A multi-component spatially-distributed model of two-phase flow for estimation and control of fuel cell water dynamics

The critical task of controlling the water distribution within the gas diffusion layer of a fuel cell suggests a partial differential equation (PDE) approach. Starting from first principles, the model of a fuel cell is represented as a boundary value problem for a set of three coupled, nonlinear, second-order PDEs. These three PDEs are approximated, with justification rooted in linear systems theory and a time-scale decomposition approach, by a single nonlinear PDE. A hybrid set of numerical transient, analytic transient, and analytic steady-state solutions for both the original and single PDE- based model are presented, and a more accurate estimate of the liquid water distribution is obtained using the single PDE-based model. The single PDE derived represents our main contribution on which future development of control, estimation, and diagnostics algorithms can be based.