An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

Analytical vortex and source surface distributions for flow about elliptical cylinders

Summary A cylindrical body is introduced into a potential flow and the resulting disturbance is treated using only an analytical singularity distribution on the surface of the body. Conformai transformation methods, using previously published results for singularity distributions on a circular cylinder, enable the derivation of the required form of vorticity distribution on the transformed body. This approach, however, does not facilitate the derivation of the analogous source/sink distribution. For an elliptic cylinder, examples of vorticity distributions are presented and a new solution is obtained giving the source/sink distribution on the surface of the cylinder in a uniform stream at incidence.