Nuclear Engineering and Design

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1 Nuclear Engineering and Design Contents lists availale at SciVerse ScienceDirect Nuclear Engineering and Design j ourna l ho me page:.elsevier.com/locate/nucengdes Pressure drop and friction factor correlations of supercritical flo Xiande Fang,Yu Xu, Xianghui Su, Rongrong Shi Institute of Air Conditioning and Refrigeration, Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing , China a r t i c l e i n f o Article history: Received 5 April 2011 Received in revised form 6 August 2011 Accepted 16 Octoer 2011 a s t r a c t The determination of the in-tue friction pressure drop under supercritical conditions is important to the design, analysis and simulation of transcritical cycles of air conditioning and heat pump systems, nuclear reactor cooling systems and some other systems. A numer of correlations for supercritical friction factors have een proposed. Their accuracy and applicaility should e examined. This paper provides a comprehensive survey of experimental investigations into the pressure drop of supercritical flo in the past decade and a comparative study of supercritical friction factor correlations. Our analysis shos that none of the existing correlations is completely satisfactory, that there are contradictions eteen the existing experimental results and thus more elaorate experiments are needed, and that the tue roughness should e considered. A ne friction factor correlation for supercritical tue flo is proposed ased on 390 experimental data from the availale literature, including 263 data of supercritical R410A cooling, 45 data of supercritical R404A cooling, 64 data of supercritical caron dioxide CO 2 cooling and 18 data of supercritical R22 heating. Compared ith the est existing model, the ne correlation increases the accuracy y more than 10% Elsevier B.V. All rights reserved. 1. Introduction Supercritical pipe flo has many applications. To cool nuclear reactors, supercritical ater has een used for several decades Pioro et al., 2004, and supercritical CO 2 also has some applications Pioro et al., 2004; Duffey and Pioro, Since CO 2 ecame a promising alternative refrigerant due to the phaseout of conventional refrigerants that have ozone depleting effects and gloal-arming potential, the study of supercritical CO 2 cooling has attracted reneal interest Fang et al., 2001; Cheng et al., 2008; Oh and Son, 2010; Dang and Hihara, 2004; Huai et al., There are other interests in supercritical cooling and heating. For example, supercritical CO 2 is used in solar collectors Niu et al., 2011, hypersonic aircraft may use supercritical H 2 for active cooling Dziedzic et al., 1993, and some promising alternative refrigerants like R410A and R404A may also operate ith transcritical cycles Garimella, 2008; Andresen, 2006; Mitra, 2005; Jiang, Under supercritical pressures, the flo pattern is somehat similar to the conventional single-phase flo, and no phase change takes place. Hoever, the thermophysical properties of fluids change drastically during supercritical heating and cooling processes. In these circumstances, the pressure drop is greatly dependent on the local fluid temperature and the inner all Corresponding author: Tel.: ; fax: address: xd fang@yahoo.com X. Fang. temperature, hich makes the conventional single-phase friction factor correlations unsuitale. The friction factor is not only used to calculate pressure drop, ut also used to calculate heat transfer. For example, the idely used Gnielinski 1976 equation, hich applies to single-phase turulent isothermal tue flo, is of the form f/8re 1000Pr Nu = 1a f/8 1/2 Pr 2/3 1 here the Darcy Weisach friction factor friction factor for short f is defined y Eq. 3, and the Nusselt numer Nu and the Reynolds numer Re are defined as the folloing, respectively: Nu = D 1 Re = VD 1c The single-phase isothermal heat transfer equations are the ase of supercritical heat transfer models Fang et al., 2001; Cheng et al., There are a numer of experimental investigations related to the pressure drop under supercritical flo, especially in supercritical CO 2 cooling. Pioro et al conducted a survey of hydraulic resistance of fluids floing in channels at supercritical pressures. Duffey and Pioro 2005 conducted a survey of experimental heat transfer of supercritical CO 2 floing inside channels. They listed no pressure drop experimental study after year There are /$ see front matter 2011 Elsevier B.V. All rights reserved. doi: /j.nucengdes

2 324 X. Fang et al. / Nuclear Engineering and Design Nomenclature C f Fanning friction factor c p specific heat at constant pressure J/kg K D inner diameter m f Darcy Weisach friction factor f ac acceleration factor g acceleration due to gravity m/s 2 G mass flux kg/m 2 s h specific enthalpy J/kg L tue length m Nu Nusselt numer p pressure Pa Pr Prandtl numer q heat flux from fluid to all W/m 2 Re Reynolds numer T temperature K V velocity m/s Greek symols heat transfer coefficient W/m 2 K ˇ thermal expansion coefficient 1/K thermal conductivity W/m K p pressure drop Pa ε average roughness height of tues m dynamic viscosity Pa s density kg/m 3 Suscripts ac acceleration at fluid ulk temperature f at film temperature, T f = T + T /2 fr friction g gravity h hydraulic in inlet iso isothermal out outlet pc at pseudo-critical temperature t total at inner all temperature some issues regarding the recent experimental study that should e addressed. Pioro et al. s 2004 survey listed several friction factor correlations for supercritical flo. This is the only paper found hich offered a systematic revie in this regard. Hoever, they only listed some correlations pulished efore 1990 and gave no detailed analysis, evaluation or comparison. Therefore, it is necessary to carry out a comprehensive revie and comparative study of existing supercritical friction factor correlations. Among the availale literature for the pressure drop of supercritical flo, only Pettersen et al explicitly considered tue all roughness. They estimated the roughness of the mm multi-port extruded circular tues at ε = 1 m. Hoever, they did not propose any correlation of supercritical friction factors. The effect of the tue roughness on supercritical friction factors should e considered, especially for flo in minichannels at large Reynolds numer. Moody 1944 gave a roughness of ε = 1.5 m for draing tuing of macro-size. Matkovic et al tested a commercial copper tue ith an inner diameter of 0.96 mm. They measured the friction factor during adiaatic flo of sucooled liquid and superheated vapour and found the internal surface average roughness ε = 1.3 m. Soierska et al conducted experiments of flo oiling of ater in a vertical microchannel ith dimension of mm 2 idth depth, hydraulic diameter D h = 1.2 mm. The surface roughness of the channel as determined to e ε < 1 m. Steiner and Taorek 1992 proposed a correlation for flo oiling. For using the correlation, they gave channel surface roughness ε = m and standard value of ε = 1 m if the surface roughness is unknon Fernando et al., Thome and Hajal 2004 studied flo oiling heat transfer model for horizontal intue evaporation specifically for CO 2 and proposed a correlation for nucleate pool oiling ith an assumption of ε = 1 m. Cavallini et al emphasized roughness issue in to-phase pressure drop calculations. This paper conducts a critical revie of the pulished literature in the experimental study of supercritical flo in the past decade and supercritical friction factor correlations. A ne supercritical friction factor correlation, hich considers the tue roughness, is to e proposed ased on 390 experimental data from the availale literature, among hich 263 data are from supercritical R410A cooling Garimella, 2008; Andresen, 2006; Mitra, 2005, 45 data from supercritical R404A cooling Garimella, 2008; Jiang, 2004, 64 data from supercritical CO 2 cooling Dang and Hihara, 2004 and 18 data from supercritical R22 heating Yamshita et al., The detailed analysis of the existing correlations and the ne correlation is performed thereafter using the same data ank. 2. Pressure drop equation Attention should e made regarding the difference eteen the friction pressure drop and the acceleration pressure drop. The majority of recent experimental investigations into supercritical CO 2 did not distinguish them ithout any reasoning Dang and Hihara, 2004; Huai et al., 2005; Yoon et al., 2003; Son and Park, 2006; Dang et al., 2007, 2010; Yun et al., The total pressure drop of a straight pipe ith a constant section area can e calculated ith p t = p fr + p ac + p g 2 here p fr is the friction pressure drop, p ac is the acceleration pressure drop, and p g is the pressure drop due to the gravity. p fr = G2 2 L D f 3 p ac = G2 2 L p g = ±g out + in 2 D f ac 4 L sin 5 here f ac is the acceleration factor, is the pipe inclination angle to the horizontal plane, the sign + is for the upard flo, and the sign is for the donard flo. The arithmetic average value of densities can e used only for short pipes in the case of strongly nonlinear dependency of the density versus temperature. The friction factor f is not to e confused ith the friction coefficient, sometimes called the Fanning friction factor. Denoted the Fanning friction factor y C f, it follos that f = 4C f 6 For long pipes at high heat fluxes and in critical and pseudocritical regions, the integral value of densities should e used. Ornatskiy et al proposed to calculate p g at supercritical pressures as follos: hout out + h p g = ±g in in L sin 7 h out + h in

3 X. Fang et al. / Nuclear Engineering and Design Fig. 1. Comparison of friction factors: supercritical vs. isothermal. For cooling processes, f ac can e approximated ith the one-dimensional approximation model Petrov and Popov, 1988; Polyakov, 1991 as follos: d f ac 2D dl 1 = 8q G ˇ c p here d is the differential symol. Sustituting Eq. 8 into Eq. 4, it follos that 1 p ac = G 2 1 9,out,in The p ac equation aove is also used for heating Pioro et al., 2004, from hich it can e seen that f ac < 0 for cooling and f ac > 0 for heating. 3. Recent experimental study of supercritical pressure drop Our extensive literature survey found that most of experimental investigations into the pressure drop of supercritical flo in the past decade are supercritical CO 2 cooling, as shon in Tales 1 and 2. Tale 1 shos the experiments of pure CO 2, hile Tale 2 lists those of CO 2 and oil mixture. The experimental investigations into in-tue supercritical pressure drop other than supercritical CO 2 cooling in the past decade are presented in Tale 3. Only Yamshita et al. s 2003 supercritical R22 heating and Garimella s group s Garimella, 2008; Andresen, 2006; Mitra, 2005; Jiang, 2004 supercritical R410A and R404A cooling are found. From the information provided y the literature listed in Tales 1 3, the folloing can e otained: 1 The majority of the experimental study of the pressure drop of supercritical CO 2 cooling Dang and Hihara, 2004; Huai et al., 2005; Yoon et al., 2003; Son and Park, 2006; Dang et al., 2007, 2010; Yun et al., 2007 in the past decade used an isothermal single-phase friction factor correlation to calculate the comining pressure drop of the friction and acceleration. The rationality of this practice lacks reasoning. 2 In the same Re, the friction factor of supercritical cooling is higher than that of the isothermal condition, and the friction factor of supercritical heating is loer than that of the isothermal counterpart, as shon in Fig. 1, here the R410A data are those of D = 3.05 mm from Garimella 2008 and Andresen 2006, the R22 data are those from Yamshita et al. 2003, and the isothermal 8 Fig. 2. Effect of tue sizes on supercritical friction factors. single-phase friction factor for smooth tues is calculated ith the equation nely proposed y Fang et al [ ] f = 0.25 log Re Re hich has the mean asolute relative deviation MARD of 0.02% and the maximum relative deviation RD of 0.05% in the range of Re = compared ith the folloing Nikuradse 1933 equation 1 = 2 logre f f RD = yi pred yi exp 12 yi exp N MARD = 1 yi pred yi exp N 13 yi exp i=1 here y pred is the predicted value, y exp is the measured value, and N is the total data points. 3 Effects of tue sizes on supercritical friction factors ere contradictorily reported. From Liao and Zhao 2002 data, the friction factor reduces y around 15% as the tue diameter decreases from 2.16 mm to 0.5 mm, hile the Dang and Hihara 2004 data sho that the 1-mm tue has igger fiction factors than those of the 2- mm tue, as shon in Fig. 2. Mitra 2005 studied and 9.4-mm tues and proposed a correlation ith size correction as follos f = af iso, Dactual D aseline c 14 here f iso, is the isothermal single-phase friction factor calculated ith Churchill 1977 equation at the fluid ulk temperature, D actual is the actual channel inner diameter, D aseline equals to 9.4 mm, the maximum diameter in the experiments, and the exponent c is negative, hich suggests that the smaller diameter has igger friction factors. After tested 0.76-, and 3.05-mm tues, it turned out to e that the D correction does not hold. Therefore, Garimella 2008 and Andresen 2006 aandoned it in their final reports. 4 Pettersen et al addressed the tue roughness issue. Their test section is multi-port extruded circular tues ith the inner diameter of mm, hich is commonly used in moile air conditioning. They compared their measured data ith the predictions of single-phase friction factor equations for smooth tues

4 326 X. Fang et al. / Nuclear Engineering and Design Tale 1 Experiments of pressure drop of supercritical CO 2 cooling. Reference Flo parameter: T in C/p in MPa/G kg/m 2 s/q kw/m 2 Flo geometry: D mm/l mm/orientation/geometry Results Pettersen et al / / / /540/horizontal/multi-port extruded circular tues Assuming ε = 1 m, the Colerook correlation predicted ell. Liao and Zhao /7.4 12/ /not mentioned 0.50, 0.70, 1.10, 1.40, 1.55, 2.16/110/horizontal/single circular tue The friction factor is seen to drop as the tue size reduced from 2.16 mm to 0.5 mm. Yoon et al / / /not mentioned 7.73/500/horizontal/single circular tue Blasius correlation has under-prediction. Deviations increase as Re increasing. Dang and Hihara /8 10/ /6 33 1, 2/500/horizontal/single circular tue The 1-mm tue has igger fiction factors than the 2-mm tue. Huai et al / / / /500/horizontal/multi-port extruded circular tues Predictions of Blasius equation are generally ithin 25%. Son and Park /7.5 10/ /not mentioned 7.75/500/horizontal/single circular tue Blasius correlation has under-prediction. Deviations increase as Re increasing. and for rough tues, respectively. For the rough conditions, they assumed the roughness to e 1 m. The mean relative deviation MRD is 6% for the smooth assumption and 1% for the rough assumption, and the MARD is 6% for the smooth assumption and 2% for the rough assumption. Pettersen et al. did not mention ho they estimated the roughness. It can e reasoned that they overestimated the roughness ecause they used the single-phase isothermal correlations to calculate the pressure drop of supercritical flo. MRD = 1 N N i=1 yi pred yi exp 15 yi exp 5 Containing oil increases the pressure drop Dang et al., 2007, 2010; Yun et al., 2007; Kuang et al., The pressure drop increase sharply ith an increase from 1% in the oil concentration Dang et al., 2007; Yun et al., Some contradictions exist eteen different experiments. Therefore, more elaorate experiments are needed. 4. Revie of supercritical friction factor correlations Andresen 2006 and Garimella 2008 otained the folloing supercritical friction factor correlation from experiments of supercritical R410A and R404A cooling f = af iso, 16 Tale 2 Experiments of pressure drop of supercritical cooling of CO 2 ith oil. Reference Flo parameter: T in C/p in MPa/G kg/m 2 s/q kw/m 2 /oil conc. Flo geometry: D mm/l mm/orientation/geometry Results Dang et al /8 10/ /12 24/oil up to 5% Yun et al / / /20 25/oil up to 4% Dang et al /8 10/ /12 24/oil up to 5% Kuang et al /9/890/not clear/oil up to 5% 1, 2/500/horizontal/single circular tue, copper 1/600/horizontal/multi-port extruded circular tues 2/500/horizontal/single grooved tue ith 6.3 helix angle p do not increase consideraly until the oil concentration reaches 1%, ut increases sharply ith an increase from 1% in the oil concentration When oil concentration increased from 0% to 4%, p increased y 4.8 times p for the grooved tue areproportional to those for a smooth tue D = 0.79 mm microchannels Immiscile oil has more negative influence on the pressure drops than the miscile oil Tale 3 Experiments of in-tue pressure drop of supercritical flo other than supercritical CO 2. Reference Flo parameter: T in C/p in /G kg/m 2 s/q kw/m 2 Flo geometry: D mm/l mm/orientation/geometry Sustance Yamshita et al /5.5 Mpa/700/ /600/vertical/single circular tue Garimella 2008, Andresen 2006, Mitra 2005, Jiang /1.0, 1.1, 0.76, 1.2 p crit / /not 1.52/ /horizontal/multiport availale. extruded circular tues. 3.05, 6.22, 9.4/323.8, 292/horizontal/single circular tue. R22 R410A D = mm. R404A D = 6.22, 9.4 mm.

5 X. Fang et al. / Nuclear Engineering and Design here the constant a and the exponent are equal to 1.16 and 0.91 for the liquid-like region, 1.31 and 0.25 for the pseudo-critical transition region, and 1.19 and 0.17 for the gas-like region, respectively, and f iso, is the friction factor calculated ith the folloing Churchill 1977 equation at the fluid ulk temperature ithout considering roughness ε: [ 8 12 ] 1/12 f iso = 8 + A 3/2 17a Re 37, { A = ln Re [ 7 Re 0.9 ]} ε 17 D Yamshita et al investigated experimentally the heat transfer and pressure drop of R22 floing in a uniformly heated vertical tue of a diameter 4.4 mm under supercritical pressure. They found that the measured friction factors ere loer than those predicted ith the isothermal friction factor equation and otained a correlation ith the deviation of ±15% as follos 0.72 f = f iso, 18 here f iso is calculated ith f iso = log Re + log Re 2 19 Petrov and Popov 1988 calculated the pressure drop of the ater, helium, and caron dioxide at supercritical pressures in the oundary conditions of the all temperature T = constant and the heat flux q = constant, ased on hich they otained f 1/4 1/3 fac = f iso, f iso, here f iso is calculated ith the Filonenko equation f iso = 0.79 ln Re Earlier in 1985, Petrov and Popov calculated the pressure drop of the turulent pipe flo of supercritical CO 2 cooling in the range of Re = and Re = , and otained a friction factor correlation of the form s f = f iso, 22a here f iso is calculated ith the Filonenko equation, and q 0.42 s = G Tarasova and Leont ev 1968 studied the friction factor in heated pipes at supercritical pressures and proposed that 0.22 f = f iso, 23 They reported a deviation of ±5% eteen experimental points and their fitting. Popov 1967 proposed to calculate the frictional factor of supercritical CO 2 ith the correlation of the form f 0.74 f = f iso, 24 here f iso is calculated ith the Filonenko equation, and the suscript f denotes evaluated at the film temperature T f. T f = T + T /2. The author reported that the equation had uncertainty of ±5%. Kutateladze 1962 proposed the equation of the form 2 2 f = f iso, 25 T /T + 1 Mikheev 1956 introduced that the friction factor of nonisothermal flo of ater and other fluids could e calculated ith Pr 1/3 f = f iso, 26 Pr here f iso is calculated ith the Filonenko equation. 5. A ne supercritical friction factor correlation A ne supercritical friction factor correlation is proposed ased on the regression analysis of 390 experimental data, including 263 data of R410A and 45 data of R404A under supercritical cooling Garimella, 2008; Andresen, 2006, 64 data of supercritical CO 2 cooling Dang and Hihara, 2004, and 18 data of supercritical R22 heating Yamshita et al., 2003, all of hich ere given graphically. The commercial softare GetData Graph Digitizer is used to translate the experimental data points on the figures into digital data, and the NIST REFPROP is used to determine the fluid thermophysical properties corresponding to the given experimental conditions of pressures and temperatures. Extensive computer tests have een conducted to develop a ne correlation ased on the 390 experimental data, using the regression analysis methodology descried y Fang et al and Fang and Xu 2011a. The methodology is summarized as the folloing: 1 To choose independent variales among those in Eqs To construct possile correlations ased on the chosen independent variales. 3 To conduct regression analysis using availale softare and data ank to find out the est model that has the highest corrected coefficient of determination Rc 2 and the loest MARD. The corrected coefficient of determination R 2 c is defined as R 2 c = 1 N 11 R 2 N m = 1 N 1s 2 SS Total 27 here m is the numer of parameters estimated, N is the numer of total samples, R 2 is the coefficient of determination, SS Total is the total sum of squares, and s 2 is the residual mean square Myers, The softare used for the regression is 1stOpt First Optimization, a leading orldide softare platform for numerical optimization analysis, especially in the area of curve fitting, nonlinear regression and parameter estimation of nonlinear complex engineering models 7D-Soft High Technology Inc., The data source files do not give any roughness information. Assuming ε = 1 m for the multi-port extruded circular tues and ε = 0.5 m for the single circular tues and using the regression analysis methodology descried aove, a ne correlation is otained as follos f pc f = f iso, here f iso is the isothermal single-phase friction factor for rough tues, hich is calculated ith the equation nely proposed y Fang et al [ ε f iso = ln D Re Re ] 2 29 here the actual channel roughness should e used. If the actual channel roughness is not knon, it is suggested to assume ε = 1 m for multi-port extruded channels and ε = 0.5 m for single channel tues. For non-circular channels, the hydraulic diameter should e used.

6 Tale 4 Evaluation of the availale models ased on the experimental data. Correlation Ne correlation Yamashitah Petrov Popov 1988 Andresen Garimella Popov Tarasova Leont ev Kutateladze Mikheev Petrov Popov 1985 All Data MARD 17.6 d MRD a c R410A MARD 17.5 d MRD a c R404A MARD 18.6 d MRD a c CO 2 MARD 19.0 d MRD a c R22 MARD 12.5 d MRD a c Isothermal smooth 328 X. Fang et al. / Nuclear Engineering and Design a Percentage of data points ithin the RD of ±10%. Percentage of data points ithin the RD of ±20%. c Percentage of data points ithin the RD of ±30%. d A old line is the first line of the given data group.

7 X. Fang et al. / Nuclear Engineering and Design Conclusions Fig. 3. Comparison of predicted values of the ne equation ith the 390 experimental data. Eq. 29 has the MARD of 0.2% and the maximum RD of 0.6% in the range of Re = and ε/d = compared ith Colerook equation 1 f = 2 log ε/d Re f 30 As indicated in Tale 4, the proposed ne equation has an MRAD of 17.6%, increasing the accuracy y more than 10% compared ith the Yamshita et al. s model, hich is the est existing model as evaluated in the folloing section. The majority of the ne model predictions have a RD of 20% Fig. 3. In generating a heat transfer equation for in-tue supercritical CO 2 cooling, the ne equation produced the est results Fang and Xu, Evaluation of availale supercritical friction factor correlations The same ank of the 390 experimental data is used for the evaluation. The comparative results of the availale models are shon in Tale 4, here the MARD, MRD and the percentile of data points ithin the RD of ±10%, ±20% and ±30% are listed and the isothermal smooth means the single-phase friction factor correlation for isothermal flo in smooth tues. The order in Tale 4 reflects the rank of the correlations ased on their overall performances. The ne correlation is the est, folloed y Yamshita et al. s 2003 and Petrov Popov s For all data, the Andresen Garimella correlation has the loer MARD than the Yamshita et al. correlation and the Petrov and Popov 1988 correlation have. Hoever, the Andresen Garimella correlation has much igger MARDs for CO 2 and R22, hich loers its rank. Besides, 79% of the data used for the comparison are those for correlating the Andresen Garimella model, hich makes it overranked. The Petrov Popov 1985 correlation has the iggest MARD ecause it ehaves anormally hen the / is too ig or too small. The correlations of Kutateladze, Mikheev and the singlephase friction factor correlation for isothermal flo in smooth tues are very close. The predictions of the single-phase friction factor correlation for isothermal flo in smooth tues are listed for reference. Most of experimental investigations into the pressure drop of supercritical flo in the past decade are supercritical CO 2 cooling ithout or ith oil, other than hich only Yamshita et al. s supercritical R22 heating and Garimella s group s supercritical R410A and R404A cooling are found. In dealing ith the supercritical CO 2 cooling, the majority of the study in the past decade did not differentiate the friction pressure drop and the acceleration pressure drop, using an isothermal single-phase friction factor correlation to calculate the comining pressure drop of the to types. This ill cause more errors. The experimental results of supercritical flo are not consistent ell, such as the contradiction of the effect of the tue diameter on the friction factor Fig. 2. More experiments are necessary to otain the correlation ith higher accuracy. The effect of tue roughness on supercritical friction factors has not properly addressed. The Andresen Garimella correlation uses the Churchill single-phase friction factor model, hich ould provide the opportunity to consider roughness. Hoever, the Andresen Garimella correlation as developed assuming smooth tues and using the coefficient a during the curve fitting. The coefficient a already reflects the effect of roughness and thus prohiits the user from using roughness in calculation. There are 8 existing correlations availale to deal ith supercritical friction factors. Based on the 390 experimental data of supercritical R410A, R404A and CO 2 cooling and supercritical R22 heating, the top to existing correlations are Yamshita et al. s 2003 and Petrov Popov s The folloing ne correlation for supercritical friction factors is proposed f pc f = f iso, It reduces the MARD y more than 10% compared ith the est existing model. References Andresen, U.C., Supercritical gas cooling and near-critical-pressure condensation of refrigerant lends in micochannels. Ph.D. thesis. G.W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology. Cavallini, A., Col, D., Matkovic, M., Rossetto, L., Pressure drop during to-phase flo of R134a and R32 in a single minichannel. ASME Journal of Heat Transfer 131, Cheng, L.X., Riatskia, G., Thome, J.R., Analysis of supercritical CO 2 cooling in macro- and micro-channels. International Journal of Refrigeration 31, Churchill, S.W., Friction-factor equation spans all fluid-flo regimes. 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Experimental Thermal and Fluid Science 31 2, Son, C.H., Park, S.-J., An experimental study on heat transfer and pressure drop characteristics of caron dioxide during gas cooling process in a horizontal tue. International Journal of Refrigeration 29, Steiner, D., Taorek, J., Flo oiling heat transfer in vertical tues correlated y an asymptotic model. Heat Transfer Engineering 13 2, Tarasova, N.V., Leont ev, A.I., Hydraulic resistance during flo of ater in heated pipes at supercritical pressures. High Temperature 6 4, Thome, J.R., Hajal, J.E., Flo oiling heat transfer to caron dioxide: general prediction method. International Journal of Refrigeration , Yamshita, T., Mori, H., Yoshida, S., Ohno, M., Heat transfer and pressure drop of a supercritical pressure fluid floing in a tue of small diameter. Memoirs of the Faculty of Engineering, Kyushu University 63 4, Yoon, S.H., Kim, J.H., Hang, Y.W., Kim, M.S., Min, K., Kim, Y., Heat transfer and pressure drop characteristics during the in-tue cooling process of caron dioxide in the supercritical region. International Journal of Refrigeration 26, Yun, R., Hang, Y., Radermacher, R., Convective gas cooling heat transfer and pressure drop characteristics of supercritical CO 2/oil mixture in a minichannel tue. International Journal of Heat Mass Transfer 50, Xiande Fang is a professor at the Institute of Air Conditioning and Refrigeration, Nanjing University of Aeronautics and Astronautics NUAA, China. Ph.D. in Engineering Thermophysics from University of Science and Technology of China. M.Sc. in Thermal Engineering from Tsinghua University, China. B. Eng. in Environmental Control Engineering from NUAA. His research areas are air conditioning and refrigeration, thermo-fluid engineering, and environmental control engineering. Yu Xu is a graduate student under the supervision of Prof. Xiande Fang. He received his B. Eng. in Environmental Control Engineering from NUAA. Xianghui Su is an associate professor at the Institute of Air Conditioning and Refrigeration of NUAA, China. Ph.D. in Man-Machine and Environmental Engineering from NUAA. M. Sci. and B. Eng. in Aircraft Environmental Control Engineering from Beijing University of Aeronautics and Astronautics, China. Her research areas are air contitioning and refrigeration, thermo-fluid engineering, and environmental control engineering. Rongrong Shi is a graduate student under the supervision of Prof. Xiande Fang. She received her B. Eng. in Environmental Control Engineering from NUAA.