Inviscid transonic flow over airfoils

Abstract

A procedure is presented to calculate steady supercritical planar flows over lifting airfoils using an unsteady approach, where the steady flow is obtained as the asymptotic flow for large times. The unsteady flow is generated by impulsively imposing the airfoil boundary condition in an initially uniform flow. The resulting flow is calculated by a finite difference analogue to the unsteady Euler equations using a diffusing second-order difference scheme. Here an artificial viscosity appears by which shock waves acquire a steep profile. The procedure is used to calculate the flows over one of the nonlifting symmetrical shockless profiles derived by Nieuwland, using the hodograph method, and over a lifting NAG A 64A-410 profile. Results agree well with experiments, with local differences accountable by a BusemannGuderley instability in the first case, and by viscous effects in the second case.