## 3 Results and Discussion  
### Flow Characteristics through Flow Visualization Experiment and Numerical Analysis  
Figure 7 shows the flow of the electrolyte in the flow visualization experiment. The electrolyte passed through the flow channel, and it was first discharged from the outlets on the right owing to the shape of the flow channel, as shown in Figure 7a. Subsequently, as more electrolyte was added, it was discharged from the outlets on the left and the flow was spread throughout the area, as shown in Figure 7b. The flow characteristics obtained through numerical analysis are shown in Figure 8. The results of the experiment and numerical analysis were in good agreement. In particular, the flow in the electrode, which was not visualized in the experiment, was initially concentrated at the outlets on the right. The distribution of the electrolyte throughout the electrode became uniform over time (Figure 8a,b). The results of the flow visualization experiment and numerical analysis show that the vertical guides before the final outlets create vertical flow and induce the electrolyte to enter the electrode from the right. As a result, flow may be non-uniform from right to left. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Model** & **Accuracy** \\ \hline Rate flow meter & Dwyer, RMA-25\_SSV & \(\pm\)4\% \\ Liquid pump & KNF, NF 1300 & \(\pm\)1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Instruments used for the experiment. Figure 7: Results of flow visualization experiment. (**a**) Flow time t = 3 s; (**b**) Flow time t = 4 s.  
Figure 10: Velocity contours in the (**a**) inlet channel and (**b**) outlet channel of the electrode. Figure 9: Velocity distribution in the basic configuration of vanadium redox flow battery. (**a**) Flow distribution; (**b**) Velocity vectors in the curved section of the S-shaped inlet channel. To analyze the flow rate of the electrolyte discharged from the inlet channel outlet to the electrode, the average velocity distribution was determined at three locations, as shown in Figure 11. Calculate location A was the starting point of the electrode, where the characteristics of the flow discharged from the inlet channel to the electrode were observed. Location B was located at the distance of 10 mm from the start of the electrode, where the change in flow owing to the porosity of the electrode was observed. Finally, Location C was located at the center of the electrode, where the average flow characteristics in the electrode were analyzed as the electrolyte flowed upward. Figure 12 shows the profiles of the average y-velocity at the three locations. The maximum velocity was at the outlet on the right at location A, where the channel and electrode were connected, and the velocity distribution was uniform toward the left, as shown in Figure 12. This indicates that the flow in the final part of the curved path was deflected to the right because of the square vane located in the curved path and the shape of the flow channel, as shown through the preceding flow visualization. The average velocity at location A was higher than that at locations B and C. This was because the total area of the outlets was approximately 50% of the area of the electrode, and the average velocity increased owing to the reduction in area at the same flow rate. In addition, the uniformity of flow significantly increased from location A to C owing to the characteristics of the porous medium in the electrode. Flow uniformity was evaluated based on the variability range coefficient (\(R_{i}\)) and maximum velocity deviation (\(D_{v}\)) given by Equations (8) and (9) through the discharge flow rates at 90 outlets of the inlet channel. When the variability range coefficient (\(R_{i}\)) was calculated for electrode, the position A exhibited the highest value of 0.072 m/s. The maximum velocity deviation (\(D_{v}\)) was 11.89%, which indicated low uniformity.