Unsteady Kutta condition and vortex-sheet generation

Abstract eng:
Vortex method has been widely used for low-Reynolds-number flights as it reduces the computation domain from the entire flow field to only finite vortical structures. An essential challenge of the vortex method lies in the prediction of the vortex sheets separated from the solid body. To tackle this problem, this study extends the classical Kutta condition to unsteady situations based on the physical sense that flow cannot turn around a sharp edge. This unsteady Kutta condition can be readily applied to an airfoil with cusped trailing edge, where the forming vortex sheet is known to be tangential to the trailing edge. For a finite-angle trailing edge, previous studies indicate that the direction of the forming vortex sheet is ambiguous. Therefore, this study proposes a novel analytical formulation to determine the angle of the trailing-edge vortex sheet based on momentum conservation in the direction normal to the forming vortex sheet.

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