Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T04:24:54.294Z Has data issue: false hasContentIssue false
  • English
  • Français

Leading-edge effects in bypass transition

Published online by Cambridge University Press:  23 January 2007

S. NAGARAJAN ,
S. K. LELE  and
J. H. FERZIGER
S. NAGARAJAN
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
S. K. LELE
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
J. H. FERZIGER*
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
*
Professor Joel H. Ferziger passed away on August 16, 2004 while this paper was being written.
Get access Rights & Permissions [Opens in a new window]

Abstract

The effect of a blunt leading edge on bypass transition is studied by numerical simulation. A mixed direct and large-eddy simulation of a flat plate with a super-ellipse leading edge is carried out at various conditions. Onset and completion of transition is seen to move upstream with increasing bluntness. For sharper leading edges, at lower levels of turbulence, transition usually occurs through instabilities on low-speed streaks as observed by Jacobs & Durbin (2001) and Brandt et al. (2004) whereas increasing either the turbulence intensity or the leading-edge bluntness brings into play another mechanism. Free-stream vortices are amplified at the leading edge because of stretching. In the case of particularly strong vortices, this interaction induces a localized streamwise vortical disturbance in the boundary layer which then grows as it convects downstream and eventually breaks down to form a turbulent spot. These disturbances, which are localized and hence wavepacket-like, move at speeds in the range 0.55 U∞–0.65 U∞ and occur in the lower portion of the boundary layer. Simulations conducted with isolated vortices confirm such a response of the boundary layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 471 - 504
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

Abu-Ghannam, B. J. & Shaw, R. 1980 Natural transition of boundary layers – the effects of turbulence, pressure gradient, and flow history. J. Mech. Engng Sci. 22 (5), 213–228.CrossRefGoogle Scholar
Amini, J. & Lespinard, G. 1982 Experimental study of an ‘incipient spot’ in a transitional boundary layer. Phys. Fluids 25, 1743–1750.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
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.CrossRefGoogle Scholar
Aris, R. 1989 Vectors, Tensors, and the Basic Equations of Fluid Mechanics. Dover.Google 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
Benney, D. J. & Gustavsson, L. H. 1981 A new mechanism for linear and nonlinear hydrodynamic instability. Stud. Appl. Math. 64, 185–209.CrossRefGoogle Scholar
Brandt, L., Cossu, C., Chomaz, J.-M., Huerre, P. & Henningson, D. S. 2003 On the convectively unstable nature of optimal streaks in boundary layers. J. Fluid Mech. 485, 221–242.CrossRefGoogle Scholar
Brandt, L. & Henningson, D. S. 2002 Transition of streamwise streaks in zero-pressure-gradient boundary layers. J. Fluid Mech. 472, 229–261.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
Breuer, K. S. & Haritonidis, J. H. 1990 The evolution of a localized disturbance in a laminar boundary layer. Part 2. 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
Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous flow. Phys. Fluids 4, 1637–1650.CrossRefGoogle Scholar
Cohen, J., Breuer, K. S. & Haritonidis, J. H. 1991 On the evolution of a wavepacket in a laminar boundary layer. J. Fluid Mech. 225, 575–606.CrossRefGoogle Scholar
Collis, S. S. 1997 A computational investigation of receptivity in high-speed flow near a swept leading-edge. PhD thesis, Stanford University.Google Scholar
Crow, S. C. 1966 The spanwise perturbation of two-dimensional boundary layers. J. Fluid Mech. 24, 153–164.CrossRefGoogle Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Dryden, H. L. 1936 Airflow in the boundary layer near a plate. NACA Rep. 562. National Advisory Committee for Aeronautics.Google Scholar
Gaster, M. 1968 The development of three-dimensional wavepackets in a boundary layer. J. Fluid Mech. 32, 173–184.CrossRefGoogle Scholar
Gaster, M. & Grant, I. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. 347, 253–269.Google Scholar
Giles, M. B. 1990 Nonreflecting boundary conditions for Euler equation calculations. AIAA J. 28, 2050–2058.CrossRefGoogle Scholar
Goldstein, M. E. & Wundrow, D. W. 1998 On the environmental realizability of algebraically growing disturbances and their relation to Klebanoff modes. Theor. Comput. Fluid Dyn. 10, 171–186.CrossRefGoogle Scholar
Govindarajan, R. & Narasimha, R. 1995 Stability of spatially developing boundary layers in pressure gradients. J. Fluid Mech. 300, 117–147.CrossRefGoogle Scholar
Grosch, C. E. & Salwen, H. 1981 The continuous spectrum of the Orr-Sommerfeld equation. Part 2. Eigenfunction expansions. J. Fluid Mech. 104, 445–465.Google 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, 169–207.CrossRefGoogle Scholar
Hultgren, L. S. & Gustavsson, L. H. 1981 Algebraic growth of disturbances in a laminar boundary layer. Phys. Fluids 104, 1000–1004.CrossRefGoogle Scholar
Hunt, J. C. R. & Durbin, P. A. 1999 Perturbed vortical layers and shear sheltering. Fluid Dyn. Res. 24, 375–404.CrossRefGoogle Scholar
Jacobs, R. G. & Durbin, P. A. 1998 Shear sheltering and the continuous spectrum of the Orr-Sommerfeld equation. Phys. Fluids 10, 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
Johnson, M. W. & Ercan, A. H. 1999 A physical model for bypass transition. Intl J. Heat Fluid Flow 20, 95–104.CrossRefGoogle Scholar
Jonas, P., Mazur, O. & Uruba, V. 2000 On the receptivity of the by-pass transition to the length scale of the outer stream turbulence. Eur. J. Mech. B Fluids 19, 707–722.CrossRefGoogle Scholar
Jordinson, R. 1970 The flat plate boundary layer. Part 1. Numerical integration of the Orr-Sommerfeld equation. J. Fluid Mech. 43, 801–811.CrossRefGoogle Scholar
Kendall, J. M. 1985 Experimental study of disturbances produced in a pre-transitional boundary layer by weak free-stream turbulence. AIAA Paper 85-1695.CrossRefGoogle Scholar
Kendall, J. M. 1991 Studies on laminar boundary-layer receptivity to freestream turbulence near a leading edge. In Boundary Layer Stability and Transition to Turbulence (ed. Reda, D. C., Reed, H. L. & Kobayashi, R.), pp. 23–30. ASME.Google Scholar
Kendall, J. M. 1998 Experiments on boundary-layer receptivity to freestream turbulence. AIAA Paper 98-0530.CrossRefGoogle Scholar
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1–24.CrossRefGoogle Scholar
Klingmann, B. G. B., Boiko, A. V., Westin, K. J. A., Kozlov, V. V. & Alfredsson, P. H. 1993 Experiments on the stability of Tollmien-Schlichting waves. Eur. J. Mech. B Fluids 12, 493–514.Google Scholar
Leib, S. J., Wundrow, D. W. & Goldstein, M. E. 1999 Effect of free-stream turbulence and other vortical disturbances on a laminar boundary layer. J. Fluid Mech. 380, 169–203.CrossRefGoogle Scholar
Luchini, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289–309.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
Mohamed, M. S. & LaRue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.CrossRefGoogle Scholar
Morkovin, M. V. 1969 The many faces of transition. In Viscous Drag Reduction (ed. Wells, C. S.). Plenum Press.Google Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order method for large eddy simulation. J. Comput. Phys. 191, 392–419.CrossRefGoogle Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2004 A high-order method for mixed direct and large-eddy simulation of turbulent and transitional flows. In preparation.Google Scholar
Reddy, S. C. & Henningson, D. S. 1993 Energy growth in viscous channel flows. J. Fluid Mech. 252, 209–238.CrossRefGoogle Scholar
Roach, P. E. & Brierley, D. H. 1992 The influence of a turbulent free-stream on zero pressure gradient transitional boundary layer development Part 1: Test cases T3A and T3B. In Numerical Simulation of Unsteady Flows and Transition to Turbulence (ed. Pironneau, O., Rodi, W. & Ryhming, I. L.), pp. 319–347. Cambridge University Press.Google Scholar
Schmid, P. J. & Henningson, D. J. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
Taylor, G. I. 1918 On the dissipation of eddies. R&M 598. British Aeronautical Research Committee.Google Scholar
Taylor, G. I. 1939 Some recent developments in the study of turbulence. In Proc. Fifth Intl Congress for Applied Mathematics (ed. Hartog, J. P. D. & Peters, H.), pp. 294–310. Wiley.Google Scholar
Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578.CrossRefGoogle ScholarPubMed
Vasudeva, B. R. 1967 Boundary-layer instability experiment with localized disturbance. J. Fluid Mech. 29, 745–763.CrossRefGoogle Scholar
Watmuff, J. 1997 Detrimental effects of almost immeasurably small free-stream nonuniformities generated by wind tunnel screens. AIAA Paper 97-0228.CrossRefGoogle Scholar
Wazzan, A. R. 1975 Spatial stability of tollmien-schlichting waves. Prog. Aerospace Sci. 16, 99–127.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, F. M. 1991 Viscous Fluid Flow. McGraw-Hill.Google Scholar
Wundrow, D. W. & Goldstein, M. E. 2001 Effect on a laminar boundary layer of small-amplitude streamwise vorticity in the upstream flow. J. Fluid Mech. 426, 229–262.CrossRefGoogle Scholar
Xiong, Z. 2004 Stagnation point flow and heat transfer under free-stream turbulence. PhD thesis, Stanford University.CrossRefGoogle Scholar
Xiong, Z., Nagarajan, S. & Lele, S. K. 2004 A simple method for generating inflow turbulence. AIAA J. 42, 2164–2166.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