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 refinements over a uniform background grid of 40x40x160 cells. The background grid defines the refinement level 0, which thus corresponds to 1.25 cells per bubble diameter. A computational grid with refinement 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 refined regions. In order to reduce the number of grid cells, the refinement at the maximum level has been limited to regions in the centerline of the fluid domain, along the bubble rising direction. A refinement 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 refined 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