The effect of viscosity on the free stream in transonic flow over a corner point

An asymptotic analysis of the system of Navier–Stokes equations for describing the flow which arises from the subsonic free stream in the neighbourhood of the vertex of a convex corner with curvilinear generatrices is presented for Reynolds numbers approaching infinity. It is assumed that, in limiting non-viscous flow, the subsonic free stream reaches the velocity of sound at the vertex of the corner and, in the first approximation, is described by the Vaglio–Laurin solution. It is shown that the flow can have a different form depending on the value of the pressure gradient, which is formed in the neighbourhood of the corner point. However, irrespective of the steady form of the flow, as a result of the interaction of the Vaglio–Laurin flow with the boundary layer, the latter induces perturbations in the outer flow, which “rounds off” the vertex of the corner when there is a transonic flow around it.