Hysing benchmark by Lionel Gamet

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Hysing benchmark

isosurface alpha=0.5 colored by U t=3.5s


This case is a reference test case for VoF simulations. It is the case number 26 of the 3D quantitative benchmark configuration by [1]. The case is also available as an example from the Basilisk website [1] and is detailed in the article of Cano-Lozano [1]. It consists in a single rising bubble in a large tank. In the physical conditions of this case, the rising bubble undergoes a spiralling path.

Setting up the test case in OpenFOAM

The bubble rises along +z direction and is initialized as a sphere at z_0/D_0 = 3:5, where D_0 is the bubble initial diameter. The fluid domain is of size 32x32x128 D_0.

The density ratio ρ_1/rho;_2 between the fluids is 1000 and the dynamic viscosity ratio μ_1/mu;_2 is 100. Index 1 refers to the continuous liquid phase while index 2 refers to the gas phase. The chosen Bond/Eotvos number Bo = ρ_1 g D_0^2= 10 and Galilei number Ga = (ρ_1 g^{1/2} D_0^{3/2})/μ_1 = 100.25 classify the current bubble in the oscillatory dynamics regime, with dominant inertial forces [2]. In the simulations, the gravity g and first phase density ρ_1 are taken as unity, which gives a surface tension σ = 0.1Nm^{-1} and a rise velocity of the order of unity.

The computational grid is obtained by local re�nements over a uniform background grid of 40x40x160 cells. The background grid defines the re�finement level 0, which thus corresponds to 1.25 cells per bubble diameter. A computational grid with re�finement level up to 4 in regions where the bubble can be present is then created with the snappyHexMesh mesh generator. The level 4 corresponds to a division of cells by a factor 2^4, and so to 20 cells per bubble initial diameter in the re�fined regions. In order to reduce the number of grid cells, the re�finement at the maximum level has been limited to regions in the centerline of the fluid domain, along the bubble rising direction. A re�finement cylindrical region of diameter 2D_0 is imposed for 2 < z/D_0 < 32. Then a cone of diameter varying between 2 and 4D_0 is used above for 32 < z/D_0 < 64. The top of the fluid domain is re�ned within a cylindrical region of diameter 4D_0 for 64 < z/D_0 < 126. The transition between levels is done through buffer layers of two cells (parameter nCellsBetweenLevels equal to 2 in snappyHexMeshDict). This method conducts to an overall grid size of 9.6 million cells.

A video of the case can be downloaded here.

The starting case case can be downloaded here.

The results can be found here.


[1] J. Cano-Lozano, C. Mart��nez-Baz�an, J. Magnaudet, and J. Tchoufag, Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability," Physical Review Fluids, vol. 1, no. 5, 2016. [2] M. K. Tripathi, K. C. Sahu, and R. Govindarajan, Dynamics of an initially spherical bubble rising in quiescent liquid," Nature Communications, vol. 6, 2015. [3] H. Scheuer and J. Roenby, Accurate and effcient surface reconstruction from volume fraction data on general meshes," J. Comp. Phys., vol. 383, pp.1-23, 2019. [4] L. Gamet, M. Scala, J. Roenby, H. Scheuer, and J.-L. Pierson, Validation of volume-of-fluid OpenFOAM isoAdvector solvers using single bubble benchmarks, Submitted to Computers and Fluids, 2020.

liquid phase fraction t=3s