7.1.1 Species Transport Equations

When you choose to solve conservation equations for chemical species, ANSYS FLUENT predicts the local mass fraction of each species, $Y_i$, through the solution of a convection-diffusion equation for the $i$th species. This conservation equation takes the following general form:

where $R_{i}$ is the net rate of production of species $i$ by chemical reaction (described later in this section) and $S_{i}$ is the rate of creation by addition from the dispersed phase plus any user-defined sources. An equation of this form will be solved for $N-1$ species where $N$ is the total number of fluid phase chemical species present in the system. Since the mass fraction of the species must sum to unity, the $N$th mass fraction is determined as one minus the sum of the $N-1$ solved mass fractions. To minimize numerical error, the $N$th species should be selected as that species with the overall largest mass fraction, such as N $_2$ when the oxidizer is air.

Mass Diffusion in Laminar Flows

In Equation  7.1-1, $\vec{J}_{i}$ is the diffusion flux of species $i$, which arises due to gradients of concentration and temperature. By default, ANSYS FLUENT uses the dilute approximation (also called Fick's law) to model mass diffusion due to concentration gradients, under which the diffusion flux can be written as

Here $D_{i,m}$ is the mass diffusion coefficient for species $i$ in the mixture, and $D_{T,i}$ is the thermal (Soret) diffusion coefficient.

For certain laminar flows, the dilute approximation may not be acceptable, and full multicomponent diffusion is required. In such cases, the Maxwell-Stefan equations can be solved; see this section in the separate User's Guide for details.

Mass Diffusion in Turbulent Flows

In turbulent flows, ANSYS FLUENT computes the mass diffusion in the following form:

where ${\rm Sc}_t$ is the turbulent Schmidt number ( $\frac{\mu_t}{\rho D_t}$ where $\mu_t$ is the turbulent viscosity and $D_t$ is the turbulent diffusivity). The default ${\rm Sc}_t$ is 0.7. Note that turbulent diffusion generally overwhelms laminar diffusion, and the specification of detailed laminar diffusion properties in turbulent flows is generally not necessary.

Treatment of Species Transport in the Energy Equation

For many multicomponent mixing flows, the transport of enthalpy due to species diffusion

can have a significant effect on the enthalpy field and should not be neglected. In particular, when the Lewis number

for any species is far from unity, neglecting this term can lead to significant errors. ANSYS FLUENT will include this term by default. In Equation  7.1-4, $k$ is the thermal conductivity.

Diffusion at Inlets

For the pressure-based solver in ANSYS FLUENT, the net transport of species at inlets consists of both convection and diffusion components. (For the density-based solvers, only the convection component is included.) The convection component is fixed by the inlet species mass fraction specified by you. The diffusion component, however, depends on the gradient of the computed species field at the inlet. Thus the diffusion component (and therefore the net inlet transport) is not specified a priori. For information about specifying the net inlet transport of species, see this section in the separate User's Guide.