Modeling transport of membrane water in PEMFC and energy loss analysis at −20 °C based on mathematical boundedness

This work analyzes why the classic cold start-up model cannot match experimental data well in high initial membrane water content due to the unboundedness of membrane water content conservation equation, and a mathematical framework to ensure the boundedness of membrane water content is developed to solve these issues. Based on vehicle mechanism and Grotthuss mechanism, a “traffic jam” model is applied to describe the transport of membrane water reaching its maximum content. To keep the membrane water content within the upper bound, a new governing equation is proposed and the corresponding boundary conditions and discretization schemes are set. This model has been proved in eleven cases by comparing with experimental data including different initial membrane water content and different current density. Some of these cases are considered impossible to exist in classical cold start-up theory. The results illustrate that the boundedness model can show a clearer physical process and obtain more accurate and reasonable calculation results.