This section describes the Volume-of-Fluid (or “VOF”) model, which is one type of the Eulerian two-phase flow model. The VOF model [38] uses a different transport model than the mixture Eulerian two-phase model. It is designed to track the interface between the two phases in an accurate manner. In computational cells where both phases are present, the two phases are assumed to be immiscible, and an interface is constructed. The transport of liquid and gas mass (or volumes) is calculated by considering how the interface is positioned in the cell.

The VOF model in Ansys Forte uses liquid volume fraction () to track the phase concentrations in the flow field. We consider liquid and gas as two immiscible fluids, and that . The evolution of liquid volume fraction is governed by the following transport equation:

(11–17)

where is the flow velocity, and is a source term due to compressibility effects. The equation indicates that the liquid volume fraction is affected by flow transport and is subject to local compressibility effects. For simplicity of presentation, we drop the variables' notations for turbulence modeling in this section.

Convection of the liquid volume fraction should be computed with very limited numerical diffusion in order to preserve the sharpness of interface. For this purpose, the “Compressive Interface Capturing Scheme for Arbitrary Meshes” (CICSAM) by Ubbink [99] is used. This method is described in Convection Scheme for the Volume Fraction Equation.

Convection of liquid and gas mass should be computed consistently with that of liquid volume fraction. In cases where liquid and gas are mixtures of species, the following species conservation equations are used to convect the liquid and gas species:

(11–18)

(11–19)

where is the mass fraction of species in the liquid mixture, and is the mass fraction of species in the gas mixture. The effects of species diffusion, turbulence, and chemistry are not considered in the species transport. Computing Equation 11–18 and Equation 11–19 requires the liquid and gas volumes convected across the control volume faces, which have been obtained from the solutions of Equation 11–17 and the method described in Convection Scheme for the Volume Fraction Equation. The liquid and gas density and species mass fractions at the control volume faces are estimated using an upwind method.

In Ansys Forte, the above convection calculations occur in the "rezone" stage (or Stage 3), as mentioned in Temporal Differencing Method in the Ansys Forte Theory Manual. Therefore, as in the methods for non-VOF models, the convection calculations are fully explicit. However, the described explicit method used for the VOF model is different from the "quasi-second-order upwind" (QSOU) method referred to in Convective Flux Discretization.

In the transport equation for the volume fraction (Equation 11–17), the source term used for compressibility effects () is applied by enforcing pressure equilibrium between the two phases (that is, ), as well as the Equation-of-State for the gas (Equation 11–3) and liquid (Equation 11–5), respectively.

It is also assumed that the two phases are in momentum equilibrium, such that they have the same flow velocity. Therefore, the Momentum Conservation Equation, (Equation 2–3 and Equation 2–4) are applied to the VOF model.

The two phases are also assumed to have the same temperature. The energy conservation Equation 2–5, Equation 2–6 can be modified for the VOF model and written as:

(11–20)

where is the specific internal energy of the liquid mixture and is the specific internal energy of the gas mixture. Their relations with the temperature are given by Equation 11–6 and Equation 11–4, respectively, and they are related to the two-phase mixture's specific internal energy () by Equation 11–2. While the source terms related to combustion and sprays are omitted, the terms on the right hand side of Equation 11–20 are the same as those in Equation 2–5, because the same physics, such as pressure work, heat conduction, enthalpy diffusion and turbulent dissipation, are considered.

If any turbulence model is used, the liquid and gas phases are assumed to have the same turbulence quantities (such as turbulent kinetic energy and turbulent dissipation rate) in the cell. The same transport equations for the turbulence quantities as presented in Turbulence Models are applied in the VOF model.