Method of calculating inviscid flow around arbitrary airfoils in upstream shear

Abstract

In this method the inviscid flow field is decomposed into two parts: a known field with constant vorticity representing the upstream shear and an unknown irrotational field representing the disturbance flow caused by the airfoil. The unknown field is handled by mapping the airfoil into a near-circular shape with a known normal velocity distribution. The flow around this shape is solved by means of a complex potential made of a vortex, a doublet and a number of quadruplets. The solution is then transformed back to the airfoil plane where it is added to the known upstream flow field. The method is general and is not limited to a particular airfoil geometry as in previous work. Results of numerous test cases indicate that the method is both accurate and numerically efficient over a wide range of angles of attack and shear rates. Comparison is also made with the limited experimental data available.