Exact solutions of core-annular laminar inclined flows

Ayelet Goldstein, Amos Ullmann*, Neima Brauner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An exact solution for laminar two-phase eccentric core-annular flows (CAF) in inclined pipes is derived. This solution complements the exact solutions that were obtained for inclined stratified flows with curved interfaces as to provide a set of solutions for two-phase laminar separated flows. A unified set of three dimensionless parameters for separated flows is defined and used to explore the effects of the system parameters and separated flow configurations on the velocity profiles and the resulting holdup, pressure gradient and pumping power requirement in horizontal and inclined concurrent and countercurrent flows. It is shown that similarly to stratified flows, also in CAF multiple solutions for the holdup and the associated flow characteristics can be obtained in inclined flows. The boundaries of the multiple solution regions are mapped and the effect of the core eccentricity and system parameters boundaries are demonstrated and discussed. The benefits of adding a lubricating phase for transportation of a viscous fluid in inclined CAFs is investigated. An adverse effect of the upward pipe inclination on the power savings in all of the separate flow configurations is demonstrated. Independently of the density of the lubricant, namely, whether it is lighter or heavier than the viscous fluid, the effect of hydrostatic pressure gradient always hinders the possibility of reducing the pumping requirement for transporting the viscous phase. However, surprisingly, a heavier lubricant is preferable form the view point of power saving. The implications of turbulent flow of the lubricating phase and the susceptibility to Ledinegg instability on the potential power savings are also considered and discussed. The application of the model for the analysis of experimental data of the holdup and pressure drop obtained in horizontal and inclined CAF is also demonstrated.

Original languageEnglish
Pages (from-to)178-204
Number of pages27
JournalInternational Journal of Multiphase Flow
StatePublished - 2017


  • Inclined pipes
  • Ledinegg instability
  • Lubrication
  • Multiple solutions
  • Two-phase core annular flow


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