Lift evaluation of a two-dimensional pitching flat plate

Abstract

Several previous experimental and theoretical studies have shown that a leading edge vortex (LEV) on an airfoil or wing can provide lift enhancement. In this paper, unsteady two-dimensional (2D) potential flow theory is employed to model the flow field of a pitching flat plate wing. A multi-vortices model is developed to model both the leading edge and trailing edge vortices (TEVs), which offers improved accuracy compared with using only single vortex at each separation location. The lift is obtained by integrating the unsteady Blasius equation. It is found that the motion of vortices contributes significantly to the overall aerodynamic force on the flat plate. A Kutta-like condition is used to determine the vortex intensity and location at the leading edge for large angle of attack cases; however, it is proposed to relax this condition for small angle of attack cases and apply a 2D shear layer model to calculate the circulation of the new added vortex. The results of the simulation are then compared with classical numerical, theoretical, and experimental data for canonical unsteady flat plat problems. Good agreement with these data is observed. Moreover, these results suggested that the leading edge vortex shedding for small angles of attack should be modeled differently than that for large angles of attack. Finally, the results of vortex motion vs. lift indicate that the slow convection of the LEV creates less negative lift while the rapid shedding of the TEV creates more positive lift. The difference between these two contributions of lift results in a total positive lift that lasts for about two chord-length travel of the plate. It is therefore concluded that the lift enhancement during the LEV “stabilization” above the wing is a combined effect of both the LEV and TEV motion. This also provides the insights for future active flow control of micro aerial vehicles (MAVs) that the formation and shedding process of LEVs and TEVs can be manipulated to provide lift enhancement.