31 May 2021 to 4 June 2021
Europe/Berlin timezone

An energy-preserving MAC numerical scheme for the Volume Of Fluid method and application on Taylor flows

2 Jun 2021, 15:00
15m
Oral Presentation (MS6-B) Interfacial phenomena in multiphase systems MS6-B

Speaker

Mohamed Id Moulay (Institut Des Mécaniques Des Fluides De Toulouse)

Description

This work focuses on numerical simulations of two-phase flows in porous media at pore-scale in the framework of Volume Of Fluids (VOF) methods. The numerical scheme consists in solving on staggered grids the transport equation for the color function using an alternate directions algorithm together with the variable density incompressible Navier-Stokes equations using a pressure correction technique. A particular attention is paid to the discretization of the surface tension forcing term performed within the Continuum Surface Force formalism. Following the pioneering work of Jacqmin [1], we propose here an energy-conserving numerical scheme that consists in estimating the capillary force following a convex combination of the curvature with respect to the color function.The implementation is carried out in the CAFIF3S platform, a parallel open-source multiphase flow solver developed by IRSN and used for a wide range applications, including laminar or turbulent flows [2].
To validate our approach, we evaluate our results against several benchmark and test cases available in the literature. We first compare the energy-balanced discretization to the CSF Brackbill for a static bubble. An advanced comparison is carried out for the quantification of spurious currents using dimensionless velocity and vorticity for different Laplace numbers. We find that our scheme reduces spurious currents compared to CSF and generally performs well against other approaches that do not use a surface reconstruction (Abadie & al [3]). In a second step, we focus on the drainage of a liquid phase in a vertical cylindrical tube for a range of capillary numbers. We compare our results for film thickness against numerical approaches in the literature and the Bretherton model, as presented in Lasseux [4]. We find good agreement for several capillary numbers with Horgue & al [5], Lasseux [4] and the Bretherton model. We further discuss the robustness of our approach and general guidelines for optimizing mesh.
At last, we consider Taylor bubbles in a horizontal cylindrical tube, as presented in Gupta & al [6]. This type of flow is characterized by the presence of elongated bubbles, with diameters close to the width of the tube, that are separated by liquid plugs. The flow also features liquid films along the wall, which depend on the capillary number and can be extremely thin, thus posing a numerical challenge. A mesh convergence study is carried out for the calculation of film thicknesses. Our results are in good agreement with those of the benchmark. We also study of spurious currents at the interface as well as bubble shapes and gas hold-up.

References

[1] D. Jacqmin, Calculation of two-phase Navier–Stokes flows using phase-field modeling, J. Comput. Phys. 155 (1) 96–127, 1999.
[2] CALIF3S web page: https://gforge.irsn.fr/gf/project/calif3s
[3] T. Abadie, J. Aubin, D. Legendre, On the combined effects of surface tension force calculation and interface advection on spurious currents within Volume of Fluid and Level Set frameworks. Journal of Computational Physics. 297. 2016.
[4] D. Lasseux, Caractérisation expérimentale, analytique et numérique d’un film dynamique lors du drainage d’un capillaire, Ph.D. thesis, Université de Bordeaux I, 1990.
[5] P. Horgue, F. Augier, M. Quintard, M. Prat, A suitable parametrization to simulate slug flows with the Volume-Of-Fluid method. Comptes Rendus Mécanique. 340. 411 - 419; 2012.
[6] R. Gupta, D. Fletcher, B. Haynes, On the cfd modelling of Taylor flow in microchannels, Chem. Eng. Sci. 64.2941–2950, 2009.

Time Block Preference Time Block B (14:00-17:00 CET)
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Primary authors

Mohamed Id Moulay (Institut Des Mécaniques Des Fluides De Toulouse) Yohan Davit (Institut de Mécanique des Fluides de Toulouse) Mr Fabien Duval (Institut de Radioprotection et de Sûreté Nucléaire (IRSN)) Mr Jean-Claude Latché (Institut de Radioprotection et de Sûreté Nucléaire (IRSN)) Michel Quintard (Institut de Mécanique des Fluides de Toulouse)

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