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Tutorial:Supersonic flow over a wedge using OpenFOAM

Script : Arvind N

Narration: Rahul Joshi

Keywords: Video tutorial,CFD,Wedge,Mach number,Compressible flows.

Visual Cue Narration
Slide 1 Hello and welcome to the spoken tutorial on Supersonic flow over a wedge using OpenFOAM
Slide 2: Learning Objectives In this tutorial I will show you
  • how to solve a compressible flow problem of supersonic flow over a wedge
  • how post process the results in paraView.
Slide 3:

System Requirement

To record this tutorial, I am using
  • Linux Operating system Ubuntu version 10.04
  • OpenFOAM version 2.1.0
  • ParaView version 3.12.0
Slide 4:

System Requirement

The tutorials were recorded using the versions specified in previous slide.

Subsequently the tutorials were edited to latest versions.

To install latest system requirements go to Installation Sheet.

Slide 5:


To practice this tutorial a learner should have some basic knowledge of
  • Compressible flows and
  • Gas Dynamics
Let us now solve
  • supersonic flow over a wedge using OpenFOAM and
  • see the shock structure formed using ParaView
Slide 6 : Boundary Conditions The problem consists of a wedge with semi-angle of 15 degrees kept in a uniform supersonic flow.
Inlet velocity 5m/s Inlet velocity is 5 meters per second
Boundary conditions as shown in the figure The boundary conditions are set as shown in the figure.
Slide 7 : Solver The type of solver I am using here is rhoCentralFoam.
It is a Density-based compressible flow solver.

It is based on central- upwind schemes of Kurganov and Tadmor

Switch to the Terminal by Ctrl+Alt+T Open a command terminal .

To do this press Ctrl+Alt+T keys simultaneously on your keyboard.

In the terminal type path for supersonic flow over a wedge.
In command terminal:

Type run and press Enter.

Problem is already set in OpenFOAM

In the terminal type 'run' and press Enter.
Type cd tutorial and press enter Now type cd tutorial - Press Enter.
Type cd compressible - Press Enter cd compressible - Press Enter.
Type cd rhoCentralFoam - Press Enter cd rhoCentralFoam - Press Enter.
Type cd wedge and press enter cd wedge15Ma5
This is the name of the folder of supersonic flow over a wedge in rhoCentralFoam.

And press Enter.

Type ls Now type ls and press Enter.
You will see three folders : 0,constant and system.
Type cd constant and press enter Now open the blockMeshDict file.

To do this, type cd space constant and press Enter.

Type cd polyMesh and press enter cd space polyMesh

Note that M here is capital and press Enter.

Type ls and press enter Now type ls and press Enter.

You can see the blockMeshDict file.

Type gedit blockMeshDict and press enter Type gedit space blockMeshDict.

Note that M and D here are capital and press Enter.

Drag and scroll down. Let me drag this to the capture area.

Scroll down.

enter the data in vertices but it i already set up in the problem In this you need to calculate the co-ordinates for the wedge.

This is already been calculated and set up in the problem.

The rest of the data remain the same.
Boundary names similar to that in slide 5 In boundary patches the boundaries are set as shown in the figure.
Close the blockMeshDict file.
Type : cd .. (twice) and press Enter >> wedge folder In the command terminal, type

cd ..(dot dot) twice to return back to the wedge folder.

Now open the 0 folder.
Type cd 0 and press enter To do this type cd space 0 and press Enter.
type ls and press enter Type ls and press Enter.
This contains initial boundary condition for pressure,velocity and temprature.
type cd .. and press enter Type cd .. (dot dot) and press Enter.
Now we need to mesh the geometry.
Mesh the geometry.

type: blockMesh

To do this in the command terminal,

type blockMesh and press Enter.

Meshing has been done.

Terminal : type paraFoam and press enter Now to view the geometry in the terminal, type paraFoam and press Enter.

This will open the ParaView window.

Paraview window On the left hand side of object inspector menu click APPLY.
About wedge geometry In this you can see the geometry is which is a rectangular section upstream.

changes to a wedge downstream.

Close the ParaView window.

Now run the solver 'rhoCentralFoam'
Terminal : rehoCentralFoam and press enter To do this in the command terminal, type rhoCentralFoam and press Enter.
Iterations in terminal window The iterations running can be seen in the terminal window.
Iterations running will stop after it converges.

Or at the end of the time step.

Now the solving has been done.

open paraview

To visualise these results let us open the ParaView window once again.
type: paraFoam and press enter In the command terminal, type “paraFoam” and press Enter.
Click APPLY in object inspector menu Again on the left hand side of object inspector menu click APPLY.
Solid geometry in drop down menu

Select U

On the left side top in active variable control menu, you will see a dropdown menu showing Solid Color.

Now click on it and change from solid color to capital U.

Make the color legend ON Now make the color legend ON by clicking on the left hand side top of active variable control menu.

And make the color legend ON.

Click on it.

On top of the ParaView window, you can see the VCR control.

Click on PLAY.

In the paraview window You can see the final results of U velocity.
In object inspector menu Now scroll down the Properties in Object inspector menu on the left hand side.

Now click on Display besides Properties.

Click on rescale to size Scroll down and click on Rescale to Size.
You can see the final value of Velocity magnitude.
Select pressure in drop dwon menu (p)

Similarly you can select pressure.

You can see the final result of pressure.

Now close the ParaView window.

Calculate the Mach number

in terminal type Mach

You can also calculate the Mach number for the flow.

To do this we can use the Openfoam utility by typing Mach in the command terminal.

Type mach in terminal.

mach number for each time step

Type Mach in the command terminal.

Note that M here is capital and press Enter.

You can see that Mach number is calculated for each time step.

Open paraview window.

type paraFoam

click APPLY

Now again open the ParaView window by typing in the command terminal paraFoam.

And press Enter.

Click APPLY.

In object inspector menu, check the Ma check box.

change from solid color to Ma

Scroll down.

In volume fields check the Ma box and again click APPLY.

On top of active variable control menu click on Solid Color and change it to Ma.

In VCR control click on play button >> make the color legend ON In the VCR control menu click on PLAY and make the color legend ON.
In paraview window You can see the Mach number in the color legend and corresponding colours.
We notice here that when the wedge is kept in a supersonic flow,
  • it produces a shock across which the flow properties
    • temperature
    • pressure
    • and density
  • drastically changes.
Slide 8: For validation Let me switch back to the slides.

The solved tutorial can be validated with exact solution available in basic books of Aerodynamics by John D Anderson.

Slide 9: Summary In this tutorial we learnt:
  • Solving a compressible flow problem
  • Velocity and pressure contour for the wedge
  • OpenFOAM utility for calculating the Mach number
Slide 10 : Assignment Assignment:

  1. Vary the wedge angle between 10 ° to 15 °
  2. to view the shock characteristic for the flow.
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Slide 17:


Spoken Tutorials are part of Talk to a Teacher project.

It is supported by the National Mission on Education through ICT, MHRD, Government of India.

More information on the same is available at the following URL link

About the contributor This script has been contributed by Arvind N.

And this is Rahul Joshi from IIT BOMBAY signing off.

Thanks for joining.

Contributors and Content Editors

Chandrika, DeepaVedartham, Nancyvarkey, Rahuljoshi