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π»π =βππ£ βπ½ππ£2 (3.6) ππΎππ Where Ξ² is a coefficient. Numerous studies have investigated the mechanism behind the Forchheimer term. The latest narrative on what is this mechanism is that the Forchheimer term represents the microscopic form drag force due to the presence of solid obstacles. [89β92] Ruth and Ma have the same opinion on what Forchheimer term represents, however, they challenge the uniqueness of this solution and present complicated solutions. Moreover, they present a similar dimensionless number to Reynolds number, which considers both the amount of flow rate and the geometric structure of the porous medium, to evaluate the necessity of Forchheimer term. However, the classic form of Forchheimer term is still used in the literature due to its simplicity and accuracy. [38,43,79] Several studies suggested equations to calculate Ξ². [90,92] However, Josephβs and Nieldβs modification to Darcyβs law is an established one: [38,93] π»π =βππ£ βπΆπΉπ|π£|π£ (3.6a) π πΎπβπΎππ Where CF is the Forchheimer coefficient. The maximum value of the Forchheimer coefficient is 0.55, however, it can be less than 0.55 if the diameter of solid particles in porous media is in order of one-tenth of the hydraulic diameter of porous media. [88] In this study, the Forchheimer coefficient is assumed to be 0.55 due to the high porosity of the electrodes in the RFB systems. Another facet that Darcyβs law overlooks is the viscous shear stress of the fluid that opposes the flow. Brinkman introduced a term, adapted from steady state N-S equations, to account for the above-mentioned effect: [94] π»π =βππ£ +πΜβ2π£ (3.7) ππΎππ 21PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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