A Dynamic Semi-Analytic Channel-to-Channel Model of Two-Phase Water Distribution for a Unit Fuel Cell

The critical task of controlling the water accumulation within the gas diffusion layer (GDL) and the channels of a polymer-electrolyte-membrane (PEM) fuel cell is shown to benefit from a partial-differential-equation (PDE) approach. Starting from first principles, a model of a fuel cell is represented as a boundary value problem for a set of three coupled nonlinear second-order PDEs for mass transport across the GDL of each electrode. These three PDEs are approximated, with justification founded in linear systems theory and a time-scale decomposition approach, by a semianalytic model that requires less than one-third the number of states to be numerically integrated. A set of numerical transient, analytic transient, and analytic steady-state solutions for the semianalytic model are presented, and an experimental verification of the cell voltage prediction due to liquid-water accumulation is demonstrated. The semianalytic model derived and the associated analysis represent our main contribution for which future expansion of along-the-channel dynamics and statistical consideration of cell-to-cell variations can be implemented for application to control, estimation, and diagnostic algorithms.