Computational Study of Supersonic Flow Over Backward-Facing Steps at High Reynolds Number

摘要

The problem of laminar separated flow over a backward-facing step is solved numerically for the limiting case of infinite Reynolds number. The flow model adopted is that deduced by Batchelor for incompressible flow: an inviscid rotational eddy confined within the recirculation portion of the separated shear layer. It is argued that the reattachment process is essentially inviscid in the limit R approaches infinity, and the flow field in the reattachment zone is computed on this basis. The computed results support Chapman's model of the reattachment process as the correct limit case, to second-order accuracy, as the flow angle entering the reattachment zone approaches zero. For the recirculation zone, the boundary-layer equations are simplified by assuming a constant pressure eddy. The Dorodnitsyn transformation is applied and numerical solutions obtained using an implicit finite-difference scheme. The solutions are carried out from station-to-station in the direction of flow over a complete cycle of recirculation. Iteration yields the unique value of the vorticity in the inviscid layer upstream of separation, including the effects of corner expansion and recirculation on the development of the separated shear layer. (Author)