Computational Study of Free Flight of Low Reynolds Number Pitching Airfoils and Wings Undergoing Reverse Hysteresis

The unsteady low Reynolds number pitching of airfoils and wings about zero mean angle of attack have been investigated using moving overlapping meshes for a wide range of reduced frequencies for which lift hysteresis loops have been obtained. In this work, it is shown that pitching the airfoils and wings above a certain critical reduced frequency reverses the lift hysteresis curve thereby causing the lift to decrease with increasing angle of attack and vice-versa. This is accompanied by a large amount of phase lag which is evident from the time history of lift coefficient. It is also shown that this phase lag is a function of reduced frequency and that the bounds on this phase lag can be determined by a simple mathematical model which compares well with computed solutions. This phenomenon is further verified using three-dimensional computations for a pitching wing with an elliptical cross-section. Aerodynamic coefficients for two- and three-dimensional test cases have also been compared. Free flight of the airfoils and wings has also been analyzed in the context of a fixed centre of mass and partially constrained motion. It is seen that the high frequency pitching motion generates a plunging motion with reduced phase lag increment.