A numerical framework for linear stability analysis of two-phase stratified pipe flows

Ilya Barmak, Alexander Gelfgat, Neima Brauner

Research output: Contribution to journalArticlepeer-review


Abstract: A numerical framework for rigorous linear stability analysis of two-phase stratified flows of two immiscible fluids in horizontal circular pipes is presented. For the first time, three-dimensional disturbances, including those at the interface between two fluids, are considered. The proposed numerical framework is based on a finite volume method and allows solving the problem numerically in bipolar cylindrical coordinates. In these coordinates, both the pipe wall and the unperturbed interface (of a constant curvature, e.g., plane interface, as considered in this work) coincide with the coordinate surfaces. Thereby, the no-slip as well as the interfacial boundary conditions can be imposed easily. It also enables investigation of the local behavior of the flow field and shear stresses in the vicinity of the triple points, where the interface contacts the pipe wall. The results obtained in the bipolar coordinates are verified by an independent numerical solution based on the problem formulation in Cartesian coordinates, where the pipe wall is treated by the immersed boundary method. Two representative examples of gas–liquid and liquid–liquid flows are included to demonstrate the applicability of the proposed numerical technique for analyzing the flow stability. Graphical abstract: [Figure not available: see fulltext.].

Original languageEnglish
Pages (from-to)559-587
Number of pages29
JournalTheoretical and Computational Fluid Dynamics
Issue number5
StatePublished - Oct 2023


  • Bipolar coordinates
  • Circular pipe
  • Immersed boundary method
  • Stability
  • Two-phase stratified flow

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • General Engineering
  • Fluid Flow and Transfer Processes
  • Computational Mechanics


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