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.
Figure 23.12.1: The
Secondary Phase Panel for a Nongranular Phase
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.
Figure 23.12.2: The
Secondary Phase Panel for a Granular Phase
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.
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 (
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 (
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 (
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
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,
, 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
(23.12-1)
with
, 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 (
). 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 (
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,
, 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
(23.12-2)
with
.
Packing Limit specifies the maximum volume fraction for the granular phase (
). 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.
Figure 23.12.3: The
Phase Interaction Panel for the Eulerian Model
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 (
in Equation
23.5-43 and
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 (
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.
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'' (
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.