View source for OpenFOAM-version-7/C3/Flow-in-a-Convergent-Divergent-Nozzle/English

'''Title of the script''': Flow in a Convergent-Divergent Nozzle

'''Author''': Ashley Melvin, Biraj Khadka

'''Keywords''': OpenFOAM, ParaView, CFD, computational fluid dynamics, blockMesh, axi-symmetry, wedge geometry, spline, compressible flow, inviscid, convergent-divergent nozzle, rhoCentralFoam, shock, FOSSEE, spoken tutorial, video tutorial

{| border=1
|- 
|| '''Visual Cue'''
|| '''Narration'''
|- 
|| '''Slide''': 
'''Opening Slide'''
| Welcome to the spoken tutorial on '''Flow in a Convergent-Divergent Nozzle'''.
|-
|
'''Slide:'''

'''Learning Objective'''
|
In this tutorial, we will learn to:


Create an '''axi-symmetric''' geometry using '''blockMesh'''
Create '''spline''' curved edge using '''blockMesh''', and
Set up and run a case of '''compressible flow'''
|-
|
'''Slide:'''

'''System Specifications'''
|
To record this tutorial, I am using,


* '''Ubuntu Linux''' OS version 22.04

* '''OpenFOAM''' version 9

* '''ParaView''' version 5.6.3, and

* '''gedit''' Text editor
|-
|
'''Slide:'''

'''Prerequisites'''

'''https://spoken-tutorial.org'''
|
As a prerequisite:


* You should have basic knowledge of '''compressible flows''' and '''gas dynamics'''.

* You should be familiar with '''setting up a case''' and '''creating a mesh''' in '''OpenFOAM'''.

* If not, please go through the prerequisite '''OpenFOAM''' tutorials on this website.
|-
|
'''Slide:'''

'''Code Files'''
|
* The files used in this tutorial are available in the '''Code''' '''Files''' link on the tutorial page

* Please download and extract them

* Make a copy and then use them while practising.
|-
|
'''Slide:'''

'''Convergent-Divergent Nozzle'''
|
We will be solving flow through a '''convergent-divergent nozzle'''.

Note that:


at the '''inlet''', '''total pressure''' is specified, and
at the '''outlet''', '''static pressure''' is specified.
|-
|
'''Slide:'''

'''Convergent-Divergent Nozzle'''
| The geometry is a '''converging-diverging''' duct.
|-
|
'''Slide:'''

'''Convergent-Divergent Nozzle'''
| Variation of the cross-sectional area is given by this '''cosine''' function along the length.
|-
| Press CTRL + ALT + T keys.
| Open the '''terminal''' by pressing '''Ctrl''', '''Alt''' and '''T''' keys together.
|-
|
[Terminal] Type:

'''cd $FOAM_RUN'''
| At the prompt type this '''command''' and press '''Enter''' to go into the '''run directory'''.
|-
|
[Terminal] Type:

'''cp -r ~/Downloads/Nozzle .'''
|
We have downloaded and extracted the case folder.

Let’s now copy it into the '''run directory'''.
|-
|
[Terminal] Type:

'''cd Nozzle'''
| Let’s move into the case folder using the '''cd''' '''command'''.
|-
|
[Terminal] Type:

'''gedit system/blockMeshDict'''
| Let’s open the '''blockMeshDict''' file in a text editor.
|-
|
'''Slide:'''

'''Axi-symmetric Geometry'''
|

'''Axi-symmetric''' geometry can be created in '''OpenFOAM''' using the '''wedge''' patch type.
The geometry is a '''wedge''' of a small angle, usually less than '''5<sup>o</sup>'''.
It has '''1 cell''' normal to the '''planes of symmetry'''.
|-
|
'''Slide:'''

'''Axi-symmetric Geometry'''
| A typical '''wedge''' geometry is shown in the figure.
|-
|
'''Slide:'''

'''Axi-symmetric Geometry'''
| The '''wedge''' geometry used for the '''convergent-divergent nozzle''' is shown in the figure.
|-
|
'''Slide:'''

'''Vertices'''
|
The geometry has '''6 vertices'''.

The '''vertices''' of the geometry are numbered as shown.
|-
|
'''Slide:'''

'''Vertex Coordinates'''
| Let us consider the '''inlet''' plane.
|-
|
'''Slide:'''

'''Vertex Coordinates-Inlet'''
|

The '''inlet''' is along the '''y-z-plane''' at '''x = 0'''.
'''Vertex 0''' is at the '''origin'''.
The cross-sectional area at the '''inlet''' is '''2.5 m<sup>2</sup>'''.
The radius at the '''inlet''' is therefore, '''0.892 m'''.
The '''y''' and '''z coordinates''' of '''vertex 1''' are as indicated in the diagram.
Similarly, the coordinates of '''vertex 2''' are evaluated.
|-
|
'''Slide:'''

'''Vertex Coordinates-Outlet'''
|
The '''outlet''' is along the '''yz-plane''' at '''x = 10''' and its cross-sectional area is '''2.5 m<sup>2</sup>'''.

The '''vertices''' of the '''outlet''' plane are indicated in the diagram.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

Vertices List [https://imgur.com/w77RPX6 <span class="underline">Link</span>]
| The '''6 vertices''' are entered in the ascending order of their '''vertex numbers''' as shown.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''0 3 5 2''' [https://imgur.com/pPDfXQ5 <span class="underline">Link</span>]
|
Let’s define the '''block'''.

We first enter the '''vertices''' of the lower '''xy-plane'''.

In this case, that would be the lower plane, when viewed along the '''negative z direction'''.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''0 3 4 1''' [https://imgur.com/UegK4aR <span class="underline">Link</span>]
| Similarly, the '''vertices''' of the '''front''' plane are ordered as shown.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''100 20''' [https://imgur.com/undefined <span class="underline">Link</span>]
|
The '''axis''' of the '''nozzle''' is along the '''x direction'''.

There are '''100 cells''' along the '''x direction''' and '''20 cells''' along the '''y direction'''.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''1''' [https://imgur.com/WVkOqWV <span class="underline">Link</span>]
|
The '''z direction''' is normal to the '''plane of symmetry''', also known as the '''azimuthal direction'''.

There is only '''1 cell''' along the '''z axis'''.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''edges''' [https://imgur.com/q3hgXOI <span class="underline">Link</span>]
|
We have '''curved edges''' that define the '''nozzle'''.

We need to specify these '''edges'''.
|-
| Slide: '''Spline'''
|
'''Spline''' curves can be created in '''blockMesh''' using the keyword '''spline'''.

It requires:


The '''2 vertices''' that '''edge''' connects, and
The '''interpolation points''' through which '''edge''' passes
|-
| Slide: '''Front Edge'''
|
Let’s look at the '''front edge''' of the '''nozzle'''.

'''Front edge''' connects the '''vertices 1''' and '''4'''.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''spline 1 4''' [https://imgur.com/3eURiww <span class="underline">Link</span>]
| We have used the keyword '''spline''' to indicate that a '''spline''' curve connects the '''vertices 1''' and '''4'''.
|-
| Slide: '''Interpolation Points'''
|
Let us calculate the '''interpolation points''' for the '''front edge''':


Let us calculate the coordinates of a point on the '''edge''' at '''x = 1'''.
From the '''cosine''' relation, at '''x = 1''', the cross-sectional area is '''2.357 m<sup>2</sup>'''.
The radius of the '''nozzle''' is therefore '''0.866 m'''.
We follow the same procedure as calculating the '''vertex''' coordinates earlier.


The '''y''' and '''z coordinates''' are found to be '''0.865''' and '''0.0378'''.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

'''spline 2 5''' [https://imgur.com/s1iuZPN <span class="underline">Link</span>]
| Using the same procedure, we define the '''spline edge''' connecting '''vertices 2''' and '''5'''.
|-
| Slide: '''Boundary'''
|
The '''boundaries''' of the geometry are:


'''inlet''' and '''outlet'''
'''nozzle'''
'''back''', and
'''front'''
|-
|
[gedit - '''blockMeshDict'''] Highlight:

Boundaries List [https://i.imgur.com/sRRBRAj.png <span class="underline">Link</span>]
| We define the '''5 boundaries''' as shown.
|-
|
[gedit - '''blockMeshDict'''] Highlight:

wedge &gt;&gt; wedge [https://i.imgur.com/gG8r6RO.png <span class="underline">Link</span>]
|
Note that the '''back''' and '''front faces''' are of the type '''wedge'''.

This indicates that the '''front''' and '''back faces''' are '''axi-symmetric wedge planes'''.
|-
|
[gedit - '''blockMeshDict''']

Close the window
| Close the '''blockMeshDict''' file.
|-
| [Terminal] Type: '''gedit 0/p'''
| Let’s view the initial and '''boundary''' '''values''' of '''pressure'''.
|-
|
[gedit - '''p'''] Highlight:

'''internalField uniform 10000''' [https://i.imgur.com/EhEocHs.png <span class="underline">Link</span>]
| The '''domain''' is '''initialized''' with 10,000 '''Pa'''.
|-
|
[gedit - '''p'''] Highlight:

'''type totalPressure''' [https://i.imgur.com/RBvQXkt.png <span class="underline">Link</span>]
| At the '''inlet''', we have the '''total pressure''' condition.
|-
|
[gedit - '''p'''] Highlight:

'''gamma 1.4''' [https://i.imgur.com/hF1Cnr9.png <span class="underline">Link</span>]
|
Since the flow is compressible, we need to specify the '''ratio of specific heats'''.

We consider the fluid to be '''air''' in this simulation.

The '''ratio of specific heats''', '''gamma''', of '''air''' is '''1.4'''.
|-
|
[gedit - '''p'''] Highlight:

'''p0 uniform 10000''' [https://i.imgur.com/qMpO2T2.png <span class="underline">Link</span>]
| The '''total pressure''' at the '''inlet''' is set to 10,000 '''Pa'''.
|-
|
[gedit - '''p'''] Highlight:

'''value uniform 10000''' [https://i.imgur.com/sxEMkAv.png <span class="underline">Link</span>]
| For the '''type totalPressure''', '''value''' is just a '''placeholder''' for the first '''time-step'''.
|-
|
[gedit - '''p'''] Highlight:

back and front BC [https://i.imgur.com/41FTbr3.png <span class="underline">Link</span>]
|
The '''back''' and '''front faces''' are the '''axi-symmetric wedge planes'''.

Therefore, the '''wedge''' '''boundary condition''' is used.
|-
| [gedit - '''p'''] Close the window
| Close the '''p''' file.
|-
| Slide: '''Boundary Conditions'''
|
Let’s now look at the '''boundary values''' of '''temperature''' and '''velocity'''.


They are tabulated as shown.
|-
|
Slide: Boundary Conditions

Highlight: '''slip''' [https://i.imgur.com/N48sg9z.png <span class="underline">Link</span>]
| Note that '''slip''' condition is imposed at the '''nozzle wall''' as the flow is '''inviscid'''.
|-
| Slide: '''Thermophysical Properties'''
|

The '''molecular weight''' of '''air''' is '''29 g/mol'''.
The '''specific heat at constant pressure''' ('''c<sub>p</sub>''') is '''1005 J/kg-K'''.
Since we don’t consider any '''phase change''', the '''heat of fusion''' ('''H<sub>f</sub>''') can be taken as '''0'''.
|-
| Slide: '''Transport Properties'''
|
Since the flow is '''inviscid''', '''viscosity''' and '''thermal conductivity''' effects are ignored.


'''Viscosity''' ('''μ''') can be taken as '''0''', and
The '''Prandtl number''' ('''Pr''') can be taken as '''1'''.

You may assign any other '''non-zero''' value for the '''Prandtl number'''.
|-
| [Terminal] Type: '''gedit constant/thermophysicalProperties'''
| Now, let’s view the '''thermophysicalProperties''' file.
|-
| [gedit - '''thermophysicalProperties'''] Highlight: Properties values [https://i.imgur.com/64PTynu.png <span class="underline">Link</span>]
| The '''thermophysical properties''' are entered as shown.
|-
|
[gedit - '''thermophysicalProperties''']

Close the window
| Close the '''thermophysicalProperties''' file.
|-
|
[Terminal] Type:

'''gedit system/controlDict'''
| Let’s open the '''controlDict''' file.
|-
|
[gedit - '''controlDict'''] Highlight:

'''adjustTimeStep yes''' [https://i.imgur.com/gMwalLV.png <span class="underline">Link</span>]
|
We have enabled the '''adjustTimeStep'''.

It calculates '''time step''' after every iteration based on the specified '''maximum Courant number'''.
|-
|
[gedit - '''controlDict'''] Highlight:

'''maxCo 0.9''' [https://i.imgur.com/blWSJNN.png <span class="underline">Link</span>]
| The '''maximum Courant number''' is set as '''0.9'''.
|-
|
[gedit - '''controlDict'''] Highlight:

'''maxDeltaT 1''' [https://i.imgur.com/oTWQKiS.png <span class="underline">Link</span>]
| The '''maximum time step''' is set as '''1'''.
|-
|
[gedit - '''controlDict'''] Highlight:

'''writeControl adjustableRunTime''' [https://i.imgur.com/UFZqUOt.png <span class="underline">Link</span>]
| Since the '''time step''' is not constant, the '''write control''' is also made adjustable.
|-
|
[gedit - '''controlDict'''] Highlight:

'''deltaT 1e-6''' [https://i.imgur.com/CVmHtlG.png <span class="underline">Link</span>]
|
The first '''time step''' is '''1 micro second'''.

Value is chosen such that the '''Courant number''' is less than '''0.9''' for the first '''time step'''.
|-
|
[gedit - '''controlDict''']

Close the window
| Close the '''controlDict''' file.
|-
| [Terminal] Type: '''blockMesh'''
| Let’s '''mesh''' the geometry using the '''blockMesh''' '''command'''.
|-
| Slide: '''rhoCentralFoam'''
|
We will be using the '''rhoCentralFoam''' solver in this simulation.

It is:


A '''density-based''' '''compressible flow''' solver
Based on '''central-upwind schemes''' of '''Kurganov''' and '''Tadmor'''
|-
| [Terminal] Type: '''rhoCentralFoam'''
| Let’s start the simulation using the following '''command'''.
|-
| Cursor in the terminal.
| The simulation may take some time to complete.
|-
| [Terminal] Highlight: '''End'''
| The simulation is now complete.
|-
| [Terminal] Type: '''paraFoam'''
|
Let’s view the simulated results in '''ParaView'''.

Type '''paraFoam''' at the prompt.
|-
|
[ParaView] '''Properties''' '''Tab'''

Click on '''Apply'''
| Click on the '''Apply''' button to view the geometry.
|-
|
[ParaView] '''Active Variable Controls'''

Click on '''vtkBlockColors''' &gt;&gt; Click on '''p'''
|
Let’s view the '''pressure contours''' for the simulation.

Click on the '''vtkBlockColors''' dropdown in the '''Active Variable Controls''' and select '''p'''.

Click on the '''p''' option with a '''point icon''' and not the '''box icon''', in the dropdown.
|-
|
[ParaView] '''VCR Controls'''

Click on '''Last Frame'''
|
Let’s view the '''contours''' at the end of the simulation.

Click on the '''Last Frame''' button in the '''VCR Controls'''.

You can now see the '''steady-state pressure contour'''.
|-
|
[ParaView] '''Active Variable Controls'''

Click on '''Rescale to Data Range'''
| Click on '''Rescale to Data Range'''
|-
|
[ParaView] '''Layout Window'''

Point to Shock
|
Notice the sudden jump in '''pressure''' in the '''diverging section''' of the '''nozzle'''.

This jump indicates the presence of '''normal shock''' in the '''nozzle'''.
|-
| [ParaView] '''Close ParaView'''
| Close the '''ParaView''' window.
|-
| Only Narration
|
With this we have come to the end of the tutorial.

Let’s summarize.
|-
| Slide: '''Summary'''
|
In this tutorial, we have learnt to:


Create an '''axi-symmetric''' geometry using '''blockMesh'''
Create '''spline''' curved edge using '''blockMesh''', and
Set up and run a case of '''compressible flow'''
|-
| Slide: '''Assignment'''
|
As an assignment:


Change the '''outlet pressure''' to '''8900 Pa'''.
Keep all the other parameters the same and run the simulation.
View the '''steady-state pressure contour''' in '''ParaView'''
|-
| Slide: '''About the Spoken Tutorial Project'''
|
The video at the following link summarises the Spoken Tutorial project.

Please download and watch it.
|-
| Slide: '''Spoken Tutorial Workshops'''
|
We conduct workshops using Spoken Tutorials and give certificates.

Please contact us.
|-
| Slide: '''Spoken Tutorial Forum'''
| Please post your timed queries in this forum.
|-
| Slide: '''FOSSEE Forum'''
|

Do you have any general/technical questions?
Please visit the forum given in the link.
|-
| Slide: '''FOSSEE Case Study Project'''
|

The FOSSEE team coordinates solving feasible CFD problems of reasonable complexity using OpenFOAM.
We give honorarium and certificates to those who do this.
For more details, please visit these sites.
|-
| Slide: '''Acknowledgements'''
| The Spoken Tutorial Project was established by the Ministry of Education, Govt. of India.
|-
| Only Narration
| This tutorial is contributed by Ashutosh P. Shridhar, Binayak Lohani, Biraj Khadka and Payel Mukherjee from IIT Bombay. Thanks for joining.
|}