# Dynamic Stall Mechanisms of Pitching Airfoil: IDDES Study Across Different Mach Numbers
## 3 Aerodynamics at a Mach Number of 0.283
### Flowfield Feature at Ma = 0.283  
Spanwise-averaged pressure coefficient contours shown in Figure 8 reveal four sequential events during the pitching cycle: (a) trailing-edge separation (TES) propagation, (b) collapse of the leading-edge suction pressure peak, (c) leading-edge vortex (LEV) development, and (d) trailing-edge vortex (TEV) emergence. Following the collapse of the leading-edge suction pressure peak, an LEV forms, generating a new low-pressure region that progressively expands and transports downstream. As the LEV approaches the trailing edge, a TEV is induced, creating an additional low-pressure region. During the pitching-up circle, the suction pressure peak exceeds the critical pressure coefficient (\(Cp_{\text{cr}}=-7.9\)), reaching a minimum value of approximately \(-13.0\). This observation indicates the occurrence of localized supercritical flow near the leading edge. Figure 6: Calculated forces of the pitching airfoil at \(Ma=0.283\): (**a**) _Cl_; (**b**) _Cd_; (**c**) _Cm_. Figure 9 presents Mach number and pressure coefficient contours for the center section at an AoA of 18.26\({}^{\circ}\), corresponding to the highest suction pressure peak. The upward-pointing arrow '\(\uparrow\)' following the AoA value denotes the upstroke circle, while the downward-pointing one '\(\downarrow\)' denotes the downstroke circle. A supersonic region (\(Ma>1\), gray-shaded in Figure 9a) forms near the leading edge, yet no shock structures are observed in the AoA. The bottom panel shows the same behavior as the one in Figure 9a. (Figure 9b). This suggests that the airfoil undergoes compressibility effects while experiencing a deep dynamic stall regime characterized by a strong adverse pressure gradient. Figure 10 shows the iso-surfaces of the \(\lambda_{2}\)-criterion (\(\lambda_{2}=-0.0001\)) in the pitching-up stage, displaying the evolution of vortical structures. In Figure 10a,b, both the LEV and TES exhibit quasi-two-dimensional characteristics during their incipient stages. As the AoA increases, the LEV experiences substantial growth and downstream convection (Figure 10c-e), which directly associated with the moment stall. During this period, the LEV evolves into multi-scale vortex structures dominated by pronounced three-dimensional interactions. Simultaneously, the TES develops into three-dimensional turbulent separation (TS), as illustrated in Figure 10d. Upon reaching the peak AoA of 24.79\({}^{\circ}\), the LEV is displaced upward, while a TEV forms near the airfoil's trailing edge. Figure 11 shows streamlines and z-vorticity contours for the center section in the pitching-up stage. At an AoA of 19.12\({}^{\circ}\), a separation bubble (SB) forms near the leading edge. At the same time, multiple separation vortices are observed near the trailing edge, forming the trailing edge separation. These vortices induce pressure perturbations and pre-stall moment coefficient fluctuations (Figure 6c). The subsequent downstream convection and structural evolution of the LEV are detailed in Figure 11b-e, revealing a compact vortex structure. At the maximum AoA (Figure 11f), the presence of the TEV causes the upward displacement and subsequent breakdown of the LEV. Figure 9: Mach number and pressure coefficient contours for the center section at \(Ma=0.283\), \(\alpha=18.26^{\circ}\)\(\uparrow\): (**a**) Mach number contour; (**b**) pressure coefficient contour. Figure 12 illustrates the pressure coefficient distribution along the upper airfoil surface at AoAs of 23.71\({}^{\circ}\) and 24.79\({}^{\circ}\) during the pitch-up maneuver. The chordwise pressure distribution demonstrates near-uniform characteristics, which can be attributed to flow separation induced by LEV shedding. As the maximum AoA is attained, a distinct low-pressure region develops near the trailing edge.