# Section 1 - What Will You Learn in This Tutorial?

In this tutorial, you will learn how to set up a simple 2D model of a PZT disc residing in a water tank using the designer mode basic geometry shapes.

You will learn:

• The Basic Simulation Workflow in Onscale Designer
• How to set up a 2D axi-symmetric model
• How to create a simple geometry
• How to simulate piezoelectric materials
• How to display and post-process your results
What is PZT?: Lead zirconate titanate is an inorganic compound with the chemical formula Pb[ZrxTi1-x]O3 (0≤x≤1). Also called PZT, it is a ceramic perovskite material that shows a marked piezoelectric effect, meaning that the compound changes shape when an electric field is applied. It is used in a number of practical applications such as ultrasonic transducers and piezoelectric resonators. It is a white to off-white solid.

# Section 2- Model Definition

### Characteristics of the model:

 Model: PZT Disc of dimensions 10 mm x 2 mm  Water of dimensions 14mm x 10mm Mesh Size: 0.1 mm Output Results: - Time History of Acoustic Pressure on top of the disc at [0, 6] mm - Maximum Y displacement data array

### Material Data:

 Name Water at 25C CTS 3203HD Code Name watr pmt3 Density 1000 kg.m-3 7820 kg.m-3 Bulk Velocity 1496 ms-1 4708.36 ms-1 Shear Velocity 0 ms-1 1687.891 ms-1

Note: Material Data in OnScale are generally defined using the bulk velocity and the shear velocity parameters instead of the more traditional Elastic Modulus and Poisson's Ratio. You can check this page if you want to understand the relation between those parameters.

# Section 3 - Why This Simulation?

PZT material is a piezo-electric material, it can thus deform under a certain voltage.

In this simulation we will apply 2 electrodes on both sides of the PZT Disk and observe the deformation of the disc in function of the voltage load applied.

The water around the PZT Disc will vibrate according to the vibration of the disc.
The model is a Disc in Lead Zirconate Titanate (PZT) inside a cylindrical water tank.

It is a 2D axi-symmetric model, which means that our model will be in 2D, but it will be transformed by the solver into a 3D model by automatically revolving the 2D model around the given Symmetry Axis (Y-Axis here).

In the results, the model will appear as a half cylinder when plotted in the post processor.

Important: Make Sure that you select the correct Axis of Symmetry from the beginning in the New project window because it is impossible to change afterwards in the designer mode.

# Section 4 - The Simulation Process:

Let's go through the step by step tutorial and see how to simulate this PZT Disc in OnScale!

## Step 1 - Create a New Project

1. Click New Project to open up the New Project window
2. Give the project a name
3. Set Project working units
4. Change Model Type to 2D Model
5. Chose the project save location click '...' and choose an appropriate save location
6. Click OK to save the dialog window

## Step 2 - Add the Materials from the Material DB

First we will add the materials needed from the material database. We will use pmt3 and water in this tutorial.

1. Click Project Materials to open the database
2. Expand Fluid and add Water at 25C to the Project Materials (double click)
3. Expand Piezoelectric and add pmt3
4. Expand pmt3 and change the poling direction to Y+
5. Click Done

## Step 3 - Create Basic Geometry Shapes

Note: After making changes to X and Y right click the workspace and select Reset View

1. Click Rectangle
2. Change Material to watr
3. Set End (mm): X (mm) = 14
4. Set End (mm): Y (mm) = 10
1. Right click primitive_1 and select Duplicate Selection
2. Click primitive_2
3. Change material from watr to pmt3
4. Set Begin (mm): Y(mm) = 4
5. Set End (mm): X(mm) = 10 and Y(mm) = 6

## Step 4 - Define a Time Function

We will now add a Ricker Wavelet drive function for later use as out loads require a time function be set.

1. Click '+' to open the Define Input Time function window
2. Change to Ricker Wavelet
3. Click Insert to close the window. A record called timefunc_1 will be added to the window

## Step 5 - Choose the right Mesh Size

We will now change the mesh settings to use 15 elements per wavelength

1. Select Configuration
3. Set Elements Per Wavelength to 15

## Step 6 - Create the two electrodes

1.  Click '+' to open the Load Definition window
2. Change Creation Mode to Geometry Interface
3. Change Geometry to primitive_2 (pmt3)
4. Change Interfacing Item to primitive_1 (watr)
6. Repeat steps 3-5

We will need to edit the loads to create 2 electrodes, where we are driving the top and grounding the bottom.

### Change the properties of the electrode 1

2. Change Load Type to Voltage
3. Change Area Scaling to 2
4. Change Termination to timefunc_1
5. Change Amplitude Scale Factor to 1
6. Change Y (mm) to 6

Important: The Area scaling is an important factor used to take in account the fact that the disc geometry in 2D is just a half model, thus we need to apply an area scaling of 2 to consider the "half surface" loading.

### Change the properties of the electrode 2

2. Change Load Type to Voltage
3. Change Area Scaling to 2
4. Change Termination to Ground
5. Change Y (mm) to 4

## Step 7 - Define the Boundary Conditions

We will need to change the X minimum boundary condition to Symmetry as this model is symmetrical along that axis.

1. Click Domain Boundaries
2. Change the X Minimum boundary condition to Symmetry. All others will be absorbing
3. Change remaining boundary conditions to Absorbing

## Step 8 - Define the Analysis Simulation Time

We will now set the model simulation time to be 5e-5 seconds

1. Click Analysis
2. Change Simulation Run Time (s) to 5e-04

## Step 9 - Define the Output Results

We will now define 2 outputs, a time history of the acoustic pressure on top of the piezo disc will be recorded and the maximum pressure array will be outputted

### Output Result 1 : Time History Graph of Acoustic Pressure at Y=6

1. Click '+' this will create a new output
2. Change Output Type to Time History
3. Set Array Type to Acoustic Pressure
4. Set Y = 6

### Output Result 2: Maximum Y Displacement Field

1. Click '+' this will create a new output
2. Change Output Type to Field Data
3. Change Array Type to Displacement and Array Component to Y
4. Change Field Type to Maximum

## Step 10 - Run on the Cloud

At this point the model is completely set up and it can now be run on the cloud.

1. Click Run on Cloud
2. The option to rename your job. This is how it will appear in the storage
3. Click Estimate
4. Click Run

### How to Get the Simulation Results?

The simulation results will need to be downloaded from the cloud storage in order to analyse the results in the post processor. More experience users may also be able to process Time Histories in Review.

1. Click Storage this opens the window shown above
2. Locate the job

Choose an appropriate save location when the file explorer pops up and click Select Folder to close the window.

## Step 11 - Check the Simulation Results

### Switch to the Post Processor

1. Click this icon to access the Post Processor

### Open Results

1. Click File Explorer
3. Double click the flxdato and flxhst file to open them
4. Click Results Manager

### Plot Data Array (Maximum Displacement in Y)

1. Double click ydmx to plot the maximum pressure data array
2. Click the work-space to rotate the model

### Plot Time History

1. Click Reset Viewport and choose Reset All Viewports
2. Double click piez load1:Charge to plot the charge time trace
3. Change Plot Title to Charge Top Electrode (optional you can choose)
4. Change Y-Axis Label to Piezoelectric Charge (optional you can choose)

# Section 5 - Try For Yourself

Now that we have introduced you to the tutorial try have a play around with some of the settings, add some other outputs, or use this model as a starting point for your own.

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