Condensation heat transfer and pressure drop of refrigerant R-410A flow in a vertical plate heat exchanger

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Condensation heat transfer and pressure drop of refrigerant

R-410A ﬂow in a vertical plate heat exchanger

W.S. Kuo

a

,Y.M. Lie

a

,Y.Y. Hsieh

b

,T.F. Lin

a,*

a

Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan, ROC b_{Department of Mechanical Engineering, Nan Kai Institute of Technology, Nantou, Taiwan, ROC}

Received 4 June 2005; received in revised form 30 July 2005 Available online 27 September 2005

Abstract

Heat transfer and associated frictional pressure drop in the condensing flow of the ozone friendly refrigerant R-410A in a vertical plate heat exchanger (PHE) are investigated experimentally in the present study. In the experiment two vertical counter flow channels are formed in the exchanger by three plates of commercial geometry with a corrugated sinusoidal shape of a chevron angle of 60. Downflow of the condensing refrigerant R-410A in one channel releases heat to the upflow of cold water in the other channel. The effects of the refrigerant mass flux,imposed heat flux,system pres-sure (saturated temperature) and mean vapor quality of R-410A on the meapres-sured data are explored in detail. The results indicate that the R-410A condensation heat transfer coefficient and associated frictional pressure drop in the PHE increase almost linearly with the mean vapor quality,but the system pressure only exhibits rather slight effects. Furthermore,increases in the refrigerant mass flux and imposed heat flux result in better condensation heat transfer accompanying with a larger frictional pressure drop. Besides,the imposed heat flux exhibits stronger effects on the heat transfer coefficient and pressure drop than the refrigerant mass flux especially at low refrigerant vapor quality. The fric-tion factor is found to be strongly influenced by the refrigerant mass flux and vapor quality,but is almost independent of the imposed heat flux and saturated pressure. Finally,an empirical correlation for the R-410A condensation heat transfer coefficient in the PHE is proposed. In addition,results for the friction factor are correlated against the Boiling number and equivalent Reynolds number of the two-phase condensing flow.

1. Introduction

Over the past decades among various hydrochloro-ﬂuorocarbon (HCFC) refrigerants,R-22 (CHClF2) has

been the most extensively used working ﬂuid in air conditioning and refrigeration systems because of its excellent thermal properties. However,many evidences

show the destruction of the ozone layer and the global warming problems related to R-22. This popular refrig-erant will be phased out in a short period of time (before 2020) since the chlorine it contains has an ozone deple-tion potential (ODP) of 0.055 and comparatively high global warming potential (GWP) of 1500 based on the time horizons of 100 years[1,2]. As a result,the search for a replacement for R-22 has been intensiﬁed in recent years. The technical committee for the Alternative Refrigerants Evaluation Program (AREP) has proposed an updated list of the potential alternatives to R-22.

*

Corresponding author. Tel.: +886 35 712121 55118; fax: +886 35 726 440.

E-mail address:tﬂin@mail.nctu.edu.tw(T.F. Lin).

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Some of the alternatives on the AREPÕs list are R-410A, R-410B,R-407C and R-507. Among these alternatives to R-22,refrigerant R-410A is the most widely used zero ODP refrigerant and is currently recognized as the main replacement to R-22. It is a mixture of R-32 and R-125 (50% by mass) which exhibits azeotropic behavior with a small temperature glide of about 0.1C. In order to properly use these new refrigerants,we need to know their thermodynamic,thermophysical,transport and heat transfer properties. Speciﬁcally,the detailed heat transfer characteristics of the condensation and boiling heat transfer and associated frictional pressure drops are very important in the design of heat exchangers used in many refrigeration and air conditioning systems. The main purpose of this study is to investigate the conden-sation heat transfer and associated frictional pressure drop for refrigerant R-410A in a vertical plate heat exchanger.

Several studies have been reported in the open litera-tures on the condensation heat transfer for refrigerant R-22 ﬂow in various enhanced tubes,especially the micro-ﬁn tubes[3–6],and the results were compared with

those for refrigerant R-134a. In the following the rele-vant literature on the forced convective condensation heat transfer for R-410A is briefly reviewed. Sami and Poirier[7]compared the evaporation and condensation heat transfer data for several refrigerant blends proposed as substitutes for R-22,including R-410A,R-410B, R-507 and the quaternary mixture R-32/125/143a/134a inside enhanced-surface tubings. They showed that the two-phase heat transfer coefficients and pressure drops increased with the refrigerant mass flux for all refriger-ants tested. The condensation heat transfer coefficients for R-410A,R-407C and R-22 flowing inside a horizon-tal smooth tube measured by Ebisu and Torikoshi [8]

indicated that the condensation heat transfer coefficient of R-410A was slightly lower than that of R-22. More-over,the R-410A condensation pressure drop was about 30% lower than that for R-22. The quantitative differ-ences in the pressure drops between R-410A and R-22 were mainly attributed to the differences in vapor density of two refrigerants. Similar study was carried out by Wijaya and Spatz[9]for refrigerants R-22 and R-410A in a horizontal smooth copper tube. They indicated that Nomenclature

A heat transfer area of the plate,m2 b channel spacing,m Bo Boiling number,dimensionless Co Convection number,dimensionless cp specific heat,J/kgC Dh hydraulic diameter, Dh= 2b, m f friction factor Fr Froude number,dimensionless g acceleration due to gravity,m/s2 G refrigerant mass flux,kg/m2s Geq equivalent all liquid mass flux

h heat transfer coeﬃcient,W/m2C ifg enthalpy of vaporization,J/kg

k conductivity,W/mC

L length from center of inlet port to center of exit port,m

LMTD log mean temperature diﬀerence,C

P pressure,Pa

Pr Prandtl number,dimensionless Q heat transfer rate,W

q imposed heat ﬂux,W/m2 Rwall thermal resistance of the wall

Rel Reynolds number, Rel¼GDllh,dimensionless Reeq equivalent all liquid Reynolds number,

dimensionless T temperature,C

U overall heat transfer coeﬃcient,W/m2_C

u velocity,m/s

v speciﬁc volume,m3_/kg

W mass ﬂow rate,kg/s X vapor quality Greek symbols DP pressure drop

DX total quality change in the exchanger q density,kg/m3 l viscosity,Ns/m2 Subscripts ave average de deceleration ele elevation exp experiment f frictional

fg diﬀerence between liquid phase and vapor phase

g vapor phase

i,o at inlet and exit of test section

l liquid phase

m average value for the two phase mixture or between the inlet and exit

man the test section inlet and exit manifolds and ports

p preheater

r refrigerant

tp two phase

w water

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the condensation heat transfer coefficients for R-410A were slightly higher than those for R-22,while the R-410A pressure drops were significantly lower than those for R-22. Condensation heat transfer and pressure drop of R-410A and R-22 inside a herringbone-type mi-cro-fin tube examined by Miyara et al.[10]showed that both the condensation heat transfer coefficient and pres-sure drop for R-410A and R-22 in the herringbone-type fin tube were higher than that in the helical micro-fin tube in the higher mass velocity region. For smooth horizontal tubes Chitti and Anand [11] showed that R-410A had about 15–20% higher regionally averaged condensation heat transfer coefficient when compared to R-22 at a given refrigerant mass flux rate. In a contin-uing study[12,13],Guo and Anand examined the con-densation of R-410A in a rectangular channel focusing on the measurement and prediction of condensation heat transfer coefficients and on the relationship between the heat transfer coefficient and two-phase flow regimes. Besides,the R-410A condensation heat transfer coeffi-cient was found to decrease with decreases in local qual-ity and refrigerant mass flux.

It is well known that plate heat exchangers (PHEs) have been extensively used in food processing,chemical reaction processes and many other industrial applications for many years due to their effectiveness,compactness, flexibility,cost competitiveness,and the accessibility of the heat-exchanger surface. Although they are used primarily for liquid-to-liquid heat transfer,their perfor-mance is also good in boiling and condensation applica-tions. Therefore,they have been introduced to the refrigeration and air conditioning systems as evaporators or condensers. The basic construction,plate patterns, flow arrangements,advantages and limitations of PHEs were clearly described by Shah and Focke[14]. Analyses of flow pattern in PHE to give some local information on the heat transfer and velocity field were carried out by Thonon et al.[15]. Besides,they proposed the heat trans-fer coefficient and pressure drop correlations for two-phase flows in PHE based on the models originally devel-oped for smooth tubes. Tribbe,Mu¨ller-Steinhagen and their colleague[16–18]recently measured pressure drop for steady adiabatic gas/liquid flow in a single channel of a plate frame heat exchanger. Their results indicated that the pressure drop was greatly influenced by the chan-nel geometry and it increased linearly with the flow quality.

In view of the scarcity in the two-phase heat transfer data for PHEs,Lin and his colleagues[19–23]recently carried out a series of experiments to investigate the evaporation,condensation,saturated and subcooled ﬂow boiling of refrigerant R-134a and R-410A in a ver-tical plate heat exchanger. Speciﬁcally,they [19,20]

experimentally measured the evaporation and condensa-tion heat transfer coeﬃcients and friccondensa-tional pressure drops for R-134a in a vertical PHE. They showed that

the evaporation heat transfer for R-134a flowing in the PHE was much better than that in circular tubes,partic-ularly in high vapor quality convection dominated re-gime. Both the heat transfer coefficient and pressure drop increased with the imposed heat flux,refrigerant mass flux and vapor quality. Furthermore,it was noted that at a higher system pressure the heat transfer coeffi-cients were slightly lower. Moreover,the rise in the heat transfer coefficient with the vapor quality was larger than that in the pressure drop. Hsieh and Lin[21] inves-tigated the saturated flow boiling heat transfer and asso-ciated pressure drop for R-410A in the PHE. Their data manifested that the saturated boiling heat transfer coef-ficient and pressure drop in the PHE increased almost linearly with the imposed heat flux and the effects of the R-410A mass flux on the heat transfer coefficient were significant at a high imposed heat flux. Later,they

[22]measured the subcooled flow boiling heat transfer of R-134a in the PHE. They also inspected the associated bubble characteristics such as bubble generation fre-quency and bubble size by visualizing the boiling flow. Finally,the measured data for the evaporation of R-410A in the PHE[23]indicated that both the evapora-tion heat transfer coefficient and fricevapora-tional pressure drop increased with the refrigerant mass flux at low vapor quality. In addition,raising the imposed heat flux was noted to significantly improve the evaporation heat transfer. However,the friction factor is insensitive to the imposed heat flux and refrigerant pressure.

The above literature review clearly reveals that although R-410A is one of the most possible substitutes for R-22,the boiling and condensation heat transfer data for R-410A are still very scarce. To complement our previous studies on the two-phase heat transfer of R-134a and R-410A in the plate heat exchanger [19– 23],the condensation heat transfer and associated pres-sure drop characteristics of refrigerant R-410A in a vertical plate heat exchanger are experimentally investi-gated in this study.

2. Experimental apparatus and procedures

The experimental apparatus established in the present study,as schematically shown inFig. 1,to investigate the condensation heat transfer and associated frictional pressure drop of refrigerant R-410A in a vertical PHE consists of four independent loops and a data acquisition system. It includes a refrigerant loop,two water loops (one for preheater and another for the test section), and a cold water–glycol loop. Refrigerant R-410A is cir-culated in the refrigerant loop. To obtain various test conditions of R-410A (including the imposed heat flux, refrigerant mass flux,system pressure and inlet vapor quality) in the test section,we need to control the temper-ature and flow rate in the other three loops.

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2.1. Refrigerant ﬂow loop

The refrigerant loop contains a variable-speed refrig-erant pump that delivers the subcooled refrigrefrig-erant to the preheater. The refrigerant mass flow rate is mainly con-trolled by an AC motor through the change of the inver-ter frequency. The flow rate can be further adjusted by regulating the bypass valve in the flow path from the refrigerant pump. To measure the refrigerant mass flow rate,an accurate mass flux meter (Micromotion,model DS12S-100SU) is installed between the refrigerant pump and preheater with a reading accuracy of ±1%. The pre-heater is used to evaporate the subcooled liquid refriger-ant R-410A to a specified vapor quality at the test section inlet by receiving heat from the hot water in the water loop. Finally,the vapor–liquid refrigerant mixture leaving the test section is condensed and sub-cooled by the low temperature water–glycol in the shell-and-coil heat exchangers acting as condenser and subcooler. An accumulator is connected to a high-pres-sure nitrogen tank to dampen the fluctuations of the flow rate and pressure. In addition,the loop also equips with a receiver,a filter/dryer,a release valve,a degassed valve and four sight glasses. The pressure of the refriger-ant loop can be controlled by varying the temperature

and ﬂow rate of the water–glycol in the condenser and subcooler. Two absolute pressure transducers are installed at the inlet and exit of the test section with res-olution up to ±2 kPa. Furthermore,a calibrated diﬀer-ential pressure transducer is used to measure the overall pressure drop across the refrigerant side of the vertical PHE. All the water and refrigerant temperatures are measured by Type T (copper–constantan) thermo-couples with a calibrated accuracy of ±0.2C. A poly-ethylene insulation layer of 5-cm thick is wrapped around the whole loop to reduce the heat loss to the ambient.

2.2. Plate heat exchanger

Three commercial SS-316 plates manufactured by the Kaori Heat Treatment Co. Ltd.,Taiwan,form the plate heat exchanger for the R-410A condensation heat trans-fer test. The plate surfaces are pressed to become grooved with a corrugated sinusoidal shape and 60 of chevron angle,which is the angle of V-grooves to the vertical axis of the plate. The detailed conﬁguration for the plate heat exchanger is illustrated schematically inFig. 2. The corrugated grooves on the right and left outer plates have a V shape but those in the middle plate

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have a contrary V shape on both sides. This arrange-ment allows the flow stream to be divided into two dif-ferent flow directions along the plates. Thus,the flow moves mainly along the grooves in each plate. Due to the contrary V shapes between two neighbor plates the flow streams near the two plates cross each other in each channel. This cross flow streams result in significant flow unsteadiness and randomness. In fact,the flow is highly turbulent even when the Reynolds number is low. In the plate heat exchanger three plates form two vertical coun-ter flow channels. Downflow of refrigerant R-410A in one channel releases heat to the upflow of the cold water in the other channel. The heat transfer rate in the test section is calculated by measuring the total temperature rise and the flow rate in the water channel.

2.3. Water loop for test section

The water loop for the test section in the experimen-tal system circulates the cold water through the test sec-tion. It contains a 40-l water thermostat with a 2.25-kW heater and an air cooled refrigeration system of 2.25-kW

cooling capacity intending to control the water temper-ature. A 0.5-hp water pump is used to drive the cold water through the test section at a specified water flow rate. To obtain the desired imposed heat flux in test sec-tion,a by-pass valve can also be used to adjust the water flow rate. The accuracy of measuring the water flow rate is ±0.5%.

2.4. Water loop for preheater

Another water loop designed for the preheater con-sists of a 125-l hot water thermostat and a water pump which drives the hot water at specified temperature and flow rate to the preheater. Similarly,a by-pass valve is also used to adjust the flow rate.

2.5. Water–glycol loop

Both the condenser and subcooler,which respectively condense and subcool the refrigerant R-410A leaving the test section,are cooled by an independent low-temperature water–glycol loop. The cooling capacity is

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3.5 kW for the water–glycol at20 C. A 0.5-hp pump is used to drive the water–glycol at a specified flow rate to the condenser as well as to the subcooler. A by-pass valve is also provided to adjust the flow rate.

2.6. Data acquisition

The data acquisition system includes a recorder (Yokogawa HR-2300),a 24 V–3 A power supply,and a controller. The water ﬂowmeter and diﬀerential pres-sure transducer need the power supply as a driver to out-put an electric current of 4–20 mA. The data signals are collected and converted by a data acquisition unit (Hy-brid recorder). The converted signals are then transmit-ted to a host computer through a GPIB interface for further calculation.

2.7. Experimental procedures

In each test the system pressure at the test section is first maintained at a specified level by adjusting the water–glycol temperature and flow rate through the con-denser and subcooler. Then,the vapor quality of R-410A at the test section inlet is kept at the desired value by adjusting the temperature and flow rate of the hot water loop in the preheater. Next,the heat transfer rate between the counterflow channels in the test section can be varied by changing the water temperature and flow-rate in the water loop for the test section. Meanwhile, by selecting the frequency of the inverter connecting to the refrigerant pump and by adjusting the by-pass valve, the R-410A mass flow rate in the test section is main-tained at a desired value.

During the test any changes of the system variables will lead to fluctuations in the temperature and pressure of the refrigerant flow. It takes about 20–100 min for the system to reach a statistically stable state at which vari-ations of the time-average inlet and outlet temperatures are both less than ±0.2C,and the variations of the pressure and imposed heat flux are within 1% and 4%, respectively. Then the data acquisition system is initiated to scan all the data channels for ten times in 50 s. The mean value of the data for each channel is used to calcu-late the condensation heat transfer coefficient and asso-ciated frictional pressure drop. Additionally,the flow rate of water in the test section should be high enough to have turbulent flow in the water side so that the asso-ciated single-phase heat transfer in it is high enough for balancing the condensation heat transfer in the refriger-ant side.

Before examining the R-410A condensation heat transfer characteristics,a preliminary test for single-phase water-to-water convective heat transfer in the ver-tical plate heat exchanger is performed. The WilsonÕs method[24]is adopted to calculate the relation between the single-phase heat transfer coeﬃcient and the ﬂow

rate from these data. The single-phase heat transfer coef-ﬁcient can then be used to analyze the data acquired from the condensation heat transfer experiments. 2.8. Uncertainty analysis

The uncertainties of the experimental results are ana-lyzed by the procedures proposed by Kline and McClin-tock [25]. The detailed results from the present uncertainty analysis for the experiments conducted here are summarized inTable 1.

3. Data reduction

The reduction of the data for the single-phase con-vection heat transfer coeﬃcient in the vertical plate heat exchanger has been performed by Hsieh and Lin[21].

The reduction procedures for the condensation heat transfer coeﬃcient from the raw data measured here are described in the following. Firstly,the total heat transfer rate between the counter ﬂows in the PHE is calculated from the cold water side,

Q_w¼ Ww cp;w ðTw;o Tw;iÞ ð1Þ

Then,the refrigerant vapor quality at the test section in-let is evaluated from the energy balance for the pre-heater. Based on the measured temperature drop and ﬂow rate on the water side,the heat transfer in the pre-heater is calculated from the relation

Qw;p¼ Ww;p cp;w ðTw;p;i Tw;p;oÞ ð2Þ

Table 1

Summary of the uncertainty analysis

Parameters Uncertainty

Absolute value Relative value (%) PHE geometry

Length,width and thickness ±5· 103m ±1.5 Area of the plate ±7· 105_m2

±2.0 Sensors Temperature, T ±0.2C ±3 Temperature diﬀerence, DT ±0.2C ±4.5 System pressure, P ±200 Pa ±1 Diﬀerential pressure, DP ±200 Pa ±1.5

Water ﬂow rate, W ±0.02 kg/s ±2

Mass ﬂux of refrigerant, G ±2 kg/m2_s _±2 Condensation heat transfer

Average vapor quality, Xm ±0.05 ±8

Boiling heat ﬂux, q ±1.5 kW/m2 ±6.5 Heat transfer coeﬃcient, hr ±300 W/m

2

C ±17.5 Frictional pressure drop, DPf ±650 Pa ±16.8

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The heat transfer from the water to the refrigerant in the preheater results in the rise of the refrigerant tempera-ture to the saturated state (sensible heat transfer) and in the evaporation of the refrigerant (latent heat trans-fer). Thus

Qw;p¼ Wr cp;r ðTr;p;o Tr;p;iÞ þ Wr ifg Xp;o ð3Þ

The above two equations can be combined to evaluate the refrigerant quality at the exit of the preheater,that is considered to be the same as the vapor quality of the refrigerant entering the test section. Speciﬁcally, Xi¼ Xp;o¼ 1 ifg Qw;p Wr cp;r ðTr;p;o Tr;p;iÞ ð4Þ The change in the refrigerant vapor quality in the test section is then deduced from the heat transfer to the refrigerant in the test section,

DX ¼ Qw

Wr ifg

ð5Þ The overall heat transfer coeﬃcient U between the two counter channel ﬂows can be expressed as

U¼ Qw

A LMTD ð6Þ

here the log-mean temperature diﬀerence (LMTD) is determined from the relation

LMTD¼ððTr;o Tw;iÞ ðTr;i Tw;oÞÞ ln ðTr;oTw;iÞ

ðTr;iTw;oÞ

h i ð7Þ

with Tr,iand Tr,obeing the saturated temperatures of

R-410A corresponding respectively to the inlet and outlet pressures in the refrigerant flow in the PHE. Finally, the condensation heat transfer coefficient in the flow of R-410A is evaluated from the equation

hr¼ 1 1 U 1 hw Rwall A ð8Þ

where hw is calculated from the single-phase

water-to-water heat transfer test.

To evaluate the friction factor associated with the R-410A condensation in the refrigerant channel in the vertical PHE,the frictional pressure drop DPf is

calcu-lated by subtracting the pressure losses at the test section inlet and exit manifolds and ports DPman,and by adding

the deceleration pressure rise during the R-410A con-densation DPde and the elevation pressure rise DPele

from the measured total pressure drop DPexp in the

refrigerant channel,

DPf¼ DPexp DPmanþ DPdeþ DPele ð9Þ

The deceleration and elevation pressure rises are esti-mated by the homogeneous model for two-phase gas– liquid ﬂow[26], DPde¼ G2 vfg DX ð10Þ DPele¼ g L vm ð11Þ where vmis the mean speciﬁc volume of the vapor–liquid

mixture in the refrigerant channel when the vapor and liquid are homogeneously mixed and is given as vm¼ ½Xm vgþ ð1 XmÞ vl ¼ ½vlþ Xm vfg ð12Þ

The pressure drop in the inlet and outlet manifolds and ports was empirically suggested by Shah and Focke[14]. It is approximately 1.5 times the head due to ﬂow expan-sion at the test section inlet

DPmanﬃ 1:5 u2 m 2vm i ð13Þ where um is the mean ﬂow velocity. With the

homoge-nous model the mean velocity is

um¼ G vm ð14Þ

Based on the above estimation,the deceleration pressure rise and the pressure losses at the test section inlet and exit manifolds and ports are found to be rather small. In fact,the summation of DPdeand DPmanranges from

1% to 3% of the total pressure drop. According to the deﬁnition ftp¼ DPf Dh 2G2_v m L ð15Þ the friction factor for the condensation heat transfer of refrigerant R-410A in the PHE is obtained.

4. Results and discussion

In the present study of R-410A condensation heat transfer in the vertical plate heat exchanger,the conden-sation temperature of R-410A is varied from 20.0C to 31.5C (saturated pressure from 1.44 MPa to 1.95 MPa) for the refrigerant mass ﬂux and imposed heat ﬂux respectively ranging from 50 kg/m2_{s to 150 kg/m}2_s

and from 5 kW/m2 to 20 kW/m2. In what follows the measured condensation heat transfer coeﬃcient and fric-tional pressure drop are presented in terms of their vari-ations with the mean vapor quality in the test section. Moreover,comparisons of the present data for R-410A with those for R-134a in the same PHE from Yan et al. [20] and with the results for R-410A in a smooth pipe from Ebisu and Torikoshi [8]and Wijaya and Spatz [9] are also conducted. Finally,correlation equations for the present data are proposed.

4.1. Condensation heat transfer

Effects of the refrigerant mass flux,imposed heat flux and system pressure (refrigerant saturated temperature)

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on the R-410A condensation heat transfer in the PHE are now inspected. Selected measured data are presented

in Fig. 3 to illustrate the changes of the condensation

heat transfer coefficient with the mean vapor quality in the test section for various flow and thermal conditions. The effects of the refrigerant mass flux are illustrated first inFig. 3(a) by presenting the variations of the mea-sured condensation heat transfer coefficient with the mean vapor quality at the saturated pressure of 1.44 MPa (Tsat= 20C) and imposed heat flux of

10 kW/m2 for the refrigerant mass ﬂux ranging from 50 kg/m2s to 150 kg/m2s and the mean vapor quality varying from 0.10 to 0.80. In the plots Xmdenotes the

average vapor quality in the PHE estimated from Xi

and DX. These results indicate that at given refrigerant mass flux,imposed heat flux and system pressure,the R-410A condensation heat transfer coefficient increases almost linearly with the mean vapor quality of the refrig-erant in the PHE. This increase is rather significant. Spe-cifically,a large increase in hrwith Xmis noted for a high

refrigerant mass ﬂux (G = 150 kg/m2s). For instance,at P = 1.44 MPa, q = 10 kW/m2 _{and G = 150 kg/m}2_{s the}

condensation heat transfer coeﬃcient at the mean vapor quality of 0.80 is about 55% larger than that at Xm= 0.10. This obviously results from the simple fact

that in the higher vapor quality regime the vapor and li-quid shear stresses on the plate surface are much larger, meanwhile the liquid ﬁlm is relatively thin. This,in turn, reduces the resistance of heat transfer from the plate sur-face to the refrigerant.

The results inFig. 3(a) also demonstrate that a rise in the refrigerant mass flux always produces a significant increase in the condensation heat transfer coefficient at high vapor quality mainly due to the convective effect. High convective effect is caused by the high vapor ity and high refrigerant mass flux. In the low vapor qual-ity regime (Xm< 0.30) the condensation heat transfer

coefficient is only slightly affected by the refrigerant mass flux. As the mean vapor quality exceeds 0.4,the conden-sation heat transfer coefficient affected by the mass flux is clearly noted. Besides,for the higher G the heat trans-fer coefficient rises with the vapor quality more quickly than that for the lower mass flux. For example,the con-densation heat transfer enhances by a factor of 1.1 for G raised from 50 to 150 kg/m2_{s at X}

m= 0.10. However at

Xm= 0.80 the enhancement factor is increased to 1.5.

This is conjectured that at the high vapor quality and high refrigerant mass flux,the void fraction of the refrig-erant is very high and the vapor flow moves turbulently at a high speed,which in turn results in a substantial rise in the condensation heat transfer coefficient in the PHE. Next,the condensation heat transfer affected by the imposed heat flux is shown in Fig. 3(b) by presenting the variations of the heat transfer data with the mean vapor quality for three heat fluxes of 10,15 and 20 kW/m2at G = 100 kg/m2s and P = 1.44 MPa. Note that the condensation heat transfer coefficient increases apparently with the imposed heat flux. Compared with the refrigerant mass flux effects shown inFig. 3(a),the imposed heat flux exhibits a slightly stronger effect on

0.0 0.2 0.4 0.6 0.8 1.0 X_m 0.0 0.2 0.4 0.6 0.8 1.0 X_m 0.0 0.2 0.4 0.6 0.8 1.0 X_m 2000 4000 6000 2000 4000 6000 2000 4000 6000 hr (W/m 2 oC) at P=1.44 MPa, q=10 kW/m2 G = 50 kg/m2_s G = 100 kg/m2_s G = 150 kg/m2_s q = 10 kW/m2 q = 15 kW/m2 q = 20 kW/m2 at P=1.44 MPa, G=100 kg/m2 s at G=50 kg/m2 s, q=15kW/m2 P = 1.44 MPa P = 1.65 MPa P = 1.95 MPa

(a) Condensation Heat Transfer Coefficient of R-410A in PHE (b) Condensation Heat Transfer Coefficient of R-410A in PHE (c) Condensation Heat Transfer Coefficient of R-410A in PHE

Fig. 3. Variations of condensation heat transfer coefficient with mean vapor quality for various refrigerant mass fluxes (a),imposed heat fluxes (b),and system pressures (c).

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the condensation heat transfer coeﬃcient over the entire range of the vapor quality tested here.

Then,how the refrigerant saturated pressure affects the R-410A condensation heat transfer coefficient is exemplified in Fig. 3(c) by presenting the data at q = 15 kW/m2_{and G = 50 kg/m}2_{s at different saturated}

pressures for P = 1.44,1.65 and 1.95 MPa which respec-tively correspond to the saturated temperatures of

20C,25 C and 31.5 C for refrigerant R-410A. The re-sults indicate that an increase in the system pressure leads to a rather slight change in the condensation heat transfer coeﬃcient.

Finally,inFig. 4we compare the present data for the R-410A condensation heat transfer coeﬃcient with those for R-134a in the same PHE reported by Yan et al.[20]

and with those for R-410A in a horizontal smooth pipe

(a) Comparison of the Present data with Yan & Lin

(b) Comparison of the Present Data with Ebisu & Wijaya et al

P=1.44 MPa, G=50 kg/m2_{s, q=10 kW/m}2_{(Present data)}

P=0.70 MPa, G=60 kg/m2_{s, q=10 kW/m}2_{(Yan et al., 1999)}

P=3.04 MPa, G=300 kg/m2_{s, q=7.5kW/m (Ebisu & Torikoshi,1998)}2

P=2.80 MPa, G=481 kg/m2_{s (Wijaya & Spatz, 1995)}

0.0 0.2 0.4 0.6 0.8 1.0 2000 4000 6000 hr (W /m 2 oC ) 0.0 0.2 0.4 0.6 0.8 1.0 Xm 2000 4000 6000 8000 hr (W/m 2 oC )

Fig. 4. Comparison of the measured R-410A condensation heat transfer coeﬃcients for PHE with those for (a) R-134a in the same PHE from Yan et al. (1999) and (b) R-410A in a horizontal smooth tube from Ebisu and Torikoshi (1998) and from Wijaya and Spatz (1995).

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measured by Ebisu and Torikoshi[8]and by Wijaya and Spatz[9]. The results inFig. 4(a) manifest that both the condensation heat transfer coefficients for R-410A and R-134a in the PHE increase almost linearly with the mean vapor quality. Besides,the quality-averaged con-densation heat transfer coefficient for R-410A is about 20–30% higher than that for R-134a. However,the con-densation heat transfer coefficient for R-134a increases faster with the mean vapor quality than that for R-410A. The difference is attributed mainly to the different thermal conductivities of two refrigerants for

the liquid and vapor phases. Specifically,the liquid ther-mal conductivity of 410A is higher than that for R-134a by about 20%. However,the vapor thermal con-ductivity for R-410A is lower than that for R-134a. Hence,at lower quality the condensation heat transfer coefficient for R-410A is significantly higher than that for R-134a. The comparison given inFig. 4(b) further indicates that for R-410A the condensation heat transfer coefficient in the PHE is higher than that in a horizontal smooth tube from Ebisu and Torikoshi [8]. This en-hanced condensation is mainly attributed to the plate

0.0 0.2 0.4 0.6 0.8 1.0 0 4000 8000 12000 16000 Pf (Pa) 0.0 0.2 0.4 0.6 0.8 1.0 Xm 0 1 2 3 4 5 ftp

(a) Frictional Pressure Drop of R-410A in PHE at P=1.44 MPa, q=10 kW/m2

G=50 kg/m2_s G=100 kg/m2_s G=150 kg/m2_s

(b) Friction Factor of R-410A in PHE at P=1.44 MPa, q=10 kW/m2

G=50kg/m2_s G=100 kg/m2_s G=150 kg/m2_s

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surface corrugation and swirl ﬂow generated in the PHE. However,our condensation heat transfer coeﬃ-cient is lower than that reported by Wijaya and Spatz

[9]. This is simply due to the fact that the refrigerant mass ﬂux for the present data is only about 1/5 of their measurement[9].

4.2. Two-phase frictional pressure drop

The frictional pressure drop and friction factor associ-ated with the refrigerant R-410A condensation in the

ver-tical plate heat exchanger for various ﬂow and thermal conditions are presented inFigs. 5–7. Besides,compari-sons of the present data in the vertical PHE with those of R-134a in the same PHE and with those of R-410A in horizontal smooth tubes are shown inFig. 8.

The results for DPf given in Fig. 5(a) for diﬀerent

R-410A refrigerant mass ﬂuxes indicate that at a given G the frictional pressure drop increases almost linearly with the mean vapor quality,similar to the results for the condensation heat transfer coeﬃcient shown in

Fig. 3(a). In addition,the pressure drop is noticeably

0.0 0.2 0.4 0.6 0.8 1.0 0 4000 8000 12000 16000 Pf (Pa) 0.0 0.2 0.4 0.6 0.8 1.0 Xm 0 1 2 3 4 5 ftp

(a) Frictional Pressure Drop of R-410A in PHE at P=1.44 MPa, G=100 kg/m2_s

q=10 kW/m2

q=15 kW/m2

q=20 kW/m2

(b) Friction Factor of R-410A in PHE at P=1.44 MPa, G=100 kg/m2_s

q=10 kW/m2

q=15 kW/m2

q=20 kW/m2

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higher for a higher mass ﬂux. For instance,for the refrigerant mass ﬂux of G = 150 kg/m2s the frictional pressure drop is about 20% and 31% on average higher than those for G = 100 and 50 kg/m2s,respectively.

Fig. 5(b) presents the variations of the friction factor with the mean vapor quality. The results manifest that the friction factor decreases exponentially with the mean vapor quality. This is conjectured to result from the fact that at the low vapor quality,the mean speciﬁc volume of the vapor–liquid mixture is low,which in turn results in a higher friction factor,according to Eq.(15).

More-over,the friction factor is lower at a higher refrigerant mass flux. This simply reflects the definition of the fric-tion factor given in Eq.(15)that ftpis proportional to

G2. Next,the data inFig. 6(a) suggest that an increase in the imposed heat flux results in a small rise in the fric-tional pressure drop. The effect of the imposed heat flux on the friction factor shown inFig. 6(b) exhibits a sim-ilar trend. We further note that the two-phase frictional pressure drop is only slightly affected by the system pres-sure (Fig. 7). Finally,the data inFig. 8show that in the high vapor quality regime (Xm> 0.4),the frictional

pres-0.0 0.2 0.4 0.6 0.8 1.0 0 4000 8000 12000 16000 Pf (Pa) 0.0 0.2 0.4 0.6 0.8 1.0 Xm 0 1 2 3 4 5 ftp

(a) Frictional Pressure Drop of R-410A in PHE at G= 50 kg/m2_{s, q=15 kW/m}2

P=1.44 MPa P=1.65 MPa P=1.95 MPa

(b) Friction Factor of R-410A in PHE at G= 50 kg/m2_{s, q=15 kW/m}2

P=1.44 MPa P=1.65 MPa P=1.95 MPa

Fig. 7. Eﬀects of refrigerant saturated pressure on (a) frictional pressure drop and (b) friction factor at G = 50 kg/m2s and q = 15 kW/m2.

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sure drop of R-410A in the plate heat exchanger is lower than that for R-134a in the same PHE,but it is much higher than that in a smooth horizontal pipe for the en-tire Xmrange.

4.3. Correlation equations

According to the present data for R-410A condensa-tion in the PHE,an empirical correlacondensa-tion for the

con-densation heat transfer coefficient is proposed,which is modified from that of Kandlikar[27]. The average con-densation heat transfer coefficient is considered to be function of Convection,Froude and Boiling numbers. The proposed correlation for the R-410A condensation heat transfer coefficient is

hr¼ hr;l ½0:25 Co0:45 Fr0:25l þ 75 Bo

0:75 _ð16Þ

(a) Comparison of the Present data with Yan & Lin

(b) Comparison of the Present Data with Ebisu & Wijaya et al

P=3.04 MPa, G=300 kg/m2s, q=7.5kW/m2(Ebisu & Torikoshi, 1998) P=2.80 MPa, G=481 kg/m2_{s (Wijaya & Spatz, 1995)}

0 10000 20000 Pf (P a ) 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1 X_m .0 0 10000 20000 Pf (P a )

Fig. 8. Comparison of the measured frictional pressure drops for R-410A condensation in the PHE with those for (a) R-134a in the same PHE from Yan et al. (1999) and (b) R-410A in a horizontal smooth tube from Ebisu and Torikoshi (1998) and from Wijaya and Spatz (1995).

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and the data for the associated friction factor can be cor-related as

ftp¼ 21; 500 Re1:14eq Bo0:085 ð17Þ

The single-phase convection heat transfer coeﬃcient for liquid R-410A in this vertical plate heat exchanger has been established in our previous study[21]as

hr;l¼ 0:2092 kl Dh Re0:78 l Pr 1=3 l lave lwall 0:14 ð18Þ

In the above equations Co, Fr, Bo and Pr are respec-tively the Convection,Froude,Boiling and Prandtl numbers. They are respectively deﬁned as

-25% +25%

(a) R-410A, Condensation Heat Transfer Coefficient Proposed Correlation

h r/ hr,l=[0.25 x Co-0.45x Frl 0.25

+75 x Bo0.75]

(b) R-410A, Friction Factor Proposed Correlation ftp= 21,500 x Reeq -1.14 x Bo-0.085 -25% +25% 0 1 2

hr / hr,I (Experimental Data)

3 0 1 2 3 hr / h r, l (Proposed correlation) 0 1 2 3 4 ftp (Experimental Data) 5 0 1 2 3 4 5 ftp (Proposed correlation)

Fig. 9. Comparison of the proposed correlations with the present data for (a) condensation heat transfer coeﬃcient and (b) friction factor.

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Co¼ qg q_l ð1 XmÞ Xm 0:8 ð19Þ Frl¼ G2 q2 l g Dh ð20Þ Bo¼ q G ifg ð21Þ Prl¼ ll cp;l kl ð22Þ and Reeqis the equivalent Reynolds number regarding

all the ﬂow as liquid. Thus Reeq¼ Geq Dh ll ð23Þ in which Geq¼ G ð1 XmÞ þ Xm q_l qg !1=2 2 4 3 5 ð24Þ

A data analysis shows that most of the present data are within 25% of deviations predicted from the above cor-relations (Fig. 9). More speciﬁcally,these correlation equations can represent our data with average devia-tions of 16% and 23% for the condensation heat transfer coeﬃcient and friction factor,respectively.

5. Concluding remarks

We have measured the condensation heat transfer coefficient and frictional pressure drop of R-410A in a vertical plate heat exchanger. The effects of the refriger-ant mass flux,imposed heat flux,system pressure and vapor quality on the measured data have been examined in detail. The major results can be summarized in the following.

(1) The heat transfer coeﬃcient and associated fric-tional pressure drop for R-410A condensation in the PHE increase almost linearly with the mean vapor quality. But they are insensitive to the var-iation in the system pressure.

(2) Rises in the refrigerant mass flux and imposed heat flux result in better condensation heat trans-fer,accompanying with a larger pressure drop. Besides,the imposed heat flux exhibits stronger influences on the heat transfer coefficient and pressure drop than the refrigerant mass flux espe-cially at low vapor quality.

(3) The effects of the refrigerant mass flux and vapor quality on the friction factor is rather significant, especially in the low vapor quality region. How-ever,the imposed heat flux and refrigerant satu-rated pressure only slightly affect the friction factor.

(4) Correlation equations for condensation heat transfer coeﬃcient and associated friction factor are proposed for R-410A ﬂow in the PHE.

Acknowledgement

The ﬁnancial support of this study by the engineering division of National Science Council of Taiwan,ROC through the contract NSC 85-2221-E-009-06 is greatly appreciated.

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