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The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble

Published online by Cambridge University Press:  07 March 2011

OLAF MARXEN  and
DAN S. HENNINGSON
OLAF MARXEN*
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden Center for Turbulence Research, Stanford University, Stanford, CA 94305-3035, USA
DAN S. HENNINGSON
Affiliation:
Linné Flow Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

Short laminar separation bubbles can develop on a flat plate due to an externally imposed pressure gradient. Here, these bubbles are computed by means of direct numerical simulations. Laminar–turbulent transition occurs in the bubble, triggered by small disturbance input with fixed frequency, but varying amplitude, to keep the bubbles short. The forcing amplitudes span a range of two orders of magnitude. All resulting bubbles differ with respect to their mean flow, linear-stability characteristics and distance between transition and mean reattachment locations. Mechanisms responsible for these differences are analysed in detail. Switching off the disturbance input or reducing it below a certain, very small threshold causes the short bubble to grow continuously. Eventually, it no longer exhibits typical characteristics of a short laminar separation bubble. Instead, it is argued that bursting has occurred and the bubble displays characteristics of a long-bubble state, even though this state was not a statistically steady state. This hypothesis is backed by a comparison of numerical results with measurements. For long bubbles, the transition to turbulence is not able to reattach the flow immediately. This effect can lead to the bursting of a short bubble, which remains short only when sufficiently large disturbances are convected into the bubble. Large-scale spanwise-oriented vortices at transition are observed for short but not for long bubbles. The failure of the transition process to reattach the flow in the long-bubble case is ascribed to this difference in transitional vortical structures.

JFM classification

Boundary Layers: Boundary layer separation Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 671 , 25 March 2011 , pp. 1 - 33
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of ‘short’ laminar separation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.CrossRefGoogle Scholar
Almutairi, J. H., Jones, L. E. & Sandham, N. D. 2010 Intermittent bursting of a laminar separation bubble on an airfoil. AIAA J. 28 (2), 414–426.CrossRefGoogle Scholar
Bake, S., Meyer, D. G. W. & Rist, U. 2002 Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and numerical simulation. J. Fluid Mech. 459, 217–243.CrossRefGoogle Scholar
Boiko, A. V., Grek, G. R., Dovgal, A. V. & Kozlov, V. V. 2002 The Origin of Turbulence in Near-Wall Flows, 1st edn. Springer.CrossRefGoogle Scholar
Diwan, S. S., Chetan, S. J. & Ramesh, O. N. 2006 On the bursting criterion for laminar separation bubbles. In Sixth IUTAM Symposium on Laminar–Turbulent Transition (ed. Govindarajan, R.), Fluid Mechanics and Its Applications, vol. 78, pp. 401–407. Springer.CrossRefGoogle Scholar
Dovgal, A. V. & Kozlov, V. V. 1995 On nonlinearity of transitional boundary-layer flows. Phil. Trans. R. Soc. Lond. A 352, 473–482.Google Scholar
Dovgal, A. V., Kozlov, V. V. & Michalke, A. 1994 Laminar boundary layer separation: instability and associated phenomena. Prog. Aerosp. Sci. 30 (1), 61–94.CrossRefGoogle Scholar
Gaster, M. 1966 The structure and behaviour of laminar separation bubbles. AGARD CP-4, pp. 813–854.Google Scholar
Gaster, M. 2006 Laminar separation bubbles. In Sixth IUTAM Symposium on Laminar–Turbulent Transition (ed. Govindarajan, R.), Fluid Mechanics and Its Applications, vol. 78, pp. 1–13. Springer, Berlin, New York.Google Scholar
Häggmark, C. P., Hildings, C. & Henningson, D. S. 2001 A numerical and experimental study of a transitional separation bubble. Aerosp. Sci. Technol. 5 (5), 317–328.CrossRefGoogle Scholar
Hain, R., Kähler, C. J. & Radespiel, R. 2009 Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils. J. Fluid Mech. 630, 129–153.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jones, L. E., Sandberg, R. D. & Sandham, N. D. 2008 Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175–207.CrossRefGoogle Scholar
Kloker, M. 1998 A robust high-resolution split-type compact FD scheme for spatial direct numerical simulation of boundary-layer transition. Appl. Sci. Res. 59, 353–377.CrossRefGoogle Scholar
Lang, M., Rist, U. & Wagner, S. 2004 Investigations on controlled transition development in a laminar separation bubble by means of LDA and PIV. Exp. Fluids 36, 43–52.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Marxen, O. & Henningson, D. 2006 Numerical simulation of the bursting of a laminar separation bubble. In High Performance Computing in Science and Engineering '06 (ed. Nagel, W. E., Jäger, W. & Resch, M.), pp. 253–267. Transactions of the High Performance Computing Center Stuttgart (HLRS), Springer.Google Scholar
Marxen, O. & Henningson, D. S. 2007 Direct numerical simulation of a short laminar separation bubble and early stages of the bursting process. In New Results in Numerical and Experimental Fluid Mechanics VI (ed. Tropea, C., Jakirlic, S., Heinemann, H.-J., Henke, R. & Hönlinger, H.), Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol. 96, pp. 235–243. Springer.Google Scholar
Marxen, O., Lang, M., Rist, U., Levin, O. & Henningson, D. S. 2009 Mechanisms for spatial steady three-dimensional disturbance growth in a non-parallel and separating boundary layer. J. Fluid Mech. 634, 165–189.CrossRefGoogle Scholar
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
Marxen, O. & Rist, U. 2010 Mean flow deformation in a laminar separation bubble: separation and stability characteristics. J. Fluid Mech. 660, 37–54.CrossRefGoogle Scholar
Marxen, O., Rist, U. & Wagner, S. 2004 Effect of spanwise-modulated disturbances on transition in a separated boundary layer. AIAA J. 42 (5), 937–944.CrossRefGoogle Scholar
Maucher, U., Rist, U. & Wagner, S. 1997 A method for the identification of high-frequency oscillations in unsteady flows. ZAMM 77 (Suppl. 1), S209–S210.Google Scholar
Maucher, U., Rist, U. & Wagner, S. 2000 a Refined interaction method for direct numerical simulation of transition in separation bubbles. AIAA J. 38 (8), 1385–1393.CrossRefGoogle Scholar
Maucher, U., Rist, U. & Wagner, S. 2000 b Secondary disturbance amplification and transition in laminar separation bubbles. In Laminar–Turbulent Transition (ed. Fasel, H. & Saric, W.), pp. 657–662 (Fifth IUTAM Symposium, Sedona, AZ, USA, Sept. 13–17, 1999). Springer.CrossRefGoogle Scholar
Meyer, D., Rist, U. & Kloker, M. 2003 Investigation of the flow randomization process in a transitional boundary layer. In High Performance Computing in Science and Engineering '03 (ed. Krause, E. & Jäger, W.), pp. 239–253. Transactions of the HLRS 2003, Springer.Google Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379–405.CrossRefGoogle Scholar
Owen, P. R. & Klanfer, L. 1953 On the laminar boundary layer separation from the leading edge of a thin airfoil. Tech. Rep. Aero 2508. Royal Aircraft Establishment, UK. In Tech. Rep. C.P. 220, 1955. Auckland Regional Council.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397–411.CrossRefGoogle Scholar
Rist, U. 2002 On instabilities and transition in laminar separation bubbles. In Proceedings of the CEAS Aerospace Aerodynamics Research Conference, 10–12 June 2002, pp. 20.1–20.14. Cambridge, UK. Royal Aeronautical Society, London, CD-ROM 269.Google Scholar
Rist, U. 2003 Instability and transition mechanisms in laminar separation bubbles. In VKI/RTO-LS Low Reynolds Number Aerodynamics on Aircraft Including Applications in Emerging UAV Technology, pp. 1–29. van Karman Institut, Rhode-Saint-Genese, Belgium.Google Scholar
Rist, U. & Augustin, K. 2006 Control of laminar separation bubbles using instability waves. AIAA J. 44 (10), 2217–2223.CrossRefGoogle Scholar
Rist, U. & Maucher, U. 2002 Investigations of time-growing instabilities in laminar separation bubbles. Eur. J. Mech. B Fluids 21, 495–509.CrossRefGoogle Scholar
Rist, U., Maucher, U. & Wagner, S. 1996 Direct numerical simulation of some fundamental problems related to transition in laminar separation bubbles. In Computational Fluid Dynamics '96, pp. 319–325. ECCOMAS 96, John Wiley & Sons.Google Scholar
Sandham, N. D. 2008 Transitional separation bubbles and unsteady aspects of aerofoil stall. Aeronaut. J. 112 (1133), 395–404.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows, 1st edn. Springer.CrossRefGoogle Scholar
Spalart, P. R. & Strelets, M. K. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.CrossRefGoogle Scholar
Tani, I. 1964 Low-speed flows involving bubble separations. Prog. Aerosp. Sci. 5, 70–103.CrossRefGoogle Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aerosp. Sci. 39, 249–315.CrossRefGoogle Scholar
Wassermann, P. & Kloker, M. 2003 Transition mechanisms induced by travelling crossflow vortices in a three-dimensional boundary layer. J. Fluid Mech. 483, 67–89.CrossRefGoogle Scholar
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
Winkelmann, A. E. & Barlow, J. B. 1980 Flowfield model for a rectangular planform wing beyond stall. AIAA J. 18 (8), 1006–1008.CrossRefGoogle Scholar
Yarusevych, S., Sullivan, P. E. & Kawall, J. G. 2009 On vortex shedding from an airfoil in low-Reynolds-number flows. J. Fluid Mech. 632, 245–271.CrossRefGoogle Scholar