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Section 2.3 Concentrations of the ionic species concentrations. These side reactions include but are not limited to the oxidation of V2+ ions by atmospheric oxygen, the evolution of hydrogen and oxygen, the corrosion of carbon components, the precipitation of vanadium salts, the (electro) osmotic water drag and the vanadium crossover across the membrane as well as the shunt currents [19]. The effect of water drag and vanadium crossover can be reverted by mixing positive and negative tanks and re-conditioning the electrolytes. However, other side-reactions, such as the carbon corrosion or the precipitation of the vanadium salts are irreversible. Regarding parasitic processes that affect the species’ concentration, only the phenomena of shunt currents and vanadium crossover are considered in this work. Finally, the coupling of the tanks and the cells via the volumetric flow rate also affects the concentrations of the ionic species in the tanks and the cells. 2.3.1 Tank concentration of vanadium ions To calculate the tank concentration of the four different vanadium ions, we have to know the ionic flux, J out , leaving the stacks and entering the tanks. Due to the shunt currents, iStacks the charging and discharging current of each cell is different, as laid out in Section 2.5 on page 26. It is assumed that both half-sides of all cells receive an identical flow rate. Hence, to yield the ionic flux of the total stack, we can summarize the concentrations of all cells of the stack and multiply them with the cell flow rate. The cell flow rate is the stack flow rate over the number of cells. The ionic flux of the total stack is shown in Eq. (2-7) for the negative half-side and in Eq. (2-8) for the positive half-side. To derive the total ionic flux of all stacks, the ionic fluxes of all stacks are summarized. Wherein: cout Output concentration of vanadium species i in cell n of stack m (molm-3) Counting index for vanadium ions (-) Total ionic flux of vanadium species i from all stacks (mols-1) Counting index for cells (-) Number of cells per stack (-) Number of stacks per tank (-) Counting index for stacks (-) Volumetric flow rate of stack m (m3s-1) iCmn J out iStacks n NC NS m QSm i Jout iStacks Jout iStacks NS Q NC Smcout (2-7) (2-8) NC iCmn n=1 m=1 NS Q NC Smcout m=1 NC iCmn n=1 During the battery operation, we continuously take an ionic flux out of the tank and feed it to the stacks. Simultaneously, we collect the electrolyte coming out of the stacks and feed it back to the tank. Hence, the tank concentration of the different vanadium species i is determined by the outgoing and the incoming ionic fluxes, as shown in the Eqs. (2-9) and (2-10). The incoming ionic flux of the tank is coming out of the stacks and thus is 16PDF Image | Model-based Design Vanadium Redox Flow Batteries
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