10 th World Congress on Structural and Multidisciplinary Optimization May 19 -24, 2013, Orlando, Florida, USA 1 A 3D topology optimization model of the cathode air supply channel in planar solid oxide fuel cell Xiankai Song, Alejandro R Diaz, Andre Benard Mechanical Engineering, Michigan State University, East Lansing, Michigan, USA, diaz@egr.msu.edu 1. Abstract A 3D topology optimization model is developed to maximize the current generation of the cathode by designing the geometry of an air supply channel found in solid oxide fuel cells (SOFC). The problem is reduced to a periodic, coupled problem in consideration of a convection dominated oxygen gas transport in the air flow and oxygen ion diffusion in the solid cathode. The air flow field is calculated using a modified momentum equation with a Darcy flow term, and the result is used as a known parameter in the calculation of the oxygen gas transport. The oxygen gas transport is coupled with the oxygen ion diffusion by a design-dependent oxygen exchange boundary condition. Numerical examples discuss the effect of geometric parameters. 2. Keywords: solid oxide fuel cell, topology optimization, cathode design 3. Introduction A SOFC converts chemical energy directly into electrical power and offers the considerable potential of a high efficiency and environmental friendly electrical power source [1]. Distinguished from other types of fuel cells, the oxygen ions migrate through a solid electrolyte for the completion of electrochemical reactions in the solid electrodes. The structure of a planar SOFC is illustrated in Figure 1. Interconnect Electrode Air Channel Fuel Channel (a) Interconnect Interconnect Interconnect Interconnect Air channel Fuel channel Cathode Anode Electrolyte Electrolyte Cathode Anode Electrolyte Air flow Fuel flow Air flow with O2 Fuel flow with H 2 1/2O 2 +2e - =O 2- H 2 + O 2- = H 2 O+2e - e - e - O 2 H 2 H 2 O O 2- x z y y z z Region designed (b) (c) x Figure 1: Schematic arrangement of a planar SOFC: (a) overview (b) front view (c) side view In a SOFC, there are voltage losses associated with the ohmic resistances in the electrodes and the active polarizations on the air-cathode interface and the fuel-anode interface [2]. However, the voltage losses in a cathode usually dominate the entire stack so it is more efficient to focus on improving the cathode performance [3].Attempts in designing the cathode geometry from macro to micro scales have shown progresses in reducing the cathode resistance. Chan et al. [4] performed a sensitivity analysis for a generic macro-homogeneous polarization model of a solid oxide fuel cell to study the effect of the thickness of the fuel cell components. In a smaller scale, the advantage of using non-flat cathode-electrolyte interface is