Pergamon Heat Recovery Systems & CHP Vol. 14, No. 4, pp. 377-389, 1994 Elsevier Science Ltd Printed in Great Britain 0890-4332/94 $7.00+ .00 POROUS MEDIUM MODEL FOR TWO-PHASE FLOW IN MINI CHANNELS WITH APPLICATIONS TO MICRO HEAT PIPES CHAO-YANG WANG,* MANFRED GROLL,t STEFAN R()SLER~ and CHUAN-JING Tu~ tInstitut ffir Kernenergetik and Energiesysteme (IKE), Universit~it Stuttgart, D-70550 Stuttgart, F.R.G; and ~Dept of Energy Engineering, Zhejiang University, Hangzhou 310027, P.R.C. (Recewed 15 June 1993) Ab~trlct--ln this paper the porous medium concept is adopted to build up a fundamental model for two-phase flows inside mini channels. The capillary force which appears important for those problems is rigorously included in the model by following the same treatment as for porous media. Various applications of the developed model are demonstrated, among which are adiabatic co- and counter-current flows and heated forced and natural convective flows. Some fundamental results such as the two-phase pressure drop in a downflow, the flooding limit in a counter-current flow and dryout heat flux in natural convection boiling, are achieved and compared with previous studies available in the literature. With the main emphasis on the application to micro heat pipes, the model is used to predict the capillary limit of an operating micro heat pipe, to explain the liquid holdup phenomenon and to imply the onset and origin of the plug flow pattern. Future research needs are pointed out to refine this first version of a two-phase model and to apply it to additional practical applications. I. INTRODUCTION It was long ago recognised that the geometrical analogy between a porous medium and a capillary tube can be utilized to build up flow theories in disordered porous media. The irregular porous media in which flow channels are highly tortuous are usually simplifyingly treated as a bundle of straight capillary tubes with effective diameter dh and length Le. In this way, flow behaviours inside porous media have been estimated from tests for a single capillary model tube and then by doing some kind of ensemble for a network of these tubes. This capillary tube model provides a simple and qualitative framework for various flow theories in porous media. Their more advanced development and quantitative descriptions, however, are largely resorting to the statistical and empirical approach. One example is the commonly used macroscopic Darcy model, which focuses only on a macroscopic behaviour averaged over a representative elementary volume, while it ignores any microscopic details inside this volume. For two-phase flows within porous media [1], again the extended Darcy law does not explicitly incorporate any microscopic features, such as liquid-gas interface, flow patterns and so on. Rather, all these two-phase features are quantitatively characterized by the so-called liquid saturation and all microscopic characteristics are lumped together to form a single term known as relative permeability. This term may theoretically, of course, be attainable by analysing microscopic two-phase details, however, in practice, it is identified exclusively by correlating experimental data. Such a methodology is quite efficient and powerful at the present stage when microscopic two-phase details have yet to be well understood, because it avoids opening the "black box" of the complicated microscopic two-phase behaviour, while it still predicts the system performance and explains experimentally observed phenomena pretty well. Exactly the same is the situation in studies of two-phase flow inside mini channels which may be circular capillary tubes or non-circular, irregular channels as used recently in micro heat pipes, with diameters of the order of 0.1 to 0.3 mm. Due to the wide technical applications, a macroscopic description of the two-phase flow phenomena is desirable as a tool for analysis and design. However, there exist almost no solutions because of the complexity introduced by the irregular *Present address: Dept of Mechanical Engineering, The University of Iowa, Iowa City, Iowa 52242, U.S.A. 377