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Section 2.12 Modeling of the hydraulic circuit 2.12.3 Implementation into the MATLAB/Simulink model For an efficient implementation of the CFD simulation results, the following approach is developed. The graphite felt obviously behaves like a linear hydraulic resistance, as shown in Eq. (2-78). The straight channel parts are an additional linear hydraulic resistance if they carry a laminar flow, which is desired to keep the pressure drop low. The orifices in the channel, such as 90° and 180° bends show a quadratic dependence on the flow rate, as shown in Eq. (2-90). Hence, the function shown in Eq. (2-80) is proposed to model the non-linear hydraulic resistance of the cell. Herein, the coefficients β and γ are used, which yet have to be determined. ∆p Q γQ2 (2-80) CCC We can derive the value pair β and γ analytically by using two pairs of values of pressure drop versus flow rate from the CFD simulations. Hence, in principle, only two values have to be determined by means of CFD simulation, which saves computational resources. 80 60 40 20 a) Stack pressure drop 0 0 20 40 60 80 100 CFD, 1000 cm2/10 mm Approx., 1000 cm2/10 mm CFD, 2000 cm2/10 mm Approx., 2000 cm2/10 mm CFD, 2000 cm2/20 mm Approx., 2000 cm2/20 mm 1000 cm2/10 mm Channel 2000 cm2/10 mm Channel 2000 cm2/20 mm Channel 1 0 -1 -2 b) Relative deviation 0 20 40 60 80 100 Stack flow rate QS in Lmin-1 Figure 2-19: Stack pressure drop over flow rate for different electrode areas and different channel widths, results from CFD-simulation and approximation In the MATLAB/Simulink Simscape library, linear and non-linear hydraulic resistances are available. While the value of β can be used directly, γ has to be converted into an equivalent channel loss coefficient, kLCh, as shown in the Eqs. (2-81) and (2-82). Thereby, the cross-sectional area of the orifice, AOrifice, can be set to unity. 51 Deviation in % Pressure drop in kPaPDF Image | Model-based Design Vanadium Redox Flow Batteries
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