A simplified model for water management in a polymer electrolyte membrane ͑PEM͒ fuel cell operating under prescribed current with iso-potential plates is presented. The consumption of gases in the flow field channels, coupled to the electric potential and water content in the polymer membrane, is modeled in a two-dimensional slice from inlet to outlet and through the membrane. Both co-and counter-flowing air and fuel streams are considered, with attention paid to sensitivity of along-the-channel current density to inlet humidities, gas stream composition, and fuel and oxygen stoichiometries. The parameters describing the nonequilibrium kinetics of the membrane/catalyst interface are found to be fundamental to accurate fuel cell modeling. A new parameter which models nonequilibrium membrane water uptake rates is introduced. Four parameters, the exchange current, a membrane water transfer coefficient, an effective oxygen diffusivity, and an average membrane resistance, are fit to a subset of data and then held constant in subsequent runs which compare polarization curves, current density and membrane hydration distributions, water transfer, and stoichiometric sensitivity to the balance of the experimental data.
Abstract-We discuss the problem of the reconstruction of the profile of an inhomogeneous object from scattered field data. Our starting point is the contrast source inversion method, where the unknown contrast sources and the unknown contrast are updated by an iterative minimization of a cost functional. We discuss the possibility of the presence of local minima of the nonlinear cost functional and under which conditions they can exist. Inspired by the successful implementation of the minimization of total variation and other edgepreserving algorithms in image restoration and inverse scattering, we have explored the use of these image-enhancement techniques as an extra regularization. The drawback of adding a regularization term to the cost functional is the presence of an artificial weighting parameter in the cost functional, which can only be determined through considerable numerical experimentation. Therefore, we first discuss the regularization as a multiplicative constraint and show that the weighting parameter is now completely prescribed by the error norm of the data equation and the object equation. Secondly, inspired by the edge-preserving algorithms, we introduce a new type of regularization, based on a weighted L 2 total variation norm. The advantage is that the updating parameters in the contrast source inversion method can be determined explicitly, without the usual line minimization. In addition this new regularization shows excellent edge-preserving properties. Numerical experiments illustrate that the present multiplicative regularized inversion scheme is very robust, handling noisy as well as limited data very well, without the necessity of artificial regularization parameters.
Van den Berg and Abubakar
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