8.9.4 Mass Diffusion Coefficient Inputs

By default, the solver computes the species diffusion using Equation  8.9-1 (for laminar flows) with your inputs for $D_{i,m}$, the diffusion coefficient for species $i$ in the mixture. For turbulent flows, species diffusion is computed with Equation  8.9-3.

You can input the mass diffusion coefficients using one of the following methods:

• Constant dilute approximation (Fickian diffusion only): define one constant for all $D_{i,m}$.

• Dilute approximation (Fickian diffusion only): define each $D_{i,m}$ as a constant or as a polynomial function of temperature (if heat transfer is enabled).

• Multicomponent method: define the binary diffusion of species $i$ in each species $j$, ${\cal D}_{ij}$ as a constant or a polynomial function of temperature, or (for ideal gases only) using kinetic theory.

• User-defined function (UDF): define a single function that will apply to all mass diffusion coefficients. This is done using the DEFINE_DIFFUSIVITY macro and is explained in the separate UDF Manual.

You should choose to input $D_{i,m}$ (using one of the first two methods) if you are modeling a dilute mixture, with chemical species present at low mass fraction in a "carrier'' fluid that is present at high concentration. You may wish to define the individual binary mass diffusion coefficients, ${\cal D}_{ij}$, if you are modeling a non-dilute mixture. If you choose to define ${\cal D}_{ij}$, the solver will compute the diffusion of species $i$ in the mixture using Equation  8.9-2, unless you have enabled full multicomponent diffusion.

If you want to use the full multicomponent diffusion model described in Section  8.9.2, turn on the Full Multicomponent Diffusion option in the Species Model dialog box, and then select the multicomponent method (the third method listed above) in the Create/Edit Materials dialog box; the dilute approximation methods are not appropriate for the full multicomponent diffusion model.

You will define $D_{i,m}$ or ${\cal D}_{ij}$ for each chemical species using the Create/Edit Materials dialog box.

Materials

The diffusion coefficients have units of m $^2$/s in SI units or ft $^2$/s in British units.

Constant Dilute Approximation Inputs

To use the constant dilute approximation method, follow these steps:

1.   Select constant-dilute-appx in the drop-down list to the right of Mass Diffusivity.

2.   Enter a single value of $D_{i,m}$. The same value will be used for the diffusion coefficient of each species in the mixture.

Dilute Approximation Inputs

To use the dilute approximation method, follow the steps below:

1.   Select dilute-approx in the drop-down list to the right of Mass Diffusivity.

2.   In the resulting Mass Diffusion Coefficients dialog box (Figure  8.9.1), select the species in the Species Di list for which you are going to define the mass diffusion coefficient.

Figure 8.9.1: The Mass Diffusion Coefficients Dialog Box for Dilute Approximation

3.   You can define $D_{i,m}$ for the selected species either as a constant value or (if heat transfer is active) as a polynomial function of temperature:

• To define a constant diffusion coefficient, select constant (the default) in the drop-down list below Coefficient, and then enter the value in the field below the list.

• To define a temperature-dependent diffusion coefficient, choose polynomial in the Coefficient drop-down list and then define the polynomial coefficients as described in Section  8.2.1.

  
  

  
  

4.   Repeat steps 2 and 3 until you have defined diffusion coefficients for all species in the Species Di list in the Mass Diffusion Coefficients dialog box.

Multicomponent Method Inputs

To use the multicomponent method, and define constant or temperature-dependent diffusion coefficients, follow the steps below:

1.   Select multicomponent in the drop-down list to the right of Mass Diffusivity.

2.   In the resulting Mass Diffusion Coefficients dialog box (Figure  8.9.2), select the species in the Species Di list and the Species Dj list for which you are going to define the mass diffusion coefficient ${\cal D}_{ij}$ for species $i$ in species $j$.

Figure 8.9.2: The Mass Diffusion Coefficients Dialog Box for the Multicomponent Method

3.   You can define ${\cal D}_{ij}$ for the selected pair of species as a constant value or as a polynomial function of temperature (if heat transfer is active).

• To define a constant diffusion coefficient, select constant (the default) in the drop-down list below Coefficient, and then enter the value in the field below the list.

• To define a temperature-dependent diffusion coefficient, choose polynomial in the Coefficient drop-down list and then define the polynomial coefficients as described in Section  8.2.1.

  
  

  
  

4.   Repeat steps 2 and 3 until you have defined diffusion coefficients for all pairs of species in the Species Di and Species Dj lists in the Mass Diffusion Coefficients dialog box.

To use the multicomponent method, and define the diffusion coefficient using kinetic theory (available only when the ideal gas law is used), follow these steps:

1.   Choose kinetic-theory in the drop-down list to the right of Mass Diffusivity.

2.   Click Change/Create after completing other property definitions for the mixture material.

3.   Define the Lennard-Jones parameters, $\sigma_i$ and $(\epsilon/k_B)_i$, for each species (fluid material), as described in Section  8.13.

The solver will use a modification of the Chapman-Enskog formula [ 50] to compute the diffusion coefficient using kinetic theory:

where $p_{\rm abs}$ is the absolute pressure, and $\Omega_D$ is the diffusion collision integral, which is a measure of the interaction of the molecules in the system. $\Omega_D$ is a function of the quantity $T^*_D$, where

$k_B$ is the Boltzmann constant, which is defined as the gas constant, $R$, divided by Avogadro's number. $(\epsilon /k_B)_{ij}$ for the mixture is the geometric average:

For a binary mixture, $\sigma_{ij}$ is calculated as the arithmetic average of the individual $\sigma$s:

Thermal Diffusion Coefficient Inputs

If you have enabled thermal diffusion (in the Species Model dialog box), you can define the thermal diffusion coefficients in the Create/Edit Materials dialog box as follows:

1.   Select one of the following three methods in the drop-down list to the right of Thermal Diffusion Coefficient:

• Choose kinetic-theory to have ANSYS FLUENT compute the thermal diffusion coefficients using the empirically-based expression in Equation  8.9-13. No further inputs are required for this option.

• Choose specified to input the coefficient for each species. The Thermal Diffusion Coefficients dialog box (Figure  8.9.3) will open. Further inputs are described in the next step.

• Choose user-defined to use a user-defined function. More information about user-defined functions can be found in the separate UDF Manual.

2.   If you choose specified, select the species in the Species Thermal Di list for which you are going to define the thermal diffusion coefficient.

Figure 8.9.3: The Thermal Diffusion Coefficients Dialog Box

3.   Define $D_{T,i}$ for the selected species either as a constant value or as a polynomial function of temperature:

• To define a constant diffusion coefficient, select constant (the default) in the drop-down list below Coefficient, and then enter the value in the field below the list.

• To define a temperature-dependent diffusion coefficient, choose polynomial in the Coefficient drop-down list and then define the polynomial coefficients as described in Section  8.2.

4.   Repeat steps 2 and 3 until you have defined diffusion coefficients for all species in the Species Thermal Di list in the Thermal Diffusion Coefficients dialog box.