In many industrial applications, the flows of working fluids that are considered are turbulent, multi-phase, and chemically reactive in general. Ansys Forte applies a turbulent reacting flow representation, in which the basic fluid dynamics are governed by the Navier-Stokes equations. Model transport equations of mass, momentum, and energy conservation laws are formulated for the continuum-based compressible flows, and represent the turbulent nature of the flow. In certain applications, when liquid sprays are injected into the gas flow, exchange functions are used to account for the interaction between the gas and the liquid droplets. Beyond these models, the main assumptions made in the derivation of the governing equations are the use of thermodynamic equation of state, the use of Fick's law for mass diffusion, the assumption of Newtonian fluid, and the use of Fourier's law for thermal diffusion.

Turbulent flow is characterized by a wide range of flow length scales as well as significant and irregular variations of the flow field. Ansys Forte offers two options of turbulence modeling. The first option is the Reynolds-Averaged-Navier-Stokes (RANS) approach, which aims at capturing the ensemble average of the flow field from many realizations of flows under equivalently set conditions. Since an important effect of turbulence is more effective transport and mixing of fluid compared to a laminar flow, the ensemble average of the turbulent transport and mixing is analogous to a large-scale diffusion. The RANS approach removes the necessity of resolving small-scale structures and fluctuations seen in individual flow realizations, while retaining the main effects of turbulence on the averaged flow and combustion characteristics.

To accomplish this, the Favre average is employed to represent an instantaneous quantity, such as the flow velocity vector , into an ensemble average and a fluctuating part , as . In this approach, the average part is defined as a conventional density-weighted average by , while the fluctuation is defined to satisfy , where the over-bar represents an averaging operator.

The second option is the Large-eddy Simulation (LES) approach, which simulates individual flow realizations instead of the ensemble average of the flows. LES is expected to capture a substantial degree of unsteadiness and smaller flow length scales, which are omitted in the ensemble average. Due to the restriction on the computational cost, only the larger three-dimensional unsteady turbulent motions are directly resolved by the mesh resolution, whereas the effects of the smaller-scale motions are modelled as "sub-grid scale" (SGS) effects. In this approach, the resolved flow field is regarded as a result of filtering the actual flow field, with the filter size being the mesh size. The filtering eliminates the need to resolve the flow scales smaller than the filter size, which is accounted for by the SGS models. In general, the smaller the filter (mesh) size is, the better the scale-resolution of the turbulent flow field that is expected.

In the LES approach, the instantaneous quantity of the flow field (for example, ), is decomposed into a filtered component and a residual (or SGS) component, also denoted by and , as . In this approach, Again, the filtered part is defined by the Favre averaging , where is the filtered density field.

The governing equations in Ansys Forte are formulated to solve the ensemble-averaged flow field in the RANS approach and to solve the filtered flow field in the LES approach. The basic form of the equations for the flow field is presented in a unified way as follows, while the turbulence models themselves are described in Turbulence Models .