Tutorial 23. Using the Eulerian Granular Multiphase Model with Heat Transfer Introduction This tutorial examines the flow of air and a granular solid phase consisting of glass beads in a hot gas fluidized bed, under uniform minimum fluidization conditions. The results obtained for the local wall-to-bed heat transfer coefficient in ANSYS FLUENT can be compared with analytical results [1]. This tutorial demonstrates how to do the following: • Use the Eulerian granular model. • Set boundary conditions for internal flow. • Calculate a solution using the pressure-based solver. Prerequisites This tutorial is written with the assumption that you have completed Tutorial 1, 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. Problem Description This problem considers a hot gas fluidized bed in which air flows upwards through the bottom of the domain and through an additional small orifice next to a heated wall. A uniformly fluidized bed is examined, which you can then compare with analytical results [1]. The geometry and data for the problem are shown in Figure 23.1. Release 12.0 c ANSYS, Inc. March 12, 2009 23-1
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Tutorial 23. Using the Eulerian Granular Multiphase Modelwith Heat Transfer
Introduction
This tutorial examines the flow of air and a granular solid phase consisting of glass beadsin a hot gas fluidized bed, under uniform minimum fluidization conditions. The resultsobtained for the local wall-to-bed heat transfer coefficient in ANSYS FLUENT can becompared with analytical results [1].
This tutorial demonstrates how to do the following:
• Use the Eulerian granular model.
• Set boundary conditions for internal flow.
• Calculate a solution using the pressure-based solver.
Prerequisites
This tutorial is written with the assumption that you have completed Tutorial 1, andthat 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.
Problem Description
This problem considers a hot gas fluidized bed in which air flows upwards through thebottom of the domain and through an additional small orifice next to a heated wall. Auniformly fluidized bed is examined, which you can then compare with analytical results[1]. The geometry and data for the problem are shown in Figure 23.1.
Using the Eulerian Granular Multiphase Model with Heat Transfer
Pressure Outlet 101325 Pa
Insulated WallHeated Wall T = 373 K
Uniform Velocity Inlet u = 0.25 m/s T = 293 K
Orificeu = 0.25 m/sT = 293 K
0.598VolumeFractionof Solids
Figure 23.1: Problem Schematic
Setup and Solution
Preparation
1. Download eulerian_granular_heat.zip from the User Services Center to yourworking folder (as described in Tutorial 1).
2. Unzip eulerian_granular_heat.zip.
The files, fluid-bed.msh and conduct.c, can be found in the eulerian granular heat
folder created after unzipping the file.
3. Use FLUENT Launcher to start the 2D version of ANSYS FLUENT.
For more information about FLUENT Launcher, see Section 1.1.2 in the separateUser’s Guide.
Ensure that Setup Compilation Environment for UDF is enabled in the UDF Compilertab of the FLUENT Launcher window. This will allow you to compile the UDF.
Using the Eulerian Granular Multiphase Model with Heat Transfer
Note: The Display Options are enabled by default. Therefore, after you read in themesh, it will be displayed in the embedded graphics window.
Step 1: Mesh
1. Read the mesh file fluid-bed.msh.
File −→ Read −→Mesh...
As ANSYS FLUENT reads the mesh file, it will report the progress in the console.
Step 2: General Settings
General
1. Check the mesh.
General −→ Check
ANSYS FLUENT will perform various checks on the mesh and will report the progressin the console. Make sure that the reported minimum volume is a positive number.
Using the Eulerian Granular Multiphase Model with Heat Transfer
2. Examine the mesh (Figure 23.2).
Extra: You can use the right mouse button to check which zone number corre-sponds to each boundary. If you click the right mouse button on one of theboundaries in the graphics window, its zone number, name, and type will beprinted in the ANSYS FLUENT console. This feature is especially useful whenyou have several zones of the same type and you want to distinguish betweenthem quickly.
Figure 23.2: Mesh Display of the Fluidized Bed
3. Enable the pressure-based transient solver.
General
(a) Retain the default selection of Pressure-Based from the Type list.
The pressure-based solver must be used for multiphase calculations.
Using the Eulerian Granular Multiphase Model with Heat Transfer
3. Retain the default laminar viscous model.
Models −→ Viscous −→ Edit...
Experiments have shown negligible three-dimensional effects in the flow field for thecase modeled, suggesting very weak turbulent behavior.
Step 4: UDF
1. Compile the user-defined function, conduct.c, that will be used to define the thermalconductivity for the gas and solid phase.
Define −→ User-Defined −→ Functions −→Compiled...
(a) Click the Add... button below the Source Files option to open the Select Filedialog box.
i. Select the file conduct.c and click OK in the Select File dialog box.
(b) Click Build.
ANSYS FLUENT will create a libudf folder and compile the UDF. Also, aWarning dialog box will open asking you to make sure that UDF source file andcase/data files are in the same folder.
Using the Eulerian Granular Multiphase Model with Heat Transfer
(c) Click OK to close the Warning dialog box.
(d) Click Load to load the UDF.
Extra: If you decide to read in the case file that is provided for this tutorial on theUser Services Center, you will need to compile the UDF associated with thistutorial in your working folder. This is necessary because ANSYS FLUENT willexpect to find the correct UDF libraries in your working folder when readingthe case file.
Step 5: Materials
Materials
1. Modify the properties for air, which will be used for the primary phase.
Materials −→ air −→ Create/Edit...
The properties used for air are modified to match data used by Kuipers et al. [1]
Using the Eulerian Granular Multiphase Model with Heat Transfer
The interphase heat exchange is simulated, using a drag coefficient, the defaultrestitution coefficient for granular collisions of 0.9, and a heat transfer coeffi-cient. Granular phase lift is not very relevant in this problem, and in fact israrely used.
(c) Click OK to close the Phase Interaction dialog box.
Step 7: Boundary Conditions
Boundary Conditions
For this problem, you need to set the boundary conditions for all boundaries.
Using the Eulerian Granular Multiphase Model with Heat Transfer
1. Set the boundary conditions for the lower velocity inlet (v uniform) for the primaryphase.
Boundary Conditions −→ v uniform For the Eulerian multiphase model, youwill specify conditions at a velocity inlet that are specific to the primary and sec-ondary phases.
(a) Select air from the Phase drop-down list.
(b) Click the Edit... button to open the Velocity Inlet dialog box.
i. Retain the default selection of Magnitude, Normal to Boundary from theVelocity Specification Method drop-down list.
ii. Enter 0.25 m/s for the Velocity Magnitude.
iii. Click the Thermal tab and enter 293 K for Temperature.
iv. Click OK to close the Velocity Inlet dialog box.
2. Set the boundary conditions for the lower velocity inlet (v uniform) for the secondaryphase.
Boundary Conditions −→ v uniform
(a) Select solids from the Phase drop-down list.
(b) Click the Edit... button to open the Velocity Inlet dialog box.
Using the Eulerian Granular Multiphase Model with Heat Transfer
i. Retain the default Velocity Specification Method and Reference Frame.
ii. Retain the default value of 0 m/s for the Velocity Magnitude.
iii. Click the Thermal tab and enter 293 K for Temperature.
iv. Click the Multiphase tab and retain the default value of 0 for VolumeFraction.
v. Click OK to close the Velocity Inlet dialog box.
3. Set the boundary conditions for the orifice velocity inlet (v jet) for the primaryphase.
Boundary Conditions −→ v jet
(a) Select air from the Phase drop-down list.
(b) Click the Edit... button to open the Velocity Inlet dialog box.
i. Retain the default Velocity Specification Method and Reference Frame.
ii. Enter 0.25 m/s for the Velocity Magnitude.
In order for a comparison with analytical results [1] to be meaningful, inthis simulation you will use a uniform value for the air velocity equal tothe minimum fluidization velocity at both inlets on the bottom of the bed.
iii. Click the Thermal tab and enter 293 K for Temperature.
iv. Click OK to close the Velocity Inlet dialog box.
Using the Eulerian Granular Multiphase Model with Heat Transfer
4. Set the boundary conditions for the orifice velocity inlet (v jet) for the secondaryphase.
Boundary Conditions −→ v jet
(a) Select solids from the Phase drop-down list.
(b) Click the Edit... button to open the Velocity Inlet dialog box.
i. Retain the default Velocity Specification Method and Reference Frame.
ii. Retain the default value of 0 m/s for the Velocity Magnitude.
iii. Click the Thermal tab and enter 293 K for Temperature.
iv. Click the Multiphase tab and retain the default value of 0 for the VolumeFraction.
v. Click OK to close the Velocity Inlet dialog box.
5. Set the boundary conditions for the pressure outlet (poutlet) for the mixture phase.
Boundary Conditions −→ poutlet
For the Eulerian granular model, you will specify conditions at a pressure outlet forthe mixture and for both phases.
The thermal conditions at the pressure outlet will be used only if flow enters thedomain through this boundary. You can set them equal to the inlet values, as noflow reversal is expected at the pressure outlet. In general, however, it is importantto set reasonable values for these downstream scalar values, in case flow reversaloccurs at some point during the calculation.
(a) Select mixture from the Phase drop-down list.
(b) Click the Edit... button to open the Pressure Outlet dialog box.
i. Retain the default value of 0 Pascal for Gauge Pressure.
ii. Click OK to close the Pressure Outlet dialog box.
Using the Eulerian Granular Multiphase Model with Heat Transfer
11. Set the boundary conditions for the adiabatic wall (wall ins) for the primary phase.
Boundary Conditions −→ wall ins
For the adiabatic wall, you will retain the default thermal conditions for the mixture(zero heat flux), and set momentum conditions (zero shear) for both phases.
(a) Select air from the Phase drop-down list.
(b) Click the Edit... button to open the Wall dialog box.
i. Select Specified Shear from the Shear Condition list.
The Wall dialog box will expand.
ii. Retain the default value of 0 for X-Component and Y-Component.
iii. Click OK to close the Wall dialog box.
12. Set the boundary conditions for the adiabatic wall (wall ins) for the secondary phasesame as that of the primary phase.
Boundary Conditions −→ wall ins
For the secondary phase, you will set the same conditions of zero shear as for theprimary phase.
Using the Eulerian Granular Multiphase Model with Heat Transfer
(a) Enter 0.5 for Pressure.
(b) Enter 0.2 for Momentum.
3. Ensure that the plotting of residuals is enabled during the calculation.
Monitors −→ Residuals −→ Edit...
4. Define a custom field function for the heat transfer coefficient.
Define −→Custom Field Functions...
Initially, you will define functions for the mixture temperature, and thermal conduc-tivity, then you will use these to define a function for the heat transfer coefficient.
(a) Define the function t mix.
i. Select Temperature... and Static Temperature from the Field Functionsdrop-down lists.
ii. Ensure that air is selected from the Phase drop-down list and click Select.
iii. Click the multiplication symbol in the calculator pad.
iv. Select Phases... and Volume fraction from the Field Functions drop-downlist.
v. Ensure that air is selected from the Phase drop-down list and click Select.
vi. Click the addition symbol in the calculator pad.
vii. Similarly, add the term solids-temperature * solids-vof.
Figure 23.4: Initial Volume Fraction of Granular Phase (solids).
11. Save the case file (fluid-bed.cas.gz).
File −→ Write −→Case...
12. Set a time step size of 0.00025 s and run the calculation for 7000 time steps.
Run Calculation
The plot of the value of the mixture-averaged heat transfer coefficient in the cellnext to the heated wall versus time is in excellent agreement with results publishedfor the same case [1].
Using the Eulerian Granular Multiphase Model with Heat Transfer
Summary
This tutorial demonstrated how to set up and solve a granular multiphase problem withheat transfer, using the Eulerian model. You learned how to set boundary conditionsfor the mixture and both phases. The solution obtained is in excellent agreement withanalytical results from Kuipers et al. [1].
Further Improvements
This tutorial guides you through the steps to reach an initial solution. You may be ableto obtain a more accurate solution by using an appropriate higher-order discretizationscheme and by adapting the mesh further. Mesh adaption can also ensure that thesolution is independent of the mesh. These steps are demonstrated in Tutorial 1.
References
1. J. A. M. Kuipers, W. Prins, and W. P. M. Van Swaaij “Numerical Calculationof Wall-to-Bed Heat Transfer Coefficients in Gas-Fluidized Beds”, Department ofChemical Engineering, Twente University of Technology, in AIChE Journal, July1992, Vol. 38, No. 7.