Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-22T02:12:31.887Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental study of absolute instability of the rotating-disk boundary-layer flow

Published online by Cambridge University Press:  26 April 2006

R. J. Lingwood
R. J. Lingwood
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, the results of experiments on unsteady disturbances in the boundary-layer flow over a disk rotating in otherwise still air are presented. The flow was perturbed impulsively at a point corresponding to a Reynolds number R below the value at which transition from laminar to turbulent flow is observed. Among the frequencies excited are convectively unstable modes, which form a three-dimensional wave packet that initially convects away from the source. The wave packet consists of two families of travelling convectively unstable waves that propagate together as one packet. These two families are predicted by linear-stability theory: branch-2 modes dominate close to the source but, as the packet moves outwards into regions with higher Reynolds numbers, branch-1 modes grow preferentially and this behaviour was found in the experiment. However, the radial propagation of the trailing edge of the wave packet was observed to tend towards zero as it approaches the critical Reynolds number (about 510) for the onset of radial absolute instability. The wave packet remains convectively unstable in the circumferential direction up to this critical Reynolds number, but it is suggested that the accumulation of energy at a well-defined radius, due to the flow becoming radially absolutely unstable, causes the onset of laminar–turbulent transition. The onset of transition has been consistently observed by previous authors at an average value of 513, with only a small scatter around this value. Here, transition is also observed at about this average value, with and without artificial excitation of the boundary layer. This lack of sensitivity to the exact form of the disturbance environment is characteristic of an absolutely unstable flow, because absolute growth of disturbances can start from either noise or artificial sources to reach the same final state, which is determined by nonlinear effects.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 314 , 10 May 1996 , pp. 373 - 405
Copyright
© 1996 Cambridge University Press

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

Balachandar, S., Streett, C. L. & Malik, M. R. 1990 Secondary instability in rotating disk flow. AIAA Paper 90-1527.
Balakumar, P. & Malik, M. R. 1990 Traveling disturbances in rotating-disk flow. Theor. Comput. Fluid Dyn. 2, 125–137.Google Scholar
Bassom, A. P. & Gajjar, J. S. B. 1988 Non-stationary cross-flow vortices in three-dimensional boundary-layer flows. Proc. R. Soc. Lond. A 417, 179–212.Google Scholar
Bassom, A. P. & Hall, P. 1991 Concerning the interaction of non-stationary crossflow vortices in a three-dimensional boundary layer. Q. J. Mech. Appl. Maths 44, 147–172.Google Scholar
Briggs, R. J. 1964 Electron-Stream Interaction with Plasmas, chap. 2. MIT Press.
Chin, D. & Litt, M. 1972 An electrochemical study of flow instability on a rotating disk. J. Fluid Mech. 54, 613–625.Google Scholar
Faller, A. J. 1991 Instability and transition of the disturbed flow over a rotating disk. J. Fluid Mech. 230, 245–269.Google Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Ann. Rev. Fluid Mech. 24, 395–457.Google Scholar
Fedorov, B. I., Plavnik, G. Z., Prokhorov, I. V. & Zhukhovitskii, L. G. 1976 Transitional flow conditions on a rotating disk. J. Engng Phys. 31, 1448–1453.Google Scholar
Gaster, M. & Grant, L. 1975 An experimental investigation of the formation and development of a wave packet in a laminar boundary layer. Proc. R. Soc. Lond. A 347, 253–269.Google Scholar
Gray, W. E. 1952 The nature of the boundary layer at the nose of a swept back wing. Unpublished, Min. Aviation, London.
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155–199.Google Scholar
Healey, J. J. 1995 A new boundary layer resonance enhanced by wave modulation: theory and experiment J. Fluid Mech. 304, 231–262.Google Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.Google Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech. 22, 473–537.Google Scholar
Johansson, A. V. & Alfredsson, P. H. 1982 On the structure of turbulent channel flow. J. Fluid Mech. 122, 295–314.Google Scholar
Kármán, Th. Von 1921 Über laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 233–252.Google 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 12, 493–514.Google Scholar
Kobayashi, R., Kohama, Y. & Takamadate, Ch. 1980 Spiral vortices in boundary layer transition regime on a rotating disk. Acta Mech. 35, 71–82.Google Scholar
Koch, W. 1985 Local instability characteristics and frequency determination of self excited wake flows. J. Sound Vib. 99, 53–83.Google Scholar
Kohama, Y. 1984 Study on boundary layer transition of a rotating disk. Acta Mech. 50, 193–199.Google Scholar
Kohama, Y. 1987 Crossflow instability in rotating disk boundary layer. AIAA Paper 87-1340.
Le Gal, P. 1992 Complex demodulation applied to the transition to turbulence of the flow over a rotating disk. Phys. Fluids A 4, 2523–2528.Google Scholar
Lingwood, R. J. 1995a Absolute instability of the boundary layer on a rotating disk. J. Fluid Mech. 299, 17–33.Google Scholar
Lingwood, R. J. 1995b Stability and transition of the boundary layer on a rotating disk. PhD thesis, Cambridge University.
Mack, L. M. 1985 The wave pattern produced by point source on a rotating disk. AIAA Paper 85-0490.
MacKerrell, S. 1987 A nonlinear, asymptotic investigation of the stationary modes of instability of the three-dimensional boundary layer on a rotating disc. Proc. R. Soc. Lond. A 413, 497–513.Google Scholar
Malik, M. R., Wilkinson, S. P. & Orszag, S. A. 1981 Instability and transition in rotating disk flow. AIAA J. 19, 1131–1138.Google Scholar
Poll, D. I. A. 1985 Some observations of the transition process on the windward face of a long yawed cylinder J. Fluid Mech. 150, 329–356.Google Scholar
Shaikh, F. N. 1993 Turbulent spots in a transitional boundary layer. PhD Thesis, Cambridge University.
Smith, N. H. 1946 Exploratory investigation of the laminar-boundary-layer oscillations on a rotating disk. NACA TN 1227.Google Scholar
Theodorsen, T. & Regier, A. 1945 Experiments on drag of revolving disks, cylinders, and streamline rods at high speeds. NACA Rep. 793.
Wilkinson, S. P., Blanchard, A. E., Gaster, M., Tritz, T., Gad-el-hak, M. & Selby, G. 1989 Flow visualization of a wave packet on a rotating disk. In Instability and Transition 1 (ed. Hussaini, M. Y. & Voigt, R. G.), pp. 306–318. Springer.
Wilkinson, S. P. & Malik, M. R. 1985 Stability experiments in the flow over a rotating disk. AIAA J. 23, 588–595.Google Scholar