Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-17T13:21:00.220Z Has data issue: false hasContentIssue false
  • English
  • Français

Direct numerical simulations of two-phase flow in an inclined pipe

Published online by Cambridge University Press:  20 July 2017

Fangfang Xie Open the ORCID record for Fangfang Xie [Opens in a new window] ,
Xiaoning Zheng ,
Michael S. Triantafyllou Open the ORCID record for Michael S. Triantafyllou [Opens in a new window] ,
Yiannis Constantinides ,
Yao Zheng  and
George Em Karniadakis
Fangfang Xie
Affiliation:
School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, ZJ 310027, China Department of Mechanical Engineering, Massachusetts Institute Technology, Cambridge, MA 02139, USA
Xiaoning Zheng
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Michael S. Triantafyllou*
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute Technology, Cambridge, MA 02139, USA
Yiannis Constantinides
Affiliation:
Chevron Energy Technology Company, Houston, TX 77002, USA
Yao Zheng
Affiliation:
School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, ZJ 310027, China
George Em Karniadakis
Affiliation:
Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the instability mechanisms leading to slug flow formation in an inclined pipe subject to gravity forces. We use a phase-field approach, where the Cahn–Hillard model is used to model the interface. At the inlet, a stratified flow is imposed with a specified velocity profile. We validate our numerical results by comparing against previous theoretical models and by predicting the various flow regimes for horizontal and inclined pipes, including stratified flow, slug flow, dispersed bubble flow and annular flow. Subsequently, we focus on slug formation in an inclined pipe and connect its appearance with specific vortical dynamics. A two-dimensional channel geometry is first considered. When the heavy fluid is injected as the top layer, inverted vortex shedding emerges, which periodically impacts on the bottom wall, as it develops further downstream. The accumulation of heavy fluid in the bottom wall causes a back flow that induces rolling waves and interacts with the upstream jet. When the heavy fluid is placed as the bottom layer, the heavy fluid accumulates and initially forms a massive slug at the bottom region, close to the inlet. Subsequently, the heavy fluid slug starts to break into smaller pieces, some of which translate along the pipe. During the accumulation phase, a back flow forms also generating rolling waves. Occasionally, a rolling wave can reach the top of the pipe and form a new slug. To describe the generation of vorticity from the two-phase interface and pipe walls in the slug formation, we study the circulation dynamics and connect it with the resulting two-phase flow patterns. Finally, we conduct three-dimensional (3-D) simulations in a circular pipe and compare the differences between the 3-D flow patterns and its circulation dynamics against the 2-D simulation results.

JFM classification

Instability: Instability Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 189 - 207
Check for updates
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barnea, D. & Taitel, Y. 1993 A model for slug length distribution in gas–liquid slug flow. Intl J. Multiphase Flow 19 (5), 829–838.Google Scholar
Batchelor, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Bendiksen, K., Malnes, D., Straume, T. & Hedne, P. 1990 A non-diffusive numerical model for transient simulation of oil–gas transportation systems. In Proc. 1990 European Simulation Multiconference, pp. 508–515. SCS Europe.Google Scholar
Bratland, O.2010 Pipe Flow 2: Multi-phase Flow Assurance http://www.drbratland.com/.Google Scholar
Brøns, M., Thompson, M. C., Leweke, T. & Hourigan, K. 2014 Vorticity generation and conservation for two-dimensional interfaces and boundaries. J. Fluid Mech. 758, 63–93.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2002a Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 17–52.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2002b Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech. 466, 53–84.CrossRefGoogle Scholar
Campbell, B. K.2015 A mechanistic investigation of nonlinear interfacial instabilities leading to slug formation in multiphase flows. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Dong, S. & Shen, J. 2012 A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios. J. Comput. Phys. 231 (17), 5788–5804.Google Scholar
Dukler, A. E. & Hubbard, M. G. 1975 A model for gas–liquid slug flow in horizontal and near horizontal tubes. Ind. Engng Chem. Fundam. 14 (4), 337–347.Google Scholar
Esmaeeli, A. & Tryggvason, G. 1998 Direct numerical simulations of bubbly flows. Part 1. Low reynolds number arrays. J. Fluid Mech. 377, 313–345.CrossRefGoogle Scholar
Esmaeeli, A. & Tryggvason, G. 1999 Direct numerical simulations of bubbly flows. Part 2. Moderate reynolds number arrays. J. Fluid Mech. 385, 325–358.Google Scholar
Fabre, J. & Liné, A. 1992 Modeling of two-phase slug flow. Annu. Rev. Fluid Mech. 24 (1), 21–46.CrossRefGoogle Scholar
Guermond, J.-L., Pasquetti, R. & Popov, B. 2011 Entropy viscosity method for nonlinear conservation laws. J. Comput. Phys. 230 (11), 4248–4267.CrossRefGoogle Scholar
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (vof) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201–225.Google Scholar
Issa, R. I. & Kempf, M. H. W. 2003 Simulation of slug flow in horizontal and nearly horizontal pipes with the two-fluid model. Intl J. Multiphase Flow 29 (1), 69–95.CrossRefGoogle Scholar
Karniadakis, G. E. & Sherwin, S. J. 2013 Spectral/hp Element Methods for Computational Fluid Dynamics, 2nd edn. Oxford University Press.Google Scholar
Morton, B. R. 1984 The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28 (3–4), 277–308.CrossRefGoogle Scholar
Nagrath, S., Jansen, K. E. & Lahey, R. T. 2005 Computation of incompressible bubble dynamics with a stabilized finite element level set method. Comput. Meth. Appl. Mech. Engng 194 (42), 4565–4587.CrossRefGoogle Scholar
Rosenhead, L. 1963 Laminar Boundary Layers. Clarendon Press.Google Scholar
Sanchez-Silva, F., Carvajal-Mariscal, I., Toledo-Velázquez, M., Libreros, D. & Saidani-Scott, H. 2013 Experiments in a combined up stream downstream slug flow. In EPJ Web of Conferences, vol. 45, p. 01082. EDP Sciences.Google Scholar
Sausen, A., de Campos, M. & Sausen, P. 2012 The Slug Flow Problem in Oil Industry and Pi Level Control. INTECH Open Access Publisher.CrossRefGoogle Scholar
Shoham, O. 2006 Mechanistic Modeling of Gas–Liquid Two-Phase Flow in Pipes, Society of Petroleum Engineers.Google Scholar
Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1), 146–159.Google Scholar
Taitel, Y. & Barnea, D. 1990 Two-phase slug flow. Adv. Heat Transfer 20, 83–132.Google Scholar
Taitel, Y. & Dukler, A. E. 1976 A model for predicting flow regime transitions in horizontal and near horizontal gas–liquid flow. AIChE J. 22 (1), 47–55.Google Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y. J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759.Google Scholar
Yue, P., Feng, J. J., Liu, C. & Shen, J. 2004 A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293–317.Google Scholar
Zheng, G., Brill, J. P. & Taitel, Y. 1994 Slug flow behavior in a hilly terrain pipeline. Intl. J. Multiphase Flow 20 (1), 63–79.Google Scholar
Zheng, X., Babaee, H., Dong, S., Chryssostomidis, C. & Karniadakis, G. E. 2015 A phase-field method for 3d simulation of two-phase heat transfer. Intl J. Heat Mass Transfer 82, 282–298.Google Scholar
Zheng, X. & Karniadakis, G. E. 2016 A phase-field/ale method for simulating fluid-structure interactions in two-phase flow. Comput. Meth. Appl. Mech. Engnng 309 (1), 19–40.CrossRefGoogle Scholar

Xie et al. supplementary movie 1

Evolution of two-phase flow patterns in a 2D upward inclined channel at θ = 30◦ . At the inlet, the heavy fluid is placed at the top layer. Blue color stands for the heavy fluid, while red stands for the light fluid. See Figure 7 in the paper.

Download Xie et al. supplementary movie 1(Video)
Video 4.2 MB

Xie et al. supplementary movie 2

Evolution of vorticity contours for two-phase flow in a 2D upward inclined channel at θ = 30◦ . At the inlet, the heavy fluid is placed at the top. Note that colors denote vorticity intensity and should not be confused with the colors denoting heavy and light fluid. See Figure 8 in the paper.

Download Xie et al. supplementary movie 2(Video)
Video 4.2 MB

Xie et al. supplementary movie 3

Evolution of two-phase flow patterns in a 2D upward inclined channel θ = 30◦ . At the inlet, the heavy fluid is placed at the bottom. Blue stands for the heavy liquid, while red stands for the light fluid. See Figure 9 in the paper.

Download Xie et al. supplementary movie 3(Video)
Video 8.8 MB

Xie et al. supplementary movie 4

Evolution of vorticity contours for two-phase flow in a 2D upward inclined channel θ = 30◦ . At the inlet, the heavy fluid is placed at the bottom. See Figure 10 in the paper.

Download Xie et al. supplementary movie 4(Video)
Video 8.7 MB