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path of electrolytes in RFB cells. Hence, understanding the pressure distribution is necessary to control the flow maldistribution. Moreover, the power demand of electrolytes pumps affects the efficiency of RFB systems. Several experimental studies have concluded that pumps are responsible for up to a 10% drop in the system efficiency of a large-scale VRFB. [53,54] Pump power consumption rate (Ppump) is directly linked to the overall pressure drop of electrolytes, as Equation 1.4 demonstrates: [55,56] 𝑃 = 𝑄∆𝑃𝑅𝐹𝐵 (1.4) 𝜂𝑝𝑢𝑚𝑝 Where Q, ΔPRFB, and ηpump are the electrolyte flow rate, the overall pressure drop of the RFB, and the pump efficiency, respectively. Larger pumps are less efficient, cost more, and consume greater power rate than smaller ones. [42,57,58] Equation 1.3 suggests that higher pump power is required for electrolyte flows with larger pressure drop. Previous studies have suggested that pumps cost 5- 14% of the capital cost, [59,60] and 5-14% of the total cost of RFB systems. [61] The target total cost of energy storage systems is 100 $/KWh, and according to the studies, the total cost of pumps is at 50-120 $/KWh, exceeding the target limit at the most. Consequentially, reducing the cost and increasing the system efficiency of RFBs are motivations to study pressure distribution. 1.3.1- Literature review on modeling in RFBs and liquid-phase electrochemical devices Numerous studies have suggested improvements to RFBs and liquid-phase electrochemical devices by modeling fluid dynamics. A summary of the studied phenomena and modeling approaches in literature are presented in Table 1. 1. Although numerical approaches are more accurate than analytical ones, they are computationally more costly than analytical ones, and numerical modeling describes the system it was designed 𝑝𝑢𝑚𝑝 11PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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