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20.2.2 Governing Equations for SOx Transport

FLUENT solves the mass transport equations for the $SO_2$ species, taking into account convection, diffusion, production and consumption of $SO_2$ and related species. This approach is completely general, being derived from the fundamental principle of mass conservation. The effect of residence time in SOx mechanisms, a Lagrangian reference frame concept, is included through the convection terms in the governing equations written in the Eulerian reference frame. If all fuel sulfur is assumed to convert directly to $SO_2$ and the other product and intermediate species and assumed negligible, then only the $SO_2$ species transport equation is needed:

 \frac{\partial}{\partial t}(\rho Y_{\rm SO_2}) + \nabla \cdo... ...nabla \cdot (\rho {\cal D} \nabla Y_{\rm SO_2}) + S_{\rm SO_2} (20.2-1)

As discussed in Section  20.2.3, SOx formation mechanisms are more involved. The tracking of sulfur-containing intermediate species is important. FLUENT solves a transport equation for the $H{_2}S$, $SO_3$, SO, and SH species in addition to the $SO_2$ species:

 \frac{\partial}{\partial t} (\rho Y_{\rm H{_2}S})+ \nabla \c... ...= \nabla \cdot (\rho {\cal D} Y_{\rm H{_2}S}) + S_{\rm H{_2}S} (20.2-2)

 \frac{\partial}{\partial t} (\rho Y_{\rm SO_3})+ \nabla \cdo... ...3}) = \nabla \cdot (\rho {\cal D} Y_{\rm SO_3}) + S_{\rm SO_3} (20.2-3)

 \frac{\partial}{\partial t} (\rho Y_{\rm SO})+ \nabla \cdot ... ...rm SO}) = \nabla \cdot (\rho {\cal D} Y_{\rm SO}) + S_{\rm SO} (20.2-4)

 \frac{\partial}{\partial t} (\rho Y_{\rm SH})+ \nabla \cdot ... ...rm SH}) = \nabla \cdot (\rho {\cal D} Y_{\rm SH}) + S_{\rm SH} (20.2-5)

where $Y_{\rm SO_2}$, $Y_{\rm H{_2}S}$, $Y_{\rm SO_3}$, $Y_{\rm SO}$, and $Y_{\rm SH}$ are mass fractions of $SO_2$, $H{_2}S$, $SO_3$, SO, and SH in the gas phase. The source terms $S_{\rm SO_2}$, $S_{\rm H{_2}S}$, $S_{\rm SO_3}$, $S_{\rm SO}$, and $S_{\rm SH}$ are to be determined depending on the form of fuel sulfur release ( $SO_2$ and/or $H{_2}S$) and inclusion of $SO_3$, SO and SH in the SOx mechanism.

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