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G. Meyer, A. Kluwick:
"On the stability of pseudo-shocks in transonic flows from an asymptotic viewpoint";
Proceedings of the Institution of Mechanical Engineers Part C - Journal of Mechanical Engineering Science, 225 (2011), 10; 2312 - 2324.

The global stability properties of weak pseudo-shocks in transonic diffusers are discussed based on a mathematically consistent treatment of strong shock-boundary layer interaction. The equations governing the viscous-inviscid interactions taking place are obtained by matched asymptotic expansions starting from first principles of fluid dynamics. The global stability analysis reveals that the interaction of the pseudo-shock with a shock-induced separation bubble is at the root of self-sustained shock oscillations widely known from technical transonic diffuser flows. It is thus demonstrated that the resulting problem conserves essential properties of transonic flows through diffusers even under the restrictive set of assumptions needed in course of the problem formulation like assumption of laminar boundary flow. Therefore, the presented problem could serve as a suitable starting point to obtain a deeper theoretical insight into the problem of shock oscillations by a suitable generalization of the global linear stability analysis to the weakly non-linear case in future efforts.

transonic flow, shock, self-sustained oscillations, global stability, viscous-inviscid interactions, triple deck

http://dx.doi.org/10.1177/0954406211407250