Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-13T19:41:16.607Z Has data issue: false hasContentIssue false
  • English
  • Français

Bifurcations in shock-wave/laminar-boundary-layer interaction: global instability approach

Published online by Cambridge University Press:  02 May 2007

J.-CH. ROBINET
J.-CH. ROBINET*
Affiliation:
SINUMEF Laboratory, ENSAM CER de Paris, 151, Boulevard de l'Hôpital, 75013 Paris, France
Get access Rights & Permissions [Opens in a new window]

Abstract

The principal objective of this paper is to study some unsteady characteristics of an interaction between an incident oblique shock wave impinging on a laminar boundary layer developing on a flat plate. More precisely, this paper shows that some unsteadiness, in particular the low-frequency unsteadiness, originates in a supercritical Hopf bifurcation related to the dynamics of the separated boundary layer. Various direct numerical simulations were carried out of a shock-wave/laminar-boundary-layer interaction (SWBLI). Three-dimensional unsteady Navier–Stokes equations are numerically solved with an implicit dual time stepping for the temporal algorithm and high-order AUSMPW+ scheme for the spatial discretization. A parametric study on the oblique shock-wave angle has been performed to characterize the unsteady behaviour onset. These numerical simulations have shown that starting from the incident shock angle and the spanwise extension, the flow becomes three-dimensional and unsteady. A linearized global stability analysis is carried out in order to specify and to find some characteristics observed in the direct numerical simulation. This stability analysis permits us to show that the physical origin generating the three-dimensional characters of the flow results from the existence of a three-dimensional stationary global instability.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 579 , 25 May 2007 , pp. 85 - 112
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ackeret, J., Feldmann, F. & Rott, N. 1947 Investigation of compression shocks and boundary layers in gases moving at high speed. NACA TM 1113.Google Scholar
Alfano, D., Corre, C., de la Motte, P., Joubert, P. N. & Lerat, A. 2004 Assesment of numerical methods for unsteady shock/boundary layer interaction. Boundary and Interior Layers – Computational and Asymptotic Methods (BAIL 2004) Conference, Toulouse, July.Google Scholar
Balakumar, P., Zhao, H. & Atkins, H. 2005 Stability of hypersonic boundary layers over a compression corner. AIAA J. 43, 760–767.Google Scholar
Bedarev, I. A., Maslov, A., Sidorenko, A., Fedorova, N. N. & Shiplyuk, A. 2002 Experimental and numerical study of hypersonic separated flow in the vicinity of a cone-flare model. J. Appl. Mech. Tech. Phys. 43, 867–876.Google Scholar
Boin, J. P., Robinet, J.-Ch., Corre, Ch. & Deniau, H. 2006 3D steady and unsteady bifurcations in a shock-wave/laminar boundary layer interaction; a numerical study. Theoret. Comput. Fluid Dyn. 20, 163–180.Google Scholar
Boyd, J. P. 1999 Chebyshev and Fourier Spectral Methods. Dover.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Chapman, D. R., Kuehn, D. M. & Larson, H. K. 1958 Investigation of separated flow in supersonic and subsonic streams with emphasis on the effect of transition. NACA Rep. 1356.Google Scholar
Degrez, G., Boccadoro, C. H. & Wendt, J. F. 1987 The interaction of an oblique shock wave with a laminar boundary layer revisited. An experimental and numerical study. J. Fluid Mech. 177, 247–263.CrossRefGoogle Scholar
Délery, J. & Marvin, J. G. 1986 Shock-wave boundary layer interactions. AGARDograph.Google Scholar
Dolling, D. S. 2001 Fifty years of shock-wave/boundary-layer interaction research: What next? AIAA J. 39 (8), 1517–1531.Google Scholar
Dupont, P., Debiève, J. F., Ardissone, J. P. & Haddad, C. 2003 Some time properties in shock boundary layer interaction. West East High Speed Flows, CIMNE 1st edn, January.Google Scholar
Dupont, P., Haddad, C., Ardissone, J. P. & Debiève, J.-F. 2005 Space and time organisation of a shock wave/turbulent boundary layer interaction. Aerospace Sci. Technol. 9, 561–572.CrossRefGoogle Scholar
Dussauge, J.-P., Dupont, P. & Debiève, J.-F. 2006 Unsteadiness in shock wave boundary layer interaction with separation. Aerospace Sci. Technol. 10, 85–91.CrossRefGoogle Scholar
Eissler, W. & Bestek, H. 1996 Spatial numerical simulations of linear and weakly nonlinear wave instabilities in supersonic boundary layers. Theoret. Comput. Fluid Dyn. 8, 219–235.Google Scholar
Haddad, C., Ardissone, J. P., Dupont, P. & Debiève, J. F. 2004 Space and time organization of a shock wave/turbulent boundary layer interaction. Congrès AAAF, Aérodynamiques instationnaires, Paris.Google Scholar
Jameson, A. 1991 Time-dependent calculations using multigrid with applications to unsteady flows past airfoils and wings. AIAA Paper 1596.CrossRefGoogle Scholar
Kim, K. H., Kim, C. & Rho, O.-H. 2001 a Methods for the accurate computations of hypersonic flows i. AUSMPW+ scheme. J. Comput. Phys. 174, 38–80.Google Scholar
Kim, K. H., Kim, C. & Rho, O.-H. 2001 b Methods for the accurate computations of hypersonic flows ii. Shock-aligned grid technique. J. Comput. Phys. 174, 81–119.Google Scholar
Kosinov, A. D., Maslov, A. A. & Shevelkov, S. G. 1990 Experiments on the stability of supersonic boundary layers. J. Fluid Mech. 219, 621–633.CrossRefGoogle Scholar
Liepmann, H. W. 1946 The interaction between boundary layer and shock waves in transonic flow. J. Aeronaut. Sci. 13, 623–637.Google Scholar
Lighthill, M. J. 1950 Reflection at a laminar boundary-layer of a weak steady disturbance to a supersonic stream neglecting viscosity and heat conduction. Q. J. Mech. Appl. Maths 3, 303.Google Scholar
Lighthill, M. J. 1953 a On the boundary layer upstream influence I. A comparison between subsonic and supersonic flows. Proc. R. Soc. A 217, 344–357.Google Scholar
Lighthill, M. J. 1953 b On the boundary layer upstream influence II. Supersonic flows without separation. Proc. R. Soc. A 217, 478–507.Google Scholar
Liou, M. S. & Edwards, J. 1998 Low-diffusion flux-splitting methods for flows at all speeds. AIAA J. 36, 1610–1617.Google Scholar
Luo, H., Baum, J. D. & Lhner, R. 2001 An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids. Comput. Fluids 30, 137–159.Google Scholar
Mack, L. 1969 Boundary layer stability theory. Tech. Rep. 900-277. Jet Propulsion Laboratory, Pasadena.Google Scholar
Malik, M. R. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86, 376–413.Google Scholar
Pagella, A., Rist, U. & Wagner, S. 2002 Numerical investigations of small-amplitude disturbances in a boundary layer with impinging shock wave at Ma = 4.8. Phys. Fluids 14 (7), 2088–2101.Google Scholar
Peyret, R. & Taylor, T. 1983 Computational Methods for Fluid Flows. Springer.Google Scholar
Smits, A. J. & Dussauge, J.-P. 1996 Turbulent Shear Layers in Supersonic Flow. AIP Press, New York.Google Scholar
Stewartson, K. & Williams, P. G. 1969 Self-induced separation. Proc. R. Soc. Lond. A 312 (1508), 181206.Google Scholar
Streett, C. L. & Macaraeg, M. G. 1989 Spectral multi-domain for large-scale fluid dynamic simulations. Appl. Numer. Maths 6, 123–139.Google Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerospace Sci. 39, 249–315.CrossRefGoogle Scholar
Theofilis, V. & Colonius, T. 2004 Three-dimensional instabilities of compressible flow over open cavities: direct solution of the biglobal eigenvalue problem. AIAA Paper 2004–2544.Google Scholar