Characteristics of a series-connected two-evaporator refrigerating system

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Characteristics of a series-connected

two-evaporator refrigerating system

Chao-Jen Li, Chin-Chia Su

*

Department of Mechanical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan, ROC

Received 24 March 2004;accepted 14 July 2004 Available online 25 September 2004

Abstract

Based on the Buckingham Pi theorem, this study derives the dimensionless correlations to characterize a series-connected two-evaporator refrigerating system with propane (R-290) as the refrigerant. Experimental data are substituted into the correlations to demonstrate the most relevant factors. Simpliﬁed correlations are then obtained.

The analytical results show that the mass ﬂow rate of refrigerant ( _mr) is primarily aﬀected by the

con-densing pressure, length of the high-temperature capillary tube, and the subcooling of refrigerant, while the heat transfer coeﬃcients of refrigerant in the evaporators (hcHand hcL) are aﬀected by the condensing

pressure and the logarithmic-mean temperature diﬀerence of the speciﬁc evaporator. However, hcHand hcL

are also affected by the lengths of the low- and high-temperature capillary tube, respectively. Additionally, the ratio of the cooling capacity of the high-temperature evaporator to the total capacity (a) is primarily affected by the condensing pressure and the logarithmic-mean temperature difference of both evaporators. The differences between the calculated and experimental data are between4% and +5%, 16% and +16%, 12% and +16%, and 10% and +10% for _mr, hcH, hcL, and a, respectively.

Keywords: Two-evaporator;R-290;Refrigerating system;Dimensionless correlation

*_{Corresponding author. Tel./fax: +886 2 2368 7352.} E-mail address:chinchiasu@ntu.edu.tw(C.-C. Su).

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1. Introduction

From a thermodynamic viewpoint, a refrigerator with two evaporators in series and one cap-illary tube outperforms that with only one evaporator. Lorenz–Meutzner [1] proposed a two-evaporator refrigerator with zeotropic refrigerant R22/R11 and experimentally demonstrated a power saving of up to 20% compared to a conventional refrigerator with R-12. Simmons et al.

[2,3] proposed that the modiﬁed Lorenz–Meutzner cycle has a power saving of 6.5% over that

of the conventional refrigerator. However, the proposed models can only use zeotropic refriger-Nomenclature

Cp speciﬁc heat (J kg1K1)

d diameter of capillary tube (mm) D diameter of evaporator (mm) f frequency of the compressor (s1) hc heat transfer coeﬃcient (W m2K1) h enthalpy (J kg1)

L length of capillary tube (m)

LMTD logarithmic-mean temperature diﬀerence (K) _

m mass ﬂow rate (kg s1) Pc condensing pressure (Pa)

Q cooling capacity or heat transfer rate (W) T temperature (K)

U overall heat transfer coeﬃcient (W m2K1) x quality

DTsc subcooling (K)

q density (kg m3) l viscosity (Pa s)

a ratio of cooling capacity b range of maximum error P dimensionless parameter

Subscripts

f saturated liquid

H high-temperature evaporator or capillary tube hm heating medium

i inside o outside

in entering evaporator out leaving evaporator

L low-temperature evaporator or capillary tube r refrigerant

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ant. With pure, azeotropic, or zeotropic refrigerants, diﬀerent evaporating temperatures can be obtained by using the refrigerating system containing two capillary tubes and two evaporators connected in series[4].

The capillary tube reduces the pressure of the liquid refrigerant and regulates the ﬂow rate of refrigerant to the evaporator. Li et al.[5], Kuehl–Goldschmidt[6], and Wijaya[7]presented de-tailed test data on the performance of a family of capillary tubes charged with R-12, R-22, and R-134a, respectively.

Both homogeneous and separated models simulating the mass ﬂow rate of refrigerant through a capillary tube were developed to optimize the size of capillary tube[8–11]. However, the calculat-ing processes involved were highly complex. Dimensionless analyses[12–14]thus were applied for simplifying the calculating processes.

The performance of the evaporator in a refrigerating system can be aﬀected by the two-phase heat transfer coeﬃcient of refrigerant [15–18]. For a system with two evaporators connected in series, the distribution of the cooling load between the evaporators may vary. Further studies therefore are needed.

CFC and HCFC refrigerants, such as R-12 and R-22, with a high ozone depleting potential (ODP) and global warming potential (GWP) have had their use restricted [19]. The zero ODP and extremely low GWP characteristics of certain hydrocarbons (HCs), e.g., propane (R-290), are extremely attractive in this aspect. The refrigerating properties of R-290 closely resemble those of R-22, thus making R-290 a proposing alternative to R-22. However, the ﬂammability of R-290 in air should not be ignored.

This study develops the dimensionless correlations for the mass ﬂow rate of refrigerant ( _mr), the

heat transfer coeﬃcients of refrigerant in the high- and low-temperature evaporators (hcH and

hcL), and the ratio of the cooling capacity of the high-temperature evaporator to the total capacity

(a) based on the experimental results and Buckingham Pi theorem. Furthermore, the experimental measurements of _mr, hcH, and hcLare compared with the calculated results from the correlations

in the literature [12,15–18]. Finally, the relative errors of the correlations are analyzed.

2. Experimental apparatus

Fig. 1shows the experimental facility of a series-connected two-evaporator refrigerating system

with R-290. The test apparatus comprises a refrigerant loop and two heat-exchange fluid loops. The refrigerant loop consists of a reciprocating compressor, a condenser, a filter-dryer, a refrig-erant flow meter, a sight glass, an electromagnetic valve, two capillary tubes, two evaporators, and some valves. The states of the working fluids are monitored using T-type thermocouples and pressure gauges as illustrated inFig. 1.

The frequency converter controls the reciprocating compressor, and the output of the converter for stable operation can be adjusted between 40 and 80 Hz. The condenser is a ﬁnned-tube heat exchanger with a fan. The condensing pressure of the system is inﬂuenced by the rotating speed of the fan which is controlled via a voltage transformer.

The evaporators and capillary tubes are all made of copper and heat-insulated.Table 1lists the dimensions of these components. The two evaporators are double-tube type and have the same dimensions. Notably, Di,iand Di,odenote the inside diameters of the inner and outer tubes,

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respectively, while Do,iand Do,odenote the outside diameters of the inner and outer tubes,

respec-tively. The refrigerant ﬂows in one direction through the inner tube while the heating medium ﬂows in the opposite direction through the annular space between the inner and outer tubes. The heating media of both evaporators is a water/glycol (50/50 wt.%) mixture to avoid icing in the annular space. Notably, the low-temperature capillary tube is shorter than the high-tempera-ture counterpart, as the refrigerant within the low-temperahigh-tempera-ture capillary tube is all two-phase, while part of the refrigerant within the high-temperature capillary tube is liquid.

capillary tube (low T) power meter frequency converter flow meter P T water/glycol tank 5 T flow meter pump T 6 sight glass electromagnetic valve capillary tube (high T) evaporator (high T) P T P T 4 7 P T P T water/glycol tank T flow meter pump T 8 evaporator (low T) condenser compressor filter-dryer 2 T P T P 1 T P 3

Fig. 1. Schematic diagram of the experimental facility.

Table 1 Test conditions

Pc(kPa) f (Hz)

1764 1666 1568 1470 1372 40 50 60 70 80

dH(mm) dL(mm) Le(m) Di,i(mm) Do,i(mm) Di,o(mm) Do,o(mm)

1.0 1.4 2 8.7 9.525 14.85 15.875

LH(m) LL(m)

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Both the heat-exchange loops are composed of a refrigerator, pump, ﬂow meter, thermometer controller, and electrically heated unit. Depending on the operating conditions, the temperature of water/glycol entering the high- and low-temperature evaporators is set at around 25°C and 9.5 °C, respectively.

The experimental variables include the condensing pressure (Pc), lengths of the capillary tubes

for the high- and low-temperature evaporator (LH and LL), and compressor frequency (f). The

details of the test conditions are listed inTable 1.

3. Experimental results and analysis

3.1. Pressure-enthalpy diagram of the system

Fig. 2shows the pressure-enthalpy diagram of the system. The properties of refrigerant are

ob-tained using REFPROP designed by McLinden et al.[20]. The encircled numbers indicate the cor-responding locations as shown in Fig. 1. States 1, 2, 3, 4, and 8, are determined based on the measured pressures and temperatures. The enthalpy of state 5 (h5) equals that of state 4 (h4), since

the high-temperature capillary tube is insulated. State 5 thus is determined based on h5and the

measured P5.

Determining state 6 requires the following equations for heat transfer:

Qr ¼ _mr hð r;out hr;inÞ ð1Þ

Q_hm¼ _mhm cphm Tð hm;in Thm;outÞ ð2Þ

Fig. 2. A P–h diagram of the refrigerant within the system (Pc= 1666 kPa, LH= 2.5 m, dH= 1.0 mm, LL= 0.3 m, dL= 1.4 mm, f = 60 Hz).

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Qris assumed to be equal to Qhmsince both evaporators are insulated. For the

high-tempera-ture evaporator, _mr, water/glycol ﬂow rate ( _mhm), and the temperatures of water/glycol entering

and leaving the evaporator (Thm,inand Thm,out) are measured, while the speciﬁc heat of

water/gly-col (Cphm) is based on that in the literature[21]. Then, Qhmcan be obtained using Eq.(2). On the

other hand, hr,inequals h5. h6can thus be obtained through Eq.(1). Therefore, point 6 can be ﬁxed

using the calculated h6and measured P6. Since P7is measured and h7equals h6owing to the fact

that the expansion in the capillary tube is insulated, state 7 can then be allocated. Notably, the pressure drops in heat exchangers and pipelines are neglected. To check the inﬂuence of these pressure drops on the system performance, some tests were conducted. The experimental results showed that the pressure drop across the heat exchangers and pipelines was about 10 kPa, which is relatively small compared with that across each capillary tube (400–700 kPa).

3.2. Refrigerant ﬂow rate

The analytical process used to develop the dimensionless correlations to predict _mr in the

two-evaporator refrigerating system is based on the Buckingham Pi theorem. The Buckingham Pi the-orem describes the relation between a function expressed in terms of dimensional parameters and a related function expressed in terms of dimensionless parameters. The utilization of the Bucking-ham Pi theorem enables the important dimensionless parameters to be developed quickly and eas-ily. The ﬁrst step in this analysis is to determine the variables that may inﬂuence _mr as follows:

both the diameters and lengths of the high-temperature (dH and LH) and low-temperature

capil-lary tube (dLand LL), the inlet conditions of refrigerant (Pcand DTsc), the frequency of

compres-sor (f ), and the saturated properties of R-290 (liquid density qf, liquid viscosity lf, and liquid

speciﬁc heat cpf). Furthermore, LH and LL are non-dimensionalized by dH and dL, respectively.

However, to non-dimensionalize _mr, Pc, DTsc, and f, a new repeating variable d, based on the

def-inition of hydraulic diameter, is deﬁned as (d2_Hþ d2

LÞ ðdHþ dLÞ1. _mr can then be expressed as

_

mr¼ f1ðPc; LH; LL; dH; dL; d;DTsc;qf; cpf;lf; fÞ ð3Þ

where dH, dL, d, qf, lf, and cpf denote the repeating variables. Therefore, the dimensionless

cor-relation for _mr is P8¼ A PB1 P C 2 P D 3 P E 4 P F 5 ð4Þ

P1, P2, P3, P4, and P5in Eq.(4)denote the dimensionless parameters of Pc, LH, LL, DTsc, and

f, respectively, as shown inTable 2. The values of constant A and exponents of the P parameters are obtained by substituting the experimental values into the statistical software STATISTICA.

Table 3lists the resultant dimensionless correlations.

The range of maximum error, b, in Table 3 represents the maximum deviation of the experi-mental data from the predicted values, while the coeﬃcient of determination, R2, is a relative com-parison criterion between the experimental and predicted values. The dimensionless correlation improves as R2approaches 1.

The dimensionless correlations for the dependent parameters include both the detailed and sim-plified forms. The simsim-plified form is a function of the more important independent variables which are determined based on the relative values of the exponents of P parameters in the detailed form. Both detailed and simplified expressions of P8, Eqs. (5) and (6), are listed in Table 3.

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Moreover, R2of the simpliﬁed form of P8, Eq. (6), is 0.9521, which is comparable to that of the

detailed form, 0.9903. Therefore, Eq. (6) cannot only simplify the calculating process but also result in acceptable prediction.

Eq. (5) inTable 3shows that _mris aﬀected primarily by Pc, LH, and DTsc. Notably, _mrincreases

with Pc and DTsc, but decreases with LH. Since increasing DTsc increases the proportion of the

refrigerant in the liquid state in the capillary tube, _mr increases with DTsc. Notably, the eﬀect Table 2

Dimensionless parameters P group

Pi-groups Deﬁnition Eﬀect

P1 d2 qf Pc l2 f Condensing pressure P2 LH dH Geometry P3 LL dL Geometry P4 d2 q2 f cpf DTsc l2 f ! Subcooling P5 d2 f qf lf Compressor frequency P6 d2 q2 f cpf LMTDH l2 f ! LMTDH P7 d2 q2 f cpf LMTDL l2 f ! LMTDL P8 _ mr d lf

Mass ﬂow rate P9 hcH d cpf lf hcH P10 hcL d cpf lf hcL P11 QH QHþ QL Ratio of QH P12 1 x Quality Table 3

Dimensionless correlations of _mr, hcH, hcL, and a: Pn¼ A PB1 P C 2 P D 3 P E 4 P F 5 P G 6 P H 7 A B C D E F G H R2 _b_(%) _Eq. P8,a 101.438 0.411 0.425 0.055 0.2246 0.0243 – – 0.9903 4 to +5 (5) P8,b 101.678 0.492 0.426 – 0.164 – – – 0.9521 10 to +8 (6) P9,a 104.52 0.343 0.097 0.209 0.045 0.021 0.888 – 0.97412 16 to +16 (11) P9,b 105.535 0.389 – 0.165 – – 0.987 – 0.97181 16 to +18 (12) P10,a 106.095 0.038 0.185 0.08 0.023 0.00002 – 0.688 0.91753 12 to +16 (14) P10,b 106.451 – 0.185 – – – – 0.689 0.83736 16 to +23 (15) P11,a 101.416 0.253 0.0815 0.020 0.052 0.027 1.563 0.999 0.98818 10 to +10 (17) P11,b 100.95 0.324 – – – – 1.544 0.986 0.98611 10 to +10 (18)

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of Pc on _mr is more signiﬁcant than that of DTsc. Fig. 3shows that b for _mr using Eq. (5) is

be-tween4% and +5%, which agrees with the experimental data.

3.3. Heat transfer coeﬃcient of refrigerant

The heat transfer coeﬃcient of refrigerant (hcr) directly aﬀects the performance of the

evapo-rator, and thus a study of the heat transfer coeﬃcient of refrigerant is essential. In the experiment, the quality of refrigerant in the high- and low-temperature evaporators is diﬀerent, and the anal-ysis for hcrthus is divided into two categories (hcHand hcL).

For a given evaporator, the cooling capacity (Q) may be expressed as

Q¼ ðU AÞ ðLMTDÞ ð7Þ

where the products of the overall heat transfer coefficient (U) and the heat transfer area (A) and the logarithmic-mean temperature difference (LMTD) are defined as

ðU AÞ ¼ 1 hcr Ai þ R þ 1 hchm Ao 1 ð8Þ

ðLMTDÞ ¼ðThm;out Tr;inÞ Tð hm;in Tr;outÞ

ln ðThm;out Tr;inÞ

Thm;in Tr;out

ð Þ

ð9Þ

For both evaporators, the inside and outside heat transfer areas, Aiand Ao, are ﬁxed, while the

conduction resistances (R) are more or less constant. Keeping _mhm constant and assuming

negli-gible variations of Thm,in, the heat transfer coeﬃcients of the heating media (hchm) are more or less

ﬁxed. With all temperatures in Eq.(9)measured, the experimental values of hcHand hcL can be

obtained through Eqs.(2), (7), (8) and (9).

7 8 9 10 11 12 13 14

predicted mass flow rate (kg.h-1) 7 8 9 10 11 12 13 14

measured mass flow rate (kg

.h

-1 ₎

+5%

-4%

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For the two-phase ﬂow in the evaporator, the heat transfer involves both nucleate boiling and forced-convection. Since nucleate boiling heat transfer increases with LMTD [22] while forced-convection heat transfer increases with Reynolds number, which is proportional to _mr, the

dimen-sionless parameter of hcHis represented by P9as follows:

P9 ¼ A PB1 P C 2 P D 3 P E 4 P F 5 P G 6 ð10Þ

The dimensionless parameter of LMTDHis represented by P6, as listed inTable 2. Moreover,

Table 3lists both detailed and simpliﬁed expressions of P9, Eqs. (11) and (12).

The exponents of P parameters in Eq. (11) show that hcHis aﬀected primarily by Pc, LL, and

LMTDH. The eﬀect of Pc on hcHis more signiﬁcant than that of LL. Increasing Pc increases _mr,

and the pressure of the high-temperature evaporator, which in turn increases Tr,inin Eq.(9)since

the refrigerant in the high-temperature evaporator is two-phase. Consequently LMTDHdecreases

with Pc. The eﬀect of LMTDH induced by Pc seems to dominate that of _mr. Therefore, hcH

de-creases with Pc. Additionally, both _mr and LMTDH decreases with LL [4], which induce hcH to

decrease with LL. Intuitively, LH is a main inﬂuence on hcH. However, the pressure of the

high-temperature evaporator will decrease slightly with LH [4]. Accordingly, LMTDH increases

slightly with LH. On the other hand, _mr decreases with LH. Apparently, the eﬀects of LMTDH

and _mr induced by LH oﬀset each other. hcHtherefore is not noticeably aﬀected by LH.

R2of Eq. (12) is 0.97181, which is nearly the same as that of Eq. (11), 0.97412. Therefore, the simpliﬁed form of P9 may also result in good prediction accuracy. Fig. 4 shows that b for hcH

using Eq. (11) is between16% and +16%.

Similarly, the dimensionless parameter of hcL is expressed by P11 as

P10¼ A PB1 P C 2 P D 3 P E 4 P F 5 P H 7 ð13Þ 0 500 1000 1500 2000 2500 3000 3500 predicted hcH (W . m-2 . K-1) 0 500 1000 1500 2000 2500 3000 3500 measured hc H (W . m -2. K -1 ) + 16% -16%

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The dimensionless parameter of LMTDLis represented by P7as shown inTable 2.Table 3also

lists the detailed and simpliﬁed expressions of P10, Eqs. (14) and (15). Eq. (14) shows that LHand

LMTDL are the main factors aﬀecting hcL. hcL decreases with LH but increases with LMTDL.

Meanwhile, _mrdecreases but LMTDLincreases with LH[4]. Apparently, hcLdecreases with LHsince

the eﬀect of _mron hcLdominates that of LMTDLinduced by LH. Again, intuitively LLcould be

ex-pected to have a signiﬁcant eﬀect on hcL. However, both _mrand the pressure of the low-temperature

evaporator will decrease slightly with LL. Accordingly LMTDLincreases slightly with LL[4].

Appar-ently, the eﬀect of _mron hcLoﬀsets that of LMTDLwhen LLis changed. Therefore, hcLis not

sig-niﬁcantly changed by LL.Fig. 5shows that b for hcLusing Eq. (14) is between12% and +16%.

3.4. Ratio of the cooling capacity of the high-temperature evaporator

The relative cooling capacities of the two evaporators in the system may vary among applica-tions. Therefore, the ratio of the cooling capacity of the high-temperature evaporator to the total capacity (a) is an important system characteristic.Table 2lists the dimensionless parameter of a, whish is deﬁned as P11. Now a can be expressed as

P11¼ A PB1 P C 2 P D 3 P E 4 P F 5 P G 6 P H 7 ð16Þ

Table 3lists both detailed and simpliﬁed expressions of P9, Eqs. (17) and (18). The relative

val-ues of the exponents of P parameters in Eq. (17) show that a is primarily aﬀected by Pc, LMTDH,

and LMTDL. a decreases with Pcand LMTDLbut increases with LMTDH. However, the eﬀect of

LMTDLon a is more signiﬁcant than that of Pc. Notably, a does not change apparently with LH

and LL. When LHis increased, _mr decreases but DhHincreases. Therefore, the cooling capacity of

high-temperature evaporator, QH, remains more or less the same for diﬀerent LH [4].

Addition-ally, with increasing LL, the variation of QH will oﬀset that of QL. Therefore, a is not noticeably

aﬀected by LL. 1000 1500 2000 2500 3000 3500 4000 predicted hcL (W . m-2 . K-1) L (W . m -2 . K -1) 1000 1500 2000 2500 3000 3500 4000 measured +16% -12% hc

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R2of the simpliﬁed form of P11 is 0.98611, which is comparable to that of the detailed form,

0.98818. Therefore, a reasonable prediction may be given by Eq. (18).Fig. 6shows that b for a using Eq. (17) is between10% and +10%. The predictions are within the acceptable range from the viewpoint of heat transfer.

3.5. Correlations from literatures

For the mass flow rate of the fluid flowing through an adiabatic capillary tube, Bittle et al.[12]

developed a series of dimensionless correlations for _mr. For the subcooled inlet condition, the

cor-relation for _mr is[12]

P8;c¼ 0:0055 P0:54851 P0:36682 P 0:1624

4 ð19Þ

Fig. 7shows the comparison of _mr calculated by Eq.(19) with the present experimental

meas-urements, in which dH is used instead of d. Notably, the form of P8,cis the same as that of P8,b,

but some diﬀerences exist between the exponents of P parameters. For the two-phase inlet condition, the correlation is [12]

P8;d ¼ 1:31 104 P0:83261 P 0:2867

3 P

1:1013

12 ð20Þ

where P12= (1 x) represents the two-phase state of the entering refrigerant. Notably, the

diﬀer-ence between Eqs.(20) and (19)is the inlet state of the refrigerant.Fig. 7shows the comparison of _

mrcalculated by Eq.(20)with the present experimental measurements, in which P6and dLis used

instead of Pc and d, respectively. The analytical results show that b for _mr from Eq. (19) is

rea-sonable while that from Eq.(20) is not so good.

Notably, the correlations, Eqs. (19) and (20), can only predict _mr through one capillary tube.

Table 4 lists b induced by Eqs. (19) and (20). The analytical results show that the error range

0 20 40 60 80 100 predicted α (%) 0 20 40 60 80 100 measured α (%) +10% -10%

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between the measured and calculated results using the correlations, Eqs.(19) and (20), are wider than that using the correlation, Eq. (5).

For the two-phase heat transfer coeﬃcients in evaporators, hcHand hcL, some correlations may

be identiﬁed from various sources, such as [15–18]. Unfortunately these correlations are quite complex. Therefore, no details are listed here. However, hcH and hcL calculated by the

correla-tions from [15–18]are compared with the experimental measurements of hcH and hcL.

Table 4 lists the entire error range between the measured and calculated results using the

cor-relations from[15–18]. The analytical results show that both hcHand hcLby the correlation from [15] are over-predicted by about 0–40%, while those by the correlation from [16] are under-pre-dicted by about 0–35%. Notably, b for hcHand hcLfrom the correlations of[17,18]is smaller than

those from the correlations, Eqs. (11) and (14). However, the required variables of the correlations found here are much fewer than those of the correlations from [17,18].

Fig. 7. Measured _mr versus correlations from literature[12].

Table 4

bof _mr, hcH, and hcLcalculated by correlations with experimental data proposed by the paper

bof _mr, % bof hcH, % bof hcL, % Inlet subcooled[12] 12 to +5 – – Inlet two-phase[12] 22 to +10 – – Gungor–Winterton[15] – 40 to 8 31 to +2 Kandlikar[16] – 0 to +45 10 to +50 Steiner–Taborek[17] – 7 to +10 12 to +8 Wattelet et al.[18] – 10 to +9 11 to +9

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4. Conclusions

This study develops the dimensionless correlations for analyzing the characteristics of the ser-ies-connected two-evaporator refrigerating system with R-290 as the refrigerant. Some conclu-sions may be drawn as follows:

1. The dimensionless correlations for _mr, hcH, hcL, and a are developed based on the

experimen-tal results and Buckingham Pi theorem. Compared with the experimenexperimen-tal results, the accuracy of the dimensionless correlations for _mr is quite good, while that for hcH, hcL, and a is

acceptable.

2. _mr is primarily aﬀected by Pc, LH, and DTsc. The dominant factors for hcH are Pc, LL, and

LMTDH, while those for hcL are LH and LMTDL. As for a the dominant factors are Pc,

LMTDH, and LMTDL.

3. The frequency of the compressor is not a main inﬂuence on _mr, hcH, hcL, and a.

4. The accuracy predicted by some correlations from literatures is good. However, the speciﬁc correlations are much more complicated than those presented here.

5. The dimensionless correlations in this study may be applied to the design of a two-evaporator refrigerating system. However, the superheating degree of refrigerant may be considered a variable for further work. Moreover, the properties of other environment-friendly refriger-ants are worthy of further investigation. Additionally, the dimensionless correlations for R290 may be applied to other refrigerants with refrigerating properties close to R-290, such as R-22.

Acknowledgment

The authors would like to acknowledge the ﬁnancial support by the National Science Council of Taiwan under the contract of NSC89-2212-E-002-143.

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