## 3 Results and Discussion  
Cell simulations showed higher minimum reactant concentration, and lower differential pressure and cell voltage for cases with wedge-shaped cells and mixers. The values for each case are given in Table 5, where the minimum V\({}^{3+}\) concentration and differential pressure are for the negative half-cell. The effect of the mixer is clearly seen in Figure 4, which shows the reactant distribution at the outlet boundary. Improved availability of reactants leads to lower concentration overpotentials and a higher minimum limiting current density. The improvement due to the varied electrode compression is less visible in the concentration distribution as the benefits are derived from optimizing local material properties. The mixer mechanism is shown in Figure 5. The boundary layers are disrupted in the center of the cell by the blades, redistributing the depleted electrolyte, which carries through the cell to the outlet shown above. Figure 4: Concentration (mol m\({}^{-3}\)) of V\({}^{4+}\) (top) and V\({}^{3+}\) (bottom) at the outlet boundary for (**a**) Case 1, (**b**) Case 2 and (**c**) Case 3 showing improved electrolyte utilization during charging at high current density in a wedge-shaped cell with mixing. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Geometry** & **Electrode Compression** & **Min. V\({}^{3+}\) Concentration** & **Differential Pressure** & **Cell Voltage** \\ \hline  & & **mol m\({}^{-3}\)** & **kPa** & **V** \\ \hline
1–Uniform & 15\% & 1 & 7.7 & 1.74 \\
2—Wedge & 0\% to 30\% & 5 & 7.0 & 1.71 \\
3—Mixed Wedge & 0\% to 30\% & 13 & 6.7 & 1.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Key values for Cases 1, 2 and 3 for simulations of 200 mm long unit-width cells charged at 160 mA cm\({}^{-2}\) from 90% SOC. The improvement in the cell voltage when compared to the reference uniform geometry was \(>\)1% by applying reducing compression, and \(>\)2% improvement with the addition of a mixer as well. These results were achieved in conjunction with a reduction in parasitic pressure losses across the cell, shown in Table 6, and despite the reduction in active porous electrode volume from the inserted mixers. Simulations in this work were conducted in a stationary model to reduce computational resource requirements, so while these improvements may seem small, they can translate into much more significant benefits in an operational system over time. When wedge cells without mixers were tested in laboratory cycling experiments [18] the reduction in overpotentials resulted in a 15% increase in energy efficiency, and increased energy capacity from an improved depth of charge and discharge between voltage cutoffs. With the addition of mixers, energy efficiency improvements of over 20% would be expected. If applied to batteries at the scale of a commercial stack, such as the concepts shown below, this would equate to improvements in the order of kWs and kWhs. The capacity improvement due to the higher energy efficiency is observable in the charge-discharge curves shown in Figure 6. Digital manufacturing was used to fabricate an adjustable 25 cm\({}^{2}\) cell with uniform and wedge flow frames for variable compression of thermally treated felt. Experimental studies were conducted to measure differential pressure and electrochemical performance for each configuration at multiple flow rates in support of numerical modelling. The single cell was cycled between 0.6 and 1.7 V limits with 100 mL of 2 M vanadium electrolyte at 20, 40, 60, 80 and 100 mA cm\({}^{-2}\) then 10 cycles at 60, 80 and 120 mA cm\({}^{-2}\). While all current densities demonstrated improved performance, the greatest \begin{table}
\begin{tabular}{c c c} \hline
**Geometry** & **Pressure Drop Improvement** & **Cell Voltage Improvement** \\ \hline Wedge without mixer & 9\% & 1.6\% \\ Wedge with mixer & 12\% & 2.2\% \\ \hline \end{tabular}
\end{table}