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Stability of eccentric core–annular flow

Published online by Cambridge University Press:  26 April 2006

Adam Huang  and
Daniel D. Joseph
Adam Huang
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. S.E., Minneapolis, MN 55455, USA
Daniel D. Joseph
Affiliation:
Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. S.E., Minneapolis, MN 55455, USA
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Abstract

Perfect core-annular flows are two-phase flows, for example of oil and water, with the oil in a perfectly round core of constant radius and the water outside. Eccentric core flows can be perfect, but the centre of the core is displaced off the centre of the pipe. The flow is driven by a constant pressure gradient, and is unidirectional. This kind of flow configuration is a steady solution of the governing fluid dynamics equations in the cases when gravity is absent or the densities of the two fluids are matched. The position of the core is indeterminate so that there is a family of these eccentric core flow steady solutions. We study the linear stability of this family of flows using the finite element method to solve a group of PDEs. The large asymmetric eigenvalue problem generated by the finite element method is solved by an iterative Arnoldi's method. We find that there is no linear selection mechanism; eccentric flow is stable when concentric flow is stable. The interface shape of the most unstable mode changes from varicose to sinuous as the eccentricity increases from zero.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 233 - 245
Copyright
© 1995 Cambridge University Press

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