A two-dimensional mathematical model for vanadium redox flow battery stacks incorporating nonuniform electrolyte distribution in the flow frame

Lumped models have been widely adopted to predict the performance of the vanadium redox flow battery (VFRB) stack, which mainly due to its simplicity in modeling transient behaviors during operation cycles. However, average transport and electrochemical properties in previous lumped models make it impossible to obtain the information of electrolyte distributions in stacks. To address this issue, in this work, we report a two-dimensional mathematical model for a VRFB stack considering the effect of nonuniform electrolyte distributions in the flow frame via a flow network equivalence method. With this new model, battery performance and its temperature at different operating conditions are determined accurately. It is demonstrated that (i) temperature fluctuations of the stack reach up to 10 K at different current densities and flow rates; (ii) 25% blockage in the middle cell can lead to the capacity reduction by up to 80%.