## 4 Results
### Shape of the Cavity
#### 4.3.2 The Influence of Shape of the Cavity in Cavity-Double Tube Flow  
Figure 21 illustrates the impact of variations in \(L/D\) on the evolution of \(\overline{m}\) within the cavity-tube flow path. Similar to the cavity-single tube flow path, the influence of increasing \(L/D\) on the evolution of \(\overline{m}\) is primarily observed during the phase when \(L/D\) increases from 0.40 to 1.86. Further analysis is conducted in conjunction with the distribution of \(Ma\) within the cavity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(L/D\) & 0.15 & 0.23 & 0.40 & 0.78 & 1.86 \\ \hline \(\left(\overline{F_{A}}\right)_{\text{min}}\) & 0.53769 & 0.53585 & 0.53778 & 0.53098 & 0.51400 \\ \hline \(\left(\overline{F_{A}}\right)_{\text{max}}\) & 0.74571 & 0.75410 & 0.75796 & 0.76197 & 0.77825 \\ \hline \(\left(\overline{F_{B}}\right)_{\text{min}}\) & 0.53499 & 0.53395 & 0.53236 & 0.52255 & 0.48645 \\ \hline \(\left(\overline{F_{B}}\right)_{\text{max}}\) & 0.75064 & 0.76294 & 0.76373 & 0.77231 & 0.82115 \\ \hline \(\left(\Delta\overline{F}\right)_{\text{min}}\) & \(-\)0.04700 & \(-\)0.05992 & \(-\)0.04752 & \(-\)0.10022 & \(-\)0.16771 \\ \hline \(\left(\Delta\overline{F}\right)_{\text{max}}\) & 0.02049 & 0.01097 & 0.00756 & 0.03395 & 0.11394 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparison of parameters for different end face relative axial load variation processes. Select \(t_{s1}\) and \(t_{s2}\) as the comparison moments for the flow path during the depressurization and pressurization processes, respectively, to examine the variations in the distribution range of \(Ma\) within the cavity, as shown in Figure 22. CIDZ exhibits a minor increase during the axial distance-constrained phase and a substantial increase during the radial distance-constrained phase. Compared to the cavity-single tube flow path, the variation in \(L/D\) in the cavity-double tube flow path also influences the duration the fluid spends in the cavity, thereby having a more pronounced effect on the oscillation phases of \(\overline{F_{A}}\), \(\overline{F_{B}}\), and \(\overline{m}\). Figure 21: (**a**) Evolution of \(\overline{m}\); (**b**) Comparison of oscillation amplitude of \(\overline{m}\); (**c**) Comparison of period of \(T\). Figure 22: Cont. According to Figure 23, the influence of \(L/D\) on the axial load response during the fast transient response process of the cavity-tube flow path under the sudden change boundary is illustrated. Similar to the cavity-single tube flow path, the effect of \(L/D\) on the responses of \(\overline{F_{A}}\) and \(\overline{F_{B}}\) is primarily concentrated in the range when \(L/D\) increases from 0.78 to 1.86, during which the variation in \(L/D\) restricts the CIDZ range. Furthermore, changes in \(L/D\) continue to affect the phase difference in the responses of \(\overline{F_{A}}\) and \(\overline{F_{B}}\), resulting in variations in the response of \(\Delta\overline{F}\) with changes in \(L/D\), where \(\left(\Delta\overline{F}\right)_{\text{max}}\) increases by over 100% and \(\left(\Delta\overline{F}\right)_{\text{min}}\) decreases by over 500%. Specific parameters are presented in Table 13.  
Comparing the influence of \(L/D\) on the response of \(\Delta\overline{F}\) in the cavity-single tube flow path, it is observed that during the venting process, the cavity-tube combination flow path, having a larger volume, increases the phase difference in the responses of \(\overline{F_{A}}\) and \(\overline{F_{B}}\). Meanwhile, during the inflating process, the flow directly passes through the cavity, resulting in a higher average flow velocity within the cavity, which reduces the phase difference in the responses of \(\overline{F_{A}}\) and \(\overline{F_{B}}\). Therefore, in the cavity-tube combination flow