# Dynamic Stall Mechanisms of Pitching Airfoil: IDDES Study Across Different Mach Numbers
## 3 Aerodynamics at a Mach Number of 0.283
### Effect of Reduced Frequency at Ma = 0.283  
Figure 16 shows the airfoil aerodynamic coefficients at reduced frequencies of \(k\) = 0.1, 0.151, and 0.2. To facilitate comparative analysis, the figure includes curves illustrating the coefficient variations with AoA and azimuth angle. The oscillating airfoils at all three frequencies encounter deep stall, characterized by dramatic post-stall airload variations indicative of leading-edge stall behavior.  
Notably, increasing the reduced frequency shifts the stall and reattachment stages to larger azimuth angles. In the attached flow stage, higher k amplifies the AoA change rate at equivalent angles, enhancing camber effects and consequently increasing lift, drag, and nose-down moment coefficients. Moreover, increased k significantly delays landmark aerodynamic events, including lift stall, moment stall, drag divergence, TEV, secondary DSV, and flow reattachment. Concurrently, this is accompanied by enhanced peaks in lift, drag, and nose-down moment, suggesting the emergence of stronger DSV structures.  
Figure 17 illustrates suction surface pressure coefficients during the airfoil's pitching-up stage at different reduced frequencies. Increasing the reduced frequency delays typical aerodynamic events, including suction peak collapse and the formation, convection, and shedding of DSV. Analysis of the local negative pressure region induced by DSV shows that higher reduced frequencies yield a more pronounced region, signifying stronger DSV influence on the airfoil. Notably, as the reduced frequency increases, the airfoil attains the maximum negative pressure peak at a larger AoA. Despite this shift, the peak magnitudes of negative pressure remain consistent across different reduced frequencies, further confirming that the increased lift overshoot amplitude stems primarily from enhanced DSV strength associated with higher \(k\) values.  
Figure 15: Cycle-averaged and time-resolved aerodynamic damping for the pitching airfoil at \(Ma\) = 0.283.  
Figure 16: Calculated forces of the pitching airfoil for different reduced frequencies at \(Ma=0.283\): (**a**) \(Cl\); (**b**) \(\Cd\acute{a}\); (**c**) \(Cm\).  
Figure 17: Pressure coefficients on the suction surface during the airfoil’s pitching-up stage at \(Ma=0.283\): (**a**) \(k=0.1\); (**b**) \(k=0.151\); (**c**) \(k=0.2\).  
Figure 18 presents the cycle-averaged and time-resolved aerodynamic damping of an oscillating airfoil at different reduced frequencies. As k increases, the cycle-averaged damping decreases, turning negative when \(k\) = 0.2. Analysis of the transient damping curves reveals that with increasing k, the damping reduction stage prolongs attributed to delayed stall onset and DSV formation, yielding a more pronounced negative damping peak. Concurrently, the subsequent damping recovery stage, induced by DSV convection along the airfoil surface, is also delayed. These results indicate that for deep stall at low Mach numbers, the airfoil pitching motion tends to become unstable with the increase in reduced frequency.