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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]
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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
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Copyright
© 2017 Cambridge University Press 

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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