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Laminar entrance flow in a curved pipe

Published online by Cambridge University Press:  20 April 2006

W. Y. Soh  and
S. A. Berger
W. Y. Soh
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720
S. A. Berger
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, California 94720
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Abstract

The full elliptic Navier–Stokes equations have been solved for entrance flow into a curved pipe using the artificial compressibility technique developed by Chorin (1967). The problem is formulated for arbitrary values of the curvature ratio and the Dean number. Calculations are carried out for two curvature ratios, a/R = 1/7 and 1/20, and for Dean number ranging from 108.2 to 680.3, in a computational mesh extending from the inlet immediately adjacent to the reservoir to the fully developed downstream region.

Secondary flow separation near the inner wall is observed in the developing region of the curved pipe. The separation and the magnitude of the secondary flow are found to be greatly influenced by the curvature ratio. As observed in the experiments of Agrawal, Talbot & Gong (1978) we find: (i) two-step plateau-like axial-velocity profiles for high Dean number, due to the secondary flow separation, and (ii) doubly peaked axial-velocity profiles along the lines parallel to the plane of symmetry, due to the highly distorted secondary-flow vortex structure.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 148 , November 1984 , pp. 109 - 135
Copyright
© 1984 Cambridge University Press

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