Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2025-01-05T14:56:56.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent spots in the asymptotic suction boundary layer

Published online by Cambridge University Press:  25 July 2007

ORI LEVIN  and
DAN S. HENNINGSON
ORI LEVIN
Affiliation:
Department of Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
DAN S. HENNINGSON
Affiliation:
Department of Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

Amplitude thresholds for transition of localized disturbances, their breakdown to turbulence and the development of turbulent spots in the asymptotic suction boundary layer are studied using direct numerical simulations. A parametric study of the horizontal scales of the initial disturbance is performed and the disturbances that lead to the highest growth under the conditions investigated are used in the simulations. The Reynolds-number dependence of the threshold amplitude of a localized disturbance is investigated for 500≤ Re ≤ 1200, based on the free-stream velocity and the displacement thickness. It is found that the threshold amplitude scales as Re−1.5 for the considered Reynolds numbers. For Re ≤ 367, the localized disturbance does not lead to a turbulent spot and this provides an estimate of the critical Reynolds number for the onset of turbulence. When the localized disturbance breaks down to a turbulent spot, it happens through the development of hairpin and spiral vortices. The shape and spreading rate of the turbulent spot are determined for Re = 500, 800 and 1200. Flow visualizations reveal that the turbulent spot takes a bullet-shaped form that becomes more distinct for higher Reynolds numbers. Long streaks extend in front of the spot and in its wake a calm region exists. The spreading rate of the turbulent spot is found to increase with increasing Reynolds number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 584 , 10 August 2007 , pp. 397 - 413
Copyright
Copyright © Cambridge University Press 2007

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

Alavyoon, F., Henningson, D. S. & Alfredsson, P. H. 1986 Turbulent spots in plane Poiseuille flow–flow visualization. Phys. Fluids 29, 1328–1331.CrossRefGoogle Scholar
Andersson, P., Berggren, M. & Henningson, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134–150.CrossRefGoogle Scholar
Baggett, J. S. & Trefethen, L. N. 1997 Low-dimensional models of subcritical transition to turbulence. Phys. Fluids 9, 1043–1053.CrossRefGoogle Scholar
Balakumar, P. & Hall, P. 1999 Optimum suction distribution for transition control. Theoret. Comput. Fluid Dyn. 13, 1–19.CrossRefGoogle Scholar
Bech, K. H., Henningson, D. S. & Henkes, R. A. W. M. 1998 Linear and nonlinear development of localized disturbances in zero and adverse pressure gradient boundary-layers. Phys. Fluids 10, 1405–1418.CrossRefGoogle Scholar
Breuer, K. S. & Haritonidis, J. H. 1990 The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances. J. Fluid Mech. 220, 569–594.CrossRefGoogle Scholar
Breuer, K. S. & Landahl, M. T. 1990 The evolution of a localized disturbance in a laminar boundary layer. Part 2. Strong disturbances. J. Fluid Mech. 220, 595–621.CrossRefGoogle Scholar
Byström, M. G., Levin, O. & Henningson, D. S. 2007 Optimal disturbances in suction boundary layers. Eur. J. Mech. B/Fluids 26, 330–343.CrossRefGoogle Scholar
Cantwell, B., Coles, D. & Dimotakis, P. 1978 Structure and entrainment in the plane of symmetry of a turbulent spot. J. Fluid Mech. 87, 641–672.CrossRefGoogle Scholar
Carlson, D. R., Widnall, S. E. & Peeters, M. F. 1982 A flow-visualization of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487–505.CrossRefGoogle Scholar
Chapman, S. J. 2002 Subcritical transition in channel flows. J. Fluid Mech. 451, 35–97.CrossRefGoogle Scholar
Dauchot, O. & Daviaud, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335–343.CrossRefGoogle Scholar
Elder, J. W. 1960 An experimental investigation of turbulent spots and breakdown to turbulence. J. Fluid Mech. 9, 235–246.CrossRefGoogle Scholar
Emmons, H. W. 1951 The laminar–turbulent transition in a boundary layer. Part I. J. Aero. Sci. 18, 490–498.CrossRefGoogle Scholar
Fransson, J. H. M. & Alfredsson, P. H. 2003 On the disturbance growth in an asymptotic suction boundary layer. J. Fluid Mech. 482, 51–90.CrossRefGoogle Scholar
Fransson, J. H. M. & Corbett, P. 2003 Optimal linear growth in the asymptotic suction boundary layer. Eur. J. Mech. B/Fluids 22, 259–270.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
Griffith, A. A. & Meredith, F. W. 1936 The possible improvement in aircraft performance due to boundary layer suction. Tech. Rep. 2315. Rep. Aero. Res. Coun.Google Scholar
Henningson, D. S. & Alfredsson, P. H. 1987 The wave structure of turbulent spots in plane Poiseuille flow. J. Fluid Mech. 178, 405–421.CrossRefGoogle Scholar
Henningson, D. S. & Kim, J. 1991 On turbulent spots in plane Poiseuille flow. J. Fluid Mech. 228, 183–205.Google Scholar
Henningson, D. S., Spalart, P. & Kim, J. 1987 Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow. Phys. Fluids 30, 2914–2917.CrossRefGoogle Scholar
Henningson, D. S., Lundbladh, A. & Johansson, A. V. 1993 A mechanism for bypass transition from localized disturbances in wall-bounded shear flows. J. Fluid Mech. 250, 169–238.CrossRefGoogle Scholar
Hocking, L. M. 1975 Non-linear instability of the asymptotic suction velocity profile. Q. J. Mech. Appl. Maths 28, 341–353.CrossRefGoogle Scholar
Hof, B., Juel, A. & Mullin, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502.CrossRefGoogle Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.CrossRefGoogle Scholar
Joslin, R. D. 1998 Aircraft laminar flow control. Annu. Rev. Fluid Mech. 30, 1–29.CrossRefGoogle Scholar
Katz, Y., Seifert, A. & Wygnanski, I. 1990 On the evolution of the turbulent spot in a laminar boundary layer with a favourable pressure gradient. J. Fluid Mech. 221, 1–22.CrossRefGoogle Scholar
Kreiss, G., Lundbladh, A. & Henningson, D. S. 1994 Bounds for threshold amplitudes in subcritical shear flows. J. Fluid Mech. 270, 175–198.CrossRefGoogle Scholar
Levin, O., Davidsson, E. N. & Henningson, D. S. 2005 Transition thresholds in the asymptotic suction boundary layer. Phys. Fluids 17, 114104.CrossRefGoogle Scholar
Lundbladh, A. & Johansson, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499–516.CrossRefGoogle Scholar
Lundbladh, A., Berlin, S., Skote, M., Hildings, C., Choi, J., Kim, J. & Henningson, D. S. 1999 An efficient spectral method for simulation of incompressible flow over a flat plate. Tech. Rep. KTH, Department of Mechanics, Stockholm.Google Scholar
Lundbladh, A., Henningson, D. S. & Reddy, S. C. 1994 Threshold amplitudes for transition in channel flows. In Transition, Turbulence, and Combustion (ed. Hussaini, M. Y., Gatski, T. B. & Jackson, T. L.), vol. 1, pp. 309–318. Kluwer.CrossRefGoogle Scholar
Mariani, P., Spalart, P. & Kollmann, W. 1993 Direct simulation of a turbulent boundary layer with suction. In Near-Wall Turbulent Flows (ed. So, R. M. C., Speziale, C. G. & Launder, B. E.), pp. 347–356. Elsevier.Google Scholar
Mathew, J. & Das, A. 2000 Direct numerical simulations of spots. Current Sci. 79, 816–820.Google 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. Comput. 20, 1365–1393.CrossRefGoogle Scholar
Perry, A. E., Lim, T. T. & Teh, E. W. 1981 A visual study of turbulent spots. J. Fluid Mech. 104, 387–405.CrossRefGoogle Scholar
Pralits, J. O., Hanifi, A. & Henningson, D. S. 2002 Adjoint-based optimization of steady suction for disturbance control in incompressible flows. J. Fluid Mech. 467, 129–161.CrossRefGoogle Scholar
Reddy, S. C., Schmid, P. J., Baggett, J. S. & Henningson, D. S. 1998 On stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365, 269–303.CrossRefGoogle Scholar
Riley, J. J. & Gad-el-Hak, M. 1985 The dynamics of turbulent spots. In Frontiers in Fluid Mechanics (ed. Davis, S. H. & Lumley, J. L.), pp. 123–155. Springer.CrossRefGoogle Scholar
Sankaran, R., Sokolov, M. & Antonia, R. A. 1988 Substructures in a turbulent spot. J. Fluid Mech. 197, 389–414.CrossRefGoogle Scholar
Schrauf, G. 2004 Large-scale laminar-flow tests evaluated with linear stability theory. J. Aircraft 41, 224–230.CrossRefGoogle Scholar
Schröder, A. & Kompenhans, J. 2004 Investigation of a turbulent spot using multi-plane stereo particle image velocimetry. Exps. Fluids 36, 82–90.CrossRefGoogle Scholar
Schumacher, J. & Eckhardt, B. 2001 Evolution of turbulent spots in a parallel shear flow. Phys. Rev. E 63, 046307Google Scholar
Seifert, A. & Wygnanski, I. J. 1995 On turbulent spots in a laminar boundary layer subjected to a self-similar adverse pressure gradient. J. Fluid Mech. 296, 185–209.CrossRefGoogle Scholar
Singer, B. A. 1996 Characteristics of a young turbulent spot. Phys. Fluids 8, 509–521.CrossRefGoogle Scholar
Singer, B. A. & Joslin, R. D. 1994 Metamorphosis of a hairpin vortex into a young turbulent spot. Phys. Fluids 6, 3724–3736.CrossRefGoogle Scholar
Tillmark, N. & Alfredsson, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89–102.CrossRefGoogle Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.CrossRefGoogle ScholarPubMed
Wygnanski, I., Sokolov, M. & Friedman, D. 1976 On a turbulent ‘spot’ in a laminar boundary layer. J. Fluid Mech. 78, 785–819.CrossRefGoogle Scholar
Wygnanski, I., Haritonidis, J. H. & Kaplan, R. E. 1979 On a Tollmien–Schlichting wave packet produced by a turbulent spot. J. Fluid Mech. 92, 505–528.CrossRefGoogle Scholar
Yoshioka, S., Fransson, J. H. M. & Alfredsson, P. H. 2004 Free stream turbulence induced disturbances in boundary layers with wall suction. Phys. Fluids 16, 3530–3539.CrossRefGoogle Scholar
Zuccher, S., Luchini, P. & Bottaro, A. 2004 Algebraic growth in a Blasius boundary layer: optimal and robust control by mean suction in the nonlinear regime. J. Fluid Mech. 513, 135–160.CrossRefGoogle Scholar