A Numerical Rating Model for Thermal Design of Air …article.aascit.org/file/pdf/8250001.pdfbuild a...

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


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:



�� $%&'() (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


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�-Γ / 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:



�'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


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



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.


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

References

[1] Fischer, S. K. and Rice, C. K., “A Steady-State Computer Design Model for Air-to-Air Heat Pumps”, Oak Ridge National Laboratory, ORNL/CON-8-, Oak Ridge, TN, (1981).

[2] Domanski, P. and Didion, D., “Computer Modeling of the Vapor Compression Cycle with Constant Flow Area Expansion Device”, NBS Building Science Series 155, Washington, DC, May (1983).

[3] Domanski, P. A., “EVSIM – an Evaporator Simulation Model Accounting for Refrigerant and One Dimensional Air Distribution”, NISTIR 89-4133, U.S. Dept. of Commerce, NIST, Maryland 20899, (1989).

[4] Zietlow, D. C., Ragazzi, F., and Pedersen, C. O., “A Physically Based Computer Model for Mobile Air Conditioning Condensers Using Ozone-Safe Refrigerants”, University of Illinois at Urbana-Champaign, ACRC TR-17, April (1992).

[5] Bensafi, A. and Borg S., “Design and Simulation of Finned-Tube Heat Exchangers Using Pure and Mixed Refrigerants”, Proceedings of CLIMA 2000 Conference, August 30th to September 2nd, 1997, Belgium, Brussels, (1997).

[6] Mullen, C. E., Bridges, B. D., Porter, K. J., Hahn, G. W., Bullard, C. W., “Development and Validation of a Room Air Conditioning Simulation Model”, ASHRAE Transactions, Vol. 102, Part 2, (1998).

[7] Sadler, E. M., “Design Analysis of a Finned-Tube Condenser for a Residential Air-Conditioner using R22”, M.Sc. Thesis, Georgia Institute of Technology, (2000).



[8] Wright, M. F., “Plate-Fin-and-Tube Condenser Performance and Design for Refrigerant R-410a Air-Conditioner.”, M.Sc. Thesis, Georgia Institute of Technology, (2000).

[9] Tarrad, A. H., “A Numerical Model for Performance Prediction of Dry Cooling Conditions of Air Cooled Condensers in Thermal Power Plant Stations”, Engineering and Technology Journal, Vol. 28, No. 16, pp. 5271-5292, 2010.

[10] Altameemi, A. F., “Study and Evaluation of the Operation Characteristics for the Condensation Load Distribution in Hybrid Systems on the Condenser Side”, MSc. Thesis, Al-Mustansiriya University, Baghdad, June 2011.

[11] Tarrad A. H., Shehhab U. S., “The Prediction of Environment Effect on the Performance of a Vapour Compression Refrigeration System in Air Conditioning Application”, Journal of Engineering and Development. Vol. 11, No. 1, March 2007, pp.169-189.

[12] Tarrad, A. H., Khudor, D. S., and Abdul Wahed, M., “A Simplified Model for the Prediction of the Thermal Performance for Cross Flow Air Cooled Heat Exchangers with a New Air Side Thermal Correlation”, Journal of Engineering and Development, Vol. 12, No. 3, 2008.

[13] Tarrad, A. H., Saleh, F. A., and Abdulrasool, A. A., “A Simplified Numerical Model for a Flat Continuous Triangle Fins Air Cooled Heat Exchanger Using a Step by Step Technique”, Engineering and Development Journal, Vol. 13, No. 3, pp. 38-59, Al-Mustansiriya University, Baghdad, (2009).

[14] Tarrad, A. H. and Khudor, D. S., “A Correlation for the Air Side Heat Transfer Coefficient Assessment in Continuous Flat Plate Finned Heat Exchangers”, Transactions of the ASME, Journal of Thermal Science and Application, Vol. (7), No. 2, Paper No. TSEA-14-1194, DOI: 10.11151/1.4029459, 2015.

[15] Tarrad, A. H. and Altameemi, A. F., “Experimental and Numerical Model for Thermal Design of Air Cooled Condenser”, Global Journal of Researches in Engineering (GJRE-A), Mechanical and Mechanics Engineering, Volume 15, Issue 3, Version 1.0, pp. 11-26, 2015.

[16] Mahmood, D. M., “Experimental and Theoretical Evaluation for the Evolution in Alternatives Applications in Water Chillers”, MSc. Thesis, Mechanical Engineering Department, College of Engineering, Al-Mustansiriya University, Baghdad, Iraq, (2010).

[17] ASHRAE Handbook, “HVAC systems & Equipment”, American Society of Heating, Refrigeration, and Air Conditioning Engineers, Inc., New York, (1979).

[18] Incropera, F. P. and DeWitt, D. P., “Fundamentals of Heat and Mass Transfer”, Fourth Edition, John Wiley & Sons, New York, (1996).

[19] Kays, W. M. and London, A. L., “Compact Heat Exchangers”, Third Edition, McGraw-Hill, New York, (1984).

[20] Shah, M. M., “A General Correlation For Heat Transfer During Film Condensation Inside of Pipes”, Int. J. Heat and Mass Transfer, vol. 22, pp. 547-556, (1979).

[21] Silver, L., “Gas Cooling with Aqueous Condensation”, Trans. Inst. Chem. Eng., Vol. 25, pp. 30-42, (1947).

[22] Bell, K. J., Ghaly, M. A., “An approximate generalized design method for multi-component partial condensers”, AICHE Symposium Series, Vol. 69, pp. 72-79, (1973).

[23] Thome, J. R., “Engineering Data Book III”, Wolverine Tube Inc., (2008).

[24] Cavallini, A., Bella, B., Longo, G. A. and Rossetto, L., “Experimental Heat Transfer Coefficients during Condensation of Halogenated Refrigerants on Enhanced Tubes”, J. Enhanced Heat Transfer, Vol. 2, No. 1-2, pp. 115-125, (1995).

[25] Smit, F. J., Tome, J. R. and Meyer, J., “Heat Transfer Coefficients during Condensation of the Zeotropic Refrigerant Mixture R-22/R-142b”, J. Heat Transfer, Vol. 124, pp. 1137-1146, (2001).

[26] Gray, D. L. and Webb, R. L., “Heat Transfer and Friction Correlations for Plate Finned-Tube Heat Exchangers Having Plain Fins”, Proc. Of Eighth Int. Heat Transfer Conference, San Francisco, (1986).

[27] Nakayama, W. and Xu, L. P., “Enhanced Fins for Air-Cooled Heat Exchangers Heat Transfer and Friction Factor Correlations”, Proceedings of ASME JSME Thermal Engineering Joint Conference, p. 495, March 1983, ASME, New York, (1983).

[28] Kays, W. M. and London, A. L., “Compact Heat Exchangers”, 2nd Edition, McGraw-Hill, New York, (1964).

[29] Schmidt, T. E., “La Production Calorifique des Surfaces Munies d’ailettes”, Annexe Du bulletin De L’Institut International Du Froid, Annexe G-5, (1945).

[30] McQuiston, F. C. and Parker, J. P., “Heating, Ventilating and Air-Conditioning Analysis and Design”, John Wiley & Sons, (1994).

[31] Perrotin, T. and Clodic, D., “Fin Efficiency Calculation in Enhanced Fin-and-Tube Heat Exchangers in Dry Conditions”, Proceedings of the 21st International Congress of Refrigeration, Paper # ICR0026, August (2003).

[32] Tarrad, A. H. and Al-Nadawi, A. K., “A Rating Model for Air Cooled Condensers using Pure and Blend Refrigerants”, American Association for Science and Technology (AASCIT), American Journal for Science and Technology, 3 (1), 1-11, 2016.

[33] Tarrad, A. H., Saleh, F. A., and Mahmood, D. M., “A Thermal Assessment for Vertical Helical Immersion Coil Evaporator in a Water Chiller”, American Association for Science and Technology (AASCIT), American Journal of Energy and Power Engineering, 2 (5), pp. 62-73, September, 2015.

A Numerical Rating Model for Thermal Design of Air …article.aascit.org/file/pdf/8250001.pdfbuild a...

Documents

Transcript of A Numerical Rating Model for Thermal Design of Air …article.aascit.org/file/pdf/8250001.pdfbuild a...