Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-01T04:03:47.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence

Published online by Cambridge University Press:  08 March 2010

LARS-UVE SCHRADER ,
SUBIR AMIN  and
LUCA BRANDT
LARS-UVE SCHRADER
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
SUBIR AMIN
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
LUCA BRANDT*
Affiliation:
Linné Flow Centre, KTH Mechanics, SE-100 44 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Receptivity, disturbance growth and transition to turbulence of the three-dimensional boundary layer developing on a swept flat plate are studied by means of numerical simulations. The flow is subject to a favourable pressure gradient and represents a model for swept-wing flow downstream of the leading edge and upstream of the pressure minimum of the wing. The boundary layer is perturbed by free-stream turbulence and localized surface roughness with random distribution in the spanwise direction. The intensity of the turbulent free-stream fluctuations ranges from conditions typical for free flight to higher levels usually encountered in turbo-machinery applications. The free-stream turbulence initially excites non-modal streak-like disturbances as in two-dimensional boundary layers, soon evolving into modal instabilities in the form of unsteady crossflow modes. The crossflow modes grow faster than the streaks and dominate the downstream disturbance environment in the layer. The results show that the receptivity mechanism is linear for the disturbance amplitudes under consideration, while the subsequent growth of the primary disturbances rapidly becomes affected by nonlinear saturation in particular for free-stream fluctuations with high intensity. Transition to turbulence occurs in the form of localized turbulent spots randomly appearing in the flow. The main features of the breakdown are presented for the case of travelling crossflow vortices induced by free-stream turbulence. The flow is also receptive to localized roughness strips, exciting stationary crossflow modes. The mode with most efficient receptivity dominates the downstream disturbance environment. When both free-stream fluctuations and wall roughness act on the boundary layer at the same time, transition is dominated by steady crossflow waves unless the incoming turbulence intensity is larger than about 0.5% for roughness amplitudes of about one tenth of the boundary-layer displacement thickness. The results show that a correct prediction of the disturbance behaviour can be obtained considering the receptivity and evolution of individual modes. In addition, we provide an estimate for the amplitudes of the external disturbance sources above which a fully nonlinear receptivity analysis is necessary.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 646 , 10 March 2010 , pp. 297 - 325
Copyright
Copyright © Cambridge University Press 2010

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

REFERENCES

Bippes, H. 1999 Basic experiments on transition in three-dimensional boundary layers dominated by crossflow instability. Prog. Aerosp. Sci. 35, 363–412.CrossRefGoogle Scholar
Bonfigli, G. 2006 Numerical simulation of transition and early turbulence in a 3-d boundary layer perturbed by superposed stationary and travelling crossflow vortices. PhD thesis, Universität Stuttgart.Google Scholar
Bonfigli, G. & Kloker, M. 2007 Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation. J. Fluid Mech. 583, 229–272.CrossRefGoogle Scholar
Brandt, L. & de Lange, H. C. 2008 Streak interactions and breakdown in boundary layer flows. Phys. Fluids 20 (024107), 1–16.CrossRefGoogle Scholar
Brandt, L., Schlatter, P. & Henningson, D. S. 2004 Transition in boundary layers subject to free-stream turbulence. J. Fluid Mech. 517, 167–198.CrossRefGoogle Scholar
Chevalier, M., Schlatter, P., Lundbladh, A. & Henningson, D. S. 2007 A pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. Royal Institute of Technology (KTH), Dept. of Mechanics, Stockholm.Google Scholar
Choudhari, M. 1994 Roughness-induced generation of crossflow vortices in three-dimensional boundary layers. Theoret. Comput. Fluid Dyn. 6, 1–30.CrossRefGoogle Scholar
Collis, S. S. & Lele, S. K. 1999 Receptivity to surface roughness near a swept leading edge. J. Fluid Mech. 380, 141–168.CrossRefGoogle Scholar
Crouch, J. D. 1992 Localized receptivity of boundary layers. Phys. Fluids A 4 (7), 1408–1414.CrossRefGoogle Scholar
Crouch, J. D. 1993 Receptivity of three-dimensional boundary layers. AIAA Paper 93-0074.CrossRefGoogle Scholar
Deyhle, H. & Bippes, H. 1996 Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions. J. Fluid Mech. 316, 73–113.CrossRefGoogle Scholar
Fransson, J. H. M., Matsubara, M. & Alfredsson, P. H. 2005 Transition induced by free-stream turbulence. J. Fluid Mech. 527, 1–25.CrossRefGoogle Scholar
Haynes, T. S. & Reed, H. L. 2000 Simulation of swept-wing vortices using nonlinear parabolized stability equations. J. Fluid Mech. 405, 325–349.CrossRefGoogle Scholar
Herbert, T. 1988 Secondary instability of boundary layers. Annu. Rev. Fluid Mech. 20, 487–526.CrossRefGoogle Scholar
Hœpffner, J. & Brandt, L. 2008 Stochastic approach to the receptivity problem applied to bypass transition in boundary layers. Phys. Fluids 20 (024108), 1–4.CrossRefGoogle Scholar
Högberg, M. & Henningson, D. S. 1998 Secondary instability of crossflow vortices in Falkner–Skan–Cooke boundary layers. J. Fluid Mech. 368, 339–357.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and continuous spectrum of the Orr–Sommerfeld equation. Phys. Fluids 10 (8), 2006–2011.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185–212.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Kachanov, Y. S. 1994 Physical mechanisms of laminar boundary-layer transition. Annu. Rev. Fluid Mech. 26, 411–482.CrossRefGoogle Scholar
Klebanoff, P. S. 1971 Effect of free-stream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc. 10, 1323.Google Scholar
Malik, M. R., Li, F., Choudhari, M. M. & Chang, C.-L. 1999 Secondary instability of crossflow vortices and swept-wing boundary-layer transition. J. Fluid Mech. 399, 85–115.CrossRefGoogle Scholar
Malik, M. R., Zang, T. A. & Hussaini, M. Y. 1985 A spectral collocation method for the Navier–Stokes equations. J. Comp. Phys. 61, 64–88.CrossRefGoogle Scholar
Matsubara, M. & Alfredsson, P. H. 2001 Disturbance growth in boundary layers subjected to free-stream turbulence. J. Fluid Mech. 430, 149–168.CrossRefGoogle Scholar
Monokrousos, A., Brandt, L., Schlatter, P. & Henningson, D. S. 2008 DNS and LES of estimation and control of transition in boundary layers subject to free-stream turbulence. Intl J. Heat Fluid Flow 29, 841–855.CrossRefGoogle Scholar
Nordström, J., Nordin, N. & Henningson, D. S. 1999 The fringe region technique and the Fourier method used in the direct numerical simulation of spatially evolving viscous flows. SIAM J. Sci. Comp. 20, 1365–1393.CrossRefGoogle Scholar
Poll, D. I. A. 1984 Transition description and prediction in three-dimensional flows. Tech. Rep. AGARD Rep. 709. Von Kármán Inst., Rhode-St-Genese, Belgium.Google Scholar
Pope, S. B. 2001 Turbulent Flows. Cambridge University Press.Google Scholar
Reibert, M. S., Saric, W. S., Carillo, R. B. & Chapman, K. L. 1996 Experiments in nonlinear saturation of stationary crossflow vortices in a swept-wing boundary layer. AIAA Paper 96-0184.CrossRefGoogle Scholar
Saric, W. S. Jr., Carillo, R. B. & Reibert, M. S. 1998 Leading-edge roughness as a transition control mechanism. AIAA Paper 98-0781.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413–440.CrossRefGoogle Scholar
Schlatter, P. & Brandt, L. 2010 DNS of spatially-developing three-dimensional turbulent boundary layers. In Direct and Large Eddy Simulation VII (ed. Armenio, V., Guerts, B. J. & Fröhlich, J.) (in press).CrossRefGoogle Scholar
Schlatter, P., de Lange, H. C. & Brandt, L. 2007 Numerical study of the stabilization of Tollmien–Schlichting waves by finite amplitude streaks. In Turbulence and Shear Flow Phenomena 5 (ed. Friedrich, R., Adams, N. A., Eaton, J. K., Humphrey, J. A. C., Kasagi, N. & Leschziner, M. A.), vol. II, pp. 849–854.Google Scholar
Schlatter, P., Stolz, S. & Kleiser, L. 2004 LES of transitional flows using the approximate deconvolution model. Intl J. Heat Fluid Flow 25 (3), 549–558.CrossRefGoogle Scholar
Schlatter, P., Stolz, S. & Kleiser, L. 2006 LES of spatial transition in plane channel flow. J. Turbul. 7 (33), 1–24.CrossRefGoogle Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Schrader, L.-U., Brandt, L. & Henningson, D. S. 2009 Receptivity mechanisms in three-dimensional boundary-layer flows. J. Fluid Mech. 618, 209–241.CrossRefGoogle Scholar
Stolz, S., Adams, N. A. & Kleiser, L. 2001 An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. Fluids 13 (4), 997–1015.CrossRefGoogle Scholar
Taylor, G. I. 1939 Some recent developments in the study of turbulence. In Proceedings of the Fifth International Congress for Applied Mechanics (ed. Den Hartog, J. P. & Peters, H.), pp. 294–310. Wiley.Google Scholar
Tempelmann, D., Hanifi, A. & Henningson, D. S. 2010 Spatial optimal growth in three-dimensional boundary layers. J. Fluid Mech. 646, pp. 5–37.CrossRefGoogle Scholar
Tufo, H. M. & Fischer, P. F. 1999 Terascale spectral element algorithms and implementations. In Supercomputing, ACM/IEEE 1999 Conference. Portland, USA.Google Scholar
Wassermann, P. & Kloker, M. 2002 Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer. J. Fluid Mech. 456, 49–84.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
Westin, K. J. A., Boiko, A. V., Klingmann, B. G. B., Kozlov, V. V. & Alfredsson, P. H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 1. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193–218.CrossRefGoogle Scholar
White, E. B. & Saric, W. S. 2005 Secondary instability of crossflow vortices. J. Fluid Mech. 525, 275–308.CrossRefGoogle Scholar
White, E. B., Saric, W. S., Gladden, R. D. & Gabet, P. M. 2001 Stages of swept-wing transition. AIAA Paper 2001-0271.CrossRefGoogle Scholar
Wintergerste, T. & Kleiser, L. 1997 Breakdown of a crossflow vortex in a three-dimensional boundary layer. In Direct and Large Eddy Simulation II (ed. Chollet, J.-P.), pp. 179–190. Kluwer.CrossRefGoogle Scholar
Zaki, T. A. & Durbin, P. A. 2005 Mode interaction and the bypass route to transition. J. Fluid Mech. 531, 85–111.CrossRefGoogle Scholar
Zaki, T. A. & Saha, S. 2009 On shear sheltering and the structure of vortical modes in single- and two-fluid boundary layers. J. Fluid Mech. 626, 111–147.CrossRefGoogle Scholar