Bubble growth detachment influence temporal spacial resolution Michael Alletto

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Bubble growth detachment influence spacial and temporal resolution

You can download the case files [1] here.

Introduction

In this tutorial we will examine the influence of the grid size and the Courant number on the flow of a bubble detaching from a flat surface. In a previous tutorial (see https://wiki.openfoam.com/Bubble_growth_detachment_influence_BC_domain_size_by_Michael_Alletto) we have analyzed the influence of the boundary conditions and the domain size on the same configuration considered here. In the previous tutorial we concluded that a domain radius of approximately 10 pipe diameter from which the bubble is released is enough to have near domain size independent solutions. Furthermore we found a suitable set of boundary conditions for which the flow we analyzed behaves as expected. This two investigation should always be done as first sensitivity studies when approaching a new configuration where one is not sure of the settings to choose. The next step to investigate a new problem should be to check the influence of the grid size and the time step size (in this case we will analyze the influence of the maximum Courant number). This two parameters are intrinsically connected to the discretization errors made. Ideally the error made compared to a known solution will approach to zero when the grid size and time step size becomes small enough (of course only if we solve the correct equation an we do not make any modeling errors). Since in our case we do not have an exact analytical solution, we expect that the change of the variable of interest (the detachment time of the bubble) will not substantially change if the grid size and time step size are small enough.


Simulation setup

The setup of the simulation was already described in https://wiki.openfoam.com/Bubble_growth_detachment_influence_BC_domain_size_by_Michael_Alletto. For this reason only the parameters important for this tutorial will be analyzed in more detail. Regarding the boundary condition the we chose the sets used together with the inflowOutflow conditions for the velocity U. The reason was that if a pressureInletOutletVelocity was used, for a fine grid backflow was observed. By choosing an inflowOutflow condition and setting the inflow velocity to zero, the backflow is prevented.

The next listing shows the fvSchemes dictionary. We used a first order Euler scheme for the temporal discretization. Regarding the convective fluxes, we used a Gauss limitedLinearV 1 scheme for the convective fluxes in the momentum equation. The limited linear schemes in openfoam limit the linear schemes towards an upwind scheme in regions of rapidly changing flow (see https://cfd.direct/openfoam/user-guide/v6-fvschemes/). The basic idea of the limited schemes (which are similar to the bounded schemes) is to avoid numerical oscillation when interpolating the variable from the cell center to the face center which are common to higher order schemes. For the tails see the book of [1]. The vanLeer scheme belongs also to the class of limited schemes. The divergence of the indicator function alpha however is not used in interIsoFoam since a geometric reconstruction is used. It is used in interFoam. The same holds for the term div(phirb,alpha).

References

[1] Fadl Moukalled, L Mangani, Marwan Darwish, et al. The finite volume method in computational fluid dynamics, volume 113. Springer, 2016.

[2] Stéphane Popinet. Numerical models of surface tension. Annual Review of Fluid Mechanics, 50:49–75, 2018.

[3] Henning Scheufler and Johan Roenby. Twophaseflow: An openfoam based framework for development of two phase flow solvers. arXiv preprint arXiv:2103.00870, 2021.

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