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Section 2.4 Vanadium crossover 1600 1200 800 400 0 1600 1200 800 400 0 a) QC=0.75 Lmin-1 b) Q=1.5 Lmin-1 Tank conc., c2T Cell conc., c2C Cell output conc., cout 2C 0 50 100 150 200 Time in min Figure 2-1: V2+ concentrations during a sample cycle with 200 A between tank SoC 20 % and 80 % for two different constant flow rates In general, vanadium crossover and water transfer through the membrane is modeled using the Nernst-Planck and the Schlogl equation, which accounts for all three of the mechanisms mentioned before [18, 21–23]. For a Nafion 117 membrane, it is observed that the diffusion phenomenon causes 90- 95 % of the total vanadium crossover [18, 24]. Thereby the effect of migration is found to play a minor role. In practice, the viscosities of positive and negative electrolyte deviate from each other. Hence, an identical flow rate for positive and negative half-cell introduces a pressure gradient between two half-cells. This gives way to the crossover caused by convection. Different flow rates for the two half-cells, reflecting the different viscosities, eliminate the effect of convection [25]. For studies on a stack level, the approaches mentioned above are too complex to be solved with reasonable computational effort in a reasonable amount of time. Hence, several simplified methods have been developed. In [24], the Nernst-Planck equation and Schlogl’s equation are solved for a zero-dimensional model. This model accounts for convection, migration and diffusion of vanadium ions through the membrane. However, the comparison with the formerly presented two-dimensional model [18] reveals large differences between both modeling approaches. A similar approach is employed in [26], but the results are not valid as the work contains a unit conversion error and thus the results are off by a factor of 1,000. 19PDF Image | Model-based Design Vanadium Redox Flow Batteries
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