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Spatial optimal disturbances in swept attachment-line boundary layers

Published online by Cambridge University Press:  30 April 2008

ALAN GUÉGAN
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
PETER J. SCHMID
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France
PATRICK HUERRE
Affiliation:
Laboratoire d'Hydrodynamique (LadHyX), CNRS-École Polytechnique, F-91128 Palaiseau, France

Abstract

A formulation based on direct and adjoint parabolized equations is developed to account for the spatial evolution of perturbations in swept attachment-line boundary layers. For sweep Reynolds numbers larger than Re = 100 the dynamics is dominated by a lift-up mechanism which is responsible for large energy amplification by transforming spanwise vortices into spanwise streaks. This mechanism favours steady perturbations with a chordwise scale that quantitatively matches its counterpart for classical Blasius boundary layers.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134150.CrossRefGoogle Scholar
Bertolotti, F. P., Herbert, T. & Spalart, P. R. 1992 Linear and nonlinear stability of the Blasius boundary layer. J. Fluid Mech. 242, 441474.CrossRefGoogle Scholar
Chang, C. L. & Malik, M. R. 1993 Non-parallel stability of compressible boundary layers. AIAA Paper 93-2912.CrossRefGoogle Scholar
Cumpsty, N. A. & Head, M. R. 1969 The calculation of the three-dimensional turbulent boundary layer. Part III: Comparison of attachment-line calculations with experiment. Aero. Q. 20, 99184.CrossRefGoogle Scholar
Gaster, M. 1967 On the flow along swept leading edges. Aero. Q. 18, 165184.CrossRefGoogle Scholar
Görtler, H. 1955 Dreidimensionale Instabilität der ebenen Staupunktsströmung gegenüber wirbelartigen Störungen. In 50 Jahre Grenzschichtforschung (ed. Görtler, H. & Tollmien, W.). Vieweg, Braunschweig.CrossRefGoogle Scholar
Gregory, M. A. 1960 Transition and the spread of turbulence on a 60° swept-back wing. J. R. Aero. Soc. 64, 562.CrossRefGoogle Scholar
Guégan, A. 2007 Optimal perturbations in swept leading-edge boundary layers. PhD thesis, Ecole Polytechnique, Palaiseau, France.Google Scholar
Guégan, A., Huerre, P. & Schmid, P. J. 2007 Optimal disturbances in swept Hiemenz flow. J. Fluid Mech. 578, 223232.CrossRefGoogle Scholar
Guégan, A., Schmid, P. J. & Huerre, P. 2006 Optimal energy growth and optimal control in swept Hiemenz flow. J. Fluid Mech. 566, 1145.CrossRefGoogle Scholar
Hall, P., Malik, M. R. & Poll, D. I. A. 1984 On the stability of an infinite swept attachment line boundary layer. Proc. R. Soc. Lond. A 395, 229245.Google Scholar
Hämmerlin, G. 1955 Zur Instabilitätstheorie der ebenen Staupunktsströmung. In 50 Jahre Grenzschichtforschung (ed. Görtler, H. & Tollmien, W.). Vieweg, Braunschweig.Google Scholar
Joslin, R. D. 1995 Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers. J. Fluid Mech. 291, 369392.CrossRefGoogle Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243251.CrossRefGoogle Scholar
Lin, R.-S. & Malik, M. R. 1996 On the stability of attachment-line boundary layers. Part 1. The incompressible swept Hiemenz flow. J. Fluid Mech. 311, 239255.CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289309.CrossRefGoogle Scholar
Obrist, D. & Schmid, P. J. 2003 a On the linear stability of swept attachment-line boundary layer flow. Part 1. Spectrum and asymptotic behaviour. J. Fluid Mech. 493, 129.CrossRefGoogle Scholar
Obrist, D. & Schmid, P. J. 2003 b On the linear stability of swept attachment-line boundary layer flow. Part 2. Non-modal effects and receptivity. J. Fluid Mech. 493, 3158.CrossRefGoogle Scholar
Pfenninger, W. 1977 Laminar flow control - Laminarization. Special Course on Concepts for Drag Reduction. Tech. Rep. 654. AGARD.Google Scholar
Pfenninger, W. & Bacon, J. W. 1969 Amplified laminar boundary layer oscillations and transition at the front attachment line of a 45 deg swept flat-nosed wing with and without suction. In Viscous drag reduction (ed. Wells, C. S.), pp. 85105. Plenum.CrossRefGoogle Scholar
Theofilis, V. 1995 Spatial stability of incompressible attachment-line flow. Theor. Comput. Fluid Dyn. 7, 159171.CrossRefGoogle Scholar
Theofilis, V. 1998 On linear and nonlinear instability of the incompressible swept attachment-line boundary layer. J. Fluid Mech. 355, 193227.CrossRefGoogle Scholar
Tumin, A. & Reshotko, E. 2001 Spatial theory of optimal disturbances in boundary layers. Phys. Fluids 13, 20972104.CrossRefGoogle Scholar
Turkyilmazoglu, M. & Gajjar, J. S. B. 1999 On the absolute instability of the attachment-line and swept Hiemenz boundary layers. Theor. Comput. Fluid Dyn. 13, 5775.Google Scholar