15.1.3 Defining Properties for the Mixture and Its Constituent Species

As discussed in Section  15.1.1, if you use a mixture material from the database, most mixture and species properties will already be defined. You may follow the procedures in this section to check the current properties, modify some of the properties, or set all properties for a brand-new mixture material that you are defining from scratch.

Remember that you will need to define properties for the mixture material and also for its constituent species. It is important that you define the mixture properties before setting any properties for the constituent species, since the species property inputs may depend on the methods you use to define the properties of the mixture. The recommended sequence for property inputs is as follows:

1.   Define the mixture species, and reaction(s), and define physical properties for the mixture. Remember to click the Change/Create button when you are done setting properties for the mixture material.

2.   Define physical properties for the species in the mixture. Remember to click the Change/Create button after defining the properties for each specie.

These steps, all of which are performed in the Create/Edit Materials dialog box, are described in detail in this section.

Materials

Defining the Species in the Mixture

If you are using a mixture material from the database, the species in the mixture will already be defined for you. If you are creating your own material or modifying the species in an existing material, you will need to define them yourself.

In the Create/Edit Materials dialog box (Figure  15.1.2), check that the Material Type is set to mixture and your mixture is selected in the Fluent Mixture Materials list. Click the Edit... button to the right of Mixture Species to open the Species dialog box (Figure  15.1.3).

Figure 15.1.2: The Create/Edit Materials Dialog Box (showing a mixture material)

Figure 15.1.3: The Species Dialog Box

Overview of the Species Dialog Box

In the Species dialog box, the Selected Species list shows all of the fluid-phase species in the mixture. If you are modeling wall or particle surface reactions, the Selected Solid Species list will show all of the bulk solid species in the mixture. Solid species are species that are deposit to, or etch from, wall boundaries or discrete-phase particles (e.g., Si(s)) and do not exist as fluid-phase species. If you are modeling wall surface reactions with site balancing, where species adsorb onto the wall surface, react, and then desorb off the surface, the Selected Site Species list will show all of the site species in the mixture.

The use of solid and site species with wall surface reactions is described in Section  15.2. See Section  15.3 for information about particle surface reactions.

The order of the species in the Selected Species list is very important. ANSYS FLUENT considers the last specie in the list to be the bulk specie. You should therefore be careful to retain the most abundant specie (by mass) as the last specie when you add species to or delete species from a mixture material.

The Available Materials list shows materials that are available but not in the mixture. Generally, you will see air in this list, since air is always available by default.

Adding Species to the Mixture

If you are creating a mixture from scratch or starting from an existing mixture and adding some missing species, you will first need to load the desired species from the database (or create them, if they are not present in the database) so that they will be available to the solver. The procedure for adding species is listed below. (You will need to close the Species dialog box before you begin, since it is a "modal'' dialog box that will not allow you to do anything else when it is open.)

1.   In the Create/Edit Materials dialog box, click the Fluent Database... button to open the Fluent Database Materials dialog box and copy the desired specie, as described in Section  8.1.2. Remember that the constituent species of the mixture are fluid materials, so you should select fluid as the Material Type in the Fluent Database Materials dialog box to see the correct list of choices. Note that available solid and site species (for surface reactions) are also contained in the fluid list.

If you do not see the specie you are looking for in the database, you can create a new fluid material for that specie, following the instructions in Section  8.1.2, and then continue with step 2, below.

2.   Re-open the Species dialog box, as described above. You will see that the fluid materials you copied from the database (or created) are listed in the Available Materials list.

3.   To add a specie to the mixture, select it in the Available Materials list and click the Add button below the Selected Species list (or below the Selected Site Species or Selected Solid Species list, to define a site or solid species). The specie will be added to the end of the relevant list and removed from the Available Materials list.

4.   Repeat the previous step for all the desired species. When you are finished, click the OK button.

Adding a specie to the list will alter the order of the species. You should be sure that the last specie in the list is the bulk specie, and you should check all cell and boundary zone conditions, under-relaxation factors, and other solution parameters that you have set, as described in detail below.

Removing Species from the Mixture

To remove a specie from the mixture, simply select it in the Selected Species list (or the Selected Site Species or Selected Solid Species list) and click the Remove button below the list. The specie will be removed from the list and added to the Available Materials list.

Removing a specie from the list will alter the order of the species. You should be sure that the last specie in the list is the bulk species, and you should check any cell zone or boundary conditions, under-relaxation factors, or other solution parameters that you have set, as described in detail below.

Reordering Species

If you find that the last specie in the Selected Species list is not the most abundant specie (as it should be), you will need to rearrange the species to obtain the proper order.

1.   Remove the bulk specie from the Selected Species list. It will now appear in the Available Species list.

2.   Add the specie back in again. It will automatically be placed at the end of the list.

The Naming and Ordering of Species

As discussed above, you should retain the most abundant specie as the last one in the Selected Species list when you add or remove species. Additional considerations you should be aware of when adding and deleting species are presented here.

There are three characteristics of a specie that identify it to the solver: name, chemical formula, and position in the list of species in the Species dialog box. Changing these characteristics will have the following effects:

• You can change the Name of a specie (using the Create/Edit Materials dialog box, as described in Section  8.1.2) without any consequences.

• You should never change the given Chemical Formula of a specie.

• You will change the order of the species list if you add or remove any specie. When this occurs, all cell zone or boundary conditions, solver parameters, and solution data for species will be reset to the default values. (Solution data, cell zone or boundary conditions, and solver parameters for other flow variables will not be affected.) Thus, if you add or remove species you should take care to redefine species cell zone and boundary conditions and solution parameters for the newly defined problem. In addition, you should recognize that patched species concentrations or concentrations stored in any data file that was based on the original species ordering will be incompatible with the newly defined problem. You can use the data file as a starting guess, but you should be aware that the species concentrations in the data file may provide a poor initial guess for the newly defined model.

Defining Reactions

If your ANSYS FLUENT model involves chemical reactions, you can next define the reactions in which the defined species participate. This will be necessary only if you are creating a mixture material from scratch, you have modified the species, or you want to redefine the reactions for some other reason.

Depending on which turbulence-chemistry interaction model you selected in the Species Model dialog box (see Section  15.1.2), the appropriate reaction model will be displayed in the Reaction drop-down list in the Edit Material dialog box. If you are using the laminar finite-rate or Eddy-Dissipation Concept model, the reaction model will be finite-rate; if you are using the eddy-dissipation model, the reaction model will be eddy-dissipation; if you are using the finite-rate/eddy-dissipation model, the reaction model will be finite-rate/eddy-dissipation.

Inputs for Reaction Definition

To define the reactions, click the Edit... button to the right of Reaction. The Reactions dialog box (Figure  15.1.4) will open.

Figure 15.1.4: The Reactions Dialog Box

The steps for defining reactions are as follows:

1.   Set the total number of reactions (volumetric reactions, wall surface reactions, and particle surface reactions) in the Total Number of Reactions field. (Use the arrows to change the value, or type in the value and press RETURN.)

Note that if your model includes discrete-phase combusting particles, you should include the particulate surface reaction(s) (e.g., char burnout, multiple char oxidation) in the number of reactions only if you plan to use the multiple surface reactions model for surface combustion.

2.   Specify the Reaction Name of the reaction you want to define.

3.   Set the ID of the reaction you want to define. (Again, if you type in the value be sure to press RETURN.)

4.   If this is a fluid-phase reaction, keep the default selection of Volumetric as the Reaction Type. If this is a wall surface reaction (described in Section  15.2) or a particle surface reaction (described in Section  15.3), select Wall Surface or Particle Surface as the Reaction Type. See Section  15.3.1 for further information about defining particle surface reactions.

5.   Specify how many reactants and products are involved in the reaction by increasing the value of the Number of Reactants and the Number of Products. Select each reactant or product in the Species drop-down list and then set its stoichiometric coefficient and rate exponent in the appropriate Stoich. Coefficient and Rate Exponent fields. (The stoichiometric coefficient is the constant $\nu'_{i,r}$ or $\nu''_{i,r}$ in this equation in the separate Theory Guide and the rate exponent is the exponent on the reactant or product concentration, $\eta'_{j,r}$ or $\eta''_{j,r}$ in this equation in the separate Theory Guide.)

There are two general classes of reactions that can be handled by the Reactions dialog box, so it is important that the parameters for each reaction are entered correctly. The classes of reactions are as follows:

• Global forward reaction (no reverse reaction): Product species generally do not affect the forward rate, so the rate exponent for all products ( $\eta''_{j,r}$) should be 0. For reactant species, set the rate exponent ( $\eta'_{j,r}$) to the desired value. If such a reaction is not an elementary reaction, the rate exponent will generally not be equal to the stoichiometric coefficient ( $\nu'_{i,r}$) for that specie. An example of a global forward reaction is the combustion of methane:

  
  

  
  
  

  where $\nu'_{{\rm CH}_4}=1$, $\eta'_{{\rm CH}_4}=0.2$, $\nu'_{{\rm O}_2}=2$, $\eta'_{{\rm O}_2}=1.3$, $\nu''_{{\rm CO}_2}=1$, $\eta''_{{\rm CO}_2}=0$, $\nu''_{{\rm H}_2{\rm O}}=2$, and $\eta''_{{\rm H}_2{\rm O}}=0$.

  Figure  15.1.4 shows the coefficient inputs for the combustion of methane. (See also the methane-air mixture material in the Database Materials dialog box.)

  Note that, in certain cases, you may wish to model a reaction where product species affect the forward rate. For such cases, set the product rate exponent ( $\eta''_{j,r}$) to the desired value. An example of such a reaction is the gas-shift reaction (see the carbon-monoxide-air mixture material in the Database Materials dialog box), in which the presence of water has an effect on the reaction rate:

  ${\rm CO} + \frac{1}{2} {\rm O}_2 + {\rm H}_2{\rm O} \longrightarrow {\rm CO}_2 + {\rm H}_2{\rm O}$

  In the gas-shift reaction, the rate expression may be defined as:

  
  

  
  
  

  where $\nu'_{\rm CO}=1$, $\eta'_{\rm CO}=1$, $\nu'_{{\rm O}_2}=0.5$, $\eta'_{{\rm O}_2}=0.25$, $\nu''_{{\rm CO}_2}=1$, $\eta''_{{\rm CO}_2}=0$, $\nu''_{{\rm H}_2{\rm O}}=0$, and $\eta''_{{\rm H}_2{\rm O}}=0.5$.

• Reversible reaction: An elementary chemical reaction that assumes the rate exponent for each specie is equivalent to the stoichiometric coefficient for that specie. An example of an elementary reaction is the oxidation of SO $_2$ to SO $_3$:
  ${\rm SO}_2 + \frac{1}{2}{\rm O}_2 \rightleftharpoons {\rm SO}_3$

  where $\nu'_{{\rm SO}_2} = 1$, $\eta'_{{\rm SO}_2} = 1$, $\nu'_{{\rm O}_2} = 0.5$, $\eta'_{{\rm O}_2} = 0.5$, $\nu''_{{\rm SO}_3} = 1$, and $\eta''_{{\rm SO}_3} =1$.

  See step 6 below for information about how to enable reversible reactions.

6.   If you are using the laminar finite-rate, finite-rate/eddy-dissipation, Eddy-Dissipation Concept or PDF Transport model for the turbulence-chemistry interaction, enter the following parameters for the Arrhenius rate in the Arrhenius Rate group box:

Pre-Exponential Factor   (the constant $A_r$ in this equation in the separate Theory Guide). The units of $A_r$ must be specified such that the units of the molar reaction rate, $\hat{R}_{i,r}$ in this equation in the separate Theory Guide , are moles/volume-time (e.g., kgmol/m $^3$-s) and the units of the volumetric reaction rate, $R_i$ in this equation in the separate Theory Guide , are mass/volume-time (e.g., kg/m $^3$-s).

It is important to note that if you have selected the British units system, the Arrhenius factor should still be input in SI units. This is because ANSYS FLUENT applies no conversion factor to your input of $A_r$ (the conversion factor is 1.0) when you work in British units, as the correct conversion factor depends on your inputs for $\nu'_{i,r}$, $\beta_r$, etc.

Activation Energy   (the constant $E_r$ in the forward rate constant expression, this equation in the separate Theory Guide).

Temperature Exponent   (the value for the constant $\beta_r$ in this equation in the separate Theory Guide).

Third-Body Efficiencies   (the values for $\gamma_{j,r}$ in this equation in the separate Theory Guide). If you have accurate data for the efficiencies and want to include this effect on the reaction rate (i.e., include ${\Gamma}$ in this equation in the separate Theory Guide), enable the Third Body Efficiencies option and click the Specify... button to open the Third-Body Efficiencies dialog box (Figure  15.1.5). For each Species in the dialog box, specify the Third-Body Efficiency.

It is not necessary to include the third-body efficiencies. You should not enable the Third-Body Efficiencies option unless you have accurate data for these parameters.

Figure 15.1.5: The Third-Body Efficiencies Dialog Box

Pressure-Dependent Reaction   (if relevant) If you are using the laminar finite-rate or Eddy-Dissipation Concept model for turbulence-chemistry interaction, or have enabled the composition PDF transport model (see Chapter  19), and the reaction is a pressure fall-off reaction (see this section in the separate Theory Guide), enable the Pressure-Dependent Reaction option for the Arrhenius Rate and click the Specify... button to open the Pressure-Dependent Reaction dialog box (Figure  15.1.6).

Figure 15.1.6: The Pressure-Dependent Reaction Dialog Box

Under Reaction Parameters, select the appropriate Reaction Type ( lindemann, troe, or sri). See this section in the separate Theory Guide for details about the three methods. Next, you must specify if the Bath Gas Concentration ( $[M]$ in this equation in the separate Theory Guide) is to be defined as the concentration of the mixture, or as the concentration of one of the mixture's constituent species, by selecting the appropriate item in the drop-down list.

The parameters you specified under Arrhenius Rate in the Reactions dialog box represent the high-pressure Arrhenius parameters. You can, however, specify values for the following parameters under Low Pressure Arrhenius Rate:

ln(Pre-Exponential Factor)   ( $A_{\rm low}$ in this equation in the separate Theory Guide) The pre-exponential factor $A_{\rm low}$ is often an extremely large number, so you will input the natural logarithm of this term.

Activation Energy   ( $E_{\rm low}$ in this equation in the separate Theory Guide)

Temperature Exponent   ( $\beta_{\rm low}$ in this equation in the separate Theory Guide)

If you selected troe for the Reaction Type, you can specify values for Alpha, T1, T2, and T3 ( $\alpha$, $T_1$, $T_2$, and $T_3$ in this equation in the separate Theory Guide) under Troe parameters. If you selected sri for the Reaction Type, you can specify values for a, b, c, d, and e ( $a$, $b$, $c$, $d$, and $e$ in this equation in the separate Theory Guide) under SRI parameters.

Coverage Dependent Reaction   If you are modeling Wall Surface reactions with site-balancing and you have reaction rates that depend on site coverages, you can enable the Coverage Dependent Reaction option. Click Specify... to open the Coverage Dependent Reaction dialog box (Figure  15.1.7) and input the coverage parameters.

Figure 15.1.7: The Coverage Dependent Reaction Dialog Box

In the Coverage Dependent Reaction dialog box, all the site species of the reaction will be present with a default value of 0 for all the parameters, corresponding to no surface coverage modification. Enter the relevant values of the parameters $\mu$, $\epsilon$, and $\eta$ (as defined in this equation in the separate Theory Guide) for all the species for which the reaction has coverage dependence.

7.   If you are using the laminar finite-rate, Eddy-Dissipation Concept or PDF Transport model for turbulence-chemistry interaction, and the reaction is reversible, enable the Include Backward Reaction option for the Arrhenius Rate. When this option is enabled, you will not be able to edit the Rate Exponent for the product species, which instead will be set to be equivalent to the corresponding product Stoich. Coefficient. If you do not wish to use ANSYS FLUENT's default values, or if you are defining your own reaction, you will also need to specify the standard-state enthalpy and standard-state entropy, to be used in the calculation of the backward reaction rate constant ( this equation in the separate Theory Guide). Note that the reversible reaction option is not available for either the eddy-dissipation or the finite-rate/eddy-dissipation turbulence-chemistry interaction model.

8.   If you are using the eddy-dissipation or finite-rate/eddy-dissipation model for turbulence-chemistry interaction, you can enter values for A and B under the Mixing Rate heading. Note, however, that these values should not be changed unless you have reliable data. In most cases you will simply use the default values.

A is the constant $A$ in the turbulent mixing rate ( this equation and  this equation in the separate Theory Guide) when it is applied to a specie that appears as a reactant in this reaction. The default setting of 4.0 is based on the empirically derived values given by Magnussen et al. [ 47].

B is the constant $B$ in the turbulent mixing rate ( this equation in the separate Theory Guide) when it is applied to a specie that appears as a product in this reaction. The default setting of 0.5 is based on the empirically derived values given by Magnussen et al. [ 47].

9.   Repeat steps 2-8 for each reaction you need to define. When you are finished defining all reactions, click OK.

Defining Species and Reactions for Fuel Mixtures

Quite often, combustion systems will include fuel that is not easily described as a pure specie (such as CH $_4$ or C $_2$H $_6$). Complex hydrocarbons, including fuel oil or even wood chips, may be difficult to define in terms of such pure species. However, if you have available the heating value and the ultimate analysis (elemental composition) of the fuel, you can define an equivalent fuel specie and an equivalent heat of formation for this fuel. Consider, for example, a fuel known to contain 50% C, 6% H, and 44% O by weight. Dividing by atomic weights, you can arrive at a "fuel'' specie with the molecular formula C $_{4.17}$H $_{6}$O $_{2.75}$. You can start from a similar, existing specie or create a specie from scratch, and assign it a molecular weight of 100.04 kg/kgmol (4.17 $\times$ 12 + 6 $\times$ 1 + 2.75 $\times$ 16). The chemical reaction would be considered to be

You will need to set the appropriate stoichiometric coefficients for this reaction.

The heat of formation (or standard-state enthalpy) for the fuel specie can be calculated from the known heating value $\Delta H$ since

where $h_{i}^0$ is the standard-state enthalpy on a molar basis. Note the sign convention in Equation  15.1-1: $\Delta H$ is negative when the reaction is exothermic.

Defining Zone-Based Reaction Mechanisms

If your ANSYS FLUENT model involves reactions that are confined to a specific area of the domain, you can define "reaction mechanisms" to enable different reactions selectively in different geometrical zones. You can create reaction mechanisms by selecting reactions from those defined in the Reactions dialog box and grouping them. You can then assign a particular mechanism to a particular zone.

Inputs for Reaction Mechanism Definition

To define a reaction mechanism, click the Edit... button to the right of Mechanism. The Reaction Mechanisms dialog box (Figure  15.1.8) will open.

Figure 15.1.8: The Reaction Mechanisms Dialog Box

The steps for defining a reaction mechanism are as follows:

1.   Set the total number of mechanisms in the Number of Mechanisms field. (Use the arrows to change the value, or type the value and press RETURN.)

2.   Set the Mechanism ID of the mechanism you want to define. (Again, if you type in the value, be sure to press RETURN.)

3.   Specify the Name of the mechanism.

4.   Select the type of reaction to add to the mechanism under Reaction Type. If you select Volumetric, the Reactions list will display all available fluid-phase reactions. If you select Wall Surface or Particle Surface, the Reactions list will display all available wall surface reactions (described in Section  15.2) or particle surface reactions (described in Section  15.3). If you select All, the Reactions list will display all available reactions. (This option is meant for backward compatibility with ANSYS FLUENT 6.0 or earlier cases.)

5.   Select the reactions to be included in the mechanism.

• For Volumetric or Particle Surface reactions, select available reactions for the mechanism in the Reactions list.

• For Wall Surface reactions, use the following procedure:

  (a)   Select available wall surface reactions for the mechanism in the Reactions list.

  (b)   If any site species appear in the selected reaction(s), set the number of sites in the Number of Sites field. (Use the arrows to change the value, or type the value and press RETURN.) See this section in the separate Theory Guide for details about site species in wall surface reactions.

  (c)   If you specify a Number of Sites that is greater than zero, specify the properties of the site.

  Site Name   (optional)

  Site Density   (in kgmol/m $^2$) This value is typically in the range of 10 $^{-8}$ to 10 $^{-6}$.

  Click the Define... button. This will open the Site Parameters dialog box (Figure  15.1.9), where you will define the parameters of the site specie.

  Figure 15.1.9: The Site Parameters Dialog Box

  

  Site Name   is the optional name of the site that was specified in the Reaction Mechanisms dialog box.

  Total Number of Site Species   is the number of adsorbed species that are to be modeled at the site. (Use the arrows to change the value, or type the value and press RETURN.)

  Under Site Species, select the appropriate species from the drop-down list(s) and specify the fractional Initial Site Coverage for each specie. For steady-state calculations, it is recommended (though not strictly required) that the initial values of Initial Site Coverage sum to unity. For transient calculations, it is required that these values sum to unity.

  Click Apply in the Site Parameters dialog box to store the new values.

6.   Repeat steps 2-5 for each reaction mechanism you need to define. When you are finished defining all reaction mechanisms, click OK.

Defining Physical Properties for the Mixture

When your ANSYS FLUENT model includes chemical species, the following physical properties must be defined, either by you or by the database, for the mixture material:

• density, which you can define using the gas law or as a volume-weighted function of composition

• viscosity, which you can define as a function of composition

• thermal conductivity and specific heat (in problems involving solution of the energy equation), which you can define as functions of composition

• mass diffusion coefficients and Schmidt number, which govern the mass diffusion fluxes ( this equation and this equation in the separate Theory Guide)

Detailed descriptions of these property inputs are provided in Chapter  8.

Remember to click the Change/Create button when you are done setting the properties of the mixture material. The properties that appear for each of the constituent species will depend on your settings for the properties of the mixture material. If, for example, you specify a composition-dependent viscosity for the mixture, you will need to define viscosity for each specie.

Defining Physical Properties for the Species in the Mixture

For each of the fluid materials in the mixture, you (or the database) must define the following physical properties:

• molecular weight, which is used in the gas law and/or in the calculation of reaction rates and mole-fraction inputs or outputs

• standard-state (formation) enthalpy and reference temperature (in problems involving solution of the energy equation)

• viscosity, if you defined the viscosity of the mixture material as a function of composition

• thermal conductivity and specific heat (in problems involving solution of the energy equation), if you defined these properties of the mixture material as functions of composition

• standard-state entropy, if you are modeling reversible reactions

• thermal and momentum accommodation coefficients , if you have enabled the low-pressure boundary slip model.

Detailed descriptions of these property inputs are provided in Chapter  8.

Global reaction mechanisms with one or two steps inevitably neglect the intermediate species. In high-temperature flames, neglecting these dissociated species may cause the temperature to be overpredicted. A more realistic temperature field can be obtained by increasing the specific heat capacity for each specie. Rose and Cooper [ 66] have created a set of specific heat polynomials as a function of temperature.

The specific heat capacity for each specie is calculated as

The modified $c_p$ polynomial coefficients (J/kg-K) from [ 60] are provided in Tables  15.1.1 and 15.1.2.

Table 15.1.1: Modified $c_p$ Polynomial Coefficients (J/kg-K) [ 60]

	N $_2$	CH $_4$	CO	H $_2$
$a_0$	$\phantom{-}$1.02705e+03	$\phantom{-}$2.00500e+03	$\phantom{-}$1.04669e+03	1.4147e+04
$a_1$	$\phantom{-}$2.16182e $-$02	$-$6.81428e $-$01	$-$1.56841e $-$01	1.7372e $-$01
$a_2$	$\phantom{-}$1.48638e $-$04	$\phantom{-}$7.08589e $-$03	$\phantom{-}$5.39904e $-$04	6.9e $-$04
$a_3$	$-$4.48421e $-$08	$-$4.71368e $-$06	$-$3.01061e $-$07	---
$a_4$	---	$\phantom{-}$8.51317e $-$10	$\phantom{-}$5.05048e $-$11	---

Table 15.1.2: Modified $c_p$ Polynomial Coefficients [ 60]

	CO $_2$	H $_2$O	O $_2$
$a_0$	$\phantom{-}$5.35446e+02	$\phantom{-}$1.93780e+03	$\phantom{-}$8.76317e+02
$a_1$	$\phantom{-}$1.27867e+00	$-$1.18077e+00	$\phantom{-}$1.22828e $-$01
$a_2$	$-$5.46776e $-$04	$\phantom{-}$3.64357e $-$03	$\phantom{-}$5.58304e $-$04
$a_3$	$-$2.38224e $-$07	$-$2.86327e $-$06	$-$1.20247e $-$06
$a_4$	$\phantom{-}$1.89204e $-$10	$\phantom{-}$7.59578e $-$10	$\phantom{-}$1.14741e $-$09
$a_5$	---	---	$-$5.12377e $-$13
$a_6$	---	---	$\phantom{-}$8.56597e $-$17