### An algorithm for simulation of the performance of air-cooled heat

### exchanger applications subject to the inﬂuence of complex circuitry

### M.C. Kuo

a### , H.K. Ma

a### , S.L. Chen

a### , C.C. Wang

b,*a_{Department of Mechanical Engineering, National Taiwan University, Taipei 107, Taiwan}

b_{Energy and Resources Laboratories, Industrial Technology Research Institute, D400 ERL/ITRI Buliding 64, 195-6 Section 4,}
Chung Hsing Rd., Chutung, Hsinchu 310, Taiwan

Received 14 September 2004; accepted 21 April 2005 Available online 28 June 2005

Abstract

The present study develops an index technique to take into account the eﬀect of complex circuitry on the design of ﬁn-and-tube heat exchangers. A 4-index array technique is described in detail that is capable of handling complex circuitry up to second-order level. In addition, a complete modeling of the performance of an evaporator is made. For the performance of evaporations without curved conﬁguration, the proposed model can give good calculations with the experimental data.

2005 Elsevier Ltd. All rights reserved.

Keywords: Circuitry; Fin-and-tube heat exchanger; Evaporator

1. Introduction

In the implementation of the air-cooled heat exchang-ers in refrigeration application, complex circuitry is often encountered as shown in Fig. 1. This is because the process of heat transfer in the tube side involved phase change, giving rise to signiﬁcant volume changes were refrigerant evaporation or condensation taken place. For the same mass ﬂux, the vapor velocity is con-siderable higher than that of the liquid phase that even-tually leads to an unacceptable friction loss. As a consequence, split or combination of the refrigerant ﬂow inside the tube is a must to provide reasonable pressure drop of the refrigerant ﬂow.

In addition to the concern of frictional loss, there is another beneﬁt of employing multiple-circuitry design of the refrigerant system. As is well known, for eﬀec-tively improvement of the performance of air-cooled heat exchangers, passive enhancement techniques are

often employed. The methods includes: (1) by using en-hanced ﬁn surfaces; (2) by increasing total surface area; (3) by increasing the eﬀective mean temperature diﬀer-ence between the air ﬂow and refrigerant ﬂow. Well cir-cuitry design can provide a more uniform temperature distribution and a better heat transfer performance accordingly. Unfortunately, the design of the circuitry usually relied on experience. Rationally based methods are seldom found. There are some discrete simulation methods available in the literature, such as those

pro-posed by Mirth and Ramadhyani [1], and Vardhan

and Dhar[2], and Wang and Hihara[3]. However, these methods are applicable only to single-phase ﬂuid ﬂow system at a cross-ﬂow or a counter-cross ﬂow arrange-ment. For two-phase refrigerant based applications, extension of these methods requires keeping track of the complex circuitry. In the open literature, there was only limited experimental information concerning the circuitry design. For example, Ebisu et al. [4] reported

performances of air-cooled heat exchangers with

R-410A for three diﬀerent circuits. They reported that the heat exchanger performances for two and three

1359-4311/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2005.04.022

* _{Corresponding author. Tel.: +886 35 916 294; fax: +886 35 820 250.}
E-mail address:ccwang@itri.org.tw(C.C. Wang).

circuits surpassed that of 1-circuit design by 17% and 19%, respectively. Wang et al.[5]investigated the eﬀect of circuitry on the performance of air-cooled condens-ers. They had provided in-depth experimental informa-tion related to the eﬀect of circuitry in the air-cooled condensers. Their results showed that counter-cross ﬂow gave better performance than other arrangements for 1-circuit arrangements. However, the reversed heat con-duction from the inlet portion to the exit portion may oﬀset the beneﬁt of counter-cross arrangement. Wang et al.[6]performed experiments to examine the pressure drop of the refrigerant ﬂow in a counter, parallel, and z-shape circuitry in evaporators. Their results showed that the parallel-cross ﬂow circuit gives the largest pres-sure drop than other arrangements and generally the refrigerant-side pressure drops increase with frontal

velocities. However, for G = 200 kg/m2s, the pressure drops decrease with increase of frontal velocity. The unusual characteristics are likely related to the ﬂow pat-tern transition subjected to heat addition.

In contrast to experimental studies of the inﬂuence of the circuitry, theoretical study concerning the inﬂuence of the circuitry is even limited. Possible reason for this limitation is the lacks of eﬀective algorithm to keep track of the refrigerant ﬂow during the simulation. Domanski

[7] developed a HPSIM model that is able to handle

some limited circuitry design such as counter-current arrangement. The only algorithm available in the open literature was developed by Ellision et al.[8]. Their index is a tube-by-tube based technique and is limited to split-ting or combining from or to two tubes. As seen, Elli-sion et al.Õs eﬀort is the only general algorithm to Nomenclature

Af surface area of ﬁn (m2)

Ao total surface area (m2)

Ap,i inside surface area of tubes (m2) Ap,m mean heat transfer area of tubes (m2) Ap,o outer surface area of tubes (m2)

b0_{p} slope of a straight line between the outside
and inside tube wall temperatures (J/kg K)
b0_{r} slope of the air saturation curved at the mean

coolant temperature (J/kg K)

b0_{w;m} slope of the air saturation curve at the mean
water ﬁlm temperature of the external surface
(J/kg K)

b0_{w;p} slope of the air saturation curve at the mean
water ﬁlm temperature of the primary surface
(J/kg K)

Cp,a moist air speciﬁc heat at constant pressure

(J/kg K)

Dc tube outside diameter, include collar (m)

Di tube inside diameter (m)

F correction factor

Fp ﬁn pitch (m)

G mass ﬂux of refrigerant ﬂow (kg/m2s)

hc,o sensible heat transfer coeﬃcient for wet coils (W/m2K)

hi inside heat transfer coeﬃcient (W/m2K)

ho,w total heat transfer coeﬃcient for wet external ﬁn (W/m2K)

I, J tube index

I0 modiﬁed Bessel function solution of the ﬁrst

kind, order 0

I1 modiﬁed Bessel function solution of the ﬁrst

kind, order 1

i air enthalpy (J/kg)

ia,in inlet air enthalpy (J/kg) ia,out outlet air enthalpy (J/kg)

ifg latent heat of water vapor (J/kg)

ir,m saturated air enthalpy at the mean refrigerant temperature (J/kg)

is,p,i,m saturated air enthalpy at the mean inside tube wall temperature (J/kg)

is,p,o,m saturated air enthalpy at the mean outside tube wall temperature (J/kg)

is,w,m saturated air enthalpy at the mean water ﬁlm temperature of the external surface (J/kg)

Di mean enthalpy diﬀerence (J/kg)

K0 modiﬁed Bessel function solution of the

sec-ond kind, order 0

K1 modiﬁed Bessel function solution of the

sec-ond kind, order 1

kf thermal conductivity of ﬁn (W/m K)

kp thermal conductivity of tube (W/m K)

kw thermal conductivity of water (W/m K)

Mw parameter (1/m)

_

ma air mass ﬂow rate (kg/s)

Pl longitudinal tube pitch (m)

Pt transverse tube pitch (m)

_

Q_{wet} heat transfer rate (W)

T temperature (K)

Ta,i inlet temperature of air (K) Ta,o outlet temperature of air (K)

Tw,m mean temperature of the water ﬁlm (K)

Tp,i,m mean temperature of the inner tube wall (K) Tp,o,m mean temperature of the outer tube wall (K)

Tr,m mean temperature of refrigerant coolant (K)

Uo,w overall heat transfer coeﬃcient (kg/m2s)

xp thickness of tube wall (m)

yw thickness of the condensate water ﬁlm (m)

df ﬁn thickness (m)

index the complex circuitry. In that regard, it is the pur-pose of this study to present an alternative and simple algorithm that is capable of handling multiple splitting or combing of the tubes to record the index of the com-plex circuitry and to examine its applicability.

2. Proposed index technique

As given in the introduction, the complex circuitry in-volves splitting and combining of the refrigerant ﬂow. For easier tacking of the refrigerant ﬂow, the refrigerant ﬂow just after the expansion device is denoted as the main ﬂow. Notice that the main ﬂow before entering the heat exchangers can be of single or multiple circuits. The ﬂow is regarded as the ﬁrst level ﬂow if splitting is encountered. If there is further splitting in the ﬁrst level, the ﬂow is con-sidered as the second level. This study is limited to second level in describing the proposed algorithm. However, extending to the third or higher level is very straightfor-ward. As a consequence, an array with indices of n, i, j, and m is used and termed as [n, i, j, m]. The array is capable

of describing the index system of the refrigerant ﬂow. The indices of n, i, j, m are as follows:

n: denotes the number of main ﬂows before entering the heat exchangers.

i: refers to as the number of the ﬁrst level circuitry, and the associated values can be 0, 1, or 2. For example, the value of 0 indicates that it is at the position without splitting or is at the location where circuitry are combining at the end. The value of 1 indicates this part is inherited from the ﬁrst level. Notice that the value can be easily extended to higher value (>2) if splitting from or re-combining to for more than two tubes. The algorithm by Ellision et al. [8] is strictly limited to two tubes.

j: refers to as the number of the second level cir-cuitry, and the associated values can be 0, 1, or 2. For example, the value of 0 indicates that it is at the position without splitting or is at the loca-tion where circuitry is combining at the end. The value of 1 indicates this part is inherited from the ﬁrst level. Notice that the value can be easily extended to higher value (>2) if splitting from or re-combining to for more than two tubes.

m: denotes as the splitting/combining index, the corre-sponding value is from 0 to 6.

Relevant meaning is as follows: 0: normal node in the circuitry. 1: inlet of the heat exchanger. 2: splitting node.

3: after splitting. 4: before combining. 5: combining node.

6: outlet of the heat exchanger.

For easier understanding of the proposed index tech-nique, a couple of examples as schematically shown in

Fig. 2is adopted for demonstration. ForFig. 2(A), there
is only one main ﬂow entering the heat exchanger,
there-fore the n-index is always 1 for every node. As the
refrig-erant ﬂows further downstream, if there is no splitting,
the second index of i is 0 indicating that the ﬂow is in
the main ﬂow. As the main ﬂow meets the splitting point
at [1, 0, 0, 2] where the third index j is also 0 showing that
this node is still in the main ﬂow but the last index m is 2
showing that this node is a splitting node. Analogously,
the left branch of the circuitry all begins with an i-index
of 1 because this part belongs to the ﬁrst circuitry after
splitting whereas the right branch possesses an i-index of
2 revealing this part belongs to the second circuitry of
the ﬁrst level. Similarly, additional splitting node is
encountered at node [1, 1, 0, 2] as the refrigerant ﬂows
further downstream, thus the third index of the left
Air Flow
No tube
12
35
Inlet
**a**
38
36
37
34
32
30
16
15
14
13
28
31
33
29
26
27
25
Air Flow
4
8
10
11
9
6
7
5
24
23
22
21
20
19
18
17
Outlet
1
3
16
42
54
**b**
Inlet
55
28
27
26
53
43
44
47
48
56
52
51
50
22
21
49
46
45
25
24
23
20
19
18
17
32
2
8
3
4
7
12
40
11
10
14
41
13
39
6
9
5
36
38
15
37
34
35
33
30
29
Outlet
1 31
2

branch after node [1, 1, 0, 2] are 1 whereas the j-index of right branch is 2. Meanwhile, the third index of node [1, 2, 0, 3] and [1, 2, 0, 4] are all 0 because there is no addi-tional splitting. The j-index and m-index of node [1, 1, 0, 5] is 0 and 5 accordingly because the ﬂow is re-combining at this node. The m-index of node [1, 1, 0, 4] is 4 because this is a node before combining. For

Fig. 2(B), similar algorithm applies and the related node array is given in the Figure. Note that the present algo-rithm can subdivide the heat exchanger into smaller ele-ment as the node [1, 0, 0, 0] of Fig. 2(B) for more accurate calculations. The algorithm by Ellision et al.

[8] was unable to perform this duty. Advances of the proposed index technique are summarized as follows:

(1) The circuitry arrangement can be extended to both sides of the tube (in both active and inactive side, Ellision et al.Õs algorithm is applicable to active side only).

(2) Applicable to multiple (>2) splitting and com-bination.

(3) The proposed indexed array needs only very small storage to keep track of all the variations. (4) No restrictions to the ﬂuid ﬂow directions for

cir-cuitry arrangements, the refrigerant and air ﬂow arrangement can be of cross or counter-parallel arrangement in any instant.

(5) The proposed index technique can handle the momentum balance after splitting and re-combina-tion. As a consequence, mal-distributions within multiple circuitry are therefore predictable. To solve the refrigerant ﬂow distribution subject to the inﬂuence of circuitry, a step-by-step procedure is needed to balance the mass and pressure drop in the cir-cuitry. The following are examples showing this step-by-step procedure for the second level circuitry ofFig. 2(A):

1. For an initial assumption, the mass ﬂow in each circuit is obtained by dividing the total mass ﬂow rate to the number of the circuits.

2. Calculation of the heat transfer rate and the pres-sure drop from node [1, 0, 0, 1] to subsequent sec-tion (to node [1, 0, 0, 2]).

3. At the splitting node of [1, 0, 0, 2], the mass ﬂow rate is presumed to be equal. The initial value is the mass ﬂow rate divided by the number of cir-cuits. Calculations are then made from steps (4) to (12).

4. Solve the ﬁrst level result for node after [1, 1, 0, 3]. If the second level splitting point [1, 1, 0, 3] is encountered, perform the procedures of (5)–(9); otherwise, go to step (10).

5. Equally divide the refrigerant ﬂow rate to serve as the initial value of the entering mass ﬂow rate of [1, 1, 1, 3] and [1, 1, 2, 3].

6. Perform calculations from [1, 1, 1, 3] to [1, 1, 1, 4]. 7. Perform calculations from [1, 1, 2, 3] to [1, 1, 2, 4]. 8. Compare the outlet pressure at [1, 1, 1, 4] and

[1, 1, 2, 4]. If it is identical, go to step (9); if not, adjust the refrigerant mass ﬂow rate distribution at [1, 1, 1, 3] and [1, 1, 2, 3] and repeat procedure from (6).

9. Obtain the mean enthalpy of the refrigerant at [1, 1, 1, 4] and [1, 1, 2, 4] to serve as the initial refrig-erant enthalpy of [1, 1, 0, 5]. The total mass ﬂow rate at the combining node of [1, 1, 0, 5] is obtained from the summation of [1, 1, 1, 4] and [1, 1, 2, 4]. 10. Perform the calculation to [1, 1, 0, 4].

11. As shown in steps (4)–(10), perform the calcula-tions from [1, 2, 0, 3] to [1, 2, 0, 4].

12. Compare the outlet pressure at [1, 1, 0, 4] and [1, 1, 2, 4]. If identical, go to step (13); if not, adjust the refrigerant ﬂow distribution at [1, 1, 0, 3] and [1, 1, 2, 3] and repeat the procedures from step (4).

13. Obtain the mean enthalpy of the refrigerant at [1, 1, 0, 4] and [1, 1, 2, 4] to serve as the initial enthalpy of [1, 0, 0, 5]. The total mass ﬂow rate at the combining node of [1, 0, 0, 5] is the summation of [1, 1, 0, 4] and [1, 1, 2, 4].

14. Perform the calculation to [1, 0, 0, 6].

15. Perform the calculation for the n-branch (n = 2), return to step (2) to continue the calculation proce-dures from (2) to (14).

16. Perform the calculation until n is equal to the total number of main ﬂow. Then make a comparison of the outlet pressures for all the main ﬂow at the outlet, i.e. [1, 0, 0, 6], [2, 0, 0, 6] . . . etc. If it is not identical, adjust the mass ﬂow rate distribution of the branch of the main ﬂow rate then go to step (2) for repeating calculation.

17. Calculations are performed until convergence. Detailed ﬂow chart of the circuitry design is shown in

Fig. 3.

3. Solution algorithm of the heat exchanger model In additional to the proposed index technique, and the related balance of the refrigerant-side distribution, some additional heat transfer, and frictional equations are needed to perform the calculation. The present model focused on the performance of the evaporator. How-ever, change the simulation algorithm to the condenser should be very easy. For the heat transfer in the airside of the evaporator involves both heat and mass transfer. Thus, the enthalpy-based method proposed by Threl-keld[9]is adopted. The heat transfer rate in the evapo-rator is calculated as

_

Q_{wet}¼ _maðiai iaoÞ ð1Þ

where iaiand iaoare the inlet and outlet enthalpy of the air ﬂow. The rating equation of the dehumidifying heat exchanger, according to Threlkeld[9], is

_

Q_{wet}¼ UowAoFDim ð2Þ

where Uow is the enthalpy-based overall heat transfer coeﬃcient, F is the correction factor and Dim is the log mean enthalpy diﬀerence. For counter ﬂow arrange-ment, Dimis given as follows[10,11]:

Dim¼

ðiai iroÞ ðiao iriÞ ln iaiiro

iaoiri

ð3Þ

The enthalpy-based overall heat transfer coeﬃcient Uo,w in Eq.(2) is evaluated as[12]

Uo;w¼
b0_{r}Ao
hiAp;i
þb
0
pxpAo
kpAp;m
þ 1
ho;w
Ap;o
b0w;pAoþ
Afgf;wet
b0w;mAo
2
4
3
5
1
ð4Þ
where
ho;w¼
1
Cp;a
b0w;mhc;oþ
yw
kw
ð5Þ
Note that ywin Eq.(5)is the thickness of the
conden-sate water ﬁlm. A constant condenconden-sate ﬁlm thickness of
0.005 in., was proposed by Myers[11]. In practice,yw

kw

ac-counts only 0.5–5% comparing to Cp;a b0

w;mhc;oand is often

ne-glected by previous investigators. As a result, this term is
not included in the ﬁnal analysis. The wet ﬁn eﬃciency
in Eq.(4)is calculated as
gwet;f ¼
2rc
Mwðr2eq r2cÞ
K1ðMwrcÞI1ðMwreqÞ K1ðMwreqÞI1ðMwrcÞ
K1ðMwreqÞI0ðMwrcÞ þ K0ðMwrcÞI1ðMwreqÞ
ð6Þ
where
Mw¼
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2ho;w
kfdf
s
¼
ﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2hc;o
kfdf
s
ﬃﬃﬃﬃﬃﬃﬃﬃﬃ
b0_{w;m}
Cp;a
s
ð7Þ
rcis radius including collar and reqis the equivalent
ra-dius for circular ﬁn. For the present plate ﬁn geometry,

Threlkeld [9] recommended the following

approximation:
req¼
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
p_{t} pl
p
r
ð8Þ
Notice that the evaluation of wet ﬁn eﬃciency is quite
controversy in the open literature. Interested readers
should refer to a recent article by Lin et al. [13]for
fur-ther discussion. The present study adopts the
enthalpy-based wet ﬁn eﬃciency. Also shown in Eq. (4), there
are four quantities (b0w;m, b

0
w;p, b
0
p, and b
0
r) involving
en-thalpy–temperature ratios that must be evaluated. The
quantities of b0_{p}, and b0_{r} can be calculated as

b0_{r}¼ is;p;i;m ir;m
Tp;i;m Tr;m
ð9Þ
b0_{p}¼is;p;o;m is;p;i;m
Tp;o;m Tp;i;m
ð10Þ
The values of b0_{w;p}and b0_{w;m}are the slope of saturated
enthalpy curve evaluated at the outer mean water ﬁlm
temperature that is at the base surface and at the ﬁn
sur-face. Without loss of generality, b0_{w;p} can be
approxi-mated by the slope of saturated enthalpy curve
evaluated at the base surface temperature[12].
Unfortu-nately, there is no explicit way to evaluate b0_{w;m}, and it
must be determined by trial and error procedures. The
evaluation procedure is as follows:

(1) Assume a value of Tw,m and determine its
corre-sponding value of b0_{w;m}_{.}

(2) Obtain the overall heat transfer coeﬃcient, ho,w, from Eq.(5).

(3) Evaluate the wet ﬁn eﬃciency from Eq. (6). (4) Calculate the enthalpy-based overall heat transfer

coeﬃcient Uo,w from Eq.(4).

(5) Calculate the is,w,m using the following

equation;

is;w;m¼ i

Cp;aho;wgwet;f
b0_{w;m}hc;o
1 Uo;wAo
b0_{r}
hiAp;i
þ xpb
0
p
kpAp;m
ði ir;mÞ ð11Þ

(6) Determine Tw,mat is,w,m. If it is not the same with the assumed value, assume a new value and repeat the procedure.

circuitryanalysis start

n=1

[n,0,0,1] to [n,0,0,2] heat transfer & pressure drop

computation
meet [n,0,0,2]?
Pre-defined
*i*
*m*
*m*
*mn*,1 *n*,2 .... *n*/
.
.
.
.
=
=
=
Pre-defined
i=1
[n,i,0,3] to [n,i,0,2]
heat transfer & pressure drop

computation

meet [n,i,0,2] ?

to [n,i,0,4] heat transfer & pressure drop

computation i=Max? No No No i=i+1 P[n,1,0,4]=P[n,2,0,4]=…? No H [n,0,0,5]=summation of H [n,1,0,4],H [n,2,0,4]… to [n,0,0,6]

heat transfer & pressure drop
computation
n= Max ?
P[1,0,0,6]=P[2,0,0,6]=…?
end
No
n=n+1
...
/
2
1
1
=
=
=
=
*m*
*m*
*n*
*rate*
*flow*
*mass*
*total*
*mn*
.
.
.

Main Flow 1st Level

*i*
*m*
*m*
*m*.*n*,1=.*n*,2=....= .*n*/
Pre-defined
j=1
to [n,i,j,4]
heat transfer & pressure drop

computation
j=Max?
No
j=j+1
P[n,i,1,4]=P[n,i,2,4]=…?
No
H [n,i,0,5]=summationof
H [n,i,1,4],H [n,i,2,4]…
....
,
, 2
1*m*
*m*
*adjust*
.
. _{,} _{,}_{....}
2
,
1
, *n*
*n* *m*
*m*
*adjust*
.
. _{,} _{,}_{....}
2
,
,
1
,
,*i* *ni*
*n* *m*
*m*
*adjust*
.
.
No
2nd Level

The empirical correlations for various ﬁn patterns of the sensible heat transfer coeﬃcients ho in wet condi-tions can be summarized from a recent article by Wang et al. [14]. Calculation of the two-phase evaporation heat transfer coeﬃcient is based on the Kandlikar corre-lation[15].

4. Simulation procedures of the performance of the evaporator

For more accurate evaluation of the performance of the evaporator, the heat exchanger can be sub-divided into small elements such as shown inFig. 4. Calculation procedures of the performance of the small element are illustrated as follows:

(1) Given the inlet conditions of Tr,i, Ta,iand dAo. (2) Calculate the wet ﬁn eﬃciency from Eq.(6). (3) Assume the heat transfer rate of this element dQ.

(4) Obtain the outlet enthalpy of this element ia,o. (5) Calculate the in-tube wall temperature Tp,i. Then

b0_{r}can be obtained from Eq.(10).

(6) Calculate the in-tube wall temperature Tp,o. Then
b0_{p} can be obtained from Eq.(9).

(7) Calculate the ﬁlm temperature Tf and use the

aforementioned procedures to obtain b0_{w;m}_{.}
(8) Obtain the overall heat transfer coeﬃcient from

Eq.(4).

(9) Calculate the outlet enthalpy ia,o from the rate equation (Eq. (2)).

(10) If calculated result of ia,odoes not equal to its ori-ginal assumption from (3), then adjust the initially guessed value, repeat the procedures from (3) to (10).

(11) Continue to the next section. (12) Repeat (3)–(11).

5. Results and discussion

To verify the capability of the proposed modeling, calculated results were compared with the test results from ﬁve evaporators in the environmental chamber of Taiwan Hitachi Co. Detailed description of the test evaporators are tabulated in Table 1. Refrigerant R-22 is the working ﬂuid used for the simulation of the evap-orator. The performance tests were conducted in an envi-ronmental chamber that can provide temperature and humidity control. The schematic of the environmental

Ta,o Tr,o Tr,i Ta,i mr dma dAo

Fig. 4. Schematic of the small element of the modeled heat exchanger. Table 1

Conﬁgurations of the simulated heat exchanger and the simulated results

Item Case 1 Case 2 Case 3 Case 4 Case 5

Size and operation conditions Width (103m) 314 314 478 355 375

Height (103m) 325 325 325 325 325

No. of series 2 2 2 3 4

No. of section 13 13 14 15 16

Series spacing (103m) 21.65 21.65 21.65 21.65 21.65

Section spacing (103_{m)} _{25} _{25} _{25} _{25} _{25}

Pipe outer diameter (103_{m)} _{10.05} _{10.05} _{10.05} _{10.05} _{10.05}

Pipe thickness (103_{m)} _{0.455} _{0.455} _{0.455} _{0.455} _{0.455}

Fin pitch (103_{m)} _{1.6} _{1.5} _{1.5} _{2.0} _{1.8}

Fin thickness (103_{m)} _{0.11} _{0.11} _{0.11} _{0.11} _{0.11}

Total air ﬂow rate (CMM) 6.42 6.85 8.25 9.32 13.60

Coolant ﬂux (kg/h) 54.647 64.831 77.163 94.361 142.856

Temperature before expansion (C) 43.1 42.5 40.1 47.9 43.2

Inlet pressure (kPa) 650.2 611.0 630.6 660.0 660.0

Fin area (m2_{)} _{4.71} _{5.03} _{8.24} _{7.38} _{12.32}

Average air velocity (m/s) 1.05 1.12 0.82 1.17 1.51

Test results Outlet temperature (C) 9.1 8.2 9.2 10.3 14.2

(A) Capacity (kJ/h) 8490.4 10127.9 12346.4 14140.9 22464.2

Computation Outlet temperatur (C) 13.0 11.5 14.7 7.3 17.0

Outlet pressure (kPa) 635.3 594.1 605.7 627.5 581.5

(B) Capacity (kJ/h) 8647.3 10288.8 12605.7 12806.3 23127.8

Unit area capacity 1835.9 2045.5 1529.8 1735.3 1877.3

chamber is shown in Fig. 5. Notice that the major measuring apparatus in the environmental chamber are regularly calibrated. The test apparatus is based on the air–enthalpy method proposed by ANSI/ASHRAE standard[16]. Cooling capacity was measured from the enthalpy diﬀerence of the airﬂow rate in the indoor coil. Maximum uncertainty of the measured cooling capacity is less than 2%. The airﬂow measuring apparatus is

constructed based on ASHRAE 41.2 standard [17].

Refrigerant temperatures were measured by T-type ther-mocouples mounted on the surface of the copper tubes and are well-insulated from the ambient. Two pressure transducers were installed at the entrance and exit of the compressor to measure the discharge and suction pressure. The corresponding measurement uncertainties

of temperatures and pressure are 0.1C and 1 kPa,

respectively. Performance tests were conducted at stan-dard condition:

Indoor : 27 0.1 C DB; 19.5 0.1 C WB

Outdoor : 35 0.1 C DB; 24 0.1 C WB

Comparisons between the experimental results and the calculated results are tabulated in Table 1 and in

Fig. 6. As shown in the table and in Fig. 6, for cases 1–3 and case 5, the predictive cooling capacity of the proposed model against the test results is within 3%. This validates the predicted ability of the present model and the related index technique. However, one can see an under-prediction of 9.4% of the cooling capacity is seen for case 4. This is because of the curved

conﬁgura-tion of the evaporator in case 4 whereas the rest are of straight conﬁguration. In this regard, the related inﬂu-ence of airﬂow mal-distribution for case 4 is more pronounced.

6. Conclusion

The present study develops an index technique to take into account the eﬀect of complex circuitry and a relevant model to simulate the performance of the evap-orator. The proposed 4-index array technique is de-scribed in the present study that is capable of handling ROOM CONDITIONING APPARATUS FLOW AIR AIR FLOW MEASURING APPARATUS COIL SECTION

INDOOR SIDE TEST ROOM

OUTDOOR UNIT SECTION TEMPERATURE MEASURING INSTRUMENTS MANOMETER INDOOR TEST ROOM OUTDOOR SIDE

Fig. 5. Schematic of the test apparatus.

Fig. 6. Comparison of the simulated results with the experimental data.

complex circuitry up to the second-order level. A de-tailed example is given to describe the proposed tech-nique. The present index technique is capable of handling splitting or combining from more than two tubes and can have further subdivisions along the refrig-erant pass for more accurate calculation. In addition, a complete modeling of the performance of an evaporator is made. For the performance of evaporations without curved conﬁguration, the proposed model gives suﬃ-ciently accurate calculations with the experimental data.

Acknowledgements

This research was funded by the National Science Council (NSC 91-2623-7-002-020-ET) and Taiwan Hit-achi Co. (1999–2001). Dr. C.C. Wang wishes to thank the Energy R&D foundation funding from the Energy Bureau of the Ministry of Economic Aﬀairs, Taiwan, for supporting this work.

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