Experimental Thermal and Fluid Science 54 (2014) 279–289

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Experimental Thermal and Fluid Science

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Condensation of R-134a inside a helically coiled tube-in-shell heatexchanger

0894-1777/$ - see front matter � 2014 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.expthermflusci.2014.01.003

⇑ Corresponding author. Tel.: +91 9458947100; fax: +91 1332 285665.E-mail address: abhinavrac77@gmail.com (A. Gupta).

Abhinav Gupta ⇑, Ravi Kumar, Akhilesh GuptaDepartment of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee 247667, India

a r t i c l e i n f o

Article history:Received 14 June 2013Received in revised form 4 January 2014Accepted 4 January 2014Available online 11 January 2014

Keywords:Helical coilCondensationHeat transferPressure dropR-134aEnhancement parameter

a b s t r a c t

This article presents an experimental investigation of heat transfer and pressure drop characteristics ofR-134a condensing inside a horizontal helical coil tube with the cooling water flowing in the shell incounter flow direction. The test runs are performed at vapor saturation temperature 35 ± 0.5 and40 ± 0.5 �C for the mass flux varying from 100 to 350 kg m�2 s�1 and vapor quality ranging from 0.1 to0.9. The flow regimes observed during the experiment have been plotted on Taitel and Dukler and massflux versus vapor quality flow map. The transitions between different flow regimes have also been dis-cussed. The effect of mass flux, vapor quality and saturation temperature on the heat transfer coefficientand pressure drop have been investigated. The experimental results of the helical coil tube are comparedto straight tube. The thermodynamic advantage of helical coil over straight tube is evaluated in terms ofenhancement parameter. The enhancement parameter is higher than one for mass fluxes lower than200 kg m�2 s�1. The correlations have been developed to predict two-phase Nusselt number andfrictional pressure drop multiplier during condensation of R-134a inside horizontal helical coil tube.

� 2014 Elsevier Inc. All rights reserved.

1. Introduction

The condenser is an integral part of any refrigeration and air-conditioning system and the development of high performancecondensers with the least pressure drop has always been a primarydesign consideration for engineers. The film resistance during con-densation of refrigerants inside a tube often governs the overallheat transfer coefficient of any water cooled condenser. Therefore,the improvement of refrigerant side heat transfer coefficient shallimprove the overall heat transfer coefficient of the condenser.The passive techniques to improve the refrigerant side heat trans-fer coefficient such as rough surfaces, swirl flow devices, coiledtubes do not require any external energy. Coiled tubes are essen-tially swirl flow devices, which facilitate forced convection heattransfer by creating secondary flows inside the tube [1]. The two-phase condensation phenomenon in helical tube is more complexthan in the straight tube attributable to the centrifugal force dueto its curvature. The vapor phase of the fluid that flows at a highvelocity in the tube experiences high centrifugal force than the li-quid phase at the tube wall. Under the influence of centrifugalforce, the vapor is drawn along the surface of the liquid film. Theliquid at the top of the film is directed to the inner wall of the tubeand then back to inner core [2]. This circulatory flow normal to

main axial flow is termed as secondary flow, which exists all alongthe length of the coil.

An intensive literature review on condensation of refrigerantvapor inside and outside smooth and enhanced tubes has been re-ported by Cavallini [3]. Jung et al. [4] measured flow condensationheat transfer coefficients of R-22, R-134a, R-407C, and R-410A in-side horizontal straight and micro-fin tubes of 9.52 mm outsidediameter and 1 m length at saturation temperature of 40 �C withmass fluxes of 100, 200, and 300 kg m�2 s�1 and a heat flux of7.7 to 7.9 kW m�2. Heat transfer coefficients of the micro-fin tubewere 2–3 times higher than those of a straight tube and the heattransfer enhancement factor decreased as the mass flux increasedfor all refrigerants tested. Sapali and Patil [5] measured condensa-tion heat transfer coefficient of R-134a and R-404A in smooth andmicro-fin tubes for different mass flux between 90 and800 kg m�2 s�1 and condensing temperature ranging from 35 to60 �C. The heat transfer coefficient increases with increasing massflux and decreases with increasing condensing temperature. Theheat transfer coefficients of R-134a are greater than that ofR-404A at a similar mass flux and condensing temperature. Theenhancement factors for R-134a and R-404A vary from 1.5 to 2.5and 1.3 to 2.01 respectively. Akhavan-Behabad et al. [6] carriedout an experimental investigation to find the heat transfer coeffi-cient during condensation of R-134a vapor inside a horizontal plaintube and tubes with twisted tape with different twisted ratios of 6,9, 12 and 15. Test runs were carried out for the mass flux of 92, 110,128 and 147 kg m�2 s�1. An empirical correlation was developed to

Nomenclature

A heat transfer area (m2) (=pdil)Bo boiling numberCP specific heat at constant pressure (J kg�1 K�1)d tube diameter (mm)D coil mean diameter (mm)di/D curvature ratio (�)Frv vapor Froud number (�)f friction factor (�)G mass flux (kg m�2 s�1)h heat transfer coefficient (kW m�2 K�1)i enthalpy (kJ kg�1)k thermal conductivity (W K�1 m�1)l length (m)m mass flow rate (kg s�1)Nu Nusselt number (�)p pressure (kPa)Pr Prandtl number (-)pr reduced pressure (�)Q heat transfer rate (W)Re Reynolds number (�)T temperature (�C)x vapor quality (�)pred predictedph pre-heaterR refrigerants saturationst straighttp two-phasets test-section

tt turbulent–turbulentv vaporw wallW water

Greek symbols

a void fraction (�)v Martinelli parameter (�)q density (kg m�3)D difference (�)/ two-phase multiplier (�)r surface tension (N m�1)l viscosity (Pa s)

Subscriptsa accelerationalcrit criticalexp experimentalf frictionalg gravitationalh homogeneoushe helicali innerin inletl liquidlv latent heat of vaporizationo outerout outlet

280 A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289

predict the heat transfer coefficient. Olivier et al. [7] presented anexperimental study of heat transfer, pressure drop, and flow pat-tern during condensation of refrigerants R-22, R-407C, and R-134a inside smooth, helical micro-fin, and herringbone tubes.The refrigerant condensed at an average saturation temperatureof 40 �C with mass fluxes ranging from 400 to 800 kg m�2 s�1.The results illustrated that the herringbone tube had an averageheat transfer enhancement factor of 1.7 for the three refrigerantsagainst the smooth tube. The enhancement factor was in the orderof 1.4 for the herringbone tube against the helical micro-fin tube.

A few papers are also published on the condensation insidehelically coiled concentric tube-in-tube heat exchanger reportingheat transfer and pressure drop characteristics of R-134a. Conden-sation heat transfer and pressure drop characteristics of R-134a forthe mass fluxes from 100 to 400 kg m�2 s�1 and cooling water Rey-nolds number between 1500 and 9000 inside a helicoidal tube atrefrigerant saturation temperature 33 �C and the tube wall temper-ature at 12 and 22 �C has been experimentally investigated byKang et al. [8]. They observed that the refrigerant-side heat transfercoefficients decreased with the increase of cooling water mass flux,although the overall heat transfer coefficient increased. When thecooling tube wall temperature increased from 12 to 22 �C, heattransfer and pressure drop decreased by nearly 30%. Yu et al. [9]presented an experimental investigation of condensation heattransfer of R-134a flowing inside a helical pipe with cooling waterthrough the concentric annular passage in counter-flow directionwith the helix axis of the test-section in vertical, inclined andhorizontal directions with refrigerant mass flux in the range of100–400 kg m�2 s�1 and cooling water Reynolds number in therange from 1500 to 10000. The results revealed that the orientationof the test-section had a significant effect on heat transfer coeffi-cients. The refrigerant side heat transfer coefficient for an inclinedtube was found 6–7 times greater than the vertical position. Han

et al. [10] conducted an experimental investigation into thecondensation heat transfer and pressure drop characteristics ofR-134a in the annular helical tube at three different saturated tem-peratures 35, 40, and 46 �C with the mass flux of R-134a rangingfrom 100 to 420 kg m�2 s�1. The results showed that the refriger-ant-side condensation heat transfer coefficients and pressure dropsof R-134a increased with the refrigerant mass flux. The condensa-tion heat transfer coefficients of R-134a in the annular tube de-creased with increase in saturated temperature. Wongwises andPolsongkram [11] have experimentally investigated two-phasecondensation heat transfer and pressure drop of R-134a in a heli-cally coiled concentric tube-in-tube heat exchanger. The test runswere carried out at saturation temperatures 40 and 50 �C. The massflux was between 400 and 800 kg m�2 s�1 and the heat fluxes werebetween 5 and 10 kW m�2. It was found that the percentage in-crease of the average heat transfer coefficient and the pressuredrop of the helically coiled concentric tube-in-tube heat exchanger,compared with that of the straight tube-in-tube heat exchanger,were in the range of 33–53% and 29–46%, respectively. The corre-lations to predict the condensation heat transfer coefficient andpressure drop were also proposed. Lin and Ebadian [12] conductedexperimental investigations to determine the condensation heattransfer and pressure drop of refrigerant R-134a in annular helicoi-dal pipe at three inclination angles viz. horizontal (0�), vertical(90�) and inclined (45�) with the mass flux of R-134a ranging from60 to 200 kg m�2 s�1, and Reynolds number of cooling water from3600 to 22,000; condensation temperatures of R-134a at 30 and35 �C, and cooling water at 16, 20 and 24 �C. The Nusselt numberwas higher at lower refrigerant saturation temperature, and wouldincrease with the increase of mass flow rates of both refrigerantand cooling water. When the orientation of the helicoidal pipechanged from 0 to 90�, the Nusselt number of the refrigerant-sidefor 0 to 45� orientation accounted for more than two times of that

A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289 281

from 45 to 90�. The pressure drop in the annular helicoidal pipewas not affected significantly due to orientation. The refrigerantheat transfer coefficient of the annular helicoidal tube could betwo times larger than that of smooth straight tubes when therefrigerant mass flux was larger than 150 kg m�2 s�1. Shao et al.[13] conducted an experimental investigation on condensationheat transfer of R-134a in a horizontal straight and helically coiledtube-in-tube heat exchangers at three saturation temperatures 35,40 and 45 �C with the refrigerant mass flux varying from 100 to400 kg m�2 s�1 and the vapor quality ranging from 0.1 to 0.8. Theheat transfer coefficients were higher at the low saturation tem-perature at a different mass flux of refrigerant. The condensationheat transfer coefficients of the helical tube were 4–13.8% higherthan that of the straight tube. Al-Hajeri et al. [14] reported anexperimental investigation of condensation heat transfer and pres-sure drop R-134a, inside a helical tube at three different saturationtemperatures 36, 42 and 48 �C on mass flux ranges from 50 to680 kg m�2 s�1. The overall heat transfer coefficient and refrigerantside heat transfer coefficient decreased as the saturation tempera-ture increased. The pressure drops increased as the mass flux ofrefrigerant increased. Al-Hajeri et al. [15] investigated the effectof coolant temperature on the condensation of the refrigerant R-134a. The study presents an experimental investigation into con-densation heat transfer and pressure drop of R-134a flowingthrough an annular helicoidal tube for refrigerant mass fluxesranging from 150 to 650 kg m�2 s�1, with a cooling water flow Rey-nolds number range of 950–15,000 at saturation temperature of42 �C and tube wall temperatures of 5, 10, and 20 �C. The resultsrevealed that with an increase of refrigerant mass flux, the overallheat transfer coefficients increased, and the pressure drops also in-creased. However, with the increase of mass flux of cooling water,the refrigerant-side heat transfer coefficients decreased. At lowtube wall temperature, a higher refrigerant-side heat transfer coef-ficient was observed. Also, as the tube wall temperature increased,the pressure drop in the helical tube decreased. El-Sayed Mosaadet al. [16] carried out an experimental study to investigate conden-sation heat transfer and pressure drop characteristics of R-134a atan inlet pressure of 815 kPa in a coiled double tube oriented withits helix axis in the vertical direction. Results were obtained forrefrigerant mass flux ranging from 95 to 710 kg m�2 s�1 and cool-ing water Reynolds number varying from 1000 to 14,000. The re-sults illustrated that the condensation heat transfer coefficient ofR-134a in a helical coil increased with the increase of refrigerantmass flux and decreased with a rise in saturation temperature dif-ference. The pressure drops across the test-section also rise withthe increase of mass flux. An empirical correlation was proposedfor predicting condensation heat transfer coefficient. Xin et al.[17] studied the single-phase and two-phase air–water flow pres-sure drop in annular helicoidal pipes with vertical and horizontalorientations. The experiments were performed for the superficialair Reynolds number from 30 to 30,000 and superficial water Rey-nolds number from 210 to 23,000. A friction factor correlation forsingle-phase flow in laminar, transition and turbulent flow regimewas proposed. The two-phase flow pressure drop multiplier in theannular helicoidal pipe was found to be dependent on the flow rateof air or water and the Lockhart–Martinelli parameter. The effect ofcentrifugal acceleration on the flow regime of air–water two-phaseflow in helically coiled tubes was investigated experimentally byMuraia et al. [18]. The interfacial structure was photographed bya high-speed video system with measurement of local pressurefluctuations. The centrifugal acceleration due to the curvature ofthe tube considerably quickened the flow transition from bubblyto plug flow as compared to that in a straight tube. The pressurefluctuation of total pressure loss was high in the case of a high voidfraction due to the effect of the complex motion inside the helicallycoiled tubes. Genic et al. [19] presented the results of experimental

research on shell-side heat transfer coefficient concerning threeheat exchangers with helical coils. The shell-side heat transfercoefficient was strongly influenced by geometric parameters suchas winding angle, pitch and axial pitch. A correlation for shell-sideheat transfer coefficients based on shell side hydraulic diameterwas proposed, because the shell side hydraulic diameter includedthe number of shell side geometric parameters. The shell-side foul-ing factors of eight heat exchangers with parallel helical coils wereinvestigated experimentally by Genic et al. [20]. They found valuesof fouling factors were somewhat less than the usual values fortypical shell-and-tube heat exchangers with straight pipes.

Despite above described research activities, any investigationfor condensation of refrigerant vapor inside helically coiled tubein a tube-in-shell heat exchanger has not been reported. In severalapplications, where space is limited and the condenser is supposedto be placed in a horizontal orientation with a lower center of grav-ity, horizontally oriented helical coil tube-in-shell is a good option.Therefore, it is essential that for the optimal design and operatingperformance, condensation heat transfer and pressure drop char-acteristics of R-134a are investigated in helically coiled tube-in-shell heat exchangers oriented in the horizontal direction. Since,the two-phase heat transfer and pressure drop is influenced bythe flow regime; the flow regime observed during condensationis plotted on Taitel and Dukler [21] and mass flux versus vaporquality flow map. Different geometries of helical coil are expectedto offer unique heat transfer and pressure drop performances. Theobjective of current experimental research is to estimate the con-densation performance of R-134a inside a helical coil having a cur-vature ratio (di/D) 0.092 and pitch 22.5 mm over the straightsmooth tube.

2. Experimental set-up and procedure

The experimental set-up was designed and fabricated to studycondensation of R-134a inside a helical coil. The schematic dia-gram of experimental set-up is shown in Fig. 1. The test-sectionwas a condenser having a helical coil placed in a shell. The test-sec-tion was connected to the post-condenser. A chiller unit was in-stalled to supply cold water to post-condenser. A sight glass wasprovided after the post-condenser to observe the state of therefrigerant. The refrigerant was circulated in the system with thehelp of a gear pump. A bank of three pumps connected in a parallelarrangement. These pumps were magnetically coupled with themotor. A Coriolis mass flow meter was provided after the pumpto measure the refrigerant flow rate, which was further connectedwith a pre-heater. The pre-heater was fabricated from a 6 m longstainless steel tube of 12.5 mm internal diameter. The heating ofpre-heater was accomplished through supplying high current atlow voltage with the help of an auto-transformer. The sight glasses,one each at the inlet and outlet of the test-section were installed toobserve flow regimes. The inner diameter of the sight glasses wassame as that of the test-tube. A filter cum drier was fitted betweenpre-heater and test-section for removal of any moisture or foreignparticle present in the refrigerant loop. The entire pre-heater, test-section and refrigerant line joining these two components wereinsulated to prevent heat leakage to the surroundings.

As seen in Fig. 2, the helical coil of the test-section was fabri-cated by bending a 2 m long straight copper tube over a woodenmandrel. The outer diameter of the tube was 9.52 mm, and thewall thickness was 0.6 mm. The diameter of the helical coil andthe coil pitch was 100 mm and 22.5 mm respectively. The helicalcoil was housed in the middle of the annular space of a cylindricalshell. Since the thermal capacity of cooling water is high, the annu-lar cylindrical shell was chosen to avoid stratification of water atlow flow rates. The shell of the heat exchanger was fabricated from

Fig. 1. Schematic diagram of experimental set-up.

Fig. 2. Schematic diagram of test-section.

282 A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289

mild steel. The inner and outer diameter of shell was 80 mm and120 mm respectively. Hence, an annular space of 20 mm was avail-able in the shell. The length of the shell was 185 mm. Both thesides of the cylindrical shell were closed with the flanges and thetest-section was integrated in the set-up with a horizontal orienta-tion. The helical coil was instrumented with T-type (copper–con-stantan) thermocouples on the outer wall of the tube at sixstations. At each station four thermocouples were soldered 90�apart at the top, bottom, and two sides of the tube to take careof any circumferential temperature variations, then water resistantglue was applied on thermocouples to avert them being biased bycooling water. These thermocouples were taken out through thegaskets used for tightening the flanges at both the ends of thetest-section. The dimension of the test-section is listed in Table 1.

Refrigerant temperatures at the inlet and outlet of the test tube,pre-heater and at other locations were also measured with T-type

Table 1Specifications of test-section.

Parameters Dimensions

Outer diameter of tube (mm) 9.52Inner diameter of tube (mm) 8.33Coil mean diameter (mm) 90.48Coil pitch (mm) 22.5Number of turns 6Curvature ratio (�) 0.092Length of copper tube (mm) 2000Outer diameter of shell (mm) 120Inner diameter of shell (mm) 80Length of shell (mm) 185

thermocouples and were calibrated to an accuracy of 0.1 �C prior toinstallation. The water temperature rise in the test-section wasmeasured by four junction copper–constantan thermopiles. Theaccuracy of thermopiles was around 0.03 �C. The pressure of therefrigerant at the inlet of test-section and at the entrance and exitof pre-heater was gauged by pressure transducers, while the pres-sure drop across the test-section was measured by a differentialpressure transducer. The pressure transducers and differentialpressure transducers were accurate to 0.25% of full scale. Therefrigerant mass flow rate was measured by a Coriolis flow metercalibrated to an accuracy of 0.1% of full scale. The water flow ratein test-section was measured by a turbine flow meter having anaccuracy of 1% of full scale.

Initially the set-up was tested under pneumatic pressure of2.0 MPa and a vacuum of 600 mm of mercury for 24 h to ensurethat there is no leakage. Refrigerant R-134a was charged in theset-up under a vacuum of 600 mm of mercury. After nearly 12 hinterval the purge valve was crack opened and the air accumulatedin the upper portion of the set-up was purged. The process was re-peated several times and complete removal of air from the systemwas ensured after verifying that the pressure inside the tubematches the value corresponding to saturation temperature of R-134a. When the air was completely removed from the system,the magnetic gear pump was turned onto deliver liquid refrigerantfrom post-condenser to pre-heater. The cooling water to post-con-denser and test-section was also turned on. The liquid refrigerantwas evaporated in the pre-heater by the resistance heating. Theelectric power to pre-heater for a given refrigerant flow rate wassupplied through an auto-transformer. The refrigerant comingout of the pre-heater entered the test-section. In the test-section,

Table 2Range of operating parameters.

Parameter Range

Condensation temperature (�C) 35 ± 0.5 and 40 ± 0.5Refrigerant mass flux (kg m�2 s�1) 100–350Cooling heat flux (kW m�2) 2–10Average vapor quality (�) 0.1–0.9Coolant water flow rate (kg s�1) 0.032–0.09Coolant water inlet temperature (�C) 27 ± 1

A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289 283

the vapor of R-134a condensed inside the copper coil tube bytransferring heat to the cooling water flowing in the shell in counterflow direction. The two-phase refrigerant leaving the test-sectionwas directed to post-condenser where it was sub-cooled to a liquidstate by transporting heat to cold water circulated from the chillerunit through a centrifugal pump. The liquid state of the refrigerantwas confirmed through the pressure and temperature readings atthe inlet of the pump. The mass flow rate of refrigerant was con-trolled by manipulating the speed of the pump through frequencyinverter. The cooling water flow rate through the test-section wasregulated by a manually operated valve. The municipal water wasutilized for the cooling purpose. The heating of the supply water totest-section was controlled by the variac of 2 kW capacity, whichultimately controlled the temperature of inlet water. This arrange-ment was necessary to avoid the condensation of the entire vaporin the test-section. The data were acquired when a steady statewas achieved. Steady state was presumed when the readings ofpressures, temperatures and mass flows of refrigerant and waterremained stable for at least 15 min. The vapor saturation temper-ature for each test run was adjusted by varying the power suppliedto pre-heater. For a particular refrigerant flow rate and saturationtemperature, the first data were usually taken on the qualities nearto 0.1–0.2. The power to pre-heater was increased to generate dataat higher qualities for a given refrigerant flow rate. Thus, total 92test runs were carried out to cover the overall quality range ofroughly 0.1–0.9 for different refrigerant flow rates at saturationtemperature 35 ± 0.5 and 40 ± 0.5 �C. All the data were collectedby a multi channel data acquisition system with virtual instrumen-tation facility and were stored for further data reduction. Thedetails of operating parameters are shown in Table 2.

3. Data reduction and uncertainty analysis

The data reduction analysis is imperative to determine the aver-age heat transfer coefficient, frictional pressure drop and averagevapor quality during each test run at steady state. Thermo-physicalproperties of refrigerant have been evaluated using REFPROP-7[22] and the range of experimental test condition is reported inTable 2. The average two-phase heat transfer coefficient iscomputed from the following equation:

htp ¼Q W

AiðTs � TwiÞð1Þ

The two-phase heat transfer coefficient, htp is averaged on theentire length of the test tube. Ts is the saturation temperature cor-responding to the average saturation pressure of the refrigerant inthe test-section. This value is compared to average of temperaturesmeasured in the adiabatic segments at the inlet and outlet of thetest tube. A variation of less than 0.2 �C is found by these twomethods. This difference is possibly due to the low mass flux ofrefrigerant flow. A similar observation has been enunciated byMohseni and Akhavan-Behabadi [23]. The average inside tube walltemperature, Twi of the test tube is calculated from the average out-side tube wall temperature, Two by taking one dimension radialconduction effect into account, according to the following

equation:

Twi ¼ Two þQ W di lnðdo=diÞ

2Aikð2Þ

The average outside tube wall temperature, Two is determinedby taking the arithmetic mean of temperatures at 24 measurementspots on the coil tube. The heat transfer rate, QW, is determinedfrom temperature gain and mass flow rate of water flowing inthe annulus of the shell.

QW ¼ mW CPWðTout � TinÞW ð3Þ

The average vapor quality, x of the refrigerant in the test-sectionis calculated as follows:

x ¼ xin �Q W

2mRilvð4Þ

where the inlet vapor quality, xin is determined from the energy bal-ance at the pre-heater as below:

xin ¼1ilv

iin;ph þQ ph � Q loss

mR

� �� il

� �ð5Þ

The electric power, Qph supplied to pre-heater is measured di-rectly and the heat loss, Qloss through the insulating ceramic woolbetween the pre-heater and the test-section inlet is calculatedfrom the one-dimensional radial conduction equation. The enthal-py, iin,ph is evaluated at the temperature and pressure of sub-cooledrefrigerant at the inlet of the pre-heater. The enthalpy of saturatedliquid, il and enthalpy of vaporization, ilv of refrigerant is deter-mined based on the temperature at the inlet of the test-section.

The two-phase pressure gradient for flows inside a tube is ex-pressed as the sum of three contributions given by followingequation:

DpDl

� �tp¼ Dp

Dl

� �tp;fþ Dp

Dl

� �tp;aþ Dp

Dl

� �tp;g

ð6Þ

The three terms in the right side of the above equation are fric-tional, accelerational, and gravitational parts of the total pressuregradient. The accelerational term is determined using one-dimen-sional two-phase separated-flow analysis as follows:

DpDl

� �tp;a

¼ G2 ddl

x2

aqvþ ð1� xÞ2

ð1� aÞql

" #ð7Þ

The void fraction, a, in the preceding equation is estimated fromthe correlation developed by Abdul-Razzak et al. [24] as:

a ¼ ð1þ 0:49v0:3036tt Þ�1 ð8Þ

The gravitational component for a complete turn is zero as theorientation of the coil is horizontal in the present investigation.The experimental two-phase frictional pressure gradient has beencalculated from Eq. (6) by subtracting the accelerational compo-nent from the measured total pressure gradient. The experimentaltwo-phase frictional pressure gradient multiplier, /2

l is calculatedfrom the following equation:

/2l ¼ðDp=DlÞtp;fðDp=DlÞl;f

ð9Þ

The experimental two-phase frictional pressure gradient,(Dp/Dl)tp,f is obtained as described above. The liquid phasefrictional pressure gradient (Dp/Dl)l,f is calculated assuming thatonly liquid of the two-phase mixture is flowing in the tube. Theliquid phase frictional pressure gradient is calculated as below:

DpDl

� �l;f¼ fl

G2ð1� xÞ2

diqlð10Þ

Table 3Experimental uncertainties.

Measurement Uncertainty

Refrigerant temperature (�C) 0.1Water temperature (�C) 0.03Pressure (kPa) 5.171Pressure drop (kPa) 0.125Refrigerant mass flow rate (kg s�1) 0.048 � 10�3

Water mass flow rate (kg s�1) 1.38 � 10�3

Average vapor quality (�) 3%Heat transfer rate at test-section (kW m�2) 5%Heat transfer rate at pre-heater (kW m�2) 6.6%Heat transfer coefficient (kW m�2 K�1) 16%

284 A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289

The liquid friction factor fl is calculated from the correlationproposed by Srinivasan et al. [25] for the coil, applicable for therange Rel(di/D)2 < 700 and 7 < (D/di) < 104.

flDdi

� �12

¼ 0:084 Reldi

D

� �2" #�1

5

ð11Þ

where Liquid Reynolds number, Rel is defined by the followingequation:

Rel ¼Gð1� xÞdi

llð12Þ

Temperatures, pressures, pressure drop, mass flow rate ofrefrigerant and cooling water have been measured directly, so,the experimental uncertainties of these parameters are those ofthe devices engaged to gauge them. On the other hand, heat trans-fer rate, average vapor quality, average heat transfer coefficientand the frictional pressure drop are calculated indirectly as de-scribed in foregoing equations; therefore, their uncertainties areestimated by the methodology suggested by Kline and McClintock[26]. Uncertainties of different parameters of the present experi-ment are enlisted in Table 3.

4. Results and discussion

The experimental database for R-134a condensation in helicalcoil tube for different saturation temperature, plotted on Taiteland Dukler [21] flow map is reported in Fig. 3. The abscissa andordinate are Martinelli parameter, vtt and vapor Froud number,Frv, respectively and their expressions are as follows:

vtt ¼1� x

x

� �0:9 qvql

� �0:5 ll

lv

� �0:1

ð13Þ

χ tt, Martinelli parameter

0.01 0.1 1 10

F v,

Vap

or F

roud

e nu

mbe

r

0.01

0.1

1

10

Ts, °C

Annular

Stratified -wavy Inte

rmitt

ent

Stratified -wavy

35 °C 40 °C

Intermittent

Annular

Transition line from Taitel and Dukler [21]

Transition line from Cui et al. [27]

Fig. 3. Taitel and Dukler [21] flow map for the experimental data.

Frv ¼Gxffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

qvdigðql � qvÞp ð14Þ

The continuous line in Fig. 3 conveys flow regime transitioncriteria proposed by Taitel and Dukler. The transition from strati-fied-wavy to annular flow is well predicted by Taitel and Dukler.Intermittent flow also fall in the annular region of the map. Thismay be because Taitel and Dukler validated their predictive flowmap against air–water experimental database, which is thermo-physically different from R-134a studied in the present work. Thetransition between different experimental flow regimes agreeswell with the observations made by Cui et al. [27] for flow boilingof R-134a inside a micro-finned helical coil, which is shown bydotted lines in Fig. 3. They proposed while the value of theMartinelli parameter, vtt is less than 0.7, transition from annularto intermittent flow takes place. In the present experiment,Martinelli parameter is found to be 0.65, where the transition offlow from annular to intermittent occurs.

To identify flow regime during the condensation process at dif-ferent mass fluxes, the axes of the Taitel and Dukler flow map havebeen converted to mass flux versus vapor quality. Such kind of flowmap is shown in Fig. 4. It is observed that at 100 kg m�2 s�1 massflux, the flow is stratified-wavy at low vapor quality, then changesto annular at high vapor quality without the presence of any inter-mittent flow. Cavallini et al. [3] reported a similar observation forthe same mass flux for R-134a flow condensation in horizontal mi-cro-fin tube. Furthermore, as mass flux increases, the flow regimesvary from intermittent to annular with the vapor quality. The tran-sition from intermittent to annular takes place at lower values ofvapor quality with increasing mass flux. The transition of flow pat-ter from intermittent to annular occurs at vapor quality around0.2–0.27. This finding shows a good agreement with Cui et al.[27]. They have identified the vapor quality range 0.2–0.3 as thetransition criteria from intermittent to annular flow. Olivier et al.[7] proposed this transition at vapor quality of 0.46 for R-134a con-densation inside straight tube. The helical coil quickened the tran-sition from intermittent to annular flow. This may be expected asthe centrifugal effect of the helical coil changes the conditions oftransition from intermittent to annular flow. When plotting theexperimental flow visualization database at different saturationtemperature, the transitions between different flow regimes arenot much affected.

The effect of vapor quality and mass flux on the heat transfercoefficient inside the helical coil tube at different saturation tem-perature is illustrated in Fig. 5a and b. The heat transfer coefficientascends modestly with a rise in vapor quality at the lowest massflux of 100 kg m�2 s�1. An identical dependence on vapor quality

x, Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

G, m

ass

flux

, kg

m-2

s-1

0

100

200

300

400

AnnularIntermittent

Statified -wavy

Ts , °C

35 °C 40 °C

Stratified -wavy

IntermittentAnnular

Fig. 4. G-x flow regime map for experimental data.

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

8

100150200250300350

G, kg m-2s-1 Ts= 35 °C

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Ave

rage

hea

t tra

nsfe

r co

effi

cien

t, kW

m-2

K-1

Ave

rage

hea

t tra

nsfe

r co

effi

cien

t, kW

m-2

K-1

0

1

2

3

4

5

6

7

8

100150200250300350

G, kg m-2s-1 Ts= 40 °C

(a)

(b)

Fig. 5. Heat transfer coefficient versus vapor quality for helical coil tube at differentcondensation temperature (a) 35 �C and (b) 40 �C.

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.01

2

3

4

5

6

7

8

100, Ts=35 °C

100, Ts=40 °C

150, Ts=35 °C

150, Ts=40 °C

200, Ts=35 °C

200, Ts=40 °C

G, kg m-2s-1

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Ave

rage

hea

t tra

nsfe

r co

effi

cien

t, kW

m-2

K-1

Ave

rage

hea

t tra

nsfe

r co

effi

cien

t, kW

m-2

K-1

1

2

3

4

5

6

7

8

250, Ts=35 °C

250, Ts=40 °C

300, Ts=35 °C

300, Ts=40 °C

350, Ts=35 °C

350, Ts=40 °C

G, kg m-2s-1

(a)

(b)

Fig. 6. Effect of saturation temperature on heat transfer coefficient at different massflux (a) 100, 150 and 200 kg m�2 s�1 and (b) 250, 300 and 350 kg m�2 s�1.

A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289 285

is also exhibited for a mass of 150 kg m�2 s�1. As the mass flux israised to 200 kg m�2 s�1, a different trend emerges. Even at lowerqualities, the heat transfer coefficients fairly high than lower massflux cases. As the vapor quality increases to 0.5, heat transfer coef-ficient starts to display a pronounced effect on vapor quality. Athigh vapor quality the velocity of vapor is also high; this makesthe secondary flows stronger. At high vapor quality the secondaryflows generate high shear stress resulting in more waves on thesurface of the liquid film and consequently, increase the surfacearea for heat transfer. Further, liquid film becomes thinner due toentrainment of liquid droplets in the vapor phase due to increasedshear stress, which in turn, lowers the thermal resistance in liquidfilm [11]. As a result of this, the heat transfer coefficient is in-creased in the helical coil with a rise in vapor quality. The depen-dence of heat transfer coefficients on vapor quality remains similarat mass fluxes above 200 kg m�2 s�1.

The effect of refrigerant mass flux on the heat transfer coeffi-cient at different saturation temperature is also apparent fromFig. 5a and b. The heat transfer coefficient increases with the risein mass flux at a given vapor quality. The experimental data showsas the mass flux increases from 100 to 350 kg m�2 s�1, the heattransfer coefficient rises around 2.6 and 2.7 times for all rangesof vapor quality at saturation temperature 35 ± 0.5 and40 ± 0.5 �C respectively.

The effect of saturation temperature on the average heat trans-fer coefficient at different mass flux is evident in Fig. 6a and b. Theaverage heat transfer coefficient at the same mass flux decreasesslightly when the condensation saturation temperature increasesfrom 35 ± 0.5 to 40 ± 0.5 �C. This is due to decrease of specific volume

of refrigerant vapor with the rise in the saturation temperature,which in turn lower the vapor flow velocity. Hence, the turbulenceis also decreased. Moreover, when the saturation temperatureincreases, the refrigerant will have lower thermal conductivity,which in turn, lowers the average heat transfer coefficient.

The heat transfer characteristics of helical coil tube are investi-gated in terms of the heat transfer enhancement factor (EF). The EFis defined as the ratio between heat transfer coefficient inside thehelical coil tube and that of a smooth tube at the same operatingcondition (vapor quality, refrigerant mass flux, and saturation tem-perature) and same inside diameter. Shah [28] correlation is usedto evaluate condensation heat transfer data for the straight tube.Fig. 7 shows the effect of vapor quality and mass flux on EF atdifferent saturation temperature. The enhancement factors aregreater than unity at all the mass fluxes. Peak points of EF are spot-ted and these points vary as mass flux is changed. EF increases withvapor quality in the lower vapor quality region and decreases afterreaching a peak value. This phenomenon can be explained by tur-bulence generation in the helical coil tube. With vapor qualityincreasing, helical coil tube generates higher turbulence over thestraight tube; however the rate of rise of turbulence decreases athigh vapor quality. The enhancement factor decreases with the in-crease in mass flux. The enhancement factor is higher at the lowermass flux region as compared to the higher mass flux. The satura-tion temperature does not make a significant difference on the EF.

Fig. 8a and b depict the effects of vapor quality and mass flux ontwo-phase pressure drop in the helical coil at different saturationtemperature. The pressure drop increases moderately with vaporquality at low mass flux of 100 and 150 kg m�2 s�1. The pressure

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Enh

ance

men

t fac

tor

(-)

1.0

1.5

2.0

2.5

3.0G, kg m-2s-1

Ts , °C, 35 40

100

150

200

250

300

350

Fig. 7. Enhancement factor versus vapor quality.

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

100150200250300350

G, kg m-2s-1 Ts = 35 °C

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Tot

al p

ress

ure

grad

ient

, kPa

m-1

Tot

al p

ress

ure

grad

ient

, kPa

m-1

0

1

2

3

4

5

6

7

100150200250300350

G, kg m-2s-1 Ts = 40 °C

(a)

(b)

Fig. 8. Total pressure gradient versus vapor quality for helical coil tube at differentcondensation temperature (a) 35 �C and (b) 40 �C.

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

100, Ts=35 °C

100, Ts=40 °C

150, Ts=35 °C

150, Ts=40 °C

200, Ts=35 °C

200, Ts=40 °C

G, kg m-2s-1

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Tot

al p

ress

ure

grad

ient

, kPa

m-1

Tot

al p

ress

ure

grad

ient

, kPa

m-1

0

1

2

3

4

5

6

7

250, Ts=35 °C

250, Ts=40 °C

300, Ts=35 °C

300, Ts=40 °C

350, Ts=35 °C

350, Ts=40 °C

G, kg m-2s-1

(a)

(b)

Fig. 9. Effect of saturation temperature on pressure drop at different mass flux(a) 100, 150 and 200 kg m�2 s�1 and (b) 250, 300 and 350 kg m�2 s�1.

286 A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289

drop increases significantly with vapor quality at high mass fluxesabove 150 kg m�2 s�1. At high vapor quality, the pressure drop issoaring due to higher interfacial shear stress created by high veloc-ity vapor generating friction against the liquid film. Furthermore,interfacial shear stress tends to generate vortices within the liquidfilm, which in addition increases the pressure drop. As the vaporquality decreases the liquid and vapor velocities become similar,resulting in a much lower pressure gradient.

It is also evident from Fig. 8a and b that the pressure drop in ahelical coil is strongly affected by the increases in mass flux. This is

owing to the increase in vapor and liquid velocities at higher massfluxes. At the same vapor quality, secondary flow in helical coil in-creases with rise of mass flux. This causes a higher pressure dropdue to higher shear stress at the interface of vapor and liquid film.Pressure drop increases around 8.2 folds with the rise in mass fluxfrom 100 to 350 kg m�2 s�1 for all ranges of vapor quality for satu-ration temperature 35 ± 0.5 �C. While, this rise in pressure drop forsaturation temperature 40 ± 0.5 �C is around 7.3 and 9.1 times atvapor quality 0.2 and 0.8 respectively.

Fig. 9a and b shows the effect of saturation temperature onpressure drop at different mass flux. It is found that when the sat-uration temperature of condensation increases, the pressure dropdecreases. This is because the increased saturation temperaturelowers the specific volume of refrigerant vapor and consequently,decreases the vapor velocity. Accordingly, the secondary flow turnsout to be weaker, both the shear stress at the interface of vapor andliquid film and the turbulence also reduce. Another significantconsequence of the increase of saturation temperature is the lowerviscosity of liquid refrigerant which, in turn, reduces the flowresistance. All these factors lower the pressure drop when thecondensation temperature increases.

Frictional pressure drop characteristics of helical coil tube areexamined in terms of the pressure drop penalty factor (PF). ThePF is the ratio of frictional pressure drop per unit length of a helicalcoil tube and that of a straight tube at the same inside diameterand operating conditions. The Müller-Steinhangen and Heck [29]correlation is used to calculate the corresponding straight tubepressure drop. Fig. 10 shows the effect of vapor quality and massflux on the PF at different saturation temperature. The effect of

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Pena

lty f

acto

r (-

)

1.0

1.2

1.4

1.6

1.8

2.0

G, kg m-2s-1Ts , °C, 35 40

100

150

200

250

300

350

Fig. 10. Penalty factor versus vapor quality.

Average vapor quality (-)

0.0 0.2 0.4 0.6 0.8 1.0

Enh

ance

men

t par

amet

er (

-)

0.4

0.6

0.8

1.0

1.2

1.4

1.6

G, kg m-2s-1Ts , °C, 35 40

100

150

200

250

300

350

Fig. 11. Enhancement parameter versus vapor quality.

A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289 287

vapor quality and mass flux are quite similar to those of the heattransfer enhancement factor. This implies that the pressure dropin mechanism is closely related to heat transfer the tested helicalcoil tube like heat-momentum analogy in the single-phase. Thepenalty factor is greater than unity at any given mass flux. Theswirls and turbulences generated by secondary flows in a helicalcoil cause a higher pressure drop compared to the straight tube.It is noteworthy that the pressure penalty factor is comparativelysmall in the low vapor quality range and reaches a peak in theintermediate range of vapor quality from 0.7 to 0.5 at a particularmass flux. The penalty factor declines after reaching the peak. Thismay be due to comparable pressure drop in the straight tube in thehigh vapor quality region. Han and Lee [30] have reported similartrends of heat transfer enhancement factor and pressure drop pen-alty factor with vapor quality and mass flux.

The foregoing result discussions have shown two general trendsconcerning the performance of coiled tubes against their straightcounterpart: higher heat transfer coefficient; and higher pressuredrop. However, in order to verify the thermodynamic advantageof helical coil over straight tube it is necessary to analyze the aboveexperimental results in term of performance evaluation criterion.Recently, Bandarra Filho and Saiz Jabardo [31] proposed enhance-ment parameter, E, for the same purpose. Here, the performancewill be evaluated in terms of an enhancement parameter, E, de-fined as the ratio between the relative heat transfer and pressuredrop of the helical coil against straight tube, that is,

E ¼ ðhtp;he=htp;stÞðDPtp;he=DPtp;stÞ

ð15Þ

The values of E higher than 1 would designate that the particu-lar coil geometry would be an attractive alternate for the straightone as the heat transfer coefficient augmentation against thestraight tube would be higher than the pressure drop increment.The variation of the enhancement parameter with vapor qualityand mass flux at different saturation temperature is shown inFig. 11. The enhancement parameters weaken with vapor quality,as the rate of pressure drop increment with vapor quality is higher.The enhancement parameter also declined with the mass flux. It isremarkable that for the mass fluxes above of 200 kg m�2 s�1, E isgenerally less than 1 beyond the vapor quality of 0.5. This suggeststhat gain in heat transfer enhancement is less than the rate of pres-sure drop increment. The effect of saturation temperature is notsignificant on enhancement parameter.

The correlation to predict the two-phase condensation heattransfer coefficient of refrigerant for helical coil in shell condenserhas not been reported in open literature. Current experimental re-

sults are compared with Wongwises and Polsongkram [11] andEl-Sayed Mosaad et al. [16] correlations based on the flow conden-sation of R-134a in a coiled double tube. The correlation to predicttwo-phase Nusselt number by Wongwises and Polsongkram [11] isgiven below:

Nutp ¼ 0:1352 De0:7654Eq Pr0:8144

l v0:0432tt p�0:3356

r ðBo� 104Þ0:112 ð16Þ

where Martinelli parameter, vtt is defined in Eq. (13). EquivalentDean number, DeEq is evaluated from following equation:

DeEq ¼ Rel þ Revlvll

� �ql

qv

� �0:5" #

di

D

� �0:5

ð17Þ

Liquid Reynolds number, Rel, is defined in Eq. (12) and VaporReynolds number, Rev, is calculated from:

Rev ¼Gxdi

lvð18Þ

Liquid Prandtl number, Prl is defined as below:

Prl ¼Cplll

klð19Þ

Reduced pressure, pr is calculated from:

pr ¼ps

pcritð20Þ

And boiling number, Bo is defined as:

Bo ¼ qGilv

ð21Þ

El-Sayed Mosaad et al. [16] proposed following correlation topredict two-phase Nusselt number for condensation of R-134a ina coiled double tube:

Nu ¼ 6:39Re�

0:4Pr1=3l 1� 0:85

DTs

Ts

� �0:9" #

ð22Þ

Applicable range is 0.3 6 DTsTs6 0.6 and 1200 6 Re

�6 95,000

where

Re�¼ Gdi

l1ð1� xÞ þ x

ffiffiffiffiffiffiq1

qv

r� �ð23Þ

Prl is defined in the Eq. (19). Ts is the condensation saturationtemperature, and DTs is the difference between condensation sat-uration and coolant water temperature.

Fig. 12 shows the results of the comparison between the exper-imental Nusselt numbers with predicted values. Wongwises and

Experimental Nusselt number (-)

0 200 400 600 800 1000

Pre

dict

ed N

usse

lt nu

mbe

r (-

)

0

200

400

600

800

1000

Wongwises and Polsongkram [11]El-Sayed Mosaad et al. [16]

-30%

+ 30%

Fig. 12. Comparison of experimental Nusselt number with Wongwises andPolsongkram [11] and El-Sayed Mosaad et al. [16].

Nutp, e, experimental Nusselt number

0 200 400 600 800 1000

Nu tp

, p, p

redi

cted

Nus

selt

num

ber

0

200

400

600

800

1000+15%

-15%

MBE = 4.34RMSE = 16.72

Fig. 14. Comparison of experimental Nusselt number with data predicted byproposed correlation.

288 A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289

Polsongkram [11] correlation over predicts most of the data up-to+20%. El-Sayed Mosaad et al. [16] correlation predicts majority ofthe experimental data in the error band of ±30%. This may bedue to different operating conditions and coil geometry used inthe present experiment.

Fig. 13 displays two-phase frictional pressure gradient multi-plier for the helical coil calculated in the present study, Eq. (9)and the correlation proposed by Wongwises and Polsongkram[11] for helically coiled concentric tube-in-tube heat exchanger,for the sake of comparison. The two-phase frictional pressure gra-dient multiplier proposed by Wongwises and Polsongkram is asfollows:

/2l ¼ 1þ 1:569

v1:496tt

þ 1v2

ttð24Þ

As shown in Fig. 13, it could be observed that the experimentaltwo-phase frictional pressure gradient multipliers are well pre-dicted by Wongwises and Polsongkram [11].

Based on the present data under given experimental conditionsand coil configuration two-phase Nusselt number correlation forR-134a is proposed, the expression of which is given as follows:

Nutp

Nul¼ 0:4 1þ 3:024

v0:8tt

� �p�0:63

r ð25Þ

Single-phase Nusselt number, Nul is calculated from thecorrelation proposed by Mori and Nakayama [32] for Prl > 1 andRel(di/D)2.5 > 0.4 as below:

χ tt, Martinelli parameter (-)

0.01 0.1 1 10

φ l2 , liq

uid

two-

phas

e fr

ictio

nal m

ultip

lier

(-)

1

10

100

1000

10000

Experimental data

Wongwises and Polsongkram [11]

Fig. 13. Comparison of experimental two-phase frictional pressure gradientmultiplier with Wongwises and Polsongkram [11].

Nul ¼1

41Re

56l Pr0:4

ldi

D

� � 112

1þ 0:061 Reldi

D

� �2:5" #�1

6

8<:

9=; ð26Þ

where the liquid Reynolds number, Rel is defined in Eq. (12) andPrandtl number, Prl is defined in Eq. (19).

A comparison between the experimental Nusselt numbers withthat predicted by the proposed correlation is shown in Fig. 14. Thecorrelation predicts the values within ±15% of experimental data.The accuracy of the correlation is also assessed by means of twowidely used statistical tools: mean bias (MBE) and root meansquare error (RMSE).

MBE ¼ 1n

R Nupred � Nuexp� �

ð27Þ

RMSE ¼ 1n

XNupred � Nuexp� �2

� �� �12

ð28Þ

The MBE and RMSE for Nusselt number values of the proposedcorrelation are 4.34 and 16.72 respectively. The value of MBEshows small over-estimate by the correlation. The value of RMSEis higher than MBE as error distribution becomes uneven.

In the present study, a new correlation is developed to predicttwo-phase frictional pressure gradient multiplier for the helicalcoil tube. For this purpose, based on the correlation proposed by

Experimental frictional pressure gradient, kPa m-10 1 2 3 4 5 6

Pred

icte

d fr

ictio

nal p

ress

ure

grad

ient

, kPa

m-1

0

1

2

3

4

5

6+15%

-15%

MBE = -0.037RMSE = 0.149

Fig. 15. Comparison of experimental frictional pressure gradient with datapredicted by proposed correlation.

A. Gupta et al. / Experimental Thermal and Fluid Science 54 (2014) 279–289 289

Wongwises and Polsongkram [11] and by using the experimentaldata, following correlation is proposed:

/2l ¼ 2:76 1þ 7:094

v1:378tt

þ 1v2

tt

� �p0:7

r ð29Þ

The reduced pressure drop term, pr is incorporated in the gen-eration of correlation to include the effect of variation in saturationpressure. A comparison of experimental two-phase frictional pres-sure gradient with the data predicted by the proposed correlationis shown in Fig. 15. The correlation predicts the experimental datawithin an error band of ±15%. The MBE and RMSE for frictionalmultiplier values of the proposed correlation are �0.037 kPa m�1

and 0.149 kPa m�1 respectively.

5. Conclusions

i. The flow regimes observed during condensation of R-134a ina helical coil is classified into three categories: stratified-wavy, intermittent, and annular flow. The experimentaltwo-phase flow regime is plotted on Taitel and Dukler flowmap and mass flux versus vapor quality flow map. Martinelliparameter is used to indicate the transition from intermit-tent to annular flow, which is vtt = 0.65. The transition fromstratified-wavy to intermittent or annular flow is identifiedin mass flux versus vapor quality flow map.

ii. The average heat transfer coefficient and pressure drop ofhelical coil tube increase with increasing average vaporquality and mass flux. On the contrary, these characteristicsdecrease with increase in saturation temperature.

iii. High heat transfer and pressure drop in the helical coil is dueto the secondary flow, increasing the turbulence as well asprolonging the annular flow regime to much lower qualitieswhen compared to the straight tube.

iv. Enhancement parameter diminishes with vapor quality andmass flux. Enhancement parameter is greater than 1 formass fluxes below 200 kg m�2 s�1. So, the helical coil tubeis a satisfactory substitute for the straight ones for low massfluxes.

v. The correlations to predict two-phase Nusselt number andfrictional pressure gradient multiplier are proposed by fit-ting experimental data obtained in the mass flux range of100–350 kg m�2 s�1. However, further investigations arestill needed to extend this correlation to account for theeffect of coil dimensions.

Acknowledgments

The authors are grateful to Department of Science & Technol-ogy, Ministry of Science &Technology, New Delhi, India for provid-ing the financial support for this project work.

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