Symscape

Compare theoretical and SymLab simulation results (generated by the Panel Flow add-on) of the pressure coefficient on a sphere.

Goals

In this tutorial, you will learn how to:

• Read a file into SymLab
• Generate equations
• Export and import the data from an XY plot
• Compare the results of your simulation with a theoretical calculation of the same quantity

Assumptions

1. You have activated the SymLab Panel Flow add-on or SymLab Professional.
2. You are familiar with SymLab essentials.
3. You have completed the Fluid Flow Around a Sphere tutorial and saved your simulation file, or you have downloaded the flow-over-sphere.sym file.

Read the Simulation File into SymLab

In the Menu Bar, select File->Open.... Navigate to the location of the flow-over-sphere.sym file. Double-click on flow-over-sphere.sym to load it into SymLab.

Plot Pressure Coefficient on the Sphere Versus theta

In the tutorial Fluid Flow Around a Sphere, you plotted pressure coefficient versus x-position along the curved edge of the sphere shown in the diagram below. In the first step of this tutorial, you will plot the pressure coefficient (as calculated in your SymLab simulation) versus theta, where theta is defined in the diagram below. (theta=0 is in the y-direction.)

The steps to calculate values of theta are:

1. Create scalar R (the radius of the sphere)
2. Create x/R, which is equal to sin(theta)
3. Create theta, which is equal to arcsin(sin(theta))

Create Scalar R, the Radius of the Sphere

In the Toolbar, click on the New icon and select Result.

In the Create Result dialog, select the Constant tab. For Units, select Length.

Click Create to create a scalar.

Select the Results Tool Palette. Select Scalar Variables->Scalar (the scalar variable you just created), click on it again to make its name editable, and change Scalar to R.

In the Properties Panel, set the Value of R to 5. Press Enter on the keyboard to apply the changes to the Properties Panel.

Create sin(theta)

Remember that sin(theta)=x/R.

In the Create Result dialog, select the Binary tab. Select Divide from the list.

In the Results tool palette, select Vector Fields->Position. Verify that X is selected as the Scalar in the Properties Panel. Drag and drop Vector Fields->Position onto the left-hand target in the Create Result dialog. Select Scalar to specify the x-position as the left-hand variable for the equation.

Drag Scalar Variables->R from the Results tool palette and drop it onto the right-hand target in the Create Result dialog.

Click Create to create the scalar field x/R, which is equal to sin(theta). In the Results tool palette, select Scalar Fields->(Position:X / R), rename it sin(theta), and press Enter on the keyboard.

Create theta

Remember that theta=arcsin(sin(theta)).

In the Create Result dialog, select the Unary tab. Select aSin from the list. Drag Scalar Variables->sin(theta) from the Results tool palette and drop it onto the target in the Create Result dialog.

Click Create to create the scalar field theta. Click Close to close the dialog.

In the Results tool palette, select Scalar Fields->aSin(sin(theta)), rename it theta, and press Enter on the keyboard.

Plot Pressure Coefficient Versus theta

Select the Pressure Coefficient Plot View Window (if it is not already selected). Drag and drop Scalar Fields->theta onto the background of the View Window. Select X Axis to display values of theta along the x-axis of the XY plot.

This is the SymLab simulation result of pressure coefficient versus theta for the sphere.

Calculate the Theoretical Values of Pressure Coefficient on the Sphere

In this step, you will use SymLab to perform a theoretical calculation of pressure coefficient on the sphere. The theory for this calculation is described in the example Potential Flow Around a Sphere.

The steps to calculate the theoretical values of pressure coefficient (Cp) are:

1. Create scalars 1 and 9/4 (2.25)
2. Create y/R, which is equal to cos(theta)
3. Create cos²(theta)
4. Create the equation Cp = 1 - 9/4 x cos²(theta)

Create the Scalars 1 and 9/4

In the Toolbar, click on the New icon and select Result.

In the Create Result dialog, select the Constant tab. For Units, select None.

Click Create to create a scalar. Click Create again to create a second scalar.

In the Results Tool Palette, select Scalar Variables->Scalar. Click on it again to make its name editable, and change Scalar to 1.

In the Properties Panel, set the Value of 1 to 1 and press Enter on the keyboard.

In the Results Tool Palette, rename Scalar Variables->Scalar to be 9/4. In the Properties panel, set its value to 2.25.

Create cos(theta)

Remember that cos(theta)=y/R.

In the Create Result dialog, select the Binary tab. Select Divide from the list.

In the Results tool palette, select Vector Fields->Position. In the Properties panel, select Y as the Scalar.

Drag and drop Vector Fields->Position onto the left-hand target in the Create Result dialog. Select Scalar to specify the y-position as the left-hand variable for the equation.

Drag Scalar Variables->R from the Results tool palette and drop it onto the right-hand target in the Create Result dialog.

Click Create to create the scalar field y/R. In the Results tool palette, select Scalar Fields->(Position:Y / R), rename it cos(theta), and press Enter.

You have now created all the elements necessary to calculate the theoretical values of pressure coefficient. Next you will assemble the parts of the equation Cp = 1 - 9/4 x cos²(theta).

Create cos²(theta)

In the Create Result dialog, select the Binary tab, and select Multiply from the list.

In the Results tool palette, select Scalar Fields->cos(theta), and drag and drop it onto the left-hand target in the Create Result dialog. Repeat the process to drop the Scalar Fields->cos(theta) tool onto the right-hand target. Click Create to create the scalar field cos²(theta). In the Results tool palette, select Scalar Fields->(cos(theta) x cos(theta)), rename it cos^2(theta), and press Enter.

Create 9/4 x cos²(theta)

In the Create Result dialog, select the Binary tab, and select Multiply from the list.

In the Results tool palette, select Scalar Variables->9/4, and drag and drop it onto the left-hand target in the Create Result dialog. Drag and drop the Scalar Fields->cos^2(theta) tool onto the right-hand target.

Click Create to create the (9/4 x cos^2(theta)) tool in the Results tool palette.

Create Cp = 1 - 9/4 x cos²(theta)

In the Create Result dialog, select the Binary tab, and select Subtract from the list.

In the Results tool palette, select Scalar Variables->1, and drag and drop it onto the left-hand target in the Create Result dialog. Drag and drop the Scalar Fields->(9/4 x cos^2(theta)) tool onto the right-hand target.

Click Create to create Cp. Click Close in the Create Result dialog.

In the Results tool palette, select Scalar Fields->(1 - (9/4 x cos^2(theta))), rename it Theory, and press Enter.

Plot Theoretical Values of Pressure Coefficient Versus theta

Select the view-sim View Window. Drag the Scalar Fields->Theory tool from the Results tool palette and drop it onto the edge of the sphere highlighted in the diagram below.

Double-click the edge in the Select dialog and select XY Plot to create an XY plot of pressure coefficient versus y-position.

Note that the plot has Position: Y along the x-axis. By default, a variable is plotted against the scalar variable selected for Position. In a previous step, you selected Y as the scalar for Position.

Drag and drop the Scalar Fields->theta tool onto the background of the View Window and select X Axis to plot theta along the x-axis.

Compare Theoretical and SymLab Simulation Pressure Coefficients

To compare the pressure coefficient values from your SymLab simulation with the theoretical values, you need to plot both data sets on the same XY plot. To do this, you will first export the theoretical results, reload them into SymLab as imported data, and then plot them on the same XY plot as the SymLab simulation results.

Export the Theoretical Pressure Coefficient Data

In the menubar, select File->Export.... Select the location to save the theoretical plot data, specify a File name (sphere-cp-theory) and select Plot Series (*.csv) as the file type. Click Save to export the theoretical pressure coefficient data.

Import the Theoretical Pressure Coefficient Data

In the menubar, select File->Import.... Select the location of the plot data you just saved. For the file type, select Plot Series (*.csv). Double-click on sphere-cp-theory.csv to import it into SymLab.

The plot series will be visible in the Results tool palette, under Imported.

Plot the Imported Data and the SymLab Simulation Data on the Same XY Plot

Select the Pressure Coefficient Plot View Window. Drag and drop the Imported->sphere-cp-theory.csv tool onto the View Window and select Done to plot the theoretical data on the same XY plot as the simulation data.

In the View Window, select the word next to the red symbol at the bottom of the window (edge in this example), and rename it to be Theory.

In the View Window, select the red symbol at the bottom of the window next to Theory. In the Properties panel, select None for the Line type, and select Circle Open for the Symbol.

In the View Window, select the word next to the black symbol at the bottom of the window, and rename it to be Computation.

In the View Window, select the black symbol at the bottom of the window next to Computation. In the Properties panel, select None for the Symbol.

Notice the good agreement between the computational and theoretical values of pressure coefficient.