In order to model fluid flow turbulence, the Euler–Euler Model, Turbulent Flow interface uses the k-ε turbulence model. This is realized by solving transport equations for the kinetic energy k (SI unit: m2/s2) and the dissipation rate of turbulent kinetic energy ε (SI unit: m2/s3).

The interface includes the possibility to model the turbulent flow of the two-phase mixture, or to solve for turbulent flow of each phase separately. In the former case, one set of k-ε equations are solved, while in the latter two sets of k-ε equations are solved for, one for each phase.

Mixture turbulence assumes that the turbulence effects on both the continuous and dispersed phase can be modeled by solving for the turbulence of the resulting two-phase mixture. Here this is done using a two-equation k-ε model where the transport of turbulence quantities is based on based on the mass-averaged mixture velocity

Setting the Two-phase turbulence interface property to Mixture, the turbulence of the two-phase flow is modeled by solving the following k and ε equations:

The equations correspond to the standard two-equation k-ε model including realizability constraints.

where Cμ is a model constant. The viscous stress tensors for the phases are hence defined as

where σT is a turbulent particle Schmidt number (dimensionless).

The phase specific Two-phase turbulence model assumes that the turbulent flow of the continuous and dispersed phase can be modeled by solving for the turbulence of each phase separately by using two sets of k-ε equations. The model implies that the time scales of the turbulent flow of each phase can differ, but it is also computationally more expensive than assuming solving one set of k-ε equations for the mixture.

Setting the Two-phase turbulence interface property to Phase specific, the turbulent flow of the two phases is modeled by solving two sets of k and ε equations, one for each phase. For the continuous phase, the transport equations for k and ε are

The equations for each phase correspond to the standard two-equation k-ε model including realizability constraints.

where Cμ,c and Cμ,d are model constants. The viscous stress tensors for the phases are hence defined as

As in the case of mixture turbulence, the dispersion of the particulate phase by the turbulent fluctuations is modeled using a gradient based hypothesis (Equation 6-89). For phase-specific turbulence the dispersion coefficient is modeled as a volume average of the respective turbulent diffusivity of each phase

using a turbulent particle Schmidt number σT,d (dimensionless).