ACU-T: 5402 Piezoelectric Flow Energy Harvester with Rigid Body Rotation

This tutorial provides the instructions for setting up, solving and viewing results for a simulation of a piezoelectric fluid harvester. In this simulation, a piezoelectric flow harvester is placed in a fluid flow channel. The harvester is attached to a cylinder mount which also acts as a bluff body causing vortices in the fluid flow. In addition, the cylinder and the harvester are imparted with a sinusoidal rotation motion. The interaction between the pressure fields generated by the vortices and the flow harvester structure is simulated in this tutorial. Arbitrary Lagrangian Eulerian (ALE) approach is used to compute the mesh deformation in the fluid domain as it interacts with the deforming structure.

The basic steps in any CFD simulation are shown in ACU-T: 2000 Turbulent Flow in a Mixing Elbow. The following additional capabilities of AcuSolve are introduced in this tutorial:
  • Defining rigid body rotation motion
  • Implementation of P-FSI in conjunction with rigid body rotation
In this tutorial you will do the following:
  • Analyze the problem
  • Start AcuConsole and read the simulation database of the Piezoelectric Flow Harvester
  • Modify general problem parameters
  • Create multiplier function for rigid body mesh motion
  • Create mesh motion for rigid body rotation
  • Apply mesh motion to the surface attributes
  • Assign rigid body motion to the surface and node attributes
  • Change the inlet velocity
  • Add a time history output point
  • Run AcuSolve
  • Monitor the solution with AcuProbe
  • Post-processing the nodal output with AcuFieldView

Prerequisites

You should have already run through the tutorials ACU-T: 2000 Turbulent Flow in a Mixing Elbow and ACU-T: 5400 Piezoelectric Flow Energy Harvester: A Fluid-Structure Interaction (P-FSI). It is assumed that you have some familiarity with AcuConsole, AcuSolve and AcuFieldView. You will also need access to a licensed version of AcuSolve.

Prior to running through this tutorial, copy AcuConsole_tutorial_inputs.zip from <Altair_installation_directory>\hwcfdsolvers\acusolve\win64\model_files\tutorials\AcuSolve to a local directory. Extract piezo_harvester_P-FSI.acs from AcuConsole_tutorial_inputs.zip. The file piezo_harvester_P-FSI.acs stores the complete setup as described in Piezoelectric Flow Harvester, which includes purely flexible body simulation. In this tutorial, you will start from that database and add a rigid body rotation and then simulate the flow phenomenon.

Analyze the Problem

An important step in any CFD simulation is to examine the engineering problem at hand and determine the important parameters that need to be provided to AcuSolve.

The CFD model contains a cantilever beam and a rigid cylindrical body. The beam along with the cylinder is placed in a water flow stream. This cylindrical body acts a bluff body placed in the flow and stimulates vortex shedding in the flow downstream as it passes over the cylinder. The alternating shedding of vortices creates a zone of alternating asymmetric pressure distribution on either side of the beam. Such an alternating pressure distribution exerts an oscillating force on the beam, creating a sustainable oscillating vibration in the beam.

In this tutorial, in the addition to the flexible motion of the beam adopted in Piezoelectric Flow Harvester Tutorial-1, you will incorporate the rigid body rotation of the cylinder and the beam. The cylinder and the beam are enforced with a sinusoidal oscillatory rotation about the center of the cylinder with a maximum angle of rotation as 100 (i.e. 0.174 rad) with a frequency of 22 rad/sec (3.5 Hz). The axis of rotation is along axis of cylinder. The variation of the rotation angle (θ) is given as:

θ=0.174×sin( 22×t )

Where, t is the time (sec).

Since this tutorial has a rotation motion in addition to flexible motion of beam, you can achieve higher displacements (and hence strains) at lower velocity. Therefore, you will reduce the inlet velocity to 4 m/sec instead of 10 m/sec in Piezoelectric Flow Harvester Tutorial-1.

The schematics of the problem which will be addressed in this tutorial is shown in Figure 1. The modeled domain consists of a fluid volume. The fluid solver does not require the solid body to be modeled. However, the results of the structural solver will be used to define the solid body and the surfaces where the fluid interacts with the solid will be allowed to deform according to the Eigen modes of the beam. Figure 2 shows the arrangement of the beam with its various layers.


Figure 1. Schematic of the Problem


Figure 2. The Beam with its Various Layers

Define the Simulation Parameters

Start AcuConsole and Open the Simulation Database

In the next steps you will start AcuConsole and open a database that is set up for a P-FSI simulation of a non-rotating piezoelectric harvester. You will then make appropriate changes to the database to take into account the rigid body rotation of the harvester in addition to the flexible body motion.

  1. Start OptiStruct from the Windows Start menu by clicking Start > Altair <version> > OptiStruct.
  2. Browse to the location that you would like to use as your working directory.
    This directory is where all files related to the simulation will be stored. The AcuConsole database file (.acs) is stored in this directory. Once the mesh and solution are created, additional files and directories will be created within this directory.
  3. Create a new directory in this location. Name it P-FSI_with_rigid_body_motion.
  4. Click File > Open and open piezo_harvester_P-FSI.acs.
  5. Click File > Save As and enter P-FSI_with_rigid_body_rotation as the file name for the database.

Set General Simulation Attributes

In the next steps you will modify global settings needed for the rigid body rotation of the piezoelectric harvester.

  1. Click BAS in the Data Tree Manager to switch to basic view in the Data Tree.


    Figure 3.
  2. Double-click the Global Data Tree item to expand it.
    Tip: You can also expand a tree item by clicking next to the item name.


    Figure 4.
  3. Double-click Problem Description to open the Problem Description detail panel.
    Tip: You can also open a panel by right-clicking a tree item and clicking Open on the context menu.
  4. Enter P-FSI with rigid body rotation as the Sub title.


    Figure 5.

Create a Multiplier Function for Mesh Motion

The variation of the rotation angle ( θ = 0.174 × sin ( 22 × t ) ) is modeled using a multiplier function using the following steps.

  1. Click PB* in the Data Tree Manager to display all the available settings related to general problem setup in the Data Tree.
  2. Right-click Multiplier Function and click New to create a new multiplier function.
    A new entry, Multiplier Function 1, will be created in the Data Tree under the Multiplier Function branch.
  3. Rename the new multiplier function.
    1. Right-click Multiplier Function 1.
    2. Click Rename.
    3. Type Rotation_multiplier and press Enter.
  4. Double-click Rotation_multiplier to open the detail panel.
  5. Change Type to Sine Series.
  6. Click Open Array next to Sine coefficients.
  7. Fill in the values as follows:
    In the Array Editor, the first column refers to the amplitude of the sine function, second column refers to the frequency of the sine function and the third column refers to phase of the sine wave.


    Figure 6.
  8. Click OK to close the dialog.

Create Mesh Motion for Rigid Body Rotation

In the next steps you will define the rigid body rotation of the cylinder and the beam.

  1. Click ALE in the Data Tree Manager to see all the settings related to mesh motion.
  2. Right-click Mesh Motion and click New to create a new mesh motion.
  3. Rename the new reference frame as Rigid_body_rotation.
  4. Double-click Rigid_body_rotation to open the detail panel.
  5. Change the Type to Rotation.
  6. Click the Open Array button next to Rotation center to open the Array Editor.
  7. Enter -0.1 as the X-coordinate.


    Figure 7.
  8. Click OK to close the dialog.
    Note: (x, y, z) = (-0.1, 0, 0) is the center of the cylinder.
  9. Click the Open Array button next to Angular velocity to open the Array Editor.
  10. Enter 1.0 as the Z-coordinate.


    Figure 8.
  11. Click OK to close the dialog.
  12. Set the Rotation variable to Multiplier Function.
  13. Set the Rotation multiplier function to Rotation_multiplier.


    Figure 9.
    Using the mesh motion Type = Rotation defines the variation of the rotation angle which is used by AcuSolve in evaluating the coordinates of the beam and cylinder. The rotation angle is evaluated by multiplying the value of Rotation Variable with the components of Angular Velocity. Therefore, for this tutorial, the rotation angle comes out to be:(1) R o t a t i o n   a n g l e   ( θ ) = ( R o t a t i o n   V a r i a b l e ) × ( A n g u l a r   V e l o c i t y )

    θ = 1 × 0.174 × sin ( 22 × t ) about z-axis

    For a point with initial coordinates, located on the cylinder or beam, the coordinates at a given time, t, is given by:(2) x = x 0 cos ( θ ) − y 0   sin ( θ ) (3) y = y 0 cos ( θ ) + x 0 sin ( θ ) (4) z = z 0

Assign Rigid Body Motion to the Beam Surface

  1. Click BAS in the Data Tree Manager to switch to basic view in the Data Tree.
  2. Expand Model > Surfaces > Beam.
  3. Double-click Simple Boundary Condition to open the detail panel.
  4. Set the Mesh motion to Rigid_body_rotation.


    Figure 10.

Assign Rigid Body Motion to the Cylinder Surface

  1. Expand Model > Surfaces > Cylinder.
  2. Double-click Simple Boundary Condition to open the detail panel.
  3. Set the Mesh motion to Rigid_body_rotation.


    Figure 11.
  4. Click Save to save the database.

Reduce the Inlet Velocity

As mentioned in Analyze the Problem, you will set the inlet velocity to 4 m/sec.

  1. Expand Model > Surfaces > Inlet.
  2. Double-click Simple Boundary Condition to open the detail panel.
  3. Set the X velocity to 4.0 m/sec.


    Figure 12.

Set Initial Conditions

In the next steps you will set the initial conditions.

  1. Under Global in the Data Tree, double-click Nodal Initial Condition to open the dialog in the detail panel.
  2. Set the X velocity to 4 m/sec.
  3. Verify that the Eddy viscosity is set to 1e-005 m2/sec.


    Figure 13.
  4. Save the database.

Add Time History Output Point

Time History Output commands enables you to extract the nodal solution at any point within the domain. In this simulation, it would be interesting to observe the displacement at the tip and root of the cantilever beam. The .acs database you started with has a monitor point at the tip of the cantilever beam.

The following steps will create a similar monitor point at the root of the cantilever beam.

  1. Double-click the Global Data Tree item to expand it.
  2. Double-click Output.
  3. Right-click on Time History Output, and select New.
  4. Rename the new time history output to Root_MonitorPoint.
  5. Double-click Root_MonitorPoint to open the detail panel.
  6. Change the Type to Coordinates.
  7. Click Open Array next to Coordinates, and update the fields in the Array Editor dialog, as follows:


    Figure 14.
  8. Set Time step frequency to 1.
  9. Click Save to save the database.


    Figure 15.

Compute the Solution and Review the Results

Run AcuSolve

In the next steps you will launch AcuSolve to compute the solution for this case.

  1. Click on the toolbar to open the Launch AcuSolve dialog.
  2. Click Ok to start the solution process.

    While computing the solution, an AcuTail window opens. Solution progress is reported in this window. A summary of the solution process indicates that the run has been completed.

    The information provided in the summary is based on the number of processors used by AcuSolve. If you use a different number of processors than indicated in this tutorial, the summary for your run may be slightly different than the summary shown.



    Figure 16.
  3. Close the AcuTail window and save the database to create a backup of your settings.

Post-Process with AcuProbe

AcuProbe can be used to monitor various variables over solution time.

  1. Open AcuProbe by clicking on the toolbar.
  2. In the Data Tree on the left, expand Time History > Root_MonitorPoint > node 1.
  3. Right-click on mesh_y_displacement and select Plot.
    Note: You might need to click on the toolbar in order to properly display the plot.
  4. Repeat the above steps to plot the mesh_y_displacement for the Tip_MonitorPoint.


    Figure 17.

    The plot above shows the displacement of the tip and the root of the beam, due to the fluid forces as the beam interacts with the flow. The above plot also shows the displacement at the root and at the tip are not in phase, hence maximizing the bending stress (hence, strains) for a lower inlet velocity.

  5. You can also save the plots as an image.
    1. From the AcuProbe dialog, click File > Save.
    2. Enter a name for the image and click Save.
  6. The time series data of the variables can also be exported as a text file for further post-processing.
    1. Right-click on the variable that you want to export and click Export.
    2. Enter a File name and choose .txt for the Save as type.
    3. Click Save.

Post-Process with AcuFieldView

The tutorial has been written with the assumption that you have become familiar with AcuFieldView and basic operations. In general, it will be helpful to understand the following basics:
  • How to find the data readers in the File menu and open up the desired reader panel for data input.
  • How to find the visualization panels either from the Side toolbar or the Visualization panel on the Main menu to create and modify surfaces in AcuFieldView.
  • How to move the data around the modeling window using mouse actions to translate, rotate and zoom in to the data.

Start AcuFieldView

Click on the AcuConsole toolbar to open the Launch AcuFieldView dialog.
You will see that the pressure contours have already been displayed on all of the boundary surfaces with mesh. When results of a transient simulation are loaded in AcuConsole, the displayed results correspond to the last time step of the simulation.


Figure 18.

Set Up AcuFieldView

  1. Close the Boundary Surface dialog.
  2. Click Viewer Options.


    Figure 19.
  3. In the Viewer Options dialog:
    1. Turn off perspective view by deselecting the Perspective check box.
    2. Disable the axis markers by clicking Axis Markers.


      Figure 20.
  4. Click Close to close the dialog.
  5. Click the Scalar Colormap Specification icon on the toolbar.
  6. In the Scalar Colormap Specification dialog, click Background.


    Figure 21.
  7. In the Background Color dialog, select the color white.


    Figure 22.
  8. Close the dialogs.
  9. Click the icon to turn off the outline display.
    Your model should now look like this:


    Figure 23.

Visualize and Save an Animation of the Beam Displacement

  1. Click to open the Boundary Surface dialog.
  2. Turn off the visibility for the active boundary surfaces.
  3. Click to open the Coordinate Surface dialog.
  4. Create a new coordinate surface at the mid -Z coordinate plane.
    The coordinate surface created is the mid plane between the z_neg and z-pos surfaces.
  5. Set the Coloring to Scalar.
  6. Set the Display Type to Smooth.
  7. Select x-velocity as the Scalar Function to be displayed.
  8. Select Z as the Coord Plane.
  9. In the Colormap tab, change Scalar Coloring to Local.
  10. From the Defined Views, select +Z as the viewing direction.
    Your model should look like the image below. The visible shape of the beam is its deformed shape at the end of last time step in the simulation.


    Figure 24.
  11. Close the dialog.
  12. Click Tools > Flipbook Build Mode.
  13. Click OK to close the Flipbook Size Warning dialog.
  14. Click Tools > Transient Data.
    The Transient Data Controls dialog opens.


    Figure 25.
    If the Sweep Control in this dialog shows Sweep instead of Build, the Flipbook Build mode is not active. In Sweep mode, you will be able to create and visualize the animation, but you will not be able to save it. To be able to save the animation, enable the Flipbook Build Mode.
  15. Drag the time step slider to its left most position. Alternatively, type 0 for the Time Step or Solution Time.
  16. Click Apply.
    The displayed state now corresponds to the initial state of the domain.


    Figure 26.
  17. Click Build.
    AcuFieldView will build the frame by frame animation of the solution progressing through all of the available time steps. You will be able to see the progress in a Building Flipbook dialog.

Summary

In this tutorial you worked through a basic workflow to set up a flexible body motion of a rotating beam in the wake of a cylinder. You started with the piezo_harvester_P-FSI.acs file from the tutorial Piezoelectric Flow Harvester and modified the set up to accommodate the rigid body rotation of the beam and the cylinder. Once the case was set up, you generated a solution using AcuSolve. Results were post-processed in AcuFieldView to allow you to create animation of the beam displacements with time.

New features introduced in this tutorial included:
  • Creating rigid body type mesh motion for rotation
  • Implementation of P-FSI in conjunction of rigid body rotation