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Transition near the edge of a rotating disk

Published online by Cambridge University Press:  19 November 2013

Benoît Pier*
Affiliation:
Laboratoire de mécanique des fluides et d’acoustique, École centrale de Lyon – CNRS – Université de Lyon 1 – INSA Lyon, 36 avenue Guy-de-Collongue, 69134 Écully CEDEX, France
*
Email address for correspondence: benoit.pier@ec-lyon.fr

Abstract

The rotating-disk boundary layer is generally considered as an example of a flow that displays a robust transition from laminar to turbulent régimes. By taking into account disks of finite radius, Healey (J. Fluid Mech., vol. 663, 2010, pp. 148–159) has predicted a stabilizing effect of the boundary condition, but Imayama et al. (J. Fluid Mech., vol. 716, 2013, pp. 638–657) were unable to confirm this prediction experimentally. Following these contradictory results, the present experimental investigation revisits the rotating-disk boundary layer, without any artificially imposed excitation, and studies in further detail the dynamics prevailing in the region closely surrounding the edge of the disk, as well as the flow beyond the disk. Azimuthal mean velocities and fluctuation amplitudes are recorded with small steps in radial and axial directions for a wide range of disk sizes. An objective criterion is used to define the onset of fluctuations consistently over a large data set. Two distinct mechanisms for the onset of fluctuations are identified. In particular, it is found that the flow over the edge of the disk acts as a strong source of fluctuations. Explanations and suggestions for a possible reconciliation of previous studies are given.

Type
Rapids
Copyright
©2013 Cambridge University Press 

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References

Chin, D.-T. & Litt, M. 1972 An electrochemical study of flow instability on a rotating disk. J. Fluid Mech. 54, 613625.CrossRefGoogle Scholar
Davies, C. & Carpenter, P. W. 2003 Global behaviour corresponding to the absolute instability of the rotating-disk boundary layer. J. Fluid Mech. 486, 287329.CrossRefGoogle 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, 14481453.CrossRefGoogle Scholar
Garrett, S. J. 2002 The stability and transition of the boundary layer on rotating bodies. PhD thesis, University of Cambridge.CrossRefGoogle Scholar
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, 155199.Google Scholar
Healey, J. J. 2010 Model for unstable global modes in the rotating-disk boundary layer. J. Fluid Mech. 663, 148159.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473537.CrossRefGoogle Scholar
Imayama, S., Alfredsson, P. H. & Lingwood, R. J. 2012 A new way to describe the transition characteristics of a rotating-disk boundary-layer flow. Phys. Fluids 24, 031701.CrossRefGoogle Scholar
Imayama, S., Alfredsson, P. H. & Lingwood, R. J. 2013 An experimental study of edge effects on rotating-disk transition. J. Fluid Mech. 716, 638657.CrossRefGoogle Scholar
von Kármán, Th. 1921 Über laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 233252.CrossRefGoogle Scholar
Kobayashi, R., Kohama, Y. & Takamadate, C. 1980 Spiral vortices in boundary layer transition regime on a rotating disk. Acta Mechanica 35, 7182.CrossRefGoogle Scholar
Launder, B., Poncet, S. & Serre, E. 2010 Laminar, transitional, and turbulent flows in rotor-stator cavities. Annu. Rev. Fluid Mech. 42, 229248.CrossRefGoogle Scholar
Lingwood, R. J. 1995 Absolute instability of the boundary layer on a rotating disk. J. Fluid Mech. 299, 1733.CrossRefGoogle Scholar
Lingwood, R. J. 1996 An experimental study of absolute instability of the rotating-disk boundary-layer flow. J. Fluid Mech. 314, 373405.CrossRefGoogle Scholar
Malik, M. R., Wilkinson, S. P. & Orszag, S. A. 1981 Instability and transition in rotating disk flow. AIAA J. 19, 11311138.CrossRefGoogle Scholar
Othman, H. & Corke, T. 2006 Experimental investigation of absolute instability of a rotating-disk boundary layer. J. Fluid Mech. 565, 6394.CrossRefGoogle Scholar
Pier, B. 2003 Finite-amplitude crossflow vortices, secondary instability and transition in the rotating-disk boundary layer. J. Fluid Mech. 487, 315343.CrossRefGoogle Scholar
Pier, B. & Huerre, P. 2001 Nonlinear synchronization in open flows. J. Fluids Struct. 15, 471480.CrossRefGoogle Scholar
Pier, B., Huerre, P. & Chomaz, J.-M. 2001 Bifurcation to fully nonlinear synchronized structures in slowly varying media. Physica D 148, 4996.CrossRefGoogle Scholar
Reed, H. L. & Saric, W. S. 1989 Stability of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 21, 235284.CrossRefGoogle Scholar
Saric, W. S., Reed, H. L. & White, E. B. 2003 Stability and transition of three-dimensional boundary layers. Annu. Rev. Fluid Mech. 35, 413440.CrossRefGoogle Scholar
Siddiqui, M. E. 2011 Experimental study of natural and forced instabilities and transition of a rotating-disk boundary-layer flow. PhD thesis, École centrale de Lyon, Écully, France.Google Scholar
Siddiqui, M. E., Mukund, V., Scott, J. & Pier, B. 2013 Experimental characterization of transition region in rotating-disk boundary layer. Phys. Fluids 25, 034102.CrossRefGoogle Scholar
Smith, N. H. 1947 Exploratory investigation of laminar-boundary-layer oscillations in a rotating disk. NACA Tech. Rep. TN 1227.Google Scholar
Theodorsen, T. & Regier, A. 1944 Experiments on drag of revolving disks, cylinders, and streamline rods at high speeds. NACA Tech. Rep. 793.Google Scholar
Wilkinson, S. P. & Malik, M. R. 1985 Stability experiments in the flow over a rotating disk. AIAA J. 23, 588595.CrossRefGoogle Scholar