Axisymmetric Wavy Core Flow in a Heavy Viscous Oil

  • R. Bai
  • D. D. Joseph
  • K. Kelkar
Conference paper
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 43)


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 low pressure region at lee side of the crest. The simulation gives excellent agreement with the experiments of Bai et al.[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 holdup 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 wave front. It is suggested that the positive pressure force is required to levitate the core off the wall when the densities are not matched and to center 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.


Reynolds Number Interfacial Tension Direct Numerical Simulation Pressure Force Water Flow Rate 
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  1. 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, 97–142.ADSCrossRefGoogle Scholar
  2. Feng, J., Huang, P. Y., & Joseph, D. D. (1995) Dynamic simulation of the motion of capsules in pipelines. J. Fluid Mech. 286, 201–227.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. Huang, A. & Joseph, D. D. (1995) Stability of eccentric core annular flow. J. Fluid Mech. 282, 233–245.MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 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.ADSzbMATHCrossRefGoogle Scholar
  5. Joseph, D. D., & Renardy, Y. Y. (1993) Fundamentals of two-fluid dynamics. Springer-Verlag New York.Google Scholar
  6. Liu, H. (1982) A theory of capsule lift-off in pipeline. J. Pipelines 2, 23–33.Google Scholar
  7. Oliemans, R. V. A. (1986) The lubricating film model for core-annular flow. Delft University Press.Google Scholar
  8. Oliemans, R. V. A. & Ooms, G. (1986) Core-annular flow of oil and water through a pipeline. Multiphase Science and Technology. vol. 2, eds. Hewitt, G. F., Delhaye, J. M. & Zuber, N., Hemisphere Publishing Corporation.Google Scholar
  9. 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. Int. J. Multiphase Flow 10, 41–60.zbMATHCrossRefGoogle Scholar
  10. 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. Int. J. Multiphase Flow 11, 481–502.zbMATHCrossRefGoogle Scholar
  11. Patankar, S. V. (1980) Numerical Heat Transfer and Fluid Flow. Hemisphere.Google Scholar
  12. 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.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • R. Bai
    • 1
  • D. D. Joseph
    • 1
  • K. Kelkar
    • 2
  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Innovative Research, Inc.MinneapolisUSA

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