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Section 2.5 Shunt currents of the standard electrolyte has been measured and published by two research groups. The Eqs. (2-28) to (2-31) describe the conductivity for a temperature of 298 K. Fraunhofer ICT, Germany [40]: σ 19.6 Sm-1 10.7 Sm-1 ⋅ SoC σ 30.8 Sm-1 14.6 Sm-1 ⋅ SoC University of New South Wales, Australia [41]: σ 18.8 Sm-1 7.3 Sm-1 ⋅ SoC σ 28.9 Sm-1 13.9 Sm-1 ⋅ SoC In this work, the arithmetic mean value of both measurements is employed, as shown in the Eqs. (2-32) and (2-33): σ 19.2 Sm-1 9.0 Sm-1 ⋅ SoC (2-32) respectively, in the particular object where the resistance is computed. Due to the strong impact of the SoC on the electrolyte conductivity, the model explicitly considers the different SoCs in the battery system. Hence, the electrolyte conductivity is calculated for each inlet and outlet channel, as well as for the forward and backward piping from and to the tanks. 2.5.4 Shunt current resistance of manifolds and pipes The electric resistances of hydraulic elements are computed using their dimensions and the electrolyte conductivity, as shown in Eq. (2-34). Herein, subscript ‘O’ denotes the respective object (channel, manifold or external circuitry). Object’s length is lO, and object’s cross sectional area is CSAO. The quotient of length over cross sectional area is called geometry factor. 1 lO RO+/ σ+/ ⋅ CSA (2-34) O For the meander-shaped channel, the geometry factor is derived using finite-element- analysis (FEA). The cell, consisting of inlet channel, distribution funnel, porous flow- through graphite electrode, collection funnel and outlet channel is modeled using the ANSYS Workbench. To determine the geometry factor, the cell model is set up in ANSYS Maxwell, which allows for the computation of electric fields and currents. ANSYS Maxwell is in particular suited for this task because it supports a flexible geometry parametrization. Hence, it adapts the cell model to the key parameters electrode width, height, and thickness, manifold diameter, channel height and channel width. For determining the geometry factor, the following procedure is developed. An ideal conductor represents the electrode to which an excitation voltage, ETest = 10 V is σ 29.9 Sm-1 14.3 Sm-1 ⋅ SoC Herein, SoC− and SoC+ denote the SoC of the negative and the positive electrolyte, (2-28) (2-29) (2-30) (2-31) (2-33) 2.5.5 Shunt current resistance of the channels 28PDF Image | Model-based Design Vanadium Redox Flow Batteries
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