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two parameters (hp and K) for tuning KĖ . Therefore, it is easier to use for designing and controlling experiments or predicting the behavior of the system while scaling up. 3.3- Assumptions for further analysis of the fluid dynamics in the RFBs i. RFB systems are in steady state. The charging and discharging cycles for RFBs usually take hours, and they reach a steady state in a couple of minutes. Therefore, this assumption is a strong one for simplification of the modeling process. ii. The flow is laminar. Based on the literature, the maximum Reynolds number for the laminar flow in a round pipe is around 2100. Reynolds numbers between 2100 to 4000 signifies a transitional flow, and flows with Reynolds numbers beyond 4000 are turbulent. [101] It is a strong assumption for the RFB cells with IFF due to possessing numerous parallel channels in their designs, but it can be a weak one for SSFF and MSFF, where the electrolyte flow passes through one channel and a couple of parallel channels, respectively. iii. The entrance region in channels is negligible. In the entrance region, boundary layer, which viscous forces are dominant, is not fully developed. For a laminar flow, the length of the entrance region is predicted as: ðð = 0.06ð ð (3.14) ð· The strength of this assumption is investigated in Section 3.2.2. iv. The flow velocity vector direction is in the direction of the length of channels (x-direction) and the velocity gradient direction is in the direction of the thickness and height of channels (z- and y-direction, respectively). The strength of this assumption is supported by employing scaling analysis on the fluid continuity equation, as done in Section 3.1.4. 26PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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