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3.4.3- Flow rate proportion in the porous and non-porous media of the flow field As stated in Assumption v, the pressure at the interface of porous and non-porous media is a continuous entity. Therefore, the magnitude of pressure gradients in both media must be in the same order, too: (3.26) βπ π£Μ π£Μ βπΜ π£Μ Μ π =π( π + π)=π΄ π,π΄ =πππππ π‘πππ‘πππ‘hππππππππ1 πΏ π€2 h2 1 πΎ 1 By applying the properties of the RFBs in the lab, Equation 3.26 is reached: Μ 3 ππΜ ππ=π΄1ππΓ10,ππππ ,π΄1=π(1) ππ Equation 3.26 demonstrates that more than 99% of the flow in the channel passes the non-porous medium, and less than 1% diffuse in the porous medium above the channels. This result justifies the following assumption that the amount of flow passing the electrode above the channels is negligible. The fundamentals of the hydraulic-electrical analogous model are based on this assumption. However, the model is modified further to relax the error of this assumption. 3.5- Hydraulic-electrical analogous model (HEAM) HEAM is developed by assuming the electrode above the channels acts like an impermeable wall justified by the small amount of flow diffusing in the electrode. Moreover, it is assumed that the entrance region is negligible, therefore, viscous forces are the only dominant forces in the channels. For Round pipes, the Hagen-Poiseuille profile is obtained by applying the Newtonβs second law of motion: [101] π£(π) = (βπππ·2) [1 β (2π)2] (3.27) 16ππ π· 33PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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