On laminar separation at a corner point in transonic flow

The separation of the laminar boundary layer from a convex corner on a rigi d body contour in transonic flow is studied based on the asymptotic analysi s of the Navier-Stokes equations at large values of the Reynolds number. It is shown that the flow in a small vicinity of the separation point is gove rned, as usual, by strong interaction between the boundary layer and the in viscid part of the flow. Outside the interaction region the Karman-Guderley equation describing transonic inviscid flow admits a self-similar solution with the pressure on the body surface being proportional to the cubic root of the distance from the separation point. Analysis of the boundary layer driven by this pressure shows that as the interaction region is approached the boundary layer splits into two parts: the near-wall viscous sublayer an d the main body of the boundary layer where the flow is locally inviscid. I t is interesting that contrary to what happens in subsonic and supersonic f lows, the displacement effect of the boundary layer is primarily due to the inviscid part. The contribution of the viscous sublayer proves to be negli gible to the leading order. Consequently, the flow in the interaction regio n is governed by the inviscid-inviscid interaction. To describe this flow o ne needs to solve the Karman-Guderley equation for the potential flow regio n outside the boundary layer; the solution in the main part of the boundary layer was found in an analytical form, thanks to which the interaction bet ween the boundary layer and external how can be expressed via the correspon ding boundary condition for the Karman-Guderley equation. Formulation of th e interaction problem involves one similarity parameter which in essence is the Karman-Guderley parameter suitably modified for the flow at hand. The solution of the interaction problem has been constructed numerically.