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Hydrodynamic instability of viscous flow between rotating coaxial cylinders with fully developed axial flow

Published online by Cambridge University Press:  12 April 2006

K. C. Chung  and
K. N. Astill
K. C. Chung
Affiliation:
Department of Mechanical Engineering, Tufts University, Medford, Massachusetts 02155
K. N. Astill
Affiliation:
Department of Mechanical Engineering, Tufts University, Medford, Massachusetts 02155
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Abstract

A linear stability analysis is presented for flow between concentric cylinders when a fully developed axial flow is present. Small perturbations are assumed to be nonaxisymmetric. This leads to an eigenvalue problem with four eigenvalues: the critical Taylor number, an amplification factor and two wavenumbers. The presence of the tangential wavenumber permits prediction of the stability of spiral flow. This made it possible to model the flow more accurately and to extend the range of calculations to higher axial Reynolds numbers than had previously been attainable. Calculations were carried out for radius ratios from 0·95 to 0·1, Reynolds numbers as large as 300 and cases with co-rotation and counter-rotation of the cylinders.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 81 , Issue 4 , 5 August 1977 , pp. 641 - 655
Copyright
© 1977 Cambridge University Press

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References

Astill, K. N. 1964 J. Heat Transfer, Trans. A.S.M.E. C 86, 383.
Astill, K. N. & Chung, K. C. 1976 A.S.M.E. Paper no. 76-FE-27.
Chandrasekhar, S. 1960 Proc. Nat. Acad. Sci. 46, 141.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press.
Chandrasekhar, S. 1962 Proc. Roy. Soc. A 265, 188.
Chung, K. C. 1976 Ph.D. thesis, Tufts University, Massachusetts.
Coney, J. E. R. & Mobbs, F. R. 1970 Proc. Inst. Mech. Engng 184 (3L), 10.
Datta, S. L. 1965 J. Fluid Mech. 21, 635.
Diprima, R. C. 1960 J. Fluid Mech. 9, 621.
Donnelly, R. J. & Fultz, D. 1960 Proc. Nat. Acad. Sci. 46, 1150.
Elliot, L. 1973 Phys. Fluids 16, 577.
Hasoon, M. A. & Martin, B. W. 1977 Proc. Roy. Soc. A 352, 351.
Hughes, T. H. & Reid, W. H. 1968 Phil. Trans. Roy. Soc. A 263, 57.
Kaye, J. & Elgar, E. C. 1958 Trans. A.S.M.E. 80, 753.
Krueger, E. R. & DiPrima, R. C. 1964 J. Fluid Mech. 19, 528.
Snyder, H. A. 1962 Proc. Roy. Soc. A 265, 198.
Snyder, H. A. 1965 Ann. Phys. 31 (2), 292.
Sparrow, E. M., Munro, W. D. & Jonsson, V. K. 1964 J. Fluid Mech. 20, 35.
Taylor, G. I. 1923 Phil. Trans. Roy. Soc. A 223, 289.
Thomas, A. D. 1974 Ph.D. thesis, University of Western Australia.