Mathematical Modeling Including CFD

As pointed out earlier in Chapter 3 and will be covered in more detail later on in this chapter, the flow in a rotary kiln is typically gas-solid turbulent flow with chemical reactions, mainly combustion. The building blocks behind the user-defined functions (UDF) in commercial CFD codes applied to rotary kiln combustion modeling consist of renormalization group (RNG) k-s turbulent model for gas phase and, in the case of pulverized combustion particles, the statistical (stochastic) trajectory model for homogeneous volatile and heterogeneous solid-phase char combustion. The underlying equations are discussed in the next section. 

The set of conservation equations that are solved in most CFD analyses are as presented earlier but expanded to include the stress generation as in Equations (6.40) through (6.45) (Wang et al., 2(X)6). 

Turbulence modeling is implemented as a closure model for the Reynolds stress with the most commonly used k-e turbulence model being 

In order to include temperature distribution, the Navier Stokes equations are accompanied by an energy equation that solves for enthalpy (h = CpT). The balance equation for enthalpy is 

The source term, S, includes combustion, that is, the heat source and the heat transfer within the system that affect temperature. In rotary kilns, the dominant heat transfer mode is radiation and there are several models to evaluate its value, some of which will be examined in detail later. 

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