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Analysis of Fluid Flow in Redox Flow Batteries

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Analysis of Fluid Flow in Redox Flow Batteries ( analysis-fluid-flow-redox-flow-batteries )

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βˆ†π‘ƒπ‘š =πœ‡ 𝑣𝑐 +πœ‡ 𝑣𝑐 β†’βˆ†π‘ƒ =𝑂(𝐿(πœ‡ 𝑣𝑐 +πœ‡ 𝑣𝑐 )) (3.18) 𝐿 h𝑐2 𝑀𝑐2 π‘š h𝑐2 𝑀𝑐2 A DN is formed by dividing the first term over the second one to find the dominant term on the RHS: πœ‡ 𝑣𝑐 h𝑐2 = 𝑀𝑐2 = 𝑀̃ , 𝑀̃ = π‘‰π‘–π‘ π‘π‘œπ‘’π‘  πΉπ‘œπ‘Ÿπ‘π‘’π‘  𝑖𝑛 π‘¦βˆ’π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› (3.19) πœ‡ 𝑣𝑐2 h𝑐2 𝑐 𝑐 π‘‰π‘–π‘ π‘π‘œπ‘’π‘  πΉπ‘œπ‘Ÿπ‘π‘’π‘  𝑖𝑛 π‘§βˆ’π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› 𝑀𝑐 wΜƒc is in order of 1 for the most cases studied, therefore, both terms are considered for further analysis. The governing equation is reiterated as: π‘‘π‘ƒπ‘š =πœ‡π‘‘2𝑣𝑐 +πœ‡π‘‘2𝑣𝑐 𝑑π‘₯ 𝑑𝑦2 𝑑𝑧2 3.4.2- Analysis of the fluid dynamics in the porous medium The governing equation for the fluid dynamics in the porous medium is: π‘‘π‘ƒπ‘š = πœ‡ 𝑣 +0.55𝜌|𝑣 |𝑣 +πœ‡πœ•2𝑣𝑝 +πœ‡πœ•2𝑣𝑝 +πœ‡πœ•2𝑣𝑝 𝑑π‘₯πΎπ‘βˆšπΎπ‘π‘πœ•π‘₯2 πœ•π‘¦2 πœ•π‘¦2 By implementing a scaling analysis, Equation 3.22 is produced: (3.20) (3.21) (3.22) DNs are formed by dividing each term over the others to find the dominant terms on the RHS: βˆ†π‘ƒπ‘š = πœ‡ 𝑣 + 0.55 πœŒπ‘£ 2 + πœ‡ 𝑣𝑝 + πœ‡ 𝑣𝑝 + πœ‡ 𝑣𝑝 𝐿 𝐾𝑝 √𝐾 𝑝 h𝑝2 𝑑𝑝2 𝑙𝑝2 πœ‡ 𝑣𝑝 h𝑝2 𝐾 𝐷𝑁1 = πœ‡π‘£ = h2 = π΅π‘Ÿπ‘–π‘›π‘˜π‘šπ‘Žπ‘›π‘› 𝑖𝑛 π‘¦βˆ’π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› π·π‘Žπ‘Ÿπ‘π‘¦β€²π‘  π‘™π‘Žπ‘€ π΅π‘Ÿπ‘–π‘›π‘˜π‘šπ‘Žπ‘›π‘› 𝑖𝑛 π‘₯βˆ’π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› π·π‘Žπ‘Ÿπ‘π‘¦β€²π‘ π‘™π‘Žπ‘€ 𝐾𝑝𝑝 πœ‡ 𝑣𝑝 𝑑𝑝2 𝐾 𝐷𝑁2=πœ‡π‘£ =𝑑2= 𝐾𝑝𝑝 (3.23) πœ‡π‘£π‘ 𝐷𝑁3 = 𝑙𝑝2 = 𝐾 = π΅π‘Ÿπ‘–π‘›π‘˜π‘šπ‘Žπ‘›π‘› 𝑖𝑛 π‘§βˆ’π‘‘π‘–π‘Ÿπ‘’π‘π‘‘π‘–π‘œπ‘› { πœ‡2β€² 𝐾𝑣𝑝 𝑙𝑝 π·π‘Žπ‘Ÿπ‘π‘¦ π‘ π‘™π‘Žπ‘€ 30

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