Air-Forced Flow in Proton Exchange Membrane Fuel Cells: Calculation of Fan-Induced Friction in Open-Cathode Conduits with Virtual Roughness

Measurements of pressure drop during experiments with fan-induced air flow in the open-cathode proton exchange membrane fuel cells (PEMFCs) show that flow friction in its open-cathode side follows logarithmic law similar to Colebrook's model for flow through pipes. The stable symbolic regression model for both laminar and turbulent flow presented in this article correlates air flow and pressure drop as a function of the variable flow friction factor which further depends on the Reynolds number and the virtual roughness. To follow the measured data, virtual inner roughness related to the mesh of conduits of fuel cell used in the mentioned experiment is 0.03086, whereas for pipes, real physical roughness of their inner pipe surface goes practically from 0 to 0.05. Numerical experiments indicate that the novel approximation of the Wright-ω function reduced the computational time from half of a minute to fragments of a second. The relative error of the estimated friction flow factor is less than 0.5%.