ANSYS Polyflow Tutorial Guide

ANSYS Polyflow Tutorial Guide

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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. Creating a Fluid Flow Analysis System in ANSYS Workbench ................................................ 6 1.4.3. Preparing the Geometry in ANSYS DesignModeler ............................................................ 10 1.4.4. Meshing the Geometry in the ANSYS Meshing Application ................................................ 12 1.4.5. Setting Up the CFD Simulation in ANSYS Polydata ............................................................. 24 1.4.6. Solution ........................................................................................................................... 28 1.4.7. Postprocessing ................................................................................................................. 28 1.4.8. Exploring Additional Solutions ......................................................................................... 43 1.5. Summary .................................................................................................................................. 48 II. Extrusion ............................................................................................................................................... 49 1. 2.5D Axisymmetric Extrusion .......................................................................................................... 51 1.1. Introduction ............................................................................................................................. 51 1.2. Prerequisites ............................................................................................................................. 51 1.3. Problem Description ................................................................................................................. 51 1.4. Preparation ............................................................................................................................... 54 1.5. Setup and Solution ................................................................................................................... 54 1.5.1. Project and Mesh ............................................................................................................. 55 1.5.2. Define a Task .................................................................................................................... 57 1.5.3. Material Data ................................................................................................................... 59 1.5.4. Boundary Conditions ....................................................................................................... 61 1.5.5. Remeshing ....................................................................................................................... 66 1.5.6. Stream Function ............................................................................................................... 69 1.5.7. Outputs ........................................................................................................................... 70 1.5.8. Save and Exit Polydata ...................................................................................................... 71 1.5.9. Solution ........................................................................................................................... 72 1.5.10. Postprocessing ............................................................................................................... 73 1.6. Summary .................................................................................................................................. 84 2. Fluid Flow and Conjugate Heat Transfer ......................................................................................... 85 2.1. Introduction ............................................................................................................................. 85 2.2. Prerequisites ............................................................................................................................. 85 2.3. Problem Description ................................................................................................................. 85 2.4. Setup and Solution ................................................................................................................... 87 2.4.1. Preparation ...................................................................................................................... 87 2.4.2. Project and Mesh ............................................................................................................. 88 2.4.3. Create a Task for the Model ............................................................................................... 88 2.4.4. Fluid Sub-Task 1 ............................................................................................................... 89 2.4.5. Die Sub-Task .................................................................................................................... 97 2.4.6. Save and Exit Polydata .................................................................................................... 100 2.4.7. Solution ......................................................................................................................... 101 2.4.8. Postprocessing ............................................................................................................... 101 Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Tutorial Guide 2.5. Summary ................................................................................................................................ 110 3. Non-Isothermal Flow Through a Cooled Die ................................................................................. 111 3.1. Introduction ........................................................................................................................... 111 3.2. Prerequisites ........................................................................................................................... 111 3.3. Problem Description ............................................................................................................... 111 3.4. Setup and Solution ................................................................................................................. 114 3.4.1. Preparation .................................................................................................................... 114 3.4.2. Project and Mesh ........................................................................................................... 114 3.4.3. Create a Task for the Model ............................................................................................. 115 3.4.4. Fluid Sub-Task 1 ............................................................................................................. 115 3.4.5. Die Sub-Task .................................................................................................................. 126 3.4.6. Numerical Parameters .................................................................................................... 129 3.4.7. Outputs ......................................................................................................................... 129 3.4.8. Save and Exit Polydata .................................................................................................... 129 3.4.9. Solution ......................................................................................................................... 130 3.4.10. Postprocessing ............................................................................................................. 130 3.5. Summary ................................................................................................................................ 142 3.6. Appendix: Nonlinearity and Evolution ...................................................................................... 142 4. 3D Extrusion .................................................................................................................................. 143 4.1. Introduction ........................................................................................................................... 143 4.2. Prerequisites ........................................................................................................................... 143 4.3. Problem Description ............................................................................................................... 143 4.4. Preparation ............................................................................................................................. 145 4.5. Setup and Solution ................................................................................................................. 146 4.5.1. Project and Mesh ........................................................................................................... 146 4.5.2. Define a Task .................................................................................................................. 146 4.5.3. Material Data ................................................................................................................. 148 4.5.4. Boundary Conditions ...................................................................................................... 150 4.5.5. Remeshing ..................................................................................................................... 152 4.5.6. Save and Exit Polydata .................................................................................................... 155 4.5.7. Solution ......................................................................................................................... 156 4.5.8. Postprocessing ............................................................................................................... 156 4.6. Summary ................................................................................................................................ 170 5. Direct Extrusion ............................................................................................................................ 171 5.1. Introduction ........................................................................................................................... 171 5.2. Prerequisites ........................................................................................................................... 171 5.3. Problem Description ............................................................................................................... 171 5.4. Setup and Solution ................................................................................................................. 173 5.4.1. Preparation .................................................................................................................... 173 5.4.2. Project and Mesh ........................................................................................................... 174 5.4.3. Create a Task for the Model ............................................................................................. 174 5.4.4. Material Data ................................................................................................................. 175 5.4.5. Boundary Conditions ...................................................................................................... 176 5.4.6. Remeshing ..................................................................................................................... 178 5.4.7. Numerical Parameters .................................................................................................... 180 5.4.8. Outputs ......................................................................................................................... 181 5.4.9. Save and Exit Polydata .................................................................................................... 181 5.4.10. Solution ....................................................................................................................... 181 5.4.11. Postprocessing ............................................................................................................. 182 5.5. Summary ................................................................................................................................ 192 5.6. Appendix ................................................................................................................................ 192 5.6.1. Power Law ..................................................................................................................... 193

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Tutorial Guide 5.6.2. Optimesh Remeshing Technique .................................................................................... 193 5.6.3. Evolution Scheme .......................................................................................................... 193 5.6.4. IGES Output ................................................................................................................... 193 6. Inverse Extrusion ........................................................................................................................... 195 6.1. Introduction ........................................................................................................................... 195 6.2. Prerequisites ........................................................................................................................... 195 6.3. Problem Description ............................................................................................................... 195 6.4. Setup and Solution ................................................................................................................. 197 6.4.1. Preparation .................................................................................................................... 197 6.4.2. Project and Mesh ........................................................................................................... 198 6.4.3. Create a Task for the Model ............................................................................................. 198 6.4.4. Material Data ................................................................................................................. 199 6.4.5. Boundary Conditions ...................................................................................................... 200 6.4.6. Remeshing ..................................................................................................................... 203 6.4.7. Numerical Parameters .................................................................................................... 205 6.4.8. Outputs ......................................................................................................................... 206 6.4.9. Save and Exit Polydata .................................................................................................... 207 6.4.10. Solution ....................................................................................................................... 207 6.4.11. Postprocessing ............................................................................................................. 207 6.5. Summary ................................................................................................................................ 218 6.6. Appendix ................................................................................................................................ 219 6.6.1. Power Law ..................................................................................................................... 219 6.6.2. Evolution Scheme .......................................................................................................... 219 6.6.3. Remeshing Technique .................................................................................................... 220 6.6.4. Optimesh Remeshing Technique .................................................................................... 220 6.6.5. IGES Output ................................................................................................................... 220 7. Flow of Two Immiscible Fluids ....................................................................................................... 221 7.1. Introduction ........................................................................................................................... 221 7.2. Prerequisites ........................................................................................................................... 221 7.3. Problem Description ............................................................................................................... 221 7.4. Setup and Solution ................................................................................................................. 224 7.4.1. Preparation .................................................................................................................... 224 7.4.2. Project and Mesh ........................................................................................................... 224 7.4.3. Create a Task for the Model ............................................................................................. 225 7.4.4. Fluid 1 Sub-Task ............................................................................................................. 225 7.4.5. Fluid 2 Sub-Task ............................................................................................................. 232 7.4.6. Save and Exit Polydata .................................................................................................... 235 7.4.7. Solution ......................................................................................................................... 236 7.4.8. Postprocessing ............................................................................................................... 236 7.5. Summary ................................................................................................................................ 242 8. Flow of Two Immiscible Fluids by Species Method ....................................................................... 243 8.1. Introduction ........................................................................................................................... 243 8.2. Prerequisites ........................................................................................................................... 243 8.3. Problem Description ............................................................................................................... 243 8.4. Setup and Solution ................................................................................................................. 246 8.4.1. Preparation .................................................................................................................... 246 8.4.2. Project and Mesh ........................................................................................................... 247 8.4.3. Create a Task for the Model ............................................................................................. 247 8.4.4. Species and Species Transport Sub-task .......................................................................... 247 8.4.5. Fluids Sub-task ............................................................................................................... 252 8.4.6. Save and Exit Polydata .................................................................................................... 257 8.4.7. Solution ......................................................................................................................... 258 Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Tutorial Guide 8.4.8. Postprocessing ............................................................................................................... 258 8.5. Summary ................................................................................................................................ 265 III. Blow Molding ..................................................................................................................................... 267 1. 3D Thermoforming of a Blister ...................................................................................................... 269 1.1. Prerequisites ........................................................................................................................... 269 1.2. Problem Description ............................................................................................................... 269 1.3. Setup and Solution ................................................................................................................. 272 1.3.1. Preparation .................................................................................................................... 272 1.3.2. Project and Mesh ........................................................................................................... 273 1.3.3. Mold Sub-Task ................................................................................................................ 273 1.3.4. Film Sub-Task ................................................................................................................. 277 1.3.5. Postprocessing Sub-Tasks ............................................................................................... 283 1.3.6. Numerical Parameters .................................................................................................... 285 1.3.7. Outputs ......................................................................................................................... 286 1.3.8. Save and Exit Polydata .................................................................................................... 286 1.3.9. Solution ......................................................................................................................... 287 1.3.10. Postprocessing ............................................................................................................. 288 1.4. Summary ................................................................................................................................ 299 1.5. Further Improvements ............................................................................................................ 299 1.6. Appendix ................................................................................................................................ 300 1.6.1. Contact Boundary Conditions ......................................................................................... 300 1.6.2. Remark on the Penalty Coefficient .................................................................................. 301 1.6.3. Remeshing ..................................................................................................................... 301 2. 2D Axisymmetric Blow Molding .................................................................................................... 303 2.1. Introduction ........................................................................................................................... 303 2.2. Prerequisites ........................................................................................................................... 303 2.3. Problem Description ............................................................................................................... 304 2.4. Setup and Solution ................................................................................................................. 305 2.4.1. Preparation .................................................................................................................... 306 2.4.2. Project and Mesh ........................................................................................................... 306 2.4.3. Create a Task for the Model ............................................................................................. 306 2.4.4. Material Data ................................................................................................................. 309 2.4.5. Boundary Conditions ...................................................................................................... 311 2.4.6. Remeshing ..................................................................................................................... 314 2.4.7. Numerical Parameters .................................................................................................... 315 2.4.8. Outputs ......................................................................................................................... 317 2.4.9. Thickness Postprocessor ................................................................................................. 318 2.4.10. Save and Exit Polydata .................................................................................................. 319 2.4.11. Solution ....................................................................................................................... 319 2.4.12. Postprocessing ............................................................................................................. 319 2.5. Summary ................................................................................................................................ 331 2.6. Appendix ................................................................................................................................ 332 2.6.1. Remeshing Technique .................................................................................................... 332 2.6.2. Time Marching Scheme .................................................................................................. 332 3. Plug-Assisted Thermoforming of a Blister .................................................................................... 333 3.1. Prerequisites ........................................................................................................................... 333 3.2. Problem Description ............................................................................................................... 333 3.3. Setup and Solution ................................................................................................................. 336 3.3.1. Preparation .................................................................................................................... 336 3.3.2. Project and Mesh ........................................................................................................... 337 3.3.3. Mold Sub-Task ................................................................................................................ 337 3.3.4. Plug Sub-Task ................................................................................................................. 342

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Tutorial Guide 3.3.5. Blister Sub-Task .............................................................................................................. 346 3.3.6. Numerical Parameters .................................................................................................... 353 3.3.7. Outputs ......................................................................................................................... 354 3.3.8. Save and Exit Polydata .................................................................................................... 354 3.3.9. Solution ......................................................................................................................... 354 3.3.10. Postprocessing ............................................................................................................. 355 3.4. Summary ................................................................................................................................ 366 3.5. Appendix ................................................................................................................................ 366 3.5.1. Contact Boundary Conditions ......................................................................................... 366 3.5.2. Remark on the Penalty Coefficient .................................................................................. 366 3.5.3. Remeshing ..................................................................................................................... 367 4. 3D Blow Molding of a Bottle ......................................................................................................... 369 4.1. Prerequisites ........................................................................................................................... 369 4.2. Description ............................................................................................................................. 369 4.3. Setup and Solution ................................................................................................................. 371 4.3.1. Preparation .................................................................................................................... 371 4.3.2. Project and Mesh ........................................................................................................... 372 4.3.3. Right Mold ..................................................................................................................... 372 4.3.4. Left Mold ....................................................................................................................... 377 4.3.5. Parison Sub-Task ............................................................................................................ 380 4.3.6. Numerical Parameters .................................................................................................... 388 4.3.7. Outputs ......................................................................................................................... 389 4.3.8. Save and Exit Polydata .................................................................................................... 389 4.3.9. Solution ......................................................................................................................... 389 4.3.10. Postprocessing ............................................................................................................. 390 4.4. Summary ................................................................................................................................ 400 4.5. Further Improvements ............................................................................................................ 400 4.6. Appendix ................................................................................................................................ 401 4.6.1. Contact Boundary Conditions ......................................................................................... 401 4.6.2. Remark on the Penalty Coefficient .................................................................................. 402 4.6.3. Remeshing ..................................................................................................................... 402 4.6.4. Evolutions ...................................................................................................................... 402

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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. These manuals are all available on the ANSYS Customer Portal (http://support.ansys.com/documentation). • 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 instructions, commentary, and postprocessing of results. Tutorials for release 18.0 are available on the ANSYS Customer Portal. To access tutorials and their input files on the ANSYS Customer Portal, go to http://support.ansys.com/training. • 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 Polyflow Examples Manual provides overviews of solutions to a variety of problem types and is available on the ANSYS Customer Portal. To access documentation files on the ANSYS Customer Portal, go to http://support.ansys.com/documentation. • 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. For details on how to access the ANSYS Polyflow manuals, see the ANSYS Polyflow documentation section of the separate Polyflow User's Guide.

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Using This Manual 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. To use this feature, enter relevant text (error message, etc.) in the Knowledge Resources Search box and click the magnifying glass icon. These Knowledge Resources provide solutions and guidance on how to resolve installation and licensing issues quickly. NORTH AMERICA All ANSYS Products except Esterel, Apache and Reaction Design products Web: Go to the ANSYS Customer Portal (http://support.ansys.com) and select the appropriate option. Toll-Free Telephone: 1.800.711.7199 (Please have your Customer or Contact ID ready.) Support for University customers is provided only through the ANSYS Customer Portal. GERMANY ANSYS Mechanical Products Telephone: +49 (0) 8092 7005-55 (CADFEM) Email: [email protected] All ANSYS Products Web: Go to the ANSYS Customer Portal (http://support.ansys.com) and select the appropriate option. National Toll-Free Telephone: (Please have your Customer or Contact ID ready.) German language: 0800 181 8499 English language: 0800 181 1565 Austria: 0800 297 835 Switzerland: 0800 564 318 International Telephone: (Please have your Customer or Contact ID ready.) German language: +49 6151 152 9981 English language: +49 6151 152 9982 Email: [email protected] UNITED KINGDOM All ANSYS Products Web: Go to the ANSYS Customer Portal (http://support.ansys.com) and select the appropriate option. Telephone: Please have your Customer or Contact ID ready. UK: 0800 048 0462 Republic of Ireland: 1800 065 6642 Outside UK: +44 1235 420130 Email: [email protected] Support for University customers is provided only through the ANSYS Customer Portal. JAPAN CFX and Mechanical Products Telephone: +81-3-5324-7305 Email: x

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Using This Manual Web: Go to the ANSYS Customer Portal (http://support.ansys.com) and select the appropriate option. Spain: Toll-Free Telephone: 900 933 407 Toll Number: +34 9178 78350 (Please have your Customer or Contact ID ready.) Portugal: Toll-Free Telephone: 800 880 513 (Portugal) Email: [email protected], [email protected] Support for University customers is provided only through the ANSYS Customer Portal. ITALY All ANSYS Products Web: Go to the ANSYS Customer Portal (http://support.ansys.com) and select the appropriate option. Toll-Free Telephone: 800 789 531 Toll Number: +39 02 00621386 (Please have your Customer or Contact ID ready.) Email: [email protected] Support for University customers is provided only through the ANSYS Customer Portal. TAIWAN, REPUBLIC OF CHINA Telephone: 866 22725 5828 K0REA Telephone: 82-2-3441-5000 CHINA Toll-Free Telephone: 400 819 8999 Toll Number: +86 10 82861715

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

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. 143). 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 CFDPost. • 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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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

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Setup and Solution Figure 1.2: The Boundary Set for the Problem

1.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 1.4.1. Preparation 1.4.2. Creating a Fluid Flow Analysis System in ANSYS Workbench 1.4.3. Preparing the Geometry in ANSYS DesignModeler 1.4.4. Meshing the Geometry in the ANSYS Meshing Application 1.4.5. Setting Up the CFD Simulation in ANSYS Polydata 1.4.6. Solution 1.4.7. Postprocessing 1.4.8. Exploring Additional Solutions

1.4.1. 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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the ext3d-workbench_R180.zip link to download the input and solution files.

7.

Unzip the ext3d-workbench_R180.zip file you have downloaded to your working folder. The extracted files include the geometry file ext3d.x_t , the data file polyflow.dat , and a solution 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. Creating a Fluid Flow Analysis System in ANSYS Workbench 1.

From the Windows Start menu, select Start > All Programs > ANSYS 18.0 > Workbench 18.0 to start ANSYS Workbench. 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 message 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.

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Create a new fluid flow analysis system by double-clicking the Fluid Flow (Polyflow) option under Analysis Systems in the Toolbox.

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Setup and Solution 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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion Figure 1.4: ANSYS Workbench with a New ANSYS Polyflow-Based Fluid Flow Analysis System

Note The ANSYS Polyflow-based fluid flow analysis system 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 descriptions 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. • 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 Attention 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 regenerated. For example, after you launch ANSYS Meshing from the Mesh cell in a Fluid Flow (Polyflow)

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Setup and Solution analysis system that has a valid geometry, the Mesh cell appears as Update Required because the Mesh cell has all the data it requires to generate an ANSYS Polyflow mesh file, but the ANSYS Polyflow 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 finishes 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 Upto-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 ( and so the cell must be refreshed.

) indicates that the last attempt to refresh cell input data failed,

• Update Failed, Update Required ( ) indicates that the last attempt to update the cell and calculate output data failed, and so the cell must 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.

4.

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.

Save the project. a.

Select the Save option under the File menu in ANSYS Workbench. 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 supporting files for the project.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 5.

View the files generated by ANSYS Workbench, by enabling the Files option under the View menu. View → Files The Files view is 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 separate Polyflow in Workbench User's Guide and the ANSYS Workbench online help. To access documentation files on the ANSYS Customer Portal, go to http://support.ansys.com/documentation.

1.4.3. Preparing the Geometry in ANSYS DesignModeler In the following steps 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.

10

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....

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Setup and Solution 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 Meshing the Geometry in the ANSYS Meshing Application (p. 12).

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. Right-click the Geometry cell in the ext3d fluid flow analysis system, and select Edit Geometry in DesignModeler..., to launch the ANSYS DesignModeler application.

3.

Finish importing the geometry file by clicking Generate in the ANSYS DesignModeler toolbar. The geometry will be displayed in the Graphics window. 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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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. 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. 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 the following steps 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.

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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. 14), 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, view.

, to assist when rotating the

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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 Preference 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. 15). Ensure

d.

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is enabled in the ANSYS Meshing toolbar, for face selection.

Right-click and select the Create Named Selection option (from the menu that opens) to open the Selection Name dialog box.

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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 highlighted in green in Figure 1.10: The Zero Velocity Faces Selected (p. 16)), then create a selection named die wall in a manner similar to the previous steps. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion Figure 1.10: The Zero Velocity Faces Selected

g.

16

Hold down the Ctrl key, select the 2 faces that will represent the free surface boundary (as highlighted in green in Figure 1.11: The Free Surface Faces Selected (p. 17)), and create a selection named free surface in a manner similar to the previous steps.

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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. 17), by holding the center mouse button and moving your pointer in the geometry window. Figure 1.12: Rotated View

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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. 18)), 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.

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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. 19)), and create a selection named symmetry 2 in a manner similar to the previous steps.

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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. 20)), and create a selection named outlet in a manner similar to the previous steps.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion Figure 1.15: The Flow Exit Face Selected

3.

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Set the appropriate meshing parameters for the ANSYS Meshing application in the Details view.

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Setup and Solution

4.

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.

c.

Select Adaptive from the Size Function drop-down list.

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 automatically 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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

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.

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Setup and Solution 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).

6.

View the files generated by ANSYS Workbench, as displayed in the Project Schematic.

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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

1.4.5. Setting Up the CFD Simulation in ANSYS Polydata 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. 143). 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 polyflow.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 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.

2.

View the files generated by ANSYS Workbench, as displayed in the Project Schematic.

Note the addition of the data file (polyflow.dat) to the list of files. 3.

Start ANSYS Polydata. 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.

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Setup and Solution 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. 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 enter values for the velocity, 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. 5.

Close the panel and click the Menus tab at the bottom of the Polydata window.

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.

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25

ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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.

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.

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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.

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Setup and Solution j. 6.

Click Upper level menu four times to return to the main Polydata menu.

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

7.

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, respectively (which is consistent with the values used in setting up the data file).

d.

Click Upper level menu twice to return to the main Polydata menu.

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. 8.

View the files generated by ANSYS Workbench, as displayed in the Project Schematic.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion Note the addition of the template file (templates.upd) to the list of files.

1.4.6. Solution 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.

2.

View the files generated by ANSYS Workbench, as displayed in the Project Schematic.

Note the addition of the listing file (polyflow.lst), the ANSYS Polyflow results file (res), the output mesh file (res.msh), the CFD-Post file (cfx.res), and the automatically generated probe files (.prb) to the list of files. For more information about ANSYS Polyflow (and the files associated with it), see files written and read by ANSYSPolydata in the Polyflow User's Guide. To access documentation files on the ANSYS Customer Portal, go to http://support.ansys.com/documentation.

1.4.7. Postprocessing In the following steps 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.

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Setup and Solution 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. Figure 1.18: The Extrusion Geometry Loaded into ANSYS CFD-Post

2.

Obtain the view shown in Figure 1.19: Rotating the View (p. 29). 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.

),

Figure 1.19: Rotating the View

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29

ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 3.

Display contours of velocity magnitude on the boundaries (Figure 1.20: Contours of Velocity Magnitude (p. 32)). 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. 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.

30

Open the Location Selector dialog box by clicking the location editor button ( Locations drop-down list in the Geometry tab.

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) next to the

Setup and Solution

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).

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 crosssection. The transition between these two states can be seen in the first third of the extrudate.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion Figure 1.20: Contours of Velocity Magnitude

4.

Display contours of velocity in cross-sections (Figure 1.21: Velocity Profiles at cross-sections (p. 37)). a.

32

Disable Contour 1 under User Locations and Plots in the Outline tab of the Tree view.

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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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

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

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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 ( Locations drop-down list in the Geometry tab.

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) next to the

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

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 rearrangement is the source of the deformation of the extrudate.

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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 parameter 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.

i.

Enter maxvelocity for Name.

ii.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

38

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.

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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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

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 10-4m/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. 41).

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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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

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

8.

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View the files generated by ANSYS Workbench, as displayed in the Project Schematic.

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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. Exploring Additional Solutions At this point you have run the simulation with an initial inlet flow rate. In the following steps 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. 44)). 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 Parameter Set bar and selecting the Edit... option in the context menu that opens.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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 DP0 (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 DP0 (Current) design point (cell C3 ).

b.

Right-click the cell under P2 - maxvelocity for the DP0 (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.

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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 DP0 (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.

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion

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. 46)). Figure 1.25: The Chart of the Current Design Point

4.

Create more design points for a range of inlet flow rates. a.

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Enter 1E-5 for P1 - flow rate in the row beneath the DP0 (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.

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Setup and Solution 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 By default, Workbench only saves the calculated data for the design point in the row labeled Current. You can specify that the data generated for any other design points is saved within the project by enabling the Retain option in column D. After the design points are updated, you can then right-click a design point in the Table of Design Points and select Set as Current to access the data.

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. 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. 47)) 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

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ANSYS Polyflow in ANSYS Workbench Tutorial: 3D Extrusion 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.

8.

View the files generated by ANSYS Workbench, as displayed in the Project Schematic. 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 documentation.

1.5. 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 computational 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.

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Part II: Extrusion The following extrusion tutorials are available: 1. 2.5D Axisymmetric Extrusion (p. 51) 2. Fluid Flow and Conjugate Heat Transfer (p. 85) 3. Non-Isothermal Flow Through a Cooled Die (p. 111) 4. 3D Extrusion (p. 143) 5. Direct Extrusion (p. 171) 6. Inverse Extrusion (p. 195) 7. Flow of Two Immiscible Fluids (p. 221) 8. Flow of Two Immiscible Fluids by Species Method (p. 243)

Chapter 1: 2.5D Axisymmetric Extrusion This tutorial is divided into the following sections: 1.1. Introduction 1.2. Prerequisites 1.3. Problem Description 1.4. Preparation 1.5. Setup and Solution 1.6. 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 involves 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.

1.3. Problem Description The problem to be considered is shown schematically in Figure 1.1: Problem Schematic (p. 52). 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.

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2.5D Axisymmetric Extrusion 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. 53)

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Problem Description 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. 53), 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

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2.5D Axisymmetric Extrusion • 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the 25–Axi-Extrusion_R180.zip link to download the input and solution files.

7.

Unzip the 25-Axi-Extrusion_R180.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 18.0 > Workbench 18.0.

1.5. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 1.5.1. Project and Mesh 1.5.2. Define a Task 1.5.3. Material Data 1.5.4. Boundary Conditions 1.5.5. Remeshing 1.5.6. Stream Function 1.5.7. Outputs 1.5.8. Save and Exit Polydata 1.5.9. Solution 1.5.10. Postprocessing

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Setup and Solution

1.5.1. 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.

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-extrusion_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, hover over Import Mesh File… and click Browse....

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2.5D Axisymmetric Extrusion

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.

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Setup and Solution

1.5.2. Define a Task In the following steps you will first define a new task representing the 2.5D axisymmetric steady-state model. Then you will 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 information 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.

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2.5D Axisymmetric Extrusion 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 dialog box 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.

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Setup and Solution 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.

1.5.3. 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 1. Click Shear-rate dependence of viscosity.

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2.5D Axisymmetric Extrusion 2. Click Cross law. The viscosity is given by the Cross law: (1.1) where: = zero-shear-rate viscosity = 85000 = natural time = 0.2 = Cross law index = 0.3 = shear rate 3. Specify the value , referred to as “fac” in the graphical user interface (compare the equation at the top of the Cross law menu to Equation 1.1 (p. 60)). Modify fac

Enter 85000 [units: poise] as the New value and click OK. 4. Specify the value for , referred to as “tnat” in the graphical user interface. Modify tnat

Enter 0.2 [units: s] as the New value and click OK.

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Setup and Solution 5. Specify the value for

, referred to as “expom” in the graphical user interface.

Modify expom

Enter 0.3 as the New value and click OK. 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.

1.5.4. Boundary Conditions The following steps will show you how to 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. Flow boundary conditions

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2.5D Axisymmetric Extrusion

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 [units: cm3/s] 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 boundary condition requires that the computational domain be built in such a way that the basic

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Setup and Solution 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, = 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. a. Select Zero wall velocity (vn=vs=0) along BS_3 and click Modify. 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 appropriate. In situations involving pulling velocity or force or gravity, the corresponding boundary condition should be selected. a. Select Zero wall velocity (vn=vs=0) along BS_4 and click Modify. b. Click Normal and tangential forces imposed (fn, fs). Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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2.5D Axisymmetric Extrusion c. Accept the default value of 0 for the normal force d. Accept the default value of 0 for the tangential force

by clicking Upper level menu. 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). 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 = .

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Setup and Solution a. Select Zero wall velocity (vn=vs=0) along BS_6 and click Modify. 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 [units: cm/s] for the constant A by clicking OK.

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2.5D Axisymmetric Extrusion g. Enter 6.2832 [units: rad/s] as the New value for the constant B and click OK.

h. Accept the default value of 0 [units: rad/s] 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.

1.5.5. 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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Setup and Solution

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. b. Click Upper level menu. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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2.5D Axisymmetric Extrusion 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 SD_1 and click Modify. i.

Select Part of inlet section.

ii. Select Upper level menu. b. Specify the outlet for the system of spines. Select BS_4 and click Modify. i.

Select Part of outlet section.

ii. Select Upper level menu.

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Setup and Solution 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.

1.5.6. 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.

2. Enter 5 [units: cm] as the New value of X.

3. Retain the default value of 0 [units: cm] for Y.

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2.5D Axisymmetric Extrusion

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.

1.5.7. 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. c. Click Upper level menu twice.

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Setup and Solution

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.

1.5.8. Save and Exit Polydata Save and exit. 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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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2.5D Axisymmetric Extrusion 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 postprocessing, and for the Polyflow format results file ( res ).

1.5.9. Solution 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 dialog box, which displays the listing file. b. In the View listing file dialog box, 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 converged. See the Polyflow User's Guide for more information on convergence.

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Setup and Solution

1.5.10. 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. 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, hover over Predefined Camera in the context 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 zoom to an area. 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.

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2.5D Axisymmetric Extrusion

c. In the details view for Contour 1, specify the following settings under Geometry: i.

Next to Locations, click the ellipsis button ( (use Ctrl to select multiple items).

) on the right and select SD_1_surf and SD_2_surf

Click OK to close the Location Selector dialog box. ii. Select PRESSURE from the Variable drop-down list, or click the ellipsis button ( and select PRESSURE. iii. Click Apply.

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) on the right

Setup and Solution Figure 1.3: Contours of Static Pressure

d. Rotate about the Y axis to view a true cross-section of the results. i.

Double-click Default Transform in the Outline tab.

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2.5D Axisymmetric Extrusion

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. Increase Number of Graphical Instances to 2. iv. Select Y from the Axis drop-down list in the Axis Definition group box. v. Decrease the Number of Passages to 2 in the Instance Definition group box. vi. Retain the rest of the default settings. vii. Click Apply. 76

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Setup and Solution 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.

iii. Enter Polyflow Results for Text String in the Definition tab of the details view.

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2.5D Axisymmetric Extrusion iv. In the Location tab, select Top for Y Justification. v. Possibly check the Appearance tab. vi. Click Apply. Figure 1.4: Contours of Static Pressure after Applying Rotation

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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Setup and Solution

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 ( and select VELOCITIES.

) on the right

iii. Click Apply. iv. Define the attributes of vectors: in the Symbol tab, set Symbol to Arrow3D and Symbol Size to 3. v. Click Apply. e. Remove the annotation. i.

Deselect Text 1 in the Outline tab, under User locations and plots.

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2.5D Axisymmetric Extrusion Figure 1.5: Velocity Vectors

f.

Modify the view to better visualize the velocity vectors. i.

Rotate to the isometric view by clicking the cyan-blue dot in the axis triad (bottom right of the graphics window). This allows you to better visualize the magnitude of the velocity vectors.

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Setup and Solution

ii. Enable Normalize Symbols in the Symbol tab of the details view for Vector 1. This allows you to better visualize the direction of the velocity vectors.

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2.5D Axisymmetric Extrusion

The velocity vectors take all components of the velocity into account. Along the screw tip, the rotational component is important, leading to long vectors that are not in the xy plane. 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. g. Display the mesh. i.

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In the Outline tab, select SD_1_surf and double-click.

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Setup and Solution

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. h. Make the mesh lines more visible. i.

Double-click Vector 1 under User Locations and Plots in the Outline tab.

ii. Under the Symbol tab, deselect Normalize Symbols. iii. Click Apply. i.

Right-click a blank area in the graphics window, hover over Predefined Camera in the context menu, and select View from +Z.

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2.5D Axisymmetric Extrusion Figure 1.6: Velocity Vectors with Mesh

j.

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. Click and move the mouse slowly to the right-hand side.

1.6. 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 CFDPost to examine the flow behavior associated with the problem.

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Chapter 2: Fluid Flow and Conjugate Heat Transfer This tutorial is divided into the following sections: 2.1. Introduction 2.2. Prerequisites 2.3. Problem Description 2.4. Setup and Solution 2.5. 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 welldefined 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. In this tutorial you will learn how to: • 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. 51). Some steps in the set up procedure will not be shown explicitly.

2.3. Problem Description 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. 86), the melt enters the domain at a fixed temperature and a given flow rate of

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Fluid Flow and Conjugate Heat Transfer = 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 subtasks 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-˚C)

•

= thermal conductivity (0.5 W/m-˚C)

Viscous heating is taken into account. For the solid region, the thermal conductivity

is 35 W/m-˚C.

The boundary sets for the problem are shown in Figure 2.2: Boundaries and Sub-domains (p. 87), and the conditions at the boundaries of the domains are as follows: • boundary 1: flow inlet, 86

= 180°C,

= 0.6 × 10−6 m3/s

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Setup and Solution • 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. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 2.4.1. Preparation 2.4.2. Project and Mesh 2.4.3. Create a Task for the Model 2.4.4. Fluid Sub-Task 1 2.4.5. Die Sub-Task 2.4.6. Save and Exit Polydata 2.4.7. Solution 2.4.8. Postprocessing

2.4.1. Preparation To prepare for running this tutorial: 1.

Prepare a working folder for your simulation.

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Fluid Flow and Conjugate Heat Transfer 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Fluid-Solid_R180.zip link to download the input and solution files.

7.

Unzip the Fluid-Solid_R180.zip file you have downloaded to your working folder. The mesh file flusol.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

2.4.2. Project and Mesh 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.

2.4.3. Create a Task for the Model 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. 1.

Create a task for the model. Create a new task

2.

Select the following options: • F.E.M. task

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Setup and Solution • Steady-state problem(s) • 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. 3.

Click Accept the current setup. The Create a sub-task menu item is highlighted.

2.4.4. Fluid Sub-Task 1 In the following steps you will 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.

Note Be sure you are selecting the non-isothermal flow problem. A dialog box 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.

2.

Define the domain where the sub-task applies. 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, Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Fluid Flow and Conjugate Heat Transfer since SUBDOMAIN_1 represents the fluid (as shown in Figure 2.2: Boundaries and Sub-domains (p. 87)). Domain of the sub-task a.

Select SUBDOMAIN_2 and click Remove.

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.

90

Click Constant viscosity.

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Setup and Solution ii.

Specify the value for , referred to as “fac” in the graphical user interface. Modify fac Polydata prompts for the new value of .

b.

iii.

Enter 2500 [units: Pa•s] as the New value and click OK.

iv.

Click Upper level menu two times to continue the Material Data specification.

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.

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Fluid Flow and Conjugate Heat Transfer

c.

ii.

Click OK.

iii.

Click Upper level menu to continue the Material Data specification.

Click Density. In this problem, specify a constant value for the density. Modification of density

d.

i.

Enter 950 [units: kg/m3] as the New value and click OK.

ii.

Click Upper level menu to continue the Material Data specification.

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) where

is the temperature and

is a reference temperature.

In this problem, the thermal conductivity is assumed to be a constant for the fluid so only the constant coefficient is modified. Modify a

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Setup and Solution

e.

i.

Enter 0.5 [units: W/m-˚C] as the New value and click OK.

ii.

Click Upper level menu to continue with the Material Data specification.

Click Heat capacity per unit mass. As shown at the top of the menu, the heat capacity per unit mass is defined as a nonlinear function of temperature: (2.2) where

is the temperature and

is a reference temperature.

The temperature variation of differs with the nature of the polymer melts. In this problem, assumed to be constant, so only the constant coefficient is modified.

is

Modify a

f.

i.

Enter 2300 [units: J/kg-˚C] as the New value and click OK.

ii.

Click Upper level menu to continue with the Material Data specification.

Click Viscous (+ Wall friction) 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.

g.

i.

Select Viscous + wall friction heating will be taken into account.

ii.

Click Upper level menu to return to the Material Data specification.

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. Flow boundary conditions Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Fluid Flow and Conjugate Heat Transfer

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.

b.

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Retain the default condition Zero wall velocity (vn=vs=0) along SUBDOMAIN_2.

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.

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Setup and Solution v.

Enter 0.6e-06 [units: m3/s] 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. c.

Click Upper level menu.

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 appropriate. This condition imposes a zero normal force, (which includes a pressure term), and zero tangential velocity, .

d.

i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_5 and click Modify.

ii.

Click Outflow.

Retain the default, Axis of symmetry along BOUNDARY_6. For axisymmetric models, Polydata recognizes the axis of symmetry from the mesh file, and automatically 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

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Fluid Flow and Conjugate Heat Transfer

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.

b.

Set the conditions at the flow inlet (BOUNDARY_1). 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. Polydata prompts you for the new value of the constant temperature.

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Setup and Solution

c.

iv.

Enter 180 [units: ˚C] as the New value and click OK.

v.

Click Upper level menu to return to the Thermal boundary conditions menu.

Set the conditions at the flow outlet (BOUNDARY_5). A zero conductive heat flux is imposed along this boundary. i.

Select Temperature imposed along BOUNDARY_5 and click Modify.

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.

2.4.5. Die Sub-Task In the following steps you will 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.

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Fluid Flow and Conjugate Heat Transfer b.

Click No, since this sub-task has different parameters associated with it.

c.

Click Heat conduction problem. A small dialog box appears asking for the title of the problem.

d.

Enter solid as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies (SUBDOMAIN_2). Domain of the sub-task a.

Select SUBDOMAIN_1 and click Remove.

b.

Click Upper level menu. The Material data menu item is highlighted.

3.

Specify the material properties for the solid. Material Data In this problem, specify a constant value for the thermal conductivity . a.

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Click Thermal conductivity.

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Setup and Solution In this problem, thermal conductivity is assumed to be a constant, so only the constant coefficient is modified.

b. 4.

i.

Select Modify a.

ii.

Enter 35 [units: W/m-˚C] as the New value and click OK.

Click Upper level menu two times to return to the solid menu.

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. Thermal boundary conditions a.

Set the conditions at the intersection of SUBDOMAIN_1 and SUBDOMAIN_2. An interface condition is set at the intersection of the sub-domains.

b.

i.

Select Temperature imposed along SUBDOMAIN_1 and click Modify.

ii.

Click Interface.

iii.

Click Upper level menu to accept the default option for continuity of temperature and heat flux.

Set the conditions at the bottom boundary of the solid (BOUNDARY_2). A zero conductive heat flux is imposed along this boundary.

c.

i.

Select Temperature imposed along BOUNDARY_2 and click Modify.

ii.

Click Insulated boundary / symmetry.

Set the conditions at the outer boundary of the solid (BOUNDARY_3). A constant value for the temperature is imposed along this boundary.

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Fluid Flow and Conjugate Heat Transfer i.

Select Temperature imposed along BOUNDARY_3 and click Modify.

ii.

Click Temperature imposed.

iii.

Select Constant. Polydata prompts you for the new value of the constant temperature.

d.

iv.

Enter 100 [units: ˚C] as the New value and click OK.

v.

Click Upper level menu to return to the Thermal boundary conditions menu.

Set the conditions at the top boundary of the solid (BOUNDARY_4). A zero conductive heat flux is imposed along this boundary.

e.

i.

Select Temperature imposed along BOUNDARY_4 and click Modify.

ii.

Click Insulated boundary / symmetry.

Click Upper level menu three times to return to the top-level Polydata menu.

2.4.6. Save and Exit Polydata After defining your model in Polydata, save the data file. 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 Modify system of Units.

2.

Select Set to metric_MKSA+Celsius.

3.

Click Upper level menu twice. A dialog box appears, asking if you want to activate convergence strategy.

4.

100

Click No.

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Setup and Solution In this instance, the convergence strategy will not assist Polyflow in reaching a solution as the problem is quasi-linear. 5.

Click Accept. This confirms that the default Current field(s) are correct.

6.

Click Continue. This accepts the default names for graphical output files (cfx.res) that are to be saved for postprocessing, and for the Polyflow format results file (res).

2.4.7. Solution 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. 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.... Workbench opens the View listing file dialog box, 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.

2.4.8. Postprocessing 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.)

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 display the details view below the Outline tab.

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Fluid Flow and Conjugate Heat Transfer

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). Click OK to close the Location Selector dialog box.

ii.

Select PRESSURE from the Variable drop-down list, or click the ellipsis button ( right and select PRESSURE.

iii.

Click Apply.

) on the

Most of the pressure drop occurs in the upper part of the die where the cross-section is smallest (Figure 2.3: Pressure Contours (p. 103)). 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.

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Setup and Solution 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. 104)). It reaches a maximum value in the center of the thin tube.

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Fluid Flow and Conjugate Heat Transfer Figure 2.4: Velocity Distribution

5.

104

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

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.

button next to Locations.

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Setup and Solution Figure 2.5: Velocity Vectors

The flow is fully developed in the downstream part of the die (Figure 2.5: Velocity Vectors (p. 105)). 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 Vector 1 in the Outline tab under User Locations and plots.

b.

Double-click Contour 1 (in the Outline tab under User Locations and plots.

c.

In the details view for Contour 1, specify the following settings under Geometry: i.

Ensure SUBDOMAIN_1_surf and SUBDOMAIN_2_surf are selected for Locations, (click the ellipsis button

on the right to confirm).

Click OK to close the Location Selector dialog box. ii.

Select Temperature from the Variable drop-down list, or click the ellipsis button ( right and select Temperature.

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) on the

105

Fluid Flow and Conjugate Heat Transfer iii.

Click Apply.

Figure 2.6: Temperature Distribution (Celsius)

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Setup and Solution 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. 106)). 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.

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Fluid Flow and Conjugate Heat Transfer

iii.

Retain the default of Two Points for Method.

iv.

Enter 0, 0.006, and 0 for Point 1 and enter 0.008, 0.006, and 0 for Point 2.

Note You will need to ensure that your unit of length is set to meter in CFD-Post.

v. b.

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Click Apply.

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.

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Setup and Solution

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.

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Fluid Flow and Conjugate Heat Transfer 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.

2.5. 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).

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Chapter 3: Non-Isothermal Flow Through a Cooled Die This tutorial is divided into the following sections: 3.1. Introduction 3.2. Prerequisites 3.3. Problem Description 3.4. Setup and Solution 3.5. Summary 3.6. Appendix: Nonlinearity 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 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. 51). Some steps in the set up procedure will not be shown explicitly.

3.3. Problem Description 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. 112), the melt enters the domain at a fixed temperature, = 200°C and at a given flow rate, = 5 10−6m3/s. 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 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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

111

Non-Isothermal Flow Through a Cooled Die Figure 3.1: Problem Description

The high flow rate introduces strong nonlinearity 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 nonlinear 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: = density (950 kg/m3) = heat capacity per unit mass (2300 J/kg-°C) = thermal conductivity (0.5 W/m-°C) 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/m-°C.

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Problem Description The boundary sets for the problem are shown in Figure 3.2: Boundaries and Subdomains (p. 113), 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 2: symmetry axis • boundary 3: insulated, zero force • boundary 4: free surface with convective heat transfer to surroundings ( = 20 W/m2-°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)

α=

20°C)

Figure 3.2: Boundaries and Subdomains

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113

Non-Isothermal Flow Through a Cooled Die

3.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 3.4.1. Preparation 3.4.2. Project and Mesh 3.4.3. Create a Task for the Model 3.4.4. Fluid Sub-Task 1 3.4.5. Die Sub-Task 3.4.6. Numerical Parameters 3.4.7. Outputs 3.4.8. Save and Exit Polydata 3.4.9. Solution 3.4.10. Postprocessing

3.4.1. 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Non-Iso-Flow_R180.zip link to download the input and solution files.

7.

Unzip the Non-Iso-Flow_R180.zip file you have downloaded to your working folder. The mesh file die.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

3.4.2. Project and Mesh 1.

Create a Fluid Flow (Polyflow) analysis system by drag and drop in Workbench.

2.

Save the ANSYS Workbench project using File → Save, entering non-iso-flow as the name of the project.

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Setup and Solution 3.

Import the mesh file (die.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.

3.4.3. Create a Task for the Model 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. 1.

Create a task for the model. Create a new task Select the following options: • F.E.M. task • Evolution problem(s) • 2D axisymmetric geometry 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.

2.

Click Accept the current setup. The Create a sub-task menu item is highlighted.

3.4.4. Fluid Sub-Task 1 In the following steps you will 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.

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Non-Isothermal Flow Through a Cooled Die

b.

Enter fluid as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies. 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. Domain of the sub-task a.

116

Select SUBDOMAIN_3 and click Remove.

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Setup and Solution 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. The Material data menu item is highlighted.

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 (3.1) where

is the viscosity at zero shear rate,

index, and ii.

is the shear rate,

is the Bird-Carreau law

is the natural time.

Specify the value , referred to as “fac” in the graphical user interface (compare the equation at the top of the Bird-Carreau law menu to Equation 3.1 (p. 117)). Modify fac

Enter 5000 [units: Pa•s] as the New value and click OK. iii.

Specify the value , referred to as “tnat” in the graphical user interface.

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117

Non-Isothermal Flow Through a Cooled Die Modify tnat Enter 0.4 [units: s] as the New Value and click OK. iv.

Specify the value for

, referred to as “expo” in the graphical user interface.

Modify expo Enter 0.41 as the New Value and click OK. v.

Click Upper level menu. When you click Upper level menu , Polydata displays the following warning message:

For this tutorial, you will 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

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Setup and Solution

(3.2) where is the ratio of the activation energy to the thermodynamic constant and is a reference 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 Equation 3.2 (p. 119)). Modify alfa Enter 2300 [units: 1/°C] as the New Value and click OK.

iii.

Specify the value for

, referred to as “talfa” by the graphical user interface.

Modify talfa Enter 200 [units: °C] as the New Value and click OK. iv.

Specify the value for

, referred to as “t0” by the graphical user interface.

Modify t0 Enter -273 [units: °C] as the New Value and click OK. v. c.

Click Upper level menu two times to continue with the Material Data specification.

Click Density. Specify a constant value for density. Modification of density

d.

i.

Enter 950 [units: kg/m3] as the New value and click OK.

ii.

Click Upper level menu to continue with the Material Data specification.

Click Thermal conductivity. Thermal conductivity is defined as a nonlinear 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 [units: W/m-°C] as the New Value and click OK. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Non-Isothermal Flow Through a Cooled Die ii. e.

Click Upper level menu to continue with the Material Data specification.

Click Heat capacity per unit mass. The heat capacity per unit mass is defined as a nonlinear function of temperature: (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

f.

i.

Enter 2300 [units: J/kg-°C] as the New value and click OK.

ii.

Click Upper level menu to continue with the Material Data specification.

Click Viscous (+ Wall friction) 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 phenomenon must be taken into account.

g.

i.

Select Viscous + wall friction heating will be taken into account.

ii.

Click Upper level menu to return to the Material Data specification.

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 the fluid. Flow boundary conditions 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 default condition.

b.

=

= 0 along all boundaries. No action is required to accept the

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 EVOL at the top of the Polydata menu to enable the evolution inputs for the flow rate. For information on nonlinearity and evolution, see Appendix: Nonlinearity and Evolution (p. 142).

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Setup and Solution 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 [units: m3/s] as the New Value and click OK.

vi.

Select Automatic option. When the Automatic option is selected, Polydata automatically chooses the most appropriate method to compute the inflow condition.

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.

c.

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.

Retain the default condition, Axis of symmetry along BOUNDARY_2. For axisymmetric models, Polydata recognizes the axis of symmetry from the mesh file, and automatically 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.

e.

i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_3 and click Modify.

ii.

Click Normal and tangential forces imposed (fn, fs).

iii.

Click Upper level menu to accept the default value of 0 [units: Pa] for

.

iv.

Click Upper level menu to accept the default value of 0 [units: Pa] for

.

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 SUBDOMAIN_3 (see Figure 3.2: Boundaries and Subdomains (p. 113) ). i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_4 and click Modify. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Non-Isothermal Flow Through a Cooled Die 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. 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. 5.

Click Upper level menu to return to the fluid menu.

Specify the thermal boundary conditions for the fluid. For non-isothermal problems, specify either the temperature or the heat flux on each boundary set. Thermal boundary conditions

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Setup and Solution

a.

Set the conditions at the intersection of SUBDOMAIN_1 and SUBDOMAIN_3. 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. i.

Select Temperature imposed along SUBDOMAIN_3 and click Modify.

ii.

Click Interface.

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 nonzero 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). i.

Select Temperature imposed along BOUNDARY_1 and click Modify.

ii.

Click Temperature imposed.

iii.

Select Constant. Polydata prompts for the value of the temperature.

iv.

Enter 200 [units: °C] as the New Value and click OK.

v.

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Non-Isothermal Flow Through a Cooled Die c.

Retain the default condition, Axis of symmetry along BOUNDARY_2.

d.

Set the conditions at the flow exit (BOUNDARY_3).

e.

i.

Select Temperature imposed along BOUNDARY_3 and click Modify.

ii.

Click Insulated boundary/symmetry.

Set the conditions at the free surface (BOUNDARY_4) i.

Select Temperature imposed along BOUNDARY_4 and click Modify.

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 . Modify alpha Enter 20 [units: W/m2-°C] as the New value and click OK.

iv.

Specify the value of

.

Modify Talpha Enter 20 [units: °C] as the New value and click OK. v. f.

Click Upper level menu to return to the Thermal boundary conditions menu.

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 a.

Specify the region where the remeshing is to be performed (SUBDOMAIN_2). 1-st local remeshing

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Setup and Solution 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 encounters. 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.

ii.

Specify the inlet for the system of spines by selecting SUBDOMAIN_1 and clicking Modify. A.

Select Part of inlet section.

B.

Select Upper level menu.

Specify the outlet for the system of spines by selecting BOUNDARY_3 and clicking Modify. A.

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Non-Isothermal Flow Through a Cooled Die B. iii.

Select Upper level menu.

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. 7.

Click Upper level menu to return to the fluid menu.

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 temperature 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.

3.4.5. Die Sub-Task In the following steps you will 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.

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Polydata asks if you want to copy data from an existing sub-task.

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Setup and Solution b.

Click No, since this sub-task has different parameters associated with it.

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. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies (SUBDOMAIN_3). Domain of the sub-task a.

Select SUBDOMAIN_1 and click Remove.

b.

Select SUBDOMAIN_2 and click Remove.

c.

Click Upper level menu at the top of the Domain of the sub-task menu. The Material data menu item is highlighted.

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 [units: W/m-°C] 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.. Thermal boundary conditions a.

Set the conditions at the intersection of SUBDOMAIN_1 and SUBDOMAIN_3. Set an interface condition at the intersection of the subdomains.

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Non-Isothermal Flow Through a Cooled Die

b.

i.

Select Temperature imposed along SUBDOMAIN_1 and click Modify.

ii.

Click Interface.

iii.

Click Upper level menu to accept the default option for continuity of temperature and heat flux.

Set the conditions on the outer boundary of the die (BOUNDARY_5). i.

Select Temperature imposed along BOUNDARY_5 and click Modify.

ii.

Click Flux density imposed. Take only the heat convection into account: see Equation 3.5 (p. 124) .

iii.

Specify the value of . Modifiy alpha Enter 20 [units: W/m2-°C] as the New Value and click OK.

iv.

Specify the value of

.

Modifiy Talpha Enter 20 [units: °C] as the New Value and click OK. v. c.

Click Upper level menu to return to the Thermal boundary conditions menu.

Set the conditions at the inner boundary of the die (BOUNDARY_6). i.

Select Temperature imposed along BOUNDARY_6 and click Modify.

ii.

Select Flux density imposed.

iii.

Specify the value of . Modify alpha Enter 20 [units: W/m2-°C] as the New value and click OK.

iv.

Specify the value of

.

Modifiy Talpha Enter 20 [units: °C] as the New Value and click OK. v.

5.

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Click Upper level menu to return to the Thermal boundary conditions menu.

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Setup and Solution

3.4.6. 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 Enter 0.01 as the New value and click OK. b.

Define the starting solution for the iterative scheme in the calculation of the inflow condition. Modify the initial value of delta-S Retain the default of 0.01 by clicking OK.

2.

Click Upper level menu three times to return to the top-level Polydata menu.

3.4.7. Outputs 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

2.

Click Upper level menu three times to return to the top-level Polydata menu.

3.4.8. Save and Exit Polydata Save and exit A panel appears, asking if you want to activate convergence strategy.

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Non-Isothermal Flow Through a Cooled Die

Click No, as you have already defined an evolution strategy on the flow rate. 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 postprocessing, and for the Polyflow format results file (res).

3.4.9. Solution 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. 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). Ten CFD-Post files are created, corresponding to the ten evolution steps in the problem.

2.

Check for convergence in the listing file. 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.

3.4.10. Postprocessing 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. In the graphical window, right-click, and select the option Predefined Camera.

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Setup and Solution

3.

a.

Right-click in the graphical window and select View from +Z under Predefined Camera.

b.

To remove the ruler right-click in the graphical window, select Viewer Options, and disable Ruler Visibility.

Display contours of pressure in the fluid region (SUBDOMAIN_1 and SUBDOMAIN_2). a.

Click the Insert menu and select Contour or click the

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.

button.

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).

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Click OK to close the Location Selector dialog box.

132

ii.

Select PRESSURE from the Variable drop-down list, or click the ellipsis button ( right and select PRESSURE.

iii.

Click Apply.

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) on the

Setup and Solution 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.

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133

Non-Isothermal Flow Through a Cooled Die 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.

134

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

c.

Click OK to accept the default name (Vector 1) and open the details view below the Outline tab.

button.

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Setup and Solution

d.

Perform the following steps in the details view of Vector 1: i.

In the Geometry tab, click the dialog box.

button next to Locations to open the Location Selector

ii.

Select SUBDOMAIN_1_surf and SUBDOMAIN_2_surf (use Ctrl to select multiple items). Click OK to close the Location Selector dialog box.

iii.

In the Symbol tab, select Arrow3D and retain the default Symbol Size of 1.0.

iv.

Click Apply.

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135

Non-Isothermal Flow Through a Cooled Die Figure 3.5: Velocity Vectors

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. 136)). Also, the important velocity re-arrangement takes place at the die exit. This leads to the swelling of the extrudate. 6.

136

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.

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Setup and Solution

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). Click OK to close the Location Selector dialog box.

ii.

Select TEMPERATURE from the Variable drop-down list.

iii.

Click Apply.

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137

Non-Isothermal Flow Through a Cooled Die Figure 3.6: Temperature Profile

138

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Setup and Solution Figure 3.7: Temperature Profile Near the Die Exit

Figure 3.7: Temperature Profile Near the Die Exit (p. 139) 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). i.

Select Line from the Location menu (

).

ii.

Click OK to accept the default name (Line 1) and display the details view below the Outline tab.

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Non-Isothermal Flow Through a Cooled Die

c.

140

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.

Create a plot. i.

Click the chart button

.

ii.

Click OK to accept the default name (Chart 1) and display the details view below the Outline tab.

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Setup and Solution

iii.

In the General tab of the details view, ensure XY is selected 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.

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. 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.

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141

Non-Isothermal Flow Through a Cooled Die Figure 3.8: Temperature Profile Across the Die

3.5. 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.

3.6. Appendix: Nonlinearity and Evolution The kinematic equation introduces nonlinear terms into the problem that might lead to convergence difficulties. In Polyflow, an evolution scheme is available to solve such highly nonlinear problems. The calculation is started with a reduced value of the parameter(s) causing the nonlinearity. Starting from the first solution, Polyflow increments the parameter(s) causing the nonlinearity 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 .

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Chapter 4: 3D Extrusion This tutorial is divided into the following sections: 4.1. Introduction 4.2. Prerequisites 4.3. Problem Description 4.4. Preparation 4.5. Setup and Solution 4.6. 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. In this tutorial you will learn how to: • Create a sub-task to define a 3D extrusion problem. • Set material properties and boundary conditions for a 3D extrusion problem. • Select a remeshing method.

4.2. 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. 51). Some steps in the setup procedure will not be shown explicitly.

4.3. 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. The melt enters the die as shown in Figure 4.1: Problem Description (p. 144) at a flow rate of

= 10

3

cm /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 any further. It is assumed that subdomain 2 is long enough to account for all the deformation of the extrudate.

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3D Extrusion Figure 4.1: 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 4.1: Problem Description (p. 144)) 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. 145), 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 4: symmetry plane • boundary 5: free surface • boundary 6: flow exit

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Preparation Figure 4.2: Boundary Sets for the Problem

4.4. 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the 3D-Extrusion_R180.zip link to download the input and solution files.

7.

Unzip the 3D-Extrusion_R180.zip file you have downloaded to your working folder. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

145

3D Extrusion The mesh file ext3d.msh can be found in the unzipped folder. 8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

4.5. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 4.5.1. Project and Mesh 4.5.2. Define a Task 4.5.3. Material Data 4.5.4. Boundary Conditions 4.5.5. Remeshing 4.5.6. Save and Exit Polydata 4.5.7. Solution 4.5.8. Postprocessing

4.5.1. Project and Mesh 1.

Create a Fluid Flow (Polyflow) analysis system by drag and drop in Workbench.

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.

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.

4.5.2. Define a Task Define a new task representing the 3D 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.

Retain the following (default) options: • F.E.M. task • Steady-state problem(s) 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 steadystate condition is assumed for the problem.

b.

Click Accept the current setup. The Create a sub-task menu item is highlighted.

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Setup and Solution 2.

Create a sub-task for the isothermal flow. Create a sub-task a.

Select Generalized Newtonian isothermal flow problem. A dialog box appears asking for the title of the problem.

b.

Enter 3D die swell as the New value and click OK. The Domain of the sub-task menu item is highlighted.

3.

Define the domain where the sub-task applies. 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. Domain of the sub-task

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3D Extrusion

Accept the default selection of both subdomains (SUBDOMAIN_1 and SUBDOMAIN_2) by clicking Upper level menu. The Material data menu item is highlighted.

4.5.3. Material Data 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. For this model you will only define the viscosity of the material. Material Data 1.

Click Shear-rate dependence of viscosity.

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 poise = natural time = 0.2 s = Cross law index = 0.3

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Setup and Solution = shear rate 3.

Specify the value , referred to as “fac” in the graphical user interface (compare the equation at the top of the Cross law menu to Equation 4.1 (p. 148)). Modify fac

Enter 85000 [units: poise] as the New value and click OK. 4.

Specify the value for , referred to as “tnat” in the graphical user interface. Modify tnat

Enter 0.2 [units: s] as the New value and click OK. 5.

Specify the value for

, referred to as “expom” in the graphical user interface.

Modify expom

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3D Extrusion

Enter 0.3 as the New value and click OK. 6.

Select Upper level menu three times to return to the 3D die swell menu. The Flow boundary conditions menu item is highlighted.

4.5.4. Boundary Conditions In the following steps you will 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. Flow boundary conditions

1.

150

Set the conditions at the flow inlet (BOUNDARY_1). a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_1 and click Modify.

b.

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Setup and Solution c.

Retain the default settings, Automatic and Volumetric flow rate.

d.

Click Modify volumetric flow rate.

Enter 10 [units: cm3/s] as the New Value and click OK. When the Automatic option is selected, Polydata automatically chooses the most appropriate method to compute the inflow condition. e. 2.

Click Upper level menu.

Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY_2 at the wall of SUBDOMAIN_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 condition because the liquid is assumed to adhere to the wall, and hence, has no velocity relative to the wall. By default, Polydata imposes condition.

3.

=

= 0 along all boundaries. No action is required to accept the default

Set the conditions at the first symmetry plane (BOUNDARY_3). In 2D axisymmetric problems, Polydata automatically identifies the axis of symmetry, 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.

4.

a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_3 and click Modify.

b.

Click Plane of symmetry (fs=0, vn=0).

Set the conditions at the second symmetry plane (BOUNDARY_4). a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_4 and click Modify.

b.

Click Plane of symmetry (fs=0, vn=0).

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3D Extrusion 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, . 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 Figure 4.2: Boundary Sets for the Problem (p. 145)).

6.

a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_5 and click Modify.

b.

Click Free surface.

c.

Click Boundary conditions on the moving surface.

d.

Select No condition along BOUNDARY_2 and click Modify.

e.

Select Position imposed.

f.

Click Upper level menu.

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.

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 externally applied stress at the exit, so the condition of zero normal and tangential forces is selected. a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_6 and click Modify.

b.

Click Normal and tangential forces imposed (fn, fs).

c.

Accept the default value of 0 for the normal force,

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.

, by clicking Upper level menu. , by clicking Upper level menu.

4.5.5. Remeshing This model involves a free surface, whose shape is unknown a priori, which will be calculated together with the flow equations. A portion of the mesh is affected by the relocation of this boundary, so a remeshing technique is applied on this part of the mesh. The free surface is entirely contained within subdomain 2, therefore only subdomain 2 is affected by the relocation of the free surface. Global remeshing 1.

Specify the region where the remeshing is to be performed (SUBDOMAIN_2). In general, only one local remeshing is required for direct extrusion simulations. It becomes necessary to define multiple local remeshings for inverse extrusion simulations. A single local remeshing is sufficient for this case.

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Setup and Solution 1–st local remeshing a.

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.

b. 2.

Click Upper level menu.

Define the parameters for the remeshing method. 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, 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 SUBDOMAIN_1 and clicking Modify. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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3D Extrusion

b.

154

i.

Select Part of inlet section.

ii.

Select Upper level menu.

Specify the final plane for the optimesh remeshing technique, by selecting BOUNDARY_6 and clicking Modify.

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Setup and Solution

c.

i.

Select Part of outlet section.

ii.

Select Upper level menu.

Click Upper level menu. Polydata asks if you want to change from the surface kinematic condition to the line kinematic condition.

d.

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.

e.

Click Upper level menu three times. The top-level Polydata menu is displayed.

4.5.6. Save and Exit Polydata 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.

Specify the system of units for the simulation. a.

Click Modify system of units.

b.

Select Set to metric cm/g/s/A+Celsius

c.

Click Upper level menu twice.

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3D Extrusion

2.

Click Accept. This confirms that the default Current field(s) are correct.

3.

Click Continue. This accepts the default names for graphical output files (cfx.res) that are to be saved for postprocessing, and for the Polyflow format results file (res).

4.5.7. Solution 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. 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.... Workbench opens the View listing file dialog box, 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.

4.5.8. Postprocessing 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.

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Setup and Solution 2.

Display the velocity distribution on the boundaries. a.

Click the Insert menu and select Contour or click the

button.

b.

Click OK to accept the default name (Contour 1) and display the details view below the Outline 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. 158), 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.

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157

3D Extrusion Figure 4.3: Contours of Velocity Magnitude

3.

Display contours of velocity in cross-sections. a.

158

Deselect Contour 1 in the Outline tree tab under User Locations and Plots.

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Setup and Solution

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.

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3D Extrusion iii.

In the Geometry tab of the details view of Plane 1, ensure XY Plane is selected 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

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: i.

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In the Geometry tab, click the

button.

button next to Locations.

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Setup and Solution

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. 162)). 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 developed, but it is not yet flat either. The velocity rearrangement is the source of the deformation of the extrudate.

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3D Extrusion Figure 4.4: Velocity Profiles at Cross-Sections

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.

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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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Setup and Solution

iii.

In the Geometry tab of the details view, select Boundary Intersection from the Method dropdown list.

iv.

Click next to Boundary List and select SUBDOMAIN_1_BOUNDARY_2, SUBDOMAIN_1_BOUNDARY_3, SUBDOMAIN_1_BOUNDARY_4 (use Shift for multiple selection). Click OK to close the Location Selector dialog box.

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. i.

Select Polyline from the Location drop-down menu (

).

ii.

Click OK to accept the default name (Polyline 2) and display the details view below the Outline tab.

iii.

In the Geometry tab of the details view, select Boundary Intersection from the Method dropdown list.

iv.

Click next to Boundary List and select SUBDOMAIN_2_BOUNDARY_3, SUBDOMAIN_2_BOUNDARY_4, SUBDOMAIN_2_BOUNDARY_5 (use Shift for multiple selection).

v.

Select SUBDOMAIN_2_BOUNDARY_6 from the Intersect With drop-down list.

vi.

Click Apply.

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3D Extrusion d.

On the axis triad in the graphics window click +Z to view from Z-direction. 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. 164)) is only due to reorganization of the velocity profile at the die exit. Fluid from the high-speed region moves to the 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.

164

i.

Select Line from the Location drop-down menu (

).

ii.

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Setup and Solution

b.

iii.

Enter 0, 0.1, 0.1 for Point 1 and 0.1, 0, 0.1 for Point 2.

iv.

Click Apply.

Create a plot. i.

Click the chart button

.

ii.

Click OK to accept the default name (Chart 1) and display the details view below the Outline tab.

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3D Extrusion

iii.

In the General tab of the details view, ensure XY is selected for 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).

v.

In the X Axis tab, select X from the Variable drop-down list.

vi.

In the Y Axis tab, select VELOCITIES from the Variable drop-down list.

vii. Click Apply.

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Setup and Solution 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. 167) 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.

b.

Define the line of the plot with the points (0.08, 0.02, 0.00) and (0.08, 0.02, 0.50). i.

Select Line from the Location drop-down menu (

).

ii.

Click OK to accept the default name (Line 2) and display the details view below the Outline tab.

iii.

Enter 0.08, 0.02, 0 for Point 1 and 0.08, 0.02, 0.5 for Point 2.

iv.

Click Apply.

Create a plot. i.

Click the chart button

.

ii.

Click OK to accept the default name (Chart 2) and display the details view below the Outline tab.

iii.

In the General tab of the details view, ensure XY is selected for Type, and disable Display Title.

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3D Extrusion iv.

In the Data Series tab, select Line 2 from the Locations drop-down list for Series 1.

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.

168

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.

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Setup and Solution 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. 170) 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. 168) and Figure 4.8: Y-Velocities Along a Line Close to the Center of the Die (p. 169) 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.

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3D Extrusion Figure 4.9: Velocities Along a Line Close to the Center of the Die

4.6. 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.

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Chapter 5: Direct Extrusion This tutorial is divided into the following sections: 5.1. Introduction 5.2. Prerequisites 5.3. Problem Description 5.4. Setup and Solution 5.5. Summary 5.6. Appendix

5.1. Introduction This tutorial is similar to the 3D extrusion problem solved in 3D Extrusion (p. 143), 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 nonlinear 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. In this tutorial you will learn how to: • Define an evolution problem. • 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 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. 51). Some steps in the set up procedure will not be shown explicitly.

5.3. Problem Description 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 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. 172) at a flow rate = 10 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.

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171

Direct Extrusion Figure 5.1: 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 5.1: Problem Description (p. 172)) 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. 173), and the conditions at the boundaries of the domains are: • boundary 1: flow inlet, volumetric flow rate

= 10 cm3/s

• boundary 2: symmetry plane • boundary 3: symmetry plane • boundary 4: zero velocity • boundary 5: free surface • boundary 6: flow exit

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Setup and Solution Figure 5.2: Boundary Set for the Problem

5.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 5.4.1. Preparation 5.4.2. Project and Mesh 5.4.3. Create a Task for the Model 5.4.4. Material Data 5.4.5. Boundary Conditions 5.4.6. Remeshing 5.4.7. Numerical Parameters 5.4.8. Outputs 5.4.9. Save and Exit Polydata 5.4.10. Solution 5.4.11. Postprocessing

5.4.1. Preparation To prepare for running this tutorial: 1.

Prepare a working folder for your simulation.

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Direct Extrusion 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Direct-Extrusion_R180.zip link to download the input and solution files.

7.

Unzip the Direct-Extrusion_R180.zip file you have downloaded to your working folder. The mesh file dirext.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

5.4.2. Project and Mesh 1.

Create a Fluid Flow - Extrusion (Polyflow) analysis system by drag and drop in Workbench.

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).

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.

5.4.3. Create a Task for the Model In the following steps you will define a new task representing the evolution model. Then, you will 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

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Setup and Solution • Evolution problem(s) The complex geometry associated with the free surface of the extrudate introduces nonlinear terms into the kinematic condition equation used to find its location. An evolution scheme is used to handle the nonlinear problem. b.

Click Accept the current setup. The Create a sub-task menu item is highlighted.

2.

Create a sub-task for the isothermal flow. Create a sub-task a.

Select Generalized Newtonian isothermal flow problem. A dialog box appears asking for the title of the problem.

b.

Enter Direct extrusion as the New value and click OK. The Domain of the sub-task menu item is highlighted.

3.

Define the domain where the sub-task applies. 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. Domain of the sub-task Accept the default selection of both subdomains by clicking Upper level menu. The Material data menu item is highlighted.

5.4.4. Material Data Polydata indicates the material properties that are relevant for your sub-task by graying out 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. Material Data 1.

Click Shear-rate dependence of viscosity.

2.

Click Power law. The viscosity in this tutorial is given by the power law. For information on power law, see Appendix (p. 192) .

3.

Specify the value for , referred to as “fac” in the graphical user interface (compare the equation at the top of the Power law menu to the equation shown in the Appendix (p. 192)).

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175

Direct Extrusion Modify fac

Enter 3e+05 [units: poise] as the New value and click OK. 4.

Retain the default value for , referred to as “tnat” in the graphical user interface. Modify tnat Click OK to retain the default value of 1 [units: s].

5.

Specify the value for , referred to as “expo” in the graphical user interface. Modify expo

Enter 0.75 as the New value and click OK. 6.

Click Upper level menu three times to return to the Direct extrusion menu. The Flow boundary conditions menu item is highlighted.

5.4.5. Boundary Conditions In the following steps you will 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. Flow boundary conditions 1.

176

Set the conditions at the flow inlet (BOUNDARY_1). Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Setup and Solution a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_1 and click Modify.

b.

Click Inflow.

c.

Ensure Volumetric flow rate is selected and click Modify volumetric flow rate. Polydata prompts you for the volumetric flow rate.

d.

Enter 10 [units: cm3/s] as the New value and click OK.

e.

Ensure Automatic is selected and click Upper level menu. When the Automatic option is selected, Polydata chooses the most appropriate method to compute the inflow condition.

2.

Set the conditions at the first symmetry plane (BOUNDARY_2). 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.

3.

4.

a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_2 and click Modify.

b.

Click Plane of symmetry (fs=0, vn=0).

Set the conditions at the second symmetry plane (BOUNDARY_3). a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_3 and click Modify.

b.

Click Plane of symmetry (fs=0, vn=0).

Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY_4 at the wall of SUBDOMAIN_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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Direct Extrusion By default, Polydata imposes condition. 5.

=

= 0 along all boundaries. No action is required to accept the default

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, = 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 Figure 5.2: Boundary Set for the Problem (p. 173)).

6.

a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_5 and click Modify.

b.

Click Free surface.

c.

Click Boundary conditions on the moving surface.

d.

Select No condition along BOUNDARY_4 (the boundary where the free surface starts) and click Modify.

e.

Select Position imposed.

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.

Set the conditions at the flow exit (BOUNDARY_6). 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. a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_6 and click Modify.

b.

Click Normal and tangential forces imposed (fn, fs).

c.

Accept the default value of 0 for the normal force,

d.

Accept the default value of 0 for the tangential force,

e.

Click Upper level menu to return to the Direct extrusion menu.

, by clicking Upper level menu. , by clicking Upper level menu.

The Global remeshing menu item is highlighted.

5.4.6. Remeshing This model involves a free surface, whose shape is unknown a priori, which will be calculated together with the flow equations. A portion of the mesh is affected by the relocation of this boundary, so a remeshing technique is applied on this part of the mesh. The free surface is entirely contained within subdomain 2, therefore only subdomain 2 is affected by the relocation of the free surface. Global remeshing 1. 178

Specify the region where the remeshing is to be performed (SUBDOMAIN_2). Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Setup and Solution In general, only one local remeshing is required for direct extrusion simulations. It becomes necessary to define multiple local remeshings for inverse extrusion simulations. A single local remeshing is sufficient for this case. 1–st local remeshing a.

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.

b. 2.

Click Upper level menu.

Define the parameters for the remeshing method. 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, 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 the Appendix (p. 192). Optimesh-3D (extrusion only) a.

b.

Specify the initial plane for the optimesh remeshing technique, by selecting SUBDOMAIN_1 and clicking Modify. i.

Select Part of inlet section.

ii.

Select Upper level menu.

Specify the final plane for remeshing technique, by selecting BOUNDARY_6 and clicking Modify. i.

Select Part of outlet section.

ii.

Select Upper level menu twice.

Polydata asks if you want to change from the surface kinematic condition to the line kinematic condition.

c.

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179

Direct Extrusion The line kinematic condition is recommended for extrusion problems, and must be used in combination 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.

5.4.7. 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.

Click Enable evolution on moving boundaries to enable the evolution scheme. For information on the evolution scheme, see Appendix (p. 192).

2.

Specify the evolution parameters. Modify the evolution 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 the number of evolution steps and to speed up the calculation. Modify the initial value of delta-S Polydata prompts you for the initial value of

180

.

b.

Enter 0.1 for the New value and click OK.

c.

Click Upper level menu to return to the Numerical parameters menu. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

(

) to reduce

Setup and Solution 3.

Click Upper level menu two times to return to the top-level Polydata menu.

5.4.8. Outputs 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. 192). Polydata asks you to confirm the current system units and fields that are to be saved to the results file for postprocessing.

2.

Specify the system of units for the simulation. a.

Click Modify system of units.

b.

Select Set to metric_cm/g/s/A+Celsius.

c.

Click Upper level menu three times. The top-level Polydata menu is displayed.

5.4.9. Save and Exit Polydata Save and exit Polydata asks you 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 postprocessing, and for the Polyflow format results file (res).

5.4.10. Solution 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. 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).

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Direct Extrusion 2.

Check for convergence in the listing file. a.

Right-click the Solution cell and select Listing Viewer.... Workbench opens the View listing file dialog box, 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.

5.4.11. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 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.

2.

Display the velocity distribution on the boundaries. Deselect Wireframe in the Outline tree tab, under User Locations and Plots. a.

Click the Insert menu and select Contour or click the

b.

Click OK to accept the default name (Contour 1) and display the details view below the Outline tab.

c.

Perform the following steps in the Geometry tab of the details view of Contour 1: i.

182

Click the

button.

button next to Locations.

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Setup and Solution

d.

ii.

Select all topological entities under Fluid Flow Extrusion Polyflow in the Location Selector dialog box (use Shift for multiple selection) and click OK.

iii.

Select VELOCITIES from the Variable drop-down list (or by clicking

iv.

Click Apply.

).

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. 183).

Figure 5.3: Contours of Velocity Magnitude

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 extrudate. 3.

Display contours of velocity in cross-sections. a.

Deselect the contours previously defined.

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183

Direct Extrusion

In the Outline tree tab, under User Locations and Plots, deselect Contour 1. b.

184

Create the cross-sectional planes, at Z = 0, 3, 7, and 20 cm. 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.

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Setup and Solution

iii.

In the Geometry tab of the details view, ensure XY Plane is selected from the Method dropdown 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.

vii. In the Outline tree tab, under User Locations and Plots, deselect Plane 1, Plane 2, Plane 3, and Plane 4.

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Direct Extrusion

c.

186

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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Setup and Solution

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. 188) shows the velocity profiles at the flow inlet, the flow outlet, and at the planes just before and just after the die exit.

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187

Direct Extrusion Figure 5.4: Velocity Profiles at Cross-Sections

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 rearrangement is the source of the deformation of the extrudate. 4.

Compare the cross-sectional shape of the extrudate with the die. a.

Simplify the display. In the Outline tree tab, under User Locations and Plots, deselect Contour 2 and Wireframe.

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Setup and Solution

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.

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.

v.

Select SUBDOMAIN_1_BOUNDARY_1 from the Intersect With drop-down list.

vi.

In the Color tab, click

next to Color and select dark blue.

vii. Click Apply. c.

Display the extrudate shape using a polyline. i.

Select Polyline from the Location drop-down menu (

).

ii.

Click OK to accept the default name (Polyline 2) and display the details view below the Outline tab. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Direct Extrusion

d.

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.

v.

Select SUBDOMAIN_2_BOUNDARY_6 from the Intersect With drop-down list.

vi.

Click Apply.

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.

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Restore the symmetry. a.

Click the Insert menu and select Instance Transform, or click the

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.

button.

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Setup and Solution iii.

Ensure Apply Rotation is selected.

iv.

Ensure Method is set to Principal Axis and Z is selected 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 double-click Polyline 2).

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.

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191

Direct Extrusion Figure 5.5: Swelling of the Extrudate

The deformations come from the rearrangement of the velocity profile. Particles coming from highspeed 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 enlarged 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 numerical simulation is necessary for a moderate to high complexity die.

5.5. 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 nonlinear problem was solved using an evolution technique to reach the convergence.

5.6. Appendix The appendix contains the following sections: 5.6.1. Power Law 5.6.2. Optimesh Remeshing Technique 5.6.3. Evolution Scheme 192

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Appendix 5.6.4. IGES Output

5.6.1. 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.

5.6.2. Optimesh Remeshing Technique 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 will be 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).

5.6.3. Evolution Scheme The kinematic equation introduces nonlinear terms in the problem that might lead to convergence difficulties. An evolution scheme is available in Polyflow to solve such highly nonlinear problems. Start the calculation with a reduced value of the parameter(s) causing the nonlinearity. Beginning with the first solution, Polyflow increments the parameter(s) causing the nonlinearity and computes a second solution. Starting from this new solution, Polyflow increments the parameter(s) again and computes a 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

.

5.6.4. 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.

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193

194

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Chapter 6: Inverse Extrusion This tutorial is divided into the following sections: 6.1. Introduction 6.2. Prerequisites 6.3. Problem Description 6.4. Setup and Solution 6.5. Summary 6.6. 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. In this tutorial you will learn how to: • Define an evolution problem. • 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 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. 51). Some steps in the set up procedure will not be shown explicitly.

6.3. 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 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. 196) at a flow rate (a quarter of the actual flow rate) and the extrudate is obtained at the exit.

= 10 cm3/s

The incompressibility and momentum equations are solved over the computational domain. The domain for the problem is divided into two sub-domains (as shown in Figure 6.1: Problem Description (p. 196)) 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

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195

Inverse Extrusion 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. Figure 6.1: Problem Description

Figure 6.2: Boundary Set for the Problem

The boundary set for the problem are shown in Figure 6.2: Boundary Set for the Problem (p. 196), and the conditions at the boundaries of the domains are given below boundaries of the domains are: • boundary 1: flow inlet, volumetric flow rate

196

= 10 cm3/s

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Setup and Solution • boundary 2: symmetry plane • boundary 3: symmetry plane • boundary 4: slip conditions along the wall • boundary 5: free surface • boundary 6: flow exit

6.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 6.4.1. Preparation 6.4.2. Project and Mesh 6.4.3. Create a Task for the Model 6.4.4. Material Data 6.4.5. Boundary Conditions 6.4.6. Remeshing 6.4.7. Numerical Parameters 6.4.8. Outputs 6.4.9. Save and Exit Polydata 6.4.10. Solution 6.4.11. Postprocessing

6.4.1. 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Inverse-Extrusion_R180.zip link to download the input and solution files.

7.

Unzip the Inverse-Extrusion_R180.zip file you have downloaded to your working folder.

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197

Inverse Extrusion The mesh file invext.msh can be found in the unzipped folder. 8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

6.4.2. Project and Mesh 1.

Create a Fluid Flow - Extrusion(Polyflow) analysis system by drag and drop in Workbench.

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).

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.

6.4.3. Create a Task for the Model In the following steps you will define a new task representing the inverse extrusion 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 • Evolution problem(s) Apply the evolution scheme on the slip coefficient along the outer wall of the die (boundary 4) when you define the slip boundary conditions.

b.

Click Accept the current setup. The Create a sub-task menu item is highlighted.

2.

Create a sub-task for the isothermal flow. Create a sub-task a.

Click Generalized Newtonian isothermal flow problem. A dialog box appears asking for the title of the problem.

198

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Setup and Solution

b.

Enter Inverse Extrusion as the New value and click OK. The Domain of the sub-task menu item is highlighted.

3.

Define the domain where the sub-task applies. 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. Domain of the sub-task Accept the default selection of both subdomains by clicking Upper level menu. The Material data menu item is highlighted.

6.4.4. Material Data Polydata indicates which material properties are relevant for your sub-task by graying out the irrelevant properties. In this case, viscosity, density, inertia terms, and gravity are available for specification. For this model you will only define the viscosity of the material. Material Data 1.

Click Shear-rate dependence of viscosity.

2.

Click Power law. The viscosity in this tutorial is given by the power law. For information on power law, see Power Law (p. 219) .

3.

Specify the value of , referred to as “fac” in the graphical user interface (compare the equation at the top of the Power law menu to the equation shown in the Power Law (p. 219)). Modify fac

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Inverse Extrusion

Enter 300000 [units: poise] as the New value and click OK. 4.

Retain the default value for , referred to as “tnat” in the graphical user interface. Modify tnat Click OK to retain the default value of 1.

5.

Specify the value for , referred to as “expo” in the graphical user interface. Modify expo Enter 0.75 as the New value and click OK.

6.

Click Upper level menu three times to return to the Inverse Extrusion menu. The Flow boundary conditions menu item is highlighted.

6.4.5. Boundary Conditions In the following steps you will 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. Flow boundary conditions 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.

Click Modify volumetric flow rate. Polydata prompts you for the volumetric flow rate.

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Setup and Solution

d.

Enter 10 [units: cm3/s] as the New value and click OK.

e.

Retain the default options of Automatic and Volumetric flow rate.

f.

Click Upper level menu. When the Automatic option is selected, Polydata chooses the most appropriate method to compute the inflow condition.

2.

Set the conditions at the first symmetry plane (BOUNDARY_2). 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.

3.

4.

a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_2 and click Modify.

b.

Click Plane of symmetry (fs=0, vn=0).

Set the conditions at the second symmetry plane (BOUNDARY_3). a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_3 and click Modify.

b.

Click Plane of symmetry (fs=0, vn=0).

Set the conditions along the outer wall of the die (BOUNDARY_4). a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_4 and click Modify.

b.

Enable the evolution scheme on the slip coefficient. The evolution scheme is used to aid with convergence by starting with a low value for the slip coefficient and slowly increasing the value of the coefficient to reach a no-slip condition. With a low value for the slip coefficient there is no swelling of the extrudate, simplifying the calculation. As the slip coefficient increases, the extrudate begins to swell because the fluid in contact with the

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201

Inverse Extrusion wall slows down, which increases the velocity of the fluid in the center of the die. For more information on the evolution scheme, see Evolution Scheme (p. 219). i.

Click EVOL at the top of the Polydata menu to enable the evolution inputs for the slip coefficient.

ii.

Click Slip conditions.

iii.

Click F(v) = Generalized Navier’s law. For information on Navier’s law, see Appendix (p. 219).

iv.

Specify the value of

.

Modify k A dialog box 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 dialog box 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 dialog box 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.

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, = 0. This equation requires an initial condition (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 Figure 5.2: Boundary Set for the Problem (p. 173)). a.

202

Select Zero wall velocity (vn=vs=0) along BOUNDARY_5 and click Modify. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Setup and Solution b.

Click Free surface.

c.

Click Boundary conditions on the moving surface.

d.

Select No condition along BOUNDARY_4 (the boundary where the free surface starts) and click Modify.

e.

Select Position imposed.

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.

6.

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.

Set the conditions at the flow exit (BOUNDARY_6). 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.

7.

a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY_6 and click Modify.

b.

Click Normal and tangential forces imposed (fn, fs).

c.

Accept the default value of 0 for the normal force,

d.

Accept the default value of 0 for the tangential force,

, by clicking Upper level menu. , by clicking Upper level menu.

Click Upper level menu at the top of the Flow boundary conditions menu. The Global remeshing menu item is highlighted.

6.4.6. Remeshing 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, since a part of the mesh is deformed. For information on remeshing technique, see Appendix (p. 219). Global remeshing 1.

Specify the region where the remeshing is to be performed (SUBDOMAIN_2). 1–st local remeshing Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Inverse Extrusion a.

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.

b. 2.

Click Upper level menu.

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. 219). Optimesh-3D (extrusion only) a.

b.

Specify the initial plane for the optimesh remeshing technique, by selecting SUBDOMAIN_1 and clicking Modify. i.

Select Part of inlet section.

ii.

Select Upper level menu.

Specify the final plane for the remeshing technique, by selecting BOUNDARY_6 and clicking Modify. i.

Select Part of outlet section.

ii.

Select Upper level menu twice.

c.

Polydata asks if you want to change from the surface kinematic condition to the line kinematic condition.

d.

Click Yes to use the line kinematic condition. The line kinematic condition is recommended for extrusion problems, and must be used in combination with the optimesh remeshing technique.

e.

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.

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Setup and Solution 3.

Activate the inverse prediction. 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.

b. 4.

5.

Click Upper level menu.

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.

Click Upper level menu two times. The F.E.M. Task 1 menu is displayed.

6.4.7. 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 evolution parameters. Modify the evolution parameters a.

Specify the final value of . Modify the upper limit of S Enter 20 for the New value and click OK.

Note Setting the final value of equal to 20 creates a large enough slip coefficient that it is equivalent to a no-slip condition at the die wall (BOUNDARY_4, as discussed in a previous step).

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Inverse Extrusion b.

Specify the initial value of

.

Modify the initial value of delta-S Enter 2 for the New value and click OK. c.

Specify the minimum value of

.

Modify the min value of delta-S Enter 0.1 for the New value and click OK. d.

Specify the maximum value of

.

Modify the max value of delta-S Enter 3 for the New value and click OK. e.

Specify the maximum number of successful steps. Modify the max number of successful steps Enter 30 for the New value and click OK.

2.

Click Upper level menu three times to return to the top-level Polydata menu.

6.4.8. Outputs 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. 219). Polydata asks you to confirm the current system units and fields that are to be saved to the results file for postprocessing.

2.

Specify the system of units for the simulation. a.

Click Modify system of units.

b.

Select Set to metric_cm/g/s/A+Celsius.

c.

Click Upper level menu three times. The top-level Polydata menu is displayed.

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Setup and Solution

6.4.9. Save and Exit Polydata Save and exit 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 postprocessing, and for the Polyflow format results file (res).

6.4.10. Solution 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. 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). A cfx.res file (corresponding to the eight evolution steps of the flow case) will be created.

2.

Check for convergence in the listing file. a.

Right-click the Solution cell and select Listing Viewer.... Workbench opens the View listing file dialog box, 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.

6.4.11. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 1.

Double-click the Results tab 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.

Display the velocity distribution on the boundaries. a.

Deselect Wireframe in the Outline tree tab, under User Locations and Plots.

b.

Click the Insert menu and select Contour or click the

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.

button.

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Inverse Extrusion

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.

iii.

Select VELOCITIES from the Variable drop-down list (or by clicking

iv.

Click Apply.

).

You can see in Figure 6.3: Contours of Velocity Magnitude (p. 209) 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.

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Setup and Solution Figure 6.3: Contours of Velocity Magnitude

3.

Display contours of velocity in cross-sections. a.

Deselect the contours previously defined.

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Inverse Extrusion

In the Outline tree tab, under User Locations and Plots deselect Contour 1. b.

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Create the cross-section planes, at Z = 0, 3, 7 and 20 cm. 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.

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Setup and Solution

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.

vii. In the Outline tree tab, under User Locations and Plots, deselect Plane 1, Plane 2, Plane 3, and Plane 4.

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Inverse Extrusion

c.

Click the Insert menu and select Contour or click the

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. i.

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In the Geometry tab, click the

button.

button next to Locations.

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Setup and Solution

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. 214). 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.

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Inverse Extrusion Figure 6.4: Velocity Profile Planes

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.

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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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Setup and Solution

iii.

In the Geometry tab of the details view, select Boundary Intersection from the Method dropdown list.

iv.

Click next to Boundary List and select SUBDOMAIN_1_BOUNDARY_4. Click OK to close the Location Selector dialog box.

v.

Select SUBDOMAIN_1_BOUNDARY_1 from the Intersect With drop-down list.

vi.

In the Color tab, click

next to Color and select dark blue.

vii. Click Apply. c.

d.

Display the extrudate shape using a polyline. i.

Select Polyline from the Location drop-down menu (

).

ii.

Click OK to accept the default name (Polyline 2) and display the details view below the Outline tab.

iii.

In the Geometry tab of the details view, select Boundary Intersection from the Method dropdown list.

iv.

Select SUBDOMAIN_2_BOUNDARY_5 from the Boundary List drop-down list.

v.

Select SUBDOMAIN_2_BOUNDARY_6 from the Intersect With drop-down list.

vi.

Click Apply.

Right-click in the graphic window and select View From +Z under Predefined Camera.

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Inverse Extrusion

5.

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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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Setup and Solution

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.

Ensure Principal Axis and Z are selected for Method and Axis in the Axis Definition group box.

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 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 double-click Polyline 2).

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.

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Inverse Extrusion

You can also click the fit view button (

) to properly center the image.

Figure 6.5: Swelling of the Extrudate

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 regions 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. 218), 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.

6.5. 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

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Appendix used multiple domain calculations with remeshing methods most suited to 3D inverse extrusion problems. The nonlinear problem was solved using an evolution technique to aid convergence.

6.6. Appendix The appendix contains the following sections: 6.6.1. Power Law 6.6.2. Evolution Scheme 6.6.3. Remeshing Technique 6.6.4. Optimesh Remeshing Technique 6.6.5. IGES Output

6.6.1. 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.

6.6.2. Evolution Scheme The kinematic equation introduces nonlinear terms in the problem that might lead to convergence difficulties. An evolution scheme is available in Polyflow to solve such highly nonlinear problems. Start the calculation with a reduced value of the parameter(s) causing the nonlinearity. Starting from the first solution, Polyflow increments the parameter(s) causing the nonlinearity and computes a second solution. Starting from this new solution, Polyflow increments the parameter(s) again and computes a 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 = tangential velocity of the wall = material parameters

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Inverse Extrusion = material parameters = 0 (assumed zero, by default

6.6.3. Remeshing Technique 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 subdomain. 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.

6.6.4. Optimesh Remeshing Technique 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 will be 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).

6.6.5. 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.

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Chapter 7: Flow of Two Immiscible Fluids This tutorial is divided into the following sections: 7.1. Introduction 7.2. Prerequisites 7.3. Problem Description 7.4. Setup and Solution 7.5. 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. In this tutorial you will learn how to: • Define a moving interface problem. • Create multiple sub-tasks. • Set material properties and boundary conditions for a moving interface problem. • Select a remeshing method.

7.2. 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. 51). Some steps in the set up procedure will not be shown explicitly.

7.3. Problem Description 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. 222). The melts are fed into the die through boundaries 1 and 3 (see Figure 7.2: Boundary Sets and Subdomains for the Problem (p. 223)). 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. 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 subtask 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 FigRelease 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

221

Flow of Two Immiscible Fluids ure 7.2: Boundary Sets and Subdomains for the Problem (p. 223)). 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. 223).

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Problem Description 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 • boundary 3: flow inlet for fluid 2, volumetric flow rate

= 1 cm3/s

• boundary 4: outer wall common to subdomain 3 and subdomain 4: zero velocity • boundary 5: flow exit for both fluids • boundary 6: outer wall common to subdomain 1 and subdomain 2: zero velocity 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.

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Flow of Two Immiscible Fluids

7.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 7.4.1. Preparation 7.4.2. Project and Mesh 7.4.3. Create a Task for the Model 7.4.4. Fluid 1 Sub-Task 7.4.5. Fluid 2 Sub-Task 7.4.6. Save and Exit Polydata 7.4.7. Solution 7.4.8. Postprocessing

7.4.1. 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Two-Fluids_R180.zip link to download the input and solution files.

7.

Unzip the Two-Fluids_R180.zip file you have downloaded to your working folder. The mesh file fluids.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

7.4.2. Project and Mesh 1.

Create a Fluid Flow - Extrusion (Polyflow) analysis system by drag and drop in Workbench.

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).

4.

Double-click the Setup cell to start Polydata.

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Setup and Solution 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.

7.4.3. Create a Task for the Model In the following steps 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 subtasks (one for each fluid) in subsequent sections. Create a task for the model. Create a new task 1.

Select the following options: • F.E.M. task • Steady-state problem(s) • 2D axisymmetric geometry

2.

Click Accept the current setup. The Create a sub-task menu item is highlighted.

7.4.4. Fluid 1 Sub-Task In the following steps you will 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. A small dialog box appears asking for the title of the problem.

b.

Enter fluid 1 as the New value and click OK.

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Flow of Two Immiscible Fluids The Domain of the sub-task menu item is highlighted. 2.

Define the domain where the sub-task applies. 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. 223). Domain of the sub-task a.

Select SUBDOMAIN3 and click Remove.

b.

Select SUBDOMAIN4 and click Remove.

c.

Click Upper level menu. The Material data menu item is highlighted.

3.

Specify the material data properties for fluid 1. Material Data Polydata indicates which material properties are relevant for your sub-task by graying out 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. Click Shear-rate dependence of viscosity.

4.

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Setup and Solution 5.

Specify the value for , referred to as “fac” in the graphical user interface. Modify fac Polydata prompts for a new value of .

Enter 10000 [units: poise] as the New value and click OK. 6.

Click Upper level menu three times to return to the fluid 1 menu. The Flow boundary conditions menu item is highlighted.

7.

Specify the flow boundary conditions for fluid 1 (SUBDOMAIN1 and SUBDOMAIN2). Flow boundary conditions

a.

Set the conditions along the intersection of SUBDOMAIN2 and SUBDOMAIN4.

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Flow of Two Immiscible Fluids 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. 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 satisfy 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.

ii.

Click Interface.

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.

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Setup and Solution x. b.

Click Accept the current setup to return to the Flow boundary conditions menu.

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. Polydata prompts you for the volumetric flow rate.

iv.

Enter 3 [units: cm3/s] as the New value and click OK.

v.

Ensure Automatic is selected and 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 therefore has no velocity relative to the wall. By default, Polydata imposes Zero wall velocity (

c.

=

= 0) along all boundaries.

Set the conditions at the flow outlet (BOUNDARY5). It is assumed that a fully developed velocity profile is reached at the exit, so the outflow condition is appropriate. This condition essentially imposes a zero normal force ( ) that includes a pressure term, and zero tangential velocity ( ). i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY5 and click Modify.

ii.

Click Outflow.

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Flow of Two Immiscible Fluids d.

Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY6 at the outer wall common to SUBDOMAIN1 and SUBDOMAIN2 (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.

e. 8.

Click Upper level menu to return to the fluid 1 menu.

Define remeshing for SUBDOMAIN2. This model involves a free surface, whose shape is unknown a priori, which will be calculated together with the flow equations. 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 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. 1–st local remeshing i.

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Select SUBDOMAIN1 and click Remove.

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Setup and Solution 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 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.

ii.

iii.

To specify the inlet for the system of spines, select SUBDOMAIN1 and click Modify. A.

Select Part of inlet section.

B.

Select Upper level menu.

Specify the outlet for the system of spines, select BOUNDARY5 and click Modify. A.

Select Part of outlet section.

B.

Select Upper level menu.

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Flow of Two Immiscible Fluids The F.E.M. Task 1 menu is displayed.

7.4.5. Fluid 2 Sub-Task In the following steps you will define the nature of the flow problem, identify the domain of definition, set the relevant material 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.

b.

Click No, since this sub-task has different parameters associated with it.

c.

Click Generalized Newtonian isothermal flow problem. A small dialog box appears asking for the title of the problem.

d.

Enter fluid 2 as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies. Domain of the sub-task a.

Select SUBDOMAIN1 and click Remove.

b.

Select SUBDOMAIN2 and click Remove.

c.

Click Upper level menu. The Material data menu item is highlighted.

3.

Specify the material data properties for fluid 2. Material Data

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Setup and Solution For this model, define only the viscosity of the material. a.

Click Shear-rate dependence of viscosity.

b.

Click Constant viscosity.

c.

Specify the value for , referred to as “fac” in the graphical user interface. Modify fac Polydata prompts for a new value of .

Enter 5000 [units: poise] as the New value and click OK. d.

Click Upper level menu three times to return to the fluid 2 menu. The Flow boundary conditions menu item is highlighted.

4.

Specify the flow boundary conditions for fluid 2 (SUBDOMAIN3 and SUBDOMAIN4). Flow boundary conditions a.

Set the conditions along the intersection of SUBDOMAIN2 and SUBDOMAIN4. i.

Select Zero wall velocity (vn=vs=0) along SUBDOMAIN2 and click Modify.

ii.

Click Interface. The interface condition was defined as a moving interface when setting the boundary conditions 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). i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY3 and click Modify.

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Flow of Two Immiscible Fluids ii.

Click Inflow.

iii.

Click Modify volumetric flow rate. Polydata prompts you for the volumetric flow rate.

iv.

Accept the default value of 1 [units: cm3/s] for the flow rate by clicking OK.

v.

Ensure Automatic is selected, and click Upper level menu.

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).

f.

i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY5 and click Modify.

ii.

Click Outflow.

Click Upper level menu to return to the Flow boundary conditions menu. The Global remeshing menu item is highlighted.

5.

Define remeshing for SUBDOMAIN4. Global remeshing a.

Specify the region where the remeshing is to be performed (SUBDOMAIN4). 1–st local remeshing i.

Select SUBDOMAIN3 and click Remove.

ii.

Click Upper level menu. The Method of Spines menu item is highlighted.

b.

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Define the parameters for the system of spines. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Setup and Solution 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). Method of Spines i.

ii.

c.

Specify the inlet for the system of spines by selecting SUBDOMAIN3 and click Modify. A.

Select Part of inlet section.

B.

Select Upper level menu.

Specify the outlet for the system of spines by selecting BOUNDARY5 and click Modify. A.

Select Part of outlet section.

B.

Select Upper level menu.

Click Upper level menu three times. The top-level Polydata menu is displayed.

7.4.6. Save and Exit Polydata 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.

Specify the system of units for the simulation. a.

Click Modify system of units.

b.

Select Set to metric_cm/g/s/A+Celsius.

c.

Click Upper level menu twice.

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Flow of Two Immiscible Fluids

2.

Click Accept. This confirms that the default Current field(s) are correct.

3.

Click Continue. This accepts the default names for graphical output files (cfx.res) that are to be saved for postprocessing, and for the Polyflow format results file (res).

7.4.7. Solution 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. 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.... Workbench opens the View listing file dialog box, 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.

7.4.8. Postprocessing Use CFD-Post to view the results of the Polyflow simulation.

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Setup and Solution 1.

Double-click the Results tab 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.

3.

Align the view. a.

In the graphical window, right-click, and select the option Predefined Camera.

b.

Select View from +Z.

Display contours of velocity magnitude. a.

Click the Insert menu and select Contour or click the

button.

b.

Click OK to accept the default name (Contour 1) and display the details view below the Outline tab.

c.

Perform the following steps in the details view: i.

In the Geometry tab, click the

button next to Locations.

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.

iii.

Select VELOCITIES from the Variable drop-down list (or by clicking

iv.

Click Apply.

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).

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Flow of Two Immiscible Fluids Figure 7.3: Contours of Velocity Magnitude

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. • 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.

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Setup and Solution 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 Vector or click the

button.

c.

Click OK to accept the default name (Vector 1) and display the details view below the Outline tab.

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Flow of Two Immiscible Fluids

d.

240

Perform the following steps in the details view: i.

In the Geometry tab, click the

button next to Locations.

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 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.

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Setup and Solution Figure 7.4: Velocity Vectors

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241

Flow of Two Immiscible Fluids 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.

7.5. Summary This tutorial introduced the concept of fluid layers flowing 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 coextrusion die).

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Chapter 8: Flow of Two Immiscible Fluids by Species Method This tutorial is divided into the following sections: 8.1. Introduction 8.2. Prerequisites 8.3. Problem Description 8.4. Setup and Solution 8.5. 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. In this tutorial you will learn how to: • Define a species. • Define a species transport problem. • Create multiple sub-tasks. • Define a PMAT function. • Define an EVOLUTION task.

8.2. 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. 51). Some steps in the set up procedure will not be shown explicitly.

8.3. Problem Description 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. 244). The melts are fed into the die through boundaries 1 and 3 (see Figure 8.2: Boundary Sets and Subdomains for the Problem (p. 245)). 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. 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 the scalar value is greater than 0.5, material properties of first fluid are used and if the scalar value is less than 0.5, material properties of second species are used. A Scalar value of 0.5 determines the location of interface. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

243

Flow of Two Immiscible Fluids by Species Method Note that the same problem has been solved using the interface tracking method (see Flow of Two Immiscible Fluids (p. 221)). The advantage of this method over the interface tracking method is that it can be used for more complex geometries, and it is less computationally expensive than the interface tracking method (no remeshing method must be defined). However 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. 221) is used. Fluid 1 has a viscosity of

= 10000 poise, and fluid 2 has a viscosity of

= 5000 poise.

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. 245).

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Problem Description Figure 8.2: 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 • boundary 3: flow inlet for fluid 2, volumetric flow rate,

= 1 cm3/s

• boundary 4: outer wall common to subdomain 3 and subdomain 4: zero velocity • boundary 5: flow exit for both fluids • boundary 6: outer wall common to subdomain 1 and subdomain 2: zero velocity The conditions at the boundaries of the domains for species transport: • boundary 1: scalar value equal to 1 Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

245

Flow of Two Immiscible Fluids by Species Method • boundary 3: scalar value equal to zero • Insulated condition at all other boundaries Note that when using this method for a sharp interface, you should ensure that the scalar doesn't diffuse much into the domain. To ensure this, an evolution is applied on scalar diffusivity starting from a large value and gradually decreasing it to a very small number.

8.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 8.4.1. Preparation 8.4.2. Project and Mesh 8.4.3. Create a Task for the Model 8.4.4. Species and Species Transport Sub-task 8.4.5. Fluids Sub-task 8.4.6. Save and Exit Polydata 8.4.7. Solution 8.4.8. Postprocessing

8.4.1. 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Two-Fluids-Species_R180.zip link to download the input and solution files.

7.

Unzip the Two-Fluids-Species_R180.zip file you have downloaded to your working folder. The mesh file fluids.msh can be found in the unzipped folder.

8.

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Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

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Setup and Solution

8.4.2. Project and Mesh 1.

Create a Fluid Flow - Extrusion(Polyflow) analysis system by drag and drop in Workbench.

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).

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.

8.4.3. Create a Task for the Model In the following steps 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 subtasks (one for each fluid) in the following sections. 1.

Create a task for the model. Create a new task

2.

Select the following options: • F.E.M. task • Evolution problem(s) • 2D axisymmetric geometry

3.

Click Accept the current setup.

8.4.4. Species and Species Transport Sub-task In the following steps you will 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 dialog box appears asking for the name of the species.

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Flow of Two Immiscible Fluids by Species Method

a.

Enter Species A as the name of the species. A dialog box appears asking for the nickname of the species.

b.

Enter spea as the nickname of the species.

c.

Click Upper level menu. The Create a sub-task menu item is highlighted.

3.

Create a sub-task for transport of the species. Create a sub-task a.

Click Transport of species. Polydata asks you to select a species.

b.

Click SpeciesA. The Domain of the sub-task menu item is highlighted.

4.

Define the domain where the sub-task applies. Species transport equation is solved in all the subdomains. Domain of the sub-task Click Upper level menu to select all of the subdomains.

5.

Specify the material properties for species. Material data

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Setup and Solution Polydata indicates the material properties that are relevant for the sub-task by graying out the irrelevant properties. For this model, you will only define the diffusivity of the species. The evolution will be applied on diffusivity with an initial high value (1) and decreases it to a small value (1e-9).

a.

Click Diffusivity.

b.

Click EVOL button at the top of Polydata menu to enable evolution inputs.

c.

Click Modify diffusivity. A dialog box appears asking for New value of diffusivity.

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Flow of Two Immiscible Fluids by Species Method

d.

Click OK to accept the default value of 1. Polydata will take you to evolution panel. Here you will make species diffusivity a function of evolution parameter . Since the diffusivity must be decreased by several orders of magnitude, is selected.

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

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Setup and Solution

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 dialog box appears asking for the new value of concentration.

b.

iv.

Set New value to 1 and click OK.

v.

Click Upper level menu.

Set insulated conditions at BOUNDARY2. i.

Select Mass fraction imposed along BOUNDARY2 and click Modify.

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Flow of Two Immiscible Fluids by Species Method ii. c.

Click Insulated boundary.

Set mass fraction at BOUNDARY3 equal to 0. i.

Select Mass fraction imposed along BOUNDARY3 and click Modify.

ii.

Click Mass fraction imposed.

iii.

Click Constant. A dialog box appears asking for the new value of concentration.

d.

iv.

Click OK to accept the default value of 0.

v.

Click Upper level menu.

Set insulated conditions at BOUNDARY4, BOUNDARY5, and BOUNDARY6. i.

Select Mass fraction imposed along BOUNDARY4 and click Modify.

ii.

Click Insulated boundary.

iii.

Repeat step (i) and step (ii) for BOUNDARY5 and BOUNDARY6.

iv.

Click Upper level menu twice.

8.4.5. Fluids Sub-task In the following steps you will define the nature of the flow problem, identify the domain of definition, set the relevant material 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. A dialog box appears asking for the title of the problem.

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Setup and Solution b.

Enter fluid 1 and 2 as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies. This Sub-task is defined for all the subdomains. Domain of the sub-task Click Upper level menu to select all of the subdomains. The Material data menu item is highlighted.

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. a.

Click Shear-rate dependence of viscosity.

b.

Click Constant viscosity.

c.

Click the PMAT button at the top of Polydata.

d.

Specify the value for , referred to as “fac” in the graphical user interface. Modify fac Polydata prompts for the new value of .

Click OK to accept the default value of 1. e.

Polydata will take you to PMAT menu as shown below.

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Flow of Two Immiscible Fluids by Species Method

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 Polydata will ask to define pairs of values. A minimum of two pairs must be defined. Here you will define (0.495, 5000) and (0.505, 10000), where the first index stands for species concentration and the second index stands for viscosity [units: poise] value.

i.

Define new pairs. Define new pairs (X1, f(X1)) Polydata prompts for X1 and f(X1) sequentially.

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Setup and Solution

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 the PMAT button at the top of Polydata.

p.

Click Upper level menu six times to return to the fluid 1 and 2 menu. The Flow boundary conditions menu item is highlighted.

4.

Specify the flow boundary conditions for the fluids. Flow boundary conditions

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Flow of Two Immiscible Fluids by Species Method

a.

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. Polydata prompts for the new value of the volumetric flow rate.

iv.

Enter 3 [units: cm3/s] as the New value and click OK.

v.

Ensure Automatic is selected and click Upper level menu. When the Automatic option is selected, Polydata automatically chooses the most appropriate method to compute the inflow condition.

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Setup and Solution 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 (

c.

=

= 0) along all boundaries.

Set the conditions at the flow inlet for fluid 2 (BOUNDARY3). i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY3 and click Modify.

ii.

Click Inflow.

iii.

Click Modify volumetric flow rate. Polydata prompts for the new value of the volumetric flow rate.

iv.

Click OK to accept the default value of 1 [units: cm3/s] for New Value.

v.

Ensure Automatic is selected and click Upper level menu.

d.

Retain the default condition Zero wall velocity (vn=vs=0) along BOUNDARY4.

e.

Set the conditions at the flow outlet (BOUNDARY5). It is assumed that a fully developed velocity profile is reached at the exit, so the outflow condition is appropriate. This condition essentially imposes a zero normal force ( ) that includes a pressure term, and a zero tangential velocity ( ).

f.

i.

Select Zero wall velocity (vn=vs=0) along BOUNDARY5 and click Modify.

ii.

Click Outflow.

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 three times to return to the top-level Polydata menu.

8.4.6. Save and Exit Polydata 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.

Specify the system of units for the simulation. a.

Click Modify system of Units.

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Flow of Two Immiscible Fluids by Species Method

2.

b.

Click Set to metric_cm/g/s/A+Celsius.

c.

Click Upper level menu twice.

Click Accept. This confirms that the default Current field(s) are correct.

3.

Click Continue. This accepts the default names for graphical output files (cfx.res) that are to be saved for postprocessing, and the Polyflow format results file (res).

8.4.7. Solution 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. 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 click Listing Viewer.... Workbench opens theView listing filedialog box, 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.

8.4.8. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 1.

Double-click the Results tab 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. In the graphical window, right-click, and select View from +Z under Predefined Camera.

3.

258

Display contours of velocity magnitude. a.

Click the Insert menu and select Contour or click the Contour button (

).

b.

Click OK to accept the default name (Contour 1) and display the details view below the Outline tab.

c.

Perform the following steps in the details view of Contour 1:

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Setup and Solution

i.

In the Geometry tab, click the

button next to Locations.

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 click OK.

iii.

Select VELOCITIES from the Variable drop-down list.

iv.

Click Apply.

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259

Flow of Two Immiscible Fluids by Species Method Figure 8.3: Contours of Velocity Magnitude

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. • 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.

260

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Setup and Solution 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

c.

Click OK to accept the default name (Vector 1) and display the details view below the Outline tab.

d.

Perform the following steps in the details view of Vector 1:

button.

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 selections) 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.

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Flow of Two Immiscible Fluids by Species Method Figure 8.4: 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. 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: i.

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Click the

).

button next to Locations.

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Setup and Solution 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.

iii.

Click the

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.

button next to Variable.

vii. Click Apply. Figure 8.5: Contours of Species A

6.

Display the interface line. a.

In Outline tree tab, under User Locations and Plots, deselect Contour 2.

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Flow of Two Immiscible Fluids by Species Method

264

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.

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Summary Figure 8.6: Location of Interface

8.5. Summary This tutorial introduced the concept of fluid layers flowing in the same duct. In Polydata, you learned how to set up a species transport equation, a PMAT function, and you learned how to define a coextrusion 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 when the die has a complex shape. For more accurate results, the interface tracking method, as demonstrated in Flow of Two Immiscible Fluids (p. 221), should be used. Generating a mesh for a 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 coextrusion die).

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Part III: Blow Molding The following blow molding tutorials are available: 1. 3D Thermoforming of a Blister (p. 269) 2. 2D Axisymmetric Blow Molding (p. 303) 3. Plug-Assisted Thermoforming of a Blister (p. 333) 4. 3D Blow Molding of a Bottle (p. 369)

Chapter 1: 3D Thermoforming of a Blister This tutorial is divided into the following sections: 1.1. Prerequisites 1.2. Problem Description 1.3. Setup and Solution 1.4. Summary 1.5. Further Improvements 1.6. Appendix

1.1. 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. 51). Some steps in the setup procedure will not be shown explicitly.

1.2. Problem Description This tutorial simulates a typical thermoforming situation for a blister. Figure 1.1: Thermoforming of a Blister, Sheet (blue) and Mold (red) (p. 270) shows a view of the process in the initial configuration.

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3D Thermoforming of a Blister 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. 270). 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.

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Problem Description The finite element mesh and the boundary conditions are displayed in Figure 1.2: Finite Element Mesh, Subdomains and Boundary Sets (p. 271). 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. 271), 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)

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271

3D Thermoforming of a Blister • 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. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 1.3.1. Preparation 1.3.2. Project and Mesh 1.3.3. Mold Sub-Task 1.3.4. Film Sub-Task 1.3.5. Postprocessing Sub-Tasks 1.3.6. Numerical Parameters 1.3.7. Outputs 1.3.8. Save and Exit Polydata 1.3.9. Solution 1.3.10. Postprocessing

1.3.1. 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.

5.

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a.

Click ANSYS Polyflow under Product.

b.

Click 18.0 under Version.

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Setup and Solution 6.

Click the 3D-Thermo-Blister_R180.zip link to download the input and solution files.

7.

Unzip the 3D-Thermo-Blister_R180.zip file you have downloaded to your working folder. The mesh file blister.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

1.3.2. Project and Mesh 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.

3.

Import the mesh file (blister.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.

1.3.3. Mold Sub-Task In the following steps you will define the task representing the mold. 1.

Create a task for the model. Create a new task a.

Select the following options: • F.E.M. task • Time-dependent problem(s) • 2D shell geometry

b. 2.

Click Accept the current setup.

Define the molds. Define molds a.

Create the new mold. Create a new mold Click Adiabatic mold. A dialog box opens, asking for the title of the mold.

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3D Thermoforming of a Blister

b.

Click OK to accept the default name, Mold 1. The Domain of the mold menu item is highlighted.

3.

Define the domain where the mold applies. Domain of the mold

4.

a.

Select Subdomain 1 and click Remove.

b.

Click Upper level menu at the top of the Domain of the mold menu.

Define the contact boundary conditions. Contact conditions

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Setup and Solution

5.

a.

Select No contact along Subdomain 2 and click Modify.

b.

Select Contact and click Upper level menu twice.

Define the motion of the mold. Mold motion a.

Click Mold motion type : fixed mold A dialog box opens, asking you to specify the type of mold motion.

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.

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3D Thermoforming of a Blister c.

Set the mold translation velocity. Modify translation velocity Polydata prompts for velocity-x. i.

Specify the x-velocity.

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 [units: 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.

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Setup and Solution Enter 0.097 as the New value and click OK. vi.

In a similar manner, set the values for b, c, and d to 1.0, 0.103, and 0, respectively. Figure 1.3: Ramp Function for Mold Velocity

Figure 1.3: Ramp Function for Mold Velocity (p. 277) 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. The Create a sub-task menu item is highlighted.

1.3.4. Film Sub-Task In the following steps you will define the nature of 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.

Select Shell model : Gen. Newtonian isothermal. A dialog box opens, asking for the title of the problem.

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3D Thermoforming of a Blister

b.

Enter Blister as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies. Domain of the sub-task a.

Select Subdomain 2 and click Remove.

b.

Click Upper level menu button at the top of the Domain of the sub-task menu. The Flow boundary conditions menu item is highlighted.

3.

Specify the flow boundary conditions. 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.

c.

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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.

Select Zero wall velocity (vn=vs=0) along Boundary 4 and click Modify. i.

Click Plane of symmetry ( fs=0, vn=0 ).

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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

Setup and Solution A dialog box opens, asking for the new value of the constant.

Enter 100000 [units: Pa] as the New value and click OK. f.

Click the EVOL button at the top of the Polydata menu to enable evolution inputs.

g.

Click Upper level menu. 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. 279) 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.

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3D Thermoforming of a Blister 4.

Define the contacts of the blister. 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.

c.

Define the contact wall. i.

Click Select a contact wall.

ii.

Select Mold 1 : Contact along Subdomain 2 and click Select.

Specify the coefficients and accuracy. i.

Click Modify slipping coefficient. Enter 1e+10 as the New value and click OK.

ii.

Click Modify penalty coefficient. Enter 1e+10 as the New value and click OK.

iii.

Click Modify penetration accuracy. Enter 0.05 as the New value and click OK.

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.

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Setup and Solution

iii.

Click No in the dialog box 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 dialog box, 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 dialog box opens, saying that velocity prediction must be disabled, and that the modification has automatically been done.

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3D Thermoforming of a Blister

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 dialog box 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. Enter 100000 [units:

] as the New value and click OK.

iv.

Click Upper level menu twice to continue with material data specification.

v.

Click Density.

vi.

Click Modification of density. Enter 0.001 [units: g/mm3] as the New value and click OK.

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Setup and Solution vii. Click Upper level menu to continue with the material data specification. 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 [units: g-mm/s/mm2] as the New value and click OK.

xi. c.

Click Upper level menu twice to return to the blister menu.

Specify the initial thickness. Initial thickness i.

Click Constant. Enter 0.35 [units: mm] as the New value and click OK.

ii.

Click Upper level menu four times to return to the F.E.M. Task 1 menu.

1.3.5. Postprocessing Sub-Tasks In the following steps 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. Subtasks 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 dialog box 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 dialog box 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 Subdomain 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.

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3D Thermoforming of a Blister The plane is calculated by the following equation (which is displayed at the top of the Restriction of Layers by cutting planes menu). (1.1) Polydata asks for the values of Coefficients A, B, C, and D sequentially.

2.

e.

Enter 0 for A, 0 for B, -1 for C, and 25.9 for D.

f.

Click Upper level menu.

g.

Click Upper level menu to ignore contact with Subdomain 2.

Set a task to report the permeability of the blown product. Create a sub-task Click No in the dialog box that opens asking if you want to copy the data of an existing sub-task. a.

Click Postprocessor. Enter Permeability of product as the New value in the dialog box that asks for the title of the sub-task and click OK.

b.

Click Permeability of blown product. Click OK in the dialog box that opens saying that the calculation will be performed on Subdomain 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. Polydata asks for the values of Coefficients A, B, C, and D sequentially. See Equation 1.1 (p. 284) for more information on the coefficients.

3.

e.

Enter 0 for A, 0 for B, -1 for C, and 25.9 for D.

f.

Click Upper level menu.

g.

Click Upper level menu to ignore contact with Subdomain 2.

Set a task to report the volume of the blown product. Create a sub-task Click No in the dialog box that opens asking if you want to copy the data of an existing sub-task. a.

Click Postprocessor. Enter Volume of product as the New value in the dialog box that asks for the title of the sub-task and click OK.

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Setup and Solution b.

Click Capacity of blown product. Click OK in the dialog box that opens saying that the calculation will be performed on Subdomain 1.

c.

Click Add a new plane. Polydata asks for the values of Coefficients A, B, C, and D sequentially. See Equation 1.1 (p. 284) 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.

1.3.6. Numerical Parameters 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 [units: s] as the New value.

3.

Click Modify the upper time limit. Enter 0.6 [units: s] as the New value and click OK.

4.

Click Modify the initial value of the time-step. Enter 0.001 [units: s] as the New value and click OK.

5.

Click Modify the min value of the time-step. Click OK to retain the default value of 0.0001 [units: s] as the New Value.

6.

Click Modify the max value of the time-step. Enter 0.01 [units: s] as the New value and click OK.

7.

Click Modify the tolerance. Click OK to retain the default of 0.01 [units: s] 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.

9.

Click Upper level menu three times to return to the top-level Polydata menu.

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3D Thermoforming of a Blister

1.3.7. Outputs 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_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.

1.3.8. Save and Exit Polydata Save and exit 1.

Click Accept.

2.

Click Continue. This accepts the default names for graphical output files (cfx.res) that are to be saved for postprocessing, and the Polyflow format results file (res).

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Setup and Solution

1.3.9. Solution 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. 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.... Workbench opens the View listing file dialog box, 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.

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. Here you can see the results of the postprocessor sub-tasks you created in Polydata. For additional information on postprocessing sub-tasks, see Postprocessing Sub-Tasks (p. 283) and derived quantities in the Polyflow User's Guide. To access documentation files on the ANSYS Customer Portal, go to http:// support.ansys.com/documentation.. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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3D Thermoforming of a Blister

1.3.10. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 1.

Double-click the Results cell in the Workbench analysis system. CFD-Post reads the solution fields that were saved to the results file.

2.

Align the view as shown in the following figure.

3.

Display contours of thickness in the fluid region (Subdomain1).

288

a.

Insert → Contour or click the

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.

button.

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Setup and Solution

c.

Specify the following settings in the Geometry tab: i.

Select Subdomain_1_surf from the Locations drop-down list.

ii.

Ensure THICKNESS is selected from the Variable 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.

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3D Thermoforming of a Blister Figure 1.5: Contours of Thickness 1/4 Geometry

4.

Show the contours of thickness on the full mold. a.

290

Double-click Default Transform in the Outline tree tab, under User Locations and Plots (or rightclick Default Transform and select Edit).

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Setup and Solution

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.

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291

3D Thermoforming of a Blister 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.

292

a.

Click the Timestep Selector icon (

).

b.

Scroll up in the Timestep Selector dialog box and select Step 1.

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Setup and Solution

c.

Click Apply.

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3D Thermoforming of a Blister Figure 1.7: Thickness of the Film at Time=0.001 s

d.

294

Repeat steps a.–c. for timesteps 30, 50, and 73.

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Setup and Solution Figure 1.8: Contours of Thickness at Time = 0.2338 s

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3D Thermoforming of a Blister Figure 1.9: Contours of Thickness at Time = 0.4239 s

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Setup and Solution Figure 1.10: Contours of Thickness at Time = 0.6000 s

6.

Create an animation for the contour plot. a.

Click the animation icon (

).

b.

Ensure Timestep Animation is selected in the Animation dialog box.

c.

To save the animation, expand the dialog box by clicking the button at the lower-right.

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3D Thermoforming of a Blister

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.

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iii.

Disable

to save only one cycle of animations.

iv.

Click the play button, to play the animation and save it as a file.

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Further Improvements

1.4. 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 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.

1.5. Further Improvements 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.wbpz in the 3D-Thermo-Blister_R180\solution folder you unzipped in Preparation (p. 272). 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 in the Polyflow User's Guide. To access documentation files on the ANSYS Customer Portal, go to http://support.ansys.com/documentation. The results are shown in Figure 1.11: Effect of Adaption on Final Mesh and Thickness Variation (p. 300). 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.

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3D Thermoforming of a Blister Figure 1.11: Effect of Adaption on Final Mesh and Thickness Variation

1.6. Appendix The appendix contains the following topics: 1.6.1. Contact Boundary Conditions 1.6.2. Remark on the Penalty Coefficient 1.6.3. Remeshing

1.6.1. Contact Boundary Conditions 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 300

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Appendix 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.

1.6.2. Remark on the Penalty Coefficient 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:

1.6.3. 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.

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Chapter 2: 2D Axisymmetric Blow Molding This tutorial contains the following sections: 2.1. Introduction 2.2. Prerequisites 2.3. Problem Description 2.4. Setup and Solution 2.5. Summary 2.6. 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 homogeneity 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. In this tutorial you will learn how to: • 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.

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. 51). Some steps in the setup procedure will not be shown explicitly.

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2.3. Problem Description 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. 304)) 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 10 cm. Figure 2.1: Problem Description

The domain for the problem is divided into two subdomains: one for the fluid preform (subdomain 1) and the other for the mold (subdomain 2). Incompressibility and momentum equations are solved in 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 the effects of gravity will be included in the calculation.

= 100000 poise. Inertia terms and

The boundary sets for the problem are shown in Figure 2.2: Boundary Set for the Problem (p. 305), and the conditions at the boundaries of the domain (for the preform) are: • boundary 1: symmetry axis

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Setup and Solution • boundary 2: free surface • boundary 3: zero normal velocity and zero surface force • boundary 4: free surface Figure 2.2: Boundary Set for the Problem

2.4. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 2.4.1. Preparation 2.4.2. Project and Mesh 2.4.3. Create a Task for the Model 2.4.4. Material Data 2.4.5. Boundary Conditions 2.4.6. Remeshing 2.4.7. Numerical Parameters 2.4.8. Outputs 2.4.9.Thickness Postprocessor 2.4.10. Save and Exit Polydata 2.4.11. Solution 2.4.12. Postprocessing

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2D Axisymmetric Blow Molding

2.4.1. 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the 2D-Axi-Blow-Molding_R180.zip link to download the input and solution files.

7.

Unzip the 2D-Axi-Blow-Molding_R180.zip file you have downloaded to your working folder. The mesh file 2d-axi-blowmold.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

2.4.2. Project and Mesh 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 Final-blow-mold as the name of the project.

3.

Import the mesh file (2d-axi-blowmold.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.

2.4.3. Create a Task for the Model In the following steps you will define a new task representing the 2D axisymmetric time-dependent model. Then, define the mold and a sub-task for the isothermal flow calculation. 1.

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Create a task for the model.

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Setup and Solution Create a new task a.

Select the following options: • F.E.M. task • Time-dependent problem(s) • 2D axisymmetric geometry 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.

b. 2.

Click Accept the current setup.

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. e.

Click Upper level menu at the top of the menu.

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.

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2D Axisymmetric Blow Molding 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. 305)).

ii. f. 3.

Select Contact.

Click Upper level menu four times to return to the F.E.M. Task 1 menu.

Create a sub-task for the isothermal flow. Create a sub-task a.

Select Generalized Newtonian isothermal flow problem. A dialog box opens, asking for the title of the problem.

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Setup and Solution b.

Enter blow molding as the New value and click OK. The Domain of the sub-task menu item is highlighted.

4.

Define the domain where the sub-task applies. 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. Domain of the sub-task a.

Select SUBDOMAIN_2 and click Remove.

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. The Material data menu item is highlighted.

2.4.4. Material Data 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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2D Axisymmetric Blow Molding a.

Click Shear-rate dependence of viscosity.

b.

Click Constant viscosity.

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.

2.

d.

Enter 100000 [units: poise] as the New value and click OK.

e.

Click Upper level menu two times to continue with the Material Data specification.

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.

3.

310

c.

Enter 1 [units: g/cm3] as the New value and click OK.

d.

Click Upper level menu to continue with the Material Data specification.

Enable the calculation of the inertia terms in the momentum equation.

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Setup and Solution 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.

4.

a.

Click Inertia terms.

b.

Select Inertia will be taken into account.

c.

Click Upper level menu to continue with the Material Data specification.

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 [units: cm/s2] as the New value and click OK.

d.

Click Upper level menu two times to return to the blow molding menu. The Flow boundary conditions menu item is highlighted.

2.4.5. Boundary Conditions In the following steps you will 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. Flow boundary conditions 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 Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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2D Axisymmetric Blow Molding • the contact wall (the boundary of the mold along which the contact is detected) • the penalty coefficient 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.

b.

Click Free surface.

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. 305), the free surface (BOUNDARY2) of the preform 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

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Setup and Solution the prediction of the velocity field in such cases destroys the prediction scheme, you can continue by clicking OK.

e. 3.

4.

Click OK to accept the warning and continue.

Set the conditions at the top part of the preform (BOUNDARY3). a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY3 and click Modify.

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,

. .

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. a.

Select Zero wall velocity (vn=vs=0) along BOUNDARY4 and click Modify.

b.

Click Free surface.

c.

Specify the normal force. i.

Click Normal force.

ii.

Select Constant. Polydata prompts for the new value of the normal force. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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d. 5.

iii.

Enter -2e06 as the New value and click OK.

iv.

Click Upper level menu.

Click Upper level menu to return to the Flow boundary conditions menu.

Click Upper level menu to return to the blow molding menu. The Global remeshing menu item is highlighted.

2.4.6. Remeshing 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 1.

Specify the region where the remeshing is to be performed (SUBDOMAIN_1). 1–st local remeshing

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Setup and Solution

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. 332). 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.

2.4.7. Numerical Parameters In the following steps you will define the numerical parameters for the simulation. Numerical parameters 1.

Specify the parameters for the iterative scheme in the calculation of the free surface. Modify the transient iterative parameters

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2D Axisymmetric Blow Molding

For information on time marching scheme, see Appendix (p. 332). 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. Enter 0.1 [units: s] as the New value and click OK.

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 [units: s] 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 Enter 1e-07 [units: s] as the New value and click OK.

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Setup and Solution 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 Enter 1e-03 [units: s] as the New value and click OK.

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 0.01 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. 2.

Enable Use of the implicit Euler method.

Click Upper level menu three times to return to the top-level Polydata menu.

2.4.8. Outputs You can specify how often Polyflow saves the solution data when it calculates a solution. In this tutorial, save the results at every 4 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. a.

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2D Axisymmetric Blow Molding b. 4.

Click Set to metric_cm/g/s/A+Celsius.

Click Upper level menu twice to return to the top-level Polydata menu.

2.4.9. Thickness Postprocessor In the following steps you will 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. Domain of the sub-task 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

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a.

Select BOUNDARY2: not used and click Modify.

b.

Click Starting border.

c.

Select BOUNDARY4: not used and click Modify.

d.

Click Ending border.

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Setup and Solution 7.

Click Upper level menu five times to return to the top-level Polydata menu.

2.4.10. Save and Exit Polydata Save and exit Polydata asks you 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 postprocessing, and the Polyflow format results file is (res).

2.4.11. Solution In the following steps you will 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. 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.... Workbench opens the View listing file dialog box, 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.

2.4.12. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 1.

Double-click the Results cell in the Workbench analysis system. CFD-Post reads the solution fields that were saved to the results file.

2.

Align the view as shown in the following figure.

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2D Axisymmetric Blow Molding

3.

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Display contours of thickness in the fluid region (SUBDOMAIN_1). a.

Click the Insert menu and select Contour or click the

button.

b.

In the box that opens, click OK to accept the default name (Contour 1) and display the details below the Outline tree.

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Setup and Solution

c.

d.

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.

)

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.

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2D Axisymmetric Blow Molding 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. a.

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Double-click Default Transform in the Outline tree tab, under User Locations and Plots (or rightclick Default Transform and select Edit).

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Setup and Solution

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.

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2D Axisymmetric Blow Molding 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

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button.

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Setup and Solution

a.

Select the 20 th timestep and click Apply.

b.

Select the 40 th timestep and click Apply.

c.

Select the 60 th timestep and click Apply.

d.

Select the final timestep and click Apply. 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.

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2D Axisymmetric Blow Molding Figure 2.5: Contours of Thickness at the 20th Timestep

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Setup and Solution Figure 2.6: Contours of Thickness at the 40th Timestep

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2D Axisymmetric Blow Molding Figure 2.7: Contours of Thickness at the 60th Timestep

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Setup and Solution 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 Timestep Animation in the Animation dialog box.

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2D Axisymmetric Blow Molding

7.

c.

Enable Save Movie to save the animation as a file.

d.

Disable

e.

Click the start button

to save only one cycle of animations. .

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. At the final time of the simulation,

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Summary 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. 269). Figure 2.9: Final Velocity Distribution

2.5. 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.

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2D Axisymmetric Blow Molding

2.6. Appendix The appendix covers the following topics: 2.6.1. Remeshing Technique 2.6.2.Time Marching Scheme

2.6.1. Remeshing Technique The purpose of the remeshing technique is to relocate internal nodes according to the displacement of the boundary nodes due to the motion of the free surface. In blow molding applications, the finiteelement mesh undergoes large deformations, especially extension. When a thin fluid region is considered, the shear component is essentially absent from the flow kinematics. Because this application involves contact occurring over time, a Lagrangian representation is used for the free surface that undergoes the contact; this improves the robustness of the contact algorithm. The Lagrangian on the border only technique remeshes based on the combination of a Lagrangian representation on the border of the fluid domain and a minimum-pseudo-energy representation for the inner mesh nodes. For additional information on this technique, see Lagrangian method on borders in the Polyflow User's Guide. To access documentation files on the ANSYS Customer Portal, go to http:// support.ansys.com/documentation.

2.6.2. 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.

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Chapter 3: Plug-Assisted Thermoforming of a Blister This tutorial is divided into the following sections: 3.1. Prerequisites 3.2. Problem Description 3.3. Setup and Solution 3.4. Summary 3.5. Appendix

3.1. 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. 51). Some steps in the setup procedure will not be shown explicitly.

3.2. Problem Description 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. 334) shows a sketch of the process in the initial configuration.

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Plug-Assisted Thermoforming of a Blister 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. 334). 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.

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Problem Description 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. That is, each mesh node is a material point. The finite element mesh and the boundary conditions are displayed in Figure 3.2: Finite Element Mesh, Subdomains and Boundary Sets (p. 335). 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

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335

Plug-Assisted Thermoforming of a Blister As seen in Figure 3.2: Finite Element Mesh, Subdomains and Boundary Sets (p. 335), 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 acquiring its shape.

3.3. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 3.3.1. Preparation 3.3.2. Project and Mesh 3.3.3. Mold Sub-Task 3.3.4. Plug Sub-Task 3.3.5. Blister Sub-Task 3.3.6. Numerical Parameters 3.3.7. Outputs 3.3.8. Save and Exit Polydata 3.3.9. Solution 3.3.10. Postprocessing

3.3.1. 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.

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Setup and Solution 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the Plug-Thermo-Blister_R180.zip link to download the input and solution files.

7.

Unzip the Plug-Thermo-Blister_R180.zip file you have downloaded to your working folder. The mesh file plugblister.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

3.3.2. Project and Mesh 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-plug-assist as the name of the project.

3.

Import the mesh file (plugblister.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.

3.3.3. Mold Sub-Task In the following steps you will define the task representing the mold. 1.

Create a task for the model. Create a new task a.

Select the following options: • F.E.M. task • Time-dependent problem(s) • 2D shell geometry

b. 2.

Click Accept the current setup.

Define the molds.

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Plug-Assisted Thermoforming of a Blister Define molds a.

Create the new mold. Create a new mold

b.

Click Adiabatic mold. A dialog box opens, asking for the title of the mold.

c.

Click OK to accept the default name, Mold 1. The Domain of the mold menu item is highlighted.

3.

Define the domain where the mold applies. Domain of the mold

338

a.

Select Subdomain 1 and click Remove.

b.

Select Subdomain 3 and click Remove.

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Setup and Solution

c. 4.

Click Upper level menu at the top of the Domain of the mold menu.

Define the contact boundary conditions. Contact conditions

5.

a.

Select No contact along Subdomain 2 and click Modify.

b.

Select Contact and click Upper level menu twice.

Define the motion of the mold. Mold motion a.

Click Mold motion type : fixed mold. A dialog box opens, asking you to specify the type of mold motion.

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Plug-Assisted Thermoforming of a Blister

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.

340

Specify the x-velocity.

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Setup and Solution

Click OK to accept the default value of 0 [units: mm/s] 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 [units: mm/s] 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 [units: 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.

Enter 0.097 as the New value and click OK. vi.

In a similar manner, set the values for b, c, and d to 1.0, 0.103, and 0, respectively. Figure 3.3: Ramp Function for Mold Velocity (p. 342) shows the ramp function you just defined.

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Plug-Assisted Thermoforming of a Blister Figure 3.3: Ramp Function for Mold Velocity

Click Upper level menu to return the Mold motion menu. vii. Click the EVOL button at the top of the menu to disable evolution inputs. viii. Click Upper level menu two times to return to the Define molds menu.

3.3.4. Plug Sub-Task In the following steps you will define the task representing the plug. 1.

Create the new mold. Create a new mold A dialog box 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. The Domain of the mold menu item is highlighted.

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Setup and Solution 2.

Define the domain where the mold applies. Domain of the mold

3.

a.

Select Subdomain 1 and click Remove.

b.

Select Subdomain 2 and click Remove.

c.

Click Upper level menu at the top of the Domain of the mold menu.

Define the contact boundary conditions. Contact conditions

4.

a.

Select No contact along Subdomain 3 and click Modify.

b.

Select Contact and click Upper level menu twice.

Define the motion of the plug. Mold motion a.

Click Mold motion type : fixed mold. A dialog box opens, asking you to specify the type of mold motion.

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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Plug-Assisted Thermoforming of a Blister

Click OK to accept the default value of 0 [units: mm/s] 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 [units: mm/s] 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 -500 [units: mm/s] for the New value of velocity-z and click OK.

iv.

Specify the time dependence of the z-velocity. 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.

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Setup and Solution

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. 345) shows the multi-ramp function you just defined. Figure 3.4: Multi-Ramp Function for Plug Velocity

Click Upper level menu three times to return 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. The Create a sub-task menu item is highlighted.

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Plug-Assisted Thermoforming of a Blister

3.3.5. Blister Sub-Task In the following steps you will define the nature of 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.

Select Shell model : Gen. Newtonian isothermal. A dialog box opens, asking for the title of the problem.

b.

Enter Blister as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies. Domain of the sub-task a.

Select Subdomain 2 and click Remove.

b.

Select Subdomain 3 and click Remove.

c.

Click Upper level menu button at the top of the Domain of the sub-task menu. The Flow boundary conditions menu item is highlighted.

3.

Specify the flow boundary conditions. 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.

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Click Plane of symmetry ( fs=0, vn=0 ).

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Setup and Solution

c.

ii.

Select normal direction along X axis.

iii.

Click Upper level menu to continue specifying flow boundary conditions.

Select Zero wall velocity (vn=vs=0) along Boundary 4 and click Modify. i.

Click Plane of symmetry ( fs=0, vn=0 ).

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 dialog box opens, asking for the new value of the constant.

Enter 1e05 [units: Pa] as the New value and click OK. f.

Click the EVOL button at the top of the Polydata menu to enable evolution inputs.

g.

Click Upper level menu. 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 0.14 as the New value.

iii.

In a similar manner, set constants b, c, and d to 0, 0.15, and 1.0 respectively. Figure 3.5: Ramp Function for Pressure (p. 348) shows the ramp function you just defined.

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Plug-Assisted Thermoforming of a Blister Figure 3.5: Ramp Function for Pressure

h.

Click Upper level menu. Click the EVOL button at the top of the Polydata menu to disable evolution inputs.

i. 4.

Click Upper level menu to return to the Blister menu.

Define the contact of the mold. 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.

c.

Define the contact wall. i.

Click Select a contact wall.

ii.

Select Mold 1 : Contact along Subdomain 2 and click Select.

Specify the coefficients and accuracy. i.

Click Modify slipping coefficient. Retain the default of 1e+09 and click OK.

ii.

Click Modify penalty coefficient. Retain the default of 1e+09 and click OK.

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Setup and Solution iii.

Click Modify penetration accuracy. Enter 0.05 as the New value and click OK.

d.

Define the orientation of the mold. 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. Darts will be displayed in the Graphics Display window, as shown in the following figure.

iv.

Click No in the dialog box 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 dialog box, rotate the view and/or change the magnification, click Specify mold side / cavity side again, and then answer the question appropriately.

v.

Click Upper level menu to return to the Define contacts menu. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Plug-Assisted Thermoforming of a Blister 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.

b.

Define the contact wall. i.

Click Select a contact wall.

ii.

Select plug : Contact along Subdomain 3 and click Select.

Activate contact release and specify the coefficients and accuracy. i.

Click Modify adhesion force density. Click Yes in the dialog box that asks if you want to activate contact release. Enter 10 as the New value for adhesion force density.

ii.

Click Modify slipping coefficient. Retain the default of 1e+09 and click OK.

iii.

Click Modify penalty coefficient. Retain the default of 1e+09 and click OK.

iv.

Click Modify penetration accuracy. Enter 0.05 as the New value and click OK.

c.

Define the orientation of the plug. i.

Rotate the view and change the magnification so that you can see the plug.

ii.

Click Specify mold side / cavity side. Darts will be displayed in the Graphics Display window, as shown in the following figure.

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Setup and Solution

iii.

Click Yes in the dialog box that opens, to verify that the darts are pointing toward the plug body (away from contact with the film). If the direction of the darts is not clear to you, you can close the dialog box, rotate the view and/or change the magnification, click Specify mold side / cavity side again, and then answer the question appropriately.

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.

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Plug-Assisted Thermoforming of a Blister

6.

Define the layers of the blister. Define layers a.

Click Create a new layer. Enter blister as the New value in the dialog box 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 i.

Click Shear-rate dependence of viscosity.

ii.

Click Constant viscosity.

iii.

Click Modify fac. Enter 1e05 [units:

] the New value and click OK.

iv.

Click Upper level menu twice to continue with material data specification.

v.

Click Density.

vi.

Click Modification of density. Enter 0.001 [units: g/mm3] as the New value and click OK.

vii. Click Upper level menu to continue with the material data specification. 352

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Setup and Solution viii. Click Inertia terms.

c.

ix.

Select Inertia will be taken into account.

x.

Click Upper level menu twice to return to the blister menu.

Specify the initial thickness. Initial thickness i.

Click Constant. Enter 0.35 [units: mm] as the New value and click OK.

ii.

Click Upper level menu four times to return to the F.E.M. Task 1 menu.

3.3.6. Numerical Parameters Numerical parameters 1.

Click Modify the transient iterative parameters.

2.

Click Modify the initial time value. Retain the default of 0.0 [units: s] and click OK.

3.

Click Modify the upper time limit. Retain the default of 1.0 [units: s] and click OK.

4.

Click Modify the initial value of the time-step. Enter 0.0001 [units: s] as the New value and click OK.

5.

Click Modify the min value of the time-step. Enter 1e-05 [units: s] as the New value and click OK.

6.

Click Modify the max value of the time-step. Enter 0.01 [units: s] as the New value and click OK.

7.

Click Modify the tolerance. Retain the default of 0.01 and click OK.

8.

Click Modify the max number of successful steps. Enter 400 as the New value and click OK. The maximum number of steps must be increased due to the case containing two contacts and “sharp” changes in the kinematics. This higher number was determined by running the problem with a maximum of 200 steps and observing that more steps were required to reach the final time. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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Plug-Assisted Thermoforming of a Blister 9.

Click Upper level menu to return to the Numerical Parameters menu.

10. Click Modify numerical parameters for iterations. 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. 12. Click Upper level menu three times to return to the top-level Polydata menu.

3.3.7. Outputs Outputs 1.

Set the system of units to output to CFD-Post. Set units for CFD-Post, Ansys Mapper or Iges

2.

Modify the current system of units. Modify system of Units

3.

Specify the new system of units. Set to metric_mm/g/s/mA+Celsius

4.

Click Upper level menu three times to return to the top-level Polydata menu.

3.3.8. Save and Exit Polydata 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 postprocessing, and the Polyflow format results file (res).

3.3.9. Solution 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. 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.

354

Check for convergence in the listing file.

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Setup and Solution a.

Right-click the Solution cell and select Listing Viewer.... Workbench opens the View listing file dialog box, 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.

3.3.10. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 1.

Double-click the Results cell in the Workbench analysis system. CFD-Post reads the solution fields that were saved to the results file.

2.

Align the view as shown in the following figure.

3.

Display contours of thickness in the fluid region (Subdomain 1).

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Plug-Assisted Thermoforming of a Blister

356

a.

Click the Insert menu and select Contour or click the

button.

b.

In the box that opens, click OK to accept the default name (Contour 1) and display the details view below the Outline tree.

c.

Perform the following steps 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 ( 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.

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) on the

Setup and Solution Figure 3.6: 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 rightclick Default Transform and select Edit).

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Plug-Assisted Thermoforming of a Blister

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.

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Rotate the view and change the magnification, as shown in Figure 3.7: Contours of Thickness on the Whole Thermoformed Blister (p. 359).

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Setup and Solution Figure 3.7: Contours of Thickness on the Whole Thermoformed Blister

5.

Display contours of thickness at various time steps. Polydata exported a total of 166 time steps to CFD-Post. a.

Click the Timestep Selector icon (

).

b.

Scroll up in the Timestep Selector dialog box and select Step 1.

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Plug-Assisted Thermoforming of a Blister

c.

360

Click Apply.

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Setup and Solution Figure 3.8: Thickness of the Film at Time = 0.0001 s

d.

Repeat steps 5. a.–c. for timesteps 40, 60, and 166.

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Plug-Assisted Thermoforming of a Blister Figure 3.9: Contours of Thickness at Time = 0.1208 s

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Setup and Solution Figure 3.10: Contours of Thickness at Time = 0.1291 s

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Plug-Assisted Thermoforming of a Blister Figure 3.11: Contours of Thickness at Time = 1.0 s

6.

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Create an animation for the contour plot. a.

Click the animation icon (

).

b.

Ensure Timestep Animation is selected in the Animation dialog box.

c.

To save the animation, expand the dialog box by clicking the button at the lower-right.

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Setup and Solution

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.

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Plug-Assisted Thermoforming of a Blister

3.4. 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 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.

3.5. Appendix The appendix covers the following topics: 3.5.1. Contact Boundary Conditions 3.5.2. Remark on the Penalty Coefficient 3.5.3. Remeshing

3.5.1. Contact Boundary Conditions 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 algorithm 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.

3.5.2. Remark on the Penalty Coefficient 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

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Appendix 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:

3.5.3. Remeshing The results of this tutorial could be refined and improved with the use of adaptive meshing. In the context of the membrane element, a Lagrangian representation is applied where all mesh nodes are considered material points. Therefore, the only available remeshing technique is Lagrangian and is the one that should be specified for this case.

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Chapter 4: 3D Blow Molding of a Bottle This tutorial is divided into the following sections: 4.1. Prerequisites 4.2. Description 4.3. Setup and Solution 4.4. Summary 4.5. Further Improvements 4.6. Appendix

4.1. 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. 51). Some steps in the setup procedure will not be shown explicitly.

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. 370) shows a sketch of the process in the initial configuration, before the pinchoff and parison inflation.

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3D Blow Molding of a Bottle 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. That is, each mesh node is a material point. The finite element mesh and the boundary conditions are displayed in Figure 4.2: Finite Element Mesh, Subdomains, and Boundary Sets (p. 371). 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 important 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

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Setup and Solution Figure 4.2: Finite Element Mesh, Subdomains, and Boundary Sets

As seen in Figure 4.2: Finite Element Mesh, Subdomains, and Boundary Sets (p. 371), 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 representing the parison.

4.3. Setup and Solution The following sections describe the setup and solution steps for this tutorial: 4.3.1. Preparation 4.3.2. Project and Mesh 4.3.3. Right Mold 4.3.4. Left Mold 4.3.5. Parison Sub-Task 4.3.6. Numerical Parameters 4.3.7. Outputs 4.3.8. Save and Exit Polydata 4.3.9. Solution 4.3.10. Postprocessing

4.3.1. Preparation To prepare for running this tutorial: 1.

Prepare a working folder for your simulation. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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3D Blow Molding of a Bottle 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 18.0 under Version.

5.

Select this tutorial from the list.

6.

Click the 3D-Blow-Molding-Bottle_R180.zip link to download the input and solution files.

7.

Unzip the 3D-Blow-Molding-Bottle_R180.zip file you have downloaded to your working folder. The mesh file bottle.msh can be found in the unzipped folder.

8.

Start Workbench from Start > All Programs > ANSYS 18.0 > Workbench 18.0.

4.3.2. Project and Mesh 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 instanet-PF-only as the name of the project.

3.

Import the mesh file (bottle.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.

4.3.3. Right Mold In the following steps you will define the task representing the right half of the mold. 1.

Create a task for the model. Create a new task a.

Select the following options: • F.E.M. task • Time-dependent problem(s)

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Setup and Solution • 2D shell geometry b. 2.

Click Accept the current setup.

Define the right mold. Define molds a.

Create the new mold. Create a new mold Click Mold with constant and uniform temperature. A dialog box opens, asking for the title of the mold.

b.

Enter Mold-Right and click OK. The Domain of the mold menu item is highlighted.

3.

Define the domain where the mold applies. Domain of the mold a.

Select MOLDLEFT and click Remove.

b.

Select PARISON and click Remove.

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3D Blow Molding of a Bottle

c. 4.

Click Upper level menu at the top of the Domain of the mold menu.

Define the contact boundary conditions. Contact conditions

5.

a.

Select No contact along MOLDRIGHT and click Modify.

b.

Select Contact and click Upper level menu twice.

Define the motion of the mold. Mold motion a.

Click Mold motion type : fixed mold. A small dialog box opens, asking you to specify the type of mold motion.

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Setup and Solution

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.

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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 0.736842 [units: m/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.

Enter 0.09 as the New value 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. 377) shows the ramp function you just defined.

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Setup and Solution Figure 4.3: Ramp Function for Right Mold Velocity

Click Upper level menu to return the Mold motion menu. vii. Click the EVOL button at the top of the menu to disable evolution inputs. viii. Click Upper level menu two times to return to the Define molds menu.

4.3.4. Left Mold In the following steps you will define the task representing the left half of the mold. 1.

Create the new mold. Create a new mold A dialog box opens, asking if you want to copy the data of an existing mold.

Click No. a.

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3D Blow Molding of a Bottle b.

Enter Mold-Left as the New value and click OK. The Domain of the mold menu item is highlighted.

2.

Define the domain where the mold applies. Domain of the mold

3.

a.

Select MOLDRIGHT and click Remove.

b.

Select PARISON and click Remove.

c.

Click Upper level menu at the top of the Domain of the mold menu.

Define the contact boundary conditions. Contact conditions

4.

a.

Select No contact along MOLDLEFT and click Modify.

b.

Select Contact and click Upper level menu twice.

Define the motion of the left mold. Mold motion a.

Click Mold motion type : fixed mold. A small dialog box opens, asking you to specify the type of mold motion.

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

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Setup and Solution Polydata prompts for velocity-x. i.

Specify the x-velocity.

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 0.736842 [units: m/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.

Enter 0.09 as the New value and click OK. vi.

In a similar manner, set the values for b, c, and d to 1.0, 0.1, and 0, respectively.

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3D Blow Molding of a Bottle Figure 4.4: Ramp Function for Left Mold Velocity (p. 380) shows the ramp function you just defined. 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. The Create a sub-task menu item is highlighted.

4.3.5. Parison Sub-Task In the following steps you will define the nature of 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.

Select Shell model : Gen. Newtonian isothermal. A small dialog box opens, asking for the title of the problem.

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Setup and Solution

b.

Enter Parison as the New value and click OK. The Domain of the sub-task menu item is highlighted.

2.

Define the domain where the sub-task applies. Domain of the sub-task 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. The Flow boundary conditions menu item is highlighted.

3.

Specify the flow boundary conditions. Flow boundary conditions a.

b.

c.

Select Zero wall velocity (vn=vs=0) along BOTTOMEDGE and click Modify. i.

Click Plane of symmetry ( fs=0, vn=0 ).

ii.

Select normal direction along Y axis.

iii.

Click Upper level menu to continue specifying flow boundary conditions.

Select Zero wall velocity (vn=vs=0) along TOPEDGE and click Modify. i.

Click Plane of symmetry ( fs=0, vn=0 ).

ii.

Select normal direction along Y axis.

iii.

Click Upper level menu to return to the Flow boundary conditions menu.

Click Inflation pressure imposed at the bottom of the Flow boundary conditions menu.

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3D Blow Molding of a Bottle 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.

e.

Click Constant for the inflation pressure. A dialog box opens, asking for the new value of the constant.

Enter -1e4 [units: Pa] as the New value and click OK.

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Setup and Solution The pressure is negative due to the orientation of the darts. f.

Click the EVOL button at the top of the Polydata menu to enable evolution inputs.

g.

Click Upper level menu.

h.

Define the settings in the Time dependence of inflation pressure menu that opens. i.

Select f(t) = Ramp function.

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. Figure 4.5: Ramp Function for Pressure (p. 383) shows the ramp function you just defined. Figure 4.5: Ramp Function for Pressure

4.

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.

Define the contact with the right mold. 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. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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3D Blow Molding of a Bottle b.

c.

Define the contact wall. i.

Click Select a contact wall.

ii.

Select Mold-Right : Contact along MOLDRIGHT and click Select.

Specify the coefficients and accuracy. i.

Click Modify slipping coefficient. Retain the default of 1e+09 and click OK.

ii.

Click Modify penalty coefficient. Retain the default of 1e+09 and click OK.

iii.

Click Modify penetration accuracy. Enter 0.001 as the New value and click OK.

d.

Define the orientation of the mold. 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. Darts will be displayed in the Graphics Display window, as shown in the following figure.

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Setup and Solution

iv.

Click No in the dialog box 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 dialog box, rotate the view and/or change the magnification, click Specify mold side / cavity side again, and then answer the question appropriately.

v.

5.

Click Upper level menu to return to the Define contacts menu.

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.

b.

Define the contact wall. i.

Click Select a contact wall.

ii.

Select Mold-Left : Contact along MOLDLEFT and click Select.

Specify the coefficients and accuracy. Release 18.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential information of ANSYS, Inc. and its subsidiaries and affiliates.

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3D Blow Molding of a Bottle i.

Click Modify slipping coefficient. Retain the default of 1e+09 and click OK.

ii.

Click Modify penalty coefficient. Retain the default of 1e+09 and click OK.

iii.

Click Modify penetration accuracy. Enter 0.001 as the New value and click OK.

c.

Define the orientation of the mold. i.

Rotate the view slightly to display the bottle-shaped cavity from an oblique angle.

ii.

Click Specify mold side / cavity side. Darts will be displayed in the Graphics Display window, as shown in the following figure.

iii.

386

Click No in the dialog box that opens, to specify that the darts are not pointing towards the mold body.

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Setup and Solution If the direction of the darts is not clear to you, you can close the dialog box, rotate the view and/or change the magnification, click Specify mold side / cavity side again, and then answer the question appropriately. iv.

6.

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 disabled.

Define the layers of the parison. Define layers a.

Click Create a new layer. In the dialog box 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 i.

Click Shear-rate dependence of viscosity.

ii.

Click Constant viscosity.

iii.

Click Modify fac.

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3D Blow Molding of a Bottle Enter 10000 [units:

] as the New value and click OK.

iv.

Click Upper level menu twice to continue with material data specification.

v.

Click Density.

vi.

Click Modification of density. Enter 900 [units: kg/m3] as the New value and click OK.

vii. Click Upper level menu to continue with the material data specification. viii. Click Inertia terms. ix.

c.

Select Inertia will be taken into account and click Upper level menu twice to return to the parison menu.

Specify the initial thickness. Initial thickness i.

Click Constant. Enter 0.003 [units: m] as the New value and click OK.

ii.

Click Upper level menu four times to return to the F.E.M. Task 1 menu.

4.3.6. Numerical Parameters Numerical parameters 1.

Click Modify the transient iterative parameters.

2.

Click Modify the initial time value. Retain the default of 0.0 [units: s] and click OK.

3.

Click Modify the upper time limit. Enter 2.0 [units: s] as the New value and click OK.

4.

Click Modify the initial value of the time-step. Retain the default of 0.01 [units: s] and click OK.

5.

Click Modify the min value of the time-step. Retain the default of 0.0001 [units: s] and click OK.

6.

Click Modify the max value of the time-step. Retain the default of 0.25 [units: s] and click OK.

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Setup and Solution 7.

Click Modify the tolerance. Retain the default of 0.01 [units: s] and click OK.

8.

Click Modify the max number of successful steps. Retain the default of 200 [units: s] and click OK.

9.

Click Upper level menu three times to return to the top-level Polydata menu.

4.3.7. Outputs Outputs 1.

Set the system of units to output to CFD-Post. Set units for CFD-Post, Ansys Mapper or Iges

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.

3.

Click Upper level menu twice to return to the top-level Polydata menu.

4.3.8. Save and Exit Polydata 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 postprocessing, and the Polyflow format results file (res).

4.3.9. Solution 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. 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.... Workbench opens the View listing file dialog box, 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.

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3D Blow Molding of a Bottle

4.3.10. Postprocessing Use CFD-Post to view the results of the Polyflow simulation. 1.

Double-click the Results cell in the Workbench analysis system. CFD-Post reads the solution fields that were saved to the results file.

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).

390

a.

Click the Insert menu and select 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 view below the Outline tree.

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Setup and Solution

c.

d.

Specify the following settings in the Geometry tab: i.

Select PARISON_surf from the Locations drop-down list.

ii.

Ensure THICKNESS is selected from the Variable 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.

Disable the Wireframe in the Outline tree tab, under User Locations and Plots. This makes for a cleaner image by removing the Wireframe lines.

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391

3D Blow Molding of a Bottle Figure 4.6: Contours of Thickness on the Parison

4.

Display the parison with the mold. a.

392

Enable and double-click MOLDLEFT_surf in the Outline tree tab, under Fluid Flow Blow Molding Polyflow at 2s.

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Setup and Solution

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.

5.

c.

Click Apply.

d.

In a similar manner, display MOLDRIGHT_surf.

Display contours of thickness at various time steps. Polydata exported a total of 81 time steps to CFD-Post. a.

Click the Timestep Selector icon (

).

b.

Scroll up in the Timestep Selector dialog box and select Step 1.

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3D Blow Molding of a Bottle

c.

394

Click Apply.

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Setup and Solution Figure 4.7: Thickness of the Film at Time = 0.01 s

d.

Repeat steps 5. a.–c. for timesteps 28, 58, and 81.

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3D Blow Molding of a Bottle Figure 4.8: Contours of Thickness at Time = 0.09253 s

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Setup and Solution Figure 4.9: Contours of Thickness at Time = 0.23409 s

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397

3D Blow Molding of a Bottle Figure 4.10: Contours of Thickness at Time = 2.0 s

6.

398

Create an animation for the contour plot. a.

Click the animation icon (

).

b.

Enable Timestep Animation in the Animation dialog box.

c.

To save the animation, expand the dialog box by clicking the button at the lower-right.

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Setup and Solution

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.

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399

3D Blow Molding of a Bottle

4.4. 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 parison. 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 interpolated 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.

4.5. Further Improvements 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.wbpz in the 3D-Blow-Molding-Bottle_R180\solution folder you unzipped in Preparation (p. 272). 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 in the Polyflow User's Guide. To access documentation files on the ANSYS Customer Portal, go to http://support.ansys.com/documentation. The results are shown in Figure 4.11: Effect of Adaption on Final Mesh and Thickness Variation (p. 401).

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Appendix Figure 4.11: Effect of Adaption on Final Mesh and Thickness Variation

4.6. Appendix The appendix contains the following topics: 4.6.1. Contact Boundary Conditions 4.6.2. Remark on the Penalty Coefficient 4.6.3. Remeshing 4.6.4. Evolutions

4.6.1. Contact Boundary Conditions 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

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401

3D Blow Molding of a Bottle 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.

4.6.2. Remark on the Penalty Coefficient 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 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. 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 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:

4.6.3. Remeshing In the context of the membrane element, a Lagrangian representation is applied where all mesh nodes are considered material points. Therefore, the only available remeshing technique is Lagrangian and is the one that should be specified for this case.

4.6.4. 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 direction 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

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Appendix 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.

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403

404

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