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20.2.7 SOx Formation in Turbulent Flows

The kinetic mechanisms of SOx formation and destruction are obtained from laboratory experiments in a similar fashion to the NOx model. In any practical combustion system, however, the flow is highly turbulent. The turbulent mixing process results in temporal fluctuations in temperature and species concentration that will influence the characteristics of the flame.

The relationships among SOx formation rate, temperature, and species concentration are highly nonlinear. Hence, if time-averaged composition and temperature are employed in any model to predict the mean SOx formation rate, significant errors will result. Temperature and composition fluctuations must be taken into account by considering the probability density functions which describe the time variation.



The Turbulence-Chemistry Interaction Model


In turbulent combustion calculations, FLUENT solves the density-weighted time-averaged Navier-Stokes equations for temperature, velocity, and species concentrations or mean mixture fraction and variance. To calculate $SO_2$ concentration, a time-averaged $SO_2$ formation rate must be computed at each point in the domain using the averaged flow-field information.



The PDF Approach


The PDF method has proven very useful in the theoretical description of turbulent flow [ 164]. In the FLUENT SOx model, a single- or joint-variable PDF in terms of a normalized temperature, species mass fraction, or the combination of both is used to predict the SOx emission. If the nonpremixed combustion model is used to model combustion, then a one- or two-variable PDF in terms of mixture fraction(s) is also available. The mean values of the independent variables needed for the PDF construction are obtained from the solution of the transport equations.



The Mean Reaction Rate


The mean turbulent reaction rate described in Section  20.1.9 for the NOx model also applies to the SOx model. The PDF is used for weighting against the instantaneous rates of production of $SO_2$ and subsequent integration over suitable ranges to obtain the mean turbulent reaction rate as described in Equations  20.1-104 and 20.1-105 for NOx.



The Beta PDF Assumption


As is the case with the NOx model, $P$ is assumed to be a two-moment beta function as appropriate for combustion calculations [ 135, 245]. Equations  20.1-107 - 20.1-109 apply to the SOx model as well, with the variance $\sigma^2$ computed by solving a transport equation during the combustion calculation stage, using the approach outlined in the derivation of Equation  20.1-110.


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