Spanwise propagation of upstream influence in conical swept shock/boundary-layer interactions

Abstract

It is shown that the motion within any boundary layer underlying an exactly conical inviscid flow with a swept shock cannot be conical at an arbitrary radial distance r from the origin, and that the resulting viscous-inviscid interaction from the displacement effect of this layer would violate the inviscid conicity. However, the far-field behavior at large radial distances beyond a certain inception length is shown to approach a quasi-twodimensional state in conical arc length coordinates, a state compatible with the corresponding far-field conical behavior of the overlying inviscid flow including viscous-inviscid interaction effects. Based on an analysis of the governing flow equations for large r, we establish that this inception length is proportional to the product of the interaction zone width (normal to the shock line) and the tangent of the shock sweep angle. These conclusions apply to a wide range of attached shock inviscid flow conditions and boundary-layer states independently of the turbulence modeling, heat transfer, or separation.