Scaling analysis of diffusion–reaction process in proton exchange membrane fuel cell with the second Damköhler number

Abstract

Diffusion-reaction coupling process in flow fields dominates the performance of proton exchange membrane fuel cell. This paper defined a new second mechanistic Damköhler number (DaII,mech) to compare the similarity and efficiency between different flow fields. Dimensionless model and numerical model were combined together to analyze the single channels, parallel and single-serpentine channels. According to trends of DaII,mech curves over current density, the diffusion–reaction interaction can be divided into three states: reaction-enhanced (DaII,mech ∼ 1000), transition and diffusion-limited states (DaII,mech ∼ 100). With the enlargement of active area, almost the same Damköhler curves and contours demonstrate the similarity of diffusion–reaction process in single channel and parallel channels. But there is no obvious scaling invariance over active area for single-serpentine channels due to its asymmetric structure. A new efficiency evaluation criterion (EEC) based on Damköhler number and Euler number is proposed to comprehensively compare the fuel cell performance. The EEC curves also present three-state characteristics. And the EEC values of parallel channels are several orders of magnitude higher than that of single-serpentine channels. This scaling method is expected to be further generalized to other flow fields and operating conditions to accelerate the fuel cell design and optimization.