## 4 Simulation Research on the Temperature Distribution of the Arrester
### Influence of Air Velocity on the Temperature Distribution on the Arrester  
The high-speed airflow during the operation of EMU may have an influence on the temperature distribution of the arrester to some extent, which will affect the heat transfer between the arrester sheath and the outside air. The forced convective heat transfer of fluid around a cylinder follows the Zhukauskas formula [31].  
\[\begin{array}{c}N_{\text{u}}=CR_{\text{e}}^{\text{n}}P_{\text{r}}^{\text{pm}} \\ N_{\text{u}}=\frac{hd}{h}\\ R_{\text{e}}=\frac{hd}{v}\end{array} \tag{7}\]  
where \(N_{\text{u}}\) is the mean Nusselt number of the fluid around a cylinder, \(R_{\text{e}}\) is the Reynolds number, \(h\) is the convective heat transfer coefficient, \(d\) is the diameter of the arrester, \(\lambda\) is the thermal conductivity, \(u\) is the air velocity, \(v\) is the kinematic viscosity and \(P_{\text{r}}\) is the Prandtl number. The values and simplified formulas of \(C\), \(n\) and \(m\) are shown in Table 4.  
When the ambient temperature is 20 \({}^{\circ}\)C, the thermal conductivity of the air is 0.0259 W/(m-K), the kinematic viscosity \(v\) is 15.06 \(\times\) 10\({}^{-6}\) m\({}^{2}\)/s and the Prandtl number \(P_{\text{r}}\) is 0.703. According to the simplified formula in Table 4 combined with the Zhukauskas formula, the convective heat transfer coefficient of airs with different velocities can be calculated, as shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Condition** & \(C\) & \(n\) & \(m\) & \(\begin{array}{c}\textbf{Simplified}\\ \textbf{Formula}\end{array}\) \\ \hline \(5<R_{\text{e}}<10^{3}\) & 0.5 & 0.5 & 0.38 & \(N_{\text{u}}=0.44R_{\text{e}}^{0.5}\) \\ \(10^{5}<R_{\text{e}}<2\times 10^{5}\) & 0.26 & 0.6 & 0.38 & \(N_{\text{u}}=0.22R_{\text{e}}^{0.5}\) \\ \(2\times 10^{5}<R_{\text{e}}<2\times 10^{6}\) & 0.023 & 0.8 & 0.37 & \(N_{\text{u}}=0.02R_{\text{e}}^{0.5}\) \\ \hline \end{tabular}
\end{table}
Table 4: \(C\), \(n\) and \(m\) and their simplified formula.  
Figure 19: The influence of the defective valve plate number on the temperature rise.  
It can be seen from the above analysis that the passing section overvoltage and steep impulse overvoltage have a high amplitude, and the probability of occurrence is also high; therefore, these two overvoltage forms are applied to the normal arrester. The internal temperature distribution of the arrester under three different velocities is calculated, and the results are shown in Figure 20.  
It can be seen from Figure 20 that, under the action of passing section overvoltage and steep impulse overvoltage, the maximum temperature of the valve plate is 36.57 \({}^{\circ}\)C and 241 \({}^{\circ}\)C, respectively, when the air is still, and it is 35.97 \({}^{\circ}\)C and 240.94 \({}^{\circ}\)C, respectively, when the air velocity is 250 km/h. Although the air velocity strengthens the convection heat dissipation, the temperature rise of the arrester is mainly caused by the heating of its internal valve column, which is wrapped in the sheath and other insulating materials, so the air velocity has little effect on its temperature. When the EMU is attacked by overvoltage during static or high-speed operation, the difference in temperature distribution is small.