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Unsteady inviscid flow models of wings and airfoils have been developed tostudy the aerodynamics of natural and man-made flyers. Vortex methods have beenextensively applied to reduce the dimensionality of these aerodynamic models,based on the proper estimation of the strength and distribution of the vorticesin the wake. In such modeling approaches, one of the most fundamental questionsis how the vortex sheets are generated and released from sharp edges. Todetermine the formation of the trailing-edge vortex sheet, the classical Kuttacondition can be extended to unsteady situations by realizing that a flowcannot turn abruptly around a sharp edge. This condition can be readily appliedto a flat plate or an airfoil with cusped trailing edge since the direction ofthe forming vortex sheet is known to be tangential to the trailing edge.However, for a finite-angle trailing edge, or in the case of flow separationaway from a sharp corner, the direction of the forming vortex sheet isambiguous. To remove any ad-hoc implementation, the unsteady Kutta condition,the conservation of circulation, as well as the conservation laws of mass andmomentum are coupled to analytically solve for the angle, strength, andrelative velocity of the trailing-edge vortex sheet. The two-dimensionalaerodynamic model together with the proposed vortex-sheet formation conditionis verified by comparing flow structures and force calculations withexperimental results for airfoils in steady and unsteady background flows.

Unsteady Aerodynamics and Vortex-sheet Formation of A Two-dimensional Airfoil