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23.12.2 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  23.10.3 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 Phase list.

2.   Click Set... to open the Secondary Phase panel (Figure  23.12.1) .

Figure 23.12.1: The Secondary Phase Panel for a Nongranular Phase
figure

3.   In the Secondary Phase panel, 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  23.10.3).

6.   In the Secondary Phase panel, 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 panel.



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 Phase list.

2.   Click Set... to open the Secondary Phase panel (Figure  23.12.2) .

Figure 23.12.2: The Secondary Phase Panel for a Granular Phase
figure

3.   In the Secondary Phase panel, 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  23.10.3). For a granular phase (which must be placed in the fluid materials category, as mentioned in Section  23.9), you need to specify only the density; you can ignore the values for the other properties, since they will not be used.

figure   

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.   Turn on the Granular option.

7.   (optional) Turn on 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 Section  23.5.8 for details.

9.   In the Secondary Phase panel, 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 Equation  23.5-62). You can select constant (the default) in the drop-down list and specify a constant value, select syamlal-obrien to compute the value using Equation  23.5-64, select gidaspow to compute the value using Equation  23.5-65, or select user-defined to use a user-defined function.

Granular Bulk Viscosity    specifies the solids bulk viscosity ( $\lambda_q$ in Equation  23.5-6). 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 Equation  23.5-66, 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 Equation  23.5-62). 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 Equation  23.5-67, select johnson-et-al to compute the value using Equation  23.5-72, 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 (Equation  23.5-67). 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 Equation  23.5-72, syamlal-obrien to apply Equation  23.5-30, based-ktgf, where the frictional pressure is defined by the kinetic theory [ 81]. 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
 G = \frac{\partial P_{friction}}{\partial \alpha_{friction}} (23.12-1)

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 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 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.

Granular Conductivity    specifies the solids granular conductivity ( $k_{\Theta_s}$ in Equation  23.5-75). You can select syamlal-obrien to compute the value using Equation  23.5-76, select gidaspow to compute the value using Equation  23.5-77, or select user-defined to use a user-defined function. Note, however, that FLUENT currently uses an algebraic relation for the granular temperature. This has been obtained by neglecting convection and diffusion in the transport equation, Equation  23.5-75 [ 364].

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
 G = \frac{\partial P_s}{\partial \alpha_s} (23.12-2)

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 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 panel.



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 panel (Figure  23.12.3).

Figure 23.12.3: The Phase Interaction Panel for the Eulerian Model
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Specifying the Drag Function

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

1.   Click the Drag tab to display the Drag Function inputs.

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 Equation  23.5-18. 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 Equation  23.5-22. 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
    Equation  23.5-27. 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.

  • Select wen-yu to use the fluid-solid drag function described by Equation  23.5-39. 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
    Equation  23.5-41. The Gidaspow model is recommended for dense fluidized beds.

  • Select syamlal-obrien to use the fluid-solid drag function described by Equation  23.5-31. 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 Equation  23.5-43. 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 Equation  23.5-43 and $e_{ss}$ in Equation  23.5-44). 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 Equation  23.5-8) 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.

figure   

Note that the lift force will be more significant for larger particles, but the 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 the Virtual Mass Force

For both granular and nongranular flows, it is possible to include the "virtual mass force'' ( ${\vec F}_{\rm vm}$ in Equation  23.5-9) 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 panel. The virtual mass effect will be included for all secondary phases; it is not possible to enable it just for a particular phase.


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