Pressure Distribution on the Trailing Edge of an Airfoil Oscillating in a Shear Layer

Abstract
The problem of calculating the pressure distribution on an oscillating plate in a uniform parallel subsonic shear layer is idealized as a layer of fluid with constant velocity and temperature that are different from the free stream conditions. An approximate solution is developed for the case where the shear layer velocity defect (displacement thickness/shear layer thickness) is small. The results are valid for arbitrary length scale of the surface deflection. The problem is a model of an airfoil trailing edge immersed in a fully developed turbulent layer and wake. The lowest-order steady state solution is calculated for a linearly deflected flap and an exponential flap. The lowest-order unsteady exponential flap and the first-order steady state exponential flap are also solved in detail. The first-order pressure decreases as the square root of the distance from the trailing edge like the lowest-order result, and in accordance with a full application of the Kutta condition. The amplitude of the correction involves the ration of the shear layer thickness to flap length. It is shown how the total lift on any section of the trailing edge of length L and flap length increases in the absence of a shear layer. An experiment to determine how the shear layer limits the growth of lift is suggested.

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