Calculation of aerodynamic characteristics of a wing profile with discharge of a controllable jet into the external flow

Abstract

A wing profile of infinite span, whose lower surface is replaced by a system of guide vanes, is placed in a flow of an ideal incompressible fluid. Fluid flows out through the system of guide vanes from the internal cavity of the wing into the external stream, forming a jet in the wake (Fig. 1). The total pressure in the wing cavity and in the jet differs from the total pressure in the outer free stream. The jet boundaries are streamlines extending to infinity, along which there is a discontinuity of the velocity value. The flow of fluid in the internal wing cavity is simulated by a flow caused by a system of suitably located sources, and the system of guide vanes is replaced by discrete vortices. The form of the profile arc is selected so that the fluid flow from the sources in the direction which is nearly opposite the direction of the freestream velocity is restrained by the segment of the contour with high curvature in the vicinity of the leading edge. We consider the flow regime about the profile with an exhausting jet for which the two ends of the arc the points of detachment of the stream and the velocity discontinuity line (profile arc, jet boundary) is a smooth curve, which imposes an additional condition on the magnitude of the circulation. As the model for the study of the flow about a profile with jet blowing we take the arc of a logarithmic spiral. Formulas are obtained for determining the over-all characteristics of the stream forces acting on the profile in the presence of the jet and the total pressure discontinuity. On the basis of the calculations made for a thin wing a qualitative analysis is made for the stream force acting on the profile.