7.3.2 ANSYS FLUENT Model Formulation

A particle undergoing an exothermic reaction in the gas phase is shown schematically in Figure  7.3.1. $T_p$ and $T_{\infty}$ are the temperatures in Equation  15.4-78.

Figure 7.3.1: A Reacting Particle in the Multiple Surface Reactions Model

Based on the analysis above, ANSYS FLUENT uses the following equation to describe the rate of reaction $r$ of a particle surface species $j$ with the gas phase species $n$. The reaction stoichiometry of reaction $r$ in this case is described by

and the rate of reaction is given as

where

$\overline{{\cal R}}_{j,r}$	=	rate of particle surface species depletion (kg/s)
$A_p$	=	particle surface area (m $^2$)
$Y_j$	=	mass fraction of surface species $j$ in the particle
$\eta_r$	=	effectiveness factor (dimensionless)
${\cal R}_{j,r}$	=	rate of particle surface species reaction per unit area (kg/m $^2$-s)
$p_{n}$	=	bulk partial pressure of the gas phase species (Pa)
$D_{0,r}$	=	diffusion rate coefficient for reaction  $r$
${\cal R}_{{\rm kin},r}$	=	kinetic rate of reaction $r$ (units vary)
$N_r$	=	apparent order of reaction $r$

The effectiveness factor, $\eta_r$, is related to the surface area, and can be used in each reaction in the case of multiple reactions. $D_{0,r}$ is given by

The kinetic rate of reaction $r$ is defined as

The rate of the particle surface species depletion for reaction order $N_r =1$ is given by

For reaction order $N_r =0$,