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Direct simulation of interfacial waves in a high-viscosity-ratio and axisymmetric core–annular flow

Published online by Cambridge University Press:  26 April 2006

Runyuan Bai
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Kanchan Kelkar
Affiliation:
Innovative Research, Inc., 2800 University Avenue SE, Minneapolis, MN 55414, USA
Daniel D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA

Abstract

A direct numerical simulation of spatially periodic wavy core flows is carried out under the assumption that the densities of the two fluids are identical and that the viscosity of the oil core is so large that it moves as a rigid solid which may nevertheless be deformed by pressure forces in the water. The waves which develop are asymmetric with steep slopes in the high-pressure region at the front face of the wave crest and shallower slopes at the low-pressure region at the lee side of the crest. The simulation gives excellent agreement with the experiments of Bai, Chen & Joseph (1992) on up flow in vertical core flow where axisymmetric bamboo waves are observed. We define a threshold Reynolds number and explore its utility; the pressure force of the water on the core relative to a fixed reference pressure is negative for Reynolds numbers below the threshold and is positive above. The wave length increases with the hold-up ratio when the Reynolds number is smaller than a second threshold and decreases for larger Reynolds numbers. We verify that very high pressures are generated at stagnation points on the wavefront. It is suggested that a positive pressure force is required to levitate the core off the wall when the densities are not matched and to centre the core when they are. A further conjecture is that the principal features which govern wavy core flows cannot be obtained from any theory in which inertia is neglected.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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References

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, 97142.Google Scholar
Feng, J., Huang, P. Y. & Joseph, D. D. 1995 Dynamic simulation of the motion of capsules in pipelines. J. Fluid Mech. 286. 201227.Google Scholar
Huang, A. & Joseph, D. D. 1995 Stability of eccentric core anular flow. J. Fluid Mech. 282, 233245.Google Scholar
Joseph, D. D. & Renardy, Y. Y. 1993 Fundamentals of Two-Fluid Dynamics. Springer.
Liu, H. 1982 A theory of capsule lift-off in pipeline. J. Pipelines 2, 2333.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. Multiphase Science and Technology (ed. G. F. Hewitt, J. M. Delhaye & N. Zuber), vol. 2. Hemisphere.
Ooms, G., Segal, A., Cheung, S. Y. & Oliemans, R. V. A. 1985 Propagation of long waves of finite amplitude at the interface of two viscous fluids. Intl J. Multiphase Flow 11, 481502.Google Scholar
Ooms, G., Segal, A., Van Der Wees, A. J., Meerhoff, R. & Oliemans, R. V. A. 1984 A theoretical model for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe. Intl J. Multiphase Flow 10, 4160.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Patankar, S. V., Liu, C. H. & Sparrow, E. M. 1977 Fully developed flow and heat transfer in ducts having streamwise-periodic variations of cross-section area. J. Heat Transfer 99, 180.Google Scholar