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Boundary-layer transition at high free-stream disturbance levels – beyond Klebanoff modes

Published online by Cambridge University Press:  01 October 2008

M. E. GOLDSTEIN  and
ADRIAN SESCU
M. E. GOLDSTEIN
Affiliation:
National Aeronautics and Space Administration, Glenn Research Center, Cleveland, OH 44135, USA
ADRIAN SESCU
Affiliation:
University of Toledo, Department of Mechanical Industrial & Manufacturing Engineering, Toledo, OH 43606, USA
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Abstract

We consider a nominally uniform flow over a semi-infinite flat plate and show how a small slowly modulated (predominantly streamwise) disturbance of the upstream flow is amplified by leading-edge bluntness effects and eventually develops into a small-amplitude but nonlinear spanwise motion far downstream from the edge. This motion is then imposed on the viscous boundary layer at the surface of the plate – causing an order-one change in its profile shape, which can reduce the wall shear to zero and thereby causes the boundary layer to separate. The present study is similar to an earlier steady flow analysis, but the unsteady effects now cause the upstream boundary layer to develop inflectional profiles which can support rapidly growing inviscid instabilities that give rise to transition before the separation can occur.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 613 , 25 October 2008 , pp. 95 - 124
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Agarwal, A. & Morris, P. J. 2006 Numerical computation of the linear convective and absolute stability of free-shear flow. Computers Fluids 35, 1282–1289.CrossRefGoogle Scholar
Carrier, G. F., Krook, M. & Pearson, C. E. 1966 Functions of a Complex Variable. McGraw–Hill.Google Scholar
Cebeci, T., Khattab, A. K. & Stewartson, K. 1981 Three-dimensional laminar boundary layers and the ok of accessibility. J. Fluid Mech. 107, 57–87.CrossRefGoogle Scholar
Cebeci, T. & Smith, A. M. O. 1974 Analysis of Turbulent Boundary Layers. Academic.Google Scholar
Cowley, S. J. 1985 High Frequency Rayleigh Instability of Stoked Layers, Stability of Time Dependent and Spatially Varying Flows (ed. Dwoyer, D. L. & Hussaini, M. I.). Springer.Google Scholar
Crow, S. C. 1966 The spanwise perturbation of two-dimensional boundary layers. J. Fluid Mech. 24, 153–164.CrossRefGoogle Scholar
Darwin, C. 1954 A note on hydrodynamics. Proc. Camb. Phil. Soc. 49, 342–354.CrossRefGoogle Scholar
Gaitonde, A. L. 1998 A Dual-time method for two-dimensional unsteady incompressible flow calculation. Intl J. Number Meth. Engng 41, 1153–1166.3.0.CO;2-9>CrossRefGoogle Scholar
Garabedian, P. R. 1964 Partial Differential Equations. John Wiley.Google Scholar
Goldstein, M. E. 1978 Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles. J. Fluid Mech. 89, 433–468.CrossRefGoogle Scholar
Goldstein, M. E. 1979 Turbulence generated by the interaction of entropy fluctuations with non-uniform mean flows. J. Fluid Mech. 93, 209–224.CrossRefGoogle Scholar
Goldstein, M. E. 1997 Response of the pre-transitional laminar boundary layer to free stream turbulence. Otto Laporte Lecture, Bull. Am. Phys. Soc. 42, 2150.Google Scholar
Goldstein, M. E. & Lieb, S. J. 1993 Three-dimensional boundary-layer instability and separation induced by small-amplitude streamwise vorticity in the upstream flow. J. Fluid Mech. 246, 21–41.CrossRefGoogle Scholar
Goldstein, M. E., Lieb, S. J. & Cowley, S. J. 1992 Distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate. J. Fluid Mech. 237, 231–260.CrossRefGoogle Scholar
Hunt, J. C. R. & Carruthers, D. H. 1990 Rapid distortion theory and the ‘problems’ of turbulence. J. Fluid Mech. 212, 497–532.CrossRefGoogle Scholar
Jameson, A. 1991 Time-dependent calculation using multigrid with application to unsteady flow past airfoils and wings. AIAA Paper 91-1596.CrossRefGoogle Scholar
Jameson, A., Schmidt, W., Turkel, E. 1981 Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes. AIAA Paper 81-1259.CrossRefGoogle Scholar
Keller, H. B. & Cebeci, T. 1972 Accurate numerical methods for boundary layer flows. AIAA J. 10, 1193–1199.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. & Kabayashi, R). PP. 23–30. ASME.Google Scholar
Kennedy, C. A. & Carpenter, M. H. 1994 Several new numerical methods for compressible shear layer simulations. Appl. Num. Maths 14, 397–433.CrossRefGoogle Scholar
Kingmann, 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, 493–514Google Scholar
Kupfer, K., Bers, A. & Ram, A. K. 1987 The cusp map in the complex-frequency plane for absolute instabilities. Phys. Fluids 30, 3075–3082.CrossRefGoogle Scholar
Lighthill, M. J. 1956 Drift. J. Fluid Mech. 1, 31–33.CrossRefGoogle Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2007 Leading-edge effects in bypass transition. J. Fluid Mech. 572, 471–504.CrossRefGoogle Scholar
Nayfeh, A. H. 1973 Perturbation Methods. John Wiley.Google Scholar
Suslov, S. A. 2006 Numerical aspects of searching convective/absolute instability transition. J. Comput. Phys. 212, 188–217.CrossRefGoogle Scholar
Toomre, A. 1960 The viscous secondary flow ahead of an infinite cylinder in a uniform parallel shear flow. J. Fluid Mech. 7, 145–155.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
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
Wu, X. 1992 The Nonlinear evolution of high-frequency resonant-triad waves in an oscillatory Stokes layer at high Reynolds number, J. Fluid Mech. 245, 553–597.CrossRefGoogle Scholar
Wu, X. & Choudhari, M. 2003 Linear and nonlinear instabilities of a Blasius boundary layer perturbed streamwise vortices. Part 2. Intermittent instability induced by long wavelength Klebanoff modes. J. Fluid Mech. 483, 249–286.CrossRefGoogle Scholar
Wu, X. Lee, S. S. & Cowley, S. J. 1993 On the weakly nonlinear three-dimensional instability of shear layers to pairs of oblique modes: the Stokes layer as a paradigm. J. Fluid Mech. 253, 681–721.CrossRefGoogle 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