Research on the hysteresis properties of a pitching NACA0012 airfoil under low transonic ground effect

Based on an investigation of pitch oscillation encountered during electromagnetic-assisted near-ground takeoff of a NACA0012 airfoil, this study proposes a layering criterion for transonic static ground effects. First, the flow patterns and aerodynamic characteristics within each layer were examined. Subsequently, the influences of ground effects and reduced frequencies on pitch hysteresis properties were analyzed, with emphasis on the mechanisms governing variations in hysteresis loop morphology, steering direction, and fullness. The results indicate that the difference between the flow channel contraction ratio beneath the airfoil and the isentropic limit serves as a critical parameter for characterizing ground effects and determining flow regimes. Under varying angles of attack, transonic static ground effects can be categorized into three distinct layers: Layer 1, with unobstructed flow throughout; Layer 2, exhibiting alternating unobstructed and choked states; and Layer 3, demonstrating fully choked flow. Correspondingly, near-ground pitch hysteresis characteristics show layer-dependent behaviors. In Layer 1, hysteresis properties resemble those in free space due to weak ground effects. In Layer 2, intensified ground effects induce choking, causing the oscillating shock wave S2 to become stationary or shift toward the trailing edge, which results in hysteresis loop contraction or translational displacement, respectively. In Layer 3, severe choking and overflow lead to significant differences between oscillating shock waves S1 and S2 at positive angles of attack but minimal differences at negative angles, transforming hysteresis loops from elliptical to "water droplet" shapes. Increasing the reduced frequency can revert this morphology to elliptical. Common characteristics persist across all layers, including counterclockwise-rotating moment hysteresis loops, lift hysteresis loop steering synchronized with changes in the sign of the curve phase, quasi-steady behavior during low-frequency pitching, and pronounced hysteresis at high frequencies.