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Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability

Published online by Cambridge University Press:  26 April 2006

M. R. Malik ,
F. Li  and
C.-L. Chang
M. R. Malik
Affiliation:
High Technology Corporation, PO Box 7262, Hampton, VA 23666, USA
F. Li
Affiliation:
High Technology Corporation, PO Box 7262, Hampton, VA 23666, USA
C.-L. Chang
Affiliation:
High Technology Corporation, PO Box 7262, Hampton, VA 23666, USA
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Abstract

Nonlinear stability of a model swept-wing boundary layer, subject to crossflow instability, is investigated by numerically solving the governing partial differential equations. The three-dimensional boundary layer is unstable to both stationary and travelling crossflow disturbances. Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble quite well the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in these calculations. Nonlinear interaction of the stationary and travelling waves is also studied. When initial amplitude of the stationary vortex is larger than the travelling mode, the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the travelling mode dominates the downstream development owing to its higher growth rate. It is also found that, prior to laminar/turbulent transition, the three-dimensional boundary layer is subject to a high-frequency secondary instability, which is in agreement with the experiments of Poll (1985) and Kohama, Saric & Hoos (1991). The frequency of this secondary instability, which resides on top of the stationary crossflow vortex, is an order of magnitude higher than the frequency of the most-amplified travelling crossflow mode.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 268 , 10 June 1994 , pp. 1 - 36
Copyright
© 1994 Cambridge University Press

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References

Arnal, D. & Juillen, J. C. 1987 AIAA Paper 87-1335.
Balachandar, S., Streett, C. L. & Malik, M. R. 1992 J. Fluid Mech. 242, 323.
Bertolotti, F. P., Herbert, Th. & Spalart, P. R. 1992 J. Fluid Mech. 242, 441.
Bippes, H. 1991 In R. Aeronaut. Soc. Conf. on Boundary Layer Transition & Control, Cambridge, UK.
Chang, C.-L., Malik, M. R., Erlebacher, G. & Hussaini, M. Y. 1991 AIAA Paper 91-1636.
Choudhari, M. M. 1993 Theor. Comput. Fluid Dyn. 5, 487.
Choudhari, M. M. & Streett, C. 1990 AIAA Paper 90-5258.
Dagenhart, J. R., Saric, W. S., Mousseux, M. C. & Stack, J. P. 1989 AIAA Paper 89-1892.
Fischer, T. M. & Dallmann, U. 1991 Phys. Fluids A 3, 2378.
Gray, W. E. 1952 R. Aeronaut. Establ. Tech. Memo. (Aero) 256.
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 Phil. Trans. R. Soc. Lond. A 248, 155.
Hall, P. & Horseman, N. J. 1991 J. Fluid Mech. 232, 357.
Hall, P., Malik, M. R. & Poll, D. I. A. 1984 Proc. R. Soc. Lond. A 395, 229.
Herbert, Th. 1983 Phys. Fluids 26, 871.
Herbert, Th. 1991 AIAA Paper 91-0737.
Joslin, R. D., Streett, C. L. & Chang, C.-L. 1992 NASA TP-3205.
Kohama, Y. 1984 Acta Mechanica 50, 193.
Kohama, Y. 1987 AIAA Paper 87-1340.
Kohama, Y., Saric, W. S. & Hoos, J. A. 1991 In Proc. R. Aeronaut. Soc. Conf. on Boundary Layer Transition & Control, Cambridge, UK, p. 4.1.
Mack, L. M. 1985 AIAA Paper 85-0490.
Malik, M. R. 1986 In 10th Intl Conf. on Numerical Methods in Fluid Dynamics (ed. F. G. Zhuang & Y. L. Zhu), p. 455. Springer.
Malik, M. R., Chuang, S. & Hussaini, M. Y. 1982 Z. Angew. Math. Phys. 33, 189.
Malik, M. R. & Li, F. 1992 SAE Paper 921991.
Malik, M. R. & Li, F. 1993 AIAA Paper 93-0077.
Meyer, F. & Kleiser, L. 1988 In AGARD Conf. Proc. 438, p. 16–1.
Michel, J. M., Arnal, D. & Juillen, J. C. 1985 In Laminar Turbulent Transition (ed. V. V. Kozlov), p. 553. Springer.
Müller, B. 1989 Laminar-Turbulent Transition (ed. D. Arnal & R. Michel), p. 489. Springer.
Müller, B. & Bippes, H. 1988 In AGARD Conf. Proc. 438, p. 13–1.
Peerhossaini, H. & Wesfreid, J. E. 1988 Intl J. Heat Fluid Flow 9, 12.
Poll, D. I. A. 1985 J. Fluid Mech. 150, 329.
Reed, H. L. 1987 Phys. Fluids 30, 3419.
Saric, W. S., Dagenhart, J. R. & Mousseux, M. C. 1989 In Numerical and Physical Aspects of Aerodynamic Flows 4 (ed. T. Cebeci). Springer.
Spalart, P. R. 1988 In AGARD Conf. Proc. 438, p. 5–1.
Spalart, P. R. 1989 In Laminar-Turbulent Transition (ed. D. Arnal & R. Michel), p. 622. Springer.
Swearingen, J. D. & Blackwelder, R. F. 1987 J. Fluid Mech. 182, 255.
Wilson, S. D. R. & Gladwell, I. 1978 J. Fluid Mech. 84, 517.