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Section 2.8 Activation overpotential Figure 2-13: Numerical examples of activation overpotential, derived with three different parameter datasets for an electrode height of 4 mm Specific surface area, transfer coefficient and electrochemical rate constant from Shah et al. [22] (sF=2·106 m-1, α=0.5, kRC−= 1.75·10−7 ms-1, kRC+= 3·10−9 ms-1), Knehr et al. [18] (sF=2·106 m−1, α−=0.45, α+=0.55, kRC−= 7·10−8 ms-1, kRC+= 2.5·10−8 ms-1) and You et al. [57] (sF=1.62·104 m-1, α=0.5, kRC−= 1.7·10−7 ms-1, kRC+= 6.8·10−7 ms-1) In this work, the activation overpotential is not considered any further for the following reasons: 1. The variety of values for each parameter makes it impossible to identify the correct parameter set for the considered materials without conducting material research and additional experiments. 2. No spatial variation of any quantity is considered within the cell. For the application of the Butler-Volmer equation, this means that the current transfer density is equal all over the cell. As shown in [51] for the cross-flow direction, this is not the case. The current density close to the current collectors is larger than close to the membrane. In spatially resolved models, this can be considered, and the Butler-Volmer equation applies to a large number of small volume elements to compute the individual overpotential in each one of them. In the lumped-parameter model, the equation describes the total cell volume at once. The error which is introduced by this simplification cannot be determined without extensively comparing the lumped- parameter model to a spatially resolved model. 3. For the purpose of the presented model, the activation overpotential only plays a minor role. As presented above, it is mainly influenced by material parameters, which are not subject to change in this work. Hence, the relative differences between any design variation are not influenced by the activation overpotential. Only the absolute values of the results such as the efficiency might show some deviations. Note that this is only valid, because the temperature is constant for all considerations. Different temperatures would cause fluctuations in the activation overpotential and thus affect the comparability of the results. However, this is not the case in the present work. 40PDF Image | Model-based Design Vanadium Redox Flow Batteries
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