Hostname: page-component-76fb5796d-5g6vh Total loading time: 0 Render date: 2024-04-27T14:27:09.370Z Has data issue: false hasContentIssue false
  • English
  • Français

Vortex formation and vortex breakup in a laminar separation bubble

Published online by Cambridge University Press:  01 July 2013

Olaf Marxen ,
Matthias Lang  and
Ulrich Rist
Olaf Marxen
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany Aeronautics and Aerospace Department, von Kármán Institute for Fluid Dynamics, Chaussée de Waterloo 72, B-1640 Rhode-St-Genèse, Belgium
Matthias Lang
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
Ulrich Rist
Affiliation:
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

The convective primary amplification of a forced two-dimensional perturbation initiates the formation of essentially two-dimensional large-scale vortices in a laminar separation bubble. These vortices are then shed from the bubble with the forcing frequency. Immediately downstream of their formation, the vortices get distorted in the spanwise direction and quickly disintegrate into small-scale turbulence. The laminar–turbulent transition in a forced laminar separation bubble is dominated by this vortex formation and breakup process. Using numerical and experimental data, we give an in-depth characterization of this process in physical space as well as in Fourier space, exploiting the largely periodic character of the flow in time as well as in the spanwise direction. We present evidence that a combination of more than one secondary instability mechanism is active during this process. The first instability mechanism is the elliptic instability of vortex cores, leading to a spanwise deformation of the cores with a spanwise wavelength of the order of the size of the vortex. Another mechanism, potentially an instability of flow in between two consecutive vortices, is responsible for three-dimensionality in the braid region. The corresponding disturbances possess a much smaller spanwise wavelength as compared to those amplified through elliptic instability. The secondary instability mechanisms occur for both fundamental and subharmonic frequency, respectively, even in the absence of continuous forcing, indicative of temporal amplification in the region of vortex formation.

JFM classification

Boundary Layers: Boundary layer separation Instability: Nonlinear instability Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 728 , 10 August 2013 , pp. 58 - 90
Copyright
©2013 Cambridge University Press 

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

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.Google Scholar
Boiko, A., Dovgal, A., Hein, S. & Henning, A. 2011 Particle image velocimetry of a low-Reynolds-number separation bubble. Exp. Fluids 50, 13–21.Google 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.Google Scholar
Caulfield, C. P. & Kerswell, R. R. 2000 The nonlinear development of three-dimensional disturbances at hyperbolic stagnation points: a model of the braid region in mixing layers. Phys. Fluids 12 (5), 1032–1043.Google Scholar
Cherubini, S., Robinet, J.-C. & De Palma, P. 2010 The effects of non-normality and nonlinearity of the Navier–Stokes operator on the dynamics of a large laminar separation bubble. Phys. Fluids 22, 014102.Google Scholar
Craik, A. D. D. & Criminale, W. O. 1986 Evolution of wavelike disturbances in shear flows: a class of exact solutions of the Navier–Stokes equations. Proc. R. Soc. Lond. A 406 (1830), 13–26.Google Scholar
Fitzgerald, E. J. & Mueller, T. J. 1988 Measurements in a separation bubble on an airfoil using laser velocimetry. AIAA J. 28 (4), 584–592.CrossRefGoogle Scholar
Gaster, M. 1967 The structure and behaviour of separation bubbles. Aeronautical Research Council, Reports and Memoranda No. 3595, London.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.Google 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.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Ho, C.-M. & Huerre, P. 1984 Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424.Google 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
Kerswell, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83–113.Google Scholar
Kloker, M. J. 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.Google Scholar
Lagnado, R. R., Phan-Thien, N. & Leal, L. G. 1984 The stability of two-dimensional linear flows. Phys. Fluids 27 (5), 1094–1101.Google 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
Marxen, O. 2005 Numerical studies of physical effects related to the controlled transition process in laminar separation bubbles. Dissertation, Universität Stuttgart.Google Scholar
Marxen, O. & Henningson, D. S. 2011 The effect of small-amplitude convective disturbances on the size and bursting of a laminar separation bubble. J. Fluid Mech. 671, 1–33.CrossRefGoogle Scholar
Marxen, O., Lang, M. & Rist, U. 2012 Discrete linear local eigenmodes in a separating laminar boundary layer. J. Fluid Mech. 711, 1–26.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.Google 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.Google Scholar
Marxen, O. & Rist, U. 2010 Mean flow deformation in a laminar separation bubble: separation and stability characteristics. J. Fluid Mech. 660, 37–54.Google Scholar
Marxen, O., Rist, U. & Henningson, D. S. 2006 Steady three-dimensional streaks and their optimal growth in a laminar separation bubble. In New Results in Numerical and Experimental Fluid Mechanics V (ed. Rath, H. J., Holze, C., Heinemann, H.-J., Henke, R. & Hönlinger, H.). Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol. 92, Contributions to the 14th STAB/DGLR Symposium, 16–18 November 2004. Springer.Google 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.Google Scholar
Mashayek, A. & Peltier, W. R. 2012 The ‘zoo’ of secondary instabilities precursory to stratified shear flow transition. Part 1. Shear aligned convection, pairing, and braid instabilities. J. Fluid Mech. 708, 5–44.CrossRefGoogle Scholar
Maucher, U., Rist, U. & Wagner, S. 2000a 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. 2000b Secondary disturbance amplification and transition in laminar separation bubbles. In Laminar–Turbulent Transition (ed. Fasel, H. & Saric, W.), Proceedings of the 5th IUTAM Symposium, Sedona, AZ, 13–17 September 1999, pp. 657–662. Springer.Google 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.), Transactions of the HLRS 2003, pp. 239–253. Springer.Google Scholar
Ortiz, S. & Chomaz, J.-M. 2011 Transient growth of secondary instabilities in parallel wakes: anti lift-up mechanism and hyperbolic instability. Phys. Fluids 23, 114106.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
Postl, D., Balzer, W. & Fasel, H. F. 2011 Control of laminar separation using pulsed vortex generator jets: direct numerical simulations. J. Fluid Mech. 676, 81–109.Google Scholar
Rist, U. & Augustin, K. 2006 Control of laminar separation bubbles using instability waves. AIAA J. 44 (10), 2217–2223.Google Scholar
Rodríguez, D. & Theofilis, V. 2010 Structural changes of laminar separation bubbles induced by global linear instability. J. Fluid Mech. 655, 280–305.Google Scholar
Theofilis, V. 2011 Global linear instability. Annu. Rev. Fluid Mech. 43, 319–352.Google 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
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.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.Google Scholar
Yon, S. & Katz, J. 1998 Study of the unsteady flow features on a stalled wing. AIAA J. 36 (3), 305–312.Google Scholar
Zaman, K. B. M. Q., McKinzie, D. J. & Rumsey, C. L. 1989 A natural low-frequency oscillation of the flow over an airfoil near stalling conditions. J. Fluid Mech. 202, 403–442.Google Scholar
Zhang, W., Hain, R. & Kähler, C. J. 2008 Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil. Exp. Fluids 45, 725–743.CrossRefGoogle Scholar