Interaction theory for hypersonic separation and supersonic flow past a flexible wall

Asymptotic methods of analysis have been extensively used in theoretical gas and fluid mechanics for more than forty years. All approaches are based on some sort of limiting process. For instance, if one or several dimensionless governing parameters of the problem are small enough, the solution may be represented in the form of an asymptotic expansion, with the small parameter being treated as asymptotically small. Approximate results obtained using asymptotic theory may be rather inaccurate on occasion, since the parameters involved may not be sufficiently small in real applications so that the leading-order asymptotic analysis gives good quantitative results. However, at worst, the theory provides an understanding of the physical mechanisms associated with the phenomena of interest and in addition reveals the characteristic regions of the flow. In general, fully numerical approaches for the solution of the flow problem should take into account, or even directly use the results of asymptotic analysis.; In the first part of this thesis (Chapters 2 and 3) separation of a hypersonic boundary layer over a cold wall for the compression-ramp geometry is considered. For small ramp angles the flow is governed by a triple-deck structure. However, it is shown that for the wall temperatures lower than a certain critical range, the streamwise extent of the interaction region is much shorter than that of the triple-deck structure. As a result, it emerges that the inner interaction region is described by the marginal separation theory. It is demonstrated that the flow over the compression ramp exhibits separation for ramp angles above a critical value. Marginal separation theory fails in the vicinity of the reattachment point and a revision of the reattachment problem is required in order to relieve the singularity. Calculated results obtained for the nonlinear reattachment region show that the flow finally breaks down in the form of the reversed-flow singularity, associated with a discontinuity in pressure distribution.; The second part (Chapter 4) is devoted to the local interaction of a supersonic boundary layer with a flexible wall. Special attention is focused on how stability of the flow is affected by the properties of the compliant surface. The particular case of supersonic flow over a compliant wall for compression ramp is considered. For small ramp angles, the flow is governed by the triple-deck structure and the interaction law is coupled with an equation representing the motion of the surface. The problem has been studied numerically and the solutions tend to suggest a sufficiently flexible surface can delay or suppress instability of the flow.