Supersonic Boundary Layer in Regions with Small Temperature Perturbations on the Wall
The problem of disturbed flow in the laminar boundary layer when heating elements are located on the surface is investigated. The flow is described by the theory of viscous-inviscid interaction with full Navier–Stokes equations. We apply the triple-deck model of the flow and describe asymptotic multiscale structure for the supersonic case. Using this structure as a base, we construct the solution to the flat stationary problem by means of Fourier transform and analysis in the complex plane. It is also shown that localization of a heating element may arrive at a singularity of the pressure downstream. Results of numerical and analytic analysis are presented. Using these elements gives us the opportunity to develop a novel method for the separation control of the boundary layer.
Laminar flow over a small hump on a flat plate
A boundary layer flows over a flat plate which has on it a small hump situated downstream of the leading edge. The description of the boundary-layer flow, based upon a triple-deck structure, shows how the presence of the hump generates an interaction between the inviscid region just outside the layer and the viscous region near the hump. The pressure force dominant in the boundary layer and the connexion of the local flow with the main stream develop together and are self-perpetuating, and both remain of primary significance for a wide range of hump sizes, even for a hump buried well inside the boundary layer. By consideration of the limiting cases of very small and very large humps, a consistent account of the nature of the disturbances due to the various sizes of hump is produced. The forces and couples on the hump are also evaluated.
On the viscous flow near the trailing edge of a flat plate
At the present time, there exists no exact solution of the Navier-Stokes equations for the viscous flow past a finite body submerged in the uniform flow of fluid. The most satisfactory of the approximate solutions now available seems to be that for the flow past a flat plate set parallel to the uniform flow which is obtained on the basis of Prandtl’s boundary-layer theory. In fact, sufficiently accurate analytical expressions have been obtained for the skin friction at the surface and the total drag of the plate as well as the velocity distribution near the plate.