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On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions

Published online by Cambridge University Press:  06 July 2015

Jan Matheis
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85747 Garching bei München, Germany
Stefan Hickel*
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85747 Garching bei München, Germany Faculty of Aerospace Engineering, Technische Universiteit Delft, P.O. Box 5058, 2600 GB Delft, The Netherlands
Email address for correspondence:


The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of $\mathit{Ma}_{0}=2$. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of $\mathit{Ma}_{0}=3$ confirm the existence of the dual-solution domain predicted by theory.

© 2015 Cambridge University Press 

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