- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Instability of stratified air-water flows in circular pipes

Ilya Barmak*

Alexander Gelfgat† and Neima Brauner‡

  • *Contact author: ilyab@tauex.tau.ac.il
  • †Contact author: gelfgat@tauex.tau.ac.il
  • ‡Contact author: brauner@tauex.tau.ac.il
PDF

Phys. Rev. Fluids 9, 093901 – Published 5 September, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.093901

Abstract

This work deals with the stability of two-phase stratified air-water flows in horizontal circular pipes. For this purpose, we performed a linear stability analysis, which considers all possible three-dimensional infinitesimal disturbances and takes into account deformations of the air-water interface. The main results are presented in the form of stability maps, which compare well with the available experimental data. The neutral stability curves are accompanied by the corresponding wavenumbers and wave speeds of the critical perturbations, as well as by spatial patterns of their velocity components. Accordingly, several modes of the critical perturbation are revealed. Long waves are found to be the critical perturbation over part of the stability boundary, and they are affected by the surface tension due to the confinement effect of the lateral direction. Exploring the effect of pipe diameter on the stability boundary and critical perturbations shows that for small water holdups (i.e., thin water film) the scaling of the critical gas velocity by the gas Froude number is valid for pipe diameters larger than about 0.1 m, where the surface tension effects due to the lateral confinement become negligible. Comparing results obtained in pipe, square-duct, and two-plate geometries, we show that there are cases where the simplified geometry of two parallel plates can be employed to model the realistic geometry reasonably well.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. I. Barmak, A. Gelfgat, H. Vitoshkin, A. Ullmann, and N. Brauner, Stability of stratified two-phase flows in horizontal channels, Phys. Fluids 28, 044101 (2016).
  2. I. Barmak, A. Y. Gelfgat, A. Ullmann, and N. Brauner, Stability of stratified two-phase flows in inclined channels, Phys. Fluids 28, 084101 (2016).
  3. I. Barmak, A. Gelfgat, A. Ullmann, and N. Brauner, Non-modal stability analysis of stratified two-phase channel flows, Int. J. Multiphase Flow 111, 122 (2019).
  4. A. Gelfgat and N. Brauner, Instability of stratified two-phase flows in rectangular ducts, Int. J. Multiphase Flow 131, 103395 (2020).
  5. A. Gelfgat, I. Barmak, and N. Brauner, Instability of stratified two-phase flows in inclined rectangular ducts, Int. J. Multiphase Flow 138, 103586 (2021).
  6. C. Pozrikidis, Instability of multi-layer channel and film flows, Adv. Appl. Mech. 40, 179 (2004).
  7. Y. Zhao, G. Chen, and Q. Yuan, Liquid-liquid two-phase flow patterns in a rectangular microchannel, AIChE J. 52, 4052 (2006).
  8. L. Raimondi, Stratified gas-liquid flow-–an analysis of steady state and dynamic simulation for gas-condensate systems, Petroleum 5, 128 (2019).
  9. Y. Taitel and D. Barnea, Hydrodynamic models based on flow patterns, in Encyclopedia of Two-Phase Heat Transfer and Flow, Volume 1, edited by J. R. Thime (World Scientific, Singapore, 2015), Chap. 4, pp. 23–99.
  10. N. Brauner, Liquid-liquid two-phase flow systems, in Modelling and Experimentation in Two-Phase Flow, edited by V. Bertola (Springer-Verlag, Vienna, 2003), pp. 221–279.
  11. J. Mandhane, G. Gregory, and K. Aziz, A flow pattern map for gas–liquid flow in horizontal pipes, Int. J. Multiphase Flow 1, 537 (1974).
  12. D. Barnea, O. Shoham, Y. Taitel, and A. Dukler, Flow pattern transition for gas-liquid flow in horizontal and inclined pipes. Comparison of experimental data with theory, Int. J. Multiphase Flow 6, 217 (1980).
  13. D. Barnea, O. Shoham, and Y. Taitel, Flow pattern transition for downward inclined two phase flow; horizontal to vertical, Chem. Eng. Sci. 37, 735 (1982).
  14. I. Barmak, A. Gelfgat, and N. Brauner, A numerical framework for linear stability analysis of two-phase stratified pipe flows, Theor. Comput. Fluid Dyn. 37, 559 (2023).
  15. N. Andritsos, L. Williams, and T. Hanratty, Effect of liquid viscosity on the stratified-slug transition in horizontal pipe flow, Int. J. Multiphase Flow 15, 877 (1989).
  16. N. Brauner and D. M. Maron, Analysis of stratified/nonstratified transitional boundaries in horizontal gas–liquid flows, Chem. Eng. Sci. 46, 1849 (1991).
  17. D. Barnea and Y. Taitel, Kelvin-Helmholtz stability criteria for stratified flow: Viscous versus non-viscous (inviscid) approaches, Int. J. Multiphase Flow 19, 639 (1993).
  18. A. Ullmann and N. Brauner, Closure relations for two-fluid models for two-phase stratified smooth and stratified wavy flows, Int. J. Multiphase Flow 32, 82 (2006).
  19. R. Kushnir, V. Segal, A. Ullmann, and N. Brauner, Closure relations effects on the prediction of the stratified two-phase flow stability via the two-fluid model, Int. J. Multiphase Flow 97, 78 (2017).
  20. R. Kushnir, V. Segal, A. Ullmann, and N. Brauner, Inclined two-layered stratified channel flows: Long wave stability analysis of multiple solution regions, Int. J. Multiphase Flow 62, 17 (2014).
  21. S. G. Yiantsios and B. G. Higgins, Linear stability of plane Poiseuille flow of two superposed fluids, Phys. Fluids 31, 3225 (1988).
  22. B. S. Tilley, S. H. Davis, and S. G. Bankoff, Nonlinear long-wave stability of superposed fluids in an inclined channel, J. Fluid Mech. 277, 55 (1994).
  23. L. Ó Náraigh, P. Valluri, D. M. Scott, I. Bethune, and P. D. M. Spelt, Linear instability, nonlinear instability and ligament dynamics in three-dimensional laminar two-layer liquid-liquid flows, J. Fluid Mech. 750, 464 (2014).
  24. A. Kaffel and A. Riaz, Eigenspectra and mode coalescence of temporal instability in two-phase channel flow, Phys. Fluids 27, 042101 (2015).
  25. T. Tatsumi and T. Yoshimura, Stability of the laminar flow in a rectangular duct, J. Fluid Mech. 212, 437 (1990).
  26. V. Theofilis, P. W. Duck, and J. Owen, Viscous linear stability analysis of rectangular duct and cavity flows, J. Fluid Mech. 505, 249 (2004).
  27. T. Adachi, Linear stability of flow in rectangular ducts in the vicinity of the critical aspect ratio, Eur. J. Mech. B Fluids 41, 163 (2013).
  28. S. A. Orszag, Accurate solution of the Orr-Sommerfeld stability equation, J. Fluid Mech. 50, 689 (1971).
  29. Y. Nezihovski, A. Gelfgat, A. Ullmann, and N. Brauner, Experimental measurements versus linear stability analysis for primary instability of stratified two-phase flows in a square rectangular duct, Int. J. Multiphase Flow 153, 104061 (2022).
  30. D. Gorelik and N. Brauner, The interface configuration in two-phase stratified pipe flows, Int. J. Multiphase Flow 25, 977 (1999).
  31. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review (Courier Corporation, New York, 2000).
  32. A. Goldstein, A. Ullmann, and N. Brauner, Characteristics of stratified laminar flows in inclined pipes, Int. J. Multiphase Flow 75, 267 (2015).
  33. R. Lechouq, D. Sorensen, and C. Yang, ARPACK users' guide: Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods, Technical Report (1998).
  34. A. Goldstein, O. Eyal, A. Ullmann, and N. Brauner, Wall and interfacial shear stresses in laminar two-phase stratified flow in pipes, Int. J. Multiphase Flow 143, 103677 (2021).
  35. A. Goldstein and O. Eyal, Local behavior near triple point in a laminar two-phase flow in an arbitrary tube cross-section, Appl. Math. Modell. 99, 739 (2021).

Outline

Information

Phys. Rev. Fluids 9, 093901– Published 5 September, 2024
  • Received 10 March 2024
  • Accepted 21 August 2024
Crossmark - Check for updates button

©2024 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation