Unsteady Aerodynamics and Trailing-edge Vortex Sheet of An Airfoil

Unsteady flow models of wings and airfoils have been studied to understand the aerodynamic performance of natural flyers and provide improved maneuverability for micro aerial vehicles (MAVs). Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the distribution and evolution of the vortices in the wake. In such modeling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from the leading and trailing edges. To study the formation of the trailing-edge vortex sheet, the classical Kutta condition is extended to unsteady situations following the physical sense that flow cannot turn around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a non-cusped trailing edge, the direction of the forming vortex sheet is ambiguous. In this study, to remove any ad-hoc condition, a novel analytical formulation is provided to determine the angle of the trailingedge vortex sheet. The derivation of this equation only requires momentum conservation in the direction normal to the forming vortex sheet. The aerodynamic model together with the proposed unsteady Kutta condition is verified by comparing flow structures and force calculations with experimental results for airfoils in steady and unsteady background flows.