft^2]"A_o_c=A_t_c+A_f_c {the total heat transfer area -air-side and refrigerant}
{evaporator Characteristics}{Variable Evaporator characteristics}h_f_e=1 "[in]" {tube vertical spacing on centers, in}t_e=.006/12 "[ft]" {thickness of fins, ft}eta_e=12*12 "[1/ft]" {evaporator fin pitch, fins/ft}d_f_e=.625 "[in]" {evaporator fin depth per tube, in}Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {evaporator depth, ft}tpc_e=2 {number of tubes per refrigerant flow parallel circuit}nrow_e=4 {number of rows of tubing}ncircuit_e=9L_e=Width_e*nrow_e*ncircuit_e {evaporator tube length} "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft "[ft]" {height of evaporator ft}TubeType_e=2
212
V_e=width_e*h_e*dep_e "[ft^3]" {Volume of evaporator}A_e=Width_e*H_e "[ft^2]" {frontal area of evaporator ft^2}CALL Surf_eff(D_o_e, h_bar_ae,h_f_e, d_f_e,t_e, A_f_e,A_o_e:phi_f_e,phi_e) {callsthe fin efficiency and tube surface efficiency for the evaporator}Call tubing(TubeType_e:D_i_e,D_o_e) {calls the tube diameter based on the 4 tubtypes for the evaporator}d_fft_e=d_f_e*convert(in,ft) "[ft]"h_fft_e=h_f_e*convert(in,ft "[ft]"A_i_e=L_e*D_i_e*pi*tpc_e "[ft^2]" {the evaporator refrigerant-side inner tubeheat transfer area}A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_ {the total refrigerant side tube heat transferarea for the evaporator} "[ft^2]"A_f_e=2*h_fft_e*tpc_e*d_fft_e*eta_e*L_e-2*pi*(D_o_e/2)^2*eta_e*L_e*tpc_e {thetotal fin heat transfer area for the evaporator} "[ft^2]"A_o_e=A_t_e+A_f_e {the total heat transfer area -air-side and refrigerant}
"[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) {the total refrigerantflow area for the evaporator}"[ft^2]"
{***********************************************************Begin Cycle Analysis -analyzes the vapor-compression refrigeration cycle************************************************************}
{Condenser Equations}P2a=P2-DELTAP_22a-DELTAP_b_22a {pressure of refrigerant exiting thesuperheated portion of the condenser} "[psia]"P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b {pressure of refrigerant exiting thesaturated portion of the condenser}"[psia]"P3=P2b-DELTAP_2b3-DELTAP_b_2b3 {pressure of refrigerant exiting the sub-cooled portion of the condenser} "[psia]"
213
{Superheated portion of condenser}T2a=temperature(R410A, P=P2a, x=x2a) {Temperature of refrigerant exiting thesuperheated portion of the condenser} "[F]"h2a=enthalpy(R410A, T=T2a, x=x2a) {Enthalpy of refrigerant exiting thsuperheated portion of the condenser} "[Btu/lbm]"Q_22a=m_dot_r*(h2-h2a) "[Btu/hr]"Q_22a=E_22a*min(C_22a,C_a22a)*(T2-Tac1) "[Btu/hr]"C_a22a=m_ac*specheat(AIR, T=Tac1)*L_22a/L_c "[Btu/hr-R]"C_22a=m_dot_r*specheat(R410A, T=T2, P=P2) "[Btu/hr-R]"Call exch_size_un_un(C_a22a, C_22a,UA_22a:E_22a)
{Total Refrigerant Side Pressure Drop for condenser}DELTAP_Residecondnser_total= DELTAP_22a+DELTAP_b_22a+DELTAP_2a2b+DELTAP_b_2a2b+DELTAP_2b3+DELTAP_b_2b3 "[psia]"
{Total Refrigerant Side Pressure Drop Due To Bends in the Condenser}
{Cost Factors for metalsFins made from pure aluminumTubes made from pure copper}Cf_cu=.8 "[1/lbm]" {copper is about $0.8/lb on the London MetalsExchange}Cf_al=.7 "[1/lbm]" {aluminum is about $0.7/lb}rho_al=2702*convert(kg/m^3,lbm/ft^3) "[lbm/ft^3]"{Incropera and DeWitt}rho_cu=8933*convert(kg/m^3, lbm/ft^3) "[lbm/ft^3]"V_cu=L_c*pi*(D_o_c^2/4-D_i_c^2/4)*tpc_c+L_e*pi*(D_o_e^2/4-D_i_e^2/4)*tpc_e
Module WithSubcool(Tac1, PD, A_e, A_c, m_sys, V_ac, h_f_c, t_c, eta_c, d_f_c, tpc_c,nrow_c, Tubetype_c, ncircuit_c: Den_COPseas_i, Tsc){This module returns the seasonal COP of the system and the sub-cool in the condenserfor the various ambient temperatures for a system whose compressor has been sized for asystem capacity of 30,000 Btu/hr at 95 F ambient temperature}
x4a=1x2a=1Tsh=10 "[F]" {refrigerant superheat in evaporator from states 4a-1, F}Tc_ave=(T2a+T2b)/2 "[F]"e=.000005 "[ft]" {roughness for drawn tubing (White), ft}m_r_t=m_dot_r/tpc_c "[lbm/hr]" {mass flow rate per tube}
{Air flow over Condenser}V_ac=V_dot_ac*convert(1/min,1/sec)/A_c {Air velocity over condenser} "[ft/s]"mu_ac=viscosity(AIR, T=Tac1)*convert(1/hr,1/s) {viscosity of air flowing over thecondenser} “[lbm/ft-s]"rho_ac1=density(AIR, T=Tac1, P=Pac1) "{density of air flowing over the condenser}[lbm/ft^3]"m_dot_ac=m_ac*convert(1/hr,1/s) "{mass flow rate of air flowing over the condenser}[bm/s]"m_ac=V_dot_ac*convert(1/min,1/hr)*rho_ac1 "{mass of air flowing over thecondenser} [lbm/hr]"h_bar_ac=ha(h_c, eta_c,t_c, width_c,m_dot_ac, mu_ac, D_o_c, A_o_c,A_t_c, C_p_air,Pr_ac, nrow_c) {air-side heat transfer coefficient over the condenser} "[Btu/hr-ft^2-R]"c_p_air=specheat(AIR, T=Tac1) {specific heat at constant pressure of air flowing overthe condenser} "[Btu/lbm-R]"Pr_ac=prandtl(AIR, T=Tac1) {Prandtl number of air flowing over the condenser}
{Air Flow over Evaporator}Tae1=80 "[F]" {Air inlet T into Evaporator}V_dot_ae=30000*400/12000 "[cfm]" {air flow rate over evaporator in cfmassuming 400 cfm/ton at design Q_e of 30,000 BTU/hr}V_ae=V_dot_ae*convert(1/min,1/sec)/A_e "{Velocity of air flow over evaporator}[ft/sec]"rho_ae1=density(AIR, T=Tae1, P=14.7) {Density of air flow over the evaporator}
"[lbm/ft^3]"m_ae=V_dot_ae*convert(1/min,1/hr)*rho_ae1 {mass of air flowing over theevaporator} "[lbm/hr]"m_dot_ae=m_ae*convert(1/hr,1/s) {mass flow rate of air flowing over theevaporator} "[lbm/s]"
219
mu_ae=viscosity(AIR, T=Tae1)*convert(1/hr,1/sec) {Viscosity of are flowing over theevaporatr} "[lbm/ft-s]"h_bar_ae=ha(h_e, eta_e,t_e, width_e,m_dot_ae, mu_ae, D_o_e, A_o_e, A_t_e, C_p_air,Pr_ac, nrow_e) {heat transfer coefficient of air flowing over the evaporator} "[Btu/hr-ft^2-R]"W_dot_fe=365*V_dot_ae*convert(W, BTU/hr)/1000
gamma_R410A=1.16 {specific heat ratio of Cp/Cv}Clearance=.05 "[%]" {Percent}v1=volume(R410A, P=P1,T=T1)"[ft^3/lbm]"v2=volume(R410A, P=P2,T=T2)"[ft^3/lbm]"nv=1-R*(v1/v2-1) {Compressor volumetric efficiency, Klein}R=.025 {ratio of clearance volume to displacement}PD=m_dot_r*v1/nv "[ft^3/hr]" {compressor piston displacement}
{condenser Characteristics}{Variable Condenser characteristics}spac_rat=h_f_c/d_f_c {tube spacing ratio-horizontal to vertical tube spacing}Dep_c=d_fft_c*nrow_c "[ft]" {condenser depth, ft}L_c=Width_c*nrow_c*ncircuit_c "[ft]" {Total length of condenser}H_c=h_fft_c*tpc_c*ncircuit_c "[ft]" {height of condenser, ft}V_c=Width_c*h_c*dep_c "[ft^3]" {Volume of Condenser}A_c=Width_c*H_c "[ft^2]" {frontal area of condenser, ft^2}CALL Surf_eff(D_o_c, h_bar_ac,h_f_c, d_f_c,t_c, A_f_c,A_o_c:phi_f,phi_c) {calls thefin efficiency and tube surface efficiency for the condenser}Call tubing(TubeType_c:D_i_c,D_o_c) {calls the tube diameter based on the 4 tubetypes for the condenser}A_i_c=L_c*D_i_c*pi*tpc_c {the condenser refrigerant-side inner tube heat transferarea} "[ft^2]"A_t_c=D_o_c*pi*L_c*(1-t_c*eta_c)*tpc_c "[ft^2]"A_f_c=2*L_c*eta_c*tpc_c*(h_fft_c*d_fft_c-pi*(D_o_c/2)^2) {the total fin heattransfer area} "[ft^2]"A_o_c=A_t_c+A_f_c {the total heat transfer area -air-side and refrigerant}
{evaporator Characteristics}{Variable Evaporator charcteristics}h_f_e=1 "[in]" {tube vertical spacing on centers, in}t_e=.006/12 "[ft]" {thickness of fins, ft}eta_e=12*12 "[1/ft]" {evaporator fin pitch, fins/ft}d_f_e=.625 "[in]" {evaporator fin depth per tube, in}Dep_e=d_f_e*nrow_e*convert(in,ft) "[ft]" {evaporator depth, ft}tpc_e=2 {number of tubes per refrigerant flow parallel circuit}nrow_e=4 {number of rows of tubing}ncircuit_e=9L_e=Width_e*nrow_e*ncircuit_e {evaporator tube length} "[ft]"H_e=h_f_e*tpc_e*ncircuit_e*convert(in,ft "[ft]" {height of evaporator ft}TubeType_e=2V_e=width_e*h_e*dep_e "[ft^3]" {Volume of evaporator}A_e=Width_e*H_e "[ft^2]" {frontal area of evaporator ft^2}CALL Surf_eff(D_o_e, h_bar_ae,h_f_e, d_f_e,t_e, A_f_e,A_o_e:phi_f_e,phi_e) {callsthe fin efficiency and tube surface efficiency for the evaporator}Call tubing(TubeType_e:D_i_e,D_o_e) {calls the tube diameter based on the 4 tubtypes for the evaporator}d_fft_e=d_f_e*convert(in,ft) "[ft]"h_fft_e=h_f_e*convert(in,ft "[ft]"A_i_e=L_e*D_i_e*pi*tpc_e "[ft^2]" {the evaporator refrigerant-side inner tubeheat transfer area}A_t_e=D_o_e*pi*L_e*(1-t_e*eta_e)*tpc_ {the total refrigerant side tube heat transferarea for the evaporator} "[ft^2]"A_f_e=2*h_fft_e*tpc_e*d_fft_e*eta_e*L_e-2*pi*(D_o_e/2)^2*eta_e*L_e*tpc_e {thetotal fin heat transfer area for the evaporator} "[ft^2]"A_o_e=A_t_e+A_f_e {the total heat transfer area -air-side and refrigerant}
"[ft^2]"A_flow_e=width_e*(1-eta_e*t_e)*(H_e-D_o_e*ncircuit_e*tpc_e) {the total refrigerantflow area for the evaporator}"[ft^2]"
{***********************************************************Begin Cycle Analysis -analyzes the vapor-compression refrigeration cycle************************************************************}
{Condenser Equations}P2a=P2-DELTAP_22a-DELTAP_b_22a {pressure of refrigerant exiting thesuperheated portion of the condenser} "[psia]"P2b=P2a-DELTAP_2a2b-DELTAP_b_2a2b {pressure of refrigerant exiting thesaturated portion of the condenser}"[psia]"P3=P2b-DELTAP_2b3-DELTAP_b_2b3 {pressure of refrigerant exiting the sub-cooled portion of the condenser} "[psia]"
{Superheated portion of condenser}T2a=temperature(R410A, P=P2a, x=x2a) {Temperature of refrigerant exiting thesuperheated portion of the condenser} "[F]"h2a=enthalpy(R410A, T=T2a, x=x2a) {Enthalpy of refrigerant exiting thsuperheated portion of the condenser} "[Btu/lbm]"Q_22a=m_dot_r*(h2-h2a) "[Btu/hr]"Q_22a=E_22a*min(C_22a,C_a22a)*(T2-Tac1) "[Btu/hr]"C_a22a=m_ac*specheat(AIR, T=Tac1)*L_22a/L_c "[Btu/hr-R]"C_22a=m_dot_r*specheat(R410A, T=T2, P=P2) "[Btu/hr-R]"Call exch_size_un_un(C_a22a, C_22a,UA_22a:E_22a)
{Total Refrigerant Side Pressure Drop for condenser}DELTAP_Residecondnser_total= DELTAP_22a+DELTAP_b_22a+DELTAP_2a2b+DELTAP_b_2a2b+DELTAP_2b3+DELTAP_b_2b3 "[psia]"
{Total Refrigerant Side Pressure Drop Due To Bends in the Condenser}DELTAP_ResideBEND_total=DELTAP_b_22a+DELTAP_b_2a2b+DELTAP_b_2b3
"[psia]"
{Valve Equation}h4=h3 "[Btu/lbm]"
{Evaporator Equations}{Neglect Pressure drop across evaporator}P4=P4a "[psia]"P4=P1 "[psia]"Q_dot_e=Q_44a+Q_4a1"[Btu/hr]"A_i_e=A_i_44a+A_i_4a1 "[ft^2]"{A_o_e=A_i_e*D_o_1/D_i_c}T4=T4a"[F]"P4=pressure(R410A, T=T4, h=h4) "[psia]"{m_ae=V_dot_ae*convert(1/min,1/hr)/volume(AIR, T=Tac1, P=14.7)}x4=quality(R410A, T=T4, h=h4)
Tsc=15 “[F]” {Sub-cool in the condenser}V_ac=8 “[ft/s]” {Air velocity over condenser, ft/s}h_f_c=1.25 "[in]" {tube vertical spacing on centers, in}t_c=.006/12 "[ft]" {thickness of fins, ft}eta_c=12*convert(1/in,1/ft) "[1/ft]" {condenser fin pitch, fins/ft}d_f_c=1.083 "[in]" {condenser fin depth per tube, in}tpc_c=2 {number of rows per refrigerant flow parallel circuit}nrow_c=3 {number of columns of tubing}TubeType_c=2 {Indicates tube diameter for standard copper pipe}ncircuit_c=12 {indicates number of refrigerant flow parallel circuits}
227
REFERENCES
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Chen, J. J. J. and Spedding, P. L., 1981. “An Extension of the Lockhart-MartinelliTheory of 2-Phase Pressure Drop and Holdup,” Int. J. Multiphase Flo , vol. 7,no. 6, pp. 659-675.
Chi, K., Wang, C. C., Chang, Y. J., and Chang, Y. P., 1998. “A Comparison Study ofCompact Plate Fin-and-Tube Heat Exchangers,” ASHRAE Transactions, vol. 104,no. 2, pp. 548-555.
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