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International Communications in Heat and Mass Transfer 35 (2008) 1147–1152 Contents lists available at ScienceDirect International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t Two-phase friction factor in vertical downward flow in high mass flux region of refrigerant HFC-134a during condensation☆ A.S. Dalkilic a,⁎, S. Laohalertdecha b, S. Wongwises b,⁎ a Heat and Thermodynamics Division, Department of Mechanical Engineering, Yildiz Technical University, Yildiz, Istanbul 34349, Turkey Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, King Mongkut's University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand b A R T I C L E I N F O Available online 15 July 2008 Keywords: Condensation Two-phase pressure drop Friction factor Vertical downward flow HFC-134a Equivalent Reynolds number model A B S T R A C T The two-phase pressure drop of the pure refrigerant HFC-134a during condensation inside a vertical tube-intube heat exchanger was investigated. The double tube test section was 0.5 m long with refrigerant flowing in the inner tube and cooling water flowing in the annulus. The inner tube was constructed from smooth copper tubing of 8.1 mm inner diameter and 9.52 mm outer diameter. The test runs were performed at average condensing temperatures of 40–50 °C. The mass fluxes were between 260 and 515 kg m− 2 s− 1 and the heat fluxes between 11.3 and 55.3 kW m− 2. The quality of the refrigerant in the test section was calculated using the temperature and pressure obtained from the experiment. The pressure drop across the test section was directly measured by a differential pressure transducer. A new correlation for the two-phase friction factor of R134a flow is proposed by means of the equivalent Reynolds number model. The effects of heat flux, mass flux and condensation temperature on the pressure drop are also discussed. © 2008 Published by Elsevier Ltd. 1. Introduction The heat transfer and pressure drop characteristics of refrigerants have been studied by a large number of researchers. However, study of the pressure drop of refrigerants during downward condensation in small diameter vertical tubes has received comparatively little attention in the literature. A brief summary of pressure drop studies of downward condensation is given as follows: Goodykoontz and Dorsch [1] investigated the local condensation heat transfer coefficients and pressure distribution of R113 for the mass fluxes of 21–455 kg m− 2 s− 1 in a 7.4–15.9 mm i.d. vertical tube. Kim and No [2] developed a turbulent film condensation model including pressure drop for high pressure steam in a 46 mm i.d. vertical tube. Ma et al. [3] studied the two-phase friction factors of downward flow of R113 for the mass fluxes of 400–800 kg m− 2 s− 1 in a 20.8 mm i.d. smooth and micro-fin tubes. Akers et al. [4] developed a two-phase multiplier by assuming that two-phase flows are similar to single-phase flows. Their correlation predicts a frictional two-phase pressure drop by means of a multiplying factor, which uses the same rationale as the Lockhart–Martinelli multiplier [5]. Their model is known as the “equivalent Reynolds number model”. It can be used for an annular flow regime. According to this model, the equivalent all liquid flow produces the same wall shear ☆ Communicated by W.J. Minkowycz. ⁎ Corresponding authors. E-mail addresses: [email protected] (A.S. Dalkilic), [email protected] (S. Wongwises). 0735-1933/$ – see front matter © 2008 Published by Elsevier Ltd. doi:10.1016/j.icheatmasstransfer.2008.06.002 stress as that of the two-phase flow. Several researchers have used this model in their work, for example, Moser et al. [6]. To the best of the authors' knowledge, there has been insufficient work dealing with the two-phase pressure drop during downward condensation in small diameter tubes. Although some information is currently available on the two-phase friction factor in annular flow, there still remains room to further discuss whether it gives reliable predictions of friction factors in the high mass flux region. Therefore, the main aim of this study was to extend the existing pressure drop data for R134a during downward condensation to the high mass flux region. The results from the large amount of experimental data were correlated with the equivalent Reynolds number and presented as a new empirical correlation to predict the two-phase friction factor. The effects of various relevant parameters on pressure drop are also discussed. 2. Experimental apparatus and method A schematic diagram of the test apparatus is shown in Fig. 1. The refrigerant loop consists of a pre-heating loop, test section, cooling loop and chilling loop. The refrigerant is circulated by a gear pump controlled by an inverter. The refrigerant flows in series through a filter/dryer, a sight glass tube, a refrigerant flow meter and a preheater and enters the test section. A spiral counter-flow double tube heat exchanger is designed to supply heat to control the inlet quality of the refrigerant before entering the test section. After exiting the test section, the chilling loop condenses and sub-cools the refrigerant and removes the heat input from the pre-heater and test section, and ejects it into the surroundings. After leaving the chilling loop, the 1148 A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152 Nomenclature cp d f G f g i ifg L m Re S T Q q x ΔP ΔT specific heat, J kg− 1 K− 1 internal tube diameter, m friction factor mass flux, kg m− 2 s− 1 friction factor gravitational acceleration, m s− 2 enthalphy, J kg− 1 latent heat of condensation, J kg− 1 length of test tube, m mass flow rate, kg s− 1 Reynolds number slip ratio temperature, °C heat transfer rate, W mean heat flux, kW m− 2 mean vapour quality pressure drop, Pa vapour side temperature difference, Tsat − Twi, °C meters. The uncertainty of the temperature measurements is ±0.1 °C. All static pressure taps are mounted on the tube wall. The refrigerant flow meter is a variable area type. The flow meter was calibrated in the range of 0–2.2 gal min− 1 for HFC-134a by the manufacturer. Pressure drop is measured by a differential pressure transducer installed between the inlet and outlet of the test section. The length between pressure taps is 0.7 m. A low temperature thermostat is used to control the system pressure of the refrigerant flow. The differential pressure transducer and pressure gauges are calibrated against a primary standard, the dead weight tester. All signals from thermocouples and pressure transducers are recorded by a data logger. Tests are performed in the steady state. 3. Data reduction The data reduction of the measured results can be analysed as follows: 3.1. The inlet vapour quality of the test section (xTS,i) xTS;i ¼ Greek symbols ρ density, kg m− 3 μ dynamic viscosity, kg m− 1 s− 1 α void fraction Subscripts eq equivalent Exp measured F frictional term g gas/vapour G gravitational term i inlet l liquid M momentum term o outlet ph pre-heater ref refrigerant sat saturation TS test section T total tp two phase w water wi inner wall refrigerant changes from the two-phase refrigerant to a sub-cooled state. Eventually, the refrigerant returns to the refrigerant pump to complete the cycle. The test section is a vertical counter-flow tube-in-tube heat exchanger with refrigerant flowing downward in the inner tube and cooling water flowing upward in the annulus. The inner and outer tubes are made from smooth vertical copper having inner diameters of 8.1 and 26 mm respectively. The length of the heat exchanger is 0.5 m. Fig. 2 shows the detailed dimensions of the heat exchanger and the location of the thermocouples. T-type thermocouples are used to measure refrigerant temperature and the tube wall temperatures in the test section. A total of ten thermocouples are located on the side wall at five points along the test tube. A thermostat is used to control the inlet temperature of the water. All the temperature-measuring devices are calibrated in a controlled temperature bath using standard precision mercury glass thermo- iTS;i −il@TTS;i ifg@TTS;i ð1Þ where il@TTS,i is the enthalpy of the saturated liquid based on the temperature of the test section inlet, ifg@TTS,i is the enthalpy of vapourisation based on the temperature of the test section inlet, and iTS,i is the refrigerant enthalpy at the test section inlet, given by: iTS;i ¼ iph;i þ Qph mref ð2Þ where iph,i is the inlet enthalpy of the liquid refrigerant before entering the pre-heater, mref is the mass flow rate of the refrigerant, and Qph is the heat transfer rate in the pre-heater: Qph ¼ mw;ph cp;w Tw;i −Tw;o ph ð3Þ where mw,ph is the mass flow rate of the water entering the preheater, cp,w is the specific heat of water, and (Tw,i − Tw,o)ph is the temperature difference between inlet and outlet positions of the preheater. 3.2. The outlet vapour quality of the test section (xTS,o) xTS;o ¼ iTS;o −il@TTS;o ifg@TTS;o ð4Þ where iTS,o is the refrigerant enthalpy at the test section outlet, il@TTS,o is the enthalpy of the saturated liquid based on the temperature of the test section outlet, and ifg@TTS,o is the enthalpy of vapourisation. The outlet enthalpy of the refrigerant flow is calculated from iTS;o ¼ iTS;i − QTS mref ð5Þ where the heat transfer rate, QTS, in the test section is obtained from: QTS ¼ mw;TS cp;w Tw;o −Tw;i TS ð6Þ where mw,TS is the mass flow rate of the water entering the test section, and (Tw,o − Tw,i)TS is the temperature difference between water at the outlet and inlet positions. A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152 1149 Fig. 1. Schematic diagram of experimental apparatus. Fig. 2. Schematic diagram of test section. 3.3. The equivalent Reynolds number model approach for two-phase friction factor tum pressure gradient and the frictional pressure gradient as follows: The two-phase pressure gradient is the sum of three contributions: the gravitational pressure gradient, the momen- dP ¼ dz dP dP dP þ þ : dz G dz M dz F ð7Þ 1150 A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152 Fig. 5. Effect of various mass fluxes of R134a on measured total pressure drop at Tsat = 50 °C. Fig. 3. Comparison of heat flux for various mass fluxes of R134a at Tsat = 50 °C. Pressure drop due to gravity can be determined from [3]: ðΔP ÞG ¼ g αρg þ ð1−α Þρl L ð8Þ where the void fraction, α, can be determined from the Chisholm [7] correlation below: α¼ 1þ 1 1−xρg x ρ S ð9Þ l where S¼ 1−x þ x ρl ρg !1=2 : ð10Þ The momentum transfer term contributes to the overall pressure drop during condensation due to the mass transfer that occurs at the phase's interface. Honda et al. [8] and Sami and Schnotale [9] reported that the momentum pressure gradient can be ignored for condensation. On the other hand, the momentum pressure gradient can be Fig. 6. Effect of various mass fluxes of R134a on measured total pressure drop at Tsat = 40 °C and xinlet = 1. written according to the results of the one-dimensional two-phase separated-flow analysis which can be defined as follows [10]: " # dP x2 ð1−xÞ2 2 d þ : ¼ −G dz M dz ρg α ρ1 ð1−α Þ ð11Þ Eq. (11) can be rearranged as follows: "( ΔPM ¼ G2 ð1−xÞ2 x2 þ ρl ð1−α Þ ρg α ) ( − o ð1−xÞ2 x2 þ ρl ð1−α Þ ρg α )# : ð12Þ i The two-phase frictional pressure drop can be obtained by subtracting the gravitational and momentum terms from the total measured pressure drop as follows: dP dP dP dP ¼ − ¼ : dz F dz Exp dz G dz M ð13Þ The two-phase friction factor is calculated by the following equation based on the all liquid Reynolds number [3]: 3 Fig. 4. Change in measured total pressure drop for all mass fluxes of R134a at Tsat = 40 °C and various condensation temperature differences. ftp ¼ ðΔP ÞF d ðΔP ÞF 2ρl d ¼ G2eq =2ρl 4L Re2eq μ 2l 4L ð14Þ A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152 Fig. 7. Effect of various mass fluxes of R134a on measured total pressure drop at Tsat = 40 °C and xinlet = 1. where the all liquid equivalent Reynolds number is determined from: Reeq ¼ Geq d μl and equivalent liquid mass flux is defined as: 0 !0:5 1 ρl @ A: Geq ¼ G ð1−xÞ þ x ρg ð15Þ 1151 Fig. 9. Comparison of friction pressure drop for various mass fluxes of R134a at Tsat = 40 °C. temperature of 50 °C at various mass fluxes in a smooth tube. It can be seen that heat flux increases with increasing temperature difference (or condensation rate). The increase in heat flux increases the condensation rate. In other words, film thickness on the tube wall increases due to the constant latent heat of condensation for a specific saturation temperature of condensation (Eqs. (5)–(6)). It can also be seen that heat flux increases with increasing mass flux due to the ð16Þ 3.4. Correlation development The two-phase friction factor of R134a in a copper smooth tube having an inner diameter of 8.1 mm and length of 0.5 m during downward condensation was developed by means of Eqs. (14)–(15). The equivalent Reynolds number is considered to be the significant variable for the experiment. Regression analysis was performed with this variable and gave a convincing correlation. Based on 380 smooth tube data points, the following correlation was developed: ftp ¼ 0:0144Re−0:0087 : eq ð17Þ 4. Results and discussion Fig. 3 shows the relationship between the mean heat flux and the condensation temperature difference (Tsat − Twi) for the condensation Fig. 10. Comparison of friction pressure drop for various mass fluxes of R134a at Tsat = 50 °C. Fig. 8. Effect of condensation temperatures of R134a on measured total pressure drop for G = 260 and 515 kg m2 s− 1 and xinlet = 1. Fig. 11. Comparison of friction factors for various mass fluxes of R134a at Tsat = 40 °C. 1152 A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152 calculated frictional pressure drop values at 50 °C are lower than those at 40 °C for the same mass flux. Figs. 11–12 show the variation in two-phase friction factor versus the equivalent Reynolds number. The sequence of lines is consistent for all mass fluxes. It can be seen that the two-phase friction factor increases with decreasing equivalent Reynolds numbers. The same trend was also seen by Ma et al. [3] with different experimental conditions and parameters. It is clear that the two-phase friction factors at 50 °C are lower than those at 40 °C. The majority of the measured data falls within ±20% using the proposed correlation (Eq. (17)) for all mass fluxes and condensing saturation temperatures. 5. Conclusion Fig. 12. Comparison of friction factors for various mass fluxes of R134a at Tsat = 50 °C. increase in condensation rate. Fig. 4 shows the change in total pressure drop with various mass fluxes for the condensation temperature of 40 °C at various temperature differences. Due to the increase in shear stress at the interface of the phases, total pressure drop increases with increasing mass fluxes. Hence, increasing heat flux increases with increasing condensation rate, decreases the vapour quality, and as a result, pressure drop is decreased. Similar results were presented in [11–13]. Fig. 5 shows the relationship between total measured pressure drop and quality at the condensation temperature of 50 °C at various mass fluxes. At high vapour quality, the higher velocity of vapour flow causes more shear stress at the interface of the vapour and the liquid film. As a consequence, the total pressure drop increases with increasing vapour quality. The pressure drop per unit length shown in Figs. 6–8 is obtained from dividing the measured pressure drop by the length between pressure taps. In our apparatus, the length between pressure taps is 0.7 m. The test runs were conducted at average inlet qualities between 0.77 and 1. Figs. 6–7 show the effect of mass fluxes of R134a on the total measured pressure drop per unit length. It can be seen that at the same condensing temperature difference, total pressure drop increases with increasing mass flux. At a specific vapour quality, the increase in mass flux will increase the vapour velocity and flow turbulence. Hence, the shear stress at the interface of the vapour and liquid film increases and, as a result, the pressure drop is increased. Fig. 8 shows the effect of condensation temperature (40–50 °C) on the total measured pressure drop per unit length for low and high mass fluxes (260 kg m− 2s− 1 and 515 kg m− 2s− 1). Low mass flux conditions give less condensation pressure drop per unit length than high mass flux conditions at the same condensing temperature. In addition to this, an increase in system pressure or condensing temperature leads to some decrease in pressure drop at the same mass flux. Yan and Lin [14] found similar results. Figs. 9–10 illustrate the dependence of the frictional pressure drop determined from Eq. (13) on the average quality along the test tube for the condensation temperatures of 40–50 °C. It is clear that frictional pressure drop increases with increasing mass flux. The increase in saturation temperature decreases the specific volume of R-134a vapour, and the vapour velocity is decreased. It also decreases the viscosity of R134a, as a result of which the flow resistance is decreased. When the condensing saturation temperature increases, all of these factors lower the pressure drop. As expected, the Accurate and repeatable pressure drop data for the condensation of R134a in downward flow at high mass flux inside a smooth tube were obtained. Chisholm's [7] void fraction correlation was used to calculate the gravitational and momentum pressure drop. Frictional pressure drop was obtained from measured total pressure drop data. The effects of various relevant parameters such as condensing temperature, condensation temperature difference, vapour quality and mass flux on the pressure drop are discussed and investigated. A new correlation of the two-phase friction factor, determined using the equivalent Reynolds number model, was developed from a large amount of data. Acknowledgements The authors are indebted to the Department of Mechanical Engineering, King Mongkut's University of Technology Thonburi (KMUTT) and the Thailand Research Fund (TRF) for supporting this study. Especially, the first author wishes to thank KMUTT for providing him with a Post-doctoral fellowship. References [1] J.H. Goodykoontz, R.G. Dorsch, Local heat transfer and pressure distributions for Freon-113 condensing in downward flow in a vertical tube, NASA TN D-3952, 1967. [2] S.J. Kim, H.C. No, Turbulent film condensation of high pressure steam in a vertical tube, Internatioanal Journal of Heat and Mass Transfer 43 (2000) 4031–4042. [3] X. Ma, A. Briggs, J.W. Rose, Heat transfer and pressure drop characteristics for condensation of R113 in a vertical micro-finned tube with wire insert, International Communications in Heat and Mass Transfer 31 (2004) 619–627. [4] W.W. Akers, A. Deans, O.K. Crosser, Condensing heat transfer within horizontal tubes, Chemical Engineering Progress Symposium Series 55 (1959) 171–176. [5] R.W. Lockhart, R.C. Martinelli, Proposed correlation of data for isothermal twophase, two-component flow in pipes, Chem. Eng. Prog. 45 (1949) 39–48. [6] K. Moser, R.L. Webb, B. Na, A new equivalent Reynolds number model for condensation in smooth tubes, International Journal of Heat Transfer 120 (1998) 410–417. [7] D. Chisholm, Two Phase Flow in Pipelines and Heat Exchangers, George Godwin in association with The Institution of Chemical Engineers, London, 1983. [8] H. Honda, S. Nozu, Y. Matsuoka, H. Nakata, Condensation of R-11 and R-113 in the annuli of horizontal double-tube condensers with an enhanced inner tube, Experimental Thermal and Fluid Science 2 (1989) 173–182. [9] S.M. Sami, J. Schnotale, Prediction of forced convective condensation of nonazeotropic refrigerant mixtures inside enhanced surface tubing, Applied Scientific Research Journal 50 (1993) 149–168. [10] V.P. Carey, Liquid-vapor Phase Change Phenomena, Hemisphere Publishing, 1992. [11] K.J. Park, D. Jung, T. 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