Shock/Boundary-Layer Interaction Model for Three-Dimensional Transonic Flow Calculations

Abstract

Several widely used computer programs for calculating viscous transonic flow in both two and three dimensions use a classical direct-iteration scheme to couple an inviscid-flow solution for the outer flow with a solution to boundary-layer equations for the viscous flow near the surface. In weak solutions to the inviscid-flow equations, shocks represent discontinuities that are inappropriate as input to the boundary-layer equations. In practice, however, the inviscid solutions are generated numerically, and the shock discontinuities are smeared over several grid cells. It is a common practice to feed the inviscid solution directly into the boundary-layer equations, allowing the boundary-layer solution to respond to the smeared shock jumps just as it would to any other pressure gradient. For very weak shocks the thickening of the boundary layer through the shock predicted in this way should be very nearly correct, but for stronger shocks there are three major drawbacks to this approach:

• 1) The prediction of the viscous flow development through the shock is inaccurate because the assumptions inherent in the simple boundary-layer equations are violated in such a strong-interaction region,

• 2) the coupled solution has an unrealistic dependence on the grid spacing used in the inviscid solution. In the real flow, the smearing of the pressure rise through the shock results from the interaction of the shock with the boundary layer, while in coupled calculations the smearing depends strongly on the grid spacing of the inviscid solution, and

• 3) the boundary-layer solution will often predict separation for cases in which the shock is moderately strong, but in which no separation appears in the real flow.