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Experimental determination of the three-dimensional vorticity field in the boundary-layer transition process

Published online by Cambridge University Press:  20 April 2006

D. R. Williams ,
H. Fasel  and
F. R. Hama
D. R. Williams
Affiliation:
Princeton University, New Jersey Present address: Illinois Institute of Technology, Chicago.
H. Fasel
Affiliation:
Princeton University, New Jersey Present address: University of Arizona, Tucson.
F. R. Hama
Affiliation:
Princeton University, New Jersey Present address: Stuttgart University, Stuttgart, West Germany.
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Abstract

The vortex loop observed in flow-visualization studies of boundary-layer transition has been investigated by mapping the instantaneous velocity and vorticity fields. All three velocity components have been measured with hot-film anemometers at numerous grid points in a measuring volume centred on the location where the vortex loop appears in flow-visualizaton studies. The instantaneous vorticity field has been computed from the velocity field, and the vortex loop is revealed in the longitudinal component of vorticity. The loop propagates downstream at approximately the primary disturbance wavespeed. The fluid in the outer part of the boundary layer travels faster, and flows over the loop. This forms the inflexional high-shear layer, which breaks down into the hairpin vortices. The magnitude of the vorticity in the high-shear layer is actually about three times larger than that in the loop. These two regions of vorticity are distinguished by the direction of the instantaneous vorticity vectors, i.e. the vectors in the high-shear layer run in the spanwise direction, while the vectors in the vortex loop run primarily in the downstream direction. This also explains why the loop cannot be detected with simple ∂u/∂y measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 179 - 203
Copyright
© 1984 Cambridge University Press

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References

Betchov, R. 1960 On the mechanism of turbulent transition. Phys. Fluids 3, 1026.Google Scholar
Bradshaw, P. 1971 An Introduction to Turbulence and its Measurement. Pergamon.
Emmons, H. W. 1951 The laminar—turbulent transition in a boundary layer. J. Aero. Sci. 18, 490.Google Scholar
Görtler, H. & Witting, G. 1957 Theorie der sekundären Instabilität der laminaren Grenzschichten. In Proc. Boundary Layer Research Symp. Freiburg (ed. H. Görtler), p. 110. Springer.
Greenspan, H. P. & Benney, D. J. 1963 On shear layer instability, breakdown and transition. J. Fluid Mech. 15, 133.Google Scholar
Hama, F. R., Long, J. D. & Hegarty, J. C. 1957 On transition from laminar to turbulent flow. J. Appl. Phys. 28, 388.Google Scholar
Hama, F. R. & Nutant, J. 1963 Detailed flow-field observations in the transition process in a thick boundary layer. In Proc. 1963 Heat Transfer and Fluid Mechanics Inst., p. 77. Stanford University Press.
Hama, F. R., Williams, D. R. & Fasel, H. 1980 Flow field and energy balance according to the spatial linear stability theory for the Blasius boundary layer. In Laminar—Turbulent Transition (ed. R. Eppler & H. Fasel), p. 73. Springer.
Klebanoff, P. S., Tidstrom, K. D. & Sargent, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1.Google Scholar
Kleiser, L. 1982 Numerische Simulationen zum laminar—turbulenten Umschlagsprozess der ebenen Poiseuille-Strömung. Dissertation, Kernforschungszentrum Karlsruhe.
Komoda, H. 1967 Nonlinear development of a disturbance in a laminar boundary layer. Phys. Fluids Suppl. 10, S87.Google Scholar
Kovasznay, L. S. G., Komoda, H. & Vasudeva, B. R. 1962 Detailed flow field in fluid in transition. In Proc. 1962 Heat Transfer and Fluid Mechanics Inst., p. 1. Stanford University Press.
Nishioka, M., Asai, M. & Iida, S. 1980 An experimental investigation of the secondary instability. In Laminar—Turbulent Transition (ed. R. Eppler & H. Fasel), p. 37. Springer.
Nishioka, M., Asai, M. & Iida, S. 1981 Wall phenomena in the final stage of transition to turbulence. In Transition and Turbulence (ed. R. E. Meyer), p. 113. Academic.
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96. 159.Google Scholar
Schlichting, H. 1933 Zur Entstehung der Turbulenz bei der Plattenströmung. Nachr. Ges. Wiss., Gött., Math. Phys. Kl., p. 182.Google Scholar
Schlichting, H. 1935 Amplitudenverteilung und Energiebilanz der kleinen Störungen bei der Plattenströmung. Nachr. Ges. Wiss., Gött., Math. Phys. Kl., p. 1.Google Scholar
Schubauer, G. B. & Skramstad, H. K. 1948 Laminar boundary layer oscillations on a flat plate. NACA Rep. 909.Google Scholar
Stuart, J. T. 1965 The production of intense shear layers by vortex stretching and convection. AGARD Rep. 514.Google Scholar
Tani, I. & Komoda, H. 1962 Boundary layer transition in the presence of streamwise vortices. J. Aero. Sci. 29, 440.Google Scholar
Theodorsen, T. 1955 The structure of turbulence. 50 Jahre Grenzschichtforschung (ed. H. Görtler & W. Tollmein), p. 55. Vieweg.
Tollmien, W. 1931 The production of turbulence. NACA TM 609.Google Scholar
Tollmien, W. 1936 General instability criterion of laminar velocity distributions. NACATM 792.Google Scholar
Williams, D. R. 1982 An experimental investigation of the non-linear disturbance development in boundary layer transition. Dissertation, Princeton University.
Wortmann, F. X. 1977 The incompressible fluid motion downstream of two-dimensional Tollmien—Schlichting waves. AGARD Conf. Proc. 224, p. 12–1.Google Scholar
Wray, A. & Hussaini, M. Y. 1980 Numerical experiments in boundary-layer stability. AIAA Paper 80–0275.Google Scholar