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Section 6.5 Evaluation of all twenty-four cell designs 6.5.2 Voltage efficiency The voltage efficiency of all designs is compared for the highest applied current density, which is 100 mAcm-2. As shown in Figure 6-7, the voltage efficiency increases with electrode area and flow factor. While the latter is obvious, the positive effect of an enlarged electrode has to be further studied. As the specific ohmic resistance is identical for all electrode areas, the concentration overpotential is suspected to cause the phenomenon. If the flow rate is controlled using the instantaneously derived stoichiometric requirements according to Faraday’s first law of electrolysis, scaled by a given flow factor, the flow rate is proportional to the nominal current, as shown in Eq. (8-6) on page 125. Hence, we yield Eq. (6-2) QC ∝ IC (6-2) The nominal current density is the same for all designs, as shown in Eq. (6-3). iC IC const. (6-3) AE If we combine the Eqs. (6-2) and (6-3), we find that under the given boundaries, the applied flow rate is proportional to the electrode area, as shown in Eq. (6-4). QC ∝IC iCAE ⇔QC ∝AE (6-4) Further, the cross-sectional area of the electrode is the product of electrode thickness, δE, and electrode width, wE. For a fixes aspect ratio between electrode width and height, as it is the case in this work, the width can be computed from the electrode area and the aspect ratio. In fact, the cross-sectional area in fluid flow direction is then proportional to the square root of the electrode area, as shown in Eq. (6-5). CSAE EwE E1.5AE ⟺ CSAE ∝ AE (6-5) For the concentration overpotential, the electrolyte velocity in the electrode, vEl, is important. The velocity is equal to volumetric flow rate over cross-sectional area of the electrode in fluid flow direction, CSAE, as shown in Eq. (6-6). vEl QC (6-6) CSAE If we combine the Eqs. (6-5) and (6-6), we find the electrolyte velocity to be proportional to the square root of the electrode area, as shown in Eq. (6-7). Hence, if the flow rate is adapted to applied current and tank SoC as shown in Eq. (8-6) on page 125, the electrolyte velocity increases with the electrode area, which is counter-intuitive. vEl QC ∝ AE AE (6-7) CSAE AE 96PDF Image | Model-based Design Vanadium Redox Flow Batteries
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