Leading Edge Vortex Development on a Pitch-Up Airfoil

Abstract

The dynamics of leading edge vortex (LEV) on an airfoil due to pitch-up motion is investigated using computational fluid dynamics techniques to solve the Navier-Stokes equations on composite overlapping grids. The objectives are to (1) quantify the contribution of circulatory effects caused by vortex development, and non-circulatory effects due to rotational acceleration of the pitch up, and (2) measure the growth rate of the LEV. The pitch-up angle is from 0 to 45 degrees, an approximation of the wing motion of a perching flyer, and the Reynolds number is approximately 500. Previous studies have investigated vortex development on pitch-up airfoils, and found the development of the LEV varies with pitch rate; however this phenomenon has never been quantified. In this study we will look at how vortex generation and diffusion at lower Reynolds numbers affect circulatory forces on the wing. The Q-criterion method is used to identify and isolate vortex structures from shear vorticity in order to numerically calculate the circulation in the computation domain caused by the LEV. The calculated circulation due to vortices will then be compared to the lift force by the pitch-up motion to obtain a better understanding of the contribution to lift exclusively by vortex generation. Previous studies involving pitch-up maneuvers have hypothesized that the increase of lift with pitch rate may be due to virtual mass effects, also known as noncirculatory forces. However this increase in lift has not been quantified. Using the noncirculatory component of Theodorsen’s theory, the lift forces can be broken into parts caused by the rotation of the wing, and the aerodynamic effects. Results have shown that noncirculatory forces only contribute 10–20% of the lifting force and the remaining is due to the LEV. It was also found that the LEV growth is time dependent and not angle dependent; however the circulation strength of the LEV is a function of pitch rate. Thus the higher pitch rates have smaller, yet stronger LEVs.