Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-20T21:05:32.445Z Has data issue: false hasContentIssue false
  • English
  • Français

Tollmien–Schlichting wave growth over spanwise-periodic surface patterns

Published online by Cambridge University Press:  30 July 2014

Robert S. Downs III  and
Jens H. M. Fransson
Robert S. Downs III*
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-10044 Stockholm, Sweden
Jens H. M. Fransson
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-10044 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A novel type of surface roughness is deployed in a zero-pressure-gradient boundary layer with the goal of delaying the onset of laminar-to-turbulent transition for drag reduction purposes. This proof-of-concept experiment relies on forcing phase-triggered Tollmien–Schlichting (TS) waves across a range of initial amplitudes to produce amplified boundary-layer disturbances in a controlled and repeatable manner. Building on earlier work demonstrating attenuation of forced disturbances and delay of transition with spanwise arrays of discrete roughness and miniature vortex generators (MVGs), the present work seeks a roughness shape which might find success in a wider range of flows. Toward that end, streamwise-elongated humps are regularly spaced in the spanwise direction to form a wavy wall. By direct modulation of the mean flow, growth rates of the forced disturbances are increased or decreased, depending on the roughness configuration. Boundary-layer velocity measurements with hot-wire probes have been performed in a parametric study of the effects of roughness-field geometry and forcing amplitude on TS-wave growth and transition. The roughness field proves detrimental to passive flow control efforts in some configurations, while a reduction in the TS-wave amplitudes compared with the smooth-wall reference case is observed at other conditions. Substantial delays in the onset of transition are demonstrated when TS waves are forced with large amplitudes.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 754 , 10 September 2014 , pp. 39 - 74
Copyright
© 2014 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

Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11 (1), 134–150.Google Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.Google Scholar
Bagheri, S. & Hanifi, A. 2007 The stabilizing effect of streaks on Tollmien–Schlichting and oblique waves: a parametric study. Phys. Fluids 19 (7), 078103.Google Scholar
Bake, S., Fernholz, H. H. & Kachanov, Y. S. 2000 Resemblance of K- and N-regimes of boundary-layer transition at late stages. Eur. J. Mech. (B/Fluids) 19 (1), 1–22.Google Scholar
Bake, S., Kachanov, Y. S. & Fernholz, H. H. 1996 Subharmonic K-regime of boundary-layer breakdown. In Transitional Boundary Layers in Aeronautics (ed. Henkes, R. A. W. M. & van Ingen, J. L.), North-Holland.Google Scholar
Bechert, D. W., Bruse, M., Hage, W., van der Hoeven, J. G. T. & Hoppe, G. 1997 Experiments on drag-reducing surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338, 59–87.Google Scholar
Bennett, J. & Hall, P. 1988 On the secondary instability of Taylor–Görtler vortices to Tollmien–Schlichting waves in fully developed flows. J. Fluid Mech. 186, 445–469.Google Scholar
Borodulin, V. I., Gaponenko, V. R., Kachanov, Y. S., Meyer, D. G. W., Rist, U., Lian, Q. X. & Lee, C. B. 2002a Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. Theor. Comput. Fluid Dyn. 15 (5), 317–337.Google Scholar
Borodulin, V. I., Kachanov, Y. S. & Koptsev, D. B. 2002b Experimental study of resonant interactions of instability waves in a self-similar boundary layer with an adverse pressure gradient: I. Tuned resonances. J. Turbul. 3 (62), 1–38.Google Scholar
Corke, T. C., Bar-Sever, A. & Morkovin, M. V. 1986 Experiments on transition enhancement by distributed roughness. Phys. Fluids 29 (10), 3199–3213.Google Scholar
Cossu, C. & Brandt, L. 2004 On Tollmien–Schlichting-like waves in streaky boundary layers. Eur. J. Mech. (B/Fluids) 23 (6), 815–833.Google Scholar
Denissen, N. A. & White, E. B. 2013 Secondary instability of roughness-induced transient growth. Phys. Fluids 25 (11), 114108.Google Scholar
von Doenhoff, A. E. & Horton, E. A.1958 A low-speed experimental investigation of the effect of a sandpaper type of roughness on boundary-layer transition. NACA Tech. Rep. 1349.Google Scholar
Ergin, F. G. & White, E. B. 2006 Unsteady and transitional flows behind roughness elements. AIAA J. 44 (11), 2504–2514.Google Scholar
Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2004 Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer. Phys. Fluids 16 (10), 3627–3638.Google Scholar
Fransson, J. H. M., Brandt, L., Talamelli, A. & Cossu, C. 2005a Experimental study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks. Phys. Fluids 17 (5), 054110.Google Scholar
Fransson, J. H. M., Matsubara, M. & Alfredsson, P. H. 2005b Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.Google Scholar
Fransson, J. H. M. & Talamelli, A. 2012 On the generation of steady streamwise streaks in flat-plate boundary layers. J. Fluid Mech. 698, 211–234.Google Scholar
Fransson, J. H. M., Talamelli, A., Brandt, L. & Cossu, C. 2006 Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96 (6), 064501.Google Scholar
Gaponenko, V. R. & Kachanov, Y. S. 1994 New methods of generation of controlled spectrum instability waves in the boundary layers. In 7th International Conference on the Methods of Aerophysical Research. Proceedings. Part 1, pp. 90–97. Inst. Theor. & Appl. Mech.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011a Drag reduction by riblets. Phil. Trans. R. Soc. Lond. A 369 (1940), 1412–1427.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011b Hydrodynamic stability and breakdown of the viscous regime over riblets. J. Fluid Mech. 678, 317–347.Google Scholar
Garzon, G. A. & Roberts, M. W.2013 Effect of a small surface wave on boundary-layer transition. AIAA Paper 2013-3110.Google Scholar
Green, J. E.2008 Laminar flow control – back to the future? AIAA Paper 2008-3738.Google Scholar
Grek, G. R., Kozlov, V. V. & Titarenko, S. V. 1996 An experimental study of the influence of riblets on transition. J. Fluid Mech. 315, 31–49.Google Scholar
Grek, G. R., Kozlov, V. V., Titarenko, S. V. & Klingmann, B. G. B. 1995 The influence of riblets on a boundary layer with embedded streamwise vortices. Phys. Fluids 7 (10), 2504–2506.Google Scholar
Gürün, A. M. & White, E. B.2005 Tollmien–Schlichting wave suppression and transition delay using stationary transient disturbances. AIAA Paper 2005-5313.Google Scholar
Hall, P. & Bennett, J. 1986 Taylor–Görtler instabilities of Tollmien–Schlichting waves and other flows governed by the interactive boundary-layer equations. J. Fluid Mech. 171, 441–457.Google Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.Google Scholar
Johansson, A. V. & Alfredsson, P. H. 1982 On the structure of turbulent channel flow. J. Fluid Mech. 122, 295–314.Google Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar-boundary-layer transition. Annu. Rev. Fluid Mech. 26, 411–482.Google Scholar
Klebanoff, P. S., Cleveland, W. G. & Tidstrom, K. D. 1992 On the evolution of a turbulent boundary layer induced by a three-dimensional roughness element. J. Fluid Mech. 237, 101–187.Google Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12 (1), 1–34.Google Scholar
Klumpp, S., Meinke, M. & Schröder, W. 2010 Numerical simulation of riblet controlled spatial transition in a zero-pressure-gradient boundary layer. Flow Turbul. Combust. 85 (1), 57–71.Google Scholar
Kosorygin, V. S., Radeztsky, R. H. & Saric, W. S. 1995 Laminar boundary-layer, sound receptivity and control. In Laminar-Turbulent Transition IV (ed. Kobayashi, R.), pp. 517–524. Springer.Google Scholar
Ladd, D. M., Rohr, J. J., Reidy, L. W. & Hendricks, E. W. 1993 The effect of riblets on laminar to turbulent transition. Exp. Fluids 14 (1–2), 1–9.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (2), 243–251.Google Scholar
Lindgren, B. & Johansson, A. V.2002 Evaluation of the flow quality in the MTL wind-tunnel. Tech. Rep. TRITA-MEK 2002:13. KTH Mechanics, Stockholm.Google Scholar
Litvinenko, Y. A., Chernoray, V. G., Kozlov, V. V., Loefdahl, L., Grek, G. R. & Chun, H. H. 2006 The influence of riblets on the development of a $\varLambda $ structure and its transformation into a turbulent spot. Dokl. Phys. 51 (3), 144–147.Google Scholar
Liu, Y., Zaki, T. A. & Durbin, P. A. 2008 Floquet analysis of secondary instability of boundary layers distorted by Klebanoff streaks and Tollmien–Schlichting waves. Phys. Fluids 20 (12), 124102.Google Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.Google Scholar
Luchini, P. & Trombetta, G. 1995 Effects of riblets upon flow stability. Appl. Sci. Res. 54 (4), 313–321.Google Scholar
Malik, M. R. & Hussaini, M. Y. 1990 Numerical simulation of interactions between Görtler vortices and Tollmien–Schlichting waves. J. Fluid Mech. 210, 183–199.Google Scholar
Mendonça, M. T., Morris, P. J. & Pauley, L. L. 2000 Interaction between Görtler vortices and two-dimensional Tollmien–Schlichting waves. Phys. Fluids 12 (6), 1461–1471.Google Scholar
Morkovin, M. V. 1969 On the many faces of transition. In Viscous Drag Reduction (ed. Wells, C. S.), Plenum.Google Scholar
Nayfeh, A. H. 1981 Effect of streamwise vortices on Tollmien–Schlichting waves. J. Fluid Mech. 107, 441–453.Google Scholar
Nayfeh, A. H. & Al-Maaitah, A. 1988 Influence of streamwise vortices on Tollmien–Schlichting waves. Phys. Fluids 31 (12), 3543–3549.Google Scholar
Nayfeh, A. H. & Ashour, O. N. 1994 Acoustic receptivity of a boundary layer to Tollmien–Schlichting waves resulting from a finite-height hump at finite Reynolds numbers. Phys. Fluids 6 (11), 3705–3716.Google Scholar
Nugroho, B., Hutchins, N. & Monty, J. P. 2013 Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and directional surface roughness. Intl J. Heat Fluid Flow 41, 90–102.Google Scholar
Peltzer, I. 2008 Comparative in-flight and wind tunnel investigation of the development of natural and controlled disturbances in the laminar boundary layer of an airfoil. Exp. Fluids 44 (6), 961–972.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 2007 Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press.Google Scholar
Reshotko, E. 2001 Transient growth: a factor in bypass transition. Phys. Fluids 13 (5), 1067–1075.Google Scholar
Reshotko, E., Saric, W. S. & Nagib, H. M.1997 Flow quality issues for large wind tunnels. AIAA Paper 97-0225.Google Scholar
Riedel, H. & Sitzmann, M. 1998 In-flight investigations of atmospheric turbulence. Aerosp. Sci. Technol. 2 (5), 301–319.Google Scholar
Ruban, A. I. 1984 On the generation of Tollmien–Schlichting waves by sound. Fluid Dyn. 19 (5), 709–717.Google Scholar
Ruban, A. I., Duck, P. W. & Zhikharev, C. N.1996 The generation of Tollmien–Schlichting waves by freestream vorticity perturbations. AIAA Paper 96-2123.Google Scholar
Saric, W. S. 1994 Görtler vortices. Annu. Rev. Fluid Mech. 26, 379–409.Google Scholar
Saric, W. S. 2007 Boundary-layer stability and transition. In Springer Handbook of Experimental Fluid Mechanics (ed. Tropea, C., Yarin, A. L. & Foss, J. F.), pp. 886–896. Springer.Google Scholar
Saric, W. S., Carpenter, A. L. & Reed, H. L. 2011 Passive control of transition in three-dimensional boundary layers, with emphasis on discrete roughness elements. Phil. Trans. R. Soc. Lond. A 369 (1940), 1352–1364.Google Scholar
Saric, W. S., Carrillo, R. B. & Reibert, M. S. 1998 Nonlinear stability and transition in 3-D boundary layers. Meccanica 33 (5), 469–487.Google Scholar
Saric, W. S., Reed, H. L. & Kerschen, E. J. 2002 Boundary-layer receptivity to freestream disturbances. Annu. Rev. Fluid Mech. 34, 291–319.Google Scholar
Schlatter, P., Deusebio, E., de Lange, R. & Brandt, L. 2010 Numerical study of the stabilisation of boundary-layer disturbances by finite amplitude streaks. Intl J. Flow Control 2 (4), 259–288.Google Scholar
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.Google Scholar
Schuele, C. Y., Corke, T. C. & Matlis, E. 2013 Control of stationary cross-flow modes in a Mach 3.5 boundary layer using patterned passive and active roughness. J. Fluid Mech. 718, 5–38.Google Scholar
Shahinfar, S., Fransson, J. H. M., Sattarzadeh, S. S. & Talamelli, A. 2013 Scaling of streamwise boundary layer streaks and their ability to reduce skin-friction drag. J. Fluid Mech. 733, 1–32.Google Scholar
Shahinfar, S., Sattarzadeh, S. S. & Fransson, J. H. M. 2014 Passive boundary layer control of oblique disturbances by finite-amplitude streaks. J. Fluid Mech. 749, 1–36.Google Scholar
Shahinfar, S., Sattarzadeh, S. S., Fransson, J. H. M. & Talamelli, A. 2012 Revival of classical vortex generators now for transition delay. Phys. Rev. Lett. 109 (7), 074501.Google Scholar
Strand, J. S. & Goldstein, D. B. 2011 Direct numerical simulations of riblets to constrain the growth of turbulent spots. J. Fluid Mech. 668, 267–292.Google Scholar
Ustinov, M. V. 1995 Secondary instability modes generated by a Tollmien–Schlichting wave scattering from a bump. Theor. Comput. Fluid Dyn. 7 (5), 341–354.Google Scholar
White, E. B. 2002 Transient growth of stationary disturbances in a flat plate boundary layer. Phys. Fluids 14 (12), 4429–4439.Google Scholar
White, E. B. & Ergin, F. G. 2004 Using laminar-flow velocity profiles to locate the wall behind roughness elements. Exp. Fluids 36 (5), 805–812.Google Scholar
Wu, X. 2001 Receptivity of boundary layers with distributed roughness to vortical and acoustic disturbances: a second-order asymptotic theory and comparison with experiments. J. Fluid Mech. 431, 91–133.Google Scholar
Zverkov, I., Zanin, B. & Kozlov, V. 2008 Disturbances growth in boundary layers on classical and wavy surface wings. AIAA J. 46 (12), 3149–3158.Google Scholar