  We discuss the problem of the optimal design of a micro-tubular fuel cell
applying an inverse homogenization technique. Fuel cells are extremely clean
and efficient electrochemical power generation devices, made up of a
cathode/electrolyte/anode structure, whose energetic potential has not being
fully exploited in propulsion systems in aeronautics due to their low power
densities. Nevertheless, thanks to the recent development of additive layer
manufacturing techniques (3D printing), complex structures usually impossible
to design with conventional manufacturing techniques can be constructed with a
low cost, allowing notably to build porous or foam-type structures for fuel
cells. We seek thus to come up with the micro-structure of an arrangement of
micro-tubular cathodes which maximizes the contact surface subject to a
pressure drop and a permeability constraint. The optimal periodic design
(fluid/solid) emerges from the application of a shape gradient algorithm
coupled to a level-set method for the geometrical description of the
corresponding cell problem.
