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.
Subsonic flow past three-dimensional localised heating elements in boundary layers
The problem of subsonic flow past three-dimensional micro-electro-mechanical-type (MEMS-type) heating elements placed on a flat surface, where the MEMS devices have hump-shaped surfaces, is investigated using the triple-deck theory. The compressible Navier–Stokes equations supplemented by the energy equation are considered in the limit when the Reynolds number is large. The dimensions of the MEMS devices considered are such that the flow perturbations are governed by the three-dimensional subsonic triple-deck equations formulated with the aid of method of matched expansions. The linear analysis of these equations is presented and our results provide an insight into how the MEMS heating elements may be used to positively control the local flow properties.
On supersonic laminar boundary layers near convex corners
The structure of a laminar supersonic boundary layer is examined near a convex corner, turning the flow through an angle α*, on the assumption that α*Re½ ~ 1 where Re is the Reynolds number of the flow. In common with related problems already examined, the boundary layer takes on the character of a triple-deck with the initial pressure fall occurring upstream of the corner. Numerical studies show that as α*Re½ increases so does the proportion of the total pressure fall which occurs upstream of the corner and an analysis is given which strongly suggests that as α*Re½ -> ∞ the relative pressure fall downstream of the corner vanishes. The theory is carried over to include angles α* which are small but finite [α* ≪ 1, α*Ret ≫ 1 for all t > 0] and an earlier theory, due to Matveeva and Neiland, is made uniformly valid and completed. Comparisons with experiment are made which, while not being decisive, are encouraging.