## 3 Results
### The Effect of Height-to-Diameter Ratio  
The other two macro structural parameters of the storage tank, namely diameter, and height will also have an impact on the flow and heat transfer characteristics in the tank. The height of the tank affects the development of flow in the tank, while the diameter of the tank affects the macro characteristic parameters of flow in the tank such as the Reynolds number. In order to comprehensively consider the effects of the two, the structural parameter height to diameter ratio \(H/D\) is proposed to investigate the charging and discharging characteristics of the TES system under different structures of the storage tank. The models of the thermocline storage tank with height to diameter ratios \(H/D=0.4/0.5/0.6/0.7/0.8/0.9/1.0/1.1/1.2/1.3/1.4\) are established respectively.  
On the one hand, the increase of height-to-diameter ratio \(H/D\) means that the ratio \(D/H\) of diameter \(D\) to total height \(H\) of the storage tank decreases, causing a decrease in average Nu and thermal disturbance in the tank. On the other hand, on the premise that the total volume of the storage tank remains unchanged, the increase of the height to diameter ratio means that the diameter of the storage tank decreases. At this time, the flow rate remains unchanged, leading to an increase in the flow velocity and the Reynolds number in the storage tank, which will enhance the disturbance in the tank.  
Figure 8 shows the variation of the thermocline thickness with the height to diameter ratio at different times in the charging and discharging processes. It can be clearly seen that when the height to diameter ratio of the storage tank rises, the thermocline thickness in the tank increases. However, the performance index of the TES system continues to increase, indicating that the charging and discharging efficiency continues to improve. It is because the increase of the height to diameter ratio leads to the increase of the total height, and the increase of the total height is much greater than that of the thermocline thickness. The share of the thermocline thickness in the total height drops with the rise of the height to diameter ratio, so the efficiency of the TES system is improved. In addition, it can be seen in Figure 9 that the thermocline in discharging process is thicker than that in charging process  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Inlet Velocity**} & \multicolumn{2}{c}{**Height to Diameter Ratio: 0.4**} & \multicolumn{2}{c}{**Height to Diameter Ratio: 1.2**} \\ \cline{2-5}  & **Thermocline** & **Performance** & **Thermocline** & **Performance** \\
**Thickness/m** & **Index** & **Thickness/m** & **Index** \\ \hline
4.025 & 0.713 & 0.936 & 1.197 & 0.948 \\
4.319 & 0.741 & 0.938 & 1.283 & 0.948 \\
4.577 & 0.768 & 0.939 & 1.366 & 0.948 \\
4.810 & 0.782 & 0.941 & 1.425 & 0.949 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The thermocline thickness and performance index value of TES system in charging process at different flow rates (\(t=\) 28,800 s).  
with the same time. Obviously, the larger the height to diameter ratio \(H/D\), the thicker the thermocline will be, but as illustrated in Figure 10 that the performance of the TES system will be improved accordingly.  
Figure 8: The variation of thermocline thickness with height to diameter ratio ((**a**)-charging, (**b**)-discharging).  
Figure 9: Comparison of thermocline thickness in charging and discharging processes.