Shape optimization of the hydrogen fuel cell cathode air channels

In this paper we deal with the shape optimization of the hydrogen fuel cell cathode air channel. We consider a 2d isothermal model given by a nonlinear PDEs system, involving the oxygen and vapor concentrations,. ² the velocity of the gas mixture and the pressure. The shape energy associated to this system "measures" the concentration of the oxygen on the catalyst layer, the concentration of the vapor on the outlet and the pressure drop. By using a fixed point approach we prove the existence of solution to the PDE system without restriction on data, and the uniqueness of the solution if the inlet oxygen concentration is small. Using classical shape optimization techniques we prove the shape differentiability of the state variables and of the shape energy. By using an appropriate adjoint problem we transform the shape energy derivative to a form appropriate for numerical computations. Finally, we present several numerical solutions of optimal cathode air channel shape. 2Here concentration means mass fraction.