24.5.2 Defining the Phases for the Eulerian Model

Instructions for specifying the necessary information for the primary and secondary phases and their interaction for an Eulerian multiphase calculation are provided below.

Defining the Primary Phase

The procedure for defining the primary phase in an Eulerian multiphase 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 an Eulerian 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  24.5.1) .

Figure 24.5.1: The Secondary Phase Dialog Box for a Nongranular Phase

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).

6.   In the Secondary Phase dialog box, specify the Diameter of the bubbles or droplets of this phase. You can specify a constant value, or use a user-defined function. See the separate UDF Manual for details about user-defined functions.

7.   Click OK in the Secondary Phase dialog box.

Defining a Granular Secondary Phase

To define a granular (i.e., particulate) secondary phase in an Eulerian 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  24.5.2) .

Figure 24.5.2: The Secondary Phase Dialog Box for a Granular Phase

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.   (optional) Enable the Packed Bed option if you want to freeze the velocity field for the granular phase. Note that when you select the packed bed option for a phase, you should also use the fixed velocity option with a value of zero for all velocity components for all interior cell zones for that phase.

8.   Specify the Granular Temperature Model. Choose either the default Phase Property option or the Partial Differential Equation option. See this section in the separate Theory Guide for details.

9.   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.

Granular Bulk Viscosity    specifies the solids bulk viscosity ( $\lambda_q$ 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 lun-et-al to compute the value using this equation in the separate Theory Guide , or select user-defined to use a user-defined function.

Frictional Viscosity    specifies a shear viscosity based on the viscous-plastic flow ( $\mu_{s,{\rm fr}}$ in this equation in the separate Theory Guide). By default, the frictional viscosity is neglected, as indicated by the default selection of none in the drop-down list. If you want to include the frictional viscosity, you can select constant and specify a constant value, select schaeffer to compute the value using this equation in the separate Theory Guide , select johnson-et-al to compute the value using this equation in the separate Theory Guide , or select user-defined to use a user-defined function.

Angle of Internal Friction    specifies a constant value for the angle $\phi$ used in Schaeffer's expression for frictional viscosity ( this equation in the separate Theory Guide). This parameter is relevant only if you have selected schaeffer or user-defined for the Frictional Viscosity.

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 Conductivity    specifies the solids granular conductivity ( $k_{\Theta_s}$ in this equation in the separate Theory Guide). You can 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. Note, however, that ANSYS FLUENT currently uses an algebraic relation for the granular temperature. This has been obtained by neglecting convection and diffusion in the transport equation, this equation in the separate Theory Guide [ 80].

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, none, or a 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 $G \ge 0$.

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.

10.   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 Eulerian 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) .

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.

Growth Rate   allows you to specify the particle growth rate (m/s). You can select none, constant, or user-defined from the drop-down list. If you select constant, specify a value in the adjacent field. If you have a user-defined function (UDF) that you want to use to model the growth rate, you can choose the user-defined option and specify the appropriate UDF.

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.

Defining the Interaction Between Phases

For both granular and nongranular flows, you will need to specify the drag function to be used in the calculation of the momentum exchange coefficients. For granular flows, you will also need to specify the restitution coefficient(s) for particle collisions. It is also possible to include an optional lift force and/or virtual mass force (described below) for both granular and nongranular flows.

To specify these parameters, click Interaction... to open the Phase Interaction dialog box and visit the Drag, Collisions, and Lift tabs.

Phases Interaction...

Specifying the Drag Function

ANSYS FLUENT allows you to specify a drag function for each pair of phases. Perform the following steps:

1.   Click the Drag tab.

2.   For each pair of phases, select the appropriate drag function from the corresponding drop-down list.

• Select schiller-naumann to use the fluid-fluid drag function described by this equation in the separate Theory Guide. The Schiller and Naumann model is the default method, and it is acceptable for general use in all fluid-fluid multiphase calculations.

• Select morsi-alexander to use the fluid-fluid drag function described by this equation in the separate Theory Guide. The Morsi and Alexander model is the most complete, adjusting the function definition frequently over a large range of Reynolds numbers, but calculations with this model may be less stable than with the other models.

• Select symmetric to use the fluid-fluid drag function described by
  this equation in the separate Theory Guide. The symmetric model is recommended for flows in which the secondary (dispersed) phase in one region of the domain becomes the primary (continuous) phase in another. For example, if air is injected into the bottom of a container filled halfway with water, the air is the dispersed phase in the bottom half of the container; in the top half of the container, the air is the continuous phase. The symmetric drag law is the default method for the Immiscible Fluid Model, which is avaialble with Eulerian multiphase model.

• Select anisotropic to use the fluid-fluid drag function described in this section in the separate Theory Guide. The anisotropic drag law is recommended for free surface modeling. It is based on higher drag in the normal direction to the interface and lower drag in the tangenation direction to the interface. This is only available with Immiscible Fluid Model.

• Select universal-drag for bubble-liquid and/or droplet-gas flow when the characteristic length of the flow domain is much greater than the averaged size of the particles. The universal drag law is described using this equation in the separate Theory Guide. When universal-drag is selected, you will need to set a value for the surface tension coefficient, under the Surface Tension tab, in the Phase Interaction dialog box. This value will apply to the primary phase and the secondary phase.

• Select wen-yu to use the fluid-solid drag function described by this equation in the separate Theory Guide. The Wen and Yu model is applicable for dilute phase flows, in which the total secondary phase volume fraction is significantly lower than that of the primary phase.

• Select gidaspow to use the fluid-solid drag function described by
  this equation in the separate Theory Guide. The Gidaspow model is recommended for dense fluidized beds.

• Select syamlal-obrien to use the fluid-solid drag function described by this equation in the separate Theory Guide. The Syamlal-O'Brien model is recommended for use in conjunction with the Syamlal-O'Brien model for granular viscosity.

• Select syamlal-obrien-symmetric to use the solid-solid drag function described by this equation in the separate Theory Guide. The symmetric Syamlal-O'Brien model is appropriate for a pair of solid phases.

• Select constant to specify a constant value for the drag function, and then specify the value in the text field.

• Select user-defined to use a user-defined function for the drag function (see the separate UDF Manual for details).

• If you want to temporarily ignore the interaction between two phases, select none.

Specifying the Restitution Coefficients (Granular Flow Only)

For granular flows, you need to specify the coefficients of restitution for collisions between particles ( $e_{ls}$ in this equation and $e_{ss}$ in this equation in the separate Theory Guide). In addition to specifying the restitution coefficient for collisions between each pair of granular phases, you will also specify the restitution coefficient for collisions between particles of the same phase.

Perform the following steps:

1.   Click the Collisions tab to display the Restitution Coefficient inputs.

2.   For each pair of phases, specify a constant restitution coefficient. All restitution coefficients are equal to 0.9 by default.

Including the Lift Force

For both granular and nongranular flows, it is possible to include the effect of lift forces ( ${\vec F}_{\rm lift}$ in this equation in the separate Theory Guide) on the secondary phase particles, droplets, or bubbles. These lift forces act on a particle, droplet, or bubble mainly due to velocity gradients in the primary-phase flow field. In most cases, the lift force is insignificant compared to the drag force, so there is no reason to include it. If the lift force is significant (e.g., if the phases separate quickly), you may want to include this effect.

Note that the lift force will be more significant for larger particles, but the ANSYS FLUENT model assumes that the particle diameter is much smaller than the interparticle spacing. Thus, the inclusion of lift forces is not appropriate for closely packed particles or for very small particles.

To include the effect of lift forces, perform the following steps:

1.   Click the Lift tab to display the Lift Coefficient inputs.

2.   For each pair of phases, select the appropriate specification method from the corresponding drop-down list. Note that, since the lift forces for a particle, droplet, or bubble are due mainly to velocity gradients in the primary-phase flow field, you will not specify lift coefficients for pairs consisting of two secondary phases; lift coefficients are specified only for pairs consisting of a secondary phase and the primary phase.

• Select none (the default) to ignore the effect of lift forces.

• Select constant to specify a constant lift coefficient, and then specify the value in the text field.

• Select user-defined to use a user-defined function for the lift coefficient (see the separate UDF Manual for details).

Including Surface Tension and Wall Adhesion Effects

As discussed in this section in the separate Theory Guide , the importance of surface tension effects depends on the value of the capillary number, Ca (defined by this equation in the separate Theory Guide), or the Weber number, We (defined by this equation in the separate Theory Guide). Surface tension effects can be neglected if Ca  $\gg 1$ or We  $\gg 1$.

Note that the calculation of surface tension effects will be more accurate if you use a quadrilateral or hexahedral mesh in the area(s) of the computational domain where surface tension is significant. If you cannot use a quadrilateral or hexahedral mesh for the entire domain, then you should use a hybrid mesh, with quadrilaterals or hexahedra in the affected areas. ANSYS FLUENT also offers an option to use VOF gradients at the nodes for curvature calculations on meshes when more accuracy is desired. For more information, see this section in the separate Theory Guide.

If you want to include the effects of surface tension along the interface between one or more pairs of phases, as described in this section in the separate Theory Guide , click Interaction... to open the Phase Interaction dialog box (Figure  24.3.7).

Perform the following steps to include surface tension (and, if appropriate, wall adhesion) effects along the interface between one or more pairs of phases:

1.   Click the Surface Tension tab.

2.   For each pair of phases between which you want to include the effects of surface tension, specify a constant surface tension coefficient. Alternatively you can specify a temperature dependent, polynomial, piece-wise polynomial, piecewise linear, or a user-defined surface tension coefficient. See this section in the separate Theory Guide for more information on surface tension, and the separate UDF Manual for more information on user-defined functions. All surface tension coefficients are equal to 0 by default, representing no surface tension effects along the interface between the two phases.

3.   If you want to include wall adhesion, enable the Wall Adhesion option. When Wall Adhesion is enabled, you will need to specify the contact angle at each wall as a boundary condition (as described in Section  24.2.9).

Including the Virtual Mass Force

For both granular and nongranular flows, it is possible to include the "virtual mass force'' ( ${\vec F}_{\rm vm}$ in this equation in the separate Theory Guide) that is present when a secondary phase accelerates relative to the primary phase. The virtual mass effect is significant when the secondary phase density is much smaller than the primary phase density (e.g., for a transient bubble column).

To include the effect of the virtual mass force, turn on the Virtual Mass option in the Phase Interaction dialog box. The virtual mass effect will be included for all secondary phases; it is not possible to enable it just for a particular phase.