Three-dimensional macrohomogeneous mathematical model of an industrial-scale high-temperature PEM fuel cell stack

Mathematical modelling offers an efficient tool for the development and optimization of various technologies, including fuel cells. However, the implementation and utilization of such a model for an industrial-scale fuel cell stack is a considerable challenge. The reason is that it consists of many layers and interphases which often display stiff behaviour. Consequently, a detailed mathematical model of such a stack is computationally difficult and highly demanding on the computational power of the hardware. The macrohomogeneous (volume-averaged) approach presented assumes a continuum on a characteristic length scale of a few centimetres (cumulative thickness of a few cells of the stack) in all spatial directions. The anisotropic structure of the real system is then expressed by means of anisotropic transport parameters. In this work, the macrohomogeneous approach is applied to a three-dimensional model of an industrial-scale high-temperature polymer electrolyte membrane (PEM) fuel cell stack consisting of 100 cells with two different flow-field geometries: (a) a 5-fold serpentine and (b) a parallel channel flow field. They were selected because of the significantly different uniformity of the gas distribution in the cell. Stationary conditions, dry pure hydrogen and air at the inlet, as well as common operating conditions (160 °C, 101.325 kPa) are considered. The model approach described not only helps to provide a better understanding of the behaviour of a fuel cell stack on a local scale, but also to identify potential weaknesses in the system design.