An aerofoil design method for viscous flows

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Description/Abstract

By convention, an aerofoil design problem involves finding the aerofoil shape corresponding to a prescribed surface velocity distribution. Various design methods have been devised for inviscid flows, including one based on an expression for the stream function on an aerofoil's surface. Present work extends this method to produce a matched viscous/inviscid iterative solution for the design of aerofoils in viscous flows.

Full derivations of new formulae are presented as well as a summary of essential formulae. Techniques for solving the underlying equations are examined, with particular emphasis on achieving a stable iteration. Comparisons are made between exact inviscid solutions for Karman-Treffetz aerofoils and viscous-flow solutions for aerofoils with the same surface velocity distributions. Results are plausible when deplacement thickness effects are taken into account.