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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.

Information

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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References

Arney, M. S., Bai, R., Guevara, E., Joseph, D. D. & Lui, K. 1993 Friction factor and holdup studies for lubricated pipelining I: experiments and correlations. Intl J. Multiphase Flow 19, 1061–1076.Google Scholar
Bai, R., Chen, K. & Joseph, D. D. 1992 Lubricated pipelining: stability of core-annular flow. Part 5. Experiments and comparison with theory. J. Fluid Mech. 240, 97–132.Google Scholar
Bentwich, M. 1964 Two-phase viscous axial flow in a pipe. Trans. ASME D: J. Basic Engng 669–672.
Charles, M. E., Goviers, G. W. & Hodgson, G. W. 1961 The horizontal pipeline flow of equal density of oil-water mixtures. Can. J. Chem. Engng 39, 7–36.Google Scholar
Christodoulou, K. N. & Scriven, L. E. 1988 Finding leading modes of a viscous free surface flow: an asymmetric generalized eigenproblem. J. Sci. Comput. 3.Google Scholar
Hu, H. & Joseph, D. D. 1989 Lubricated pipelining: stability of core-annular flow, Part 2. J. Fluid Mech. 205, 359–396.Google Scholar
Huang, A., Christodoulou, C. & Joseph, D. D. 1993 Friction factor and holdup studies for lubricated pipelining II: laminar and k—ε models of eccentric core flow. Intl J. Multiphase flow (to appear).Google Scholar
Joseph, D. D., Nguyen, K. & Beavers, G. 1984 Non-uniqueness and stability of the configuration of flow of immiscible fluids with different viscosities. J. Fluid Mech. 141, 319–345.Google Scholar
Joseph, D. D. & Renardy, Y. 1992 Fundamentals of Two-Fluid Dynamics, Part I. Springer.
Joseph, D. D., Renardy, M. & Renardy, Y. 1983 Instability of the flow of immiscible liquids with different viscosities in a pipe. Math. Center Tech. Summary Rep. 2503.
Oliemens, R. V. A. & Ooms, G. 1986 Core-annular flow of oil and water through a pipeline. In Multiphase Science and Technology, vol. 2. Hemisphere.
Preziosi, L., Chen, K. & Joseph, D. D. 1989 Lubricated pipelining: stability of core-annular flow. J. Fluid Mech. 201, 323–356.Google Scholar
Russel, T. W. F. & Charles, M. E. 1959 The effect of the less viscous liquid in the laminar flow of two immiscible liquids. Can. J. Chem, Engng 39, 18–24.Google Scholar
Saad, Y. 1980 Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices. Lin. Alg. App. 34, 269–295.Google Scholar
Saad, Y. 1989 Numerical solution of large nonsymmetric eigenvalue problems. Computer Phys. Commun. 53, 71–90.Google Scholar
Salwen, H. & Grosch, C. E. 1972 The stability of Poiseuille flow in a pipe of circular cross section. J. Fluid Mech. 54, 93–112.Google Scholar