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Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction

Published online by Cambridge University Press:  28 February 2012

Muzio Grilli*
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85748 Garching, Germany
Peter J. Schmid
Affiliation:
Laboratoire d’Hydrodynamique (LadHyX), CNRS-École Polytechnique, 91128 Palaiseau, France
Stefan Hickel
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85748 Garching, Germany
Nikolaus A. Adams
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85748 Garching, Germany
*
Email address for correspondence: muzio.grilli@aer.mw.tum.de

Abstract

The unsteady behaviour in shockwave turbulent boundary layer interaction is investigated by analysing results from a large eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer. Wall pressure data are first analysed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. Furthermore, the flow dynamics are analysed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward–backward motion of the shock.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

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References

1. Adams, N. A. 2000 Direct simulation of the turbulent boundary layer along a compression ramp at and . J. Fluid Mech. 420, 4783.CrossRefGoogle Scholar
2. Beresh, S. J., Clemens, N. T. & Dolling, D. S. 2002 Relationship between upstream turbulent boundary-layer velocity fluctuations and separation shock unsteadiness. AIAA J. 40, 24122422.CrossRefGoogle Scholar
3. Dolling, D. S. & Murphy, M. T. 1983 Unsteadiness of the separation shock wave structure in a supersonic compression ramp flow field. AIAA J. 21, 16281634.CrossRefGoogle Scholar
4. Dolling, D. S. & Or, C. T. 1985 Unsteadiness of the shock wave structure in attached and separated compression ramp flows. Exp. Fluids 3, 2432.CrossRefGoogle Scholar
5. Dupont, P., Haddad, C. & Debieve, J. F. 2006 Space and time organization in a shock-induced separated boundary layer. J. Fluid Mech. 559, 255277.Google Scholar
6. Dussauge, J. P., Dupont, P. & Debieve, J. F. 2006 Unsteadiness in shock wave boundary layer interactions with separation. Aerosp. Sci. Technol. 10, 8591.CrossRefGoogle Scholar
7. Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2006 Effects of upstream boundary layer on the unsteadiness of shock induced separation. J. Fluid Mech. 585, 369394.CrossRefGoogle Scholar
8. Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2009 Low-frequency dynamics of shock-induced separation in a compression ramp interaction. J. Fluid Mech. 636, 397425.CrossRefGoogle Scholar
9. Hickel, S. 2012 Implicit subgrid-scale modelling for large eddy simulation of compressible flows and shock turbulence interaction Phys. Fluids (submitted).Google Scholar
10. Hickel, S., Adams, N. A. & Domaradzki, J. A. 2006 An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213, 413436.CrossRefGoogle Scholar
11. Huang, P. G., Coleman, G. N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech.Google Scholar
12. Loginov, M., Adams, N. A. & Zheltovodov, A. 2006 Large-eddy simulation of shock-wave/turbulent boundary layer interaction. J. Fluid Mech. 565, 133169.CrossRefGoogle Scholar
13. Piponniau, S., Dussauge, J. P., Debieve, J. F. & Dupont, P. 2009 A simple model for low-frequency unsteadiness in shock-induced separation. J. Fluid Mech. 629, 87108.CrossRefGoogle Scholar
14. Pirozzoli, S. & Grasso, F. 2006 Direct numerical simulation of impinging shock wave/turbulent boundary layer interaction at . Phys. Fluids 8, 117.Google Scholar
15. Pirozzoli, S., Larsson, J., Nichols, J. W., Bernardini, M., Morgan, B. E. & Lele, S. K. 2010 Analysis of unsteady effects in shock/boundary layer interaction. In Center for Turbulence Research Proceedings of the Summer Program. Center for Turbulence Research, Stanford University and NASA Ames Research Center, Stanford, CA.Google Scholar
16. Ringuette, M. J., Martin, M. P. & Smits, A. J. 2006 Characterization of the turbulence structure in supersonic boundary layers using DNS data. AIAA Paper 2006-3539.CrossRefGoogle Scholar
17. Rowley, C. W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 113.CrossRefGoogle Scholar
18. Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 528.CrossRefGoogle Scholar
19. Schmid, P. J. 2011 Applications of the dynamic mode decomposition to experimental data. Exp. Fluids 50, 11231130.CrossRefGoogle Scholar
20. Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to . J. Fluid Mech. 187.CrossRefGoogle Scholar
21. Touber, E. & Sandham, N. 2009 Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble. Theor. Comput. Fluid Dyn. 23, 79107.CrossRefGoogle Scholar
22. Wu, M. & Martin, M. P. 2007 Direct numerical simulation of shockwave and turbulent boundary layer interaction induced by a compression ramp. AIAA J. 45, 879889.CrossRefGoogle Scholar
23. Zheltovodov, A. A., Trofimov, V. M., Schülein, E. & Yakovlev, V. N. 1990 An experimental documentation of supersonic turbulent flows in the vicinity of forward- and backward-facing ramps. Tech. Rep. 2030. Inst. Theor. Appl. Mech., USSR Acad. Sci., Novosibirsk.Google Scholar

Grilli et al. supplementary material

Animation of the reconstructed flow field by the four dominant modes. 11 contours of velocity are shown.

Download Grilli et al. supplementary material(Video)
Video 1.8 MB

Grilli et al. supplementary material

Animation of the reconstructed flow field by the four dominant modes. 11 contours of velocity are shown.

Download Grilli et al. supplementary material(Video)
Video 2.7 MB