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Section 2.12 Modeling of the hydraulic circuit However, it is beyond the scope of this work to tackle this problem. Hence, the tank inlet is modeled as a sudden expansion and the tank outlet as a sudden contraction. In this case, the loss coefficient of the tank inlet is given by Eq. (2-91) [72]. As the exact tank geometry is not known, CSAT≫CSAP is assumed. Therefore, the loss coefficient of the tank inlet is unity. CSAP 2 kLTIn 1CSA T Wherein: CSAP Pipe cross-sectional area (m2) CSAT Tank cross-sectional area (m2) The loss coefficient of the tank outlet is given by Eq. (2-92) [72]. Again, CSAT≫CSAP is assumed. Therefore, the loss coefficient of the tank outlet is 0.42. CSAP 2 kLTOut 0.421CSA T Table 2-2: Loss coefficients for various hydraulic elements (2-92) (2-91) Component 90° bend T-junction, direct flow T-junction, branch flow Tank, inlet Tank, outlet 2.12.6 Pump efficiency and pump power k Ref. / Source 0.30 [74] 0.20 [74] 1.00 [74] 1.00 Eq. (2-91) 0.42 Eq. (2-92) In this work, two pumps apply the desired volumetric flow rate to the two electrolyte circuits. The required electric pump power is calculated with Eq. (2-93) considering a variable, flow rate dependent pump efficiency [73]. PPumps 2 ΔpTotalQPump ηPump (QPump ) (2-93) Wherein: ηPump ΔpTotal PPumps QPump Pump efficiency (-) Total pressure difference generated by the pump (Pa) Electric pump power of both pumps (W) Pump volumetric flow rate (m3s-1) The efficiency of the pump strongly depends on the flow rate, as shown Figure 2-20. The presented curves are derived from datasheets of seven different pumps from three different manufacturers. All efficiencies are derived while pumping water, not VRFB electrolyte. The pump efficiency for pumping electrolyte has not been published yet. The efficiencies of pumps from different manufacturers show a similar trend with a peak efficiency at approximately 60 % of the maximum flow rate. This point is called best- efficiency-point (BEP). However, the efficiencies of different pumps in their BEPs vary strongly. Thus, for this work, an average efficiency is calculated, as shown 54PDF Image | Model-based Design Vanadium Redox Flow Batteries
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