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Unsteadiness in transonic shock-wave/boundary-layer interactions: experimental investigation and global stability analysis

Published online by Cambridge University Press:  24 September 2015

F. Sartor ,
C. Mettot ,
R. Bur  and
D. Sipp
F. Sartor*
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
C. Mettot
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
R. Bur
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
D. Sipp
Affiliation:
ONERA/DAFE, 8 rue des Vertugadins, 92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

A transonic interaction between a shock wave and a turbulent boundary layer is experimentally and theoretically investigated. The configuration is a transonic channel flow over a bump, where a shock wave causes the separation of the boundary layer in the form of a recirculating bubble downstream of the shock foot. Different experimental techniques allow for the identification of the main unsteadiness features. As recognised in similar shock-wave/boundary-layer interactions, the flow field exhibits two distinct characteristic frequencies, whose origins are still controversial: a low-frequency motion which primarily affects the shock wave; and medium-frequency perturbations localised in the shear layer. A Fourier analysis of a series of Schlieren snapshots is performed to precisely characterise the structure of the perturbations at low- and medium-frequencies. Then, the Reynolds-averaged Navier–Stokes (RANS) equations closed with a Spalart–Allmaras turbulence model are solved to obtain a mean flow, which favourably compares with the experimental results. A global stability analysis based on the linearization of the full RANS equations is then performed. The eigenvalues of the Jacobian operator are all damped, indicating that the interaction dynamic cannot be explained by the existence of unstable global modes. The input/output behaviour of the flow is then analysed by performing a singular-value decomposition of the Resolvent operator; pseudo-resonances of the flow may be identified and optimal forcings/responses determined as a function of frequency. It is found that the flow strongly amplifies both medium-frequency perturbations, generating fluctuations in the mixing layer, and low-frequency perturbations, affecting the shock wave. The structure of the optimal perturbations and the preferred frequencies agree with the experimental observations.

JFM classification

Instability: Absolute/convective instability Compressible Flows: Compressible Flows Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 550 - 577
Copyright
© 2015 Cambridge University Press 

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