Interaction between a Supersonic Stream and a Parallel Subsonic Stream Bounded by a Fluid at Rest.

摘要

In a simplified inviscid model of shock-wave boundary-layer interaction, Tsien and Finston have replaced the boundary layer by a uniform subsonic stream bounded on one side by a solid wall and on the other side by the interface with a uniform supersonic stream of semi-infinite extent. Among other things, this model fails to simulate the separated region or 'dead-air' bubble that generally appears in a laminar boundary layer subjected to an oblique incident shock wave of moderate strength. In order to introduce a main feature of such a dead-air region, the model has been modified herein by replacing the solid wall by an interface with fluid at rest. The presence of the boundary layer sandwiched between the outer supersonic flow and the dead-air region is found scarcely to modify the shape, in the vicinity of the shock, of the expansive 'corner' turn that would exist if the shock were incident directly on the dead-air region without the intermediary of the boundary layer; there are local distortions top and bottom, but these are reduced to negligible amounts several boundary-layer thicknesses to the left or right of the effective corner. It is concluded that in a more accurate treatment of the complete region of shock boundary-layer interaction the Prandtl boundary-layer equations may be applied to the entire extent of the disturbed boundary layer, applying as a boundary condition a sudden turn of the displacement surface through deflection angle at the point of shock incidence. Thereby the flow details in the immediate vicinity of the shock will be somewhat in error, but the over-all features of the interaction are capable of being given correctly. Present unknown elements in such an application appear to be the point of transition from laminar to turbulent flow and the form of the turbulent equations where a separated bubble exists.