Linear interaction of two-dimensional free-stream disturbances with an oblique shock wave – ERRATUM

If a plane oblique shock wave, inclined to the free stream at the angle ε, is produced in two-dimensional supersonic flow of Mach number M by (for example) a wedge which deflects the flow through an angle δ, the equation connecting these quantities may be writtenIn this form, δ is given explicitly when M, ε are fixed. Similarly, we may obtain M explicitly when ε, δ are fixed; equation (1) may be written (see, for example, Liepmann and Puckett, Equation 4.27)

Download Full-text

Two-Dimensional Interaction of the Oblique Shock Wave with the Boundary and High-Entropy Layers of the Blunt Plate

49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition ◽

10.2514/6.2011-731 ◽

2011 ◽

Author(s):

Ivan Egorov ◽

I. Egorov ◽

I. Stuminskaya

Keyword(s):

Shock Wave ◽

Oblique Shock ◽

Oblique Shock Wave ◽

Two Dimensional ◽

High Entropy ◽

Dimensional Interaction

Download Full-text

Instabilities in oblique shock wave/laminar boundary-layer interactions

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.729 ◽

2016 ◽

Vol 789 ◽

pp. 1-35 ◽

Cited By ~ 25

Author(s):

F. Guiho ◽

F. Alizard ◽

J.-Ch. Robinet

Keyword(s):

Boundary Layer ◽

Shock Wave ◽

Shear Layer ◽

Laminar Boundary Layer ◽

Oblique Shock ◽

Oblique Shock Wave ◽

Two Dimensional ◽

Linear Framework ◽

Displacement Thickness ◽

The Impact

The interaction of an oblique shock wave and a laminar boundary layer developing over a flat plate is investigated by means of numerical simulation and global linear-stability analysis. Under the selected flow conditions (free-stream Mach numbers, Reynolds numbers and shock-wave angles), the incoming boundary layer undergoes separation due to the adverse pressure gradient. For a wide range of flow parameters, the oblique shock wave/boundary-layer interaction (OSWBLI) is seen to be globally stable. We show that the onset of two-dimensional large-scale structures is generated by selective noise amplification that is described for each frequency, in a linear framework, by wave-packet trains composed of several global modes. A detailed analysis of both the eigenspectrum and eigenfunctions gives some insight into the relationship between spatial scales (shape and localization) and frequencies. In particular, OSWBLI exhibits a universal behaviour. The lowest frequencies correspond to structures mainly located near the separated shock that emit radiation in the form of Mach waves and are scaled by the interaction length. The medium frequencies are associated with structures mainly localized in the shear layer and are scaled by the displacement thickness at the impact. The linear process by which OSWBLI selects frequencies is analysed by means of the global resolvent. It shows that unsteadiness are mainly associated with instabilities arising from the shear layer. For the lower frequency range, there is no particular selectivity in a linear framework. Two-dimensional numerical simulations show that the linear behaviour is modified for moderate forcing amplitudes by nonlinear mechanisms leading to a significant amplification of low frequencies. Finally, based on the present results, we draw some hypotheses concerning the onset of unsteadiness observed in shock wave/turbulent boundary-layer interactions.

Download Full-text