Computational Fluid Dynamics of Airfoils and Wings

Abstract

Transonic flow is one of the fields where computational fluid dynamics turns out to be most effective. Codes for the design and analysis of supercritical airfoils and wings have become standard tools of the aircraft industry. One of the first applications of computational fluid dynamics to transonic flow occurred in the use of the hodograph method to construct shockless airfoils. The most successful aerodynamics codes are those for the analysis of flow at off-design conditions where weak shock waves appear. Shockless airfoils have played an effective role in the development of supercritical wings for modern aircraft. In cascade, they can also be used to enhance the performance of compressor blades. The mathematical problem of transonic flow past an air-foil or wing is usually formulated in terms of a velocity potential. The variation of entropy behind any shock waves that may occur is neglected, and the Rankine−Hugoniot shock conditions are replaced by an approximation valid for Mach numbers M close to 1. The approximation is adequate because for larger Mach numbers, the boundary layer separates anyway and the flow becomes of less interest in practice.