OS-HM-T: 13010 Shape Optimization of Aluminum Fins Based on Heat Transfer Analysis

Tutorial Level: Advanced In this tutorial, shape optimization on an example of aluminum fins is performed.

A part of the fins’ base experiences a constant heat flux of q = 8000 W/m2. The temperature of the surrounding air is 283 K, with a corresponding heat transfer coefficient of H = 40 W/m2 • K. The heat conduction coefficient is K = 221 W/m • K. The temperature distribution within the fins is determined by solving the heat conduction and convection load case.
Figure 1. Model Overview


Before you begin, copy the file(s) used in this tutorial to your working directory.
The optimization problem for this tutorial is stated as:
Objective
Minimize the temperature at the center of the base.
Constraints
Volume < 1.0e-5 m2.
Design Variables
Shape design variables.
The following exercises are included:
  • Set up the shape optimization problem in HyperMesh.
  • Post-process optimization results in HyperView.

Launch HyperMesh

  1. Launch HyperMesh.
  2. In the New Session window, select HyperMesh from the list of tools.
  3. For Profile, select OptiStruct.
  4. Click Create Session.
    Figure 2. Create New Session


    This loads the user profile, including the appropriate template, menus, and functionalities of HyperMesh relevant for generating models for OptiStruct.

Import the Model

  1. On the menu bar, select File > Import > Solver Deck.
  2. In the Import File window, navigate to and select fins.fem you saved to your working directory.
  3. Click Open.
  4. In the Solver Import Options dialog, ensure the Reader is set to OptiStruct.
    Figure 3. Import Base Model in HyperMesh


  5. Accept the default settings and click Import.
    Tip: Alternatively, you can drag and drop the file from your file browser into the application window to open the model file.

Set Up the Optimization

Create Shapes in HyperMorph

The Free morphing function in Morph forms perturbations which are saved as Shapes. For a more detailed description of the functionality of the Morph page, refer to the Morph section of the HyperMesh documentation.

  1. Open the Morph ribbon and click Free.
    Figure 4. Free Tool


  2. On the guide bar, click Move > Faces.
    Figure 5. Guide Bar


  3. Select the end of one of the fins.
    Figure 6. Select End of Fin


  4. Click the arrow pointing normal to the selected element faces (X-direction).
  5. In the micro-dialog, for X, enter 0.03.
    Figure 7. Select X-direction


  6. Press Enter.
    The fin extends by the value entered in the micro-dialog.
    Figure 8. Extended Fin


  7. On the Morph ribbon, hover over the Shapes tool and select the Create satellite icon to save a shape.
    Figure 9. Select Create


  8. Hover over the Shapes tool and select the Undo All satellite icon to reset moved elements to their original positions.
    Figure 10. Select Undo All


  9. In the modeling window, right-click and select Select > Reset Selection.
    Figure 11. Reset Selection


  10. Repeat steps 2 through 9 to create 2 more shapes on the other fins, selecting the end of each fin to be the facets directly morphed.
    Figure 12. Shapes Created on Fins


    Note: To control the Shapes display, from the Model Browser you can right-click on Shapes in the list and select Hide/Show.

Create Shape Design Variables

  1. Open the Optimize ribbon and click Shapes.
    Figure 13. Shapes Tool


  2. For Shape Id, select Unspecified.
    Figure 14. Create Design Variable


  3. Click the Search tool.
  4. Select the first saved shape from the list.
  5. For Initial Value, enter 0.0.
  6. For Lower Bound, enter -1.0.
  7. For Upper Bound, enter 2.0.
    Figure 15. Design Variable Defined


  8. Click Close.
    A shape design variable is created from the first saved shape created in the previous step.
  9. Repeat steps 2 through 8 to create shape design variables from the other two saved shapes.

Create Design Responses

A volume response is created and then defined as the constraint of the optimization problem. A temperature response is created and then defined as the objective.

  1. On the Optimize ribbon, Targets tool group, click Responses.
    Figure 16. Responses Tool


  2. For Name, enter volume.
  3. For Response Type, select volume from the drop-down menu.
  4. Ensure total is selected for Property Type.
  5. Click Close.
    The total volume of the fins is created as the response.
  6. On the ribbon, click Responses.
  7. For Name, enter temperature.
  8. For Response Type, select temperature from the drop-down menu.
  9. For List of Nodes, click 0 Nodes.
  10. Click to open Advanced Selection.
  11. In the drop-down, choose to select nodes By ID and enter 2450.
    Figure 17. Select Nodes by ID


  12. Click OK.
    "1 Nodes" is now shown for List of Nodes in the dialog.
    Figure 18. List of Nodes Shows 1 Node Selected


  13. Click Close.
    The temperature response at node 2450 is created.

Define the Optimization Constraint

  1. On the Optimize ribbon, Targets tool group, click Constraints.
    Figure 19. Constraints Tool


  2. For Name, enter vol.
  3. For Response, click Unspecified.
  4. Click the Search tool.
  5. Select volume from the list of responses.
  6. For Upper Options, select Upper bound from the drop-down menu.
  7. For Upper Bound, enter 1.0e-5.
    Figure 20. Enter Upper Bound


  8. Click Close.
    A volume constraint with the upper bound of 1.0e-5 is created.

Define the Objective Function

  1. On the Optimize ribbon, Targets tool group, click Objectives.
  2. For Name, enter temp.
  3. For Objective Type, select Minimize.
  4. For Response Id, click Unspecified.
  5. Click the Search tool and select temperature from the list of responses.
  6. For Loadstep Id, click Unspecified.
  7. Click the Search tool and select heat transfer.
    Figure 21. temp Objective Parameters
  8. Click Close.
    The objective function of minimizing the temperature at node 2450 is created.

Run the Optimization

  1. From the Optimize tool, click Run.
    Figure 22. Run Optimization


  2. Select the directory where you want to write the OptiStruct model file.
  3. For File name, enter fins_opt.
    The .fem filename extension is the recommended extension for Bulk Data Format input decks.
  4. Click Save.
  5. For Export, select All.
  6. Click Export.
  7. In the Altair Compute Console, click Run.
    If the job is successful, new results files are seen in the directory where the model file was written. The fins_opt.out file is a good place to look for error messages that could help debug the input deck if any errors are present.

Post-process the Results

View Contour Plot

In this step, review the contour plot of the temperatures with the optimized shape in HyperView.

  1. After the "OptiStruct Job completed" message appears in the Run Summary window, click Results.
    This launches HyperView and loads fins_opt_des.h3d.
    Figure 23. Launch Results


  2. In the Results Browser, select the last iteration.
    Figure 24. Show Results Browser


    Figure 25. Select Last Iteration


  3. On the Results ribbon, Plot tool group, select Contour.
    Figure 26.


  4. For Result type, select Shape Change (v) and click Apply.
    Figure 27. Select Shape Change (v) Results


    The optimized shape change contour is displayed.
  5. To load the results of the heat transfer loadcase, in the Home tool group, click Open.
  6. Ensure fins_opt_des.h3d is selected for Load Model and Load Results.
  7. Click Apply, then click Yes.
    Figure 28. Open Heat Transfer Loadcase


  8. In HyperView, click Design History to expand the Page Selection dialog.
  9. Select Subcase 1 - heat transfer.
    Figure 29. Select Subcase 1


  10. From the Results ribbon, Plot tool group, click Contour.
  11. For Result type, select Grid Temperatures (s) and click Apply.
    Figure 30. Select Grid Temperature (s) Results


    The initial temperature distribution contour in the aluminum fins is displayed.
  12. In the Results Browser, select the last iteration.
  13. To overlay the optimized temperature results onto the optimized shape results, switch the Page Selection dialog to the Design History page.
    Figure 31. Page Selection


  14. On the Results ribbon, Create tool group, select DLC.
    Figure 32. DLC Tool


  15. In the Create/Edit Derived Load Case dialog, click Result Files….
    Figure 33. Click Result Files


  16. For Add result file, browse to the directory in which the file was run and select the *__s1.h3d file.
    Figure 34. Open File Browser


  17. Click Open.
  18. Click Close.
    Both the heat transfer results and design results should be visible in the left window.
    Figure 35. Results Visible in Left Window


  19. Select the last iteration of the Design results and click to load the result into the derived loadcase list to the right.
    Figure 36. Load Result into Derived Loadcase


  20. Repeat step 19 to load the last iteration of the Heat Transfer Analysis results.
  21. For derived loadcase Type, select Linear-Superposition.
    Figure 37. Select Linear-Superposition


  22. Click OK.
  23. In the Results browser, choose the newly created Derived Load Case from the drop-down menu.
    Figure 38. Select Derived Loadcase


  24. For Result type, select Grid Temperatures (s) and click Apply.
    The contour plot of grid temperature is now applied on top of the optimized shape. The following plot shows the temperature distributions in the optimized design.
    Figure 39. Temperature Distributions in Optimized Design