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20.3.3 Using the Soot Models

To compute the soot formation, you will need to start from a converged fluid-flow solution. The procedure for setting up and solving a soot formation model is outlined below, and described in detail on the pages that follow. Remember that only the steps that are pertinent to soot modeling are shown here. For information about inputs related to other models that you are using in conjunction with the soot formation model, see the appropriate sections for those models.

1.   Calculate your turbulent combustion (finite-rate or nonpremixed) problem using FLUENT as usual.

2.   Enable the desired soot formation model and set the related parameters, as described in this section.

Define $\rightarrow$ Models $\rightarrow$ Species $\rightarrow$ Soot...

3.   In the Solution Controls panel, turn off solution of all variables except soot (and nuclei, if you are using the two-step model).

Solve $\rightarrow$ Controls $\rightarrow$ Solution...

4.   Also in the Solution Controls panel, set a suitable value for the soot (and nuclei, for the two-step model) under-relaxation factor(s). A value of 0.9 is suggested, although a lower value may be required for certain problems. That is, if convergence cannot be obtained, try a lower under-relaxation value.

5.   In the Residual Monitors panel, decrease the convergence criterion for soot (and nuclei, for the two-step model) to $10^{-5}$.

Solve $\rightarrow$ Monitors $\rightarrow$ Residual...

6.   Define the boundary conditions for soot (and nuclei, for the two-step model) at flow inlets.

Define $\rightarrow$ Boundary Conditions...

7.   Perform calculations until convergence (i.e., until the soot--and nuclei, for the two-step model--residual is below $10^{-5}$) to ensure that the soot (and nuclei) field is no longer evolving.

8.   Review the mass fraction of soot (and nuclei) with alphanumerics and/or graphics tools in the usual way.

9.   Save a new set of case and data files, if desired.

10.   If you want to calculate a coupled solution for the soot and the flow field, turn on the other variables again and recompute until convergence. (See the end of this section for some advice on coupled calculations.)



Selecting the Soot Model


You can enable the calculation of soot formation by selecting a soot model in the Soot Model panel (Figure  20.3.1).

Define $\rightarrow$ Models $\rightarrow$ Species $\rightarrow$ Soot...

Figure 20.3.1: The Soot Model Panel
figure

Under Model, select either the One-Step or the Two-Step model. The panel will expand to show the appropriate inputs for the selected model.

(If you want to include the effects of soot formation on the radiation absorption coefficient, turn on the Generalized Model option under Soot-Radiation Interaction.)



Setting the Combustion Process Parameters


For both soot models, you will next define the Process Parameters, which depend on the combustion process that you are modeling. These inputs include the stoichiometry of the fuel and soot combustion and (for the two-step model only) the average size and density of the soot particles:

Mean Diameter of Soot Particle   and Mean Density of Soot Particle are the assumed average diameter and average density of the soot particles in the combustion system, used to compute the soot particle mass, $m_p$, in Equation  20.3-9 for the two-step model. Note that the default values for soot density and diameter are taken from [ 229].

These parameters will not appear when the one-step model is used.

Stoichiometry for Soot Combustion   is the mass stoichiometry, $\nu_{\rm soot}$, in Equation  20.3-6, which computes the soot combustion rate in both soot models. The default value supplied by FLUENT (2.6667) assumes that the soot is pure carbon and that the oxidizer is O $_2$.

Stoichiometry for Fuel Combustion   is the mass stoichiometry, $\nu_{\rm fuel}$, in Equation  20.3-6, which computes the soot combustion rate in both soot models. The default value supplied by FLUENT (3.6363) is for combustion of propane (C $_3$H $_8$) by oxygen (O $_2$).



Defining the Fuel and Oxidizing Species


In addition to defining the stoichiometry for the fuel and soot combustion, you need to tell FLUENT which chemical species in your model should be used as the fuel and oxidizer. In the Soot Model panel under Species Definition, select the fuel in the Fuel drop-down list and the oxidizer in the Oxidant drop-down list.

If you are using the nonpremixed model for the combustion calculation and your fuel stream consists of a mixture of components, you should choose the most appropriate species as the Fuel species for the soot formation model. Similarly, the most significant oxidizing component (e.g., O $_2$) should be selected as the Oxidant.



Setting Model Parameters for the Single-Step Model


When you choose the One-Step model for soot formation, the modeling parameters to be defined are those used in Equations  20.3-3, 20.3-5, and 20.3-6:

Soot Formation Constant   is the parameter $C_s$ in Equation  20.3-3.

Equivalence Ratio Exponent   is the exponent $r$ in Equation  20.3-3.

Equivalence Ratio Minimum   and Equivalence Ratio Maximum are the minimum and maximum values of the fuel equivalence ratio $\phi$ in Equation  20.3-3. Equation  20.3-3 will be solved only if Equivalence Ratio Minimum $< \phi <$ Equivalence Ratio Maximum; if $\phi$ is outside of this range, there is no soot formation.

Activation Temperature of Soot Formation Rate   is the term $E/R$ in Equation 20.3-3.

Magnussen Constant for Soot Combustion   is the constant $A$ used in the rate expressions governing the soot combustion rate (Equations 20.3-5 and 20.3-6).

Note that the default values for these parameters are for propane fuel [ 63, 388], and are considered to be valid for a wide range of hydrocarbon fuels.



Setting Model Parameters for the Two-Step Model


When you choose the Two-Step model for soot formation, the modeling parameters to be defined are those used in Equations  20.3-5, 20.3-6, 20.3-9, 20.3-11, and 20.3-12:

Limiting Nuclei Formation Rate   is the limiting value of the kinetic nuclei formation rate $\eta_0$ in Equation  20.3-12. Below this limiting value, the branching and termination term, ( $f-g$) in Equation  20.3-11, is not included.

Nuclei Branching-Termination Coefficient   is the term $(f - g)$ in Equation  20.3-11.

Nuclei Coefficient of Linear Termination on Soot   is the term $g_0$ in Equation  20.3-11.

Pre-Exponential Constant of Nuclei Formation   is the pre-exponential term $a_0$ in the kinetic nuclei formation term, Equation  20.3-12.

Activation Temperature of Nuclei Formation Rate   is the term $E/R$ in the kinetic nuclei formation term, Equation  20.3-12.

Constant Alpha for Soot Formation Rate   is $\alpha$, the constant in the soot formation rate equation, Equation  20.3-9.

Constant Beta for Soot Formation Rate   is $\beta$, the constant in the soot formation rate equation, Equation  20.3-9.

Magnussen Constant for Soot and Nuclei Combustion   is the constant $A$ used in the rate expressions governing the soot combustion rate (Equations 20.3-5 and 20.3-6).

The default values for the two-step model are the same as in Magnussen and Hjertager [ 229] (for an acetylene flame), except for $a_0$, which is assumed to have the original value from Tesner et al. [ 373]. If your model involves propane fuel rather that acetylene, it is recommended that you change the value of $\alpha$ to $3.5 \times 10^8$ [ 5]. For best results, you should modify both of these parameters, using empirically determined inputs for your specific combustion system.



Defining Boundary Conditions for the Soot Model


At flow inlet boundaries, you will need to specify the Soot Mass Fraction, $Ystar{\rm soot}$, in Equation  20.3-1, and (for the two-step model only) the Nuclei mass concentration, $b_{\rm nuc}^*$, in Equation  20.3-7.

Define $\rightarrow$ Boundary Conditions...

You can retain the default inlet values of zero for both quantities or you can input nonzero numbers as appropriate for your combustion system.



Calculating Coupled Soot Solutions


If you are calculating a coupled solution for the soot and the flow field, you will generally need to increase the convergence criteria for soot (and nuclei, for the two-step model) to $10^{-4}$. You may choose to keep the recommended value of $10^{-5}$ used for the uncoupled soot calculation, but be aware that the coupled solution may not be able to converge to this stricter tolerance.

For coupled calculations you should also use a lower under-relaxation factor for soot (and nuclei, for the two-step model). A value of 0.2 will be suitable in most cases.

If you are calculating a coupled solution and you are modeling radiative heat transfer using a variable absorption coefficient, you should enable the Generalized Model for Soot-Radiation Interaction in the Soot Model panel. When this option is enabled, FLUENT will include the effect of soot on the variable radiation absorption coefficient, as described in Section  13.3.8.



Reporting Soot Quantities


FLUENT provides several additional reporting options when your model includes soot formation. You can generate graphical plots or alphanumeric reports of the following items:

Both of these parameters are contained in the Soot... category of the variable selection drop-down list that appears in postprocessing panels.


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