Effects of Higher Order Derivatives on Unsteady Aerodynamics of NACA0012 Airfoil Associated with Transonic Forced Motions

Accurate and efficient unsteady aerodynamic model is of great importance during initial aircraft design process as the characteristics of flight dynamics and control system design are closely related to unsteady aerodynamics of an aircraft. In the maneuvering flight of modern aircraft, especially for the high-performance fighter aircraft, the aerodynamic characteristics may behave in a highly nonlinear manner due to unsteady separation and vortex flow. Because the aerodynamic forces and moments not only depend on the flight state parameters, such as instantaneous angle of attack, angle of slip, and Euler angles, but also relates to the time cumulative effect of these flight state parameters, therefore, it is unsuitable to model unsteady aerodynamics for modern aircraft with high agility by traditional linear superposition theory. In this paper, unsteady time histories of the unsteady lift and pitching moment for two-dimensional NACA0012 airfoil associated with single freedom of forced motions, plunging and pitching, and coupled of plunging and pitching motion at transonic condition have been investigated computationally. Furthermore, the effects of various aerodynamic derivatives on the aerodynamic model have been discussed based on the Etkin aerodynamic model. Final results demonstrate that unsteady aerodynamics in the forced single or coupled motions could be accurately regenerated if the Etkin model were expanded to the second order derivative of angle of attack and angle of pitch with respect to time.