An Algorithm for Simulation of the Performance of Air-cooled Heat Exchanger Applications Subject to the Influence of Complex Circuitry

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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,*

aDepartment of Mechanical Engineering, National Taiwan University, Taipei 107, Taiwan

bEnergy 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).

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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)

b0p slope of a straight line between the outside and inside tube wall temperatures (J/kg K) b0r slope of the air saturation curved at the mean

coolant temperature (J/kg K)

b0w;m slope of the air saturation curve at the mean water film temperature of the external surface (J/kg K)

b0w;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)

_

Qwet 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)

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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

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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).

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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

_

Qwet¼ _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

_

Qwet¼ 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 b0rAo 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 b0w;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 pt 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 b0p, and b0r can be calculated as

b0r¼ is;p;i;m ir;m Tp;i;m Tr;m ð9Þ b0p¼is;p;o;m is;p;i;m Tp;o;m Tp;i;m ð10Þ The values of b0w;pand b0w;mare 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, b0w;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 b0w;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 b0w;m.

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(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 b0w;mhc;o 1 Uo;wAo b0r 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 1m m adjust . . , ,.... 2 , 1 , n n m m adjust . . , ,.... 2 , , 1 , ,i ni n m m adjust . . No 2nd Level

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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

b0rcan be obtained from Eq.(10).

(6) Calculate the in-tube wall temperature Tp,o. Then b0p can be obtained from Eq.(9).

(7) Calculate the film temperature Tf and use the

aforementioned procedures to obtain b0w;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 (103m) 25 25 25 25 25

Pipe outer diameter (103m) 10.05 10.05 10.05 10.05 10.05

Pipe thickness (103m) 0.455 0.455 0.455 0.455 0.455

Fin pitch (103m) 1.6 1.5 1.5 2.0 1.8

Fin thickness (103m) 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

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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.

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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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數據

Fig. 1. Schematic of a refrigerant heat exchanger.
Fig. 1. Schematic of a refrigerant heat exchanger. p.3
Fig. 2. Examples of the proposed index techniques.
Fig. 2. Examples of the proposed index techniques. p.4
Fig. 3. Circuitry flow chart of the proposed index techniques.
Fig. 3. Circuitry flow chart of the proposed index techniques. p.6
Fig. 4. Schematic of the small element of the modeled heat exchanger.
Fig. 4. Schematic of the small element of the modeled heat exchanger. p.7
Fig. 5. Schematic of the test apparatus.
Fig. 5. Schematic of the test apparatus. p.8
Fig. 6. Comparison of the simulated results with the experimental data.
Fig. 6. Comparison of the simulated results with the experimental data. p.8

參考文獻

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