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Lubricated pipelining: stability of core-annular flow

Published online by Cambridge University Press:  26 April 2006

Luigi Preziosi ,
Kangping Chen  and
Daniel D. Joseph
Luigi Preziosi
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Kangping Chen
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

The stability of core-annular flow (CAF) in pipes is analysed using the linear theory of stability. Attention is confined to the potentially stable case of lubricated pipelining with the less viscous liquid, say water, in the annulus. The effects of surface tension and density are included, but gravity is excluded. We find upper and lower branches of the neutral curve in a Reynolds number (ℝ) vs. wavenumber (α) plane. A window of parameters is identified in which CAF is stable to small disturbances. When ℝ is below the lower critical value, CAF is destabilized by surface tension and long waves break up into slugs and bubbles. The sizes of slugs and bubbles of oil in water observed by Charles, Govier & Hodgson (1961) are given by the wavelength of the fastest growing long wave. This long-wave instability is a capillary instability, modified by shear, which reduces to Rayleigh's instability in the appropriate limit. At higher ℝ, the capillary instability is stabilized by shear. At yet higher ℝ, above the upper critical value, the flow is unstable to generally shorter waves which leads to emulsification, water droplets in oil. The theory agrees with experiments. The analysis seems to be applicable to the design of lubricated pipelines; for example, there is an optimum viscosity ratio for stability, greater stability can be obtained by using heavy liquid as a lubricant when the flow is unstable to capillary modes on the lower branch and by using light liquids when the flow is unstable to emulsifying disturbances on the upper branch.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 201 , April 1989 , pp. 323 - 356
Copyright
© 1989 Cambridge University Press

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References

Chandrasekhar, S. 1961 Hydrodynamics and Hydromagnetic Stability. Dover.
Charles, M. E., Govier, G. W. & Hodgson, G. W. 1961 The horizontal pipeline flow of equal density of oil-water mixtures. Can. J. Chem. Engng 39, 17–36.Google Scholar
Charles, M. E. & Lilleleht, L. U. 1966 Correlation of pressure gradients for the stratified laminar-turbulent pipeline flow of two immiscible liquids. Can. J. Chem. Engng 44, 47–49.Google Scholar
Gemmel, A. R. & Epstein, N. 1962 Numerical analysis of stratified laminar flow of two immiscible Newtonian liquids in circular pipes. Can. J. Chem. Engng 40, 215–224.Google Scholar
Hesla, T. I., Pranckh, F. R. & Preziosi, L. 1986 Squire's theorem for two stratified fluids. Phys. Fluids 29, 2808–2811.Google Scholar
Hickox, C. E. 1971 Instability due to viscosity and density stratification in axisymmetric pipe flow. Phys. Fluids 14, 251–262.Google Scholar
Hooper, A. & Boyd, W. G. 1983 Shear-flow instability at the interface between two viscous fluids. J. Fluid Mech. 128, 507–528.Google Scholar
Hooper, A. & Boyd, W. G. 1987 Shear flow instability due to a wall and a viscosity discontinuity at the interface. J. Fluid Mech. 179, 201–225.Google Scholar
Joseph, D. D., 1976 Stability of Fluid Motions. Springer.
Joseph, D. D., Nguyen, K. & Beavers, G. S. 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, M. & Renardy, Y. 1983 Instability of the flow of immisible liquids with different viscosities in a pipe. Math. Res. Center Tech. Summary Rep. 2503.
Joseph, D. D., Renardy, Y. & Renardy, M. 1984 Instability of the flow of immiscible liquids with different viscosities in a pipe. J. Fluid Mech. 141, 309–317.Google Scholar
Oliemans, R. V. A. 1986 The Lubricating Film Model for Core-annular Flow. Delft University Press.
Oliemans, R. V. A. & Ooms, G. 1986 Core-annular flow of oil and water through a pipeline In Multiphase Science & Technology, Vol. 2 (ed. G. F. Hewitt, J. M. Delhaye & N. Zuber). Hemisphere.
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159–205.Google Scholar
Rayleigh, Lord 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Renardy, M. & Joseph, D. D. 1986 Hopf bifurcation in two-component flow. SIAM J. Math. Anal. 17, 894–910.Google Scholar
Renardy, Y. 1985 Instability at the interface between two shearing fluids in a channel. Phys. Fluids 28, 3411–3443.Google Scholar
Renardy, Y. & Joseph, D. D. 1985 Couette flow of two fluids between concentric cylinders. J. Fluid Mech. 150, 381–394.Google Scholar
Russell, 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
Russell, T. W. F., Hodgson, G. W. & Govier, G. W. 1959 Horizontal pipeline flow of mixtures of oil and water. Can. J. Chem. Engng 37, 9–17.Google Scholar
Salwen, H., Cotton, F. W. & Grosch, C. E. 1980 Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98, 273–284.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
Than, P., Rosso, F. & Joseph, D. D. 1987 Instability of Poiseuille flow of two immiscible liquids with different viscosities in a channel. Intl J. Engng Sci. 25, 189.Google Scholar
Yih, C. S. 1967 Instability due to viscosity stratification. J. Fluid Mech. 27, 337.Google Scholar