# Two Phase Flow Correlation

Advances in Space Research 49 (2012) 351–364 www.elsevier.com/locate/asr

Evaluation of using two-phase frictional pressure drop correlations for normal gravity to microgravity and reduced gravity Xiande Fang ⇑, Honggang Zhang, Yu Xu, Xianghui Su

Institute of Air Conditioning and Refrigeration, Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing 210016, China Received 8 May 2011; received in revised form 15 August 2011; accepted 5 September 2011 Available online 19 October 2011

Abstract The calculation of two-phase frictional pressure drop (TPFPD) is required by two-phase systems operating under microgravity and reduced gravity. There are a large number of correlations for the TPFPD in tubes under normal gravity. However, it is hard to ﬁnd out a TPFPD correlation obtained from microgravity and/or reduced gravity conditions, and thus people have to use TPFPD correlations for normal gravity to calculate TPFPD under microgravity and reduced gravity. It is necessary to evaluate the feasibility of such practice. This paper oﬀers a comprehensive review of the TPFPD correlations for normal gravity and an up-to-data survey of the TPFPD experimental study under microgravity and reduced gravity. There are 23 TPFPD correlations for normal gravity reviewed and 135 experimental data under microgravity obtained from the literature. These experimental data are used to evaluate the reviewed TPFPD correlations. It is found that the smallest mean absolute relative deviation (MARD) of the correlations is greater than 34%. Using TPFPD correlations for normal gravity to reduced gravity and microgravity may be acceptable for the ﬁrst approximation, but correlations intended for microgravity and reduced gravity are needed and more experiments are desired to obtain more data with high accuracy. Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Two-phase; Frictional pressure drop; Microgravity; Reduced gravity; Normal gravity

1. Introduction Microgravity (or lg) is used to refer to situations that are substantially weightless, and it is more or less a synonym of weightlessness and zero-g, but indicates that g-forces are not quite zero, just very small. Normal gravity refers to Earth gravity. Often, the term reduced gravity is used to mean weightlessness as it is experienced by orbiting spacecraft, and it is also used to mean gravity less than normal gravity, such as Moon gravity (0.17 g) and Mars gravity (0.38 g). The determination of the two-phase frictional pressure drop (TPFPD) in tubes is important in the development of space thermal transport systems, power acquisition systems, and environmental control and life support systems, which has triggered research into the TPFPD under micro⇑ Corresponding author. Tel./fax: +86 25 8489 6381.

E-mail address: xd_fang@yahoo.com (X. Fang).

gravity and reduced gravity conditions. Two-phase ﬂow could meet the escalating power requirements in future thermal management and thermal control systems in spacecraft, communication and Earth observation satellites, as well as space stations. Understanding the hydrodynamic characteristics of two-phase ﬂow under microgravity and reduced gravity is essential to design such systems. The extensive theoretical and experimental study of TPFPD in tubes has been conducted in the past seven decades, and a number of correlations have been proposed for normal gravity. The methods developed so far can be classiﬁed into two categories: homogeneous and separated ﬂow approaches. The former treats two-phase ﬂow as a pseudo single-phase ﬂow characterized by suitably averaged properties of the liquid and vapor phases Shannak, 2008. The latter considers the two-phase to be artiﬁcially separated into two streams, each ﬂowing in its own pipe, with the assumption that the velocity of each phase is constant in

0273-1177/$36.00 Ó 2011 COSPAR. Published by Elsevier Ltd. All rights...

References: Bousman, W.S. Studies of two-phase gas–liquid ﬂow in microgravity. Ph. D. Dissertation, Department of Chemical Engineering, University of Houston, USA, 1994. Bousman, W.S., Dukler, A.E. Studies of gas-liquid ﬂow in microgravity: void fraction, pressure drop and ﬂow patterns, in: Proc. of 1993 ASME Winter Meeting, New Orleans, LA, 1993. Cavallini, A., Censi, G., Del Col, D., Doretti, L., Longo, G.A., Rossetto, L. Condensation of halogenated refrigerants inside smooth tubes. HVAC R. Res. 8, 429–445, 2002.

Dalkilic, A.S., Agra, O., Teke, I., Wongwises, S. Comparison of frictional pressure drop models during annular ﬂow condensation of R600a in a horizontal tube at low mass ﬂux and of R134a in a vertical tube at high mass ﬂux. Int. J. Heat Mass Transfer 53, 2052–2064, 2010. Chen, I., Downing, R., Keshock, E.G., Al-Sharif, M. Measurements and correlation of two-phase pressure drop under microgravity conditions. J. Thermophysics 5 (4), 514–523, 1991. Chen, I.Y., Yang, K.S., Chang, Y.J., Wang, C.C. Two-phase pressure drop of air–water and R-410a in small horizontal tubes. Int. J. Multiph. Flow 27, 1293–1299, 2001. Chisholm, D.A. Theoretical basis for the Lockhart–Martinelli correlation for two-phase ﬂow. Int. J. Heat Mass Transfer 10, 1767–1778, 1967. Chisholm, D. Pressure gradients due to friction during the ﬂow of evaporating two-phase mixtures in smooth tubes and channels. Int. J. Heat Mass Transfer 16, 347–348, 1973. Choi, B., Fujii, T., Asano, H., Sugimoto, K. A study of gas-liquid twophase ﬂow in a horizontal tube under microgravity. Ann. New York Acad. Sci. 974, 316–327, 2002. Cicchitti, A., Lombardi, C., Silvestri, M., Soldaini, G., Zavattarelli, R. Two-phase cooling experiments–pressure drop, heat transfer, and burnout measurements. Energia Nucleare 7 (6), 407–425, 1960. Colin, C., Fabre, J.A., Dukler, A.E. Gas–liquid ﬂow at microgravity conditions—I. Dispersed bubble and slug ﬂow. Int. J. Multiphase Flow 17, 533–544, 1991. Colin, C., Fabre, J. Gas–liquid pipe ﬂow under microgravity conditions: inﬂuence of tube diameter on ﬂow patterns and pressure drops. Adv. Space Res. 16 (7), 137–142, 1995. Dukler, A.E., Wicks, M., Cleveland, R.G. Friction pressure drop in twophase ﬂow. A. I. Ch. E. 10 (1), 38, 1964. Fang, X.D., Xu, Y., Zhou, Z.R. New correlations of single-phase friction factor for turbulent pipe ﬂow and evaluation of existing single-phase friction factor correlations. Nucl. Eng. Des. 241, 897–902, 2011. Friedel, L. Improved friction pressure drop correlation for horizontal and vertical two-phase pipe ﬂow. Eur. Two-phase Flow Group Meeting Pap. E2 18, 485–492, 1979. Garimella, S., Agarwal, A., Killion, J.D. Condensation pressure drop in circular microchannels. Heat Transfer Eng. 26, 1–8, 2005. Gronnerud, R., Investigation of liquid hold-up, ﬂow resistance and heat transfer in circulation type evaporators, part IV: Two-phase ﬂow resistance in boiling refrigerants. Annexe 1972-1, Bulletin, de l’Institut du Froid, 1979. Heppner, D. B., King, C. D., Littles, J. W. Zero-G experiments in twophase ﬂuids ﬂow patterns, in: The ICES Conf., San Francisco, CA, ASME paper No. TS-ENAs-24, 1975. Hurlbert, K.M., Witte, L.C., Best, F.R., Kurwitz, C. Scaling two-phase ﬂows to Mars and Moon gravity conditions. Int. J. Multiphase Flow 30, 351–368, 2004. Lee, H.J., Lee, S.Y. Pressure drop correlations for two-phase ﬂow within horizontal rectangular channels with small heights. Int. J. Multiphase Flow 27, 783–796, 2001. Lee, J., Mudawar, I. Two-phase ﬂow in high-heat-ﬂux micro-channel he at sink for refrigeration cooling applications: Part I—pressure drop characteristics. Int. J. Heat Mass Transfer 48, 928–940, 2005. Lockhart, R.W., Martinelli, R.C. Proposed correlation of data for isothermal two-phase, two-component ﬂow in pipes. Chem. Eng. Prog. 45 (1), 39–48, 1949. McAdams, W.H., Wood, W.K., Bryan, R.L. Vaporization inside horizontal tubes—II—Benzene-oil mixtures. Trans. ASME 66 (8), 671– 684, 1942. Miller, K.M., Ungar, E. K., Dzenitis, L. M., Wheeler, M. Microgravity two-phase pressure drop data in smooth tubing, in: Proc. ASME Winter Meeting, New Orleans, 1993. Mishima, K., Hibiki, T. Some characteristics of air–water ﬂow in small diameter vertical tubes. Int. J. Multiphase Flow 22, 703–712, 1996. Moody, L.F. Friction factors for pipe ﬂow. Trans. ASME, 671–684, 1944. Muller-Steinhagen, H., Heck, K. A simple friction pressure drop correlation for two-phase ﬂow pipes. Chem. Eng. Prog. 20, 297–308, 1986.

364

X. Fang et al. / Advances in Space Research 49 (2012) 351–364 Wilson, M.J., Newell, T.A., Chato, J.C., Ferreira, C.A.I. Refrigerant charge, pressure drop, and condensation heat transfer in ﬂattened tubes. Int. J. Refrig. 26, 442–451, 2003. Wambsganss, M.W., Jendrzejezyk, J.A., France, D.M., Obot, N.T. Frictional pressure gradients in two-phase ﬂow in a small horizontal rectangular channel. J. Exp. Therm. Fluid Sci. 5, 40–56, 1992. Wang, C.C., Chiang, C.S., Lu, D.C. Visual observation of two-phase ﬂow pattern of R-22, R-134a, and R-407C in a 65-mm smooth tube. Exp. Ther. Fluid Sci. 15, 395–405, 1997. Zhang, W., Hibiki, T., Mishima, K. Correlations of two-phase frictional pressure drop and void fraction in mini-channel. Int. J. Heat Mass Transfer 53, 453–465, 2010. Zhang, M., Webb, R.L. Correlation of two-phase friction for refrigerants in small-diameter tubes. Exp. Thermal Fluid Sci. 25, 131–139, 2001. Zhao, J.F., Lin, H., Xie, J.C., Hu, W.R. Pressure drop of bubbly twophase ﬂow in a square channel at reduced gravity. Adv. Space Res. 29 (4), 681–686, 2002. Zhao, J.F., Lin, H., Xie, J.C., Hu, W.R., Zhang, Y. Experimental study on pressure drop of two-phase gas/liquid ﬂow at microgravity conditions. J. Basic Sci. Eng. 9 (4), 373–380, 2001. Zhao, L., Rezkallahk, S. Pressure drop in gas–liquid ﬂow at microgravity conditions. Int. J. Multiphase Flow 21 (5), 837–849, 1995.

Pamitran, A.S., Choi, K.-I., Oh, J.-T., Hrnjak, P. Characteristics of twophase ﬂow pattern transitions and pressure drop of ﬁve refrigerants in horizontal circular small tubes. Int. J. Refrigeration 33 (3), 578–588, 2010. Qu, W., Mudawar, I. Measurement and prediction of pressure drop in two-phase micro-channel heat sinks. Int. J. Heat Mass Transfer 46, 2737–2753, 2003. Shannak, B.A. Frictional pressure drop of gas liquid two-phase ﬂow in pipes. Nucl. Eng. Des. 238, 3277–3284, 2008. Souza, A.L., Pimenta, M.M. Prediction of pressure drop during horizontal two-phase ﬂow of pure and mixed refrigerants, in: ASME, Cavitation and Multiphase Flow, FED-Vol. 210, pp. 161–171, 1965. Sun, L., Mishima, K. Evaluation analysis of prediction methods for twophase ﬂow pressure drop in mini-channels. Int. J. Multiphase Flow 35, 47–54, 2009. Tran, T.N., Chyu, M.C., Wambsganss, M.W., France, D.M. Two-phase pressure drop of refrigerants during ﬂow boiling in small channels: an experimental investigation and correlation development. Int. J. Multiph. Flow 26, 1739–1754, 2000. Whalley, P.B.. Boiling, Condensation and Gas–Liquid Flow. Oxford University Press, New York, 1987.

Please join StudyMode to read the full document