ANSYS Polyflow Tutorial Guide.pdf - Portal de Documentacion de ( PDFDrive ).pdf

ANSYS Polyflow Tutorial Guide
Release 15.0
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Table of Contents
Using This Manual ........................................................................................................................................ ix
1.The Contents of This Manual ............................................................................................................... ix
2.The Contents of the ANSYS Polyflow Manuals ...................................................................................... ix
3. Contacting Technical Support ............................................................................................................. ix
I. Introduction to using Polyflow in Workbench ......................................................................................... 1
1. ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion .......................................................... 3
1.1. Introduction ............................................................................................................................... 3
1.2.Prerequisites ............................................................................................................................... 3
1.3. Problem Description ................................................................................................................... 3
1.4. Setup and Solution ..................................................................................................................... 5
1.4.1. Preparation ........................................................................................................................ 5
1.4.2.Step 1: Creating a Fluid Flow Analysis System in ANSYS Workbench ..................................... 6
1.4.3. Step 2: Preparing the Geometry in ANSYS DesignModeler ................................................. 11
1.4.4.Step 3:Meshing the Geometry in the ANSYS Meshing Application ..................................... 13
1.4.5.Step 4:Setting Up the CFD Simulation in ANSYS Polydata .................................................. 24
1.4.6. Step 5: Running the CFD Simulation in ANSYS Polyflow ..................................................... 28
1.4.7.Step 6: Displaying Results in ANSYS CFD-Post .................................................................... 29
1.4.8.Step 7:Exploring Additional Solutions ............................................................................... 44
1.4.9. Step 8: Summary .............................................................................................................. 49
II. Extrusion ............................................................................................................................................... 51
1.2.5D Axisymmetric Extrusion .......................................................................................................... 53
1.1. Introduction ............................................................................................................................. 53
1.2. Prerequisites ............................................................................................................................. 53
1.3. Problem Description ................................................................................................................. 54
1.4.Preparation ............................................................................................................................... 56
1.5. Step 1: Project and Mesh ........................................................................................................... 56
1.6. Step 2: Models .......................................................................................................................... 59
1.7. Step 3: Material Data ................................................................................................................. 61
1.8. Step 4: Boundary Conditions ..................................................................................................... 63
1.9. Step 5: Remeshing .................................................................................................................... 68
1.10.Step 6:Stream Function ........................................................................................................... 71
1.11. Step 7: Outputs ....................................................................................................................... 73
1.12.Step 8: Save the Data and Exit Polydata .................................................................................... 73
1.13. Step 9: Solution ....................................................................................................................... 75
1.14.Step 10: Postprocessing ........................................................................................................... 75
1.15. Summary ................................................................................................................................ 86
2. Fluid Flow and Conjugate Heat Transfer ......................................................................................... 87
2.1. Introduction ............................................................................................................................. 87
2.2. Prerequisites ............................................................................................................................. 87
2.3. Problem Description ................................................................................................................. 88
2.4.Preparation ............................................................................................................................... 89
2.5. Step 1: Project and Mesh ........................................................................................................... 90
2.6. Step 2: Models, Material Data, and Boundary Conditions ............................................................ 90
2.7.Step 2a:Definition of Sub-Task 1 ................................................................................................ 91
2.8. Step 2b: Definition of Sub-Task 2 ............................................................................................... 99
2.10. Step 4: Solution ..................................................................................................................... 103
2.12. Summary .............................................................................................................................. 113
3. Non-Isothermal Flow Through a Cooled Die ................................................................................. 115
iii
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of ANSYS,Inc.and its subsidiaries and affiliates.

3.1. Introduction ........................................................................................................................... 115
3.2. Prerequisites ........................................................................................................................... 115
3.3. Problem Description ............................................................................................................... 115
3.4. Preparation ............................................................................................................................. 118
3.5. Step 1: Project and Mesh ......................................................................................................... 119
3.6. Step 2: Models, Materials, and Boundary Conditions ................................................................. 119
3.7. Step 3: Definition of the Fluid Sub-Task .................................................................................... 120
3.8. Step 4: Definition of the Solid Sub-Task .................................................................................... 131
3.9. Step 5: Numerical Parameters .................................................................................................. 134
3.10. Step 6: Outputs ..................................................................................................................... 134
3.11.Step 7: Save the Data and Exit Polydata .................................................................................. 134
3.12. Step 8: Solution ..................................................................................................................... 135
3.14. Summary .............................................................................................................................. 147
3.15.Appendix: Non-Linearity and Evolution .................................................................................. 147
4. 3D Extrusion .................................................................................................................................. 149
4.1. Introduction ........................................................................................................................... 149
4.2. Prerequisites ........................................................................................................................... 149
4.4. Preparation ............................................................................................................................. 151
4.6. Step 2: Models ........................................................................................................................ 152
4.7. Step 3: Material Data ............................................................................................................... 154
4.8. Step 4: Boundary Conditions ................................................................................................... 155
4.9.Step 5:Remeshing ................................................................................................................... 158
4.11. Step 7: Solution ..................................................................................................................... 162
4.13. Summary .............................................................................................................................. 176
5. Direct Extrusion ............................................................................................................................ 177
5.1. Introduction ........................................................................................................................... 177
5.2. Prerequisites ........................................................................................................................... 177
5.4. Preparation ............................................................................................................................. 179
5.6. Step 2: Models ........................................................................................................................ 180
5.9.Step 5:Remeshing ................................................................................................................... 184
5.10. Step 6: Numerical Parameters ................................................................................................ 185
5.11. Step 7: Outputs ..................................................................................................................... 186
5.13. Step 9: Solution ..................................................................................................................... 187
5.14. Step 10: Postprocessing ......................................................................................................... 187
5.15. Summary .............................................................................................................................. 198
5.16. Appendix .............................................................................................................................. 198
5.16.1.Power Law .................................................................................................................... 199
5.16.2. Optimesh Remeshing Technique .................................................................................. 199
5.16.3. Evolution Scheme ........................................................................................................ 199
5.16.4. IGES Output ................................................................................................................. 199
6.Inverse Extrusion ........................................................................................................................... 201
6.1. Introduction ........................................................................................................................... 201
iv
Tutorial Guide

6.2. Prerequisites ........................................................................................................................... 201
6.4. Preparation ............................................................................................................................. 203
6.6. Step 2: Models ........................................................................................................................ 204
6.9.Step 5:Remeshing ................................................................................................................... 209
6.11. Step 7: Outputs ..................................................................................................................... 212
6.13. Step 9: Solution ..................................................................................................................... 213
6.15. Summary .............................................................................................................................. 225
6.16. Appendix .............................................................................................................................. 225
6.16.1.Power Law .................................................................................................................... 225
6.16.2. Evolution Scheme ........................................................................................................ 225
6.16.3. Remeshing Technique .................................................................................................. 226
6.16.4. Optimesh Remeshing Technique .................................................................................. 226
6.16.5. IGES Output ................................................................................................................. 226
7.Flow of Two Immiscible Fluids ....................................................................................................... 227
7.1. Introduction ........................................................................................................................... 227
7.2. Prerequisites ........................................................................................................................... 227
7.4. Preparation ............................................................................................................................. 230
7.6.Step 2:Models,Material Data,and Boundary Conditions ........................................................... 230
7.7.Step 2a: Definition of Sub-Task 1 .............................................................................................. 231
7.8. Step 2b: Definition of Sub-Task 2 ............................................................................................. 238
7.10. Step 4: Solution ..................................................................................................................... 242
7.12. Summary .............................................................................................................................. 248
8. Flow of Two Immiscible Fluids by Species Method ....................................................................... 249
8.1. Introduction ........................................................................................................................... 249
8.2. Prerequisites ........................................................................................................................... 249
8.4. Preparation ............................................................................................................................. 253
8.6.Step 2:Models,Material Data,and Boundary Conditions ........................................................... 254
8.7. Step 2a: Definition of Species and Species Transport Sub-task .................................................. 254
8.8. Step 2b: Definition of a Sub-task .............................................................................................. 259
8.10. Step 4: Solution ..................................................................................................................... 265
8.12. Summary .............................................................................................................................. 272
III. Blow Molding ..................................................................................................................................... 273
1. 3D Thermoforming of a Blister ...................................................................................................... 275
1.1. Prerequisites ........................................................................................................................... 275
1.3. Preparation ............................................................................................................................. 278
v
Tutorial Guide

1.5. Step 2: Models ........................................................................................................................ 279
1.6. Step 3: Definition of a Sub-task ................................................................................................ 283
1.7. Step 4: Create Sub-tasks for Postprocessing ............................................................................. 289
1.8. Step 5: Specify the Numerical Parameters ................................................................................ 291
1.9. Step 6: Outputs ....................................................................................................................... 291
1.11. Step 8: Solution ..................................................................................................................... 292
1.13. Summary .............................................................................................................................. 304
1.14. Further Improvements .......................................................................................................... 305
1.15. Appendix .............................................................................................................................. 306
1.15.1. Contact Boundary Conditions ....................................................................................... 306
1.15.2. Remark on the Penalty Coefficient ................................................................................ 307
1.15.3. Remeshing ................................................................................................................... 307
2. 2D Axisymmetric Blow Molding .................................................................................................... 309
2.1. Introduction ........................................................................................................................... 309
2.2. Prerequisites ........................................................................................................................... 310
2.4. Preparation ............................................................................................................................. 311
2.6. Step 2: Models ........................................................................................................................ 312
2.9.Step 5:Remeshing ................................................................................................................... 320
2.11. Step 7: Outputs ..................................................................................................................... 323
2.12. Step 8:Thickness Postprocessor ............................................................................................. 324
2.14. Step 10: Solution ................................................................................................................... 325
2.16. Summary .............................................................................................................................. 337
2.17. Appendix .............................................................................................................................. 337
2.17.1. Remeshing Technique .................................................................................................. 338
2.17.2. Master Moving Surface ................................................................................................. 338
2.17.3.Time Marching Scheme ................................................................................................ 338
3. Plug-Assisted Thermoforming of a Blister .................................................................................... 339
3.1. Prerequisites ........................................................................................................................... 339
3.3. Preparation ............................................................................................................................. 342
3.5. Step 2: Model the Mold ........................................................................................................... 343
3.6. Step 3: Model the Plug ............................................................................................................ 348
3.7.Step 4:Definition of the Blister Sub-task ................................................................................... 351
3.9. Step 6: Outputs ....................................................................................................................... 360
3.11. Step 8: Solution ..................................................................................................................... 360
3.13. Summary .............................................................................................................................. 372
3.14. Appendix .............................................................................................................................. 373
vi
Tutorial Guide

3.14.3. Remeshing ................................................................................................................... 374
4. 3D Blow Molding of a Bottle ......................................................................................................... 375
4.1. Prerequisites ........................................................................................................................... 375
4.2. Description ............................................................................................................................. 375
4.3. Preparation ............................................................................................................................. 377
4.5. Step 2: Model the Right Mold .................................................................................................. 378
4.6.Step 3: Model the Left Mold ..................................................................................................... 383
4.7.Step 4: Definition of the Parison Sub-task ................................................................................. 386
4.9. Step 6: Outputs ....................................................................................................................... 395
4.11. Step 8: Solution ..................................................................................................................... 395
4.13. Summary .............................................................................................................................. 405
4.14. Further Improvements .......................................................................................................... 406
4.15. Appendix .............................................................................................................................. 407
4.15.3. Remeshing ................................................................................................................... 408
4.15.4. Evolutions .................................................................................................................... 408
vii
Tutorial Guide

viii

Using This Manual
1.The Contents of This Manual
The Polyflow Tutorial Guide contains a number of example problems with complete detailed instructions,
commentary, and postprocessing of results.
2.The Contents of the ANSYS Polyflow Manuals
The manuals listed below form the ANSYS Polyflow product documentation set. They include descriptions
of the procedures, commands, and theoretical details needed to use ANSYS Polyflow products.
• The Polyflow User's Guide explains how to use ANSYS Polydata and ANSYS Polyflow to set up and
solve a problem.
• The Polyflow Tutorial Guide contains a number of example problems with complete detailed instruc-
tions, commentary, and postprocessing of results.
• The Polyflow in Workbench User's Guide explains how to use the ANSYS Polyflow application within
ANSYS Workbench.
• The Polymat User's Guide explains how to use the ANSYS Polymat module for material property
evaluation.
• The Polystat User's Guide explains how to set up a MIXING task in ANSYS Polydata and how to
use the ANSYS Polystat module for statistical postprocessing of results.
• The GAMBIT manuals teach you how to use the GAMBIT preprocessor for geometry creation and mesh
generation.
• The CFD-Post User's Guide explains how to use CFD-Post to examine your results.
• The ANSYS Polyflow Examples Manual provides overviews of solutions to a variety of problem types.
For details on how to access the ANSYS Polyflow manuals, see ANSYS Polyflow Documentation in the
separate Polyflow User's Guide.
3.Contacting Technical Support
Technical Support for ANSYS, Inc. products is provided either by ANSYS, Inc. directly or by one of our
certified ANSYS Support Providers. Please check with the ANSYS Support Coordinator (ASC) at your
company to determine who provides support for your company, or go to www.ansys.com and select
Contact ANSYS > Contacts and Locations.
If your support is provided by ANSYS, Inc. directly, Technical Support can be accessed quickly and effi-
ciently from the ANSYS Customer Portal, which is available from the ANSYS Website (www.ansys.com)
under Support > Customer Portal. The direct URL is: support.ansys.com.
One of the many useful features of the Customer Portal is the Knowledge Resources Search, which can
be found on the Home page of the Customer Portal.
ix

Systems and installation Knowledge Resources are easily accessible via the Customer Portal by using
the following keywords in the search box: Systems/Installation. These Knowledge Resources
provide solutions and guidance on how to resolve installation and licensing issues quickly.
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Support for University customers is provided only through the ANSYS Customer Portal.
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Using This Manual

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xi
Contacting Technical Support

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xii
Using This Manual

Part I: Introduction to using Polyflow in Workbench
The following Workbench tutorial is available:
1. ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

ANSYS Polyflow Tutorial Guide.pdf - Portal de Documentacion de ( PDFDrive ).pdf

Chapter 1: ANSYS Polyflow in ANSYS Workbench Tutorial: 3D
Extrusion
1.1.Introduction
This tutorial illustrates how to use ANSYS Polyflow fluid flow systems in ANSYS Workbench to set up
and solve a 3D extrusion problem with a variety of inlet flow rates. This tutorial is designed to introduce
you to the ANSYS Workbench tool set using a similar geometry to that used in 3D Extrusion (p. 149). In
this tutorial, you will import the geometry and generate a computational mesh using the geometry and
meshing tools within ANSYS Workbench. Then you will use ANSYS Polydata to modify an imported data
file, solve the CFD problem using ANSYS Polyflow, and view the results in the CFD-Post postprocessing
tool. Finally, you will use the Parameter and Design Points view in ANSYS Workbench to calculate
results for multiple design points that represent different inlet flow rates.
This tutorial demonstrates how to do the following:
• Launch ANSYS Workbench.
• Create an ANSYS Polyflow fluid flow analysis system in ANSYS Workbench.
• Import and edit geometry using ANSYS DesignModeler.
• Create a computational mesh for the geometry using the ANSYS Meshing application.
• Import a data file, and modify it using ANSYS Polydata to include a user-defined template for the die inlet
flow rate.
• Calculate a solution using ANSYS Polyflow.
• View the initial results and create an output parameter for the maximum velocity of the extrudate in CFD-
Post.
• Generate results for multiple design points using the Parameter and Design Points view, and chart how
the outflow velocity varies with the inlet flow rate.
1.2.Prerequisites
This tutorial assumes that you have little to no experience with ANSYS DesignModeler, ANSYS Meshing,
ANSYS Polyflow, CFD-Post, or the Parameter and Design Points view of ANSYS Workbench, and so
each step will be explicitly described.
1.3.Problem Description
This problem deals with the flow of a Newtonian fluid through a three-dimensional die. Due to the
symmetry of the problem (the cross-section of the die is a square), the computational domain is defined
for a quarter of the geometry and two planes of symmetry are defined.
3

The melt enters the die as shown in Figure 1.1: Problem Description(p. 4) at an initial flow rate of
= cm3
/s (this flow rate is a quarter of that for the complete physical system) and the extrudate is
obtained at the exit. It is assumed that the extrudate is fully deformed at the end of the computational
domain, and that it will not deform any further (that is, subdomain 2 is long enough to account for all
the deformation of the extrudate).
Figure 1.1: Problem Description
The incompressibility and momentum equations are solved over the computational domain. The domain
for the problem is divided into two subdomains (as shown in Figure 1.1: Problem Description(p. 4))
so that a remeshing algorithm can be applied only to the portion of the mesh that will be deformed.
Subdomain 1 represents the die where the fluid is confined. Subdomain 2 corresponds to the extrudate
that is in contact with the air and can deform freely. The calculation will determine the location of the
free surface (the skin of the extrudate), as well as the velocity of the extrudate at the exit.
The boundary set for the problem is shown in Figure 1.2: The Boundary Set for the Problem(p. 5), and
the conditions at the boundaries of the domains are:
• inlet: flow inlet, initial volumetric flow rate =
cm3
/s
• die wall: zero velocity
• free surface: free surface
• symmetry 1: symmetry plane
• symmetry 2: symmetry plane
• outlet: flow exit
4
ANSYS Polyflow in ANSYS Workbench Tutorial:3D Extrusion

Figure 1.2: The Boundary Set for the Problem
1.4.Setup and Solution
1.4.1.Preparation
1. Copy the file ext3d-workbench.zip to your working directory. To access this file, begin by pointing
your web browser to
• For Windows:
pathANSYS Incv150polyflowpolyflow15.0. helpindex.htm
• For Linux:
path/ansys_inc/v150/polyflow/polyflow15.0./help/index.htm
where path is the directory in which ANSYS Polyflow has been installed and represents the ap-
propriate number for the release (for example, 0 for polyflow15.0.0).
If, for example, you are using Internet Explorer as your browser, select the File Open... menu
item and click the Browse button to browse through your directories to find the file.
5
Setup and Solution

When opened, the file displays the ANSYS Polyflow documentation “home page. Click the Download
link under the ANSYS Polyflow in ANSYS Workbench Tutorial heading, and then copy the ext3d-
workbench.zip file that is saved to your computer to your working directory.
Note
This zipped file can also be downloaded from the ANSYS Customer Portal, https://sup-
port.ansys.com/training.
2. Unzip ext3d-workbench.zip.
The extracted files include the geometry file ext3d.x_t, the data file polyflow.dat, and a
solution_files folder that contains the solution files created during the preparation of the tutorial.
Note
This tutorial is prepared using ANSYS Polyflow on a Windows system. The screen shots and
graphic images that follow may be slightly different than the appearance on your system,
depending on the operating system or graphics card.
1.4.2.Step 1: Creating a Fluid Flow Analysis System in ANSYS Workbench
In this step, you will start ANSYS Workbench, create a new fluid flow analysis system, then view the list
of files generated by ANSYS Workbench.
1. Start ANSYS Workbench by clicking the Start button, moving your pointer over All Programs, moving
your pointer over ANSYS 15.0, then clicking Workbench 15.0.
Start → All Programs → ANSYS 15.0 → Workbench 15.0
The ANSYS Workbench application window will open, containing the Toolbox on the left and the
Project Schematic on the right. The Toolbox lists the various supported analyses and applications,
and the Project Schematic provides a space to display the components of the analysis systems you
select.
Note
When you first start ANSYS Workbench, the Getting Started pop-up window is displayed,
offering assistance through the online help for using the application. You can keep the
window open, or close it by clicking the red ‘X’ icon in the upper right corner. If you
need to access the online help at any time, use the Help menu, or press the F1 key.
2. Create a new fluid flow analysis system by double-clicking the Fluid Flow (Polyflow) option under
Analysis Systems in the Toolbox.
6

Figure 1.3: Selecting the Fluid Flow (Polyflow) Analysis System in ANSYS Workbench
Extra
You can also create a new fluid flow analysis system by dragging-and-dropping the
analysis system into the Project Schematic: a green dotted outline will indicate a potential
location in the Project Schematic for the new system, which will turn into a red box
when you attempt to drop it.
A new ANSYS Polyflow-based fluid flow analysis system will be displayed in the Project Schematic.
7
Setup and Solution

Figure 1.4: ANSYS Workbench with a New ANSYS Polyflow-Based Fluid Flow Analysis System
Note
The ANSYS Polyflow-based fluid flow analysis system, for example, is composed of various
cells (Geometry, Mesh, and so on) that represent the work flow for performing the
analysis. ANSYS Workbench is composed of multiple data-integrated (for example, ANSYS
Polyflow) and native applications into a single, seamless project flow, where individual
cells can obtain data from and provide data to other cells. ANSYS Workbench provides
visual indications of a cell’s state at any given time via icons on the right side of each
cell. Because of the constant flow of data, a cell’s state can quickly change. Brief descrip-
tions of the various states are provided below. For more information about cell states,
see the ANSYS Workbench online help.
• Unfulfilled ( ) indicates that required upstream data does not exist. For example, when you first
create a new Fluid Flow (Polyflow) analysis system, all cells downstream of the Geometry cell appear
as Unfulfilled because you have not yet specified a geometry for the system.
• Refresh Required ( ) indicates that upstream data has changed since the last refresh or update.
For example, after you assign a geometry to the Geometry cell in your new Fluid Flow (Polyflow)
analysis system, the Mesh cell appears as Refresh Required since the geometry data has not yet
been passed from the Geometry cell to the Mesh cell.
8

• Attention Required ( ) indicates that the current upstream data has been passed to the cell, however,
you must take some action to proceed. For example, after you launch ANSYS Polydata from the Setup
cell in a Fluid Flow (Polyflow) analysis system that has a valid mesh, the Setup cell appears as At-
tention Required because additional data must be entered in ANSYS Polydata before you can calculate
a solution.
• Update Required ( ) indicates that local data has changed and the output of the cell must be re-
generated. For example, after you launch ANSYS Meshing from the Mesh cell in a Fluid Flow (Polyflow)
analysis system that has a valid geometry, the Mesh cell appears as Update Required because the
Mesh cell has all the data it needs to generate an ANSYS Polyflow mesh file, but the ANSYS Poly-
flow mesh file has not yet been generated.
• Up-to-Date ( ) indicates that an update has been performed on the cell and no failures have occurred
(or an interactive calculation has been completed successfully). For example, after ANSYS Polyflow fin-
ishes performing the number of necessary solver iterations, the Solution cell appears as Up-to-Date.
• Interrupted ( ) indicates that you have interrupted an update (or stopped an interactive calculation
that is in progress). For example, if you select the stop button ( ) in the Progress Monitor of ANSYS
Workbench at a point where ANSYS Polyflow has generated results but has not yet completed the
calculation (such as during a transient simulation), then verify the action in the dialog box that opens,
ANSYS Polyflow is immediately stopped and the Solution cell appears as Interrupted.
• Input Changes Pending ( ) indicates that the cell is locally up-to-date, but may change when next
updated as a result of changes made to upstream cells. For example, if you change the Mesh in an
Up-to-Date Fluid Flow (Polyflow) analysis system, the Setup cell appears as Refresh Required, and
the Solution and Results cells appear as Input Changes Pending.
• Pending ( ) indicates that a batch or asynchronous solution is in progress. This icon will only appear
when the Solution cell is in background mode.
• Refresh Failed, Refresh Required ( ) indicates that the last attempt to refresh cell input data failed,
and so the cell must be refreshed.
• Update Failed, Update Required ( ) indicates that the last attempt to update the cell and calculate
output data failed, and so the cell needs to be updated. For example, if you update the Solution cell
and the solver diverges during the calculation, the Solution cell appears as Update Failed, Update
Required.
• Update Failed, Attention Required ( ) indicates that the last attempt to update the cell and calculate
output data failed, and so the cell requires attention.
3. Name the analysis.
a. Double-click the Fluid Flow (Polyflow) label underneath the analysis system.
b. Enter ext3d for the name of the analysis system.
4. Save the project.
a. Select the Save option under the File menu in ANSYS Workbench.
9
Setup and Solution

File → Save
The Save As dialog will open, where you can browse to a specific directory and enter a specific
name for the ANSYS Workbench project.
b. In your working directory, enter ext3d-wb as the project File name and click the Save button
to save the project. ANSYS Workbench saves the project with a .wbpj extension, as well as sup-
porting files for the project.
5. View the files generated by ANSYS Workbench, by enabling the Files option under the View menu.
View → Files
The Files view will be displayed in the Project Schematic.
Figure 1.5: Displaying the Files View after Adding an ANSYS Polyflow-Based Fluid Flow
Analysis System
ANSYS Workbench allows you to easily view the files associated with your project using the Files view.
You can see the name and type of file, the ID of the cell the file is associated with, the size of the file,
the location of the file, and other information. For more information about the Files view, see the sep-
arate Polyflow in Workbench User's Guide and the ANSYS Workbench online help.
10

1.4.3.Step 2: Preparing the Geometry in ANSYS DesignModeler
In this step, you will import a previously created geometry file, modify the geometry with ANSYS
DesignModeler, then review the list of files generated by ANSYS Workbench.
Note
ANSYS DesignModeler is licensed separately from ANSYS Polyflow. If you do not have access
to ANSYS DesignModeler, you can instead import a geometry file that does not need to be
modified, as noted in step 1.c.
1. Import the geometry file.
a. Right-click the Geometry cell in the ext3d fluid flow analysis system (cell A2 in the ANSYS
Workbench Project Schematic).
b. Move your pointer over Import Geometry in the context menu that opens, and click Browse....
c. Use the Open dialog box to browse to the folder you unzipped in a previous step, select
ext3d.x_t, and click Open.
Note
If you do not have access to ANSYS DesignModeler, select PFL.agdb in the Open
dialog box instead, then skip to Step 3: Meshing the Geometry in the ANSYS
Meshing Application (p. 13).
The state of the Geometry cell becomes Up-to-Date, indicating that there is a geometry now associated
with the fluid flow analysis system.
2. Start ANSYS DesignModeler.
Double-click the Geometry cell in the ext3d fluid flow analysis system to launch the ANSYS
DesignModeler application.
Extra
You can also launch ANSYS DesignModeler by right-clicking the Geometry cell to display
the context menu then selecting the Edit Geometry... option.
3. Finish importing the geometry file by clicking Generate in the ANSYS DesignModeler toolbar. The
geometry will be displayed in the Graphics window.
11
Setup and Solution

Figure 1.6: The Imported Geometry in the ANSYS DesignModeler Application
Note that the scale at the bottom of the Graphics window can be used to confirm that the overall
length of the domain is 0.6 m.
4. Modify the geometry so that the separate domains (bodies) are treated as a single entity (a part),
by performing the following actions in the Tree Outline.
By uniting the multiple bodies of the geometry into a single part, you will create a conformal mesh
between the separate domains of the bodies.
a. Expand the 2 Parts, 2 Bodies node.
b. Click 1 so that it is highlighted.
c. Hold the Ctrl key and click 2 so that it is highlighted as well.
d. Right-click the highlighted objects and click Form New Part in the menu that opens.
12

The Tree Outline will list the geometry as 1 Part, 2 Bodies.
5. Close ANSYS DesignModeler.
You can simply close the ANSYS DesignModeler application. ANSYS Workbench automatically saves
the geometry and updates the Project Schematic accordingly.
6. View the files generated by ANSYS Workbench, as displayed in the Project Schematic.
Note the addition of the geometry file (PFL.agdb, where PFL indicates a Polyflow-based fluid flow
system) to the list of files.
1.4.4.Step 3: Meshing the Geometry in the ANSYS Meshing Application
Now that you have prepared the extrusion geometry, you need to generate a computational mesh
throughout the flow volume. In this step, you will use the ANSYS Meshing application to create a mesh
for your CFD analysis, then review the list of files generated by ANSYS Workbench.
1. Open the ANSYS Meshing application.
Double-click the Mesh cell in the ext3d fluid flow analysis system (cell A3) to launch the ANSYS
Meshing application with the extrusion geometry already loaded.
Extra
You can also right-click the Mesh cell to display the context menu where you can select
the Edit... option.
13
Setup and Solution

Figure 1.7: The ANSYS Meshing Application with the Extrusion Geometry Loaded
2. Group the faces and create named selections to match the boundary set shown in Figure 1.2: The
Boundary Set for the Problem (p. 5).
a. Rotate the view to get your display similar to that shown in Figure 1.8: Rotated View(p. 15), by
holding the center mouse button and moving your pointer in the geometry window. (You can also
manipulate the view by clicking in the ANSYS Meshing toolbar and dragging the model).
Tip
Look at the orientation of the axis triad, , to assist when rotating the
view.
14

Figure 1.8: Rotated View
b. Click Mesh under Project/Model in the Outline tree.
Information will be displayed about the mesh in the Details view below the Outline tree view.
Note
Note that since the ANSYS Meshing application automatically detects that you are
going to perform a CFD fluid flow analysis, CFD is selected from the Physics Pref-
erence drop-down list.
c. Select the face that will represent the inlet, as shown highlighted in green in Figure 1.9: Selecting
the Inlet Face (p. 16).
Ensure is enabled in the ANSYS Meshing toolbar, for face selection.
d. Right-click and select the Create Named Selection option (from the menu that opens) to open
the Selection Name dialog box.
15
Setup and Solution

Figure 1.9: Selecting the Inlet Face
e. Enter inlet for the name in the Selection Name dialog box, and click OK.
f. Hold down the Ctrl key, select the 2 faces that will represent the zero velocity boundary (as high-
lighted in green in Figure 1.10: The Zero Velocity Faces Selected(p. 17)), then create a selection
named die wall in a manner similar to the previous steps.
16

Figure 1.10: The Zero Velocity Faces Selected
g. Hold down the Ctrl key, select the 2 faces that will represent the free surface boundary (as high-
lighted in green in Figure 1.11: The Free Surface Faces Selected(p. 18)), and create a selection
named free surface in a manner similar to the previous steps.
17
Setup and Solution

Figure 1.11: The Free Surface Faces Selected
h. Rotate the view to get your display to be similar to that shown in Figure 1.12: Rotated View(p. 18),
by holding the center mouse button and moving your pointer in the geometry window.
Figure 1.12: Rotated View
18

i. Hold down the Ctrl key, select the 2 faces that will represent one of the symmetry boundaries (as
highlighted in green in Figure 1.13: The First Pair of Symmetry Faces Selected(p. 19)), and create
a selection named symmetry 1 in a manner similar to the previous steps.
Figure 1.13: The First Pair of Symmetry Faces Selected
j. Hold down the Ctrl key, select the 2 faces that will represent the other of the symmetry boundaries
(as highlighted in green in Figure 1.14: The Second Pair of Symmetry Faces Selected(p. 20)), and
create a selection named symmetry 2 in a manner similar to the previous steps.
19
Setup and Solution

Figure 1.14: The Second Pair of Symmetry Faces Selected
k. Select the face that will represent the flow exit boundary (as highlighted in green in Figure 1.15: The
Flow Exit Face Selected (p. 21)), and create a selection named outlet in a manner similar to the
previous steps.
20

Figure 1.15: The Flow Exit Face Selected
3. Set the appropriate meshing parameters for the ANSYS Meshing application in the Details view.
a. Confirm that Polyflow is selected from the Solver Preference drop-down list under Defaults.
b. Expand the Sizing node to reveal additional sizing parameters.
21
Setup and Solution

c. Select Off from the Use Advanced Size Function drop-down list.
4. Generate the mesh.
a. Right-click Mesh in the Outline tree view, and select Update in the context menu.
The geometry window will display the generated mesh.
Note
Using the Generate Mesh option from the Mesh context menu creates the mesh,
but does not actually create the relevant mesh files for the project and is optional
if you already know that the mesh is acceptable. Using the Update option automat-
ically generates the mesh and creates the relevant mesh files for your project and
updates the ANSYS Workbench cell that references this mesh.
b. Refine the mesh.
i. Enter 80 for Relevance under Defaults in the Details view.
ii. Right-click Mesh in the Outline tree view, and select Update in the context menu.
The geometry window will display the refined mesh.
Extra
After the mesh is generated, you can view the mesh statistics by expanding the Statistics
node in the Details view to reveal information about the number of nodes, the number
of elements, and other details.
22

Figure 1.16: The Computational Mesh for the Extrusion Geometry
5. Close the ANSYS Meshing application.
When you close the ANSYS Meshing application, ANSYS Workbench automatically saves the mesh
and updates the Project Schematic accordingly (the state of the Mesh cell changes from Refresh
Required to Up-to-Date, indicating that there is a mesh now associated with the fluid flow analysis
system).
Note the addition of the mesh files (PFL.1.poly and PFL.mshdb) to the list of files. The
PFL.1.poly file was created when you updated the mesh, and the PFL.mshdb file was generated
when you closed the ANSYS Meshing application.
23
Setup and Solution

1.4.5.Step 4: Setting Up the CFD Simulation in ANSYS Polydata
In this step, you will proceed to set up a CFD analysis using ANSYS Polydata, then review the list of files
generated by ANSYS Workbench.
1. Import the data file (polyflow.dat).
The data file you will import has already been set up for a 3D extrusion simulation with a single inlet
flow rate. For details on how to set up a similar data file in ANSYS Polydata, see 3D Extrusion (p. 149).
a. Right-click the Setup cell in the ext3d fluid flow analysis system, and click Import Polyflow Dat
... in the context menu that opens.
b. Use the Open dialog box to browse to the folder you unzipped in a previous step, select poly-
flow.dat, and click Open.
The state of the Setup cell remains Refresh Required, indicating that even though there is a
data file now associated with the fluid flow analysis system, you still must perform an update for
the cell.
c. Right-click the Setup cell and click Update in the context menu that opens.
After ANSYS Polydata converts the .poly mesh file into a .msh file and checks for coherence
between the mesh and data files, the state for the Setup cell becomes Up-to-Date. At this point
it would be possible to run the ANSYS Polyflow solver for your simulation; however, for this tutorial
you will first modify the data file.
Note the addition of the mesh file (convert.msh) and the data file (polyflow.dat) to the list of
files.
3. Start ANSYS Polydata.
24

Double-click the Setup cell in the ext3d fluid flow analysis system.
Extra
You can also launch ANSYS Polydata by right-clicking the Setup cell and clicking Edit...
in the context menu that opens.
Note
The mesh is automatically loaded and displayed in the Graphics Display window by
default.
Figure 1.17: The ANSYS Polydata Application
4. View the mesh information, in order to verify the unit that should be used for length when defining
your inputs for the simulation.
25
Setup and Solution

It is a good practice to always perform this step with new meshes. Polydata and Polyflow do not consider
units when calculating a solution, so it is your responsibility to ensure that you input values for the ve-
locity, material data, and other settings that are consistent with each other and with the mesh.
a. Click the Mesh tab at the bottom of the Polydata window.
b. Click the Info button to open a panel that displays the mesh information.
c. Verify that the Length Unit used to create the mesh was meters and that the dimensions of the
Bounding Box (which surrounds the mesh) are 0.1 x 0.1 x 0.6.
It is therefore recommended that you use meters for the length unit when specifying the inputs for
the simulation. Note that if you decided that you would rather work with a different length unit,
you could scale the mesh using Polyfuse, as described in the Polyflow User's Guide.
d. Close the panel and click the Menus tab at the bottom of the Polydata window.
5. Modify the data file so that the inlet flow rate is flagged as modifiable in a user-defined template (UDT).
Note
UDTs are considered input parameters by ANSYS Workbench.
a. Select the task that must be modified.
F.E.M. Task 1
b. Select the sub-task of F.E.M. Task 1 to modify.
3D die swell
3D die swell is the name that was given to the sub-task for the flow problem when the data file
was created.
c. Modify the boundary conditions.
Flow boundary conditions
d. Select Inflow along INLET in the Flow boundary conditions menu and click Modify.
e. Click the UPDT button at the top of the ANSYS Polydata application window, to enable template
inputs.
26

f. Click Inflow in the Flow boundary condition along INLET menu.
g. Retain the selections of Automatic and Volumetric flow rate in the Inflow calculation on
INLET menu, and note that the flow rate is already set to 1 x 10-5
(which, since you are using
meters for your length unit, is equal to 10 cm3
/s—that is, the initial flow rate proposed in
Problem Description (p. 3)). Then click Upper level menu.
h. Click Create a new template entry in the Create template entry menu.
i. Click the UPDT button again at the top of the ANSYS Polydata application window, to disable
template inputs.
j. Click Upper level menu four times to return to the main Polydata menu.
6. Verify the system of units that will be passed to CFD-Post for postprocessing.
It is a good practice to always perform this step before running a new simulation, to ensure consistency
with the mesh and the units you used when defining the velocity, material data, and other settings.
Outputs
a. Note that the Current output(s) in the Outputs menu indicate that CFD-Post is currently selected
as the intended postprocessor.
b. Click Set units for CFD-Post, Ansys Mapper or Iges.
c. Note that meter, kilogram, and second are currently selected for Length, Mass, and Time, respect-
ively (which is consistent with the values used in setting up the data file).
27
Setup and Solution

d. Click Upper level menu twice to return to the main Polydata menu.
7. Save the data file and close ANSYS Polydata.
Save and exit
a. Click Accept in the Field Management menu.
b. Click Continue in the File Management menu.
A Parameters cell will be added to the ext3d fluid flow analysis system in the ANSYS Workbench
Project Schematic (cell A7). Also, a Parameter Set bar will be added below the system with an inbound
arrow, indicating that an input parameter has been created.
Note the addition of the template file (templates.upd) to the list of files.
1.4.6.Step 5: Running the CFD Simulation in ANSYS Polyflow
Now that your mesh and data files are properly set up, in this step you will use the ANSYS Polyflow solver
to run the initial simulation, generate results files, then review the list of files generated by ANSYS
Workbench.
1. Start ANSYS Polyflow.
In the ANSYS Workbench Project Schematic, right-click the Solution cell in the ext3d fluid flow
analysis system (cell A5), and click Update in the context menu that opens.
The ANSYS Polyflow solver will begin running. When the calculation is complete, the state for the
Solution cell becomes Up-to-Date.
28

Note the addition of the listing file (polyflow.lst), the ANSYS Polyflow results file (res), the output
mesh file (res.msh), and the CFD-Post file (cfx.res) to the list of files. For more information about
ANSYS Polyflow (and the files associated with it), see Polyflow User's Guide in the Polyflow User's Guide.
1.4.7.Step 6: Displaying Results in ANSYS CFD-Post
In this step, you will use ANSYS CFD-Post to view the results of your initial simulation, create an expression
that can be used as an output parameter for ANSYS Workbench, then review the list of files generated
by ANSYS Workbench.
1. Start ANSYS CFD-Post.
In the ANSYS Workbench Project Schematic, double-click the Results cell in the ext3d fluid flow
analysis system (cell A6).
Extra
You can also start ANSYS CFD-Post by right-clicking the Results cell and selecting the
Edit... option in the context menu that opens.
The ANSYS CFD-Post application will launch with the extrusion geometry already loaded (displayed in
outline mode). Note that ANSYS Polyflow results are also automatically loaded into ANSYS CFD-Post.
29
Setup and Solution

Figure 1.18: The Extrusion Geometry Loaded into ANSYS CFD-Post
2. Obtain the view shown in Figure 1.19: Rotating the View(p. 31).
a. Rotate the view, by holding the center mouse button and moving your pointer in the viewer area.
b. Reduce the magnification of the view by clicking the Zoom icon at the top of the viewer area ( ),
holding the left mouse button, and moving your pointer in the viewer area.
30

Figure 1.19: Rotating the View
3. Display contours of velocity magnitude on the boundaries (Figure 1.20: Contours of Velocity Mag-
nitude (p. 33)).
a. Open the Insert Contour dialog box.
Insert → Contour
b. Retain the default entry of Contour 1 for Name and click OK to close the dialog box.
31
Setup and Solution

Information about Contour 1 will be displayed in the Details view below the Tree view in ANSYS
CFD-Post. The Details view contains all of the settings for a contour object.
c. Open the Location Selector dialog box by clicking the location editor button ( ) next to the
Locations drop-down list in the Geometry tab.
i. Select all of the boundaries listed under ext3d by clicking the first one in the list
(PART_1_1_SOL_DIE_WALL), holding the Shift key, and clicking the last one in the list
(PART_1_2_SOL_SYMMETRY_2).
32

ii. Click OK to close the Location Selector dialog box.
d. Select VELOCITIES from the Variable drop-down list.
e. Click Apply.
The velocity is 0 along the die wall (as expected) and there is a fully developed profile at the inlet of the
die. At the die outlet, the velocity profile changes to become constant throughout the extrudate cross
section. The transition between these two states can be seen in the first third of the extrudate.
Figure 1.20: Contours of Velocity Magnitude
4. Display contours of velocity in cross sections (Figure 1.21: Velocity Profiles at Cross Sections(p. 38)).
a. Disable Contour1 under User Locations and Plots in the Outline tab of the Tree view.
33
Setup and Solution

b. Create a cross section plane at =0.0 m.
i. Select Plane from the Location drop-down menu, located in the toolbar.
ii. Retain the default entry of Plane 1 for Name in the Insert Plane dialog box that opens, and
click OK.
34

Information about Plane 1 will be displayed in the Details view.
iii. Retain the default selection of XY Plane for Method in the Geometry tab of the Details view
for Plane 1.
iv. Retain the default entry of 0.0 m for Z.
v. Click Apply
c. In a similar manner, create cross section planes at =0.08 m, 0.15 m, and 0.45 m named Plane 2,
Plane 3, and Plane 4 respectively. Note that you will retain the default selection of XY Plane for
Method and enter appropriate values for Z in the Details view.
d. Disable Plane 1, Plane 2, Plane 3, and Plane 4 under User Locations and Plots in the Outline
tab of the Tree view, so that the planes are no longer colored gray in the viewer area.
e. Open the Insert Contour dialog box.
Insert → Contour
35
Setup and Solution

f. Retain the default entry of Contour 2 for Name and click OK to close the dialog box.
Information about Contour 2 will be displayed in the Details view below the Tree view.
g. Open the Location Selector dialog box by clicking the location editor button ( ) next to the
Locations drop-down list in the Geometry tab.
36

i. Select all of the planes listed under User Locations and Plots by clicking Plane 1, holding
the Shift key, and clicking Plane 4.
ii. Click OK to close the Location Selector dialog box.
h. Select VELOCITIES from the Variable drop-down list.
i. Click Apply.
Velocity profiles at the flow inlet, the flow outlet, and planes just before and just after the die exit are
displayed. Compare the velocity profile within the die to the velocity profile just after the die exit at the
end of the computational domain. In the die the flow is fully developed. The velocity profile is flat (that
is, all the particles in the cross section are at the same velocity) in the extrudate, far away from the die
exit. In the transitional zone just beyond the die exit, the velocity profile is reorganized. The velocity
profile on the plane =0.15 m is no longer fully developed, but it is not yet flat either. The velocity re-
arrangement is the source of the deformation of the extrudate.
37
Setup and Solution

Figure 1.21: Velocity Profiles at Cross Sections
5. Create an expression for the maximum velocity at the flow exit, which can be used as an output para-
meter in ANSYS Workbench.
a. Click the Expressions tab in the Tree view.
b. Right-click anywhere in the Expressions tab and click New in the menu that opens to create a
new expression.
The New Expression dialog box will open.
38

i. Enter maxvelocity for Name.
ii. Click OK to close the New Expression dialog box.
c. Right-click in the Definition tab of the Details view, move your pointer over Functions, move
your pointer over CFD-Post, and click maxVal, to specify that the function in the expression obtains
the maximum value.
d. Make sure that the cursor is between the parentheses of maxVal()@, right-click in the Details view
again, move your pointer over Variables, and click VELOCITIES, to specify that the variables obtained
in the expression are velocities.
39
Setup and Solution

e. Move the cursor so that it is after the @ symbol of maxVal (VELOCITIES)@, right-click in the Details
view again, move your pointer over Locations, and click PART_1_2_SOL_OUTLET, to specify that
the variables are obtained for the expression at the flow exit.
40

f. Click Apply.
The expression in the Definition tab of the Details view will be defined as maxVal (VELOCITIES)@
PART_1_2_SOL_OUTLET with a Value of approximately 7.8 x 10-4
m/s, and maxvelocity will
be added to the list in the Expressions tab of the Tree view, as shown in Figure 1.22: Creating an
Expression for an Output Parameter (p. 42).
41
Setup and Solution

Figure 1.22: Creating an Expression for an Output Parameter
g. Right-click maxvelocity in the Expressions tab of the Tree view and select Use as Workbench
Output Parameter in the context menu that opens.
42

An outbound arrow will be added from the Parameters cell to the Parameter Set bar in the
Project Schematic, indicating that an output parameter has been created.
6. Close the ANSYS CFD-Post application.
Note
Note that the ANSYS CFD-Post state files are automatically saved when you exit ANSYS
CFD-Post and return to ANSYS Workbench.
7. Save the ext3d-wb project in ANSYS Workbench.
File → Save
43
Setup and Solution

Figure 1.23: Displaying the Files View after Viewing Results in ANSYS CFD-Post
Note the addition of the ANSYS CFD-Post state file (ext3d.cst) to the list of files. For more information
about ANSYS CFD-Post (and the files associated with it), see the ANSYS CFD-Post documentation.
1.4.8.Step 7: Exploring Additional Solutions
At this point you have run the simulation with an initial inlet flow rate. In this step, you will create
multiple design points for various inlet flow rates, solve them with a single action, then review the list
of files generated by ANSYS Workbench.
Note
ANSYS DesignXplorer is licensed separately from ANSYS Polyflow. If you do not have access
to ANSYS DesignXplorer, you will not be able to perform some of the steps that follow, such
as computing multiple design points or plotting results in a chart.
1. Open the Parameters Set tab, which contains the Parameters and Design Points view (Figure 1.24: The
Parameters and Design Points View (p. 45)).
In the ANSYS Workbench Project Schematic, double-click the Parameter Set bar below the ext3d
fluid flow analysis system.
Extra
You can also open the Parameters and Design Points view by right-clicking the Para-
meter Set bar and selecting the Edit... option in the context menu that opens.
44

Figure 1.24: The Parameters and Design Points View
If you do not see the panes shown in the previous figure, make them visible by enabling Outline,
Properties, Table, and Chart from the View menu.
2. Run the calculation again with a new inlet flow rate for the current design point.
a. Enter 8E-6 under P1 - flow rate for the Current design point (cell B3) in the Table of Design
Points.
An Update Required icon will be added to the cell under P2- maxvelocity for the Current design
point (cell C3).
b. Right-click the cell under P2 - maxvelocity for the Current design point and select Update Selected
Design Points in the context menu that opens, to generate the maximum velocity at the flow exit
with the revised inlet flow rate.
Extra
You can also update the design point by clicking Update All Design Points in the
ANSYS Workbench toolbar.
45
Setup and Solution

A dialog box may open to inform you that some open editors may close during this process. Click
OK to proceed.
ANSYS Polydata will update the data file based on the revised inlet flow rate and ANSYS Polyflow will
run again. When the calculation is complete, the Table of Design Points will display a new value of
approximately 6.2 x 10-4
m/s under P2 - maxvelocity for the Current design point.
3. Create a chart for the updated current design point.
a. Click P1 under Input Parameters (cell A4) in the Outline of All Parameters.
The ANSYS Workbench Toolbox will display options for Parameter Charts.
b. Double-click Parameters Chart P1 vs ? in the Toolbox to open the Properties of Outline A11:0
window at the bottom of the Parameters Set tab.
The Properties of Outline A11:0 window will display an initial setup for Parameter Chart 0,
in which P1 - flow rate is selected from the X-Axis (Bottom) drop-down list.
46

c. Select P2 - maxvelocity from the Y-Axis (Left) drop-down list in the Properties of Outline A11:0
window.
The current design point will be plotted in Parameter Chart 0 (Figure 1.25: The Chart of the Current
Design Point (p. 47)).
Figure 1.25: The Chart of the Current Design Point
4. Create more design points for a range of inlet flow rates.
a. Enter 1E-5 for P1 - flow rate in the row beneath the Current design point (cell B*) in the
Table of Design Points, so that a new row is added (4) with DP 1 as the Name.
b. In a similar manner, create additional design points DP 2 and DP 3 with a P1 - flow rate of
1.1E-5 and 1.2E-5, respectively.
Extra
You can specify that the data generated for any of the added design points is saved
in a separate project file (for example, ext3d-wb_dp1.wbpj) by enabling the
Exported option in column D for the design points.
5. Generate the values for the maximum velocity at the flow exit for all of the new design points.
Click Update All Design Points in the ANSYS Workbench toolbar.
47
Setup and Solution

ANSYS Polydata will update and ANSYS Polyflow will run repeatedly to solve for each of the design
points. As each calculation completes, the Table of Design Points (Figure 1.26: Displaying Values for
All of the Design Points (p. 48)) and Parameter Chart 0 (Figure 1.27: The Chart of All of the Design
Points (p. 48)) will be updated.
Figure 1.26: Displaying Values for All of the Design Points
Figure 1.27: The Chart of All of the Design Points
6. Save the ext3d-wb project in ANSYS Workbench.
File → Save
7. Return to the Project Schematic view by clicking the Project tab above the ANSYS Workbench toolbar.
48

Figure 1.28: Displaying the Files View after Exploring Solutions
Note that the list of files shows that the design point file (designPoint.wbdp) was updated. For
more information about the files associated with ANSYS Workbench, see the ANSYS Workbench docu-
mentation.
1.4.9.Step 8: Summary
In this tutorial, portions of ANSYS Workbench were used to simulate a 3D extrusion and to compare
the flow exit velocities associated with a range of inlet flow rates.
ANSYS DesignModeler was used to prepare the geometry, ANSYS Meshing was used to create a compu-
tational mesh, ANSYS Polydata was used to set up the simulation, ANSYS Polyflow was used to calculate
the fluid flow throughout the geometry using the computational mesh, and CFD-Post was used to
analyze the results. In addition, the Parameters and Design Points view of ANSYS Workbench was
used to add additional design points and compare their associated flow exit velocities on a chart.
49
Setup and Solution

50

Part II: Extrusion
The following extrusion tutorials are available:
1. 2.5D Axisymmetric Extrusion
2. Fluid Flow and Conjugate Heat Transfer
3. Non-Isothermal Flow Through a Cooled Die
4. 3D Extrusion
5. Direct Extrusion
6. Inverse Extrusion
7. Flow of Two Immiscible Fluids
8. Flow of Two Immiscible Fluids by Species Method

Chapter 1: 2.5D Axisymmetric Extrusion
This tutorial is divided into the following sections:
1.1.Introduction
1.2.Prerequisites
1.4.Preparation
1.5.Step 1:Project and Mesh
1.6.Step 2:Models
1.7.Step 3:Material Data
1.8.Step 4:Boundary Conditions
1.9.Step 5:Remeshing
1.10.Step 6:Stream Function
1.11.Step 7:Outputs
1.12.Step 8:Save the Data and Exit Polydata
1.13.Step 9:Solution
1.14.Step 10:Postprocessing
1.15.Summary
1.1.Introduction
This tutorial illustrates the setup and solution of a 2.5D axisymmetric extrusion problem. The problem
corresponds to a simplified 2D simulation of a swirling flow that occurs around the head of an extrusion
screw. The fluid is forced through the die and exits the +extruder after a short die land. The model in-
volves a free surface, the position of which is unknown.
In this tutorial you will learn how to:
• Create a project in ANSYS Workbench.
• Start Polydata from ANSYS Workbench.
• Create a new task.
• Create a sub-task.
• Set material properties and boundary conditions for a 2.5D axisymmetric extrusion problem.
• Select a remeshing method.
• Specify output for CFD-Post.
1.2.Prerequisites
This tutorial assumes that you have little experience with Polyflow and its associated modules.
53

The problem to be considered is shown schematically in Figure 1.1: Problem Schematic(p. 54). The
fluid enters the domain at a flow rate of 10 cm3
/s. The screw rotates at an angular velocity of 2 rad/s.
In the upper part of the domain, a free surface is used to model the extrudate going out of the extrusion
die. The position of the free surface is unknown. A portion of the mesh is affected by this unknown
boundary. A remeshing technique will be applied on this part of the mesh.
Figure 1.1: Problem Schematic
Since the problem involves a free surface, the domain is divided into two subdomains: one for the region
near the free surface and the other for the rest of the domain, as shown in Figure 1.2: Subdomains and
Boundary Sets for the Problem (p. 55)
54
2.5D Axisymmetric Extrusion

Figure 1.2: Subdomains and Boundary Sets for the Problem
The boundary sets for the problem are also shown in Figure 1.2: Subdomains and Boundary Sets for the
Problem (p. 55), and the conditions at the boundaries of the domains are:
• BS1: flow inlet
• BS2: outer wall
• BS3: free surface
• BS4: flow exit
• BS5: symmetry axis
55
Problem Description

• BS6: rotating screw
1.4.Preparation
To prepare for running this tutorial:
1. Prepare a working folder for your simulation.
2. Go to the ANSYS Customer Portal, https://support.ansys.com/training.
Note
If you do not have a User Name and Password, you can register by clicking Customer
Registration on the Log In page.
3. Enter the name of this tutorial into the search bar.
4. Narrow the results by using the filter on the left side of the page.
a. Click ANSYS Polyflow under Product.
b. Click 15.0 under Version.
5. Select this tutorial from the list.
6. Click Files to download the input and solution files.
7. Unzip the 2.5-Axi-Extrusion_R150.zip file you have downloaded to your working folder.
The mesh file ext2d.msh can be found in the unzipped folder.
8. Start Workbench from Start → All Programs → ANSYS 15.0 → Workbench 15.0.
1.5.Step 1: Project and Mesh
Note
If you create the mesh in GAMBIT or a third-party CAD package, you need to convert it before
you read it into Polydata. In this tutorial, the mesh file has already been converted. So you
can read the mesh file directly into Polydata.
1. Create a Fluid Flow (Polyflow) analysis system by drag and drop in ANSYS Workbench.
56

a. Rename the project name to Tutorial 1 by double-clicking and editing the text Fluid Flow
(Polyflow).
b. Save the ANSYS Workbench project using File → Save.
c. Enter 2.5-axi-extrusion as the name of the ANSYS Workbench project.
This will create a 2.5-axi-extrusion.wbpj file and a folder named 2.5-axi-extru-
sion_files in the working directory. To reopen this project in a later ANSYS Workbench session,
use File → Open.
2. Import the mesh file for the Polydata session.
Right-click the Mesh cell and click Import Mesh File….
57
Step 1:Project and Mesh

a. Select ext2d.msh.
b. Click Open.
3. Double-click the Setup cell to start Polydata and read in the mesh. When Polydata starts, the Create a
new task menu item appears in bold text, and the geometry for the problem is displayed in the Graphics
Display window.
Note
At this point (when Create a new task appears in bold text) if you realize that you have
read the wrong mesh file, click STOP at the top of the Polydata menu and repeat the
process to access the correct mesh file.
58

1.6.Step 2: Models
In this step, first define a new task representing the 2.5D axisymmetric steady-state model. Then define a
sub-task for the isothermal flow calculation.
1. Create a task for the model.
Create a new task
a. Select the following options:
• F.E.M. task
• Steady-state problem(s)
• 2D 1/2 axisymmetric geometry
The Current setup (above the selected options) will be updated to reflect the selection. In any
problem solved using Polyflow, first an F.E.M. task is defined to calculate the flow field. If inform-
ation regarding the trajectories is necessary, specify a MIXING task after solving the problem
with the F.E.M. task specification and obtaining the results file. Then solve the problem once
again. 3D velocity components (u,v,w) are prescribed in a 2D cylindrical reference frame (r,z), so
2D 1/2 axisymmetric geometry has been chosen. A steady-state condition is assumed for this
problem.
b. Click Accept the current setup.
59
Step 2:Models

The Create a sub-task menu item appears in bold text.
Note
At this point (when Create a sub-task appears in bold text) if you realize that you
have made a mistake in the creation of the task and you need to return to that menu,
do the following:
i. Click Upper level menu to return to the top-level Polydata menu.
ii. Select Redefine global parameters of a task and make the necessary changes.
iii. Click Accept the current setup when you are satisfied with the corrected settings.
iv. Select F.E.M. Task 1.
2. Create a sub-task for the isothermal flow.
Create a sub-task
a. Select Generalized Newtonian isothermal flow problem.
A small panel appears asking for the title of the problem.
b. Enter die swell as the New value and click OK.
The Domain of the sub-task menu item appears in bold text.
Note
At this point (when Domain of the sub-task appears in bold text) if you realize that
you have made a mistake in the creation of the sub-task and you need to return to
that menu, do the following:
i. Click Upper level menu.
ii. Select Redefine global parameters of a sub-task and make the necessary changes.
iii. Click Upper level menu.
60

iv. Select die swell at the bottom of the existing menu.
The Domain of the sub-task menu item appears in bold text.
3. Define the domain where the sub-task applies.
Since this flow involves a free surface, the domain is divided into two subdomains: one for the region
near the free surface and the other for the rest of the domain. Here, the sub-task applies to both
subdomains (the default condition).
Domain of the sub-task
Accept the default selection of both subdomains by clicking Upper level menu.
The Material data menu item appears in bold text.
1.7.Step 3: Material Data
Polydata indicates the material properties that are relevant for your sub-task by dimming the irrelevant
properties. In this case, viscosity, density, inertia terms, and gravity are available for specification. For this
model, define only the viscosity of the material. Inertia effects are neglected and density is specified only
when inertia, gravity, heat convection, or natural convection is taken into account. Since gravitational effects
are not included in the model, the default value of zero is retained for gravity.
Material data
61
Step 3:Material Data

1. Click Shear-rate dependence of viscosity.
2. Click Cross law.
The viscosity is given by the Cross law:
=
+

where:
= zero-shear-rate viscosity = 85000
= natural time = 0.2
= Cross law index = 0.3
= shear rate
3. Specify the value for .
Modify fac
Enter 85000 as the New value and click OK.
Modify tnat
62

Enter 0.2 as the New value and click OK.
5. Specify the value form.
Modify expom
6. Check whether the values of the constants are correct, and repeat the previous steps if you need to
modify the constants again.
7. Click Upper level menu three times to leave the Material Data specification.
The Flow boundary conditions menu item appears in bold text.
1.8.Step 4: Boundary Conditions
In this step, set the conditions at each of the boundaries of the domain. When a boundary set is selected,
its location appears in bold text in red in the graphics window.
63
Step 4:Boundary Conditions

1. Set the conditions at the flow inlet (BS_1).
a. Select Zero wall velocity (vn=vs=0) along BS_1 and click Modify.
b. Click Inflow.
c. Click Modify volumetric flow rate.
Polydata prompts you for the volumetric flow rate.
d. Enter 10 as the New value and click OK.
e. Select Automatic and click Upper level menu.
When the Automatic option is selected, Polydata chooses the most appropriate method to compute
the inflow. In this case, Polydata will use a 1D finite-element technique to compute a 1D fully-developed
velocity profile, based on the specified material properties and flow rate. Moreover, the inflow
64

boundary condition requires that the computational domain be built in such a way that the basic
assumptions of fully-developed flow are satisfied. In axisymmetric geometries, the inflow section must
be perpendicular to the axial direction.
2. Set the conditions at the outer wall (BS_2).
The fluid is assumed to stick to the wall, since at a solid-liquid interface the velocity of the liquid is that
of the solid surface. This is commonly known as the no-slip assumption because the liquid is assumed
to adhere to the wall, and therefore has no velocity relative to the wall.
Retain the default condition Zero wall velocity (vn=vs=0) along BS_2.
3. Set the conditions at the free surface (BS_3).
In a steady-state problem, the velocity field must be tangential to a free surface, since no fluid
particles go out of the domain through the free surface. This constraint is called the kinematic
condition, v_n = 0. This equation requires an initial condition at the starting point of the free surface,
which in this case is located at the intersection of BS_2 and BS_3.
b. Click Free surface.
c. Click Boundary conditions on the moving surface.
Note
Do not select the Outlet option. It is only applicable for die design problems.
d. Select No condition along BS_2 and click Modify.
As mentioned above, the starting point of the free surface is at the intersection of BS_2 and BS_3.
e. Click Position imposed.
f. Click Upper level menu.
g. Click Upper level menu to return to the Kinematic condition menu.
h. Retain the default settings for the Normal force and Direction of motion.
i. Click Upwinding in the kinematic equation.
j. Click Upper level menu to return to the Flow boundary conditions menu.
4. Set the conditions at the flow exit (BS_4).
It is reasonable to consider that a uniform velocity profile is obtained at the exit. In most cases, a bulk
flow is obtained and thus no force is acting, so the selection of zero normal and tangential forces is ap-
propriate. In situations involving pulling velocity or force or gravity, the corresponding boundary condition
should be selected.
65

b. Click Normal and tangential forces imposed (fn, fs).
c. Accept the default value of 0 for the normal force
by clicking Upper level menu.
d. Accept the default value of 0 for the tangential force

by clicking Upper level menu.
e. Click No when prompted to confirm that the rotational velocity () is 0.
The rotational force is 0, not the rotational velocity.
f. Click 'w' force imposed.
g. Select 'w' force = constant.
h. Accept the default value of 0 by clicking OK.
i. Click Yes to confirm that the rotational force is 0.
5. Retain the default condition at the symmetry axis (Axis of symmetry along BS_5).
For axisymmetric models, the axis of symmetry is always the y axis. Polydata determines the axis of
symmetry from the mesh file, and automatically imposes the symmetry condition along the line r=0
(x=0).
6. Set the conditions at the boundary of the rotating screw (BS_6).
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Since the screw is rotating with angular velocity = 2 = 6.2832 rad/s, the rotational velocity along this
boundary is prescribed to increase linearly with (= 6.2832 ). In the equation for , X denotes the
direction and Y denotes the direction. Since the fluid sticks to the wall, = 0 = .
b. Click Normal and tangential velocities imposed (vn,vs).
c. Accept the default value of 0 for the normal velocity ( ) and tangential velocity () by selecting
Upper level menu twice.
d. Click No when prompted to confirm that the rotational velocity () is 0.
e. Click Velocity w imposed and select 'w' velocity = linear function of coordinates.
f. Accept the default value of 0 for the constant A by clicking OK.
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g. Enter 6.2832 as the New value for the constant B and click OK.
h. Accept the default value of 0 for the constant C by clicking OK.
i. Click Yes to confirm the w velocity equation.
j. Click Upper level menu at the top of the Flow boundary conditions menu.
The Global remeshing menu item appears in bold text.
1.9.Step 5: Remeshing
This model involves a free surface for which the position is unknown. A portion of the mesh is affected by
this unknown boundary. Hence a remeshing technique is applied on this part of the mesh. The free surface
is entirely contained within subdomain 2, and hence only subdomain 2 will be affected by the relocation of
the free surface.
Global remeshing
1. Specify the region where the remeshing is to be performed (SD_2).
In some cases, when the mesh is geometrically complex, it may be necessary to split it into additional
subdomains in order to define a specific remeshing method on each of them. For this purpose, Polydata
allows you to create several local remeshings. For the current problem, a single local remeshing is sufficient.
1-st local remeshing
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a. Select SD_1 and click Remove.
SD_1 is moved from the top list to the bottom list, indicating that only SD_2 will be remeshed.
If you accidentally remove the wrong subdomain, select it and click Add to restore it. Then, follow
the instructions to remove the correct subdomain.
69
Step 5:Remeshing

b. Click Upper level menu.
The Method of Spines menu item appears in bold text.
2. Define the parameters for the system of spines.
The purpose of the remeshing technique is to relocate internal nodes according to the displacement of
boundary nodes due to the motion of the free surface. Mesh nodes are organized along lines of
remeshing (spines), which are collections of nodes logically arranged in a one-dimensional manner. This
technique is most suited for 2D extrusion problems. Polydata requires the specification of the first and
last spines that the fluid encounters (inlet of spines and outlet of spines, respectively).
In this case, the inlet of spines is the intersection of subdomain 2 with subdomain 1, and the outlet of
spines is the intersection of subdomain 2 with the flow exit (boundary 4).
Method of Spines
a. Specify the inlet for the system of spines.
Select Intersection with SD_1 and click Confirm.
70

b. Specify the outlet for the system of spines.
Select Intersection with BS_4 and click Confirm.
c. Click Upper level menu twice.
At this point, if you realize that you have made a mistake in global remeshing, click die swell at the
bottom of the menu and perform this Step again.
1.10.Step 6: Stream Function
Once the velocity field is known, Polyflow calculates the stream function automatically. This calculation requires
you to specify the point where the stream function vanishes. Polydata imposes a vanishing value at the
nodal point closest to the specified position.
Assign the stream function
1. Select Condition on the stream function for field 1. Click No in the window that pops up.
71
Step 6:Stream Function

2. Enter 5 as the New value of X.
3. Retain the default value of 0 for Y.
4. Click Upper level menu twice.
If you have made a mistake in assigning the stream function, click F.E.M. Task 1 to get into that menu
and then repeat this Step.
72

1.11.Step 7: Outputs
After Polyflow calculates a solution, it can save the results in several different formats. Choose the format
that is appropriate for your postprocessor. In this case, save the outputs in the default format for ANSYS
CFD-Post.
Outputs
1. Select Listing: max.
2. Accept the default output option for CFD-Post by clicking Upper level menu.
When exiting the menu, Polydata asks you to confirm the current system units and fields that are to be
saved to the results file for postprocessing.
3. Specify the system of units for the simulation.
a. Click Modify system of units.
b. Select Set to metric_cm/g/s/A+Celsius.
If you do not enter the menu Outputs, Polydata will ask you to confirm the current system units at
the end of the session, if it is a new session.
1.12.Step 8: Save the Data and Exit Polydata
After defining your model in Polydata, you need to save the data file. In the next step, you will have to read
this data file into Polyflow and calculate a solution.
Save and exit.
73
Step 8:Save the Data and Exit Polydata

If this was not yet done before (see above), Polydata asks you to confirm the current system units. It will
also ask to confirm fields that are to be saved to the results file for postprocessing.
1. Click Accept.
This confirms that the default Current field(s) are correct.
2. Click Continue.
This accepts the default names for graphical output files (cfx.res) that are to be saved for postpro-
cessing, and for the Polyflow format results file (res).
74

1.13.Step 9: Solution
In this step, run Polyflow to calculate a solution for the model you just defined using Polydata.
1. Run Polyflow by right-clicking the Solution cell of the simulation and selecting Update from the shortcut
menu.
This executes Polyflow using the data file as standard input, and writes information about the problem
description, calculations, and convergence to a listing file (polyflow.lst).
2. Check for convergence in the listing file.
a. Right-click the Solution cell and select Listing Viewer….
ANSYS Workbench opens the View listing file panel, which displays the listing file.
b. In the View listing file panel, disable the Show only last 200 lines option and click the Manual
refresh button. Then find the SOLVER section that relates to F.E.M. Task 1; at the end of this
section, a message Convergence assumed is displayed. This indicates that the solution has con-
verged. See the Polyflow User's Guide for more information on convergence.
1.14.Step 10: Postprocessing
ANSYS CFD-Post has similar interfaces for UNIX and Windows, the postprocessing steps are illustrated for
Windows.
1. Double-click the Results cell in the ANSYS Workbench analysis and read the results files saved by Polyflow.
75
Step 10:Postprocessing

ANSYS CFD-Post reads the solution fields that were saved to the results file.
2. Align the view.
a. Right-click a blank area anywhere in the graphical window, and select Predefined Camera from the
shortcut menu, and select View From +Z.
The central mouse button allows you to zoom in and zoom out. The left mouse button allows rotating
the image. The right mouse button allows you to translate the image.
b. Also, right-click a blank area anywhere in the graphical window and deselect Ruler, if needed.
3. Display contours of pressure.
a. Click the Insert menu and select Contour or click the Contour button ( ).
b. Click OK to accept the default name (Contour 1) and open the details view below the Outline tab.
76

c. In the details view for Contour 1, specify the following settings under Geometry:
i. Next to Locations, click the ellipsis button ( ) on the right and select SD_1_surf and SD_2_surf
(use Ctrl to select multiple items).
Click OK to close the Location Selector dialog box.
ii. Select PRESSURE from the Variable drop-down list, or click the ellipsis button ( ) on the right
and select PRESSURE.
iii. Click Apply.
77

Figure 1.3: Contours of Static Pressure
d. Restore the symmetry along the Y axis.
i. In the Outline tab, double-click Default Transform.
78

The details view of Default Transform will open below the Outline tab.
ii. In the details view of Default Transform, disable Instancing Info From Domain.
iii. Disable Apply Rotation.
79

iv. Enable Apply Reflection.
v. Select YZ plane from the Method drop-down list.
vi. Leave the default value of 0.0[m] for X.
vii. Click Apply.
e. Annotate the display.
i. Click the Insert menu and select Text or click the button.
ii. Click OK to accept the default name (Text 1) and open the details view below the Outline tab.
80

iii. In the Definition tab of the details view, enter Polyflow Results for Text String.
iv. Possibly check the other tabs (Location, Appearance).
v. Click Apply.
81

Figure 1.4: Contours of Static Pressure after Mirroring
4. Display velocity vectors.
a. Deselect Contour 1.
b. Click the Insert menu and select Vector or click the Vector button ( ).
c. Click OK to accept the default name (Vector 1) and open the details view below the Outline tab.
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d. Perform the following steps in the details view of Vector 1:
i. In the Geometry tab, click the ellipsis button ( ) next to Locations, select SD_1_surf and
SD_2_surf (use Ctrl to select multiple items), and click OK.
ii. Select VELOCITIES from the Variable drop-down list, or click the ellipsis button ( ) on the
right and select VELOCITIES.
iii. Click Apply.
iv. Define the attributes of vectors: in the Symbol tab, set Symbol to Arrow3D and Symbol Size to
5.
v. Click Apply.
e. Remove the annotation.
i. On the Outline tab, under User locations and plots, deselect the item Text 1 previously defined.
The velocity vectors take all components of the velocity into account. Along the screw tip, the rota-
tional component is important, leading to long vectors that are not in the xy plane (perspective view).
After the die exit, a rearrangement of the velocity field takes place. The flow slows down along the
axis of symmetry and accelerates on the outside. This makes the particles go toward the free surface,
creating the swelling.
83

Figure 1.5: Velocity Vectors
f. Display the mesh.
i. In the Outline tab, select SD_1_surf and double-click.
84

ii. Under Render tab, deselect Show Faces and select Show Mesh Lines.
iii. Under Color tab, click the ellipsis ( ), select the color white and click OK.
iv. Click Apply.
v. Repeat operations (i) to (iii) for SD_2_surf.
85

Figure 1.6: Velocity Vectors with Mesh
g. Rotate the whole figure.
i. Move the mouse to the left-hand border of the graphic window until the cursor suggests a rotation
along a vertical line.
ii. Left-click and move the mouse slowly to the right-hand side.
1.15.Summary
This tutorial demonstrated how to set up and solve a 2.5D axisymmetric extrusion problem. It showed
how to set up a free surface problem and the associated remeshing, and demonstrated the use of CFD-
Post to examine the flow behavior associated with the problem.
86

Chapter 2: Fluid Flow and Conjugate Heat Transfer
2.1.Introduction
2.2.Prerequisites
2.4.Preparation
2.6.Step 2:Models,Material Data,and Boundary Conditions
2.7.Step 2a:Definition of Sub-Task 1
2.8.Step 2b:Definition of Sub-Task 2
2.12.Summary
2.1.Introduction
This tutorial illustrates the setup and solution of a problem involving heat transfer between a Newtonian
fluid and a cooled circular die. Along with a good die design, rheological and thermo physical properties
of the melt and the thermal settings in the die are very important in obtaining a geometrically well-
defined polymer product. The heat transfer calculation is important when temperature-sensitive polymers
are shaped and when product surface qualities are of critical importance. The temperature field at the
die exit influences the swelling and drawing behavior of the product.
In this tutorial, you will solve the non-isothermal flow problem for the fluid and the heat conduction
in the die, making some assumptions regarding the rheological and thermo physical properties of the
melt.
• Start Polydata from Workbench.
• Create a new task.
• Create multiple sub-tasks.
• Define a Newtonian non-isothermal flow problem.
• Define a Heat conduction problem.
• Set material properties and boundary conditions for a fluid-solid heat conduction and flow problem.
2.2.Prerequisites
This tutorial assumes that you are familiar with the menu structure in Polydata and Workbench and
that you have solved or read 2.5D Axisymmetric Extrusion (p. 53). Some steps in the set up procedure
will not be shown explicitly.
87

This tutorial examines the coupled problem of non-isothermal flow of a Newtonian fluid and heat
conduction in an axisymmetric steel die. As shown in Figure 2.1: A Schematic Diagram of the Fluid and
the Circular Die (p. 88), the melt enters the domain at a fixed temperature and a given flow rate of
= 180˚C and =0.6e−06 m3
/s, respectively. The problem involves flow, heat transfer by conduction
and convection, and heat generation by viscous dissipation. Energy, momentum, and incompressibility
equations are solved in the fluid domain. The energy equation for heat conduction is solved in the
solid domain.
To solve the coupled problem, two sub-tasks are defined: one for the fluid (sub-task 1) and the other
for the solid (sub-task 2). Each sub-task will contain a particular model, domain of definition, material
properties, and boundary conditions, including interface conditions with the other sub-task. The sub-
tasks are coupled, because the global solution of the problem depends on the values of the solution
variables at the intersection of the fluid and solid domains.
Figure 2.1: A Schematic Diagram of the Fluid and the Circular Die
The material properties for the fluid are as follows:
• = density (950 kg/m3
)
• = Newtonian viscosity (2500 Pa•s)
• = heat capacity per unit mass (2300 J/kg-K)
• = thermal conductivity (0.5 W/m-K)
88
Fluid Flow and Conjugate Heat Transfer

Viscous heating is taken into account. For the solid region, the thermal conductivity is 35 W/m-K.
The boundary sets for the problem are shown in Figure 2.2: Boundaries and Sub-domains(p. 89), and
the conditions at the boundaries of the domains are as follows:
• boundary 1: flow inlet, = 180°C, = 0.6 × 10−6
m3
/s
• intersection of subdomain 1 and subdomain 2: interface
• boundary 2: insulated
• boundary 3: = 100°C
• boundary 4: insulated
• boundary 5: flow exit
• boundary 6: symmetry axis
Figure 2.2: Boundaries and Sub-domains
2.4.Preparation
Note
89
Preparation

7. Unzip the Fluid-Solid_R150.zip file you have downloaded to your working folder.
The mesh file flusol.msh can be found in the unzipped folder.
1. Create a Fluid Flow (Polyflow) analysis system by drag and drop in Workbench.
2. Save the ANSYS Workbench project using File → Save, entering fluid_solid as the name of the
project.
3. Import the mesh file (flusol.msh).
4. Double-click the Setup cell to start Polydata.
When Polydata starts, the Create a new task menu item is highlighted, and the geometry for the
problem is displayed in the Graphics Display window.
2.6.Step 2: Models,Material Data,and Boundary Conditions
In this step, define a new task representing the fluid flow and conjugate heat transfer problem. The flow
problem for the fluid and the heat conduction in the solid is solved in two different sub-tasks. However, the
task attributes are the same for both the sub-tasks, so define a single task for the coupled problem.
Create a new task
2. Select the following options:
• F.E.M. task
• 2D axisymmetric geometry
Since the problem involves an axisymmetric steel die, the computational domain for the problem is
chosen to be a 2D cylindrical reference frame (r,z) with r=0 as the axis of symmetry, and involves two
velocity components (u,v); hence 2D axisymmetric geometry has been chosen. A Steady-state condition
is assumed for the problem.
90

3. Click Accept the current setup.
The Create a sub-task menu item is highlighted.
2.7.Step 2a: Definition of Sub-Task 1
In this step, define the flow problem, identify the domain of definition, set the relevant material properties
for the Newtonian fluid, and define boundary conditions along its boundaries.
1. Create the sub-task for the fluid flow.
Create a sub-task
a. Select Generalized Newtonian non-isothermal flow problem.
A panel appears asking for the title of the problem.
b. Enter fluid as the New value and click OK.
The Domain of the sub-task menu item is highlighted.
To solve the coupled problem, the computational domain is divided into two sub-domains with a
common intersection. A sub-task with its own model, material properties, and boundary conditions
is defined on each of the non-overlapping subdomains. Sub-task 1 is defined for SUBDOMAIN_1,
since SUBDOMAIN_1 represents the fluid (as shown in Figure 2.2: Boundaries and Sub-do-
mains (p. 89)).
a. Select SUBDOMAIN_2 and click Remove.
91
Step 2a:Definition of Sub-Task 1

SUBDOMAIN_2 is moved from the top list to the bottom list, indicating that subtask 1 is defined
on SUBDOMAIN_1.
b. Click Upper level menu at the top of the panel.
The Material data menu item is highlighted.
3. Specify the material properties for the fluid.
Polydata indicates which material properties are relevant for your sub-task by graying out the irrelevant
properties. In this sub-task, Polyflow solves energy, incompressibility and momentum equations, so you
have to define viscosity, density, thermal conductivity, heat capacity per unit mass, and viscous heating.
For a non-isothermal flow problem, the viscosity can depend on both shear rate and temperature. In
this case, the viscosity is constant, so it depends on neither of them.
Material Data
a. Click Shear-rate dependence of viscosity.
Since the fluid flow is Newtonian, specify a constant value for the viscosity.
i. Click Constant viscosity.
ii. Specify the value for .
Modify fac
92

Polydata prompts for the new value of .
iii. Enter 2500 as the New value and click OK.
iv. Click Upper level menu two times to continue the Material Data specification.
b. Select Temperature dependence of viscosity.
i. Select No temperature dependence.
Polydata displays the following message, confirming that there is no temperature dependence
for the viscosity.
ii. Click OK.
iii. Click Upper level menu to continue the Material Data specification.
93

c. Click Density.
In this problem, specify a constant value for the density.
Modification of density
i. Enter 950 as the New value and click OK.
ii. Click Upper level menu to continue the Material Data specification.
d. Click Thermal conductivity.
As shown at the top of the menu, the thermal conductivity is defined as a nonlinear function of
the temperature:
(2.1)
= + + +

In this problem, the thermal conductivity is assumed to be a constant for the fluid so only the
constant coefficient is modified.
Modify a
i. Enter 0.5 as the New value and click OK.
ii. Click Upper level menu to continue with the Material Data specification.
e. Click Heat capacity per unit mass.
94

As shown at the top of the menu, the heat capacity per unit mass is defined as a non-linear
function of temperature:
(2.2)
= + + +

The temperature variation of differs with the nature of the polymer melts. In this problem,
is assumed to be constant, so only the constant coefficient is modified.
Modify a
f. Click Viscous heating.
When shearing occurs in a flow, the friction of the different fluid layers generates heat. When the
fluid is highly viscous and/or the shear rate is high, the heating of the fluid caused due to this
phenomenon must be taken into account.
i. Select Viscous heating will be taken into account.
ii. Click Upper level menu to return to the Material Data specification.
g. Click Upper level menu to return to the fluid menu.
The Flow boundary conditions menu item is highlighted.
4. Specify the flow boundary conditions for SUBDOMAIN_1.
95

a. Set the conditions along the intersection of SUBDOMAIN_1 and SUBDOMAIN_2.
The intersection acts as a wall for the fluid, and since the fluid is assumed to stick to the wall, zero
normal and tangential velocities is imposed along this boundary.
i. Retain the default condition Zero wall velocity (vn=vs=0) along SUBDOMAIN_2.
b. Set the conditions at the flow inlet (BOUNDARY_1).
i. Select Zero wall velocity (vn=vs=0) along BOUNDARY_1 and click Modify.
ii. Click Inflow.
iii. Retain the default settings, Automatic and Volumetric flow rate.
iv. Click Modify volumetric flow rate.
96

v. Enter 0.6e-06 as the New value in the dialog box that appears, and click OK.
The flow rate of the melt is very low due to the highly viscous nature of the melt.
When the Automatic option is selected, Polydata automatically chooses the most appropriate
method to compute the inflow condition.
vi. Click Upper level menu.
c. Set the conditions at the flow exit (BOUNDARY_5).
It is assumed that a fully developed velocity profile is reached at the exit, so the outflow condition
is most appropriate. This condition imposes a zero normal force,
(which includes a pressure
term), and zero tangential velocity,.
ii. Click Outflow.
d. Retain the default, Axis of symmetry along BOUNDARY_6.
For axisymmetric models, Polydata recognizes the axis of symmetry from the mesh file, and auto-
matically imposes the symmetry condition along the line r=0. This condition imposes a zero normal
velocity and zero tangential force

along this boundary.
e. Click Upper level menu at the top of the Flow boundary conditions menu to return to the fluid
menu.
The Thermal boundary conditions menu item is highlighted.
5. Specify the thermal boundary conditions for SUBDOMAIN_1.
For non-isothermal problems, specify either the temperature or the heat flux on each boundary segment.
The temperature along a given boundary can be a constant or a prescribed function of coordinates.
Thermal boundary conditions
97

a. Set the conditions at the intersection of SUBDOMAIN_1 and SUBDOMAIN_2.
An interface condition is set at the intersection of subdomain 1 and subdomain 2. This condition
ensures continuity of the temperature field and of the heat flux along the interface. Since you are
solving a coupled problem, this condition of continuity is essential for the global solution of the
temperature and heat flux variables.
i. Select Temperature imposed along SUBDOMAIN_2 and click Modify.
ii. Click Interface.
iii. Click Upper level menu to accept the default setting (continuous heat flux along the interface).
In the case of an interface condition, both the heat flux and temperature are usually continuous
along the interface. It is possible to specify a nonzero value for the heat flux jump ( ), but
this is mainly used in problems where internal radiation is simulated. Here, accept the default
value for the definition of heat flux discontinuity, = 0.
A constant value for the temperature is imposed along this boundary.
i. Select Temperature imposed along BOUNDARY_1 and click Modify.
ii. Click Temperature imposed.
iii. Select Constant.
98

Polydata prompts you for the new value of the constant temperature.
iv. Enter 180 as the New value and click OK.
v. Click Upper level menu to return to the Thermal boundary conditions menu.
c. Set the conditions at the flow outlet (BOUNDARY_5).
A zero conductive heat flux is imposed along this boundary.
ii. Click Outflow.
d. Retain the default, Axis of symmetry along BOUNDARY_6.
e. Click Upper level menu twice to return to the F.E.M. Task 1 menu.
2.8.Step 2b: Definition of Sub-Task 2
In this step, define the heat conduction problem, identify the domain of definition, set the relevant material
properties for the solid, and define the boundary conditions along its boundaries.
1. Create a sub-task for the solid.
Create a sub-task
a. Polydata asks if you want to copy data from an existing sub-task.
99
Step 2b:Definition of Sub-Task 2

b. Click No, since this sub-task has different parameters associated with it.
c. Click Heat conduction problem.
d. Enter solid as the New value and click OK.
2. Define the domain where the sub-task applies (SUBDOMAIN_2).
3. Specify the material properties for the solid.
Material Data
In this problem, specify a constant value for the thermal conductivity .
100

a. Click Thermal conductivity.
In this problem, thermal conductivity is assumed to be a constant, so only the constant coefficient
is modified.
i. Select Modify a.
ii. Enter 35 as the New value and click OK.
b. Click Upper level menu two times to return to the solid menu.
4. Specify the thermal boundary conditions for SUBDOMAIN_2.
In this step, set the conditions at each of the boundaries of the domain. When a boundary set is
selected, it is highlighted in red in the graphics window.
An interface condition is set at the intersection of the sub-domains.
iii. Click Upper level menu to accept the default option for continuity of temperature and heat
flux.
b. Set the conditions at the bottom boundary of the solid (BOUNDARY_2).
ii. Click Insulated boundary / symmetry.
c. Set the conditions at the outer boundary of the solid (BOUNDARY_3).
101

A constant value for the temperature is imposed along this boundary.
Polydata prompts you for the new value of the constant temperature.
d. Set the conditions at the top boundary of the solid (BOUNDARY_4).
ii. Click Insulated boundary / symmetry.
e. Click Upper level menu three times to return to the top-level Polydata menu.
After defining your model in Polydata, save the data file. In the next step, read this data file into Polyflow
and calculate a solution.
Save and exit
Polydata asks you to confirm the current system units and fields that are to be saved to the results file
for postprocessing.
1. Click Upper level menu.
This confirms that the default units are correct.
A panel appears, asking if you want to activate convergence strategy.
2. Click No.
102

In this instance, the convergence strategy will not assist Polyflow in reaching a solution as the problem
is quasi-linear.
3. Click Accept.
4. Click Continue.
Run Polyflow to calculate a solution for the model you just defined using Polydata.
1. Run Polyflow by right-clicking the Solution cell of the simulation and selecting Update.
a. Right-click the Solution cell and select Listing Viewer....
Workbench opens the View listing file panel, which displays the listing file.
b. It is a common practice to confirm that the solution proceeded as expected by looking for the
following printed at the bottom of the listing file:
The computation succeeded.
Use CFD-Post to view the results of the Polyflow simulation.
1. Double-click the Results cell in the Workbench analysis and read the results files saved by Polyflow.
CFD-Post reads the solution fields that were saved to the results file.
2. Align the view.
Right-click the Graphics window and select View from +Z under Predefined Camera.
(Or you can click +Z on the axis triad in the graphic window.)
The central-mouse button allows you to zoom in and zoom out.
The left-mouse button allows you to rotate the image.
The right-mouse button allows you to translate the image.
3. Display contours of pressure.
103

b. Click OK to accept the default name (Contour 1) and display the details view below the Outline
tab.
c. In the details view for Contour 1, specify the following settings under Geometry:
i. Next to Locations, click the ellipsis button ( ) on the right and select SUBDOMAIN_1_surf
and SUBDOMAIN_2_surf (use Ctrl to select multiple items).
ii. Select PRESSURE from the Variable drop-down list, or click the ellipsis button ( ) on the
right and select PRESSURE.
iii. Click Apply.
Most of the pressure drop occurs in the upper part of the die where the cross section is smallest (Fig-
ure 2.3: Pressure Contours(p. 105)). The pressure is linear except in the contraction zone. The isobars are
perpendicular to the flow direction, as expected for the fully developed flow that occurs in the second
part of the die.
104

Figure 2.3: Pressure Contours
4. Display contours of velocity.
a. In the details of Contour 1, select VELOCITIES from the Variable drop-down list.
b. Click Apply.
The velocity is higher in the second part of the die where the cross-section is smaller (Figure 2.4: Velocity
Distribution (p. 106)). It reaches a maximum value in the center of the thin tube.
105

Figure 2.4: Velocity Distribution
5. Display velocity vectors.
a. In the Outline tab, under User Locations and Plots, deselect Contour 1.
b. Define the vectors.
i. Click the Insert menu and select Vector or click the button.
ii. Click OK to accept the default name, Vector 1.
iii. In the Geometry tab of the details view of Vector 1, click the button next to Locations.
iv. Select the location SUBDOMAIN_1 and click OK to close the Location Selector dialog box.
v. In the Symbol tab, select Arrow 3D and increase the Symbol Size to 3.
vi. Click Apply.
106

The flow is fully developed in the downstream part of the die (Figure 2.5: Velocity Vectors(p. 107)). Observe
the classical parabolic velocity profile. The Poiseuille flow is rapidly reached after the contraction because
inertia is not taken into account here.
6. Display of the temperature distribution in the solid and the fluid regions.
a. Deselect the vectors.
107

Deselect Vector 1 in the Outline tab under User Locations and plots.
b. Select the domain.
Select SUBDOMAIN_1 Hex and SUBDOMAIN_2 Hex in the Outline tab under Mesh Regions.
c. Define the contour plot.
i. In the graphic window, right-click the left-hand domain.
ii. Under Color, select Temperature.
iii. Repeat the above operations (i) and (ii) for the right-hand domain.
108

Figure 2.6: Temperature Distribution (Celsius)
109

Figure 2.7: Temperature Distribution (Kelvin)
As expected, the temperature gradients are larger in the fluid than in the die, (the isolines are closer
together in the fluid than in the die—see Figure 2.6: Temperature Distribution (Celsius)(p. 109)). This is
because the conductivity of the fluid is much lower than the conductivity of the solid. The temperature
isolines are perpendicular to the boundaries where the (normal) flux becomes zero. The heating of the
fluid due to viscous dissipation can be clearly seen. In order to visualize contours in Kelvin, select the
Edit/Options... menu item, click Units under Common, select K from the Temperature drop-down
menu, and click OK.
7. Plot the temperature along a line at y = 0.006 m.
a. Define the stating and ending points of the line.
i. Select Line from the Location drop-down menu ( ).
ii. Click OK to accept the default name (Line 1) and display the details view below the Outline
tab.
110

iii. Select Two Points from the Method drop-down list.
iv. Enter 0, 6, and 0 for Point 1 and enter 8, 6, and 0 for Point 2.
Note
You will need to ensure that your unit of length is set to meter in CFD-Post.
v. Click Apply.
b. Create a plot.
i. Click the Insert menu and select Chart or click the Chart button ( ).
ii. Click OK to accept the default name (Chart 1) and display the details view below the Outline
tab tree.
111

iii. In the General tab, ensure XY is selected for the Chart Type and enter Temperature
Profile for the Title.
iv. In the Data Series tab, select Line 1 from the Location drop-down list.
v. In the X Axis tab, select X from the Variable drop-down list.
vi. In the Y Axis tab, select Temperature from the Variable drop-down list.
vii. Click Apply.
112

Figure 2.8: Temperature Profile Along the Line Y = 0.006 m
The thermal boundary layer located along the die wall is clearly visible. This boundary layer is the result
of the low thermal conductivity and high heat capacity of the fluid. The temperature of the fluid at the
center is not affected by the low temperature of the solid. The heat does not diffuse quickly enough
through the fluid layer to reach the axis of symmetry, before the fluid exits the die.
2.12.Summary
This tutorial introduced the coupling of sub-tasks of different types: a non-isothermal flow problem and
a heat conduction problem in a solid. Coupled calculations like this are very useful in polymer processing
applications where thermal effects are critical (for example: extrusion, coating, fiber spinning). Coupling
can also be applied through fields other than temperature (for example: electrical potential and pressure
in porous media).
113
Summary

114

Chapter 3: Non-Isothermal Flow Through a Cooled Die
3.1.Introduction
3.2.Prerequisites
3.4.Preparation
3.6.Step 2:Models,Materials,and Boundary Conditions
3.7.Step 3:Definition of the Fluid Sub-Task
3.8.Step 4:Definition of the Solid Sub-Task
3.9.Step 5:Numerical Parameters
3.10.Step 6:Outputs
3.14.Summary
3.15.Appendix:Non-Linearity and Evolution
3.1.Introduction
This tutorial examines the flow of a polymer melt through a die. The temperature of the melt increases
due to viscous dissipation caused by the shearing taking place in the die. The temperature of the fluid
is critical for the process. The viscosity of the fluid changes with temperature, which leads to the
modification of the shape of the extrudate. The polymer might degrade if the temperature is too high,
so a numerical simulation is of great interest to optimize the operating conditions.
In this tutorial, you will learn how to:
• Define an evolution problem.
• Create multiple sub-tasks to define a 2D axisymmetric contraction flow problem.
• Set material properties and boundary conditions for the contraction flow problem.
3.2.Prerequisites
This tutorial examines the coupled problem of non-isothermal flow of a fluid and heat conduction in
an axisymmetric steel die. As shown in Figure 3.1: Problem Description(p. 116), the melt enters the domain
at a fixed temperature, = 200°C and at a given flow rate, = 5 ×10−6
m3
/s. The problem involves flow,
heat transfer by conduction and convection, and heat generation by viscous dissipation. Energy, mo-
115

mentum, and incompressibility equations are solved in the fluid domain. The energy equation for heat
transport problems is solved in the solid (die) domain.
In solving for the free surface location, the position variables are also coupled to the temperature, velocity,
and pressure fields. To solve the coupled problem, you will define two sub-tasks: one each for the fluid
(sub-task 1) and the solid (sub-task 2). Each sub-task contains a particular model, domain of definition,
material properties, and boundary conditions, including interface conditions with the other sub-task.
The sub-tasks are coupled because the global solution of the problem depends on the values of the
solution variables at the intersection of the fluid and solid domains.
The high flow rate introduces strong non-linearity in the problem, which can lead to a loss of convergence
in the iterative scheme. In Polyflow an evolution scheme is available to solve such highly non-linear
problems. In this problem, the evolution scheme is applied to the flow rate, which is increased from a
low value to the desired value. This leads to a simultaneous increase of viscous dissipation and inertia
effects.
The material properties of the generalized Newtonian fluid are:
116
Non-Isothermal Flow Through a Cooled Die

= density (950 kg/m3
)
= heat capacity per unit mass (2300 J/kg-K)
= thermal conductivity (0.5 W/m-K)
Viscous heating is taken into account and the shear-rate dependence of viscosity obeys the Bird-Carreau
law. For the solid region, the thermal conductivity () is 30 W/mK.
The boundary sets for the problem are shown in Figure 3.2: Boundaries and Subdomains(p. 118), and
the flow and thermal conditions for the fluid and the die at the boundaries of the domains are:
• intersection of SUBDOMAIN_1 and SUBDOMAIN_3: interface
• boundary 1: flow inlet (=200°C, = 5 × 10-6
m3
/s)
• boundary 3: insulated, zero force
• boundary 4: free surface with convective heat transfer to surroundings ( = 20 W/m2
-°C, α= 20°C)
• boundary 5: convective heat transfer to surroundings ( = 20 W/m2
-°C, α= 20°C)
• boundary 6: convective heat transfer to surroundings ( = 20 W/m2
-°C, α= 20°C)
117
Problem Description

Figure 3.2: Boundaries and Subdomains
3.4.Preparation
Note
118

7. Unzip the Non-Iso-Flow_R150.zip file you have downloaded to your working folder.
The mesh file die.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering non-iso-flow as the name of the
project.
3. Import the mesh file (die.msh).
3.6.Step 2: Models,Materials,and Boundary Conditions
In this step, define a new task representing the contraction flow problem. The flow problem for the generalized
Newtonian fluid and the heat conduction problem in the solid are solved in two different sub-tasks. However,
the task attributes are the same for both sub-tasks, so define a single task for the coupled problem.
Create a new task
Select the following options:
• F.E.M. task
• Evolution problem(s)
The Current setup (above the selected options) is updated to reflect your selections. Since the
problem involves an axisymmetric die, Polyflow uses a 2D cylindrical reference frame (r,z) with r=0
as the axis of symmetry. The use of evolution inputs allows the flow rate to be slowly ramped up to
ensure that the solution converges.
119
Step 2:Models,Materials,and Boundary Conditions

3.7.Step 3: Definition of the Fluid Sub-Task
In this step, define the flow problem, identify the domain of definition, set the relevant material properties
for the fluid, and define boundary conditions along its boundaries.
1. Create a sub-task for the fluid.
Create a sub-task
a. Click Generalized Newtonian non-isothermal flow problem.
Note
Be sure you are selecting the non-isothermal flow problem.
A panel appears, asking for the title of the problem.
b. Enter fluid as the New value and click OK.
To solve the coupled problem, the computational domain is divided into three subdomains. There are
two sub-tasks in this problem. Define a sub-task with its own model, material properties, and boundary
conditions for the fluid region. Since this problem involves a free surface, the domain for sub-task 1 is
divided into two subdomains: one for the region near the free surface (SUBDOMAIN_2) and the other
for the rest of the fluid domain (SUBDOMAIN_1). In this problem, sub-task 1 applies to SUBDOMAIN_1
and SUBDOMAIN_2.
120

SUBDOMAIN_3 is moved from the top list to the bottom list, indicating that subtask 1 is defined
on SUBDOMAIN_1 and SUBDOMAIN_2.
b. Click Upper level menu at the top of the Domain of the sub-task menu.
3. Specify the material properties for the fluid.
Polydata indicates the material properties that are relevant for your sub-task by graying out the irrelevant
properties. In this sub-task, Polyflow solves energy, incompressibility, and momentum equations. Hence,
define viscosity, density, thermal conductivity, and heat capacity per unit mass. For a non-isothermal
generalized Newtonian fluid, the viscosity depends on the shear rate and the temperature. Hence, define
the shear-rate dependence of viscosity and the temperature dependence of viscosity.
Material data
a. Specify the shear-rate dependence of viscosity.
Shear-rate dependence of viscosity
i. Select Bird-Carreau law.
Viscosity is defined by the Bird-Carreau law as
121
Step 3:Definition of the Fluid Sub-Task

(3.1)
= 

+ 

−

where is the viscosity at zero shear rate, is the shear rate, is the Bird-Carreau law
index, and is the natural time.
ii. Specify the value , referred to as “fac” in the graphical user interface (compare the equation
at the top of the Shear-rate dependence of viscosity menu to Equation 3.1 (p. 122)).
Modify fac
iii. Specify the value , referred to as “tnat” in the graphical user interface.
Modify tnat
Enter 0.4 as the New Value and click OK.
iv. Specify the value for , referred to as “expo” in the graphical user interface.
Modify expo
v. Click Upper level menu.
When you click Upper level menu, Polydata displays the following warning message:
122

For this tutorial, use an evolution function for the flow rate (the third recommended method).
vi. Click OK to continue.
vii. Click Upper level menu again to continue with the Material Data specification.
b. Specify the temperature dependence of viscosity.
Temperature dependence of viscosity
For this problem, assume that the dependence of viscosity on temperature follows the Arrhenius
law.
i. Click Arrhenius law.
The Arrhenius law is given as
(3.2)
=







−


 −



−








where is the ratio of the activation energy to the thermodynamic constant and is a refer-
ence temperature for which = 1. The parameter denotes the absolute 0 temperature
in your selected temperature scale. It is set to 0, when and are absolute temperatures.
In this example, specify the temperatures in Celsius, so enter a value of -273 for .
ii. Specify the value for , referred to as “alfa” in the graphical user interface (compare the
equation at the top of the Temperature dependence of viscosity menu to Equa-
tion 3.2 (p. 123)).
Modify alfa
123

Enter 2300 as the New Value and click OK.
iii. Specify the value for , referred to as “talfa” by the graphical user interface.
Modify talfa
iv. Specify the value for , referred to as “t0” by the graphical user interface.
Modify t0
Enter -273 as the New Value and click OK.
v. Click Upper level menu two times to continue with the Material Data specification.
c. Click Density.
Specify a constant value for density.
Modification of density
d. Click Thermal conductivity.
Thermal conductivity is defined as a non-linear function of the temperature:
(3.3)
= + + +

For this problem, the thermal conductivity of the fluid is assumed to be a constant. So only the
constant coefficient is modified.
Modify a
i. Enter 0.5 as the New Value and click OK.
e. Click Heat capacity per unit mass.
The heat capacity per unit mass is defined as a non-linear function of temeprature:
(3.4)
= + + +

The temperature variation of depends on the nature of the polymer melt. For this problem,
is assumed to be constant, so only the constant coefficient is modified.
Modify a
124

f. Click Viscous heating.
When shearing occurs in a flow, the friction of the different fluid layers generates heat. When the
fluid is highly viscous and/or the shear rate is high, the heating of the fluid caused by this phe-
nomenon must be taken into account.
i. Select Viscous heating will be taken into account.
ii. Click Upper level menu to return to the Material Data specification.
g. Click Upper level menu to return to the fluid menu.
4. Specify the flow boundary conditions for the fluid.
a. Retain the default condition Zero wall velocity (vn=vs=0) along SUBDOMAIN_3 at the intersection
of SUBDOMAIN_1 and SUBDOMAIN_3.
The liquid is assumed to stick to the wall, since at a solid-liquid interface the velocity of the liquid
is that of the solid surface. This is known as the no-slip assumption because the liquid is assumed
to adhere to the wall, and hence, has no velocity relative to the wall.
By default, Polydata imposes = = 0 along all boundaries. No action is required to accept the
default condition.
ii. Click EVOL at the top of the Polydata menu to enable the evolution inputs for the flow rate.
For information on non-linearity and evolution, see Appendix: Non-Linearity and Evolu-
tion (p. 147).
iii. Click Inflow.
iv. Select Volumetric flow rate.
v. Select Modify volumetric flow rate.
Polydata prompts for the new value of the volumetric /mass flow rate.
Enter 5e-06 as the New Value and click OK.
vi. Select Automatic option.
125

vii. Click Upper level menu. Polydata prompts for the evolution function .
viii. Select f(S)=S.
The Current choice (at the top of the menu) is updated to reflect your selection.
ix. Click EVOL at the top of the Polydata menu to disable the evolution inputs.
x. Click Upper level menu to return to the Flow boundary conditions menu.
c. Retain the default condition, Axis of symmetry along BOUNDARY_2.
For axisymmetric models, Polydata recognizes the axis of symmetry from the mesh file, and auto-
matically imposes the symmetry condition along the line = 0. This condition imposes a zero surface
normal velocity () and zero tangential force (

) along this boundary.
d. Set the conditions at the flow exit (BOUNDARY_3).
It is assumed that a uniform velocity profile is reached at the exit. The melt is not subjected to any
externally applied stress at the exit, so the condition of zero normal and tangential forces is selected.
ii. Click Normal and tangential forces imposed (fn, fs).
iii. Click Upper level menu to accept the default value of 0 for

.
iv. Click Upper level menu to accept the default value of 0 for .
e. Set the conditions at the free surface (BOUNDARY_4).
In a steady-state problem, the velocity field must be tangential to a free surface, since no fluid
particles leave the domain through the free surface. This constraint is called the kinematic condition,
= 0. This equation requires an initial condition, which is the starting line of the free surface.
In this problem, the starting line of the free surface is the intersection of BOUNDARY_4 and SUBDO-
MAIN_3 (see Figure 3.2: Boundaries and Subdomains(p. 118)).
ii. Click Free surface.
iii. Click Boundary conditions on the moving surface.
iv. Select No condition along SUBDOMAIN_3 and click Modify.
v. Click Position imposed.
vi. Click Upper level menu.
vii. Click Upper level menu to return to the Kinematic condition menu.
126

viii. Click Upwinding in the kinematic equation.
ix. Click Direction of motion.
x. Click No condition along whole surface and click Modify.
xi. Select Modify the constraint on the Y-component.
Polydata prompts for the new value of the Y-component of the direction-of-displacement
vector.
xii. Retain the default value of 0 and click OK.
xiii. Click Accept the current condition.
xiv. Click Upper level menu to return to the Kinematic condition menu.
xv. Click Upper level menu to return to the Flow boundary condition menu.
f. Click Upper level menu to return to the fluid menu.
5. Specify the thermal boundary conditions for the fluid.
For non-isothermal problems, specify either the temperature or the heat flux on each boundary set.
127

Set an interface condition at the intersection of SUBDOMAIN_1 and SUBDOMAIN_3. This condition
ensures the continuity of the temperature field and the heat flux along the interface. Since the
problem is coupled, the condition of continuity is essential for the global solution of the temperature
and heat flux variables.
iii. Click Upper level menu to accept the default setting (continuous heat flux along the interface).
For an interface condition, both the heat flux and temperature are usually continuous along
the interface. It is possible to specify a non-zero value for the heat flux jump ( ), but this is
mainly used in problems where internal radiation is simulated. Accept the default value for
the definition of heat flux discontinuity (=0).
b. Set the condition at the flow inlet (BOUNDARY_1).
Polydata prompts for the value of the temperature.
128

iv. Enter 200 as the New Value and click OK.
c. Retain the default condition, Axis of symmetry along BOUNDARY_2.
d. Set the conditions at the flow exit (BOUNDARY_3).
ii. Click Insulated boundary/symmetry.
e. Set the conditions at the free surface (BOUNDARY_4)
ii. Click Flux density imposed.
If the heat transfer from radiation is neglected, the heat flux can be written as
(3.5)
= −

where is the heat convection coefficient and is the reference temperature (in this case,
the temperature of the air surrounding the extrudate).
iii. Specify the value of .
Modification of alpha
iv. Specify the value of .
Modification of Talpha
f. Click Upper level menu to return to the fluid menu.
The Global remeshing menu item is highlighted.
6. Define remeshing for SUBDOMAIN_2.
This model involves a free surface for which the position is unknown. A portion of the mesh is affected
by the relocation of this boundary. Hence, a remeshing technique is applied on this part of the mesh.
The free surface is entirely contained within SUBDOMAIN_2 and hence, only SUBDOMAIN_2 is affected
by the relocation of the free surface.
Global remeshing
129

a. Specify the region where the remeshing is to be performed (SUBDOMAIN_2).
1-st local remeshing
i. Select SUBDOMAIN_1 and click Remove.
SUBDOMAIN_1 is moved from the top list to the bottom list, indicating that only SUBDOMAIN_2
will be remeshed.
ii. Click Upper level menu.
The Method of spines menu item is highlighted.
b. Define the parameters for the system of spines.
The purpose of the remeshing technique is to relocate internal nodes according to the displacement
of boundary nodes due to the motion of the free surface. Mesh nodes are organized along lines of
remeshing (spines), which are collections of nodes logically arranged in a one-dimensional manner.
Polydata requires the specification of the first and last spines (inlet and outlet) that the fluid en-
counters In this case, the inlet of spines is the intersection of SUBDOMAIN_2 with SUBDOMAIN_1,
and the outlet of spines is the intersection of SUBDOMAIN_2 with the flow exit (BOUNDARY_3).
Method of Spines
i. Specify the inlet for the system of spines by selecting Intersection with SUBDOMAIN_1 and
clicking Confirm.
130

ii. Specify the outlet for the system of spines by selecting Intersection with BOUNDARY_3 and
clicking Confirm.
iii. Click Accept the current setup in the Element distortion check menu.
The finite-element mesh can undergo great deformations. The Element distortion check
menu deals with the detection of all possible distortions of the elements.
For this problem, accept the default options and proceed to the next step.
c. Click Upper level menu to return to the fluid menu.
7. Select a suitable discretization scheme to increase the accuracy of the calculation.
Interpolation
You can expect important temperature gradients in the calculation. Therefore, you can retain the
quadratic interpolation (9 unknowns per element) for velocity and the linear interpolation (4 unknowns
per element) for pressure, but it is recommended that you select the 4x4 interpolation for temperature.
In the 4x4 discretization scheme, each finite element is divided into 16 sub-elements, with the temper-
ature being linearly interpolated over each sub-element. This leads to 25 temperature unknowns per
element.
a. Scroll down to select 4x4 element for temperature in the Interpolation menu.
The Current setup (at the top of the menu) is updated to reflect your selection.
b. Click Upper level menu two times to return to the F.E.M. Task 1 menu.
3.8.Step 4: Definition of the Solid Sub-Task
In this step, define the heat conduction problem, identify the domain of definition, set the relevant material
properties for the die, and define the boundary conditions along its boundaries.
1. Create a sub-task for the die.
Create a sub-task
a. Polydata asks if you want to copy data from an existing sub-task.
131
Step 4:Definition of the Solid Sub-Task

c. Select Heat conduction problem.
A panel appears, asking for the title of the problem.
d. Enter solid as the New Value and click OK.
2. Define the domain where the sub-task applies (SUBDOMAIN_3).
b. Select SUBDOMAIN_2 and click Remove.
c. Click Upper level menu at the top of the Domain of the sub-task menu.
3. Specify the material properties for the die.
For this problem, specify a constant value for the thermal conductivity .
Material data
a. Select Thermal conductivity.
For this problem, thermal conductivity is assumed to be a constant, so only the constant coefficient
is modified.
b. Select Modify a.
c. Enter 30 as the New value and click OK.
d. Click Upper level menu two times to return to the solid menu.
The Thermal boundary conditions menu item is highlighted.
4. Specify the thermal boundary conditions for the die.
Set the conditions at each of the boundaries of the domain. The selected boundary set will be highlighted
(in red) in the graphics window as you select them..
Set an interface condition at the intersection of the subdomains.
132

iii. Click Upper level menu to accept the default option for continuity of temperature and heat
flux.
b. Set the conditions on the outer boundary of the die (BOUNDARY_5).
ii. Click Flux density imposed.
Take only the heat convection into account: see Equation 3.5 (p. 129).
c. Set the conditions at the inner boundary of the die (BOUNDARY_6).
ii. Select Flux density imposed.
5. Click Upper level menu twice to return to the F.E.M. Task 1 menu.
133
Step 4:Definition of the Solid Sub-Task

3.9.Step 5: Numerical Parameters
All information relevant to iterative schemes (for the F.E.M. task calculations) can be modified in the
Numerical parameters menu.
Numerical parameters
1. Specify the parameters required for the evolution scheme.
Modify the evolution parameters
a. Define the initial value of (the evolution variable).
Modify the initial value of S
b. Define the starting solution for the iterative scheme in the calculation of the inflow condition.
Modify the initial value of delta-S
2. Click Upper level menu three times to return to the top-level Polydata menu.
Outputs
1. Set the system of units to output to CFD-Post.
Set units for CFD-Post, Ansys Mapper or Iges
a. Modify the current system of units.
Modify system of Units
b. Specify the new system of units.
Set to metric_MKSA+Celsius
After defining your model in Polydata, save the data file. In the next step, you will have to read this data file
into Polyflow and calculate a solution.
134

Save and exit
A panel appears, asking if you want to activate convergence strategy.
Click No, as you have already defined an evolution strategy on the flow rate.
1. Click Accept.
2. Click Continue.
Ten CFD-Post files are created, corresponding to the thirteen evolution steps in the problem.
135

2. Align the view.
In the graphical window, right-click, and select the option Predefined Camera.
a. Right-click in the graphical window and select View from +Z under Predefined Camera.
The central-mouse button allows you to zoom in and zoom out. The left-mouse button allows ro-
tating the image. The right-mouse button allows you to translate the image.
b. To remove the ruler right-click in the graphical window, select Viewer Options, and disable Ruler
Visibility.
3. Display contours of pressure in the fluid region (SUBDOMAIN_1 and SUBDOMAIN_2).
a. Click the Insert menu and select Contour or click the button.
b. In the panel that opens, click OK to accept the default name (Contour 1) display the details view
below the Outline tab.
c. Perform the following steps In the Geometry tab of the details view for Contour 1:
i. Next to Locations, click the ellipsis button ( ) on the right and select SUBDOMAIN_1_surf
and SUBDOMAIN_2_surf (use Ctrl to select multiple items).
136

ii. Select PRESSURE from the Variable drop-down list, or click the ellipsis button ( ) on the
right and select PRESSURE.
iii. Click Apply.
137

Figure 3.3: Contours of Pressure
4. Display contours of velocity in the fluid region.
a. In the details view of Contour 1, select VELOCITIES from the Variable drop-down list.
b. Click Apply.
138

Figure 3.4: Velocity Profile
The fluid experiences high velocity gradients in the narrow section of the die. This leads to important
viscous dissipation effects that cause the temperature of the melt to increase.
5. Display velocity vectors for the two fluid subdomains.
a. In the Outline tab under User Locations and Plots, disable Contour 1.
b. Click the Insert menu and select Vector or click the button.
c. Click OK to accept the default name (Vector 1) and open the details view below the Outline tab.
139

i. In the Geometry tab, click the button next to Locations to open the Location Selector
dialog box.
ii. Select SUBDOMAIN_1_surf and SUBDOMAIN_2_surf (use Ctrl to select multiple items).
iii. In the Symbol tab, select Arrow3D and retain the default Symbol Size of 1.0.
iv. Click Apply.
140

The velocity vectors in the wide section of the die are very small compared to those in the narrow section
of the die (Figure 3.5: Velocity Vectors(p. 141)). Also, the important velocity re-arrangement takes place
at the die exit. This leads to the swelling of the extrudate.
6. Display the temperature distribution in the solid and the fluid regions.
a. In the Outline tab, under User Locations and Plots, disable Vector 1 and enable and double-click
Contour 1.
b. In the details of Contour 1, define the temperature contours.
141

i. Next to Locations, click the ellipsis button ( ) on the right and select SUBDOMAIN_1_surf,
SUBDOMAIN_2_surf and SUBDOMAIN_3_surf (use Ctrl to select multiple items).
ii. Select TEMPERATURE from the Variable drop-down list.
iii. Click Apply.
142

Figure 3.6: Temperature Profile
143

Figure 3.7: Temperature Profile Near the Die Exit
Figure 3.7: Temperature Profile Near the Die Exit(p. 144) shows a magnified view of the temperature
contours near the die exit. The high velocity gradients near the die exit lead to an important viscous
dissipation effect. The temperature of the polymer melt increases from the converging zone to the die
lip. This increase in temperature must be monitored to avoid melt degradation. The simulation helps
optimize the geometry of the die, the flow section for the cooling fluid, and other conditions in order
to maximize the flow rate and the extrudate speed.
7. Create a 2D plot on a cross section of the die.
a. Verify that you have millimeters selected as your units for length in CFD-Post.
Edit → Options... → Units
b. Define the line for the plot with the points (0, 1, 0) and (15, 1, 0).
144

i. Select Line from the Location menu ( ).
tab.
iii. Enter 0, 1, 0 for Point 1 and 15, 1, 0 for Point 2.
iv. Select the Cut option button under Line Type.
v. Click Apply.
c. Create a plot.
i. Click the chart button .
tab.
145

iii. In the General tab of the details view, select XY for the chart Type and disable Display Title.
iv. In the Data Series tab, select Line 1 from the Locations drop-down list for Series 1.
vi. In the Y Axis tab, select TEMPERATURE from the Variable drop-down list.
vii. With Series 1 (Line 1) enabled under the Line Display tab, select Rectangle from the Symbols
drop-down list. Retain the default Symbol Color (green).
viii. Click Apply.
146

Figure 3.8: Temperature Profile Across the Die
3.14.Summary
In this tutorial, you solved the non-isothermal flow of a polymer melt through a cooled die. You set the
material properties for the melt and supplied suitable boundary conditions. A specific interpolation
scheme was used for the temperature in order to cope with the important gradients. You applied an
evolution scheme to solve the convergence problems caused by the viscous dissipation coupled with
the temperature-dependent viscosity law.
3.15.Appendix: Non-Linearity and Evolution
The kinematic equation introduces non-linear terms into the problem that might lead to convergence
difficulties. In Polyflow, an evolution scheme is available to solve such highly non-linear problems. The
calculation is started with a reduced value of the parameter(s) causing the non-linearity. Starting from
the first solution, Polyflow increments the parameter(s) causing the non-linearity and computes a second
solution. Starting from this new solution, Polyflow increments the parameter(s) again and computes a
third solution. Thus, Polyflow increases the value of each parameter up to its nominal value.
In Polyflow, this procedure is fully automated. The increments are automatically adapted according to
the results of previous calculations. Polyflow uses an evolution variable ( ) that is incremented during
the evolution scheme. starts at an initial value of and is increased up to a final value of . Each
parameter that you evolve is defined as =
.
147
Appendix:Non-Linearity and Evolution

148

Chapter 4: 3D Extrusion
4.1.Introduction
4.2.Prerequisites
4.4.Preparation
4.6.Step 2:Models
4.13.Summary
4.1.Introduction
This tutorial illustrates the simulation of a 3D extrusion process. Due to the velocity rearrangement that
occurs at the die exit, the shape of the extrudate is usually different from the die lip cross section.
Polyflow is capable of handling 3D free surfaces, so it can predict the extrudate shape that corresponds
to a given die geometry under prescribed operating conditions.
• Create a sub-task to define a 3D extrusion problem.
• Set material properties and boundary conditions for a 3D extrusion problem.
4.2.Prerequisites
symmetry of the problem (the cross section of the die is a square), the computational domain is defined
for a quarter of the geometry and two planes of symmetry are defined.
The melt enters the die as shown in Figure 4.1: Problem Description(p. 150) at a flow rate of = 10
cm3
/s (a quarter of the actual flow rate) and the extrudate is obtained at the exit. At the end of the
computational domain, it is assumed that the extrudate is fully deformed and that it will not deform
149

any further. It is assumed that subdomain 2 is long enough to account for all the deformation of the
extrudate.
for the problem is divided into two subdomains (as shown in Figure 4.1: Problem Description(p. 150))
so that the remeshing algorithm can be applied only to the portion of the mesh that will be deformed.
The subdomain 1 represents the die where the fluid is confined. The subdomain 2 corresponds to the
extrudate that is in contact with the air and can deform freely. The main aim of the calculation is to
find the location of the free surface (the skin of the extrudate).
The boundary sets for the problem are shown in Figure 4.2: Boundary Sets for the Problem(p. 151), and
the conditions at the boundaries of the domains are as follows.
• boundary 1: flow inlet, volumetric flow rate = 10 cm3
/s
• boundary 2: zero velocity
• boundary 3: symmetry plane
• boundary 5: free surface
150
3D Extrusion

Figure 4.2: Boundary Sets for the Problem
4.4.Preparation
Note
7. Unzip the 3D-Extrusion_R150.zip file you have downloaded to your working folder.
151
Preparation

The mesh file ext3d.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering 3D-extrusion as the name of the
project.
3. Import the mesh file (ext3d.msh).
4.6.Step 2: Models
In this step, first define a new task representing the 3D steady-state model. Then define a sub-task for
the isothermal flow calculation.
Create a new task
a. Retain the following (default) options:
• F.E.M. task
This problem is a 3D simulation of the extrusion process, that is, a three-dimensional geometry is
assumed for the die. A Cartesian (x,y,z) reference frame is used for the 3D calculations. A steady-
state condition is assumed for the problem.
Create a sub-task
152
3D Extrusion

b. Enter 3D die swell as the New value and click OK.
Since this problem involves a free surface, the domain is divided into two subdomains; one for the region
near the free surface (subdomain 2) and the other for the rest of the domain (subdomain 1). In this
problem, the sub-task applies to both subdomains, which is the default condition.
Accept the default selection of both subdomains (SUBDOMAIN_1 and SUBDOMAIN_2) by clicking
Upper level menu.
153
Step 2:Models

Polydata indicates which material properties are relevant for the sub-task by graying out the irrelevant
model, define only the viscosity of the material.
Material Data
2. Click Cross law.
The Cross law exhibits shear-thinning (the decrease in viscosity as the shear rate increases) that is a
characteristic of many polymers. The viscosity in this tutorial is given by the Cross law:
(4.1)
=
+

where:
= zero shear-rate viscosity = 85000
= natural time = 0.2
= Cross law index = 0.3
= shear rate
3. Specify the value .
Modify fac
Modify tnat
154
3D Extrusion

Modify expom
6. Select Upper level menu three times to return to the 3D die swell menu.
In this step, set the conditions at each of the boundaries of the domain. When a boundary set is selected, its
location is highlighted in red in the graphics window.
155

1. Set the conditions at the flow inlet (BOUNDARY_1).
a. Select Zero wall velocity (vn=vs=0) along BOUNDARY_1 and click Modify.
b. Click Inflow.
c. Retain the default settings, Automatic and Volumetric flow rate.
d. Click Modify volumetric flow rate.
e. Click Upper level menu.
156
3D Extrusion

2. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY_2 at the wall of SUBDO-
MAIN_1 (BOUNDARY_2).
At a solid-liquid interface, the velocity of the liquid is that of the solid surface. Hence the fluid is assumed
to stick to the wall. This is known as the no-slip assumption because the liquid is assumed to adhere
to the wall, and hence, has no velocity relative to the wall.
By default, Polydata imposes = = 0 along all boundaries. No action is required to accept the default
condition.
3. Set the conditions at the first symmetry plane (BOUNDARY_3).
In 2D axisymmetric problems, the axis of symmetry is automatically identified by Polydata, but for 3D
flows, you must manually identify a plane of symmetry.
The normal velocity () and the tangential force ( ) are set to zero on a symmetry plane. A particle
cannot cross the plane ( = 0) due to the symmetry, so the particles flow at the same velocity on both
sides of the symmetry plane, leading to a zero tangential force.
b. Click Plane of symmetry (fs=0, vn=0).
4. Set the conditions at the second symmetry plane (BOUNDARY_4).
5. Set the conditions at the free surface (BOUNDARY_5).
In a steady-state problem, the velocity field must be tangential to a free surface, since no fluid particles
go out of the domain through the free surface. This constraint is called the kinematic condition, v·n =
0. This equation requires an initial condition, that is, the starting line of the free surface. In the current
problem, the starting line of the free surface is the intersection of boundary 2 and boundary 5 (see Fig-
ure 4.2: Boundary Sets for the Problem(p. 151)).
d. Select No condition along BOUNDARY_2 and click Modify.
e. Select Position imposed.
g. Click Upper level menu to return to the Kinematic condition menu.
h. Click Upper level menu to return to the Flow boundary conditions panel.
157

6. Set the conditions at the flow outlet (BOUNDARY_6).
It is assumed that a uniform velocity profile is reached at the exit. The melt is not subjected to any ex-
ternally applied stress at the exit, so the condition of zero normal and tangential forces is selected.
c. Accept the default value of 0 for the normal force,
, by clicking Upper level menu.
d. Accept the default value of 0 for the tangential force,

e. Click Upper level menu at the top of the Flow boundary conditions panel.
This model involves a free surface, the position of which is unknown. A portion of the mesh is affected by
the relocation of this boundary. Hence a remeshing technique is applied on this part of the mesh. The free
surface is entirely contained within subdomain 2, and hence only subdomain 2 will be affected by the relo-
cation of the free surface.
Global remeshing
1. Specify the region where the remeshing is to be performed (SUBDOMAIN_2).
allows you to create several local remeshings. For the current problem, a single local remeshing is suffi-
cient.
1–st local remeshing
will be remeshed.
158
3D Extrusion

2. Define the parameters for the remeshing method.
boundary nodes due to the motion of the free surface, since a part of the mesh is deformed. For 3D
extrusion problems where large deformations of the extrudate are expected, the optimesh remeshing
technique is recommended
The optimesh remeshing technique requires the direction of extrusion to be parallel to the , , or
axis, and all slices into which the remeshing domain is cut must be perpendicular to the extrusion axis.
The domain to be remeshed is cut into a series of 2D slices (planes) in a direction perpendicular to the
direction of extrusion, and each plane is remeshed independently. For this process, Polyflow requires
the selection of the initial plane and the final plane. In this problem, the initial plane is the intersection
of subdomain 2 with subdomain 1, and the final plane is the intersection of subdomain 2 with the flow
exit (boundary 6).
Optimesh-3D (extrusion only)
a. Specify the initial plane for the optimesh remeshing technique, by selecting Intersection with
SUBDOMAIN_1 and clicking Confirm.
159
Step 5:Remeshing

b. Specify the final plane for the optimesh remeshing technique, by selecting Intersection with
BOUNDARY_6 and clicking Confirm.
Polydata asks whether you want to use the surface kinematic condition.
160
3D Extrusion

c. Click Yes to use the line kinematic condition.
The line kinematic condition is recommended for extrusion problems, and should be used in
combination with the optimesh remeshing technique.
d. Click Upper level menu three times.
The top-level Polydata menu is displayed.
Save and exit
Polydata asks you to confirm the current system units and fields that are to be saved to the results file for
postprocessing.
b. Select Set to metric cm/g/s/A+Celsius
161

Polydata asks you to confirm fields that are to be saved to the results file for postprocessing.
2. Click Accept.
3. Click Continue.
162
3D Extrusion

2. Display the velocity distribution on the boundaries.
tab.
c. In the Outline tree tab, under User Locations and Plots, deselect Wireframe.
d. Perform the following steps in the details view of Contour 1:
i. In the Geometry tab, click the button next to Locations.
ii. Select all topological entities under PFL in the Location Selector dialog box (use Shift) and
click OK.
iii. Select VELOCITIES from the Variable drop-down list (or by clicking ).
iv. In the Render tab, deselect Show Contour Lines.
v. Click Apply.
In Figure 4.3: Contours of Velocity Magnitude(p. 164), the velocity is zero along the die wall (as expected)
and there is a fully developed profile at the inlet of the die. At the die outlet, the velocity profile changes
to become constant throughout the extrudate cross section. The transition between these two states
can be seen in the beginning section of the extrudate.
163

3. Display contours of velocity in cross sections.
a. Deselect Contour 1 in the Outline tree tab under User Locations and Plots.
164
3D Extrusion

b. Create the cross section planes, at Z = 0, 0.08, 0.15, 0.45 m.
i. Select Plane from the Location drop-down menu ( ).
ii. Click OK to accept the default name (Plane 1) and display the details view below the Outline
tab.
165

iii. In the Geometry tab of the details view of Plane 1, select XY Plane from the Method drop-
down list.
iv. Enter 0 for Z.
v. Click Apply.
vi. Repeat steps 3.b.i.–v. for the other planes, at Z = 0.08, 0.15, and 0.45 m.
vii. In the Outline tree tab, under User Locations and Plots, deselect Plane 1, Plane 2, Plane 3,
and Plane 4.
c. Click the Insert menu and select Contour or click the button.
d. Click OK to accept the default name (Contour 2) and display the details view below the Outline
tab.
e. In the Outline tree tab under User Locations and Plots, select Wireframe.
f. Perform the following steps in the details view of Contour 2:
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3D Extrusion

ii. Select all planes under User Locations and Plots (use Shift for multiple selection).
iii. Click OK.
iv. Select VELOCITIES from the Variable drop-down list (or click ).
v. In the Render tab, deselect Show Contour Lines.
vi. Click Apply.
Velocity profiles at the flow inlet, the flow outlet, and planes just before and just after the die exit are
displayed (Figure 4.4: Velocity Profiles at Cross Sections(p. 168)). Compare the velocity profile within the
die to the velocity profile just after the die exit at the end of the computational domain. In the die the
flow is fully developed. The velocity profile is flat in the extrudate, far away from the die exit; all the
particles in the cross section plane are at the same velocity. Just beyond the die exit, in the transitional
zone, the velocity profile is reorganized. The velocity profile on the plane = 15 is no longer fully de-
veloped, but it is not yet flat either. The velocity rearrangement is the source of the deformation of the
extrudate.
167

4. Compare the cross section shape of the extrudate with die.
a. Simplify the display.
In the Outline tree tab, under User Locations and Plots, deselect Contour 2 and Wireframe.
b. Display the die shape using a polyline.
i. Select Polyline from the Location drop-down menu ( ).
ii. Click OK to accept the default name (Polyline 1) and display the details view below the Outline
tab.
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3D Extrusion

iii. In the Geometry tab of the details view, select Boundary Intersection from the Method
drop-down list.
iv. Click next to Boundary List and select SUBDOMAIN_1_BOUNDARY_2, SUBDO-
MAIN_1_BOUNDARY_3, SUBDOMAIN_1_BOUNDARY_4 (use Shift for multiple selection).
v. Select SUBDOMAIN_1_BOUNDARY_1 from the Intersect With drop-down list.
vi. Under the Color tab, click next to Color and select dark blue.
vii. Click Apply.
c. Display the extrudate shape using a polyline.
tab.
drop-down list.
iv. Click next to Boundary List and select SUBDOMAIN_2_BOUNDARY_3, SUBDO-
MAIN_2_BOUNDARY_4, SUBDOMAIN_2_BOUNDARY_5 (use Shift for multiple selection).
vi. Click Apply.
d. On the axis triad in the graphics window click +Z to view from Z-direction.
169

This allows you to compare the size and shape of the flow inlet with that of the flow outlet without
distortion due to perspective.
Figure 4.5: Swelling of the Extrudate
Since the model involves a generalized Newtonian fluid, there are no viscoelastic effects. The swelling
(Figure 4.5: Swelling of the Extrudate(p. 170)) is only due to reorganization of the velocity profile at the
die exit. Fluid from high-speed region moves to low-speed region and pushes the free surface to the
exterior.
5. Create a 2D plot on the diagonal of the die.
a. Define the line of the plot with the points (0.0, 0.1, 0.1) and (0.1, 0.0, 0.1).
These values are in meters.
tab.
170
3D Extrusion

iii. Enter 0, 0.1, 0.1 for Point 1 and 0.1, 0, 0.1 for Point 2.
iv. Click Apply.
b. Create a plot.
tab.
171

iii. In the General tab of the details view, select XY for the Type and enter 3D Extrusion for
Title.
iv. In the Data Series tab, for Series 1, select Line 1 from the Locations drop-down list (or by
clicking the button).
vi. In the Y Axis tab, select VELOCITIES from the Variable drop-down list.
vii. Click Apply.
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3D Extrusion

Figure 4.6: Velocity Magnitude Along a Diagonal of Die Exit Section
The shear-thinning introduced by the Cross law is not clearly visible in Figure 4.6: Velocity Magnitude
Along a Diagonal of Die Exit Section (p. 173) due to the large finite elements along the die wall. The
mesh should be refined in that zone.
6. Plot X-velocity close to center of the die.
a. Define the line of the plot with the points (0.08, 0.02, 0.00) and (0.08, 0.02, 0.50).
tab.
iii. Enter 0.08, 0.02, 0 for Point 1 and 0.08, 0.02, 0.5 for Point 2.
iv. Click Apply.
b. Create a plot.
tab.
iii. In the General tab of the details view, select XY for the Type and disable Display Title.
iv. In the Data Series tab, select Line 2 from the Locations drop-down list for Series 1.
173

v. In the X Axis tab, select Z from the Variable drop-down list.
vi. In the Y Axis tab, select VELOCITIES X from the Variable drop-down list.
vii. Click Apply.
Figure 4.7: X-Velocities Along a Line Close to the Center of the Die
7. Plot Y-velocity close to the center of the die.
a. In the Y Axis tab of the details of Chart 2, select VELOCITIES Y from the Variable drop-down list.
b. Click Apply.
174
3D Extrusion

Figure 4.8: Y-Velocities Along a Line Close to the Center of the Die
8. Plot Z-velocity close to the center of the die.
a. In the Y Axis tab of the details view of Chart 2, select VELOCITIES Z from the Variable drop-down
list.
b. Click Apply.
Figure 4.9: Velocities Along a Line Close to the Center of the Die(p. 176) shows that the flow
slows down ( decreases) after the die exit. Meanwhile, particles travel from the center of
the extrudate toward the edge, creating the swelling of the extrudate. Figure 4.7: X-Velocities
Along a Line Close to the Center of the Die (p. 174) and Figure 4.8: Y-Velocities Along a Line
Close to the Center of the Die (p. 175) show that the peak values of and are located at
the very beginning of the extrudate, and vanish at the end of the free jet.
175

Figure 4.9: Velocities Along a Line Close to the Center of the Die
4.13.Summary
This tutorial introduced the concept of a 3D extrusion problem. You solved the problem using a specific
3D geometry for the die and made suitable assumptions about the physics of the problem. You analyzed
the factors affecting the extrudate shape. In Polydata you learned how to use the optimesh remeshing
method, which is recommended for 3D extrusion problems.
176
3D Extrusion

Chapter 5: Direct Extrusion
5.1.Introduction
5.2.Prerequisites
5.4.Preparation
5.6.Step 2:Models
5.11.Step 7:Outputs
5.15.Summary
5.16.Appendix
5.1.Introduction
This tutorial is similar to the 3D extrusion problem solved in 3D Extrusion (p. 149), where the shape of
the extrudate was computed from the die geometry. In this tutorial, a complex geometry (free surface)
is associated with the exit section of the die and undergoes large deformations during the extrusion
process. Consequently, the problem becomes highly non-linear and special convergence techniques
are required to obtain a solution. This tutorial introduces the evolution procedure in Polyflow that is
used to handle nonlinear problems.
• Create a sub-task to define a direct extrusion problem.
• Set material properties and boundary conditions for a direct extrusion problem.
5.2.Prerequisites
This problem deals with the flow of a Newtonian fluid through a three-dimensional die with a complex
die lip section. Due to the symmetry of the problem (the cross section of the die is a polygon), the
177

computational domain of the fluid is defined for a quarter of the geometry and two planes of symmetry
are defined.
The melt enters the die as shown in Figure 5.1: Problem Description(p. 178) at a flow rate = 200 cm3
/s
(a quarter of the actual flow rate) and the extrudate is obtained at the exit. It is assumed that subdomain
2 is long enough to account for all the deformation of the extrudate.
for the problem is divided into two subdomain s (as shown in Figure 5.1: Problem Description(p. 178))
so that the remeshing algorithm can be applied only to the portion of the mesh that is deformed.
Subdomain 1 represents the fluid as it enters and is confined by the die. Subdomain 2 corresponds to
the extrudate that is in contact with the air (and can deform freely). The main aim of the calculation is
to find the location of the free surface (the skin of the extrudate).
The boundary set for the problem are shown in Figure 5.2: Boundary Set for the Problem(p. 179), and
the conditions at the boundaries of the domains are:
/s
• boundary 4: zero velocity
178
Direct Extrusion

Figure 5.2: Boundary Set for the Problem
5.4.Preparation
Note
179
Preparation

7. Unzip the Direct-Extrusion_R150.zip file you have downloaded to your working folder.
The mesh file dirext.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering direct-extrusion as the name of
the project.
3. Import the mesh file (dirext.msh).
5.6.Step 2: Models
In this step, define a new task representing the evolution model. Then, define a sub-task for the isothermal
flow calculation.
Create a new task
a. Retain the following (default) options:
• F.E.M. task
The complex geometry associated with the free surface of the extrudate introduces non-linear
terms into the kinematic condition equation used to find its location. An evolution scheme is
used to handle the non-linear problem.
Create a sub-task
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Direct Extrusion

b. Enter Direct extrusion as the New value and click OK.
Since this problem involves a free surface, the domain is divided into two subdomain s; one for
the region near the free surface (SUBDOMAIN_2) and the other for the rest of the domain (SUBDO-
MAIN_1). In this problem, the sub-task applies to both subdomain s, which is the default condition.
Polydata indicates the material properties that are relevant for your sub-task by graying out the irrelevant
Material Data
2. Click Power law.
The viscosity in this tutorial is given by the power law. For information on power law, see Ap-
pendix (p. 198).
Modify fac
4. Retain the default value for .
Modify tnat
181

Click OK to retain the default value of 1.
Modify expo
6. Click Upper level menu three times to return to the Direct extrusion menu.
b. Click Inflow.
c. Click Volumetric flow rate and Modify volumetric flow rate.
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Direct Extrusion

e. Select Automatic and click Upper level menu.
the inflow condition.
flows, you must manually identify a plane of symmetry. The normal velocity ( ) and the tangential
force ( ) are set to zero on a symmetry plane. A particle cannot cross the plane ( = 0) due to the
symmetry, so the particles flow at the same velocity on both sides of the symmetry plane, leading to a
zero tangential force.
4. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY_4 at the wall of SUBDO-
MAIN_1 (BOUNDARY_4).
At a solid-liquid interface, the velocity of the liquid is that of the solid surface. Hence the velocity the
fluid is assumed to stick to the wall. This is known as the no-slip assumption because the liquid is assumed
to adhere to the wall, and hence, has no velocity relative to the wall.
By default, Polydata imposes = = 0 along all boundaries. No action is required to accept the default
condition.
go out of the domain through the free surface. This constraint is called the kinematic condition,
= 0. This equation requires an initial condition, that is, the starting line of the free surface. In this
problem, the starting line of the free surface is the intersection of boundary 4 and boundary 5 (see Fig-
ure 5.2: Boundary Set for the Problem(p. 179)).
d. Select No condition along BOUNDARY_4 (the boundary where the free surface starts) and click
Modify.
183

f. Click Upper level menu to return to the Boundary conditions on the moving surface menu.
g. Click Upper level menu two times to return to the Flow boundary conditions menu.
6. Set the conditions at the flow exit (BOUNDARY_6).

e. Click Upper level menu to return to the Direct extrusion menu.
This model involves a free surface for which the position is unknown. A portion of the mesh is affected by
the relocation of this boundary. Hence a remeshing technique is applied on this part of the mesh. The free
surface is entirely contained within SUBDOMAIN_2, and hence only SUBDOMAIN_2 is affected by the relocation
of the free surface.
Global remeshing
allows you to create several local remeshings. For the current problem, a single local remeshing is suffi-
cient.
will be remeshed.
2. Define the parameters for the remeshing method.
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Direct Extrusion

boundary nodes caused due to the motion of the free surface, since a part of the mesh is deformed. For
3D extrusion problems where large deformations of the extrudate are expected, the optimesh remeshing
technique is recommended. For information on optimesh remeshing technique, refer to Appendix (p. 198).
b. Specify the final plane for remeshing technique, by selecting Intersection with BOUNDARY_6 and
clicking Confirm.
Polydata asks you whether you want to use the surface kinematic condition.
c. Click Yes to use the kinematic condition.
The line kinematic condition is recommended for extrusion problems, and must be used in combin-
ation with the optimesh remeshing technique.
d. Click Accept the current setup in the Element distortion check menu.
In complex extrusion simulations, the finite element mesh can undergo great deformations. The
Element distortion check menu deals with the detection of all possible distortions of the elements.
e. Click Upper level menu two times.
F.E.M. Task 1 menu is displayed.
All information relevant to iterative schemes (for the F.E.M. task calculations) can be modified in the Numer-
ical parameters menu.
1. Click Enable evolution on moving boundaries to enable the evolution scheme.
For information on the evolution scheme, see Appendix (p. 198).
2. Specify the evolution parameters.
185
Step 6:Numerical Parameters

a. Define the starting solution for the iterative scheme in the calculation of the free surface location.
The first calculation is performed at . Increase the value of the initial increment of () to reduce
the number of evolution steps and to speed up the calculation.
Polydata prompts you for the initial value of .
b. Enter 0.1 for the New value and click OK.
c. Click Upper level menu to return to the Numerical parameters menu.
3. Click Upper level menu two times to return to the top-level Polydata menu.
After Polyflow calculates a solution, it can save the results in several different formats. Choose the one that
is appropriate for your postprocessor. In this case, save the outputs in IGES format, as well as the default
format for CFD-Post.
Outputs
1. Retain the default output (CFD-Post) and click Enable Iges file output.
The default CFD-Post output is used for postprocessing with CFD-Post. The IGES output contains the
modified geometry of the extrudate (after remeshing) calculated at every step of the evolution procedure.
For information on IGES output, see Appendix (p. 198).
for postprocessing.
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Direct Extrusion

c. Click Upper level menu three times.
Save and exit
1. Click Accept.
2. Click Continue.
1. Double-click the Results tab in the Polyflow analysis system. This will start CFD-Post and read the results
files saved by Polyflow. CFD-Post reads the mesh information and the solution fields that were saved
to the results file.
Deselect Wireframe in the Outline tree tab, under User Locations and Plots.
187

tab.
c. Perform the following steps in the Geometry tab of the details view of Contour 1:
i. Click the button next to Locations.
ii. Select all topological entities under PFL in the Location Selector dialog box (use Shift for
multiple selection) and click OK.
iv. Click Apply.
d. Rotate the image so that you can see the fluid at the inlet of the die, as shown in Figure 5.3: Contours
of Velocity Magnitude (p. 189).
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Direct Extrusion

Observe that the velocity is zero along the die wall, as expected, and there is a fully developed profile
at the inlet of the die. At the die outlet, the velocity profile changes to become constant throughout the
extrudate cross section. The transition between these two states can be seen in the first third of the ex-
trudate.
3. Display contours of velocity in cross sections.
a. Deselect the contours previously defined.
189

In the Outline tree tab, under User Locations and Plots, deselect Contour 1.
b. Create the cross-sectional planes, at Z = 0, 3, 7, and 20 cm.
tab.
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Direct Extrusion

iii. In the Geometry tab of the details view, select XY Plane from the Method drop-down list.
iv. Enter 0 for Z.
v. Click Apply.
vi. Repeat steps 3.b.i.–v. for the other planes, at Z = 0.03, 0.07, and 0.1999 m.
and Plane 4.
191

c. Display the contours.
i. Click the Insert menu and select Contour or click the button.
ii. Click OK to accept the default name (Contour 2) and display the details view below the
Outline tab.
iii. In the Outline tree tab under User Locations and Plots, select Wireframe.
iv. In the Geometry tab of the details view of Contour 2, click the button next to Locations.
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Direct Extrusion

v. Select all planes under User Locations and Plots (use Shift for multiple selection).
vi. Click OK.
vii. Select VELOCITIES from the Variable drop-down list (or click ).
viii. In the Render tab, disable Lighting.
ix. Click Apply.
Figure 5.4: Velocity Profiles at Cross Sections(p. 194) shows the velocity profiles at the flow inlet, the flow
outlet, and at the planes just before and just after the die exit.
193

Compare the velocity profile within the die to the velocity profile just after the die exit at the end of the
computational domain. In the die the flow is fully developed. In the extrudate, far away from the die
exit, the velocity profile is flat. That is, all the particles in a cross-sectional plane are at the same speed.
Just after the die exit, there is a transitional zone where the velocity profile is reorganized. The velocity
profile on the plane Z = 7 cm is no longer fully developed, but it is not yet flat either. The velocity re-
arrangement is the source of the deformation of the extrudate.
4. Compare the cross-sectional shape of the extrudate with the die.
194
Direct Extrusion

tab.
iii. In Geometry tab of the details view, select Boundary Intersection from the Method drop-
down list.
iv. Click next to Boundary List and select SUBDOMAIN_1_BOUNDARY_4. Click OK to close
the Location Selector dialog box.
vi. In the Color tab, click next to Color and select dark blue.
vii. Click Apply.
tab.
195

iii. In Geometry tab of the details view, select Boundary Intersection from the Method drop-
down list.
iv. Select SUBDOMAIN_2_BOUNDARY_5 from the Boundary List drop-down list.
vi. Click Apply.
d. Right-click in the graphic window and select View From +Z under Predefined Camera.
This allows you to compare the size and shape of the flow inlet with that of the flow outlet without
distortion due to perspective.
5. Restore the symmetry.
a. Click the Insert menu and select Instance Transform, or click the button.
b. Click OK to accept the default name (Instance Transform 1) and display the details view below
the Outline tab.
c. Perform the following steps in the details view of Instance Transform 1:
i. Disable Instancing Info From Domain.
ii. Set Number of Graphical Instances to 4.
iii. Ensure Apply Rotation is selected.
196
Direct Extrusion

iv. Set Method to Principal Axis and select Z from the Axis drop-down list.
v. Enable Full Circle under Instance Definition.
vi. Click Apply.
d. In the Outline tree tab, under User Locations and Plots, right-click Polyline 1 and click Edit (or
double-click Polyline 1).
e. In the View tab, scroll down and enable Apply Instancing Transform.
f. Select Instance Transform 1 from the Transform drop-down list.
g. Click Apply.
h. In the Outline tree tab, under User Locations and Plots, right-click Polyline 2 and click Edit (or
i. Repeat steps 5.e.–g.
You can use the central-mouse button to zoom in and out. This allows you to compare the size and
shape of the flow inlet with that of the flow outlet without distortion due to perspective.
You can also click the fit view button ( ) to properly center the image.
197

The deformations come from the rearrangement of the velocity profile. Particles coming from high-
speed regions in the die must slow down, while particles coming from low-speed regions must
accelerate. Observe that the central part of the cross, where the fluid easily flows in the die, is en-
larged in the extrudate, while the extremities of the branches are smaller in the extrudate. Since
the combined effect of cross-sectional expansions and reductions is very difficult to guess, a nu-
merical simulation is necessary for a moderate to high complexity die.
5.15.Summary
This tutorial introduced the concept of a direct extrusion problem. You solved the problem using a
specific 3D geometry for the die, made suitable assumptions about the physics of the problem, and
analyzed the factors affecting the extrudate shape. The non-linear problem was solved using an evolution
technique to reach the convergence.
5.16.Appendix
The appendix contains the following sections:
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Direct Extrusion

5.16.1.Power Law
5.16.2.Optimesh Remeshing Technique
5.16.3.Evolution Scheme
5.16.4.IGES Output
5.16.1.Power Law
The power law exhibits shear thinning (reduction in the viscosity with an increase in shear rate) that is
a characteristic of many polymers. The viscosity in this tutorial is given by the power law:
(5.1)
= −

where:
= consistency factor
= power-law index
= natural time
is included in the equation to make the units consistent.
The optimesh remeshing technique requires the direction of extrusion to be parallel to the , , or
direction of extrusion, and each plane will be remeshed independently. For this process, Polyflow requires
of SUBDOMAIN_2 with SUBDOMAIN_1, and the final plane is the intersection of SUBDOMAIN_2 with
the flow exit (boundary 6).
The kinematic equation introduces non-linear terms in the problem that might lead to convergence
difficulties. An evolution scheme is available in Polyflow to solve such highly non-linear problems. Start
the calculation with a reduced value of the parameter(s) causing the non-linearity. Starting from the
first solution, Polyflow increments the parameter(s) causing the non-linearity and computes a second
third solution. Following this procedure, Polyflow increases the value of each parameter up to its
nominal value. In Polyflow , this procedure is fully automated; the increments are automatically adapted
according to the results of previous calculations. Polyflow uses an evolution variable that is incremented
during the evolution scheme. S starts at an initial value of and is increased to a final value of . Each
parameter that you want to evolve is defined as =

.
5.16.4.IGES Output
An IGES output allows you to import the final geometry into a CAD program. This is useful when you
are designing a die because you want to be able to manufacture the die predicted by the calculation.
In the present case, you can compare the final shape of the predicted extrudate in an IGES format with
the desired shape.
199
Appendix

200

Chapter 6: Inverse Extrusion
6.1.Introduction
6.2.Prerequisites
6.4.Preparation
6.6.Step 2:Models
6.11.Step 7:Outputs
6.15.Summary
6.16.Appendix
6.1.Introduction
Inverse extrusion deals with the computation of the shape of a die that produces an extrudate of the
desired shape. This tutorial illustrates how to handle a complex inverse extrusion problem. In this tutorial,
slip conditions along the die walls are considered and evolution on the slip coefficient is enabled to
aid convergence.
• Create a sub-task to define an inverse extrusion problem.
• Set material properties and boundary conditions for a inverse extrusion problem.
• Specify multiple local remeshing regions.
6.2.Prerequisites
201

symmetry of the problem (the cross-section of the die is a polygon), the computational domain of the
fluid is defined for a quarter of the geometry. Two planes of symmetry are defined.
The melt enters the die as shown in Figure 6.1: Problem Description(p. 202) at a flow rate = 200 cm3
/s
(a quarter of the actual flow rate) and the extrudate is obtained at the exit.
for the problem is divided into two sub-domains (as shown in Figure 6.1: Problem Description(p. 202))
so that specific remeshing algorithms can be applied in each sub-domain to accurately predict the die
profile. Subdomain 1 represents the fluid as it enters and is confined by the die. Subdomain 2 corresponds
to the extrudate that is in contact with the air (and can deform freely). The main aim of the calculation
is to compute the geometry of the die to obtain the desired extrudate.
202
Inverse Extrusion

The boundary set for the problem are shown in Figure 6.2: Boundary Set for the Problem(p. 203), and
the conditions at the boundaries of the domains are given below
boundaries of the domains are:
/s
• boundary 4: slip conditions along the wall
6.4.Preparation
203
Preparation

Note
7. Unzip the Inverse-Extrusion_R150.zip file you have downloaded to your working folder.
The mesh file invext.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering inverse-extrusion as the name
of the project.
3. Import the mesh file (invext.msh).
6.6.Step 2: Models
In this step, define a new task representing the inverse extrusion model. Then, define a sub-task for the iso-
thermal flow calculation.
Create a new task
• F.E.M. task
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Inverse Extrusion

Apply the evolution scheme on the slip coefficient along the outer wall of the die (boundary 4)
when you define the slip boundary conditions.
Create a sub-task
a. Click Generalized Newtonian isothermal flow problem.
b. Enter Inverse Extrusion as the New value and click OK.
This problem involves a free surface, so the domain is divided into two sub-domains; one for the region
near the free surface (SUBDOMAIN_2) and the other for the rest of the domain (SUBDOMAIN_1). In this
problem, the sub-task applies to both sub-domains, which is the default condition.
205

Material Data
2. Click Power law.
The viscosity in this tutorial is given by the power law. For information on power law, see Power
Law (p. 225).
3. Specify the value of .
Modify fac
4. Retain the default value for .
Modify tnat
Click OK to retain the default value of 1.
Modify expo
6. Click Upper level menu three times to return to the Inverse Extrusion menu.
206
Inverse Extrusion

b. Click Inflow.
c. Click Modify volumetric flow rate.
e. Retain the default options of Automatic and Volumetric flow rate.
the inflow condition.
flows, you must manually identify a plane of symmetry.
The normal velocity ( ) and the tangential force ( ) are set to zero on a symmetry plane. A particle
cannot cross the plane ( = 0) due to the symmetry, so the particles flow at the same velocity on both
sides of the symmetry plane, leading to a zero tangential force.
4. Set the conditions along the outer wall of the die (BOUNDARY_4).
207

b. Enable the evolution scheme on the slip coefficient.
For information on the evolution scheme, see Evolution Scheme (p. 225).
i. Click EVOL at the top of the Polydata menu to enable the evolution inputs for the slip coeffi-
cient.
ii. Click Slip conditions.
iii. Click F(v) = Generalized Navier’s law.
For information on Navier’s law, see Appendix (p. 225).
Modify k
A panel appears asking you for the value of .
v. Retain the default value of 1 for k and click OK.
vi. Select the function f(S) = a*exp(b*S) + c + d*S.
You will retain the default values for a and b, and will modify the values for c and d.
vii. Click Modify the value of c.
Hint: Scroll down to see Modify the value of c.
A panel appears asking for the new value of c.
viii. Enter 0 as the New value and click OK.
ix. Click Modify the value of d.
A panel appears asking for the new value of d.
x. Enter 0 as the New value and click OK.
xi. Click EVOL at the top of the Polydata menu to disable the evolution inputs.
xii. Click Upper level menu.
xiii. Retain the default value of 1 for e ( ).
xiv. Click Upper level menu two times to return to the Flow boundary conditions menu.
go out of the domain through the free surface. This constraint is called the kinematic condition,
= 0. This equation requires an initial condition (the starting line of the free surface). In this problem, the
208
Inverse Extrusion

starting line of the free surface is the intersection of boundary 4 and boundary 5 (see Figure 5.2: Boundary
Set for the Problem (p. 179)).
d. Select No condition along BOUNDARY_4 (the boundary where the free surface starts) and click
Modify.
f. Click Upper level menu to return to the Boundary conditions on the moving surface menu.
g. Click Upper level menu at the top of the menu.
h. Click Outlet (Inv. prediction) to define the outlet of the moving surface.
In inverse extrusion problems, you have to predict the appropriate die exit cross-section to obtain
a given extrudate cross-section. By defining the outlet of a free surface, inform Polyflow the desired
extrudate shape. Hence, you impose the outlet of the moving surface along the last section of the
free jet as the outlet of the free surface. This section will not be modified during the calculation.
i. Select BOUNDARY_6 as the outlet of the moving surface and click Confirm.
j. Click Upper level menu to return to the Flow boundary conditions menu.
6. Set the conditions at the flow exit (BOUNDARY_6).

7. Click Upper level menu at the top of the Flow boundary conditions menu.
boundary nodes due to the motion of the free surface, since a part of the mesh is deformed. For information
on remeshing technique, see Appendix (p. 225).
Global remeshing
209
Step 5:Remeshing

will be remeshed.
2. Define the parameters for the fist local remeshing method.
For 3D extrusion problems where large deformations of the extrudate are expected, the optimesh
remeshing technique is recommended. For information on optimesh remeshing technique see
Appendix (p. 225).
b. Specify the final plane for the remeshing technique, by selecting Intersection with BOUNDARY_6
and clicking Confirm.
Polydata asks you whether you want to use the surface kinematic condition.
c. Click Yes to use the kinematic condition.
The line kinematic condition is recommended for extrusion problems, and must be used in combin-
ation with the optimesh remeshing technique.
d. Click Accept the current setup in the Element distortion check menu.
In complex extrusion simulations, the finite element mesh can undergo great deformations. The
Element distortion check menu deals with the detection of all possible distortions of the elements.
Accept default options.
3. Activate the inverse prediction.
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Inverse Extrusion

Inverse prediction management
a. Click Enable the inverse prediction.
The technique of inverse prediction is selected to calculate the profile for the “constant section”
region of the die.
4. Specify a second region for remeshing (SUBDOMAIN_1).
a. Click Creation of a local remeshing.
b. Select SUBDOMAIN_1 and click Add.
c. Click Upper level menu.
d. Click Constant section for prediction.
e. Click Accept the current setup.
5. Click Upper level menu two times.
The F.E.M. Task 1 menu is displayed.
All information relevant to iterative schemes (for the F.E.M. task calculations) can be modified in the Numer-
ical parameters menu.
1. Specify the evolution parameters.
a. Specify the final value of .
Modify the upper limit of S
Enter 20 for the New value and click OK.
b. Specify the initial value of .
c. Specify the minimum value of .
Modify the min value of delta-S
211

Enter 0.1 for the New value and click OK.
d. Specify the maximum value of .
Modify the max value of delta-S
e. Specify the maximum number of successful steps.
Modify the max number of successful steps
After Polyflow calculates a solution, it can save the results in several different formats. Choose the one that
is appropriate for your postprocessor. In this case, save the outputs in IGES format, as well as the default
format for CFD-Post.
Outputs
1. Retain the default output (CFD-Post) and click Enable Iges file output.
The default CFD-Post output is used for postprocessing with CFD-Post. The IGES output contains the
modified geometry of the extrudate (after remeshing) calculated at every step of the evolution procedure.
For information on IGES output, see Appendix (p. 225).
for postprocessing.
Save and exit
1. Click Accept.
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Inverse Extrusion

2. Click Continue.
A cfx.res file (corresponding to the eight evolution steps of the flow case) will be created.
1. Double-click the Results tab in the Workbench analysis and read the results files saved by Polyflow.
a. Deselect Wireframe in the Outline tree tab, under User Locations and Plots.
b. Click the Insert menu and select Contour or click the button.
c. Click OK to accept the default name (Contour 1) and open the details view below the Outline
tab.
d. Perform the following steps In the Geometry tab of the details view.
213

ii. Select all topological entities under PFL in the Location Selector dialog box (use Shift for
multiple selection) and click OK.
iv. Click Apply.
You can see in Figure 6.3: Contours of Velocity Magnitude(p. 215) that the velocity is zero along the die
wall, as expected, and there is a fully developed profile at the inlet of the die. At the die outlet, the velocity
profile changes to become constant throughout the extrudate cross-section. The transition between
these two states can be seen at the beginning of extrudate section.
214
Inverse Extrusion

3. Display contours of velocity in cross-sections.
a. Deselect the contours previously defined.
215

In the Outline tree tab, under User Locations and Plots deselect Contour 1.
b. Create the cross-section planes, at Z = 0, 3, 7 and 20 cm.
tab.
216
Inverse Extrusion

iii. In the Geometry tab of the details view, select XY Plane from the Method drop-down list.
iv. Enter 0 for Z.
v. Click Apply.
vi. Repeat steps 3.b.i.–v. to create the other planes at Z = 0.03, 0.07, and 0.1999 m.
and Plane 4.
217

c. Click the Insert menu and select Contour or click the button.
d. Click OK to accept the default name (Contour 2) and open the details view below the Outline
tree tab.
e. In the Outline tree tab under User Locations and Plots, select Wireframe.
f. Perform the following steps in the details view of Contour 2.
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Inverse Extrusion

ii. Select all planes under User Locations and Plots (use Shift for multiple selection).
iii. Click OK.
iv. Select VELOCITIES from the Variable drop-down list (or click ).
v. In the Render tab, disable Lighting.
vi. Click Apply.
The velocity profiles planes are located at the flow inlet, the flow outlet, and planes just before and after
the die exit as shown in Figure 6.4: Velocity Profile Planes(p. 220).
Compare the velocity profile within the die to the velocity profile just after the die exit at the end of the
computational domain.
• The flow is fully developed in the die.
• The velocity profile is flat in the extrudate, far away from the die exit. All particles in the cross-section
plane are at the same velocity.
• Just after the die exit, there is a transitional zone where the velocity profile is reorganized.
• The velocity profile on the plane = 7 cm is not fully developed, but it is not flat either.
The velocity rearrangement is the source of the deformation of the extrudate.
219

Figure 6.4: Velocity Profile Planes
4. Compare the cross-section shape of the extrudate with die.
tab.
220
Inverse Extrusion

drop-down list.
iv. Click next to Boundary List and select SUBDOMAIN_1_BOUNDARY_4. Click OK to close
the Location Selector dialog box.
vi. In the Color tab, click next to Color and select dark blue.
vii. Click Apply.
tab.
drop-down list.
iv. Select SUBDOMAIN_2_BOUNDARY_5 from the Boundary List drop-down list.
vi. Click Apply.
d. Right-click in the graphic window and select View From +Z under Predefined Camera.
221

5. Restore the symmetry.
a. Click the Insert menu and select Instance Transform, or click the button.
b. Click OK to accept the default name (Instance Transform 1) and display the details view below
the Outline tab.
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Inverse Extrusion

c. Perform the following steps in the Definition tab of the details view of Instance Transform 1:
i. Disable Instancing Info From Domain.
ii. Enter 4 for Number of Graphical Instances.
iii. Ensure Apply Rotation is selected.
iv. Select Principal Axis from the Method drop-down list.
v. Select Z from the Axis drop-down list.
vi. Enable Full Circle under Instance Definition.
vii. Click Apply.
d. In the Outline tree tab, under User Locations and Plots, right-click Polyline 1 and click Edit (or
e. In the View tab of the details view, scroll down and enable Apply Instancing Transform.
f. Select Instance Transform 1 from the Transform drop-down list.
g. Click Apply.
h. In the Outline tree tab, under User Locations and Plots, right-click Polyline 2 and click Edit (or
i. Repeat steps 5..e–g.
You can use the central-mouse button to zoom in and out. This allows you to compare the size and
shape of the flow inlet with that of the flow outlet without distortion due to perspective.
223

You can also click the fit view button ( ) to properly center the image.
The deformation of the extrudate is the result of the rearrangement taking place at the die exit. Particle
coming from high-speed regions in the die must slow down, while particles coming from low-speed re-
gions must accelerate. You can change the speed by enlarging the flowing section. A tube of fluid at
high speed in the die will enlarge its cross-section in the extrudate to decrease its average velocity. A
tube of fluid at low speed in the die will reduce its cross-section in the extrudate in order to increase
average speed. In Figure 6.5: Swelling of the Extrudate(p. 224), you can see that the die design tool
compensated for these effects. The central part of the cross-section where the fluid easily flowed in the
original die has been reduced by the die design tool, while the extremities of the branches were enlarged
because the flow was much slower in the original die. Since the combined effects of the cross-sectional
enlargements and reductions are very difficult to guess, the numerical simulation is necessary to help
the die designer reduce the number of trial-and-error iterations.
224
Inverse Extrusion

6.15.Summary
This tutorial introduced the concept of an inverse extrusion problem. You solved the problem assuming
suitable conditions for the physics of the problem and Polyflow predicted the shape of the die. You
used multiple domain calculations with remeshing methods most suited to 3D inverse extrusion problems.
The non-linear problem was solved using an evolution technique to aid convergence.
6.16.Appendix
The appendix contains the following sections:
6.16.1.Power Law
6.16.3.Remeshing Technique
6.16.5.IGES Output
6.16.1.Power Law
The power law exhibits shear thinning (reduction in the viscosity with an increase in shear rate) that is
a characteristic of many polymers. The viscosity in this tutorial is given by the power law:
(6.1)
= −

where:
= consistency factor
= power-law index
= natural time
is included in the equation to make the units consistent.
The kinematic equation introduces non-linear terms in the problem that might lead to convergence
difficulties. An evolution scheme is available in Polyflow to solve such highly non-linear problems. Start
the calculation with a reduced value of the parameter(s) causing the non-linearity. Starting from the
first solution, Polyflow increments the parameter(s) causing the non-linearity and computes a second
third solution. Following this procedure, Polyflow increases the value of each parameter up to its
nominal value. In Polyflow , this procedure is fully automated; the increments are automatically adapted
according to the results of previous calculations. Polyflow uses an evolution variable that is incremented
during the evolution scheme. S starts at an initial value of and is increased to a final value of . Each
parameter l that you want to evolve is defined as =
.
Navier’s Law: The generalized Navier’s law is given by:
(6.2)

= − − −

!#
where:
$% = tangential velocity of the fluid
225
Appendix

= tangential velocity of the wall
= material parameters
= material parameters
= 0 (assumed zero, by default
Remeshing for the inverse extrusion problems is carried out in two stages. This model involves a free
surface of unknown position. A portion of the mesh will be affected by the relocation of this boundary.
Hence a remeshing technique that is suitable for 3D extrusion problems is applied to this part of the
mesh. The free surface is entirely contained within subdomain 2, and hence only subdomain 2 will be
affected by the relocation of the free surface.
This technique modifies the location of the section where the boundary conditions on the kinematic
condition apply (the die-lip region). Apply local remeshing technique to the region between the entry
section and the die-lip area (subdomain 1). In this tutorial, you define a constant section on this sub-
domain. This means that the die cross-section is constant from the die entry to the die exit (a parallel
die). Using this two-stage remeshing technique, Polyflow calculates the die profile that produces an
extrudate of the desired shape. More complex deformations of the die are available via the definition
of different local remeshings within the die.
The optimesh remeshing technique requires the direction of extrusion to be parallel to the ,, or
direction of extrusion, and each plane will be remeshed independently. For this process, Polyflow requires
of subdomain 2 with subdomain 1, and the final plane is the intersection of subdomain 2 with the flow
exit (boundary 6).
6.16.5.IGES Output
An IGES output allows you to import the final geometry into a CAD program. This is useful when you
are designing a die because you want to be able to manufacture the die predicted by the calculation.
In the present case, you can compare the final shape of the predicted extrudate in an IGES format with
the desired shape.
226
Inverse Extrusion

Chapter 7: Flow of Two Immiscible Fluids
7.1.Introduction
7.2.Prerequisites
7.4.Preparation
7.7.Step 2a:Definition of Sub-Task 1
7.8.Step 2b:Definition of Sub-Task 2
7.12.Summary
7.1.Introduction
This tutorial examines the flow of two fluids in a single die. Two polymer melts with distinct physical
properties are fed through different channels into a die. The aim of the calculation is to predict the
location of the interface between the two fluids.
• Define a moving interface problem.
• Set material properties and boundary conditions for a moving interface problem.
7.2.Prerequisites
This problem analyzes the flow of two immiscible Newtonian fluids (fluid 1 and fluid 2) through a die
of diameter 1 cm, as shown in Figure 7.1: A Schematic Diagram of the Two Fluids in the Die(p. 228). The
melts are fed into the die through boundaries 1 and 3 (see Figure 7.2: Boundary Sets and Subdomains
for the Problem (p. 229)). The flow rates for the two fluids are not equal. The fluids come into contact
in the die, creating an interface. The location of the interface is unknown and will be determined by
Polyflow. The location of the interface depends on the physical properties of the fluids, the flow rates
of the fluids, and the geometry of the die.
227

Incompressibility and momentum equations are solved in the fluid domains. To solve the fully coupled
problem, two sub-tasks are defined one each for fluid 1 (sub-task 1) and fluid 2 (sub-task 2). Each sub-
task will contain a particular model, domain of definition, material properties, and boundary conditions,
including the moving interface along the intersection of the two sub-tasks.
The domain of definition for the problem is divided into four subdomains: sub-task 1 is defined on
subdomain 1 and subdomain 2, and sub-task 2 is defined on subdomain 3 and subdomain 4 (see Fig-
ure 7.2: Boundary Sets and Subdomains for the Problem(p. 229)). Each sub-task is defined over two
subdomains to allow for the definition of the remeshing method only where it is necessary, (in the area
near the moving interface).
Fluid 1 has a viscosity of = 10000 poise, and fluid 2 has a viscosity of = 5000 poise.
Figure 7.1: A Schematic Diagram of the Two Fluids in the Die
The boundary sets for the problem are shown in Figure 7.2: Boundary Sets and Subdomains for the
Problem (p. 229).
228
Flow of Two Immiscible Fluids

Figure 7.2: Boundary Sets and Subdomains for the Problem
The conditions at the boundaries of the domains are:
• boundary 1: flow inlet for fluid 1, volumetric flow rate = 3 cm3
/s
• boundary 2: outer wall common to subdomain 1 and subdomain 3: zero velocity
/s
• boundary 5: flow exit for both fluids
An interface is defined at the intersection of subdomain 2 and subdomain 4. In this problem, the interface
is a moving one, since the exact line of separation between the fluids is unknown.
229
Problem Description

7.4.Preparation
Note
7. Unzip the Two-Fluids_R150.zip file you have downloaded to your working folder.
The mesh file fluids.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering two-fluids as the name of the
project.
3. Import the mesh file (fluids.msh).
In this step, you will define a single task that represents the global problem. Since this tutorial deals
with two fluids, each with its own physical properties, you will need to define two different sub-tasks
(one for each fluid) in steps that follow.
Create a task for the model.
230

Create a new task
• F.E.M. task
7.7.Step 2a: Definition of Sub-Task 1
In this step, define the nature of the flow problem, identify the domain of definition, set the relevant material
properties for fluid 1, and define boundary conditions along its boundaries.
1. Create a sub-task for fluid 1.
Create a sub-task
a. Click Generalized Newtonian isothermal flow problem.
b. Enter fluid 1 as the New value and click OK.
Sub-task 1 is defined for SUBDOMAIN2 (the region of fluid 1 near the moving interface) and SUBDOMAIN1
(the rest of fluid 1), as shown in Figure 7.2: Boundary Sets and Subdomains for the Problem(p. 229).
a. Select SUBDOMAIN3 and click Remove.
231

b. Select SUBDOMAIN4 and click Remove.
3. Specify the material data properties for fluid 1.
Material Data
properties. In this case, viscosity, density, inertia terms, and gravity are available for specification. For
this model, define only the viscosity of the material.
Click Shear-rate dependence of viscosity.
4. Click Constant viscosity.
Modify fac
Polydata prompts for a new value of .
232

6. Click Upper level menu three times to return to the fluid 1 menu.
7. Specify the flow boundary conditions for fluid 1 (SUBDOMAIN1 and SUBDOMAIN2).
a. Set the conditions along the intersection of SUBDOMAIN2 and SUBDOMAIN4.
The boundary uses the interface condition, which is the standard boundary condition between two
adjacent fluids. This condition establishes the continuity of the velocity field and the contact forces
in the momentum equation.
233

The position of the line separating the two fluids is unknown at the start of the problem and is
calculated as part of the solution, so the intersection will be defined as a moving interface. In
steady flows and problems involving immiscible fluids, the interface must be a streamline. To sat-
isfy this condition and to obtain the exact location of the line of separation, an additional equation,
the kinematic condition, ( = 0), is added to the system. This guarantees that the material points
do not cross the interface.
i. Select Zero wall velocity (vn=vs=0) along SUBDOMAIN4 click Modify.
iii. Select Switch to moving interface.
iv. Click Specify moving interface parameters.
v. Click Boundary conditions on the moving surface.
Polydata asks you to select the boundary or subdomain on which the position of the moving
surface is to be imposed.
vi. Select No condition along BOUNDARY2 and click Modify.
vii. Select Position imposed.
viii. Click Upper level menu twice to return to the Kinematic condition menu.
ix. Select Upwinding in the kinematic equation. Click Upper level menu.
x. Click Accept the current setup to return to the Flow boundary conditions menu.
234

b. Set the conditions at the flow inlet for fluid 1 (BOUNDARY1).
i. Select Zero wall velocity (vn=vs=0) along BOUNDARY1 and click Modify.
ii. Click Inflow.
iii. Click Modify volumetric flow rate.
v. Select Automatic. Click Upper level menu.
When this option is selected, Polydata automatically chooses the most appropriate method
to compute the inflow condition.
vi. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY2 at the outer
wall of SUBDOMAIN1 (BOUNDARY2).
At a solid-liquid interface, the velocity of the liquid is that of the solid surface. Hence the fluid
is assumed to stick to the wall. This is known as the no-slip assumption because the liquid is
assumed to adhere to the wall, and so has no velocity relative to the wall.
By default, Polydata imposes Zero wall velocity ( = = 0) along all boundaries.
c. Set the conditions at the flow outlet (BOUNDARY5).
is most appropriate. This condition essentially imposes a zero normal force ( ) that includes a
pressure term, and zero tangential velocity ().
ii. Click Outflow.
d. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY6 at the outer wall
common to SUBDOMAIN1 and SUBDOMAIN2 (BOUNDARY6).
235

The fluid is assumed to stick to the wall, since at a solid-liquid interface the velocity of the liquid
is that of the solid surface.
e. Click Upper level menu to return to the fluid 1 menu.
8. Define remeshing for SUBDOMAIN2.
This model involves a moving interface for which the position is unknown. A portion of the mesh is af-
fected by the relocation of this boundary. Hence a remeshing technique is applied on this part of the
mesh. The moving interface is entirely contained within SUBDOMAIN2, and hence only SUBDOMAIN2
will be affected by the relocation of the moving interface.
Global remeshing
a. Specify the region where the remeshing is to be performed (SUBDOMAIN2).
If you have a complex geometry, it may be necessary to split it into additional subdomains in order
to define a specific remeshing method on each of them.
For this purpose, Polydata allows you to create several local remeshings. For this problem, a single
local remeshing is sufficient.
i. Select SUBDOMAIN1 and click Remove.
236

The Method of Spines menu item is highlighted.
of boundary nodes due to the motion of the interface. Mesh nodes must be organized along lines
of remeshing (spines), which are collections of nodes logically arranged in a one-dimensional
manner. Polydata requires the specification of the first and last spines that the fluid encounters
(inlet of spines and outlet of spines, respectively). In this case, the inlet of spines is the intersection
of SUBDOMAIN2 with SUBDOMAIN1, and the outlet of spines is the intersection of SUBDOMAIN2
with the flow exit (BOUNDARY5).
Method of Spines
i. To specify the inlet for the system of spines, select Intersection with SUBDOMAIN1 and click
Confirm.
ii. Specify the outlet for the system of spines, select Intersection with BOUNDARY5 and click
Confirm.
iii. Click Upper level menu two times.
The F.E.M. Task 1 menu is displayed.
237

7.8.Step 2b: Definition of Sub-Task 2
properties for fluid 2, and define the boundary conditions along its boundaries.
1. Create a sub-task for fluid 2.
Create a sub-task
a. Polydata asks you if you want to copy data from an existing sub-task.
c. Click Generalized Newtonian isothermal flow problem.
d. Enter fluid 2 as the New value and click OK.
a. Select SUBDOMAIN1 and click Remove.
b. Select SUBDOMAIN2 and click Remove.
3. Specify the material data properties for fluid 2.
Material Data
For this model, define only the viscosity of the material.
238

b. Click Constant viscosity.
c. Specify the value for .
Modify fac
Polydata prompts for a new value of .
d. Click Upper level menu three times to return to the fluid 2 menu.
4. Specify the flow boundary conditions for fluid 2 (SUBDOMAIN3 and SUBDOMAIN4).
a. Set the conditions along the intersection of SUBDOMAIN2 and SUBDOMAIN4.
i. Select Zero wall velocity (vn=vs=0) along SUBDOMAIN2 and click Modify.
The interface condition was defined as a moving interface when setting the boundary condi-
tions for fluid 1. So further inputs are not required to define the moving interface for fluid 2.
Surface tension effects are neglected in this problem.
iii. Click Accept the current setup.
b. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY2 at the outer wall
of SUBDOMAIN3 (BOUNDARY2).
c. Set the conditions at the flow inlet for fluid 2 (BOUNDARY3).
ii. Click Inflow.
239

iv. Accept the default value of 1 for the flow rate by clicking OK.
d. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY4 at the outer wall
common to SUBDOMAIN3 and SUBDOMAIN4 (BOUNDARY4).
e. Set the conditions at the flow outlet for fluid 2 (BOUNDARY5).
ii. Click Outflow.
f. Click Upper level menu to return to the Flow boundary conditions menu.
5. Define remeshing for SUBDOMAIN4.
Global remeshing
a. Specify the region where the remeshing is to be performed (SUBDOMAIN4).
i. Select SUBDOMAIN3 and click Remove.
The Method of Spines menu item is highlighted.
In this case, the inlet of spines is the intersection of SUBDOMAIN3 with SUBDOMAIN4, and the
outlet of spines is the intersection of SUBDOMAIN4 with the flow exit (BOUNDARY5).
240

Method of Spines
i. Specify the inlet for the system of spines by selecting Intersection with SUBDOMAIN3 and
click Confirm.
ii. Specify the outlet for the system of spines by selecting Intersection with BOUNDARY5 and
click Confirm.
Save and exit
postprocessing.
2. Click Accept.
241

3. Click Continue.
2. Align the view.
a. In the graphical window, right-click, and select the option Predefined Camera.
b. Select View from +Z.
The central-mouse button allows you to zoom in and zoom out. The left-mouse button allows ro-
tating the image. The right-mouse button allows you to translate the image.
3. Display contours of velocity magnitude.
tab.
242

c. Perform the following steps in the details view:
ii. In the Location Selector dialog box that opens, select SUBDOMAIN1_surf, SUBDOMAIN2_surf,
SUBDOMAIN3_surf, and SUBDOMAIN4_surf (use Ctrl for multiple selection) and then click
OK.
iv. Click Apply.
243

The velocity is much larger at the inlet of fluid 1 than at the inlet of fluid 2. There are two reasons for
this:
• The flow rate is three times larger for fluid 1 than for fluid 2.
• You are modeling an annular die. Hence the flow section is smaller for the interior channel than for the
exterior channel.
When the two fluids come into contact with each other, the interface between the two fluids is pushed
towards the exterior of the annular die.
There are three reasons for this:
• The flow rate for fluid 1 is higher than for fluid 2.
• The die is annular, so even identical flow rates cause the interface to move in order to equilibrate the flow
sections.
244

• The viscosity of fluid 1 is higher than the viscosity of fluid 2. In the process of giving more room to the
most viscous fluid, its shearing decreases. This leads to a smaller global dissipation.
4. Display velocity vectors for the two fluids.
a. Deselect the contour previously defined.
In the Outline tree tab, under User Locations and Plots deselect Contour 1.
b. Click the Insert menu and select Contour or click the button.
c. Click OK to accept the default name (Vector 1) and display the details view below the Outline
tab.
245

d. Perform the following steps in the details view:
SUBDOMAIN3_surf, and SUBDOMAIN4_surf (use Ctrl for multiple selection) and click OK.
iii. Ensure that VELOCITIES is selected as the Variable.
iv. In the Symbol tab, set Symbol to Arrow3D and increase the Symbol Size to 3.
v. Click Apply.
246

247

Figure 7.5: Magnified View of Velocity Vectors
You can see that the velocity is continuous across the interface. As both the fluids are Newtonian, the
velocity profile is a parabola on both sides of the interface. Since the force must be continuous across
the interface, the shear stress generated within fluid 1 is equal to the shear stress generated within fluid
2 along the interface.
7.12.Summary
This tutorial introduced the concept of fluid layers owing in the same duct. In Polydata, you learned
how to set up a multiple-domain calculation, including the definition of a moving interface and associated
remeshing methods.
The location of the interface depends largely on the physical properties of the fluids involved, the
geometry of the channels, and the operating conditions (for example: flow rates of the fluids). A CFD
simulation with Polyflow allows you to test different setups (for example: in order to optimize the
feeding of a co-extrusion die).
248

Chapter 8: Flow of Two Immiscible Fluids by Species Method
8.1.Introduction
8.2.Prerequisites
8.4.Preparation
8.7.Step 2a:Definition of Species and Species Transport Sub-task
8.8.Step 2b:Definition of a Sub-task
8.12.Summary
8.1.Introduction
This tutorial examines the flow of two fluids in a single die. Two polymer melts with distinct physical
properties are fed through different channels into a die. The aim of the calculation is to predict the
location of the interface between the two fluids.
• Define a species.
• Define a species transport problem.
• Define a PMAT function.
• Define an EVOLUTION task.
8.2.Prerequisites
This problem analyzes the flow of two immiscible Newtonian fluids (fluid 1 and fluid 2) through a die
of diameter 1 cm, as shown in Figure 8.1: A Schematic Diagram of the Two Fluids in the Die(p. 251). The
melts are fed into the die through boundaries 1 and 3 (see Figure 8.2: Boundary Sets and Subdomains
for the Problem (p. 252)). The flow rates for the two fluids are not equal. The fluids come into contact
in the die, creating an interface. The location of the interface is unknown and will be determined by
249

Polyflow. The location of the interface depends on the physical properties of the fluids, the flow rates
of the fluids, and the geometry of the die.
Incompressibility and momentum equations are solved in the fluid domains. To determine the interface,
an extra scalar transport equation is solved and material properties are made functions of this scalar
using PMAT. If scalar value is greater than 0.5, material properties of first fluid are used and if scalar
value is less than 0.5, material properties of second species are used. Scalar value of 0.5 determines the
location of interface.
Note that same problem has been solved using the interface tracking method (see Flow of Two Immiscible
Fluids (p. 227)).
The advantage of this method over the interface tracking method is that you can use this method even
for complex geometries, and it is less expensive compared to interface tracking method (no remeshing
method must be defined). But this comes at a loss of accuracy. The interface tracking method gives a
very accurate position of interface, whereas the species method produces a blurred interface.
The geometry and mesh from Flow of Two Immiscible Fluids (p. 227) is used.
Fluid 1 has a viscosity of = 10000 poise, and fluid 2 has a viscosity of = 5000 poise.
250
Flow of Two Immiscible Fluids by Species Method

Figure 8.1: A Schematic Diagram of the Two Fluids in the Die
The boundary sets for the problem are shown in Figure 8.2: Boundary Sets and Subdomains for the
Problem (p. 252).
251
Problem Description

Figure 8.2: Boundary Sets and Subdomains for the Problem
The conditions at the boundaries of the domains are:
/s
• boundary 3: flow inlet for fluid 2, volumetric flow rate, = 1 cm3
/s
• boundary 5: flow exit for both fluids
The conditions at the boundaries of the domains for species transport:
• boundary 1: scalar value equal to 1
252

• boundary 3: scalar value equal to zero
• Insulated condition at all other boundaries
Note that using this method, for sharp interface it should be ensured that the scalar doesn't diffuse
much into the domain. To ensure this, evolution is applied on scalar diffusivity starting from a large
value and gradually decreasing it to a very small number.
8.4.Preparation
Note
7. Unzip the Two-Fluids-Species_R150.zip file you have downloaded to your working folder.
The mesh file fluids.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering two-fluids-species as the name
of the project.
3. Import the mesh file (fluids.msh).
253
Step 1:Project and Mesh

In this step, you will define a single task that represents the global problem. Since this tutorial deals
with two fluids, each with its own physical properties, you will need to define two different sub-tasks
(one for each fluid) in steps that follow.
Create a new task
• F.E.M. task
8.7.Step 2a: Definition of Species and Species Transport Sub-task
In this step, define a species A and set material properties as well as boundary condition along its boundaries.
1. Create a species A.
Define species
2. Create a new species.
Create a new species
A small panel appears asking for the name of the species.
a. Enter Species A as the name of the species.
A small panel appears asking for the nickname of the species.
254

b. Enter spea as the nickname of the species.
3. Create a sub-task for transport of the species.
Create a sub-task
a. Click Transport of species.
Polydata will ask to select a species.
b. Click SpeciesA.
Species transport equation is solved in all the subdomains.
Click Upper level menu to select all of the subdomains.
5. Specify the material properties for species.
Material data
Polydata indicates the material properties that are relevant for the sub-task by graying out the irrelevant
properties. For this model, you will define only the diffusivity of the species. Evolution will be applied
on diffusivity with initial high value (1) and decreasing it to a small value (1e-9).
255
Step 2a:Definition of Species and Species Transport Sub-task

a. Click Diffusivity.
b. Click EVOL button at the top of Polydata menu to enable evolution inputs.
c. Click Modify diffusivity.
A small panel appears asking for New value of diffusivity.
256

d. Click OK to accept the default value of 1.
Polydata will take you to evolution panel. Here you will make species diffusivity as a function of
evolution parameter . Since we want diffusivity to decrease by several orders of magnitude, we
use = + +
.
e. Select the function f(S) = a*exp(b*S) + c + d*S.
f. Modify the value of function parameters: a, b, c, and d to 1, –20, 0 and 0, respectively.
g. Click Upper level menu.
h. Click the EVOL button at the top of the Polydata menu to disable evolution inputs.
i. Click Upper level menu twice to return to the Transport of SpeciesA menu.
Boundary conditions of the species must be defined at all of the boundaries.
6. Specify the concentration boundary conditions for fluid 1 (SUBDOMAIN1 and SUBDOMAIN2).
Concentration boundary conditions
257
Step 2a:Definition of Species and Species Transport Sub-task

a. Set mass fraction at BOUNDARY1 equal to 1.
i. Select Mass fraction imposed along BOUNDARY1 and click Modify.
ii. Click Mass fraction imposed.
iii. Click Constant.
A small panel appears asking for the new value of concentration.
iv. Set New value to 1 and click OK.
258

b. Set insulated conditions at BOUNDARY2.
ii. Click Insulated boundary.
c. Set mass fraction at BOUNDARY3 equal to 0.
ii. Click Mass fraction imposed.
iii. Click Constant.
A small panel appears asking for the new value of concentration.
iv. Click OK to accept the default value of 0.
d. Set insulated conditions at BOUNDARY4, BOUNDARY5, and BOUNDARY6.
ii. Click Insulated boundary.
iii. Repeat step (i) and step (ii) for BOUNDARY5 and BOUNDARY6.
iv. Click Upper level menu twice.
8.8.Step 2b: Definition of a Sub-task
properties for fluid, and define boundary conditions along its boundaries.
1. Create a sub-task for the fluids.
Create a sub-task
a. Click No in the window that pops up.
Select Generalized Newtonian isothermal flow problem.
259
Step 2b:Definition of a Sub-task

b. Enter fluid 1 and 2 as the New value and click OK.
This Sub-task is defined for all the subdomains.
Click Upper level menu to select all of the subdomains.
3. Specify the material data properties for fluids.
Material Data
Polydata indicates the material properties that are relevant for the sub-task by graying out the irrelevant
properties. For this model, you will define only the viscosity of the material. The viscosity of material 1
will be used if the species concentration is greater than 0.5, otherwise the viscosity of material 2 will be
used. This can be achieved by the use of PMAT.
c. Click PMAT button at the top of Polydata.
d. Specify the value for .
Modify fac
Polydata prompts for the new value of .
260

e. Polydata will take you to PMAT menu as shown below.
f. Create a new function.
Create a new function
A new function f1(...) will be created.
g. Click f1(...).
h. Select multi-ramp function.
f(X1) = Multi-ramp function
261

Polydata will ask to define pair of values. A minimum of two pairs need to be defined. Here we
define (0.495, 5000) and (0.505, 10000) where first index stands for species concentration and
second index stands for viscosity value.
i. Define new pairs.
Define new pairs (X1, f(X1))
Polydata prompts for X1 and f(X1) sequentially.
Enter 0.495 for X1( 1), and 5000 for f(X1)( 1).
j. Define the second pair.
Insert new pair
k. Enter 0.505 for X1( 2) and 10000 for f(X1)( 2).
l. Click Upper level menu two times.
m. Change the field to species concentration.
Change field X1 = S (evol. var.)
n. Select SpeciesA.
o. Disable PMAT button at the top of Polydata.
p. Click Upper level menu six times to return to the fluid 1 and 2 menu.
262

4. Specify the flow boundary conditions for the fluids.
a. Set the conditions at the flow inlet for fluid 1 (BOUNDARY1).
ii. Click Inflow.
Polydata prompts for the new value of the volumetric flow rate.
263

When this option is selected, Polydata automatically chooses the most appropriate method
to compute the inflow condition.
b. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY2.
At a solid-liquid interface, the velocity of the liquid is that of the solid surface. Hence the fluid is
assumed to stick to the wall. This is known as the no-slip assumption because the liquid is assumed
to adhere to the wall, and so has no velocity relative to the wall.
By default, Polydata imposes Zero wall velocity ( = = 0) along all boundaries.
c. Set the conditions at the flow inlet for fluid 2 (BOUNDARY3).
ii. Click Inflow.
Polydata prompts for the new value of the volumetric flow rate.
d. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY4.
e. Set the conditions at the flow outlet (BOUNDARY5).
is most appropriate. This condition essentially imposes a zero normal force ( ) that includes a
pressure term, and a zero tangential velocity ().
ii. Click Outflow.
f. Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY6.
The fluid is assumed to stick to the wall, since at a solid-liquid interface the velocity of the liquid
is that of the solid surface.
g. Click Upper level menu to return to the fluid 1 and 2 menu.
h. Click Upper level menu two times.
The main menu of Polydata is displayed.
264

Save and exit
postprocessing.
a. Click Modify system of Units.
b. Click Set to metric_cm/g/s/A+Celsius.
2. Click Accept.
This confirms that the default Current field(s) are correct..
3. Click Continue.
cessing, and the Polyflow format results file (res).
Right-click the Solution cell and click Listing Viewer....
2. Align the view.
In the graphical window, right-click, and select View from +Z under Predefined Camera.
265

The central-mouse button allows you to zoom in and zoom out. The left-mouse button allows rotating
the image. The right-mouse button allows you to translate the image.
3. Display contours of velocity magnitude.
tab.
c. Perform the following steps in the details view of Contour 1:
266

SUBDOMAIN3_surf, and SUBDOMAIN4_surf (use Ctrl for multiple selection) and click OK.
iii. Select VELOCITIES from the Variable drop-down list.
iv. Click Apply.
The velocity is much larger at the inlet of fluid 1 than at the inlet of fluid 2. There are two reasons for
this:
• The flow rate is three times larger for fluid 1 than for fluid 2.
• You are modeling an annular die. Hence the flow section is smaller for the interior channel than for the
exterior channel.
When the two fluids come into contact with each other, the interface between the two fluids is pushed
towards the exterior of the annular die.
267

There are three reasons for this:
• The flow rate for fluid 1 is higher than for fluid 2.
• The die is annular, so even identical flow rates cause the interface to move in order to equilibrate the flow
sections.
• The viscosity of fluid 1 is higher than the viscosity of fluid 2. In the process of giving more room to the
most viscous fluid, its shearing decreases. This leads to a smaller global dissipation.
4. Display the velocity vectors for the two fluids.
a. In Outline tree tab, under User Locations and Plots, deselect Contour 1.
b. Click the Insert menu and select Vector or click the button.
c. Click OK to accept the default name (Vector 1) and display the details view below the Outline
tab.
i. In the Geometry tab, click the button next to Location.
ii. In the Location Selector dialog box that opens, select the locations SUBDOMAIN1_surf,
SUBDOMAIN2_surf, SUBDOMAIN3_surf and SUBDOMAIN4_surf (use ctrl for multiple selec-
tions) and click OK.
iii. In the Symbol tab, select Arrow 3D from the Symbol drop-down list.
iv. Set Symbol Size to 2.
v. Click Apply.
268

You can see that the velocity is continuous across the interface. As both the fluids are Newtonian, the
velocity profile is a parabola on both sides of the interface. Since the force must be continuous across
the interface, the shear stress generated within fluid 1 is equal to the shear stress generated within fluid
2 along the interface.
5. Displaying the contours of Species A.
a. In Outline tree tab, under User Locations and Plots, deselect Vector 1.
b. Click the Insert menu and select Contour or click the Contour button ( ).
c. Click OK to accept the default name (Contour 2) and display the details view below the Outline
tab.
d. Perform the following steps in the details view of Contour 2:
269

SUBDOMAIN3_surf, and SUBDOMAIN4_surf (use Ctrl for multiple selection), and then click
OK.
iii. Click the button next to Variable.
iv. In the Variable Selector dialog box that opens, select SpeciesA, and then click OK.
v. Set Range to User Specified.
vi. Enter 0 for Min and 1 for Max.
vii. Click Apply.
Figure 8.5: Contours of Species A
270

6. Display the interface line.
a. In Outline tree tab, under User Locations and Plots, deselect Contour 2.
b. Select Isosurface from the Location drop-down menu ( ).
c. Click OK to accept the default name (Isosurface 1) and display the details view below the Outline
tab.
d. Perform the following steps in the details view of Isosurface 1:
i. In the Geometry tab, click the button next to Variable and select SpeciesA.
ii. Enter 0.5 for Value in order to locate the interface line.
iii. In the Color tab, select Constant from the Mode drop-down list and select pink by clicking
next to Color.
iv. In the Render tab, select Draw As Lines from the Draw Mode drop-down list.
v. Click Apply.
vi. Right-click in the Graphics Window and deselect Default Legend.
271

Figure 8.6: Location of Interface
8.12.Summary
This tutorial introduced the concept of fluid layers owing in the same duct. In Polydata, you learned
how to set up a species transport equation, PMAT function and how to define a co-extrusion problem
using species transport and PMAT functions. This method avoids the use of the remeshing method,
which is computationally expensive.
The species method although less accurate can help in quickly finding a solution even for a complex
die. For more accurate results, the interface tracking method as demonstrated in Flow of Two Immiscible
Fluids (p. 227) should be used. Generating a mesh for complex die may be an issue with the interface
tracking method.
The location of the interface depends largely on the physical properties of the fluids involved, the
geometry of the channels, and the operating conditions (for example: flow rates of the fluids). A CFD
simulation with Polyflow allows you to test different setups (for example: in order to optimize the
feeding of a co-extrusion die).
272

Part III: Blow Molding
The following blow molding tutorials are available:
1. 3D Thermoforming of a Blister
2. 2D Axisymmetric Blow Molding
3. Plug Assist Thermoforming of a Blister
4. 3D Blow Molding of a Bottle

Chapter 1: 3D Thermoforming of a Blister
1.1.Prerequisites
1.3.Preparation
1.5.Step 2:Models
1.6.Step 3:Definition of a Sub-task
1.7.Step 4:Create Sub-tasks for Postprocessing
1.8.Step 5:Specify the Numerical Parameters
1.9.Step 6:Outputs
1.13.Summary
1.14.Further Improvements
1.15.Appendix
1.1.Prerequisites
that you have solved or read 2.5D Axisymmetric Extrusion (p. 53). Some steps in the setup procedure
This tutorial simulates a typical thermoforming situation for a blister. Figure 1.1: Thermoforming of a
Blister, Sheet (blue) and Mold (red) (p. 276) shows a view of the process in the initial configuration.
275

Figure 1.1: Thermoforming of a Blister, Sheet (blue) and Mold (red)
To reduce the computational run time, and utilizing the symmetric nature of the blister, only one quarter
of the blister/mold is modeled, Figure 1.1: Thermoforming of a Blister, Sheet (blue) and Mold (red)(p. 276).
From a geometric point of view, the initial (1/4) film has the following dimensions:
• Length = 15 mm
• Width = 5 mm
• Initial thickness = 0.35 mm
Dimensions are intentionally given in millimeters due to the small size of the object. The simulation will be
built around the system of units consisting of millimeters, grams and seconds.
The thickness compared to the length/width of the blister is rather small. This allows for the use of the
membrane (shell) element, which is suited for the analysis of 3D blow molding and thermoforming
simulations. The use of the membrane element is presently restricted to time-dependent flows and is
combined with Lagrangian representation (each mesh node is a material point). Node displacement
results from the time integration of nodal velocity.
276
3D Thermoforming of a Blister

The finite element mesh and the boundary conditions are displayed in Figure 1.2: Finite Element Mesh,
Subdomains and Boundary Sets (p. 277). A 3D surface mesh has been generated for both the mold and
the film. The most important aspect is the proper description of the inner mold surfaces that will shape
the blister.
The film has the following material properties:
• Viscosity = 105
⋅
• Density = 10-3
g/mm3
• Initial thickness = 0.35 mm
Figure 1.2: Finite Element Mesh, Subdomains and Boundary Sets
As seen in Figure 1.2: Finite Element Mesh, Subdomains and Boundary Sets(p. 277), the topology involves
two subdomains:
• Subdomain 1 = film
• Subdomain 2 = mold
and four boundary sets:
• Boundary 1: will be fixed (clamped boundary)
• Boundary 2: will be fixed (clamped boundary)
277
Problem Description

• Boundary 3: symmetry boundary condition with respect to the x-axis
• Boundary 4: symmetry boundary condition with respect to the y-axis
The inflation pressure will be defined on the subdomain representing the film (Subdomain 1).
An important new concept is introduced in this tutorial: contact with a mold. Typically, two cases may
be encountered:
• The moving mold comes in contact with the shell and the shell acquires the mold velocity.
• The shell is inflated according to a certain rate and eventually comes into contact with the mold, acquiring
its shape.
Often, both types of contact are encountered in a given application.
1.3.Preparation
Note
7. Unzip the 3D-Thermo-Blister_R150.zip file you have downloaded to your working folder.
The mesh file blister.msh can be found in the unzipped folder.
1. Create a Fluid Flow - Blow Molding (Polyflow) analysis system by drag and drop in Workbench.
2. Save the ANSYS Workbench project using File → Save, entering blister as the name of the project.
278

3. Import the mesh file (blister.msh).
1.5.Step 2: Models
In this step, define the task representing the mold.
Create a new task
• F.E.M. task
• Time-dependent problem(s)
• 2D shell geometry
2. Define the molds.
Define molds
a. Create the new mold.
Create a new mold
Click Adiabatic mold.
A panel opens, asking for the title of the mold.
b. Click OK to accept the default name, Mold 1.
279
Step 2:Models

The Domain of the mold menu item is highlighted.
3. Define the domain where the mold applies.
Domain of the mold
a. Select Subdomain 1 and click Remove.
b. Click Upper level menu at the top of the Domain of the mold menu.
4. Define the contact boundary conditions.
Contact conditions
a. Select No contact along Subdomain 2 and click Modify.
b. Select Contact and click Upper level menu twice.
5. Define the motion of the mold.
Mold motion
a. Click Mold motion type : fixed mold
A small panel opens, asking you to specify the type of mold motion.
280

Enter 1 as the New value to impose a translation velocity, and click OK.
b. Click the EVOL button at the top of the Polydata menu to enable evolution inputs.
c. Set the mold translation velocity.
Modify translation velocity
Polydata prompts for velocity-x.
i. Specify the x-velocity.
281
Step 2:Models

Click OK to accept the default value of 0 for the New value of velocity-x.
Polydata asks you to the specify the time dependence of the x-velocity. Click Upper level
menu, as there is no velocity in the x-direction.
ii. Specify the y-velocity.
Click OK to accept the default value of 0 for the New value of velocity-y, and click Upper
level menu, as there is no velocity in the y-direction.
iii. Specify the z-velocity.
Enter 10 mm/s for the New value of velocity-z and click OK.
iv. Specify the time dependence of the z-velocity.
Select f(t) = Ramp function.
v. Define the coordinate pairs (a,b) and (c,d) for the points that define the ramp function.
Click Modify the value of a.
vi. In a similar manner, set the values for b, c, and d to 1.0, 0.103, and 0, respectively.
282

Figure 1.3: Ramp Function for Mold Velocity
Figure 1.3: Ramp Function for Mold Velocity(p. 283) shows the ramp function you just defined.
Click Upper level menu to return to the Mold motion menu.
vii. Click the EVOL button at the top of the menu to disable evolution inputs.
viii. Click Upper level menu three times to return to the F.E.M. Task 1 menu.
1.6.Step 3: Definition of a Sub-task
properties for the fluid, and define boundary conditions along its boundaries.
Create a sub-task
a. Select Shell model : Gen. Newtonian isothermal.
A small panel opens, asking for the title of the problem.
283
Step 3:Definition of a Sub-task

b. Enter Blister as the New value and click OK.
b. Click Upper level menu button at the top of the Domain of the sub-task menu.
3. Specify the flow boundary conditions.
a. Retain the default settings for Boundary 1 and Boundary 2.
b. Select Zero wall velocity (vn=vs=0) along Boundary 3 and click Modify.
i. Click Plane of symmetry ( fs=0, vn=0 ).
ii. Select normal direction along X axis.
iii. Click Upper level menu to continue specifying flow boundary conditions.
c. Select Zero wall velocity (vn=vs=0) along Boundary 4 and click Modify.
ii. Select normal direction along Y axis.
iii. Click Upper level menu to return to the Flow boundary conditions menu.
d. Click Inflation pressure imposed at the bottom of the Flow boundary conditions menu.
e. Click Constant for the inflation pressure.
A panel opens, asking for the new value of the constant.
284

f. Click the EVOL button at the top of the Polydata menu to enable evolution inputs.
Polydata directs you to the Time dependence of inflation pressure menu.
i. Select f(t) = Ramp function.
ii. Click Modify the value of a, and enter 0.1 as the New value.
iii. In a similar manner, set constants b, c, and d to 0, 0.11, and 1.0, respectively.
Figure 1.4: Ramp Function for Pressure
Figure 1.4: Ramp Function for Pressure(p. 285) shows the ramp function you just defined.
h. Click Upper level menu.
Click the EVOL button at the top of the Polydata menu to disable evolution inputs.
i. Click Upper level menu to return to the Blister menu.
4. Define the contacts of the blister.
285

Define contacts
a. Click Create a new contact problem.
The Modification of a contact problem menu will open with the Select a contact wall menu
item highlighted.
b. Define the contact wall.
i. Click Select a contact wall.
ii. Select Mold 1 : Contact along Subdomain 2 and click Select.
c. Specify the coefficients and accuracy.
i. Click Modify the slipping coefficient.
Enter 1e+10 as the New value and click OK.
ii. Click Modify the penalty coefficient.
Enter 1e+10 as the New value and click OK.
iii. Click Modify the penetration accuracy.
d. Define the orientation of the mold.
i. Magnify the view of the mold to ensure that you can see the darts that will be displayed.
Alternatively, you can increase the size of the darts:
Graphical window → Sizing Darts → Size up.
ii. Click Specify mold side / cavity side.
Darts will be displayed in the Graphics Display window, as shown in the following figure.
286

iii. Click No in the panel that opens, to specify that the darts are not pointing towards the mold
body.
If the direction of the darts is not clear to you, you can close the panel, rotate the view and/or
change the magnification, click Specify mold side / cavity side again, and then answer
the question appropriately.
e. Click Upper level menu twice.
A warning panel opens, saying that velocity prediction must be disabled, and that the modification
has automatically been done.
287

Click OK.
The Define layers menu item is highlighted.
5. Define the layers of the blister.
Define layers
a. Click Create a new layer.
In the panel that opens, enter blister as the New value.
The blister menu will open with the Material data menu item highlighted.
b. Specify the material data for the blister.
Material Data
i. Click Shear-rate dependence of viscosity.
ii. Click Constant viscosity.
iii. Click Modify fac.
iv. Click Upper level menu twice to continue with material data specification.
v. Click Density.
vi. Click Modification of density.
vii. Click Upper level menu to continue with the material data specification.
288

viii. Click Inertia terms.
Select Inertia will be taken into account and click Upper level menu to continue with
material data specification.
ix. Click Layer permeability.
x. Click Modify coef. of permeability.
Enter 5e-12 g-mm/s/mm2
as the New value and click OK.
xi. Click Upper level menu twice to return to the blister menu.
c. Specify the initial thickness.
Initial thickness
i. Click Constant.
ii. Click Upper level menu four times to return to the F.E.M. Task 1 menu.
1.7.Step 4: Create Sub-tasks for Postprocessing
In this step you will create a number of sub-tasks that will report various statistics about the blown product.
The results for derived quantities that produce a single value are displayed in the listing file. Sub-tasks that
produce a field of values are exported to CFD-Post.
1. Set a task to report the mass of the blown product.
Create a sub-task
Click No in the panel that opens asking if you want to copy the data of an existing sub-task.
a. Click Postprocessor.
Enter Mass of product as the New value in the panel that asks for the title of the sub-
task and click OK.
b. Click Mass of blown product.
Click OK in the dialog box that opens saying that the calculation will be performed on Subdo-
main 1.
c. Confirm that the Density of layer [blister] is set to 1.00E-03, and click Upper level menu.
d. Click Add a new plane.
The plane is calculated by the following equation (which is displayed at the top of the Restric-
tion of Layers by cutting planes menu).
289
Step 4:Create Sub-tasks for Postprocessing

(1.1)
+ + +
Polydata asks for the values of Coefficients A, B, C, and D sequentially.
e. Enter 0 for A, 0 for B, -1 for C, and 25.9 for D.
g. Click Upper level menu to ignore contact with Subdomain 2.
2. Set a task to report the permeability of the blown product.
Create a sub-task
Enter Permeability of product as the New value in the panel that asks for the title
of the sub-task and click OK.
b. Click Permeability of blown product.
main 1.
c. Confirm that the Permeability of layer [blister] is set to 5.00E-12, and click Upper level menu.
d. Click Add a new plane.
See Equation 1.1 (p. 290) for more information on the coefficients.
e. Enter 0 for A, 0 for B, -1 for C, and 25.9 for D.
g. Click Upper level menu to ignore contact with Subdomain 2.
3. Set a task to report the volume of the blown product.
Create a sub-task
Enter Volume of product as the New value in the panel that asks for the title of the sub-
task and click OK.
b. Click Capacity of blown product.
290

main 1.
c. Click Add a new plane.
See Equation 1.1 (p. 290) for more information on the coefficients.
d. Enter 0 for A, 0 for B, -1 for C, and 25.9 for D.
e. Click Upper level menu.
f. Click Upper level menu to ignore contact with Subdomain 2 and return to F.E.M. Task 1.
1.8.Step 5: Specify the Numerical Parameters
1. Click Modify the transient iterative parameters.
2. Click Modify the initial time value.
Click OK to retain the default value of 0.0 s as the New value.
3. Click Modify the upper time limit.
Enter 0.6 s as the New value and click OK.
4. Click Modify the initial value of the time-step.
5. Click Modify the min value of the time-step.
6. Click Modify the max value of the time-step.
7. Click Modify the tolerance.
Click OK to retain the default of 0.01 as the New value.
8. Click Modify the max number of successful steps.
Click OK to retain the default of 200 as the New value.
1.9.Step 6: Outputs
Outputs
291
Step 6:Outputs

a. Modify the current system of units.
b. Specify the new system of units.
Set to metric_mm/g/s/mA+Celsius
2. Click Upper level menu two times to return to the Outputs menu.
a. Set the output triggering.
Output Triggering
b. Specify the type of output triggering.
Output after N valid steps
The Enter the number of steps menu item is highlighted.
c. Specify the number of steps.
Enter the number of steps
Click OK to retain the default of 1 for the New value.
3. Click Upper level menu twice to return to the top-level Polydata menu.
Save and exit
1. Click Accept.
2. Click Continue.
cessing, and the Polyflow format results file (res).
292

3. Scroll up to view the results of the postprocessing sub-tasks.
Scroll up in the listing file to view the results of the Postprocessors.
293
Step 8:Solution

Here you can see the results of the postprocessor sub-tasks you created in Polydata. For additional in-
formation on postprocessing sub-tasks, see Step 4: Create Sub-tasks for Postprocessing (p. 289) and
Overview of Derived Quantities in the Polyflow User's Guide.
1. Double-click the Results cell in the Workbench analysis system.
2. Align the view as shown in the following figure.
3. Display contours of thickness in the fluid region (Subdomain1).
a. Insert → Contour or click the button.
b. In the dialog box that opens, click OK to accept the default name (Contour 1) and display the
details of Contour 1 below the Outline tree.
294

c. Specify the following settings in the Geometry tab:
i. Select Subdomain_1_surf from the Locations drop-down list.
ii. Select THICKNESS from the Variable drop-down list, or click the ellipsis button ( ) on the
right and select THICKNESS.
iii. Select User Specified from the Range drop-down list.
iv. Enter 0.1 mm for Min and 0.35 mm for Max.
v. Click Apply.
295

Figure 1.5: Contours of Thickness 1/4 Geometry
4. Show the contours of thickness on the full mold.
a. Double-click Default Transform in the Outline tree tab, under User Locations and Plots (or right-
click Default Transform and select Edit).
296

b. Disable Instancing Info From Domain under the Definition tab in the details of Default Transform.
c. Enter 2 for the Number of Graphical Instances.
d. Select Value from the Determine Angle From drop-down list in the Instance Definition group
box.
e. Enter 180 for Angle.
f. Enable Apply Reflection, and select ZX Plane from the Method drop-down list.
g. Retain the default value of 0.0 m for Y.
h. Click Apply and revise the magnification of the view to show the whole mold.
297

Figure 1.6: Contours of Thickness on the Whole Mold
5. Display contours of thickness at various time steps.
Polydata exported a total of 73 time steps to CFD-Post.
a. Click the Timestep Selector icon ( ).
b. Scroll up in the Timestep Selector dialog box and select Step 1.
298

c. Click Apply.
299

Figure 1.7: Thickness of the Film at Time=0.001 s
d. Repeat steps a.–c. for timesteps 30, 50, and 73.
300

Figure 1.8: Contours of Thickness at Time = 0.2338 s
301

302

6. Create an animation for the contour plot.
a. Click the animation icon ( ).
b. Ensure Quick Animation is selected in the Animation dialog box.
c. Select Timesteps.
d. To save the animation, expand the dialog box by clicking the button at the lower-right.
303

i. Enable Save Movie.
ii. Click the file icon to the right and enter the path where you would like to save the animation.
Enter Thickness.wmv for the name of the file and click Save to close the Save Movie
dialog box.
wmv and mpg are the recommended formats.
iii. Disable to save only one cycle of animations.
iv. Click the play button, to play the animation and save it as a file.
1.13.Summary
This tutorial introduced the concept of a blow molding problem. The mold moved into contact with
the film, where a constant pressure was applied to the film. This blew the film into the mold where it
assumed the shape of the mold.
You represented the film by a shell geometry under the valid assumption that the thickness of the film
was much smaller than the other two dimensions. Polyflow linearly interpolated the process vari-
304

ables—thickness, velocity and position. By reporting the individual time steps to CFD-Post you were
able to view the thickness of the product as a function of time.
In many practical cases, the use of adaptive meshing based on contact, remeshing, or both may be
useful to selectively and automatically refine the mesh during the solution. To illustrate the effects of
such refinement, this tutorial has been run with contact adaptive meshing enabled and made available
as blister-adapt.wbpj in the 3D-Thermo-Blister_R150solution_files folder you un-
zipped in Preparation (p. 278). The following settings were specified:
F.E.M. Task 1
• Numerical parameters
– Adaptive meshing
→ Activate adaptive meshing for contacts
• Enable all the local criteria
• Switch to calculated from angle and curvature
• Modify size_min = .1
• Modify tolerance = .01
• Modify size_max = 1
• Modify dist_crit = .5
→ Modify Nstep = 4
→ Modify Maxdiv = 1, 2, and 3 (in separate analysis systems)
For additional information on adaptive meshing, see Adaptive Meshing.
The results are shown in Figure 1.11: Effect of Adaption on Final Mesh and Thickness Variation(p. 306).
Note how the mesh changes as the Maxdiv value increases. The results do not change very much as
a result of the adaption, which indicates that the original solution was already mesh independent.
305
Further Improvements

Figure 1.11: Effect of Adaption on Final Mesh and Thickness Variation
1.15.Appendix
The appendix contains the following topics:
1.15.1.Contact Boundary Conditions
1.15.2.Remark on the Penalty Coefficient
1.15.3.Remeshing
As seen, the subdomain that describes the fluid will eventually come in contact with the mold. Besides
its usual material parameters, it also receives some process parameters: inflation pressure and the contact
306

with the (moving) molds. In all forming applications (blow molding and thermoforming for example),
the definition of the contact is an important aspect, as it will eventually lead to the desired shape. The
contact involves a “what” and a “how”
. The “what” describes the geometry of the film/sheet and the
mold surface it may get in contact with (contact problem). The “how” refers to other process parameters
such as a moving mold. In this case, a velocity (possibly time-dependant) must be specified for the
mold. In some cases, the material may slip along the contact wall, which can also be taken into account.
Next to these operating attributes, some numerical parameters must be specified. A geometrical algorithm
is applied for detecting the occurrence of contact, while a penalty formation is used for the treatment
of contact. A penalty coefficient ensures that a geometrical contact is detected. It should not be too
small. A coefficient is also specified in the tangential direction. If the fluid sticks along the wall, this
tangential coefficient should preferably receive the same value as the penalty coefficient. Two additional
coefficients are also needed; a tolerance on penetration accuracy and an element dilatation.
Presently, the penalty coefficient has been set to 1010
, while the same value has been selected for the
coefficient along the tangential direction (slipping coefficient). The tolerance on penetration and element
dilatation equal 0.05 and 0.05 mm, respectively.
The large value of the penalty coefficient can never guarantee an exactly vanishing normal velocity at
the contact. Instead, a residual normal velocity will remain even after mold contact. The amplitude of
this residual velocity will depend on the penalty coefficient. In most cases, the residual velocity is as
low as 10-3
–10-6
.
In classical thermoforming applications, such residual velocity will not produce any significant numerical
penetration of the fluid film/sheet through the mold in view of the short times involved (physically, the
thermoforming process is very fast). However, some situations may involve longer time scales such as
in the glass industry.
The question that is now raised concerns the best evaluation of the penalty coefficient. The penalty
formulation mainly establishes a balance between a force (for example: the inflation pressure, ) and
a penalty force because of contact. The penalty force is simply the product of the penalty coefficient,
, and the residual velocity of the film/sheet upon contact. The other elements of the momentum
equation can be ignored for the present consideration. Assuming a typical time scale (for example:
the simulation time), and a maximum penetration depth , a good penalty coefficient can be selected
as:
=

1.15.3.Remeshing
No remeshing must be specified. In the context of the membrane element, a Lagrangian representation
is applied where all mesh nodes are considered material points.
307
Appendix

308

Chapter 2: 2D Axisymmetric Blow Molding
This tutorial contains the following sections:
2.1.Introduction
2.2.Prerequisites
2.4.Preparation
2.6.Step 2:Models
2.11.Step 7:Outputs
2.12.Step 8:Thickness Postprocessor
2.16.Summary
2.17.Appendix
Files required to work on this tutorial can be downloaded from this website: http://support.ansys.com/
training.
2.1.Introduction
Molding is a process of forcing a preform or a parison (preshaped sleeve) into a mold cavity so that the
preform assumes the shape of the cavity. There are numerous molding methods, including blow
molding, compression and transfer molding, and slush and rotational molding. These methods differ
in the formation of the preform and the filling of the mold cavity. Also, each processing method is
suitable for a specific class of polymers.
Blow molding is an important processing method for molding hollow articles such as bottles. The preform
is usually made by extrusion and forced between the mold halves by pressurization (blowing air). The
polymer solidifies upon contact with the cold mold and the finished product is then ejected. The homo-
geneity and rheological properties of the preform along with the operating conditions (temperature
and pressure variations) are crucial in this step and will affect the design of the processing machinery.
This process reflects all facets of polymer processing— the isothermal and transient flow of Newtonian
fluids in complex geometries with simultaneous structuring and solidification.
• Define a time-dependent problem.
• Set material properties and boundary conditions for a 2D axisymmetric blow molding problem.
• Set numerical parameters available in Polydata for a time-dependent problem.
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2.2.Prerequisites
This problem analyzes a blow molding simulation for a 2D axisymmetric bottle. The problem deals with
the cavity filling stage of the molding process and it is assumed that a preform has been positioned
inside the mold. The contact between the fixed mold and the preform is considered.
A large pressure is applied to the preform, which enters the mold and eventually takes its shape. The
operating conditions must account for a low pressure drop at the entrance, low material waste, and
slow cooling to avoid premature solidification of the preform.
The cylindrical geometry of the preform (Figure 2.1: Problem Description(p. 310)) has an internal radius
of 2 cm and external radius of 3 cm (the initial thickness of the preform is 1 cm). The height of the
preform is 7 cm.
The domain for the problem is divided into two subdomains: one for the fluid perform (subdomain 1)
and the other for the mold (subdomain 2). Incompressibility and momentum equations are solved in
310
2D Axisymmetric Blow Molding

subdomain 1 (the fluid preform). The problem involves two free surfaces (boundary 2 and boundary 4,
shown in Figure 2). boundary 2 will eventually come into contact with the mold, and its position is
calculated as a part of the solution.
The fluid preform has a density of =1 g/cm3
and a viscosity of = 100000 poise. Inertia terms and
the effects of gravity will be included in the calculation.
The boundary sets for the problem are shown in Figure 2.2: Boundary Set for the Problem(p. 311), and
the conditions at the boundaries of the domain (for the preform) are:
• boundary 3: zero normal velocity and zero surface force
2.4.Preparation
311
Preparation

Note
7. Unzip the 2D-Axi-Blow-Molding_R150.zip file you have downloaded to your working folder.
The mesh file 2d-axi-blowmold.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering Final-blow-mold as the name of
the project.
3. Import the mesh file (2d-axi-blowmold.msh).
2.6.Step 2: Models
In this step, define a new task representing the 2D axisymmetric time-dependent model. Then, define the
mold and a sub-task for the isothermal flow calculation.
Create a new task
• F.E.M. task
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The Current setup is updated to reflect the selected options. This example is a simulation of blow
molding for a 2D axisymmetric bottle and the mold is two-dimensional. The problem is assumed
to be time-dependent.
2. Define the mold.
Define molds
a. Create a mold.
Create a new mold
b. Select an adiabatic mold.
Adiabatic mold
c. When prompted, click OK to retain the default name for the mold (Mold 1).
d. Specify the solid region that represents the mold.
Domain of the mold
i. Select SUBDOMAIN_1 and click Remove.
SUBDOMAIN_1 is moved from the top list to the bottom list, indicating that the mold is
defined as SUBDOMAIN_2.
ii. Click Upper level menu at the top of the menu.
e. Specify the boundary that represents the part of the mold that comes into contact with the fluid.
Polyflow uses this information to determine the penetration distance (into the mold) of every
point of the free surface (BOUNDARY2).
Contact conditions
i. Select No contact along BOUNDARY5 and click Modify.
The free surface, BOUNDARY2 of the preform comes into contact with the mold wall,
BOUNDARY5 (as shown in Figure 2.2: Boundary Set for the Problem(p. 311)).
313
Step 2:Models

ii. Select Contact.
f. Click Upper level menu four times to return to the F.E.M. Task 1 menu.
Create a sub-task
A panel opens, asking for the title of the problem.
b. Enter blow molding as the New value and click OK.
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The domain is divided into two subdomains, one for the fluid preform (SUBDOMAIN_1) and the other
for the mold (SUBDOMAIN_2). In this problem, the sub-task applies only to the preform.
SUBDOMAIN_2 is moved from the top list to the bottom list, indicating that the sub-task is
defined on SUBDOMAIN_1.
b. Click Upper level menu at the top of the menu.
Polydata indicates which material properties are relevant for the sub-task by graying out the irrelevant
properties. In this case, viscosity, density, inertia terms, and gravity are available for specification.
Material data
1. Define the viscosity of the preform.
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c. Click Modify fac to specify the value of , which is referred to as “fac” in the graphical user interface.
Polydata prompts for the new value of the viscosity.
e. Click Upper level menu two times to continue with the Material Data specification.
2. Define the density of the preform.
a. Click Density.
b. Click Modification of density to specify the value of the density.
Polydata prompts for the new value of the density.
c. Enter 1 as the New value and click OK.
d. Click Upper level menu to continue with the Material Data specification.
3. Enable the calculation of the inertia terms in the momentum equation.
In this problem, inertia plays an important role. When internal pressure is applied, the preform expands,
and the fluid accelerates towards the mold. In order to obtain a realistic blowing time, inertia must be
taken into account.
316

a. Click Inertia terms.
b. Select Inertia will be taken into account.
c. Click Upper level menu to continue with the Material Data specification.
4. Include the effects of gravity in the flow.
The fluid preform flows in the negative y direction under gravity, so specify the component of gravity
along the y direction ( ).
a. Click Gravity.
b. Click Modify gy to specify the value of gravity in the y-direction.
Modify gy
Polydata prompts for the new value of the gravity along the y-axis.
c. Enter -981 as the New value and click OK.
d. Click Upper level menu two times to return to the blow molding menu.
1. Retain the default condition Axis of symmetry along BOUNDARY1.
No action is required to accept the default value. You can simply proceed to the next step. For 2D
axisymmetric models, Polydata recognizes the axis of symmetry from the mesh file and automatically
imposes the symmetry condition along the line =
.
2. Set the conditions at the outer free surface (BOUNDARY2).
The free surface boundary condition in contact detection problems is different from their simulations
in Polyflow. In blow molding problems, a free surface comes into contact with a solid mold. Polyflow
applies a contact detection algorithm at each location of the surface to detect the occurrence of the
contact.
You need to specify the following for the free surface on BOUNDARY2:
• the components of the direction of displacement along BOUNDARY1 and BOUNDARY3
• the contact wall (the boundary of the mold along which the contact is detected)
• the penalty coefficient
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This determines the accuracy of the contact; the smaller its value, the deeper the contact is.
• The slipping coefficient
The fluid may slip along the contact wall, so to take this factor into account, a slipping coefficient
must be specified along the tangential direction.
a. Select Zero wall velocity (vn=vs=0) along BOUNDARY2 and click Modify.
c. Specify the contact detection problem.
i. Click Contact (Blow mold).
ii. Click Create a new contact problem.
iii. Specify where the free surface will contact the mold.
Polyflow uses the definition of the contact wall in the determination of the penetration distance
(into the mold) of every point of the free surface (BOUNDARY2).
Click Select a contact wall.
iv. Select Mold 1 : Contact along BOUNDARY5 and click Select.
As shown in Figure 2.2: Boundary Set for the Problem(p. 311), the free surface (BOUNDARY2)
of the perform comes into contact with the mold (BOUNDARY5).
v. Define the slipping coefficient.
Modify slipping coefficient
Retain the default value of 1e+09 and click OK.
With such a high value of the slipping coefficient, the fluid will stick to the contact wall.
vi. Define the penalty coefficient.
Modify penalty coefficient
Retain the default value of 1e+09 and click OK.
vii. Click Upper level menu two times to return to the Kinematic condition menu.
d. Click Upper level menu to return to the Flow boundary conditions panel.
In contact detection problems, abrupt changes in the velocity field occur at the contact points
between the fluid preform and the mold. Polydata gives the warning message shown below. Since
the prediction of the velocity field in such cases destroys the prediction scheme, you can continue
by clicking OK.
318

e. Click OK to accept the warning and continue.
3. Set the conditions at the top part of the preform (BOUNDARY3).
b. Click Normal velocity and tangential force imposed ( vn, fs ).
c. Click Upper level menu to accept the default value of 0 for the normal velocity, .
d. Click Upper level menu to accept the default value of 0 for the tangential force, .
4. Set the conditions at the inner free surface (BOUNDARY4).
This boundary of the preform is subjected to pressure by the application of a normal force, so specify
a normal force along this boundary.
c. Specify the normal force.
i. Click Normal force.
ii. Select Constant.
Polydata prompts for the new value of the normal force.
319

iii. Enter -2e06 as the New value and click OK.
iv. Click Upper level menu.
d. Click Upper level menu to return to the Flow boundary conditions menu.
5. Click Upper level menu to return to the blow molding menu.
This model involves free surfaces for which the positions are unknown. A portion of the mesh is affected by
the relocation of these boundaries. Hence a remeshing technique is applied on this part of the mesh. The
free surfaces are entirely contained within SUBDOMAIN_1, and hence only SUBDOMAIN_1 is affected by the
relocation of the free surfaces.
Global remeshing
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Click Upper level menu to accept the default selection of SUBDOMAIN_1.
2. Click Lagrangian on the border only.
For information on remeshing techniques, see Appendix (p. 337).
a. Click Accept the current setup in the Element distortion check menu.
In blow molding simulations, the finite-element mesh can undergo great deformations. The Element
distortion check menu deals with the detection of all possible distortions of the elements. In this
problem, you can accept the default options and proceed to the next step.
b. Click Upper level menu two times to return to the F.E.M. Task 1 menu.
In this step, define the numerical parameters for the simulation.
1. Specify the parameters for the iterative scheme in the calculation of the free surface.
Modify the transient iterative parameters
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For information on time marching scheme, see Appendix (p. 337).
a. Specify the time limit.
This option specifies the time at which the solution procedure stops.
Modify the upper time limit
Polydata prompts for the new value of the time limit.
b. Specify the initial value of the time step.
This option is used to define the initial time step, which is used for the calculation of the next two
time steps. After that, the step size is automatically calculated by Polyflow. This first time step
should be set according to the characteristic time scale of the process considered.
Modify the initial value of the time-step
Enter 1e-03 as the New value and click OK.
c. Specify the minimum value for the time step.
If a calculated value for the time step falls below the minimum for the time step at any point in
the calculation, the iterative scheme stops since this might be a symptom of calculation difficulties.
Modify the min value of the time-step
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d. Specify the maximum value for the time step.
In order to guarantee accuracy of the time-marching scheme and to avoid useless calculations
(rejection of inaccurate time steps), you can limit the growth of the time increment.
Modify the max value of the time-step
e. Specify the tolerance for time marching.
The tolerance is the admissible error between the predicted solution and the exact solution at a
particular time step. A very small value of the tolerance can result in large computational costs
and a very large value can result in wrong solution.
Modify the tolerance
Retain the default value of 1e-02 and click OK.
f. Specify the maximum number of successful steps.
This option is used to select the maximum number of converged steps. If this value is reached, the
calculation stops, even if the upper time limit has not been reached.
Modify the max number of successful steps
Retain the default value of 200 and click OK.
g. Enable Use of the implicit Euler method.
You can specify how often Polyflow saves the solution data when it calculates a solution. In this tutorial,
save the results at every 10 time steps.
Outputs
1. Click Output Triggering.
a. Click Enter the number of steps.
Polydata prompts you for the number of steps.
b. Enter 4 as the New value and click OK.
2. Click Upper level menu twice.
3. Specify the system of units.
323
Step 7:Outputs

b. Click Set to metric cm/g/s/A+Celsius.
2.12.Step 8:Thickness Postprocessor
In this step create a postprocessor sub-task to compute the thickness of the blown product.
The results of this postprocessor are sent to CFD-Post as a value field.
F.E.M. Task 1
1. Create a new sub-task.
Create a sub-task
a. Click No when asked whether you want to copy an existing sub-task.
b. Click Postprocessor.
c. Enter parison thickness as the New value for the title and click OK.
2. Click Parison thickness.
3. Click parison #01.
4. Click OK twice to accept the warnings about defining the borders.
You will have to define these borders at a later stage.
5. Specify the region where the postprocessor sub-task applies.
Accept the default of SUBDOMAIN_1 by clicking Upper level menu.
6. Specify the boundary sets representing the starting and ending borders to be used in the thickness
calculation.
Polyflow evaluates the distance between these borders at a point between them to determine the
thickness at that location.
Borders for thickness calculation
a. Select BOUNDARY2: not used and click Modify.
b. Click Starting border.
c. Select BOUNDARY4: not used and click Modify.
d. Click Ending border.
324

7. Click Upper level menu five times to return to the top-level Polydata menu.
Save and exit
1. Click Accept.
2. Click Continue.
cessing, and the Polyflow format results file is (res).
325

3. Display contours of thickness in the fluid region (SUBDOMAIN_1).
b. In the box that opens, click OK to accept the default name (Contour 1) and display the details
below the Outline tree.
326

c. Specify the following settings under the Geometry tab:
i. Select SUBDOMAIN_1_surf from the Locations drop-down list.
ii. Select estim. THICKNESS from the Variable drop-down list, or click the ellipsis button ( )
on the right and select estim. THICKNESS.
iii. Click Apply.
d. Annotate the display.
i. Click the Insert menu and select Text or click the button.
ii. Click OK to accept the default name (Text 1) and display the details view below the Outline
tab.
iii. Enable Embed Auto Annotation under the Definition tab.
iv. Select Time Value from the Type drop-down list.
v. Click Apply.
327

Figure 2.3: Contours of Thickness at the Final Time-step t = 0.1 s
4. Show contours of thickness on the full blown bottle.
328

b. Disable Instancing Info From Domain under the Definition tab in the details of Default Transform.
c. Enable Apply Reflection, and select YZ Plane from the Method drop-down list.
d. Retain the default value of 0.0 m for X.
e. Click Apply.
f. Click the button to center the view.
329

Figure 2.4: Contours of Thickness on the Full Blown Bottle at t = 0.1 s
5. Display contours of thickness at various timesteps.
Display the results at several time steps to see the shape and thickness of the parison during the blow
molding process.
Tools → Timestep Selector or click the button.
330

a. Select the 20th
timestep and click Apply.
b. Select the 40th
c. Select the 60th
d. Select the final timestep and click Apply.
On these figures, the thickness is integrated from the moving master surface towards the other
free surface. This explains the color fringes appearing through the parison. The thickness decreases
as the parison inflates. At the final time step, the thickness is smallest where the parison has been
the most extended, (in the corner of the bottle). It is largest at the top where the deformation was
much less important due to the small diameter here.
331

Figure 2.5: Contours of Thickness at the 20th Timestep
332

333

334

Figure 2.8: Contours of Thickness on the Full Blown Bottle at t = 0.1 s
6. Create and save an animation.
a. Click the Tools menu and select Animation or click the button.
b. Enable Quick Animation and select Timesteps in the Animation dialog box.
335

c. Click the start button .
d. Enable Save Movie to save the animation as a file.
7. Display contours of velocity in the fluid region.
a. Double-click Contour 1 under the Outline tab to display the details view.
b. Select VELOCITIES from the Variable drop-down list and click Apply.
There is zero velocity at the contact between the parison and the mold, but the velocity magnitude
is still important where the fluid does not yet touch the mold.
There is zero velocity at the contact between the parison and the mold, but the velocity
magnitude can still be important where the fluid does not yet touch the mold. At the final
time of the simulation, the velocity is near zero, which indicates that the contact is completed.
The residual value originates from the penalty formulation used for the contact, as explained
in 3D Thermoforming of a Blister (p. 275).
336

Figure 2.9: Final Velocity Distribution
2.16.Summary
This tutorial introduced a time-dependent problem with a 2D axisymmetric geometry for the mold.
Suitable assumptions were made regarding the nature of the preform and the operating conditions.
You analyzed the factors affecting the process in the postprocessing section. An optimization of the
preform shape could be performed in order to minimize the weight of the bottle while avoiding weak
(too thin) bottle walls.
You used a remeshing method that is most suited for contact detection problems. This problem also
introduced the concept of the calculation of free surfaces for contact detection problems. You used
efficient numerical techniques to more accurately solve a time-dependent problem.
2.17.Appendix
The appendix covers the following topics:
337
Appendix

2.17.2.Master Moving Surface
2.17.3.Time Marching Scheme
of the boundary nodes due to the motion of the free surface. In blow molding applications, the finite-
element mesh undergoes large deformations, especially extension. Thin-shell remeshing is designed to
handle blow molding simulations and is able to cope with such large nodal displacements.
Remeshing is carried out in the tangential direction along the free surface that is expected to undergo
large deformations (the master moving surface) and the internal nodes are relocated along spines in a
direction normal to the master moving surface.
2.17.2.Master Moving Surface
In this problem, the intersection of SUBDOMAIN_1 with BOUNDARY2 is a free surface that comes into
direct contact with the mold. This surface undergoes maximum deformations and so it is defined as
the master moving surface.
2.17.3.Time Marching Scheme
Since this problem is time-dependent, parameters such as flow rate, boundary conditions, or material
data are time-dependent. In such problems, the solution of the partial differential equations has to be
satisfied at a discrete set of times starting from an initial time. The solution of the equations is obtained
by specific integration methods known as predictor-corrector methods. The predictor method calculates
a first guess of the solution at a specific time step. This guess is then used by the corrector method to
compute the real solution at the time step considered. The data for the time marching scheme is
provided in this menu.
338

Chapter 3: Plug-Assisted Thermoforming of a Blister
3.1.Prerequisites
3.3.Preparation
3.5.Step 2:Model the Mold
3.6.Step 3:Model the Plug
3.7.Step 4:Definition of the Blister Sub-task
3.9.Step 6:Outputs
3.13.Summary
3.14.Appendix
3.1.Prerequisites
This tutorial simulates plug-assisted thermoforming for a blister. Figure 3.1: Plug-Assisted Thermoforming
of a Blister: Plug (Orange), Sheet (Blue), and Mold (Green) in the Initial Configuration (p. 340) shows a
sketch of the process in the initial configuration.
339

Figure 3.1: Plug-Assisted Thermoforming of a Blister: Plug (Orange), Sheet (Blue), and Mold (Green)
in the Initial Configuration
To reduce the computational run time, and utilizing the symmetric nature of the blister, only one quarter
of the blister/plug/mold is modeled, Figure 3.1: Plug-Assisted Thermoforming of a Blister: Plug (Orange),
Sheet (Blue), and Mold (Green) in the Initial Configuration (p. 340). From a geometric point of view, the
initial (1/4) film has the following dimensions:
• length = 15 mm
• width = 5 mm
• initial thickness = 0.35 mm
Dimensions are intentionally given in millimeters due to the small size of the object. The simulation will be
built around the system of units consisting of millimeters, grams and seconds.
340
Plug-Assisted Thermoforming of a Blister

The thickness compared to the length/width of the blister is rather small. This allows the use of the
membrane (shell) element, which is suited for the analysis of 3D blow molding and thermoforming
simulations. The use of the membrane element is presently restricted to time-dependant flows and is
combined with Lagrangian representation. In other words, each mesh node is a material point.
Subdomains and Boundary Sets (p. 341). As shown, a full 3D finite element is built for the mold, the plug
and the film. Only a surface mesh is required for the three subdomains, but the most important aspect
remains the proper description of the inner mold surfaces which will shape the blister.
The film has the following material properties:
• model: shell model, Gen. Newtonian isothermal
• viscosity = 105
⋅
• density = 10-3
g/mm3
• inertial terms taken into account
• initial thickness = 0.35 mm
Figure 3.2: Finite Element Mesh, Subdomains and Boundary Sets
341
Problem Description

As seen in Figure 3.2: Finite Element Mesh, Subdomains and Boundary Sets(p. 341), the mesh topology
involves three subdomains:
• Subdomain 1 = film
• Subdomain 2 = mold
• Subdomain 3 = plug
and four boundary sets:
• boundary 1: will be a fixed (clamped) boundary
• boundary 2: will be a fixed (clamped) boundary
• boundary 3: symmetry boundary condition with respect to the x-axis
• boundary 4: symmetry boundary condition with respect to the y-axis
The inflation pressure will be defined on the subdomain representing the film (Subdomain 1).
An important new concept is introduced in this tutorial: plug-assisted contact with a mold. The film
acquires the mold velocity then the plug guides the film into the mold. Once inside the mold, the film
is inflated according to a certain rate where it eventually comes into contact with the mold, finally ac-
quiring its shape.
3.3.Preparation
Note
7. Unzip the Plug-Thermo-Blister_R150.zip file you have downloaded to your working folder.
342

The mesh file plugblister.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering Blister-plug-assist as the name
of the project.
3. Import the mesh file (plugblister.msh).
3.5.Step 2: Model the Mold
In this step, define the task representing the mold.
Create a new task
• F.E.M. task
2. Define the molds.
Define molds
Create a new mold
b. Click Adiabatic mold.
343
Step 2:Model the Mold

c. Click OK to accept the default name, Mold 1.
Domain of the mold
b. Select Subdomain 3 and click Remove.
c. Click Upper level menu at the top of the Domain of the mold menu.
344

Contact conditions
Mold motion
a. Click Mold motion type : fixed mold.
Enter 1 as the New value, to impose a translation velocity, and click OK.
345

346

Enter 10 mm/s for the New value of velocity-z and click OK.
Figure 3.3: Ramp Function for Mold Velocity(p. 347) shows the ramp function you just defined.
Figure 3.3: Ramp Function for Mold Velocity
Click Upper level menu to return the Mold motion menu.
viii. Click Upper level menu two times to return to the Define molds menu.
347

3.6.Step 3: Model the Plug
In this step, define the task representing the plug.
1. Create the new mold.
Create a new mold
A panel opens, asking if you want to copy the data of an existing mold.
Click No.
a. Click Adiabatic mold.
b. Enter plug as the New value and click OK.
Domain of the mold
Contact conditions
4. Define the motion of the plug.
Mold motion
348

349
Step 3:Model the Plug

Enter -500 mm/s for the New value of velocity-z and click OK.
Select f(t) = Multi-ramp function.
v. Define the four pairs that define the multi-ramp function.
Click Define new pairs ( time, f(time) ).
Polydata asks for the points of the pair sequentially.
Enter 0.11 as the New value for time( 1) and click OK.
Retain the default, 0 as the New value for f(time)( 1) and click OK.
vi. Click Insert new pair, and in a similar manner, define the following three pairs: (0.12, 1),
(0.13, 1), and (0.14, 0).
Figure 3.4: Multi-Ramp Function for Plug Velocity(p. 351) shows the multi-ramp function you
just defined.
350

Figure 3.4: Multi-Ramp Function for Plug Velocity
Click Upper level menu three times to return the Mold motion menu.
viii. Click Upper level menu three times to return to the F.E.M. Task 1 menu.
3.7.Step 4: Definition of the Blister Sub-task
Create a sub-task
351
Step 4:Definition of the Blister Sub-task

b. Enter Blister as the New value and click OK.
c. Click Upper level menu button at the top of the Domain of the sub-task menu.
a. Retain the default settings for Boundary 1 and Boundary 2.
b. Select Zero wall velocity (vn=vs=0) along Boundary 3 and click Modify.
ii. Select normal direction along X axis.
c. Select Zero wall velocity (vn=vs=0) along Boundary 4 and click Modify.
d. Click Inflation pressure imposed at the bottom of the Flow boundary conditions menu.
352

Polydata directs you to the Time dependence of inflation pressure menu.
ii. Click Modify the value of a, and enter 0.14 as the New value.
iii. In a similar manner, set constants b, c, and d to 0, 0.15, and 1.0 respectively.
353

h. Click Upper level menu.
Click the EVOL button at the top of the Polydata menu to disable evolution inputs.
i. Click Upper level menu to return to the Blister menu.
4. Define the contact of the mold.
Define contacts
item highlighted.
ii. Select Mold 1 : Contact along Subdomain 2 and click Select.
Retain the default of 1e+09 and click OK.
i. Increase the size of the darts that will be used to display the orientation, to ensure that they
are visible.
Graphical window → Sizing Darts → Size up
ii. Rotate the view to an oblique angle and zoom in on the mold.
iii. Click Specify mold side / cavity side.
354

iv. Click No in the panel that opens, to specify that the darts are not pointing towards the mold
body.
v. Click Upper level menu to return to the Define contacts menu.
5. Define the contact of the plug.
Create a new contact problem
The Modification of a contact problem menu will open with the Select a contact wall menu item
highlighted.
a. Define the contact wall.
ii. Select plug : Contact along Subdomain 3 and click Select.
355

b. Activate contact release and specify the coefficients and accuracy.
i. Click Modify the adhesion force density.
Click Yes in the panel that asks if you want to activate contact release.
Enter 10 as the New value for adhesion force density.
ii. Click Modify the slipping coefficient.
iii. Click Modify the penalty coefficient.
iv. Click Modify the penetration accuracy.
c. Define the orientation of the plug.
i. Rotate the view and change the magnification so that you can see the plug.
356

iii. Click Yes in the panel that opens, to verify that the darts are pointing toward the plug body
(away from contact with the film).
iv. Click Upper level menu to return to the Define contacts menu.
d. Click Upper level menu to return to the Blister menu.
e. Click OK in the warning box that opens, saying that velocity prediction must be disabled.
357

6. Define the layers of the blister.
Define layers
Enter blister as the New value in the panel that opens and click OK.
The blister menu will open with the Material data menu item highlighted.
b. Specify the material data for the blister.
Material Data
v. Click Density.
358

ix. Select Inertia will be taken into account.
x. Click Upper level menu twice to return to the blister menu.
Initial thickness
i. Click Constant.
Retain the default of 0.0 s and click OK.
Enter 1e-05 s as the New value and click OK.
Retain the default of 0.01 and click OK.
9. Click Upper level menu to return to the Numerical Parameters menu.
10. Click Modify numerical parameters for iterations.
359
Step 5:Specify the Numerical Parameters

11. Click Modify the convergence test.
Enter 0.0001 as the New value.
It is recommended that you specify a convergence criterion of 0.0001 or lower when contact release is
activated.
3.9.Step 6: Outputs
Outputs
2. Modify the current system of units.
3. Specify the new system of units.
Set to metric_mm/g/s/mA+Celsius
Save and exit
After defining your model in Polydata, save the data file. In the next step, you will use the Polyflow solver to
calculate a solution for this data file.
1. Click Accept.
2. Click Continue.
This accepts the default names for the graphical output files (cfx.res) that are to be saved for post-
processing, and the Polyflow format results file (res).
360

361

3. Display contours of thickness in the fluid region (Subdomain 1).
b. In the box that opens, click OK to accept the default name (Contour 1) and display the details
view below the Outline tree.
362

c. Perform the following steps in the Geometry tab:
i. Select Subdomain_1_surf from the Locations drop-down list.
iii. Select User Specified from the Range drop-down list.
iv. Enter 0.1 mm for Min and 0.35 mm for Max.
v. Click Apply.
363

Figure 3.6: Contours of Thickness 1/4 Geometry
4. Show the contours of thickness on the full mold.
364

The details view of Default Transform will be displayed below the Outline tab.
b. Perform the following steps in the Definition tab of the details view.
i. Disable the Instancing Info From Domain option.
ii. Increase the Number of Graphical Instances to 2.
iii. Select Value from the Determine Angle From drop-down list in the Instance Definition
group box.
iv. Enter 180 for Angle.
v. Enable Apply Reflection, and select ZX Plane from the Method drop-down list.
vi. Retain the default value of 0.0 m for Y.
vii. Click Apply.
c. Rotate the view and change the magnification, as shown in Figure 3.7: Contours of Thickness on
the Whole Thermoformed Blister (p. 366).
365

Figure 3.7: Contours of Thickness on the Whole Thermoformed Blister
366

c. Click Apply.
367

Figure 3.8: Thickness of the Film at Time = 0.0001 s
d. Repeat steps 5. a.–c. for timesteps 40, 60, and 166.
368

369

370

371

dialog box.
3.13.Summary
This tutorial introduced the concept of a plug-assisted blow molding problem. The mold moved into
contact with the film, where a plug guided the film into the mold, and a constant pressure was applied
to the film. This blew the film into the mold where it assumed the shape of the mold.
You represented the film by a shell geometry under the valid assumption that the thickness of the film
was much smaller than the other two dimensions. Polyflow linearly interpolated the process vari-
372

ables—thickness, velocity and position. By reporting the individual time steps to CFD-Post you were
able to view the thickness of the product as a function of time.
3.14.Appendix
The appendix covers the following topics:
3.14.3.Remeshing
As seen, the subdomain that describes the fluid will eventually come in contact with the mold and the
plug. Besides its usual material parameters, it also receives some process parameters: inflation pressure
and the contact with the (moving) molds. In all forming applications (blow molding and thermoforming
for example), the definition of the contact is an important aspect, as it will eventually lead to the desired
shape. The contact involves a what and a how. The what describes the geometry of the film/sheet
and the mold surface it may get in contact with (contact problem). The how refers to other process
parameters such as a moving mold. In this case, a velocity (that is possibly time dependant) must be
specified for both the molds. In some cases, the material may slip along the contact wall, which can
also be taken into account.
Next to these operating attributes, some numerical parameters have to be specified. A geometrical al-
gorithm is applied for detecting the occurrence of contact, while a penalty formation is used for the
treatment of contact. A penalty coefficient makes sure that a geometrical contact is detected. It should
not be too small. A coefficient is also to be specified in the tangential direction. If the fluid sticks along
the wall, this tangential coefficient should preferably receive the same value as the penalty coefficient.
Two additional coefficients are also needed; a tolerance on penetration accuracy and an element
dilatation.
Presently, the penalty coefficient has been set to 109
, while the same value has been selected for the
coefficient along the tangential direction (slipping coefficient). The tolerance on penetration and element
dilatation equal 0.05 and 0.05 mm respectively.
low as 10-3
–10-6
.
In classical thermoforming applications, such residual velocity will not produce any significant numerical
penetration of the fluid film/sheet through the mold in view of the short times involved (physically, the
thermoforming process is very fast). However, some situations may involve longer time scales such as
in the glass industry.
formulation mainly establishes a balance between a force (for example, the inflation pressure, ) and
, and the residual velocity of the film/sheet upon contact. The other elements of the momentum
equation can be ignored for the present consideration. Assuming a typical time scale (for example,
373
Appendix

the simulation time), and a maximum penetration depth , a good penalty coefficient can be selected
as:
=

3.14.3.Remeshing
No remeshing needs to be specified for this case. In the context of the membrane element, a Lagrangian
representation is applied where all mesh nodes are considered material points.
374

Chapter 4: 3D Blow Molding of a Bottle
4.1.Prerequisites
4.2.Description
4.3.Preparation
4.5.Step 2:Model the Right Mold
4.6.Step 3:Model the Left Mold
4.7.Step 4:Definition of the Parison Sub-task
4.9.Step 6:Outputs
4.13.Summary
4.15.Appendix
4.1.Prerequisites
4.2.Description
This tutorial simulates a typical blow molding situation for a bottle. In the present case, it is assumed
that a cylindrical parison with uniform thickness distribution has been extruded. The present calculation
involves two major steps; parison pinch-off due to mold closing, and inflation. Figure 4.1: Blow Molding
Initial Configuration (p. 376) shows a sketch of the process in the initial configuration, before the pinch-
off and parison inflation.
375

Figure 4.1: Blow Molding Initial Configuration
From a geometric point of view, the initial parison has the following dimensions:
• height = 0.276 m
• radius = 0.0225 m
• initial thickness = 0.003 m
The thickness of the fluid parison is much smaller than the other two dimensions of the bottle, which
allows for the use of the membrane (shell) element, which is suited for the analysis of 3D blow molding
simulations. It is important to remember when preparing the surface mesh, that the mesh elements on
the mold should not be the same order of magnitude as the expected final local thickness. The use of
the membrane element is presently restricted to time-dependant flows and is combined with Lagrangian
representation. In other words, each mesh node is a material point.
Subdomains, and Boundary Sets (p. 377). As shown, a full 3D finite element is built for both the mold
and the parison. Only a surface mesh is needed for both the mold and the parison, but the most im-
portant aspect remains the proper description of the inner mold surfaces that will shape the bottle.
The parison has the following material properties in SI units:
• model: shell model, Gen. Newtonian isothermal
• viscosity = 104
⋅
• density = 900 kg/m3
• inertial terms taken into account
376
3D Blow Molding of a Bottle

Figure 4.2: Finite Element Mesh, Subdomains, and Boundary Sets
As seen in Figure 4.2: Finite Element Mesh, Subdomains, and Boundary Sets(p. 377), the mesh topology
involves three subdomains (MoldLeft, parison, and Moldright) and two boundary sets (TopEdge and
BottomEdge). The fluid parison is covered by the subdomain named parison while MoldLeft and
MoldRight will be defined as molds. Along boundary sets TopEdge and BottomEdge, a symmetry
boundary condition will be imposed. The inflation pressure will be defined on the subdomain repres-
enting the parison.
4.3.Preparation
Note
377
Preparation

7. Unzip the 3D-Blow-Molding-Bottle_R150.zip file you have downloaded to your working folder.
The mesh file bottle.msh can be found in the unzipped folder.
2. Save the ANSYS Workbench project using File → Save, entering instanet-PF-only as the name of
the project.
3. Import the mesh file (bottle.msh).
4.5.Step 2: Model the Right Mold
In this step, define the task representing the right half of the mold.
Create a new task
• F.E.M. task
2. Define the right mold.
Define molds
Create a new mold
378

Click Mold with constant and uniform temperature.
b. Enter Mold-Right and click OK.
Domain of the mold
a. Select MOLDLEFT and click Remove.
b. Select PARISON and click Remove.
379
Step 2:Model the Right Mold

Contact conditions
a. Select No contact along MOLDRIGHT and click Modify.
Mold motion
380

381
Step 2:Model the Right Mold

Enter 0.736842 m/s for the New value of velocity-z and click OK.
vi. In a similar manner, set the values for b, c, and d to -1.0, 0.1, and 0, respectively.
Figure 4.3: Ramp Function for Right Mold Velocity(p. 382) shows the ramp function you just
defined.
Figure 4.3: Ramp Function for Right Mold Velocity
Click Upper level menu to return the Mold motion menu.
382

viii. Click Upper level menu two times to return to the Define molds menu.
4.6.Step 3: Model the Left Mold
In this step, define the task representing the left half of the mold.
1. Create the new mold.
Create a new mold
A panel opens, asking if you want to copy the data of an existing mold.
Click No.
a. Click Mold with constant and uniform temperature.
b. Enter Mold-Left as the New value and click OK.
Domain of the mold
a. Select MOLDRIGHT and click Remove.
b. Select PARISON and click Remove.
Contact conditions
a. Select No contact along MOLDLEFT and click Modify.
383
Step 3:Model the Left Mold

4. Define the motion of the left mold.
Mold motion
384

Enter 0.736842 m/s for the New value of velocity-z and click OK.
Figure 4.4: Ramp Function for Left Mold Velocity(p. 386) shows the ramp function you just
defined.
385
Step 3:Model the Left Mold

Figure 4.4: Ramp Function for Left Mold Velocity
vii. Click Upper level menu to return the Mold motion menu.
d. Click the EVOL button at the top of the menu to disable evolution inputs.
e. Click Upper level menu three times to return to the F.E.M. Task 1 menu.
4.7.Step 4: Definition of the Parison Sub-task
Create a sub-task
386

b. Enter Parison as the New value and click OK.
a. Select MOLDLEFT and click Remove.
b. Select MOLDRIGHT and click Remove.
c. Click Upper level menu button at the top of the Domain of the sub-task menu.
a. Select Zero wall velocity (vn=vs=0) along BOTTOMEDGE and click Modify.
b. Select Zero wall velocity (vn=vs=0) along TOPEDGE and click Modify.
c. Click Inflation pressure imposed at the bottom of the Flow boundary conditions menu.
387
Step 4:Definition of the Parison Sub-task

Darts will be displayed in the Graphics Display window, to indicate the orientation of the pressure
on the parison.
d. Zoom in on the darts to view their orientation.
As shown in the figure that follows, the darts point into the center of the parison.
Enter -1e4 as the New value and click OK.
388

The pressure is negative due to the orientation of the darts.
h. Define the settings in the Time dependence of inflation pressure menu that opens.
ii. Click Modify the value of a, enter 0.1 as the New value, and click OK.
iii. In a similar manner, set the values for b, c, and d to 0, 0.2, and 1.0, respectively.
i. Click Upper level menu.
j. Click the EVOL button at the top of the Polydata menu to disable evolution inputs.
k. Click Upper level menu to return to the Parison menu.
4. Define the contact with the right mold.
Define contacts
item highlighted.
389

ii. Select Mold-Right : Contact along MOLDRIGHT and click Select.
i. Increase the size of the darts that will be used to display the orientation, to ensure that they
are visible.
Graphical window → Sizing Darts → Size up
ii. Zoom out so that the bottle-shaped cavity is visible.
iii. Click Specify mold side / cavity side.
390

iv. Click No in the panel that opens, to specify that the darts are not pointing towards the mold
body.
v. Click Upper level menu to return to the Define contacts menu.
5. Define the contact with the left mold.
Create a new contact problem
The Modification of a contact problem menu will open with the Select a contact wall menu item
highlighted.
a. Define the contact wall.
ii. Select Mold-Left : Contact along MOLDLEFT and click Select.
b. Specify the coefficients and accuracy.
391

c. Define the orientation of the mold.
i. Rotate the view slightly to display the bottle-shaped cavity from an oblique angle.
iii. Click No in the panel that opens, to specify that the darts are not pointing towards the mold
body.
392

iv. Click Upper level menu to return to the Define contacts menu.
d. Click Upper level menu to return to the Parison menu.
e. Click OK in the warning box that opens, to acknowledge that the velocity prediction must be dis-
abled.
6. Define the layers of the parison.
Define layers
In the panel that opens, enter parison as the New value.
The parison menu will open with the Material data menu item highlighted.
b. Specify the material data for the parison.
Material Data
393

v. Click Density.
Enter 900 kg/m3
as the New value and click OK.
ix. Select Inertia will be taken into account and click Upper level menu twice to return to the
parison menu.
Initial thickness
i. Click Constant.
Enter 0.003 m as the New value and click OK.
394

Retain the default of 0.01 and click OK.
Retain the default of 200 s and click OK.
4.9.Step 6: Outputs
Outputs
2. Confirm that Current system is set to metric_MKSA+Kelvin.
The Current system is shown at the top of the Change system of Units for specific outputs menu.
Save and exit
1. Click Accept.
2. Click Continue.
This accepts the default names for the graphical output files (cfx.res) that are to be saved for post-
processing, and the Polyflow format results file (res).
395
Step 8:Solution

2. Change the view in the Graphics Display window as shown in the figure that follows.
3. Display contours of thickness in the fluid region (PARISON).
396

b. In the panel that opens, click OK to accept the default name (Contour 1) and display the details
view below the Outline tree.
c. Specify the following settings in the Geometry tab:
i. Select PARISON_surf from the Locations drop-down list.
iii. Change Range to User Specified.
iv. Enter 0.0006 m for Min and 0.003 m for Max.
v. Click Apply.
d. Disable the Wireframe in the Outline tree tab, under User Locations and Plots.
This makes for a cleaner image by removing the Wireframe lines.
397

Figure 4.6: Contours of Thickness on the Parison
4. Display the parison with the mold.
a. Enable and double-click MOLDLEFT_surf in the Outline tree tab, under PFL at 2s.
398

b. Enter 0.7 for Transparency in the Render tab in the details view of MOLDLEFT_surf.
The contours of thickness on the parison would not be visible without increasing the transparency
of the mold.
c. Click Apply.
d. In a similar manner, display MOLDRIGHT_surf.
399

c. Click Apply.
400

Figure 4.7: Thickness of the Film at Time = 0.01 s
d. Repeat steps 5. a.–c. for timesteps 28, 58, and 81.
401

402

403

404

dialog box.
4.13.Summary
This tutorial introduced the concept of a parison blow molding problem. The two halves of the mold
moved into contact with the parison, where it became pinched, and a vacuum was applied to the par-
ison. This blew the parison into the mold where it assumed the shape of the mold, which was a bottle
in this case.
You represented the parison by a shell geometry under the valid assumption that the thickness of the
parison was much smaller than the other two dimensions (diameter and height). Polyflow linearly inter-
405
Summary

polated the process variables—thickness, velocity and position. By reporting the individual time steps
to CFD-Post you were able to view the thickness of the product as a function of time.
In many practical cases, the use of adaptive meshing based on contact, remeshing, or both may be
useful to selectively and automatically refine the mesh during the solution. To illustrate the effects of
such refinement, this tutorial has been run with contact adaptive meshing enabled and made available
as instanet-PF-adapt.wbpj in the 3D-Blow-Molding-Bottle_R150solution_files
folder you unzipped in Preparation (p. 278). The following settings were specified:
F.E.M. Task 1
• Numerical parameters
– Adaptive meshing
→ Activate adaptive meshing for contacts
• Enable all the local criteria
• Switch to calculated from angle and curvature
• Modify size_min = 0.002
• Modify tolerance = 0.001
• Modify size_max = 0.01
• Modify dist_crit = 0.005
→ Modify Nstep = 5
→ Modify Maxdiv = 1
For additional information on adaptive meshing, see Adaptive Meshing.
The results are shown in Figure 4.11: Effect of Adaption on Final Mesh and Thickness Variation(p. 407).
406

Figure 4.11: Effect of Adaption on Final Mesh and Thickness Variation
4.15.Appendix
The appendix contains the following topics:
4.15.3.Remeshing
4.15.4.Evolutions
As seen, the parison subdomain, which describes the fluid, will eventually come in contact with the
mold. Other than its material parameters, the parison also receives some process parameters: inflation
pressure and the contact with the (moving) molds. In all blow molding and related applications, the
definition of the contact is an important aspect as it will eventually lead to the desired shape. The
407
Appendix

contact involves a what and a how. The what describes the geometry of the parison and the mold
surface it may come in contact with (contact problem). The how refers to other process parameters,
such as a moving mold. In this case, a velocity (that is possibly time dependent) must be specified for
the mold. In some cases, the material may slip along the contact wall, which can also be taken into
account.
Along with these operating attributes, some numerical parameters must be specified. A geometrical
algorithm is applied for detecting the contact, while a penalty formation is used for the treatment of
the contact. A penalty coefficient ensures that a geometrical contact is detected. It should not be too
small. A coefficient is also specified in the tangential direction. If the fluid sticks along the wall, this
tangential coefficient should preferably receive the same value as the penalty coefficient. Two additional
coefficients are also needed; a tolerance on penetration accuracy and an element dilatation.
Presently, the penalty coefficient and the slipping coefficient (tangential direction) are both set to 109
.
The tolerance on penetration and element dilatation are equal to 0.001 and 0.002 m respectively.
low as 10-3
–10-6
.
In classical blow molding applications, such residual velocity will not produce any significant numerical
penetration of the fluid parison through the mold in view of the short times involved (physically, blow
molding process is very fast). However, some situations may involve longer time scales such as in the
glass industry.
formulation mainly establishes a balance between a force (for example: the inflation pressure, ) and
, and the residual velocity of the parison upon contact. The other variables of the momentum equation
can be omitted for the present problem. Considering a typical time scale, (for example, the simulation
time), and a maximum penetration depth that can be practically accepted, , a good penalty coefficient
can be selected as:
=

4.15.3.Remeshing
No remeshing needs to be specified for this case. In the context of the membrane element, a Lagrangian
representation is applied where all mesh nodes are considered material points.
4.15.4.Evolutions
The present case involves a mold motion followed by inflation.
For the mold motion, the x and y-components are zeros. The two mold halves move only in the z-dir-
ection at the same speed but in opposite directions. The two mold halves move at 0.736842 m/s in the
z-direction. To control the duration and the direction of the motion, a simple ramp function is applied
on the mold speed. The ramp function is multiplied by the z-velocity component to give each half of
the mold the proper speed in the appropriate direction.
408

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