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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
This tutorial is divided into the following sections:
23.1. Introduction
23.2. Prerequisites
23.3. Problem Description
23.4. Setup and Solution
23.5. Summary
23.6. Further Improvements
23.1. Introduction
Mixing tanks are used to maintain solid particles or droplets of heavy fluids in suspension. Mixing may
be required to enhance reaction during chemical processing or to prevent sedimentation. In this tutorial,
you will use the Eulerian multiphase model to solve the particle suspension Eulerian
multiphase model solves momentum equations for each of the phases, which are allowed to mix in any
proportion.
This tutorial demonstrates how to do the following:
•
•
•
•
•
Use the granular Eulerian multiphase model.
Specify fixed velocities with a user-defined function (UDF) to simulate an impeller.
Set boundary conditions for internal flow.
Calculate a solution using the pressure-based solver.
Solve a time-accurate transient problem.
23.2. Prerequisites
This tutorial is written with the assumption that you have completed one or more of the introductory
tutorials found in this manual:
•
•
•
Introduction to Using ANSYS FLUENT in ANSYS Workbench: Fluid Flow and Heat Transfer in a Mixing
Elbow (p.1)
Parametric Analysis in ANSYS Workbench Using ANSYS FLUENT (p.77)
Introduction to Using ANSYS FLUENT: Fluid Flow and Heat Transfer in a Mixing Elbow (p.131)
and that you are familiar with the ANSYS FLUENT navigation pane and menu structure. Some steps in
the setup and solution procedure will not be shown explicitly.
23.3. Problem Description
The problem involves the transient startup of an impeller-driven mixing primary phase is
water, while the secondary phase consists of sand particles with a 111 micron sand is
initially settled at the bottom of the tank, to a level just above the impeller. A schematic of the mixing
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
tank and the initial sand position is shown in Figure 23.1 (p.940).The domain is modeled as 2D axisym-
metric.
Figure 23.1 Problem Specification
The fixed-values option will be used to simulate the impeller. Experimental data are used to represent
the time-averaged velocity and turbulence values at the impeller approach avoids the
need to model the impeller experimental data are provided in a user-defined function.
23.4. Setup and Solution
The following sections describe the setup and solution steps for this tutorial:
23.4.1. Preparation
23.4.2. Step 1: Mesh
23.4.3. Step 2: General Settings
23.4.4. Step 3: Models
23.4.5. Step 4: Materials
23.4.6. Step 5: Phases
23.4.7. Step 6: User-Defined Function (UDF)
23.4.8. Step 7: Cell Zone Conditions
23.4.9. Step 8: Solution
23.4.10. Step 9: Postprocessing
23.4.1. Preparation
t the eulerian_multiphase_ from the ANSYS_Fluid_Dynamics_Tu-
torial_ archive which is available from the
Customer Portal.
940
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Setup and Solution
Note
For detailed instructions on how to obtain the ANSYS_Fluid_Dynamics_Tutori-
al_ file, please refer to Preparation (p.3) in Introduction to Using ANSYS
FLUENT in ANSYS Workbench: Fluid Flow and Heat Transfer in a Mixing Elbow (p.1).
eulerian_multiphase_.
The files, and fix.c can be found in the eulerian_multiphase_granular
folder created after unzipping the file.
3.
4.
Use FLUENT Launcher to start the 2D version of ANSYS FLUENT.
Enable Double-Precision.
For more information about FLUENT Launcher, see Starting ANSYS FLUENT Using FLUENT Launcher in
the User’s Guide.
Note
The Display Options are enabled by ore, after you read in the mesh, it will
be displayed in the embedded graphics window.
Note
The double precision solver is recommended for modeling multiphase flow simulations.
23.4.2. Step 1: Mesh
the mesh file .
File ¡ Read ¡
A warning message will be displayed twice in the need not take any action at this point,
as the issue will be rectified when you define the solver settings in Step 2.
23.4.3. Step 2: General Settings
General
the mesh.
General ¡ Check
ANSYS FLUENT will perform various checks on the mesh and report the progress in the console. Ensure
that the reported minimum volume is a positive number.
e the mesh (Figure 23.2 (p.942)).
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Figure 23.2 Mesh Display
Extra
You can use the right mouse button to check which zone number corresponds to each
boundary. If you click the right mouse button on one of the boundaries in the graphics
window, its zone number, name, and type will be printed in the feature
is especially useful when you have several zones of the same type and you want to
distinguish between them quickly.
the mesh colors.
General ¡
button to open the Mesh Colors dialog box.
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Setup and Solution
You can control the colors used to draw meshes by using the options available in the Mesh Colors
dialog box.
Color by ID in the Options list.
This will assign a different color to each zone in the domain, rather than to each type of
zone.
ii.
b.
Close the Mesh Colors dialog box.
Click Display and close the Mesh Display dialog box.
The graphics display will be updated to show the mesh.
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Figure 23.3 Mesh Display Using the Color by ID Option
the view of the mesh display to show the full tank upright.
Graphics and Animations ¡
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Setup and Solution
axis from the Mirror Planes selection list and click Apply.
The mesh display will be updated to show both sides of the tank.
Auto Scale.
This option is used to scale and center the current display without changing its orientation (Figure
23.4 (p.946)).
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Figure 23.4 Mesh Display of the Tank, Mirrored and Scaled
button to open the Camera Parameters dialog box.
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Setup and Solution
i.
ii.
d.
Drag the indicator of the dial with the left mouse button in the counter-clockwise direction
until the upright view is displayed (Figure 23.5 (p.947)).
Click Apply and close the Camera Parameters dialog box.
Close the Views dialog box.
Note
While modifying the view, you may accidentally lose the view of the geometry in the
can easily revert to the default (front) view by clicking the Default button
in the Views dialog box.
Figure 23.5 Mesh Display of the Upright Tank
y a transient, axisymmetric model.
General
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
the default Pressure-Based solver.
The pressure-based solver must be used for multiphase calculations.
b.
c.
6.
a.
b.
Select Transient in the Time list.
Select Axisymmetric in the 2D Space list.
Enable Gravity.
Enter -9.81 m/ for the Gravitational Acceleration in the X direction.
Set the gravitational acceleration.
23.4.4. Step 3: Models
Models
the Eulerian multiphase model.
Models ¡ Multiphase ¡
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Setup and Solution
a.
b.
c.
2.
Select Eulerian in the Model list.
Retain the default setting of 2 for Number of Eulerian Phases.
Click OK to close the Multiphase Model dialog box.
Enable the
- turbulence model with standard wall functions.
Models ¡ Viscous ¡
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
a.
b.
Select k-epsilon (2eqn) in the Model list.
Select Standard Wall Functions in the Near-Wall Treatment list.
This problem does not require a particularly fine mesh hence, standard wall functions can be
used.
Dispersed in the Turbulence Multiphase Model list.
The dispersed turbulence model is applicable in this case because there is clearly one primary
continuous phase and the material density ratio of the phases is approximately 2.5. Furthermore,
the Stokes number is much less than ore, the kinetic energy of the particle will not differ
significantly from that of the liquid. For more information, see Model Comparisons in the Theory
Guide.
OK to close the Viscous Model dialog box.
23.4.5. Step 4: Materials
Materials
In this step, you will add liquid water to the list of fluid materials by copying it from the ANSYS FLUENT ma-
terials database and create a new material called sand.
liquid water from the FLUENT materials database so that it can be used for the primary phase.
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Setup and Solution
Materials ¡
a.
Fluid ¡
Click the button to open the FLUENT Database Materials dialog box.
water-liquid (h2o l ) from the FLUENT Fluid Materials selection list.
Scroll down the FLUENT Fluid Materials list to locate water-liquid (h2o l ).
c.
d.
2.
Click Copy to copy the information for liquid water to your model.
Close the FLUENT Database Materials dialog box.
Create a new material called sand.
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
a.
b.
c.
Enter sand for Name and delete the entry in the Chemical Formula field.
Enter 2500 kg/ for Density in the Properties group box.
Click Change/Create.
A Question dialog box will open, asking if you want to overwrite water-liquid.
No in the Question dialog box to retain water-liquid and add the new material (sand) to
the list.
The Create/Edit Materials dialog box will be updated to show the new material,sand, in the
FLUENT Fluid Materials drop-down list.
the Create/Edit Materials dialog box.
23.4.6. Step 5: Phases
Phases
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Setup and Solution
y water (water-liquid) as the primary phase.
Phases ¡ phase-1 ¡
a.
b.
c.
2.
Enter water for Name.
Select water-liquid from the Phase Material drop-down list.
Click OK to close the Primary Phase dialog box.
Specify sand (sand) as the secondary phase.
Phases ¡ phase-2 ¡
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
a.
b.
c.
d.
e.
f.
g.
h.
Enter sand for Name.
Select sand from the Phase Material drop-down list.
Enable Granular.
Retain the selection of Phase Property in the Granular Temperature Model list.
Enter 0.000111 m for Diameter.
Select syamlal-obrien from the Granular Viscosity drop-down list.
Select lun-et-al from the Granular Bulk Viscosity drop-down list.
Enter 0.6 for Packing Limit.
Scroll down in the Properties group box to locate Packing Limit.
i.
3.
Click OK to close the Secondary Phase dialog box.
Specify the drag law to be used for computing the interphase momentum transfer.
Phases ¡
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Setup and Solution
a.
b.
Select gidaspow from the Drag Coefficient drop-down list.
Click OK to close the Phase Interaction dialog box.
23.4.7. Step 6: User-Defined Function (UDF)
A UDF is used to specify the fixed velocities that simulate the values of the time-averaged impeller
velocity components and turbulence quantities are based on experimental variation of
these values may be expressed as a function of radius, and imposed as polynomials according to:
=++++…
The order of polynomial to be used depends on the behavior of the function being fitted. For this tutorial,
the polynomial coefficients shown in Table 23.1: Impeller Profile Specifications (p.955)
Table 23.1 Impeller Profile Specifications
Variable
u velocity
v velocity
kinetic energy
dissipation
A1
-7.1357e-2
3.1131e-2
2.2723e-2
-6.5819e-2
A2
54.304
-10.313
6.7989
88.845
A3
-3.1345e+3
9.5558e+2
-424.18
-5.3731e+3
A4
4.5578e+4
-2.0051e+4
9.4615e+3
1.1643e+5
A5
-1.966e+5
1.186e+5
-7.725e+4
-9.120e+5
A6
–
–
1.8410e+5
1.9567e+6
For more information about setting up a UDF using the DEFINE_PROFILE macro, refer to the separate
UDF this macro is usually used to specify a profile condition on a boundary face zone,
it is used in fix.c to specify the condition in a fluid cell zone. Hence, the arguments of the macro
have been changed accordingly.
ret the UDF source
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Define ¡ User-Defined ¡ Functions ¡
fix.c for Source File Name.
If the UDF source file is not in your working folder, you must enter the entire folder path for Source
File Name instead of just entering the file name. Alternatively, and select fix.c in
the eulerian_multiphase_granular folder that was created after you unzipped the ori-
ginal file.
Display Assembly Listing.
The Display Assembly Listing option displays the assembly language code in the console as the
function compiles.
c.
d.
Click Interpret to interpret the UDF.
Close the Interpreted UDFs dialog box.
Note
The name and contents of the UDF are stored in the case file when you save the
case file.
23.4.8. Step 7: Cell Zone Conditions
Cell Zone Conditions
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Setup and Solution
For this problem, you do not have to specify any conditions for outer the domain, there
are three fluid zones, representing the impeller region, the region where the sand is initially located, and the
rest of the are no conditions to be specified in the latter two zones, so you need to set conditions
only in the zone representing the impeller.
the boundary conditions for the fluid zone representing the impeller (fix-zone) for the primary
phase.
Cell Zone Conditions ¡ fix-zone
You will specify the conditions for water and sand separately using the default conditions
for the mixture (i.e., conditions that apply to all phases) are acceptable.
a.
b.
c.
Select fix-zone in the Zone list.
Select water from the Phase drop-down list.
Click button to open the Fluid dialog box.
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Fixed Values.
The Fluid dialog box will expand to show the related inputs.
the Fixed Values tab and set the following fixed values:
Parameter
Axial Velocity
Radial Velocity
Turbulence Kinetic En-
ergy
Turbulence Dissipation
Rate
Value
udf
fixed_u
udf
fixed_v
udf
fixed_ke
udf
fixed_diss
d.
2.
Click OK to close the Fluid dialog box.
Set the boundary conditions for the fluid zone representing the impeller (fix-zone) for the secondary
phase.
Cell Zone Conditions ¡
a.
b.
c.
fix-zone
Make sure that fix-zone is selected in the Type list.
Select sand from the Phase drop-down list.
Click button to open the Fluid dialog box.
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Setup and Solution
Fixed Values.
The Fluid dialog box will expand to show the related inputs.
the Fixed Values tab and set the following fixed values:
Parameter
Axial Velo-
city
Radial Ve-
locity
Value
udf
fixed_u
udf
fixed_v
OK to close the Fluid dialog box.
23.4.9. Step 8: Solution
the under-relaxation factors.
Solution Controls
0.5 for Pressure,0.2 for Momentum, and 0.8 for Turbulent Viscosity.
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Tip
Scroll down in the Under-Relaxation Factors group box to locate Turbulent
Viscosity.
the plotting of residuals during the calculation.
Monitors ¡ Residuals ¡
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Setup and Solution
a.
b.
3.
Ensure that the Plot is enabled in the Options group box.
Click OK to close the Residual Monitors dialog box.
Initialize the solution using the default initial values.
Solution Initialization
a.
4.
Retain the default initial values and click Initialize.
Patch the initial sand bed configuration.
Solution Initialization ¡
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
a.
b.
c.
d.
e.
5.
Select sand from the Phase drop-down list.
Select Volume Fraction from the Variable selection list.
Enter 0.56 for Value.
Select initial-sand from the Zones to Patch selection list.
Click Patch and close the Patch dialog box.
Save the initial case and data files ( and ).
File ¡ Write ¡ Case &
The problem statement is now complete. As a precaution, you should review the impeller velocity fixes
and sand bed patch after running the calculation for a single time step. Since you are using a UDF for
the velocity profiles, perform one time step in order for the profiles to be calculated and available for
viewing.
the time stepping parameters and run the calculation for 0.005 seconds.
Run Calculation
a.
b.
Enter 0.005 for Time Step Size.
Enter 1 for Number of Time Steps.
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Setup and Solution
c.
d.
7.
Enter 40 for Max Iterations/Time Step.
Click Calculate.
Examine the initial velocities and sand volume fraction.
In order to display the initial fixed velocities in the fluid zone (fix-zone), you need to create a surface
for this zone.
a surface for fix-zone.
Surface ¡
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
fix-zone from the Zone selection list and click Create.
The default name is the same as the zone name. ANSYS FLUENT will automatically assign
the default name to the new surface when it is new surface will be added to
the Surfaces selection list in the Zone Surface dialog box.
ii.
b.
Close the Zone Surface dialog box.
Display the initial impeller velocities for water (Figure 23.6 (p.966)).
Graphics and Animations ¡ Vectors ¡
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Setup and Solution
i.
ii.
iii.
iv.
v.
Retain the selection of Velocity from the Vectors of drop-down list.
Retain the selection of water from the Phase drop-down list below the Vectors of drop-
down list.
Retain the selection and Velocity Magnitude from the Color by drop-down
lists.
Retain the selection of water from the Phase drop-down list below the Color by drop-down
lists.
Select fix-zone from the Surfaces selection list and click Display.
ANSYS FLUENT will display the water velocity vectors fixes at the impeller location, as shown
in Figure 23.6 (p.966).
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Figure 23.6 Initial Impeller Velocities for Water
y the initial impeller velocities for sand (Figure 23.7 (p.967)).
Graphics and Animations ¡
i.
ii.
Vectors ¡
Select sand from the Phase drop-down lists (below the Vectors of drop-down list and Color
by drop-down lists).
Click Display (Figure 23.7 (p.967)) and close the Vectors dialog box.
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Setup and Solution
Figure 23.7 Initial Impeller Velocities for Sand
y contours of sand volume fraction (Figure 23.8 (p.969)).
Graphics and Animations ¡ Contours ¡
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
i.
ii.
iii.
iv.
Enable Filled in the Options group box.
Select sand from the Phase drop-down list.
and Volume fraction from the Contours of drop-down lists.
Click Display and close the Contours dialog box.
ANSYS FLUENT will display the initial location of the settled sand bed, as shown in Figure
23.8 (p.969).
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Setup and Solution
Figure 23.8 Initial Settled Sand Bed
the calculation for 1 second.
Run Calculation
a.
b.
Enter 199 for Number of Time Steps.
Click Calculate.
After a total of 200 time steps have been computed (1 second of operation), you will review the
results before continuing.
the case and data files ( and ).
File ¡ Write ¡ Case &
e the results of the calculation after 1 second.
y the velocity vectors for water in the whole tank (Figure 23.9 (p.970)).
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Graphics and Animations ¡
i.
ii.
iii.
Vectors ¡
Select water from the Phase drop-down lists (below the Vectors of drop-down list and
Color by drop-down lists).
Deselect fix-zone from the Surfaces selection list.
Click Display.
Figure 23.9 (p.970) shows the water velocity vectors after 1 second of circulation
is confined to the region near the impeller, and has not yet had time to develop in the upper
portions of the tank.
Figure 23.9 Water Velocity Vectors after 1 s
y the velocity vectors for the sand (Figure 23.10 (p.971)).
Graphics and Animations ¡ Vectors ¡
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Setup and Solution
i.
ii.
Select sand from the Phase drop-down lists (below the Vectors of drop-down list and Color
by drop-down lists).
Click Display and close the Vectors dialog box.
Figure 23.10 Sand Velocity Vectors after 1 s
Figure 23.10 (p.971) shows the sand velocity vectors after 1 second of circulation
of sand around the impeller is significant, but note that no sand vectors are plotted in the upper
part of the tank, where the sand is not yet present.
y contours of sand volume fraction (Figure 23.11 (p.972)).
Graphics and Animations ¡
i.
ii.
iii.
Contours ¡
Retain the selection and Volume fraction from the Contours of drop-down lists.
Retain the selection of sand from the Phase drop-down list.
Click Display and close the Contours dialog box.
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Notice that the action of the impeller draws clear fluid from above the originally settled bed and
mixes it into the compensate, the sand bed is lifted up maximum sand
volume fraction has decreased as a result of the mixing of water and sand.
Figure 23.11 Contours of Sand Volume Fraction after 1 s
ue the calculation for another 19 seconds.
Run Calculation
the Time Step Size to 0.01.
The initial calculation was performed with a very small time step size to stabilize the solution.
After the initial calculation, you can increase the time step to speed up the calculation.
b.
c.
Enter 1900 for Number of Time Steps.
Click Calculate.
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Setup and Solution
The transient calculation will continue up to 20 seconds.
the case and data files ( and ).
File ¡ Write ¡ Case &
23.4.10. Step 9: Postprocessing
You will now examine the progress of the sand and water in the mixing tank after a total of 20
mixing tank has nearly, but not quite, reached a steady flow solution.
y the velocity vectors for water (Figure 23.12 (p.974)).
Graphics and Animations ¡ Vectors ¡
Figure 23.12 (p.974) shows the water velocity vectors after 20 seconds of circulation of
water is now very strong in the lower portion of the tank, though modest near the top.
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Figure 23.12 Water Velocity Vectors after 20 s
y the velocity vectors for sand (Figure 23.13 (p.975)).
Graphics and Animations ¡ Vectors ¡
Figure 23.13 (p.975) shows the sand velocity vectors after 20 seconds of sand has now
been suspended much higher within the mixing tank, but does not reach the upper region of the tank.
The water velocity in that region is not sufficient to overcome the gravity force on the sand particles.
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Setup and Solution
Figure 23.13 Sand Velocity Vectors after 20 s
y contours of sand volume fraction (Figure 23.14 (p.976)).
Graphics and Animations ¡ Contours ¡
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Chapter 23: Using the Eulerian Multiphase Model for Granular Flow
Figure 23.14 Contours of Sand Volume Fraction after 20 s
y filled contours of static pressure for the mixture (Figure 23.15 (p.977)).
Graphics and Animations ¡
a.
b.
c.
Contours ¡
Select mixture from the Phase drop-down list.
and Static Pressure from the Contours of drop-down lists.
Click Display and close the Contours dialog box.
Figure 23.15 (p.977) shows the pressure distribution after 20 seconds of pressure
field represents the hydrostatic pressure except for some slight deviations due to the flow of the
impeller near the bottom of the tank.
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of ANSYS, Inc. and its subsidiaries and affiliates.
Further Improvements
Figure 23.15 Contours of Pressure after 20 s
23.5. Summary
This tutorial demonstrated how to set up and solve a granular multiphase problem using the Eulerian
multiphase problem involved the 2D modeling of particle suspension in a mixing tank and
postprocessing showed the near-steady-state behavior of the sand in the mixing tank, under the as-
sumptions made.
23.6. Further Improvements
This tutorial guides you through the steps to reach an initial may be able to obtain a more
accurate solution by using an appropriate higher-order discretization scheme and by adapting the mesh.
Mesh adaption can also ensure that the solution is independent of the steps are demon-
strated in Introduction to Using ANSYS FLUENT: Fluid Flow and Heat Transfer in a Mixing Elbow (p.131).
Release 14.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information
of ANSYS, Inc. and its subsidiaries and affiliates.
977
978
Release 14.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information
of ANSYS, Inc. and its subsidiaries and affiliates.
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