Difference between revisions of "The stationary droplet by Lionel Gamet"

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[[File:StDrop2D_scheme.png|280px|center|Bubble 26 trajectory for isoAdvector iso-Alpha. Courtesy from [4].]]
 
[[File:StDrop2D_scheme.png|280px|center|Bubble 26 trajectory for isoAdvector iso-Alpha. Courtesy from [4].]]
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The 2D case setup is schematized in the Figure above. The phase 1 is the liquid, while the phase 2 is the gas. Both fluids have the same viscosity μ and density ρ. The volume fraction α is set to 1 inside the droplet near the bottom left corner, and to 0 outside. The density ρ and the surface tension σ between the two fluids are both taken as unitary constant values. The droplet has an initial diameter D_0 = 2R_0 = 0.8 m. Only a quarter of the 2D geometry is simulated in a domain of size 1x1 m. The droplet is placed at the bottom left corner of the domain. All boundary conditions are symmetries. This test case can easily be extended to 3D, where 1/8th of an initially spherical droplet is then simulated.
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Ideally, the static droplet test case is not supposed to generate any velocity field and the pressure field should follow the Laplace pressure jump at the interface. However, parasitic velocities (also called spurious currents) can occur from a numerical imbalance between the discretization errors of the pressure gradient and surface tension terms.
  
 
==References==
 
==References==

Revision as of 05:19, 17 September 2020

Go back to Multiphase modeling.

The stationary droplet

The starting cases case can be downloaded here:

Reference OpenFOAM results of the stationary droplet can be found here.

Introduction

This case is a reference test case for Volume-of-Fluid (VoF) simulations. This benchmark configuration allows for quantitative measurements of the spurious currents appearing in VoF simulations. The case consists in a single static droplet in a quiescent liquid under zero gravity. It is a widely used test case in the literature, described by Popinet [1]. More details can be found in the iterature [1,2,3,4,5] and in the article in press of Gamet et al. [6].

Bubble 26 trajectory for isoAdvector iso-Alpha. Courtesy from [4].

The 2D case setup is schematized in the Figure above. The phase 1 is the liquid, while the phase 2 is the gas. Both fluids have the same viscosity μ and density ρ. The volume fraction α is set to 1 inside the droplet near the bottom left corner, and to 0 outside. The density ρ and the surface tension σ between the two fluids are both taken as unitary constant values. The droplet has an initial diameter D_0 = 2R_0 = 0.8 m. Only a quarter of the 2D geometry is simulated in a domain of size 1x1 m. The droplet is placed at the bottom left corner of the domain. All boundary conditions are symmetries. This test case can easily be extended to 3D, where 1/8th of an initially spherical droplet is then simulated.

Ideally, the static droplet test case is not supposed to generate any velocity field and the pressure field should follow the Laplace pressure jump at the interface. However, parasitic velocities (also called spurious currents) can occur from a numerical imbalance between the discretization errors of the pressure gradient and surface tension terms.

References

[1] S. Popinet: An accurate adaptive solver for surface-tension-driven interfacial flows," Journal of Computational Physics, vol. 228, no. 16, pp. 5838-5866, 2009.

[2] M. M. Francois, S. J. Cummins, E. D. Dendy, D. B. Kothe, J. M. Sicilian, and M. W. Williams: A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework," Journal of Computational Physics, vol. 213, no. 1, pp. 141-173, 2006.

[3] S. Popinet: A quadtree-adaptive multigrid solver for the serre-green-naghdi equations," Journal of Computational Physics, vol. 302, pp. 336-358, 2015.

[4] --: Numerical models of surface tension," Annual Review of Fluid Mechanics, vol. 50, pp. 49-75, 2018.

[5] T. Abadie, J. Aubin, and 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, vol. 297, pp. 611-636, 2015.

[6] L. Gamet, M. Scala, J. Roenby, H. Scheufler, and J.-L. Pierson: Validation of volume-of-Fluid OpenFOAM isoAdvector solvers using single bubble benchmarks," Submitted to Computers and Fluids, 2020.

[7] H. Scheufler and J. Roenby: Accurate and effcient surface reconstruction from volume fraction data on general meshes," J. Comp. Phys., vol. 383, pp. 1 - 23, 2019.