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Relevance of local parallel theory to the linear stability of laminar separation bubbles

Published online by Cambridge University Press:  05 April 2012

Sourabh S. Diwan  and
O. N. Ramesh
Sourabh S. Diwan
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560064, India
O. N. Ramesh*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: onr@aero.iisc.ernet.in
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Abstract

Laminar separation bubbles are thought to be highly non-parallel, and hence global stability studies start from this premise. However, experimentalists have always realized that the flow is more parallel than is commonly believed, for pressure-gradient-induced bubbles, and this is why linear parallel stability theory has been successful in describing their early stages of transition. The present experimental/numerical study re-examines this important issue and finds that the base flow in such a separation bubble becomes nearly parallel due to a strong-interaction process between the separated boundary layer and the outer potential flow. The so-called dead-air region or the region of constant pressure is a simple consequence of this strong interaction. We use triple-deck theory to qualitatively explain these features. Next, the implications of global analysis for the linear stability of separation bubbles are considered. In particular we show that in the initial portion of the bubble, where the flow is nearly parallel, local stability analysis is sufficient to capture the essential physics. It appears that the real utility of the global analysis is perhaps in the rear portion of the bubble, where the flow is highly non-parallel, and where the secondary/nonlinear instability stages are likely to dominate the dynamics.

JFM classification

Boundary Layers: Boundary layer separation Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 698 , 10 May 2012 , pp. 468 - 478
Copyright
Copyright © Cambridge University Press 2012

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References

1. Catherall, D. & Mangler, K. W. 1966 The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction. J. Fluid Mech. 26, 163–182.CrossRefGoogle Scholar
2. Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
3. Diwan, S. S. 2009 Dynamics of early stages of transition in a laminar separation bubble. PhD thesis, Department of Aerospace Engineering, Indian Institute of Science, Bangalore, India.Google Scholar
4. Diwan, S. S. & Ramesh, O. N. 2009 On the origin of the inflectional instability of a laminar separation bubble. J. Fluid Mech. 629, 263–298.CrossRefGoogle Scholar
5. Dovgal, A. V., Kozlov, V. V. & Michalke, A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aerosp. Sci. 30, 61–94.CrossRefGoogle Scholar
6. Ehrenstein, U. & Gallaire, F. 2008 Two-dimensional global low-frequency oscillations in a separating boundary-layer flow. J. Fluid Mech. 614, 315–327.CrossRefGoogle Scholar
7. Gaster, M. 1967 The structure and behaviour of separation bubbles. ARC London R&M 3595.Google Scholar
8. Haggmark, C. P., Bakchinov, A. A. & Alfredsson, P. H. 2000 Experiments on a two-dimensional laminar separation bubble. Phil. Trans. R. Soc. Lond. A 358, 3193–3205.Google Scholar
9. Hetsch, T. & Rist, U. 2009 Accuracy of local and nonlocal stability theory in swept separation bubbles. AIAA J. 47 (5), 1116–1122.CrossRefGoogle Scholar
10. Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
11. Lekoudis, S. G. 1981 Studies in three-dimensional turbulent boundary layer separation from smooth surfaces. Progress Report E-16-606. Lockheed-Georgia Company.Google Scholar
12. Lou, W. & Hourmouziadis, J. 2000 Separation bubbles under steady and periodic-unsteady main flow conditions. Trans. ASME: J. Turbomach. 122, 634–643.Google Scholar
13. Marquet, O., Lombardi, M., Chomaz, J.-M., Sipp, D. & Jacquin, L. 2009 Direct and adjoint global modes of a recirculation bubble: lift-up and convective non-normalities. J. Fluid Mech. 622, 1–21.CrossRefGoogle Scholar
14. Marxen, O., Lang, M., Rist, U. & Wagner, S. 2003 A combined experimental/numerical study of unsteady phenomena in a laminar separation bubble. Flow Turbul. Combust. 71, 133–146.CrossRefGoogle Scholar
15. Radwan, S. F. & Lekoudis, S. G. 1984 Boundary-layer calculations in the inverse mode for incompressible flows over infinite swept wings. AIAA J. 22, 737–743.CrossRefGoogle Scholar
16. Rodriguez, D. & Theofilis, V. 2010 Structural changes of laminar separation bubbles induced by global linear instability. J. Fluid Mech. 655, 280–305.CrossRefGoogle Scholar
17. Smith, F. T. 1986 Steady and unsteady boundary-layer separation. Annu. Rev. Fluid Mech. 18, 197–220.CrossRefGoogle Scholar
18. Spalart, P. R. & Strelets, M. Kh. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.CrossRefGoogle Scholar
19. Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39, 249–315.CrossRefGoogle Scholar
20. Veldman, A. E. P. 2001 Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction. J. Engng Maths 39, 189–206.Google Scholar
21. Watmuff, J. H. 1999 Evolution of a wave packet into vortex loops in a laminar separation bubble. J. Fluid Mech. 397, 119–169.CrossRefGoogle Scholar