Ansys Forte includes a generalized turbulence-chemistry interaction model that is adapted from the work of Kong et al. [[44] , [45] ], which was previously applied to simulations of Diesel engines. This model is included in Ansys Forte as an option and is intended for simulating turbulence effects on combustion kinetics.

This mixing time-scale model considers that the combustion chemistry should be partly controlled by the breakup of turbulent eddies due to the imperfect mixing of fuel and oxidizer in an actual engine process. The model assumes every species moves towards its local equilibrium values with a time scale of τ _eff and thus the effective (or actual) production rate of species k are expressed as

(2–50)

where the effective time scale is related to the chemical time scale τ _chem and the turbulent scalar mixing time scale τ _mix as

(2–51)

The local chemical time scale is defined as the time it would take the mixture to reach equilibrium under the conditions within the computational cell. The turbulent scalar mixing time scale is obtained from the local turbulent kinetic energy and dissipation rate:

(2–52)

A relationship between the effective species production rate and the kinetic-only species production rate is derived from Equation 2–54 as

(2–53)

The effective species production rates that are directly used in kinetics integration are then

(2–54)

In this way the gas composition and temperature remain consistent.

The model constant C _tki is one of the turbulence model constants and is provided as the Mixing Time Coefficient user input parameter in Ansys Forte when the Turbulence Kinetics Interaction option is turned on. A value of 1.5 is found to be appropriate, based on engine simulation studies.

To ensure that the effective species production rates do not go to zero when the turbulent mixing time scale is very large, the Turbulence Kinetics Interaction model is turned OFF when the τ _mix value is above 1 millisecond.