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Scaling analysis predicts the order of magnitude for involved parameters in modeling. [87,98] For example, Equation 3.9 is extracted from the fluid continuity equation in a long channel by utilizing scaling analysis: π»π£=0βππ£π₯ +ππ£π¦ +ππ£π§ =0,ππ£π₯ =π(π£π₯),ππ£π¦ =π(π£π¦),ππ£π§ =π(π£π§) ππ₯ ππ¦ ππ§ ππ₯ πΏ ππ¦ π€ ππ§ h π ππππππ π£π₯ π£π¦ π£π§ β πΏ +π€+h =0,π‘,hβͺπΏβπ£π¦,π£π§βͺπ£π₯ (3.9) Where L, w, and h are the channelβs length, width, and height, respectively. The performed scaling analysis suggests that the fluid velocity magnitude in the x-direction is greater than the same in y- and z-directions. By the same rationale, the velocity in y- and z-direction is neglected for further analysis in this document. 3.1.5- Studied flow field designs The analyses, models, and experiments in this study are implemented on IFFs, SSFFs, and 3- channel serpentine flow fields (3SFFs). Figure 1. 6 demonstrates schematic of these flow fields. IFFs forces the electrolytes to pass through the electrode by making them jump over FF ribs, which ensures full contact between the electrolyte flow and electrodes. However, as Wang et. al. suggested, the residence time in IFFs is lower than SFFs, which results in lower reaction extent in each cycle. [99] Moreover, as mentioned in Chapter 1, it is expected for RFB cells with SFF to have higher pressure loss than the ones with IFF. 3.2- Dimensional analysis of fluid dynamics in VRFB Based on Buckingham pi theorem, the number of DNs describing the system is the number of variables subtracted by the number of independent units. 23PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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