Available online at www.sciencedirect.com Journal of Power Sources 179 (2008) 603–617 Modeling two-phase flow in PEM fuel cell channels Yun Wang 1 , Suman Basu, Chao-Yang Wang ∗ Electrochemical Engine Center (ECEC), and Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802, USA Received 19 December 2007; received in revised form 23 January 2008; accepted 24 January 2008 Available online 3 February 2008 Abstract This paper is concerned with the simultaneous flow of liquid water and gaseous reactants in mini-channels of a proton exchange membrane (PEM) fuel cell. Envisaging the mini-channels as structured and ordered porous media, we develop a continuum model of two-phase channel flow based on two-phase Darcy’s law and the M 2 formalism, which allow estimate of the parameters key to fuel cell operation such as overall pressure drop and liquid saturation profiles along the axial flow direction. Analytical solutions of liquid water saturation and species concentrations along the channel are derived to explore the dependences of these physical variables vital to cell performance on operating parameters such as flow stoichiometric ratio and relative humility. The two-phase channel model is further implemented for three-dimensional numerical simulations of two-phase, multi-component transport in a single fuel-cell channel. Three issues critical to optimizing channel design and mitigating channel flooding in PEM fuel cells are fully discussed: liquid water buildup towards the fuel cell outlet, saturation spike in the vicinity of flow cross-sectional heterogeneity, and two-phase pressure drop. Both the two-phase model and analytical solutions presented in this paper may be applicable to more general two-phase flow phenomena through mini- and micro-channels. © 2008 Elsevier B.V. All rights reserved. Keywords: Mathematical modeling; Proton exchange membrane fuel cells; Water management; Two-phase flow; Channel flow 1. Introduction Fuel cells, converting chemical energy of fuels directly into electricity, have become an integral part of alternative energy and energy efficiency. Their noteworthy features, high- energy conversion efficiency and zero emission, meet the critical demands of a rapidly growing society [1,2]. Among all types of fuel cells, the proton exchange membrane (PEM) fuel cell, also called polymer electrolyte fuel cell (PEFC), has reached center stage, particularly for mobile and portable applications [3,4]. Besides their high-power capability, PEM fuel cells work at low temperatures, produce only water as byproduct, and can be compactly assembled, making them one of the leading candidates for the next generation power generator. A typical PEFC consists of bipolar plates, gas channels, gas diffusion layers (GDLs), and a proton-conductive membrane ∗ Corresponding author. Tel.: +1 814 863 4762; fax: +1 814 863 4848. E-mail address: cxw31@psu.edu (C.-Y. Wang). 1 Present address: Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697-3975, USA. with platinum catalyst coated on each side, called the membrane electrode assembly (MEA), as shown in Fig. 1. Gas channels are grooved in graphite or metal plates, where injected reactant streams are distributed for electrochemical reactions. The GDLs, usually coated with micro-porous layers (MPLs), play an impor- tant role in electronic connection between the bipolar plate and the electrode and provide a passage for reactant transport and heat/water removal. Protons are produced from hydrogen oxida- tion in the anode catalyst layer, and pass through the membrane, carrying water molecules via electro-osmotic drag, to the cath- ode catalyst layer where the oxygen reduction reaction (ORR) occurs with water as byproduct. Water management is a central issue in PEFC technology because while water is essential for membrane ionic conduc- tivity, excess liquid water leads to flooding of catalyst layers and GDLs [5–7] as well as channel clogging [8,9]. Given low- operating temperatures during normal startup (25 ◦ C) and hence low-saturation pressures, two-phase phenomena are unavoid- able in automotive fuel cells. Two-phase transport in a fuel cell consists of three sub-problems: catalyst layer flooding, GDL flooding, and two-phase flow in channels. To date, most of the efforts in two-phase modeling were devoted to the former two 0378-7753/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jpowsour.2008.01.047