Discrete vortex method of two-dimensional jet flaps.

Abstract

A jet flap theory is developed with the aid of a classical cooformal mapping of airfoils onto unit circles and the method is free of any restrictions on the amount of airfoil thickness, camber or angle of attack. The jet sheet is supposed to be infinitesimally thin and is approximated by a finite number of discrete vortices placed on a stagnation streamline. The strengths of vortices are determined by an iterative procedure which is set up between the transformed and the physical plane. Any one of the classical incompressible airfoil theories, such as Theodorsen and Garrick's direct method or LighthilPs inverse one, can be applied to determine the mapping function of airfoils onto unit circles. The present approximation will converge to the exact incompressible potential flow theory of two-dimensional airfoil sections with infinitesimally thin jet flaps, if the number of vortices is increased and the distances between the adjacent vortices decreased indefinitely. Furthermore, the classical Blasius formulae are modified for jet flaps with discrete vortex approximations; and lift, drag and moment of airfoils are obtained. An example of an elliptical section of 12.5% thickness chord ratio with jet flaps shows a fair agreement with Dimmock's experimental data. With the aid of Theodorsen and Garrick's direct and author's inverse method several more examples are worked out.