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Section 2.12 Modeling of the hydraulic circuit ∆p γQ 2 ρEl Q 2 1 ρ Q 2 (2-81) (2-82) Wherein: hf Head loss h Height p Pressure ρEl Electrolyte density g Gravity constant (m) (m) (Pa) 1,354 kgm-3 9.81 N(kg)-1 Wherein: f Friction factor (-) lP Pipe length (m) dP Pipe diameter (m) vP Fluid velocity (ms-1) Orifice C LCh2AOrifice C 2 LCh El C kLCh 2γ ρEl The presented approximation represents the results of the time-consuming CFD simulations very precisely, as shown in Figure 2-19. Values for the coefficients β and γ are given in the cell design section, namely in Table 5-4 on page 83. 2.12.4 Pressure drop in pipes For computing the pressure drop in the pipes, the concept of head loss is used, as shown in Eq. (2-83) [72, 73]. In this concept, the pressure drop Δp is converted into an equivalent gain or loss of height. hf hIn hOutpIn pOut∆h ∆p ρElg ρElg ρElg (2-83) In the common concept of a VRFB, the negative and the positive electrolyte circuits are closed. Hence, Δh is equal to zero over the entire hydraulic circuit. The pressure drop is then only related to the head loss, as shown in Eq. (2-84). ∆p hfρElg (2-84) For a pipe with a circular cross-section, the head loss, hfP, is given by Eq. (2-85) [72]. lP vP2 hfP f dP 2g (2-85) Combining the Eqs. (2-84) and (2-85) leads to Eq. (2-86). Therein, the fluid velocity vP in the pipe is expressed as the volumetric flow rate, QP, over the circular cross-sectional area of the pipe. ∆p 8f lP ρElQ 2 (2-86) P dP5π2P The definition of the friction factor depends on the flow regime [72]. If the Reynolds number is below 2,300, the flow is supposed to be laminar. Thus, the friction factor only depends on the duct shape and the Reynolds number, as shown in Eq. (2-87). For a 52PDF Image | Model-based Design Vanadium Redox Flow Batteries
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