The Eulerian two-phase model considers the working fluid as a two-phase mixture in general, which can be gas, liquid, or a mixture of both. Both liquid and gas are treated as a continuum. The two phases are assumed to have equal velocities, temperatures, and pressures in each computational cell, so that single momentum and energy conservation equations are applied for the two-phase mixture.

In this method, the mass, momentum, and energy conservation equations described in Basic Governing Equations can be applied for the two-phase mixture but the equation-of-state needs modifications, as described below. For simplicity, combustion and sprays are not considered in this model. A different Equation of State is needed to account for the thermodynamics of the fluid. In a general case, a computational cell is filled with a two-phase mixture. It is assumed that the masses, volumes, and internal energies of each phase add up to those of the mixture, therefore,

(11–1)

(11–2)

where and are the density and specific internal energy of the two-phase mixture, is the gas phase mass fraction which could vary between zero and one, and are the densities of the gas and liquid phases, and and are the specific internal energies of the gas and liquid phases, respectively.

The gas phase's Equation of State has been described in Gas-phase Mixture Equation of State. Both the ideal gas law and the real gas model can be applied to the gas phase in the two-phase mixture. Taking the ideal gas law as an example, the thermodynamic relations Equation 2–7 and Equation 2–8 can be applied to the gas phase in the two-phase mixture and are re-written as:

(11–3)

and

(11–4)

in which subscript refers to species in the gas phase.

For the liquid phase, a linear pressure-density relation is applied to consider the compressibility effects:

(11–5)

where is a reference density of the liquid at the reference pressure, , which is taken as one atmospheric pressure. The reference density () can be temperature-dependent or constant. Either one of the three density relations available in Ansys Chemkin (Liquid Species Density Models in the Chemkin Theory Manual) can be used to specify the reference density, depending on which type of relation is used when the liquid species are defined in the surface kinetics file. The linear coefficient is equal to , where is the speed of sound in the liquid.

The specific internal energy of the liquid mixture () is a mass-average of the specific internal energy of individual liquid species (), which are tabulated with respect to temperature:

(11–6)

Both liquid and gas phases are assumed to be compressible, therefore the Eulerian two-phase model is a compressible flow model. In pure liquid simulations, a trivial amount of gas (1e-6 by mass fraction) is assumed to be mixed with the liquid. The presence of small amounts of gas represents impurities in the liquid. In general, this inclusion is helpful in maintaining numerical stability.

Ansys Forte includes two types of Eulerian two-phase models, mixture Eulerian two-phase model, and Volume of Fluid (VOF) model. They are introduced in Mixture Eulerian Two-Phase Model and Volume-of-Fluid (VOF) Model, respectively.