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UnderstandininggththeeVVaannaaddiuimumRRedeodxoFxloFwlowBaBttaetrtiesries 31435 geometry from a reservoir into a pipe from a pipe into a reservoir bends and elbows valves Loss coefficient kL,i 0.04 - 0.9 1 0.2 - 1.5 0.15 - 10 Table 6. Loss coefficients (Munson et al., 1998; Candel, 2001). where fi is the friction factor, kL,i the loss coefficient given in Tab. 6, Li and Di are the length and diameter of the conduit. When the flow is laminar, the friction factor fi is derived from the Poiseuille law (28) and for a turbulent flow, it is obtained from the Colebrook equation (29) (Candel, 2001): 1 εi 3.7Di + 2.51 = −2log where εi is the equivalent roughness of the pipe and Rei is the Reynolds number: fi = 64 Rei [−] (28) [−] (29) Rei Re = ρVsD = VsD [−] (30) 5.2 Stack hydraulic model The stack geometry is too complex to be analytically described (Fig. 9), therefore the stack hydraulic model can only be numerically obtained with a finite element method (FEM). fi fi μν where ρ is the density, μ the dynamic viscosity and ν the kinematic viscosity. Fig. 9. Hydraulic circuit of a 2 cells stack. Note that the frame is not represented and that the colored segments represented the electrolytes (liquid). It was assumed that the flow stays laminar in the stack; although the flow might be turbulent in the manifold at high velocity. In this example, the flow stays laminar in the distribution channels where the major part of the pressure drop Δpstack occurs; therefore, the pressure drop in the stack Δpstack is proportional to the flowrate: Δpstack = QR [Pa] (31) where R is the hydraulic resistance obtained from FEM simulations.PDF Image | Understanding the Vanadium Redox Flow Batteries
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