Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. Part I: Pressure distribution

An asymptotic approach for shock-wave/transpired turbulent boundary layer interactions

“…1. This figure is similar to that given by Messiter [6] and Liou & Adamson [7] since the disturbances caused to the main flow by the blown or sucked fluid are such that the various flow regions are preserved. This feature is best understood if one realizes that multilayer theories have been developed to account for the fact that viscous terms, both turbulent and laminar, are important only in well defined regions of the flow and that this situation is not altered in any way by the blown or sucked fluid.…”

“…Note that as vwu tends to zero Eq. (1) reduces to the unblown expression used in references [6] and [7]. For this reason parameters K , n and function w ( y) assume here their classical numerical values, that is Here y is the defect layer stretched coordinate ( = Y / Ô ) and S, S denote the thickness of the defect and wall layers respectively.…”

“…These solutions lead to a skin-friction equation which is much less sensitive than the integral-momentum equation to small changes in the flow parameters. In this work we are concerned with flows at high transonic speeds and extend the approach of Messiter [6] and Adamson & Liou [7] for the permeable surface case.…”

Interacting Laminar and Turbulent Boundary Layers

“…In the latter case the flow disturbances in the velocity defect region are governed by a non-linear transonic small perturbation equation generalized to account for the rotational part of the undisturbed boundary layer profile which has to be solved numerically. Partial analytical results can be derived for stronger normal and oblique shocks having Xt ~ 1 as shown by Adamson and Messiter (1977), Messiter (1980b), Liou and Adamson (1980), Kluwick and Stross (1984). The flow near the foot ofthe shock, however, is again governed by a generalized transonic small perturbation equation there necessitating a numeric al treatment.…”

Turbulent boundary-layer interaction with a shock wave at a compression corner

“…The inviscid-flow approximation has been developed as an asymptotic approximation for the related problem of the interaction at transonic speeds between an unseparated turbulent boundary layer and a normal shock wave, by Melnik & Grossman (1974), Adamson & Feo (1975) and Messiter (1980). A review of the important ideas, as applied to this and other problems, has been given by Melnik (1981).…”