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After implementing RREF function: ρ vc hc ΔPm μ K L wc hc ρ100110000 vc 0 1 0 2 1 0 0 0 0 hp 0 0 1 0 1 2 1 1 1 𝐾𝑤𝑤h𝐿 ∆𝑃 𝜌𝑣h 𝐸𝑢=𝑓(𝑅𝑒, , 𝑟, 𝑐, 𝑐, ),𝐸𝑢= 𝑚,𝑅𝑒= 𝑐 𝑐 h2 h h h h 𝜌𝑣2 𝜇 𝑝𝑝𝑝𝑝𝑝 𝑐 (3.10) Where Eu and Re are the Euler number and the Reynolds number, respectively. A representation of K̃ is by using a DN called compression ratio (CR): 𝐶𝑅=1− h𝑝 (3.11) h𝑝,0 Which hp,0 is the uncompressed electrode thickness. Based on the literature, the permeability and the thickness of porous media has a linear correlation with each other.[38,100] This correlation leads to the following equations: 𝐾=𝐾 h𝑝 =𝐾(1−𝐶𝑅) 0 h𝑝,0 0 (3.12) (3.13) ̃ 𝐾 𝐾=h2= 𝑝 𝐾0(1−𝐶𝑅) (h𝑝,0(1−𝐶𝑅)) 𝐾0 1 ́ 𝑎̃𝑏 𝑐 𝑑̃𝑒̃𝑑 →𝐸𝑢=𝐴𝑅𝑒𝐾𝑤̃̃𝑤 𝐿h 𝑟𝑐𝑐 2=h2 1−𝐶𝑅 𝑝,0 Which K0 is the uncompressed permeability. This representation of K̃ shows the linear relationship between the permeability and the thickness of electrodes, and a single parameter (CR) substitutes 25PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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