24.4.1 Defining the Phases for the Mixture Model

Instructions for specifying the necessary information for the primary and secondary phases and their interaction for a mixture model calculation are provided below.

Recall that only one of the phases can be a compressible ideal gas. Be sure that you do not select a compressible ideal gas material (i.e., a material that uses the compressible ideal gas law for density) for more than one of the phases. See Section  24.4.3 for details.

Defining the Primary Phase

The procedure for defining the primary phase in a mixture model calculation is the same as for a VOF calculation. See Section  24.3.4 for details.

Defining a Nongranular Secondary Phase

To define a nongranular (i.e., liquid or vapor) secondary phase in a mixture multiphase calculation, perform the following steps:

1.   Select the phase (e.g., phase-2) in the Phases list.

2.   Click Edit... to open the Secondary Phase dialog box (Figure  24.4.1).

Figure 24.4.1: The Secondary Phase Dialog Box for the Mixture Model

3.   In the Secondary Phase dialog box, enter a Name for the phase.

4.   Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list.

5.   Define the material properties for the Phase Material, following the same procedure you used to set the material properties for the primary phase (see Section  24.3.4). For a particulate phase (which must be placed in the fluid materials category, as mentioned in Section  24.2), you need to specify only the density; you can ignore the values for the other properties, since they will not be used.

6.   In the Secondary Phase dialog box, specify the Diameter of the bubbles, droplets, or particles of this phase ( $d_p$ in this equation in the separate Theory Guide). You can specify a constant value, or use a user-defined function. See the separate UDF Manual for details about user-defined functions. Note that when you are using the mixture model without slip velocity, this input is not necessary, and it will not be available to you.

7.   Click OK in the Secondary Phase dialog box.

Defining a Granular Secondary Phase

To define a granular (i.e., particulate) secondary phase in a mixture model multiphase calculation, perform the following steps:

1.   Select the phase (e.g., phase-2) in the Phases list.

2.   Click Edit... to open the Secondary Phase dialog box (Figure  24.4.2) .

Figure 24.4.2: The Secondary Phase Dialog Box for a Granular Phase Using the Mixture Model

3.   In the Secondary Phase dialog box, enter a Name for the phase.

4.   Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list.

5.   Define the material properties for the Phase Material, following the same procedure you used to set the material properties for the primary phase (see Section  24.3.4). For a granular phase (which must be placed in the fluid materials category, as mentioned in Section  24.2), you need to specify only the density; you can ignore the values for the other properties, since they will not be used.

Note that all properties for granular flows can utilize user-defined functions (UDFs).

See the separate UDF Manual for details about user-defined functions.

6.   Enable the Granular option.

7.   In the Secondary Phase dialog box, specify the following properties of the particles of this phase:

Diameter   specifies the diameter of the particles. You can select constant in the drop-down list and specify a constant value, or select user-defined to use a user-defined function. See the separate UDF Manual for details about user-defined functions.

Granular Viscosity    specifies the kinetic part of the granular viscosity of the particles ( $\mu_{s,{\rm kin}}$ in this equation in the separate Theory Guide). You can select constant (the default) in the drop-down list and specify a constant value, select syamlal-obrien to compute the value using this equation in the separate Theory Guide , select gidaspow to compute the value using this equation in the separate Theory Guide , or select user-defined to use a user-defined function.

Frictional Pressure    specifies the pressure gradient term, $\nabla P_{friction}$, in the granular-phase momentum equation. Choose none to exclude frictional pressure from your calculation, johnson-et-al to apply this equation in the separate Theory Guide , syamlal-obrien to apply this equation in the separate Theory Guide , based-ktgf, where the frictional pressure is defined by the kinetic theory [ 19]. The solids pressure tends to a large value near the packing limit, depending on the model selected for the radial distribution function. You must hook a user-defined function when selecting the user-defined option. See the separate UDF manual for information on hooking a UDF.

Frictional Modulus    is defined as

with $G \ge 0$, which is the derived option. You can also specify a user-defined function for the frictional modulus.

Friction Packing Limit    specifies a threshold volume fraction at which the frictional regime becomes dominant. It is assumed that for a maximum packing limit of 0.6, the frictional regime starts at a volume fraction of about 0.5. This is only a general rule of thumb as there may be other factors involved.

Granular Temperature    specifies temperature for the solids phase and is proportional to the kinetic energy of the random motion of the particles. Choose either the algebraic, the constant, or user-defined option.

Solids Pressure    specifies the pressure gradient term, $\nabla p_s$, in the granular-phase momentum equation. Choose either the lun-et-al, the syamlal-obrien, the ma-ahmadi, or the user-defined option.

Radial Distribution    specifies a correction factor that modifies the probability of collisions between grains when the solid granular phase becomes dense. Choose either the lun-et-al, the syamlal-obrien, the ma-ahmadi, the arastoopour, or a user-defined option.

Elasticity Modulus    is defined as

with $G \ge 0$.

Choose either the derived or user-defined options.

Packing Limit    specifies the maximum volume fraction for the granular phase ( $\alpha_{s,{\rm max}}$). For monodispersed spheres, the packing limit is about 0.63, which is the default value in ANSYS FLUENT. In polydispersed cases, however, smaller spheres can fill the small gaps between larger spheres, so you may need to increase the maximum packing limit.

8.   Click OK in the Secondary Phase dialog box.

Defining the Interfacial Area Concentration

To define the interfacial area concentration on the secondary phase in the mixture model, perform the following steps:

1.   Select the phase (e.g., phase-2) in the Phases list.

2.   Click Edit... to open the Secondary Phase dialog box (Figure  24.4.3) .

Figure 24.4.3: The Secondary Phase Dialog Box Displaying the Interfacial Area Concentration Settings

3.   In the Secondary Phase dialog box, enter a Name for the phase.

4.   Specify which material the phase contains by choosing the appropriate material in the Phase Material drop-down list.

5.   Define the material properties for the Phase Material.

6.   Enable the Interfacial Area Concentration option. Make sure the Granular option is disabled for the Interfacial Area Concentration option to be visible in the interface.

7.   In the Secondary Phase dialog box, specify the following properties of the particles of this phase:

Diameter   specifies the diameter of the particles or bubbles. You can select constant in the drop-down list and specify a constant value, or select user-defined to use a user-defined function. See the separate UDF Manual for details about user-defined functions. The Diameter recommended setting is sauter-mean, allowing for the effects of the interfacial area concentration values to be considered for mass, momentum and heat transfer across the interface between phases.

Packing Limit    specifies the maximum volume fraction for the particle/bubble phase.

Surface Tension    specifies the attractive forces between the interfaces. The surface tension for the liquid-air interface is set for both the hibiki-ishii and the ishii-kim models.

Coalescence Kernal and Breakage Kernel    allows you to specify the coalescence and breakage kernels. You can select none, constant, hibiki-ishii, ishii-kim, or user-defined. The two options, hibiki-ishii and ishii-kim, are described in detail in this section in the separate Theory Guide.

In addition to specifying the hibiki-ishii and ishii-kim as the coalescence and breakage kernels, you can also tune the properties of these two models by using the /define/phases/iac-expert/hibiki-ishii-model and
/define/phases/iac-expert/ishii-kim-model text commands.

For the Hibiki-Ishii model, you can specify the following parameters:

Coefficient Gamma_c

Coefficient K_c

Coefficient Gamma_b

Coefficient K_b

alpha_max

For the Ishii-Kim model, you can specify the following parameters:

Coefficient Crc

Coefficient Cwe

Coefficient C

Coefficient Cti

alpha_max

These values are discussed in greater detail in this section in the separate Theory Guide.

Dissipation Function   gives you the option to choose the formula which calculates the dissipation rate used in the hibiki-ishii and ishii-kim models. You can choose amongst constant, wu-ishii-kim, fluent-ke, and user-defined for the dissipation function.

The wu-ishii-kim option uses a simple algebraic correlation for $\epsilon$:

where

and

where $\rho_m$, $v_m$, $\mu_m$, and $D_h$ are the mixture density, mixture velocity, mixture molecular viscosity, and hydraulic diameter of the flow path.

When you select the wu-ishii-kim model, you will set an additional input for Hydraulic Diameter.

Hydraulic Diameter   is the value used in Equation  24.4-3, should you use the wu-ishii-kim formulation.

Min/Max Diameter   are the limits of the bubble diameters.

Defining Drag Between Phases

For mixture multiphase flows with slip velocity, you can specify the drag function to be used in the calculation. The functions available here are a subset of those discussed in Section  24.5.2. See this section in the separate Theory Guide for more information.

To specify drag laws, click Interaction... to open the Phase Interaction dialog box (Figure  24.4.4) , and then click the Drag tab.

Figure 24.4.4: The Phase Interaction Dialog Box for the Mixture Model ( Drag Tab)

Defining the Slip Velocity

If you are solving for slip velocities during the mixture calculation, and you want to modify the slip velocity definition, click Interaction... to open the Phase Interaction dialog box (Figure  24.4.5) , and then click the Slip tab.

Figure 24.4.5: The Phase Interaction Dialog Box for the Mixture Model ( Slip Tab)

Under Slip Velocity, you can specify the slip velocity function for each secondary phase with respect to the primary phase by choosing the appropriate item in the adjacent drop-down list.

• Select maninnen-et-al (the default) to use the algebraic slip method of Manninen et al. [ 48], described in this section in the separate Theory Guide.

• Select none if the secondary phase has the same velocity as the primary phase (i.e., no slip velocity).

• Select user-defined to use a user-defined function for the slip velocity. See the separate UDF Manual for details.