Numerical studies in high Reynolds number aerodynamics

Abstract

Two numerical approaches are presented for the computation of viscous compressible flows at high Reynolds' numbers. In the first approach, named global approach, the whole flow field, which includes viscous and inviscid regions, is determined as the solution of a single set of equations, which may be the full Navier-Stokes equations, or some approximate form of these equations. The second approach, named coupling approach, consists in solving two different sets of equations in their respective domains simultaneously; one of the two sets governs an inviscid flow whose boundary conditions are provided by the viscous effects, determined by the other set. The discussion of the global approach is centred on two particular features of the finite-difference method used: a discretization technique, directly in the physical plane with arbitrary meshes: and a mesh adaptation technique, which combines a coordinate transformation to fit the mesh system to particular lines in the flow, and a technique of dichotomy for mesh refinement. Numerical results are presented for an axisymmetric compression corner and a shock-boundary layer interaction on a flat plate, both in supersonic regime, and for a transonic nozzle flow. For the coupling approach, emphasis is given firstly to the improvement resulting from an interacting analysis where the viscous and inviscid computations are matched, and not only patched. It is shown that the parabolic problems associated with simple viscous theories are always replaced by elliptic problems, even for supersonic flows, and that “supercritical interactions” or “critical points”, as defined by Crocco-Lees, are removed. Secondly, a new coupling method, fully automatized and capable of solving directly a well-posed problem for supersonic flow, is illustrated by examples involving shock wave-boundary layer interactions and reverse flow bubbles; they concern flows over symmetrical transonic airfoils and supersonic compression ramps.