Computation of Three-Dimensional Potential Flow Using Surface Vorticity Distribution

Abstract

An iterative method is developed using incompressible potential flow theory to compute three-dimensional velocity and pressure distributions on the surface of thick wings. The mathematical formulation is illustrated for a semi-infinite circular cylinder having a hemispherical tip. The procedure starts from a specified twodimensional vorticity distribution on the entire body and converges in three iterations to the three-dimensional distribution on the tip which merges smoothly with the two-dimensional one further inboard. The finite-element approach used here gives a continuous distribution of vorticity which is directly equivalent to the surface velocity distribution. The present method involves repeated use of the Biot-Savart law to relax the surface vorticity strength in successive iterations; whereas the more commonly used integral equation formulation requires solving a large matrix which is usually not well behaved for the surface vorticity model. A modification of the method is applied to compute the nonlifting flow on a semi-infinite NACA 0012 wing with a halt-bod}-ofrevolution tip and a NACA 0012 wing with an aspect ratio of three. The chordwise pressure coefficient distributions are presented for representative spanwise locations for all of the cases.