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Direct numerical simulations of laminar separation bubbles: investigation of absolute instability and active flow control of transition to turbulence

Published online by Cambridge University Press:  14 April 2014

Martin Embacher  and
H. F. Fasel
Martin Embacher*
Affiliation:
Institut für Aero- und Gasdynamik (IAG), Universität Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart, Germany
H. F. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, 1130 North Mountain, PO Box 210119, Tucson, AZ 85719-0119, USA
*
†Email address for correspondence: martin.embacher@gmail.com
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Abstract

Laminar separation bubbles generated on a flat plate by an adverse pressure gradient are investigated using direct numerical simulations (DNSs). Two-dimensional periodic forcing is applied at a blowing/suction slot upstream of separation. Control of separation through forcing with various frequencies and amplitudes is examined. For the investigation of absolute instability mechanisms, baseflows provided by two-dimensional Navier–Stokes calculations are analysed by introducing pulse disturbances and computing the three-dimensional flow response using DNS. The primary instability of the time-averaged flow is investigated with a local linear stability analysis. Employing a steady flow solution as baseflow, the nonlinear and non-parallel effects on the self-sustained disturbance development are illustrated, and a feedback mechanism facilitated by the upstream flow deformation is identified. Secondary instability is investigated locally using spatially periodic baseflows. The flow response to pulsed forcing indicates the existence of an absolute secondary instability mechanism, and the results indicate that this mechanism is dependent on the periodic forcing. Results from three-dimensional DNS provide insight into the global instability mechanisms of separation bubbles and complement the local analysis. A forcing strategy was devised that suppresses the temporal growth of three-dimensional disturbances, and as a consequence, breakdown to turbulence does not occur. Even for a separation bubble that has transitioned to turbulence, the flow relaminarizes when applying two-dimensional periodic forcing with proper frequencies and amplitudes.

JFM classification

Instability: Absolute/convective instability Boundary Layers: Boundary layer separation Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 141 - 185
Copyright
© 2014 Cambridge University Press 

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References

Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (6), 068102.Google Scholar
Alam, M. & Sandham, N. D. 2000 Direct numerical simulation of ‘short’ laminar separatation bubbles with turbulent reattachment. J. Fluid Mech. 410, 1–28.CrossRefGoogle Scholar
Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, Inc.Google Scholar
Bracewell, R. N. 1978 The Fourier Transform and its Applications. McGraw-Hill, Inc.Google Scholar
Brancher, P. & Chomaz, J.-M. 1997 Absolute and convective secondary instabilities in spatially periodic shear flows. Phys. Rev. Lett. 78 (4), 658–661.Google Scholar
Brevdo, L. & Bridges, T. J. 1997 Absolute and convective instabilities of spatially periodic flows. Phil. Trans. R. Soc. Lond. A 354 (1710), 1027–1064.Google Scholar
Delbende, I. & Chomaz, J.-M. 1998 Nonlinear convective/absolute instabilities in parallel two-dimensional wakes. Phys. Fluids 10 (11), 2724–2736.Google Scholar
Embacher, M.2006 Numerical investigation of secondary absolute instability in laminar separation bubbles. Master thesis, University of Arizona.Google Scholar
Eppler, R. 2003 About classical problems of airfoil drag. Aerosp. Sci. Technol. 7 (4), 289–297.Google Scholar
Fasel, H. F. 2002 Numerical investigation of the interaction of the Klebanoff-mode with a Tollmien–Schlichting wave. J. Fluid Mech. 450, 1–33.Google Scholar
Fasel, H. & Postl, D. 2006 Interaction of separation and transition in boundary layers: direct numerical simulations. In Proceedings of the Sixth IUTAM Symposium on Laminar–Turbulent Transition (ed. Govindarajan, R.), pp. 71–88. Springer.CrossRefGoogle Scholar
Fasel, H., Rist, U. & Konzelmann, U. 1990 Numerical investigation of the three-dimensional development in boundary layer transition. AIAA J. 23, 29–37.CrossRefGoogle Scholar
Gaster, M. 1966 The structure and behaviour of laminar separation bubbles. AGARD CP 4, 813–854.Google Scholar
Gaster, M. 1992 Stability of velocity profiles with reverse flow. In Instability, Transition and Turbulence, ICASE-Workshop (ed. Hussaini, M. Y., Kumar, A. & Streett, C. L.), pp. 212–215. Springer.CrossRefGoogle Scholar
Gaster, M. 2006 Laminar separation bubbles. In IUTAM Symposium on Laminar-Turbulent Transition (ed. Govindarajan, R.), Fluid Mechanics and its Applications, vol. 78, pp. 1–13. Springer.Google Scholar
Herbert, Th. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.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
Kachanov, Y. S. & Levchenko, V. Y. 1984 The resonant interaction of disturbances at laminar–turbulent transition in a boundary layer. J. Fluid Mech. 138, 209–247.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, 937–944.Google Scholar
Maucher, U.2001 Numerische Untersuchungen zur transition in der laminaren Ablöseblase einer Tragflügelgrenzschicht. PhD dissertation, Universität Stuttgart.Google Scholar
Meitz, H. L.1996 Numerical investigation of suction in a transitional flat plate boundary layer. PhD dissertation, University of Arizona.Google Scholar
Meitz, H. L. & Fasel, H. 2000 A compact-difference scheme for the Navier–Stokes equations in vorticity–velocity formulation. J. Comput. Phys. 157, 371–403.Google Scholar
Pauley, L. L., Moin, P. & Reynolds, W. C. 1990 The structure of two-dimensional separation. J. Fluid Mech. 220, 397–411.Google Scholar
Rist, U. & Maucher, U.1994 Direct numerical simulation of 2-D and 3-D instability waves in a laminar separation bubble. In Application of Direct and Large Eddy Simulation to Transition and Turbulence, AGARD-CP-551.Google Scholar
Rist, U. & Maucher, U. 2002 Investigations of time-growing instabilities in laminar separation bubbles. Eur. J. Mech. (B/Fluids) 21, 495–509.Google Scholar
Rist, U., Maucher, U. & Wagner, S. 1996 Direct numerical simulation of some fundamental problems related to transition in laminar separation bubbles. In Computational Methods in Applied Sciences’96 (ed. Désidéri, J.-A.), pp. 319–325. John Wiley & Sons Ltd.Google Scholar
Schwartz, M., Bennett, W. R. & Stein, S. 1966 Communication Systems and Techniques. McGraw-Hill.Google Scholar
Spalart, Ph. R. & Strelets, M. Kh. 2000 Mechanisms of transition and heat transfer in a separation bubble. J. Fluid Mech. 403, 329–349.Google Scholar
Wernz, S. & Fasel, H. F. 1999 Numerical investigation of resonance phenomena in wall jet transition. In Laminar–Turbulent Transition. Proceedings of the IUTAM Symposium, Sedona, AZ, 1999 (ed. Fasel, H. F. & Saric, W. S.), pp. 217–222. Springer.Google Scholar