VOF Methodology

This Eulerian multi-phase flow methodology is used to capture flows with sharp inter-faces, such as single-droplet dynamics, fuel atomisation, droplet impingement processes, droplet detachment from solid surfaces, tank-filling etc. The method is flexible and economical compared to other Eulerian multi-phase flow methodologies while it has proven reliable in simulating a wide variety of problems.  

The method is based on the solution of a transport equation for a variable “α” (often also referred as indicator function) for the liquid phase. Variable α takes value 0 in the region of pure gas and value of 1 in the region of pure liquid while the non-conservative form of the equation for the mass should be used for deriving the pressure equation. For the indicator equation α, the CICSAM scheme is used, which can handle the density changes across the interface and reduce numerical diffusion in these areas. The convective and normal diffusion terms are discretised using second order upwind schemes. The cross diffusion terms and the second order derivatives are discretised using standard central difference scheme. Time step is adjusted during the solution so that local Courant number does not exceed 0.4. The Crank–Nicholson implicit time differencing is used for the time term discretisation. Calculation of the local radii of curvature of the interface allows calculation of the surface tension forces according to the continuum surface force model CSF, which are added to the momentum equations. Moderate smoothing of the radii of curvature is also available.

To overcome the inherited disadvantage of the method that the transitional region between the liquid and the gas phase (which in reality should be close to zero) at the best case is equal to the grid distance, adaptive grid local refinement around the gas–liquid interface is used. The criterion for the mesh refinement is usually the solution accuracy and/or the gradient of a variable. The remapping or transfer of the variables from one grid to another is done by interpolating the values of the closest cells, using the inverse distance between the cell centres. This method is not conservative, but it is fast, especially when using unstructured meshes. Moreover, the grid in the vicinity of the interface does not change when creating the grid for the new time step since this is always refined up to a distance around the interface and thus, the variables in the region of interest are transferred accurately.

In addition to the standard VOF method, important modifications have been developed in order to capture flow problems with heat transfer and variable fluid properties, more than two fluids (multi-VOF) and phase-change. The multi-VOF solver, accounts for n-VOF equations to be solved for all additional n-fluids. Phase-change is considered in two different ways. In the first one evaporation through a gas-liquid interface is considered. The local vaporisation rate is calculated from kinetic theory evaporation models. In the second case, formation of vapour from the bulk of the liquid is included. This approach is used to calculate boiling processes.

Examples and validation cases using the different VOF options can be found in the following links.

    VOF Sample Cases

    VOF Validation Cases

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