[Fluent Inc. Logo] return to home search
next up previous contents index

8.9.1 Fickian Diffusion

Mass diffusion coefficients are required whenever you are solving species transport equations in multi-component flows. Mass diffusion coefficients are used to compute the diffusion flux of a chemical species in a laminar flow using (by default) Fick's law:


 J_i = - \rho D_{i,m} \nabla Y_i - D_{T,i}\frac{\nabla T}{T} (8.9-1)

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

Equation  8.9-1 is strictly valid when the mixture composition is not changing, or when $D_{i,m}$ is independent of composition. This is an acceptable approximation in dilute mixtures when $Y_i << 1$, for all $i$ except the carrier gas. FLUENT can also compute the transport of non-dilute mixtures in laminar flows by treating such mixtures as multicomponent systems. Within FLUENT, $D_{i,m}$ can be specified in a variety of ways, including by specifying ${\cal D}_{ij}$, the binary mass diffusion coefficient of component $i$ in component $j$. ${\cal D}_{ij}$ is not used directly, however; instead, the diffusion coefficient in the mixture, $D_{i,m}$, is computed as


 D_{i,m} = \frac{1 - X_i}{\displaystyle\sum_{j,j \neq i} (X_j/{\cal D}_{ij})} (8.9-2)

where $X_i$ is the mole fraction of species $i$. You can input $D_{i,m}$ or ${\cal D}_{ij}$ for each chemical species, as described in Section  8.9.4.

In turbulent flows, Equation  8.9-1 is replaced with the following form:


 J_i = -(\rho D_{i,m} + \frac{\mu_t}{{\rm Sc}_t}) \; \nabla Y_i - D_{T,i}\frac{\nabla T}{T} (8.9-3)

where ${\rm Sc}_t$ is the effective Schmidt number for the turbulent flow:


 {\rm Sc}_t = \frac{\mu_t}{\rho D_t} (8.9-4)

and $D_t$ is the effective mass diffusion coefficient due to turbulence.

In turbulent flows your mass diffusion coefficient inputs consist of defining the molecular contribution to diffusion $D_{i,m}$ using the same methods available for the laminar case, with the added option to alter the default settings for the turbulent Schmidt number. As seen from Equation  8.9-4, this parameter relates the effective mass diffusion coefficient due to turbulence with the eddy viscosity ${\mu_t}$. As discussed in Section  8.9.5, the turbulent diffusion coefficient normally overwhelms the laminar diffusion coefficient, so the default constant value for the laminar diffusion coefficient is usually acceptable.


next up previous contents index Previous: 8.9 Mass Diffusion Coefficients
Up: 8.9 Mass Diffusion Coefficients
Next: 8.9.2 Full Multicomponent Diffusion
© Fluent Inc. 2006-09-20