The Volume of Fluid (VOF) Method: An Introduction
Oil and water don’t mix, as most engineers are aware, unless you ask a computer. In a free surface analysis, multiple fluids are modeled using the volume of fluid approach in computational fluid dynamics (CFD). Our experienced engineering services ignore the antiquated VOF theory and instead concentrate on realworld application.
The volume fraction is a new transport equation that VOF adds for simulations involving two fluids. We need new boundary conditions because of the additional transport equation, and mesh modifications are also necessary for VOF modeling. Now let’s talk about the specifics of VOF modeling.
Interphase Mass Transfer between Fluids
Interphase transfer of mass (phase change), species, energy, and momentum, including surface tension, can also be included, allowing the modeling of numerous multiphase flow conditions.
Given the complexities and specific parameters required for practical application, SimuTech Group offers consulting services to businesses in need of adhoc or continuous services in free surface analysis of general fluid engineering.
Free Surface Analysis  Recent CFD Projects
Biomedical Device
Analyzed the atomization of a liquid stream into droplets before automated sorting, which captured the laminar surface tensiondriven breakup at the free surface.
Large Ocean Vessel
Calculated the transient pressure and shear loading on a large oceangoing vessel while moving through different sea states.
Spincoating
Calculated the film distribution and thickness during the spin coating process at various rotational speeds and therefore high gforce loaded films for various viscous liquids.
Mixing Tank
Calculated the height deformation of a free surface with its vortex calculation from added momentum of a highspeed impeller in a biomedical mixing tank.
Water Storage Tanks
Predicted diurnal flow patterns to ensure effective water replacement in a wastewater storage tank.
Boundary Conditions for Fluid Volume Fraction
For the volume fraction, new boundary conditions were needed for VOF modeling. Which fluid (or portion of both fluids) fills each mesh cell is indicated by this volume fraction. Over the course of the domain, the volume fraction varies. The volume fraction frequently needs to alter with vertical position in order to replicate a fluid water level.
Instead of defining the border condition as a single value, define it as a mathematical function. All of your fluid’s limits, including inlets, outlets, and your body, should be subject to the vertical variation.
The pressure equation is an additional modeling modification. Free Surface Analysis Consulting would lead engineers to understanding the boundary conditions, now taking into account hydrostatic pressure, which varies with vertical location.
To find out how your software manages the hydrostatic pressure, consult your solver. Some take hydrostatic pressure into account. Some also include it. In any event, while defining boundary conditions, hydrostatic pressure must be taken into consideration.
VOF for Ship Resistance and Free Surface Flow
Let’s now concentrate on two common uses for VOF modeling: ship resistance analyses and free surface flow. Our meshing approach and expectations for simulation stability are impacted by this application. The sole interface between air and water is a key characteristic of unrestricted surface flow.
Free surface flow simulates a single continuous contact between the air and the water, in contrast to industrial flow scenarios that might imitate bubbles. This produces a discrete area where the meshing can be concentrated.
The volume fraction should preferably shift from a value of 0 to 1 in the span of 1 to 2 cells in order to accurately represent that airwater interface. Unfortunately, reality rarely reflects idealism.
Rapid changes in volume fraction are not supported by interpolation models for volume fraction. High resolution interface compression (HRIC), developed by CFD developers, attempted to address issue, however it was not entirely successful. The CFD engineer must instead use a modeling approach.
You must focus the mesh for the modeling solution in the areas where you anticipate changes in the volume fraction. With 6–12 cells spanning the zone of transition, the vertical cell spacing is between 10–20 percent of the normal cell size. If you need to account for waves, the transition region expands.
Unreasonably high cell counts can, unfortunately, quickly result from accurate resolution of the transition area. One of the main modeling issues CFD engineers have in VOF modeling is balancing mesh resolution with mesh size.
VOF Instability Modeling
Instability is another effect of VOF modeling on the simulation.
To ensure simulation stability, you might need to switch to first order interpolation on the volume fraction. Additionally, anticipate a rise of at least 1 x 102 in all residuals in the momentum and pressure equations.
Monitors are superior to residuals when checking the convergence of VOF simulations. Simulation stability is not guaranteed by VOF modeling.
However, with supplemental field analysis provided by SimuTech Group fluids engineers, we guarantee the model will be as accurate as computationally possible.
Free Surface Post Processing  Creating an IsoSurface
Based on the Variable of the Volume Fraction
Every SimuTech Group client wants to view the free surface while post processing ship free surface models. They are often looking for a surface that delineates the boundary between the water and the air. The issue is that VOF only measures the amount of each fluid phase in each cell, not the interface.
Now, let’s quickly review making an isosurface based on the variable of the volume fraction to produce a free surface. Put the volume fraction at 0.5, which is the ratio of the two fluid phases. The boundary between air and water is here. The free surface is represented by that transition.
Check a volume plot as well as another visualization for quality assurance. Cells with a volume percent between 0.10 and 0.90 should be plotted out. The area of transition is represented by this.
The area where the fluid is clearly not water or air is known as the transition region. It looks more like spray or fog, which is not how free surface flow actually occurs. The bulk of the cells in a shipfree surface flow should be made up of either water or air, which corresponds to a volume fraction of 0 to 1.
Additionally, the transition region, where the volume fraction is between 0.10 and 0.90, should continue to be minimal. The transition region can be checked using the volume plot by the CFD engineer to make sure it stays small and the simulation accurately represents reality.
Don’t Hesitate to Ask for Advanced CFD Modeling Support
The volume of fluid approach brings up new possibilities for sophisticated modeling, which calls for more preparation on the part of the CFD engineer.
The volume fraction requires new boundary conditions that change with vertical position. Keep hydrostatic pressure in mind. The meshing method became increasingly intricate, necessitating further improvements at the free surface transition.
While we recommend Ansys Fluent, some CFD analysis software toolkit will be required for postprocessing to see the free surface. Volume of fluid (VOF), in short, is difficult to define. This is why we strongly recommend seeking advice from engineering experts for expensive projects which require computational accuracy and swift execution.
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Numerical modeling of complex free surface flows