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

Abstract

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.

Break-away separation for high turbulence intensity and large Reynolds number

“…More generally, such a flow region is also found in other types of interacting fully developed turbulent boundary layers (see e.g. Melnik & Chow 1975;Sykes 1980;Agrawal & Messiter 1984). Therefore, determining the order of magnitude of δ in terms of Re not only completes the scaling of the boundary layer but also answers the question of the existence of that blending layer, and in turn the asymptotic structure of the flow near D.…”

“…Sykes 1980) or turbulent boundary layer/shock wave interaction (cf. Agrawal & Messiter 1984 and references therein) that include separation.…”

Interacting Laminar and Turbulent Boundary Layers

“…A second new feature of compressible turbulent interactions occurs in supercritical transonic flow and is related to the position of the sonic line inside the unperturbed (a) wall pressure ), (b) wall shear (Agrawal and Messiter (1984)). …”

“…In addition to the shock induced phenomena mentioned so far local interaction processes caused by compression ramps in supercritical external flows have been investigated by Agrawal and Messiter (1984), Melnik, Siclari and Cusic (1985). Theoretical and experimental results are compared in Fig.…”

Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

“…The necessity of using logarithmic variables in problems of this type was pointed out by Lagerstrom & Casten (1972) and by Bush (1971) (see also Agrawal & Messiter 1984).…”