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Bifurcation in steady laminar flow through curved tubes

Published online by Cambridge University Press:  20 April 2006

K. Nandakumar  and
Jacob H. Masliyah
K. Nandakumar
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada
Jacob H. Masliyah
Affiliation:
Department of Chemical Engineering, University of Alberta, Edmonton, Alberta, Canada
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Abstract

The occurrence of dual solutions in curved ducts is investigated through a numerical solution of the Navier-Stokes equations in a bipolar-toroidal co-ordinate system. With the shape of duct being the region formed by the natural co-ordinate surfaces, it was possible to alter the duct geometry gradually and preserve the prevailing form of the velocity field, in a manner suggested by Benjamin (1978).

In addition to the Dean number Dn = Re/Rc½, a geometrical parameter that defines the shape of the duct was also varied systematically to study the bifurcation of a two-vortex solution into a two- and four-vortex solution. Dual solutions have been found for all geometrical shapes investigated here. Of particular interest are the shapes of a full circle and a semicircle with a curved outer wall.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 475 - 490
Copyright
© 1982 Cambridge University Press

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