American Journal of Mathematical and Computational Sciences
2016; 1(1): 18-28
http://www.aascit.org/journal/ajmcs
Keywords Condensation,
Heat Exchangers,
Air Cooled,
Modeling,
Refrigeration,
Numerical
Received: March 8, 2016
Accepted: March 21, 2016
Published: May 13, 2016
A Numerical Rating Model for Thermal Design of Air Cooled Condensers in the Industrial Applications
Ali Hussain Tarrad1, *
, Ali F. Altameemi2, Deyaa M. Mahmood
3
1Private Consultant, Thermal Engineering Specialist, Copenhagen, Denmark 2Mechanical Engineering, Adhwa Alshamal Contracting and General Trading, Baghdad, Iraq 3Technical Training Department, Technical Institute, the Foundation of Technical Institutes,
Baghdad, Iraq
Email address [email protected] (A. H. Tarrad), [email protected] (A. F. Altameemi),
[email protected] (D. M. Mahmood) *Corresponding Author
Citation Ali Hussain Tarrad, Ali F. Altameemi, Deyaa M. Mahmood. A Numerical Rating Model for
Thermal Design of Air Cooled Condensers in the Industrial Applications. American Journal of
Mathematical and Computational Sciences. Vol. 1, No. 1, 2016, pp. 18-28.
Abstract The thermal assessment of a water chiller air cooled condenser is outlined in the present
work. The steady state experimental data of a water chiller unit was implemented to
build a tube by tube model to investigate the louvered finned tube air cooled condenser
performance. The refrigerants selected for this object were R-22, R-134a, R-404A and R-
407C for the ambient dry bulb temperature range of (24 – 46)°C. The validation of the
present numerical model for pure and zeotropic mixtures showed a reasonable agreement
between experimental and those predicted values. The maximum scatter between
experimental and predicted condenser duty was within (±8)% for R-22, R-134a and R-
407C refrigerants. The predicted condenser exit air temperature showed a lower scatter
for these refrigerants to be within (±4)%. The model prediction for R-404A refrigerant
underestimated the heat duty and exit air dry bulb temperature by (30)% and (15)%
respectively.
1. Introduction
Fischer and Rice (1981) [1] developed a model for a heat pump system including
condenser and evaporator finned tube heat exchanger. The condenser was divided into
three regions; superheated, two-phase (condensation) and sub-cooled. Each region was
analyzed separately using effectiveness NTU method. Domanski and Didion (1983) [2]
presented a model of evaporator and condenser finned tube heat exchanger in a heat
pump systems. The model based on tube-by-tube approach. The model assumes a
uniform air distribution and assigns the same air mass flow rate for each tube. Domanski
(1989) [3] developed a computer simulation program of modeling evaporator finned tube
heat exchanger for air conditioning system. The model has one dimension air
distribution, each tube was assumed to have uniform air distribution over its entire
length. The percentage of discrepancy between the experimental and predicted total
cooling capacity was (-6%).
Zietlow et al. (1992) [4] developed a scheme model of condenser finned tube heat
exchanger for mobile air conditioning unit. In this model the total length of the
condenser was divided into few segments which are further divided into several models,
American Journal of Mathematical and Computational Sciences 2016; 1(1): 18-28 19
as in tube-by-tube approach. Two typical cross flow
condensers were modeled and the error between
experimental and calculated condenser capacities obtained
with the refrigerant R-134a was within (10%). Mullen et al.
(1997) [5] developed modeling of evaporator and condenser
finned tube heat exchanger in room air conditioning unit. The
condenser was divided into three zones; superheated, two-
phase (condensation) and sub-cooled, each zone was
analyzed separately using the effectiveness NTU method.
Bensafi, et al. (1997) [6] presented a computational model
of evaporator and condenser finned tube heat exchanger
using pure and mixed refrigerant. The heat exchanger was
divided into tubes and then subdivided into element. The
percentage error between experimental and predicted coil
duty for water and R-22 refrigerant was less than (5%).
Sadler (2000) [7] developed a detailed design and modeling
of the finned tube heat exchanger as condenser circulating R-
22 in residential air conditioning units. In this model the
condenser was divided into three zones; superheated,
condensation, and sub-cooled. Wright (2000)[8] developed
condenser finned tube heat exchanger models similar to that
developed by Sadler [7] but it was established for the R-410A
alternative refrigerant.
A model was suggested in a form of computer software to
be implemented for the prediction of the thermal
performance of the air cooled condensers by Tarrad (2010)
[9]. The results revealed that the cooling technique used for
the air stream before entering the condenser has a significant
effect on the thermal map. It improves the performance of the
condenser and reduces the required area for a specified
condensation load and steam loading. Altameemi (2011) [10]
accomplished experimental investigation for air cooled
condenser (ACC) and shell and tube type used as a single or
in a hybrid arrangement. He found that when the air flow rate
was doubled and its entering dry bulb temperature reduced
from (42) to (21)°C, the (ACC) average steam loading and
thermal load were increased by (22%). Pre-cooling of air
gave an increase in (ACC) steam mass flow rate of (0.58-
0.66) kg/h per each degree reduction of air dry bulb
temperature from (37.5°C) to (27°C) for constant air mass
flow rate and surface area.
The work of Tarrad and coworkers (2007-2009) [11-13]
was focused on the heat transfer performance and modeling
of air cooled heat exchangers. Their work showed that the
thermal enhancement is a dependent measure of the fin
geometric variables and row intensity of the air cooled heat
exchanger. Tarrad and Khudor (2015) [14] have presented
quite a simple and adaptable correlation for the air side heat
transfer coefficient based on a dimensional analysis. They
concluded that their correlation predicts the heat duty and
overall heat transfer coefficient of the case study heat
exchangers with total mean absolute errors of (13%) and
(10%) respectively. Tarrad and Altameemi (2015) [15]
implemented the step by step numerical technique along the
steam flow direction to rate a vertical orientation single pass
two tube rows heat exchanger. The simulated data showed
that the discrepancy for the heat duty was within (12)% and
(-5)% whereas the exit air temperature was underestimated
by (5)%.
In the present work a simulation model was built for
rating objectives of air cooled finned tube condenser used
in a water chiller unit using alternative refrigerants to R-22.
The model represents an accurate technical tool for the
thermal prediction of a suitable alternative that may be
implemented in an existing refrigeration unit without a
major modification. It depends on a marching a step by step
solution following the flow of refrigerant in a tube by tube
procedure. The most interesting and attractive result of the
present model is its capability to reveal the distribution map
of the operating conditions such as pressure, vapor quality,
air temperature and heat duty throughout heat exchanger
tube bank.
2. Experimental Rig
2.1. Overview
The used experimental rig is comprised of a water chiller
which was built for the objective of the present work. It
circulates R-22 as a refrigerant having a cooling capacity of
(1.5 kW). The apparatus arrangement together with the
instrumentation and measurement devices are shown in
figure 1. It consists of the basic components required for the
refrigeration cycle namely, evaporator, condenser,
compressor and expansion device.
Figure 1. A schematic diagram for the refrigerant side of the chiller,
Mahmood [16].
20 Ali Hussain Tarrad et al.: A Numerical Rating Model for Thermal Design of Air Cooled
Condensers in the Industrial Applications
Figure 2. A schematic diagram for the water side path of the test unit,
Mahmood [16].
The refrigerant side flow arrangement and instrumentation
are installed at selected ports around the rig on both of the
refrigerant and water sides. The water path through the
chiller is shown schematically in figure 2 for which the
temperature and flow rate were measured at the entering and
leaving sides. A water centrifugal pump is used to circulate
water between the evaporator vessel and external load. The
flow rate of the pump (5-30) lit/min with a head of (5.5-28)
m. The external load is represented by an (85) liter water tank
capacity equipped with electrical heater of (2000) watt. It is
made of insulated steel cylindrical vessel of (40) cm diameter
and (68) cm height. The water piping system was provided
with a bypass loop for the control purpose of the chiller
capacity and cycling mode tests. The condenser fan is the
axial AC type with air delivery (600/665) cfm, at rated speed
of (1400-1600) rpm. The operation temperature is in the
range of (-10 to +70)°C.
2.2. Condenser Geometry
The test condenser is shown in figure 3. It is a finned tube
heat exchanger, air cooled condenser. The physical
characteristics are shown in table 1. The tube layout and the
arrangement of refrigerant tubes are shown in figures (3.a)
and (3.b) respectively.
Figure 3. The geometry of the condenser of the test chiller.
Figure 4. A schematic diagram of the shell and coil evaporator, Mahmood
[16].
The condenser is manufactured in a way that the
refrigerant flows in single tube circuit having three tube rows
as shown in figure (3.b). A shell and coil evaporator was
designed and fabricated in the local market workshops, figure
4. The refrigerant flows inside the copper helical coil,
whereas the water is circulated on the shell side between the
evaporator and external load reservoir.
A reciprocating hermetic compressor charged with
polyolester oil as a lubricant. This type of oil is suitable to be
used with HCFC such as R-22 refrigerant and working with
the test HFC refrigerant. The expansion device was made of
(90) cm copper capillary tube of (1) mm internal diameter
and external diameter of (2) mm. It was selected and installed
American Journal of Mathematical and Computational Sciences 2016; 1(1): 18-28 21
as a part of the experimental test rig according to ASHRAE
(1979) [17]. The evaporator shell, water pump and piping
system were completely insulated with a sheet of Armaflex
having a thickness of (25) mm and thermal conductivity of (k
= 0.036) W/m.K. Full details for the experimental rig set-up
and construction may be found in Mahmood [16].
Table 1. Condenser Physical Characteristics, Mahmood [16].
Dimension specification Value
Height of the condenser, H, (mm) 279.4
width of the condenser, L, (mm) 254
depth of the condenser, Ddep, (mm) 65
Tube length (mm) 254
Inner tube diameter (mm) 7.93
Outer tube diameter (mm) 9.52
Transverse tube pitch (mm) 25.4
Longitudinal tube pitch (mm) 22.225
Number of tube circuits 1
Number of tubes per circuits 30
Total number of tubes 30
Number of tube rows 3
Number of tubes per row 10
Tube metal Copper
Tube metal thermal conductivity (W/m.K) 386
Inner tube surface Smooth
Fin thickness (mm) 0.15
Fin pitch (mm) 2
Number of fin per inch (FPI) 12
Fin type Louvered
Fin metal Aluminum
Fin metal thermal conductivity (W/m.K) 200
Total surface area of the condenser (m2) 4.074
Total bare tube surface area (m2) 0.228
Total exposed fin area (m2) 3.846
Four refrigerants, namely R-22, R-134a, R-407C and R-
404a were implemented during the tests. These refrigerants
were assessed in a drop-in technique to find out the best
alternative to the R-22 refrigerant circulated in a water
chiller. It is worth mentioning that Mahmood [16] stated that
the experimental data collected for the condenser has an
uncertainty for the measured performance parameters to fall
within (± 2%).
3. Model Methodology
Figure 5. A control volume of an individual tube.
The condenser model is based on a tube-by-tube approach
in backward scheme in view of vapor flow and cooling air
flow directions. Evaluation of performance for a single fined
tube is a basic part of the model, as in figure 5. The
performance of each tube is analyzed separately at a certain
time. Each tube is associated with refrigerant parameters,
specific air mass flow rate and inlet air temperature. In the
backward scheme, the selection of tubes for performance
evaluation is in the opposite of the refrigerant flow from the
outlet to the inlet.
Air mass flow rate was assumed to be uniformly
distributed over the whole coil face regardless of the coil and
fan respective locations. It was also assumed that there was
enough turbulence in the air stream passing through the coil
to provide effective mixing so that air of uniform properties
enters each tube bank. The idea of implementation of the step
by step technique with a detailed description in Tarrad [9],
Tarrad et al. [13] was considered in the present work for the
condenser rating methodology.
3.1. Refrigerant Side Heat Transfer
Coefficient
3.1.1. Single Phase
The Dittus-Boelter correlation was used to calculate the
single phase heat transfer coefficient for the turbulent flow,
Incropera and Dewitt (1996) [18]. For the single liquid phase
refrigerant, the heat transfer coefficient is expressed as:
�� � 0.023��.� ���.� ������ (1)
Where liquid Reynolds number and Prandtl number are
estimated as:
� � �����
(2)
�� � �������
(3)
This mathematical relation has been confirmed by
experimental data for the following conditions:
(0.7 ≤ Pr ≤ 160), (Re ≥ 10,000) and (L/di ≥ 10)
In the sub-cooled portion of the condenser in this study,
the temperature difference at the inlet and exit is usually less
than (10)°C, and the moderate temperature variation
assumption is valid. However, in the superheated portion of
the condenser, the inlet and exit temperatures can differ by as
much as (50)°C. Therefore, the more accurate Kays and
London (1984) [19] correlation was used in the present
model to predicted the heat transfer coefficient of the
superheated portion. The correlation is expressed as:
�� �� �� � �� !"# (4)
Where the coefficients ast and bst are as follows:
Laminar
Re < 3,500 ast = 1.10647, bst = -0.78992
Transition
3,500 ≤ Re ≤ 6,000 ast = 3.5194 x 10-7, bst = 1.038040
Turbulent
6,000 < Re ast = 0.2243, bst = -0.38500
The Stanton number, St is expressed as:
22 Ali Hussain Tarrad et al.: A Numerical Rating Model for Thermal Design of Air Cooled
Condensers in the Industrial Applications
�� � $%&'() (5)
The superheated vapor Reynolds and Prandtl numbers are
estimated as the following:
* � ����+
(6)
�* � �+��+�+
(7)
The thermal properties of the superheated vapor of
refrigerant are correlated in suitable curve fitting equations.
3.1.2. Two Phase
Shah (1979) [20] developed a heat transfer model for pure
fluids condensation. The condensation operating conditions
were the mass flux range to be within (11 < G < 211) kg/m2.s
and the reduced pressure of (0.002 < Pr < 0.44). He also
stated that the model should be restricted to (1< Prl < 13) and
(Rel > 350) due to limited data at lower Rel values. This
correlation was found to predict all the data considered with a
mean deviation of (17%), [20]:
� � � �� ,-1 − 01�.� +�.�34.56-78314.49(:4.;< = (8)
Where αl represent the liquid heat transfer coefficient
determined from Dittus-Boelter equation (1) and (Pr)
represent the reduce pressure. The Silver-Bell-Ghaly method,
Silver (1947) [21], Bell and Ghaly (1973) [22], is used to
predict condensation heat transfer coefficient of miscible
mixture, where all component are condensable. The effective
condensing heat transfer coefficient (αeff) for condensation of
mixture is calculated by the method as:
7>?@@ =
7>#A-31 +
B+>+ (9)
Where αtp (x) the condensation heat transfer coefficient is
obtained from Shah (1979) [20] correlation for pure fluid,
equation (8). The single phase heat transfer coefficient of the
vapor αg is calculated with the Dittus-Boelter turbulent flow
correlation using the vapor fraction of the flow in calculating
the vapor Reynolds number.
* = ���-7831�+ (10)
The parameter Zg is the ratio of the sensible cooling of the
vapor to the total cooling rate:
C* = 0DE* �FG?H�I (11)
Here (x) is the local vapor quality, (cpg) is the specific heat
of the vapor and ∆Tdew/dh is the slope of the dew point
temperature curve with respect to the enthalpy of the mixture
as it condenses. The total enthalpy change is that of the latent
heat plus sensible heat. The latter can be estimated as the
mean of the liquid and vapor specific heat applied to the
condenser temperature glide Thome (2007) [23].
Jℎ = ����L��+� �∆N*�O�' +ℎP* (12)
This method has been applied to hydrocarbon mixtures and
more recently to binary and ternary zeotropic refrigerant
blend by Cavallini et al. (1995) [24] and binary refrigerant
mixtures by Smit et al. (2001) [25].
3.2. Air Side Heat Transfer Coefficient
3.2.1. Flat Fins
The correlation of Gray and Webb (1986) [26] was
selected to calculate the air side heat transfer coefficient for
flat fins. The correlation provides an average value for the j-
factor for a heat exchanger with four or more tube depth
rows, no change in the j-factor after four rows is assumed.
The heat transfer coefficient is based on the Colburn j-factor
which is defined as:
Q = �� �� �� (13)
This relationship gives the following for the air convective
heat transfer coefficient, αa.
�R = ST�UVW��V()X ;� (14)
Where Gmax is the air mass flux through minimum flow
area calculated as:
YZR3 = ZV[\U�]
(15)
In the case of the present study, the minimum flow area is
estimated as:
^ZO_ = `a − bP�Pc-d − ef�1 (16)
And the collar diameter (Dc) is calculated as:
f� = Jg + 2�P (17)
The j-factor for four rows is calculated as:
Qh = 0.14g8�.�� �jkjl�8�.m�� � ��n�
�.��7� (18)
The Reynolds number based on the outside tube diameter
can be estimated by:
g = �UVW�n� (19)
To calculate an average value for the j-factor for heat
exchangers with less than four depth rows, jN (where N<4),
Gray and Webb (1986) [26] provided the following equation:
Q$ = 0.991Qh p2.248�.�q� �$h�8�.��7r
�.s�t-h8$1 (20)
Here j4 is obtained by equation (18). Tube-by-tube
simulation requires the availability of the air-side heat
transfer coefficient for a tube in a given row, Tarrad and
Altameemi (2015) [15]. Assuming that each row weights
equally on the average air-side heat transfer coefficient of the
American Journal of Mathematical and Computational Sciences 2016; 1(1): 18-28 23
coil, the heat transfer coefficient value for the depth row (N),
jN,R can be approximated by the formula, Domanski (1989)
[3]:
Q$,& � bQ$ −-b − 11Q$87 (21)
Where
jN, jN-1 = average j-factors for heat exchangers with (N) and
(N-1) depth rows, respectively, obtained by equation (20).
3.2.2. Lanced Fins (Louvered)
Lanced fins are those enhanced fins which have arrays of
small strips raised from the base plate. Nakayama and Xu
(1983) [27] proposed a heat transfer correlation for such fins.
Their formula is in the form of a heat transfer correlation for
a flat fin and a multiplier which provides correction for heat
transfer enhancement due to the raised strips. The lanced fin
enhancement multiplier is a function of the geometry
parameters shown in figure 6.
Figure 6. Geometry of the lanced (louverd) fin, Mahmood [16].
The proposed correlation has the following form:
vS � 1 2 1093 w�P� x7.�h
yz�.qhh8�.m� 2
1.097 � @� ��.�q yz�.�s�.�� (22)
Where
yz � -�_|871�|�|jkjl8�.�m}�nX (23.a)
The Reynolds number based on the hydraulic diameter
expressed as:
~ � ��UVW��� (23.b)
And the hydraulic diameter estimated as Kays and London
(1974) [28]:
f~ � h\U�]�G?A\n
(23.c)
^g � ^P 2^ (23.d)
^P � 2bP`df�'�c /b �}h Jg�� (23.e)
^ �b -�Jgd1 (23.f)
Where (Ao) is the total air side heat transfer area, fins and
tubes, (Af) is the fin side heat transfer area and (At) is the tube
side heat transfer area.
3.3. Fins and Surface Efficiency
In the present study the fins of condenser is continuous,
rectangular plates serving all tubes in the slab. The method
proposed by Schmidt (1945) [29], and described in
McQuiston (1994) [30], is sensitive to the pattern of tube
staggering and is employed here. The fin efficiency, ηf, is
calculated in terms of the fin root radius, ro and two
parameters, mes and φ:
�P � ����-Z?|)n�1Z?|)n� (24)
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. Staggered tube configurations.
Schmidt (1945) [29] 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:
&?)n � 1.27�-à / 0.317 �� (25)
The coefficients Ψ and Г are defined as:
� � jk�)n (26.a)
Γ � 7jk
���� 2jkXh �
7 �� (26.b)
Once the equivalent radius has been determined, the
equations for standard circular fins can be used. For this
study, the length of the fins is much greater than the fin
thickness. Therefore, the standard extended surface
parameter, mes can be expressed as:
24 Ali Hussain Tarrad et al.: A Numerical Rating Model for Thermal Design of Air Cooled
Condensers in the Industrial Applications
�'z � � I��\�
�7 �� �w�IV
� @x7 ��
(26.c)
y � �&?)n / 1��1 2 0.35 ln �&?
)n�� (26.d)
The total surface efficiency of the fin, ηs is therefore
expressed as:
�z � 1 / \@\n
`1 / �Pc (27)
For louvered fins, Perrotin and Clodic (2003) [31]
concluded that Schmidt’s circular fin approximation analysis
overestimates the fin efficiency, by up to (5%). This is
because the addition of the enhancement can alter the
conduction path through the fin. However, there is currently
no approximation method available in the open literature that
claims to be valid for enhanced fins.
3.4. NTU Effectiveness Relations
The effectiveness is the ratio of the actual amount of heat
transferred to the maximum possible amount of heat
transferred and expressed mathematically as:
� � �V�#�UVW (28)
The equations used to determine the effectiveness depend
on the temperature distribution within each fluid and on the
paths of the fluids as heat transfer takes place, i.e. parallel-
flow, counter-flow or cross-flow. For a cross-flow heat
exchanger with both fluids unmixed, the effectiveness can be
related to the number of transfer units (NTU) with the
following equation, Incropera and Dewitt (1996) [18]:
� � 1 / 0E �� 7�:�-bN�1�.���exp-/�)-bN�1�.t�1 / 1�� (29.a)
� � �[ DE (29.b)
�) � �U�]�UVW (29.c)
In the saturated portion of the condenser, the heat capacity
on the refrigerant side approaches infinity and the heat
capacity ratio goes to zero. When Cr=0, the effectiveness for
any heat exchanger configuration is:
� � 1 / 0E-/bN�1 (29.d)
The NTU is a function of the overall heat transfer
coefficient.
bN� � \�U�] (30)
7 \ � 7
¡|,V>V\V2 &@,V
¡|,V\V2¢ 2 &@,:
¡|,:\:2 7
¡|,:>:\: (31)
Where Rf,a and Rf,r is the fouling factor for the air and
refrigerant sides respectively, Rw is the wall thermal
resistance, ηs,a and ηs,r is the surface efficiency for the air and
refrigerant sides respectively. There are no fins on the
refrigerant side of the condensing tubes; therefore, the
refrigerant side surface efficiency is (1). Neglecting fouling
factors, Rf,a and Rf,r then:
�^ � w 7¡|,V>V\V
2 ¢ 2 7>:\:
x87
(32)
4. Model Results
4.1. Model Validation
The present model was verified by the implementation of
the experimental data collected for four refrigerants tested
with a water chiller. These were namely, the pure refrigerants
R-22 and R-134a and the zeotropic miscible refrigerant
mixtures R-407C and R-404A in the mode of steady state
drop-in technique. The model calculation scheme depends on
the prediction of the air exit dry bulb temperature that is
leaving the condenser on the lee side. Hence, this parameter
was considered as an indication for the uncertainty
percentage of the simulation process of the present model.
The uncertainty of each parameter and its discrepancy or
scatter from the experimental data was estimated from:
Φ¤ � ¥#¦?n:?#��V�8¥?WA?:�U?]#V�¥?WA?:�U?]#V� (33)
Here Φ represents either the exit air temperature or the
heat duty of the condenser.
Figures 8 showed a comparison for the experimental and
predicated condenser load for R-22, R-134a, R-407C and R-
404A respectively. The maximum discrepancy percentage
between experimental and predicted condenser load of R-22
was about (8%), while the predicted condenser load values of
R-134a were within (±8%). The corresponding predicted
condenser load values of R-407C were overestimated by
(8%). Therefore, the scatter of the predicted condenser load
for these refrigerants was within (±8%).
Figure 8. Comparison of the experimental and predicted condenser load.
R-404A showed the highest discrepancy, the condenser
load of R-404A was under predicted as much as (30%). This
American Journal of Mathematical and Computational Sciences 2016; 1(1): 18-28 25
could be attributed to the scatter of the predicted
condensation heat transfer coefficient of R-404A. This
concludes that the correlation used for this purpose was not
suitable or not accurate enough.
Figure 9 demonstrates the comparison for the measured
and predicated condenser air exit temperature (CAET) for R-
22, R-134a, R-407C and R-404A respectively. It is obvious
that the simulated results of the condenser air exit
temperature (CAET) were well predicted than that of the
condenser loads. The discrepancy percentage between
measured and predicted condenser air exit temperature
(CAET) of R-22 was about (-8%), whereas, the discrepancy
percentage of R-134a were within (±4%). The predicted
(CAET) of R-407C was around (4%) over predicted. R-404A
revealed the maximums discrepancy, it was under predicted
by about (15%).
Figure 9. Comparison of the measured and predicted condenser air exit
temperatures.
4.2. Visual Representation
4.2.1. Exit Air Temperature
The visual representation is considered more tangible for
the analysis presentation as presented by Domanski (1989)
[3] and Tarrad and Al-Nadawi (2015) [32]. In these figures
the assigned tubes with grey and red are the inlet and exit
ports of the refrigerant side respectively. Figures 10 showed
the (CAET) distributions over the condenser coil tubes for
the test refrigerants. The condenser layout, tube and rows are
well demonstrated by the schematic diagram shown in the
figure. The exit mean air temperature that is leaving the
condenser is also shown at the lee side of the condenser. The
data shows that as the air passes from row to row experiences
an increase in the predicted air temperature. It is obvious that
the simulated air tempera ture showed an excellent agreement
with the measured values to be within (±4)% for the R-22, R-
134a and R-407C. Whereas, the model showed a higher
scatter for the R-404A data, it underestimates the measured
exit air temperature by (15)%.
Figure 10. Condenser coil tube by tube air exit temperature distribution.
4.2.2. Heat Duty
A typical tube by tube heat duty distribution is shown in
figure 11 for the entire test refrigerants at different
operating conditions. It is obvious that lowest load is
exhibited by the tubes accommodated in row number (3),
the row where the superheated vapor enters the condenser
and the cooling air leaves. Here, the temperature difference
between both streams is low and the refrigerant heat
transfer coefficient is the lowest. Accordingly, the heat
absorbed by air at this row revealed the lowest rate among
the other rows.
Figure 12 demonstrated the total condenser coil load
variation with the tube number for R-22, R-134a, R-404A
and R-407C. The simulated refrigerants reveal the same
trend, the condenser load increased gradually in almost
linear relation. However, the condenser coil load of the first
row exhibited a higher numerical value than that of the
second and third rows. The condenser load of the simulated
refrigerant were, (2091 W), (1388 W), (2234 W) and (1768
W) for R-22, R-134a, R-407C and R-404A respectively. It
26 Ali Hussain Tarrad et al.: A Numerical Rating Model for Thermal Design of Air Cooled
Condensers in the Industrial Applications
is worth to mention here that the water chiller when
circulating R-134a throughout the unit exhibited the lowest
refrigeration load as stated by Tarrad et al. (2015) [33].
Accordingly, it reveals the lowest condenser load in
agreement with the energy conservation law in the
refrigeration cycle.
Figure 11. Condenser coil tube by tube load distribution.
Figure 12. Total condenser coil load variation with the number of tubes.
The entire group of curves showed almost the same
behavior but with different numerical values. The upper band
included the R-22, R-407C and R-404A with a close
predicted values and the R-134a revealed the lowest value of
the heat duty. Again here, R-407C showed a close
performance to that of the R-22 case due to the close values
of the refrigeration load of the chiller as shown by Tarrad et
al. (2015) [33].
4.2.3. Vapor Quality
The refrigerant vapor quality distribution (x) was
demonstrated in figure 13 for the test refrigerants. The vapor
quality variation showed a nonlinear behavior and R-134a
has a longest path for the sub-cooling stage of the refrigerant
through the condenser.
Figure 13. Refrigerant vapor quality (x) distribution.
5. Conclusions
The main findings of the present work are:
1. A simple and detailed air cooled condenser model has
been developed for pure and mixture refrigerants R-22,
R-134a, R-407C and R-404A.
2. The present model provided detailed information for the
condenser design and performance characteristic. It
offers a practical tool for the rating process of an
existing water chiller for refrigerant alternatives.
3. The model showed excellent agreement for the load
capacity and exit air temperature for the simulation of
R-22, R-134a and R-407C to be within (±8)% and
(±4)% respectively. The model underestimated the heat
load and exit air temperature for R-404A by (30)% and
(15)% respectively.
4. The model revealed its ability to predict the same trend
of the condenser heat duty in a similar fashion as that of
the refrigeration load of the water chiller measured
during the experiments.
American Journal of Mathematical and Computational Sciences 2016; 1(1): 18-28 27
Nomenclature
Symbol Description Units
A Area m2
Ac Cross sectional area m2
Af Fin area m2
Amin Minimum flow area m2
Ao Total heat transfer area on the air side m2
At Surface area of the tubes m2
ast Kays & London coefficient ---
bst Kays & London power coefficient ---
C Heat capacity W/K
cp Specific heat at constant pressure kJ/kg.K
Cr Heat capacity ratio ---
Dc Collar diameter m
Ddep Depth of heat exchanger m
DH Hydraulic diameter m
D Diameter m
Fj Lanced fin enhancement multiplier ---
G Mass flux kg/m2.s
g Gravitational acceleration m/s2
hfg Latent heat J/kg
j Colburn j-factor ---
j4 j-factor for four rows ---
k Thermal conductivity W/m.°C
L Length of tube m
ls Width of a stripe m
m˙ Mass flow rate kg/s
mes Extended surface parameter ---
N Number of rows ---
Nf Number of fins ---
Nt Number of tubes ---
Nu Nusselt number ---
ns Number of strips ---
P Pressure Pa
Pr Reduced pressure ---
Pr Prandtle number ---
Q Heat transfer W
Re Reynolds number ---
Re Fin equivalent radius m
Rf Fouling factor m2.°C/W
Rw Tube resistance m2.°C/W
ro Outside tube radius m
St Stanton number ---
S Fin spacing m
ss Length of a strip m
T Temperature °C
Tdew Dew point temperature °C
tf Fin thickness m
U Over all heat transfer coefficient W/m2.°C
V Velocity m/s
XL Longitudinal tube spacing m
XT Transverse tube spacing m
X Vapor quality ---
Zg
Ratio of the sensible cooling of the
vapor to the total cooling rate ---
Greek Symbols:
α Heat transfer coefficient W/m2.°C
αeff Effective heat transfer coefficient W/m2.°C
ε Effectiveness ---
ζ Tube per row ---
η Efficiency ---
ηf Fin efficiency ---
ηs Surface efficiency ---
λ Parameters m
µ Viscosity Pa.s
ρ Density kg/m3
τ Life time year
φ Fin efficiency parameter ---
Subscripts:
a Air
act Actual
g Vapor
in Inlet
l Liquid
max Maximum
meas Measured value
min Minimum
out Outlet
r Refrigerant
simu Simulated value
tp Two phase
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