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Numerical study of viscous flow in rotating rectangular ducts

Published online by Cambridge University Press:  20 April 2006

Charles G. Speziale
Charles G. Speziale
Affiliation:
Stevens Institute of Technology, Hoboken, NJ 07030
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Abstract

A numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted. The full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role. At weak to moderate rotation rates, a double-vortex secondary flow appears in the transverse planes of the duct whose structure is relatively independent of the aspect ratio of the duct. For Rossby numbers Ro < 100 this secondary flow is shown to lead to substantial distortions of the axial velocity profiles. For more rapid rotations (Ro < l), the Secondary flow (in a duct with an aspect ratio of two) is shown to split into an asymmetric configuration of four counter-rotating vortices similar to that which appears in curved ducts. It is demonstrated mathematically that this effect could result from a disparity in the symmetry of the convective and Coriolis terms in the equations of motion. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration and the axial velocity wumes a Taylor–Proudman configuration in the interior of the duct. Comparisons with existing experimental results are quite favourable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 122 , September 1982 , pp. 251 - 271
Copyright
© 1982 Cambridge University Press

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References

Barua, S. N. 1954 Secondary flow in a rotating straight pipe. Proc. R. Soc. Lond. A 227, 133–139.Google Scholar
Batchelor, G. K. 1967 Introduction to Fluid Dynamics. Cambridge University Press.
Benton, G. S. 1956 The effect of the earth's rotation on laminar flow in pipes. J. Appl. Mech. 23, 123–127.Google Scholar
Benton, G. S. & Boyer, D. 1966 Flow through a rapidly rotating conduit of arbitrary crosssection. J. Fluid Mech. 26, 69–79.Google Scholar
Buneman, O. 1969 A compact non-iterative Poisson solver. Stanford Univ. Inst. for Plasma Res. Rep. SUIPR no. 294.
Cheng, K. C., Lin, R. C. & Ou, J. W. 1976 Fully-developed laminar flow in curved rectangular channels. Trans. A.S.M.E. I, J. Fluids Engng 98, 41–48.Google Scholar
Dennis, S. C. R. & Ng, M. 1982 Dual solutions for steady laminar flow through a curved tube. Q. J. Mech. Appl. Math. (to appear).
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341–351.Google Scholar
Howard, J. H., Patankar, S. V. & Bordynuik, R. M. 1980 Flow prediction in rotating ducts using Coriolis-modified turbulence models. Trans. A.S.M.E. I, J. Fluids Engng 102, 456–461.Google Scholar
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533–557.Google Scholar
Lezius, D. K. & Johnston, J. P. 1976 Roll-cell instabilities in rotating laminar and turbulent channel flow. J. Fluid Mech. 77, 153–175.Google Scholar
Majumdar, A. K., Pratap, V. S. & Spalding, D. B. 1977 Numerical computation of flow in rotating ducts. Trans. A.S.M.E. I, J. Fluids Engng 99, 148–153.Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa.
Wagner, R. E. & Velkoff, H. R. 1972 Measurements of secondary flows in a rotating duct. Trans. A.S.M.E. A, J. Engng Power 95, 261–270.Google Scholar