Adjoint method for solid-oxide fuel cell simulations

Adjoint methods suitable for obtaining sensitivity derivatives for numerical simulations of solid-oxide fuel cells are presented. The adjoint method is derived, and the implementation is discussed, including a methodology for accurately obtaining all the linearizations necessary for correct implementation. Results are included for a one-dimensional anode model that includes diffusion, permeation, and relevant chemical reactions. Using this model, the accuracy of the sensitivity derivatives is demonstrated for design variables describing geometric and material properties of the anode. Finally, the adjoint method is demonstrated for a three-dimensional fuel cell geometry where sensitivity derivatives are obtained for approximately 180,000 design variables. The results are used to modify the upper and lower walls of the plenum to obtain significantly improved distribution of fluid amongst the channels.