# Research on Panel Flutter Considering the Effect of Convective Active Cooling
## 3 Panel Stability
Figure 14 plots the curves of the peak of deformation versus the freestream dynamic pressure under the condition of the forward injection and reverse injection of coolant. The injection direction mainly affects three aspects of the panel response. First, in the buckling state, the buckling deformation under forward injection is smaller than that under the reverse injection when the dynamic pressure is small, while the magnitude relationship changes when the dynamic pressure is large. There is obviously a transition point. With the increase in \(\alpha\), the values of \(\lambda\) corresponding to the transition points are 140, 94, 49.5, and 111.1, respectively. Second, the position at which the bifurcation occurs is also different. The bifurcation occurs first when the coolant is injected reversely when \(\alpha\) is equal to 0.6 and 1.0, while opposite results are obtained when \(\alpha\) is equal to 1.4 and 1.8. Third, the peak of LCO when the coolant is injected forward is larger than that when the coolant is injected reversely, and the difference between the peaks increases with the increase in \(\alpha\). Figure 3:0 The buckling deformation versus the critical dynamic pressure. Figure 15 shows the stability regions of the panel under the influence of the coolant injection direction. When \(\alpha\!=\!0.6\), the panel with a small in-plane load is more prone to bifurcation using the reverse injection method. The injection method that leads to earlier bifurcation or multiple bifurcations of the panel with a large in-plane load is correspondingly opposite. The effect of the coolant injection direction on the panel stability when \(\alpha\!=\!1.8\) is opposite to that when \(\alpha\!=\!0.6\). Table 1 shows the critical dynamic pressure of the panel without an in-plane load using different injection methods. The results are close when \(\alpha=1.4\). The result obtained by the reverse injection is smaller than that of the forward injection when \(\alpha<1.4\), and the conclusion is opposite when \(\alpha>1.4\). Figure 3:1 Peak of deformation versus dynamic pressure under different injection directions. Figure 3:2 Stability regions under different injection directions. Considering the influence of inertial and viscous resistances, Figure 16 shows the convergence process of the buckling response under different inertial and viscous resistances. It indicates that inertial resistance slows down the convergence process, while viscous resistance speeds up the convergence process. However, neither of them change the buckling deformation of the panel. Figure 17 plots the peak of deformation versus the freestream dynamic pressure under different inertial and viscous resistances, showing that the panel bifurcates from the stable state to LCO. In Figure 17a, the critical dynamic pressure of the panel decreases, and meanwhile, the peak of LCO gradually increases as inertial resistance increases, but clear changes appear only at small inertial resistances. Figure 17b shows the influence of viscous resistance, which plays the opposite role to inertial resistance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\alpha\) & 0.6 & 1.0 & 1.4 & 1.8 \\ \hline \(\lambda_{cr}\) (forward injection) & 425.4 & 369 & 344.3 & 370.9 \\ \hline \(\lambda_{cr}\) (reverse injection) & 420.5 & 364.9 & 345.2 & 380 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The critical dynamic pressure of the panel without in-plane load under different injection. Figure 16: The convergence process of the buckling response under different inertial and viscous resistances: (**a**) inertial resistances; (**b**) viscous resistances. Figure 17: Peak of deformation versus dynamic pressure under different inertial and viscous resistances: (**a**) inertial resistances; (**b**) viscous resistances. Table 2 shows the critical dynamic pressure of the panel under an in-plane load at different inertial resistances. As the in-plane load increases, the critical dynamic pressure first decreases and then tends to be stable.