The relationships for calculating char particle burning rates are presented and discussed in detail by Smith  [609]. The particle reaction rate, (-s), can be expressed as

(7–98)

In Equation 7–98, the concentration at the particle surface, , is not known, so it should be eliminated, and the expression is recast as follows:

(7–99)

This equation has to be solved by an iterative procedure, with the exception of the cases when or . When , Equation 7–99 can be written as

(7–100)

In the case of , if there is a finite concentration of reactant at the particle surface, the solid depletion rate is equal to the chemical reaction rate. If there is no reactant at the surface, the solid depletion rate changes abruptly to the diffusion-controlled rate. In this case, however, Ansys Fluent will always use the chemical reaction rate for stability reasons.

A particle undergoing an exothermic reaction in the gas phase is shown schematically in Figure 7.1: A Reacting Particle in the Multiple Surface Reactions Model. and are the temperatures in Equation 12–159.

Figure 7.1: 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 of a particle surface species with the gas phase species . The reaction stoichiometry of reaction in this case is described by

(7–101)

and the rate of reaction is given as

(7–102)

(7–103)

The effectiveness factor, , is related to the surface area, and can be used in each reaction in the case of multiple reactions. is given by

(7–104)

The kinetic rate of reaction is defined as

(7–105)

The rate of the particle surface species depletion for reaction order is given by

(7–106)

For reaction order ,

(7–107)

When more than one gas phase reactant takes part in the reaction, the reaction stoichiometry must be extended to account for this case:

(7–108)

To describe the rate of reaction of a particle surface species in the presence of gas phase species , it is necessary to define the diffusion-limited species for each solid particle reaction, that is, the species for which the concentration gradient between the bulk and the particle surface is the largest. For the rest of the species, the surface and the bulk concentrations are assumed to be equal. The concentration of the diffusion-limited species is shown as and in Figure 7.1: A Reacting Particle in the Multiple Surface Reactions Model, and the concentrations of all other species are denoted as . For stoichiometries with multiple gas phase reactants, the bulk partial pressure in Equation 7–103 and Equation 7–106 is the bulk partial pressure of the diffusion-limited species, for reaction .

The kinetic rate of reaction is then defined as

(7–109)

When this model is enabled, the constant (Equation 7–104) and the effectiveness factor (Equation 7–102) are entered in the Reactions dialog box (see User Inputs for Particle Surface Reactions in the User's Guide).

Reactions involving only particle surface reactants can be modeled, provided that the particle surface reactants and products exist on the same particle.

The reaction rate for this case is given by Equation 7–107.

The decomposition reactions of particle surface species can be modeled.

(7–110)

The reaction rate for this case is given by Equation 7–102 – Equation 7–109, where the diffusion-limited species is now the gaseous product of the reaction. If there are more than one gaseous product species in the reaction, it is necessary to define the diffusion-limited species for the particle reaction as the species for which the concentration gradient between the bulk and the particle surface is the largest.

The deposition reaction of a solid species on a particle can be modeled with the following assumptions:

(7–111)

The theoretical analysis and Equation 7–102 – Equation 7–109 are applied for the surface reaction rate calculation, with the mass fraction of the surface species set to unity in Equation 7–102, Equation 7–106, and Equation 7–107.

In Ansys Fluent, for the particle surface species to be deposited on a particle, a finite mass of the species must already exist in the particle. This allows for activation of the deposition reaction selectively to particular injection particles. It follows that, to initiate the solid species deposition reaction on a particle, the particle must be defined in the Set Injection Properties Dialog Box (or Set Multiple Injection Properties Dialog Box) to contain a small mass fraction of the solid species to be deposited. For details on defining the particle surface species mass fractions, see Using the Multiple Surface Reactions Model for Discrete-Phase Particle Combustion in the User’s Guide.

Reactions of gaseous species catalyzed on the particle surface can also be modeled following Equation 7–102 – Equation 7–109 for the surface reaction rate calculation, with the mass fraction of the surface species set to unity in Equation 7–102, Equation 7–106, and Equation 7–107. To apply this type of reaction, see Modeling Gaseous Solid Catalyzed Reactions in the User's Guide. For details on defining the particle surface species mass fractions, see Using the Multiple Surface Reactions Model for Discrete-Phase Particle Combustion in the User’s Guide.