Unsteady response of rectangular wings in spanwise uniform shear flow

Abstract

In engineering applications, it is important to estimate aerodynamic forces on wings in nonuniform flow. Wakes produced by objects ahead of wings frequently affect the performance of airplanes, turbomachines, etc. In this paper, a theory of wings oscillating in shear flow is presented. The whole flowfield is assumed to be inviscid and incompressible, and, furthermore, the shear flow velocity is assumed to vary linearly along the wing span. For this problem, lifting surface theory is applied. An integral equation, which is similar to that for potential flow, is derived under the assumption of small perturbations, arid then solved numerically by the mode function method. Generalized forces, Q^, which can be easily related to unsteady lift forces and moments, are obtained; moreover, response functions of wings to sinusoidal heaving oscillations and a sinusoidal gust are calculated for three different amounts of shear flow. The results are compared for several frequencies and show that the effect of shear is not large except in the limiting case. However, the generalized forces and gust response functions are affected by .the shear to some extent, even when the degree of shear is moderate. The effect increases as the frequency becomes larger.