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The effect of spanwise system rotation on Dean vortices

Published online by Cambridge University Press:  26 April 2006

O. John E. Matsson  and
P. Henrik Alfredsson
O. John E. Matsson
Affiliation:
Department of Mechanics/Fluid Physics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
P. Henrik Alfredsson
Affiliation:
Department of Mechanics/Fluid Physics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
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Abstract

An experimental study is reported of the flow in a high-aspect-ratio curved air channel with spanwise system rotation, utilizing hot-wire measurements and smoke visualization. The experiments were made at two different Dean numbers (De), approximately 2 and 4.5 times the critical De for which the flow becomes unstable and develops streamwise vortices. For the lower De without system rotation the primary Dean instability appeared as steady longitudinal vortices. It was shown that negative spanwise system rotation, i.e. the Coriolis force counteracts the centrifugal force, could cancel the primary Dean instability and that for high rotation rates it could give rise to vortices on the inner convex channel wall. For positive spanwise system rotation, i.e. when the Coriolis force enhanced the centrifugal force, splitting and merging of vortex pairs were observed. At the higher De secondary instabilities occurred in the form of travelling waves. The effect of spanwise system rotation on the secondary instability was studied and was found to reduce the amplitude of the twisting and undulating motions for low negative rotation. For low positive rotation the amplitude of the secondary instabilities was unaffected for most regions in parameter space.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 274 , 10 September 1994 , pp. 243 - 265
Copyright
© 1994 Cambridge University Press

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References

Alfredsson, P. H. & Persson, H. 1989 Instabilities in channel flow with system rotation. J. Fluid Mech. 202, 543–557.Google Scholar
Andereck, C. D., Dickman, R. & Swinney, H. L. 1983 New flows in a circular Couette system with co-rotating cylinders. Phys Fluids 26, 1395–1401.Google Scholar
Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Cuette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183.Google Scholar
Aouidef, A., Wesfreid, J. E. & Mutabazi, I. 1992 Coriolis effects on Görtler vortices in the boundary-layer flow on concave wall. AIAA J. 30, 2779–2782.Google Scholar
Bland, S. B. & Finlay, W. H. 1991 Transitions toward turbulence in a curved channel. Phys. Fluids A 3, 106–114.Google Scholar
Bottaro, A. 1993 On longitudinal vortices in curved channel flow. J. Fluid Mech. 251, 627–660.Google Scholar
Bottaro, A., Matsson, O. J. E. & Alfredsson, P. H. 1991 Numerical and experimental results for developing curved channel flow. Phys. Fluids A 3, 1473–1476.Google Scholar
Brewster, D. B., Grosberg, P. & Nissan, A. H. 1959 The stability of viscous flow between horizontal concentric cylinders. Proc. R. Soc. Lond. A 251, 76–91.Google Scholar
Chen, F. & Chang, M. H. 1992 Stability of Taylor-Dean flow in a small gap between rotating cylinders. J. Fluid Mech. 243, 443–455.Google Scholar
Cheng, K. C., Nakayama, J. & Akiyama, M. 1977 Effect of finite and infinite aspect ratios on flow patterns in curved rectangular channels. In Flow visualization: Proc. Int Symp. on Flow Visualization, Tokyo (ed. T. Asanuma), pp. 181–186.
Dean, W. R. 1928 Fluid motion in a curved channel. Proc. R. Soc. Lond. A 121, 402–420.Google Scholar
Finlay, W. H., Guo, Y. & Olsen, D. 1993 Inferring secondary flows from smoke or dye flow visualization: Two case studies. Phys. Fluids A 5, 2689–2701.Google Scholar
Finlay, W. H., Keller, J. B. & Ferziger, J. H. 1988 Instability and transition in curved channel flow. J. Fluid Mech. 194, 417–456.Google Scholar
Finlay, W. H. & Nandakumar, K. 1990 Onset of two-dimensional cellular flow in finite curved channels of large aspect ratio. Phys. Fluids A 2, 1163–1174.Google Scholar
Guo, Y. & Finlay, W. H. 1991 Splitting, merging and wavelength selection of vortices in curved and/ or rotating channel flow due to Eckhaus instability. J. Fluid Mech. 228, 661–691.Google Scholar
Guo, Y. & Finlay, W. H. 1994 Wavenumber selection and irregularity of spatially developing nonlinear Dean and Görtler vortices. J. Fluid Mech. 264, 1–40.Google Scholar
Kelleher, M. D., Flentie, D. L. & Mc Kee, R. J. 1980 An experimental study of the secondary flow in a curved rectangular channel. Trans. ASME I: J. Fluids Engng 102, 92–96.Google Scholar
Le Cunff, C., & Bottaro, A. 1993 Linear stability of shear profiles and relation to the secondary instability of the Dean flow. Phys. Fluids A 5, 2161–2171.Google Scholar
Ligrani, P. M., Finlay, W. H., Fields, W. A., Fuqua, S. J. & Subramanian, C. S. 1992 Features of wavy vortices in a curved channel from experimental and numerical studies. Phys. Fluids A 4, 695–709.Google Scholar
Ligrani, P. M. & Niver, R. D. 1988 Flow visualization of Dean vortices in a curved channel with 40 to 1 aspect ratio. Phys. Fluids 31, 3605–3617.Google Scholar
Masuda, S. & Matsubara, M. 1989 Visual study of boundary layer transition on rotating flat plate. In Laminar-Turbulent Transition (ed. D. Arnal & R. Michel), pp. 465–474. Springer.
Matsson, O. J. E. 1993 Time-dependent instabilities in curved rotating channel flow. Phys. Fluids A 5, 1514–1516.Google Scholar
Matsson, O. J. E. & Alfredsson, P. H. 1990 Curvature- and rotation-induced instabilities in channel flow. J. Fluid Mech. 210, 537–563.Google Scholar
Matsson, O. J. E. & Alfredsson, P. H. 1992 Experiments on instabilities in curved channel flow. Phys. Fluids A 4, 1666–1676.Google Scholar
Matsson, O. J. E. & Alfredsson, P. H. 1993 Secondary instability and breakdown to turbulence in curved channel flow. Appl. Sci. Res. 51, 9–14.Google Scholar
Matsson, O. J. E., Bottaro, A. & Alfredsson, P. H. 1991 Transition to turbulence in curved channel flow. In Eighth Symp. on Turbulent Shear Flows, Sept. 9-11, Münich, Germany, Paper 18–2.
Matsubara, M. & Masuda, S. 1990 Turbulent spots in a rotating Blasius boundary layer. In Advances in Turbulence 3 (ed. A. V. Johansson & P. H. Alfredsson), pp. 204–210. Springer.
Mutabazi, I., Hegseth, J. J., Andereck, C. D. & Wesfreid, J. E. 1988 Pattern formation in the flow between two horizontal coaxial cylinders with a partially filled gap. Phys. Rev. A 38, 4752–4760.Google Scholar
Mutabazi, I., Normand, C., Peerhossaini, H. & Wesfreid, J. E. 1989 Oscillatory modes in the flow between two horizontal corotating cylinders with a partially filled gap. Phys. Rev. A 39, 763–771.Google Scholar
Ng, L., Singer, B. A., Henningson, D. S. & Alfredsson, P. H. 1990 Instabilities in rotating channel flow. In Instability and Transition, vol. II (ed. M.Y. Hussaini & R.G. Voigt), pp. 313–329. Springer.
Zebib, A. & Bottaro, A. 1993 Goertler vortices with system rotation: linear theory. Phys. Fluids A 5, 1206–1210.Google Scholar