Difference between revisions of "OpenFOAM/C3/Turbulent-Flow-in-a-Lid-driven-Cavity/English-timed"

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|-
 
|-
 
| 00:33
 
| 00:33
 +
| 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.
 +
 +
|-
 +
| 00:38
 
| To practice this tutorial, you should have some basic knowledge of '''Turbulence modelling''', knowledge of how to solve flow in a '''Lid driven cavity'''.
 
| To practice this tutorial, you should have some basic knowledge of '''Turbulence modelling''', knowledge of how to solve flow in a '''Lid driven cavity'''.
  
 
|-
 
|-
| 00:43
+
| 00:48
 
|If not so, please refer to the relevant tutorial on our website.
 
|If not so, please refer to the relevant tutorial on our website.
  
 
|-
 
|-
| 00:50
+
| 00:55
 
| This problem is identical in '''geometry''' and '''boundary conditions''' to the ''''Lid Driven Cavity'''' problem discussed in the basic level tutorial.
 
| This problem is identical in '''geometry''' and '''boundary conditions''' to the ''''Lid Driven Cavity'''' problem discussed in the basic level tutorial.
  
 
|-
 
|-
| 00:59
+
| 01:04
 
|Please make a note this problem is already set up in''''pisoFoam' solver''' in OpenFoam directory.
 
|Please make a note this problem is already set up in''''pisoFoam' solver''' in OpenFoam directory.
  
 
|-
 
|-
| 01:07
+
| 01:12
 
|The '''boundary conditions''' are the '''Lid velocity U =1 m/s'''. We are solving this for a '''Reynolds number Re =10000'''.
 
|The '''boundary conditions''' are the '''Lid velocity U =1 m/s'''. We are solving this for a '''Reynolds number Re =10000'''.
  
 
|-
 
|-
|  01:20
+
|  01:25
 
| We are  using a transient solver for '''in-compressible, turbulent flow''' of '''Newtonian fluid'''s  called  as '''pisoFoam'''.
 
| We are  using a transient solver for '''in-compressible, turbulent flow''' of '''Newtonian fluid'''s  called  as '''pisoFoam'''.
  
 
|-
 
|-
| 01:29
+
| 01:34
 
| Now, let us open the '''terminal window''' by pressing '''Ctrl+Atl+t keys''' together.
 
| Now, let us open the '''terminal window''' by pressing '''Ctrl+Atl+t keys''' together.
  
 
|-
 
|-
| 01:37
+
| 01:42
 
| In the terminal window, type "run" and press '''Enter'''. Now type '''cd space tutorials''' and press '''Enter'''. Now, type '''cd space incompressible''' and press '''Enter'''.
 
| In the terminal window, type "run" and press '''Enter'''. Now type '''cd space tutorials''' and press '''Enter'''. Now, type '''cd space incompressible''' and press '''Enter'''.
  
 
|-
 
|-
| 01:59
+
| 02:04
 
|Now, type '''cd space pisoFoam''' (note that F here is capital ) and press '''Enter'''.
 
|Now, type '''cd space pisoFoam''' (note that F here is capital ) and press '''Enter'''.
  
 
|-  
 
|-  
| 02:10
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| 02:15
 
|Now type "ls" and press '''Enter'''. In this, you will see two folders "les" and "ras".
 
|Now type "ls" and press '''Enter'''. In this, you will see two folders "les" and "ras".
 
Our problem  setup is inside "ras" folder which is called as '''reynolds average stress'''.  
 
Our problem  setup is inside "ras" folder which is called as '''reynolds average stress'''.  
  
 
|-
 
|-
| 02:26
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| 02:31
 
| Our folder name is '''cavity'''. Now type '''cd space ras''' and press '''Enter'''. Now type "ls" and press '''Enter'''.
 
| Our folder name is '''cavity'''. Now type '''cd space ras''' and press '''Enter'''. Now type "ls" and press '''Enter'''.
  
 
|-
 
|-
| 02:39
+
| 02:44
 
|You can see the '''cavity''' folder. Let me clear this off. Now type '''cd space cavity''' and press '''Enter'''. Now type "ls" and press '''Enter'''.
 
|You can see the '''cavity''' folder. Let me clear this off. Now type '''cd space cavity''' and press '''Enter'''. Now type "ls" and press '''Enter'''.
  
 
|-
 
|-
| 02:57
+
| 03:02
 
| You can see three folders''' 0, constant''' and '''system'''. The '''initial conditions''' are specified within the files in the '0' (zero) directory.
 
| You can see three folders''' 0, constant''' and '''system'''. The '''initial conditions''' are specified within the files in the '0' (zero) directory.
  
 
|-
 
|-
| 03:08
+
| 03:13
 
|Let us take a look at the files in the '0' directory.  
 
|Let us take a look at the files in the '0' directory.  
  
 
|-
 
|-
| 03:12
+
| 03:17
 
| To do this, in the command terminal, type '''cd space 0''' and press '''Enter'''. Now type "ls" and press '''Enter'''.  
 
| To do this, in the command terminal, type '''cd space 0''' and press '''Enter'''. Now type "ls" and press '''Enter'''.  
  
 
|-
 
|-
| 03:22
+
| 03:27
 
| You can see the files named as '''epsilon, k, nut, nutilda, p, R''' and '''U'''.  
 
| You can see the files named as '''epsilon, k, nut, nutilda, p, R''' and '''U'''.  
  
 
|-
 
|-
| 03:30
+
| 03:35
 
| These files are to be kept as default until the inlet parameters don't change. If any changes are to be done please refer to the tutorial  
 
| These files are to be kept as default until the inlet parameters don't change. If any changes are to be done please refer to the tutorial  
  
 
|-
 
|-
| 03:41
+
| 03:46
 
| on '''Simulating flow in a channel using OpenFoam''' to calculate these values.  
 
| on '''Simulating flow in a channel using OpenFoam''' to calculate these values.  
  
 
|-
 
|-
|03:47
+
|03:52
 
|Now type '''cd space dot dot (..)''' and press '''Enter'''. Let me clear this off. Let us open the '''constant''' folder. To do this, type '''cd space constant''' and press '''Enter'''. Now type "ls" and press '''Enter'''.  
 
|Now type '''cd space dot dot (..)''' and press '''Enter'''. Let me clear this off. Let us open the '''constant''' folder. To do this, type '''cd space constant''' and press '''Enter'''. Now type "ls" and press '''Enter'''.  
  
 
|-
 
|-
| 04:08
+
| 04:13
 
| In this, you will see the '''polyMesh''' folder containing the geometry of the case inside '''blockMeshDict''' and the '''fluid properties'''.
 
| In this, you will see the '''polyMesh''' folder containing the geometry of the case inside '''blockMeshDict''' and the '''fluid properties'''.
  
 
|-
 
|-
| 04:19
+
| 04:24
 
|In this case, you will see two more files other than '''transportProperties''' named as '''RASProperties''' and''' turbulenceProperties'''.
 
|In this case, you will see two more files other than '''transportProperties''' named as '''RASProperties''' and''' turbulenceProperties'''.
  
 
|-
 
|-
| 04:29
+
| 04:34
 
|Let us open these two files.
 
|Let us open these two files.
  
 
|-
 
|-
| 04:32
+
| 04:37
 
| In the terminal, type''' gedit (space) RASProperties''' and press '''Enter'''. Let me drag this to the capture area.
 
| In the terminal, type''' gedit (space) RASProperties''' and press '''Enter'''. Let me drag this to the capture area.
  
 
|-
 
|-
| 04:49
+
| 04:54
 
|Scroll down. '''RASProperties''' contains the '''Reynolds average stress model''' for this case which is kept as '''kepsilon''' close this.
 
|Scroll down. '''RASProperties''' contains the '''Reynolds average stress model''' for this case which is kept as '''kepsilon''' close this.
  
 
|-
 
|-
| 05:03
+
| 05:08
 
| Now in the command terminal, type '''gedit (space) turbulentproperties''' and press '''Enter'''.
 
| Now in the command terminal, type '''gedit (space) turbulentproperties''' and press '''Enter'''.
  
 
|-
 
|-
| 05:15
+
| 05:20
 
| Scroll down. '''simulation Type''' model for this case is kept as '''RASModel'''. Close this.
 
| Scroll down. '''simulation Type''' model for this case is kept as '''RASModel'''. Close this.
  
 
|-
 
|-
| 05:25
+
| 05:30
 
| Now let us open the '''transportProperties''' model. To do this, in the terminal, type '''gedit space transportProperties '''and press '''Enter'''.
 
| Now let us open the '''transportProperties''' model. To do this, in the terminal, type '''gedit space transportProperties '''and press '''Enter'''.
  
 
|-
 
|-
| 05:36
+
| 05:41
 
|The '''transportModel '''we are using here is '''Newtonian '''and Viscosity is kept as '''1 e raise to -4'''. Close this.  
 
|The '''transportModel '''we are using here is '''Newtonian '''and Viscosity is kept as '''1 e raise to -4'''. Close this.  
  
 
|-
 
|-
| 05:46
+
| 05:51
 
| We are not changing the geometry in this case. So, we need not go inside the '''polyMesh''' folder and look at the '''blockMeshDict''' file.
 
| We are not changing the geometry in this case. So, we need not go inside the '''polyMesh''' folder and look at the '''blockMeshDict''' file.
  
 
|-
 
|-
| 05:54
+
| 05:59
 
|It can be kept as it is. In the terminal, type '''cd space (dot dot) ..''' and press '''Enter'''. We will keep the '''system''' folder default as there are no changes inside it.
 
|It can be kept as it is. In the terminal, type '''cd space (dot dot) ..''' and press '''Enter'''. We will keep the '''system''' folder default as there are no changes inside it.
  
 
|-
 
|-
| 06:08
+
| 06:13
 
|Now we are done with the setup. We can '''mesh''' the geometry. To do this, in the terminal window, type "blockMesh" and press '''Enter'''. '''Meshing '''has been done.
 
|Now we are done with the setup. We can '''mesh''' the geometry. To do this, in the terminal window, type "blockMesh" and press '''Enter'''. '''Meshing '''has been done.
  
 
|-
 
|-
| 06:22
+
| 06:27
 
| Now we can '''run''' the '''solver'''. To do this, in the terminal, type "pisoFoam" and press '''Enter'''. The '''iterations''' running can be seen in the terminal window.
 
| Now we can '''run''' the '''solver'''. To do this, in the terminal, type "pisoFoam" and press '''Enter'''. The '''iterations''' running can be seen in the terminal window.
  
 
|-
 
|-
| 06:34
+
| 06:39
 
|It may take some time for the '''iterations''' to stop.
 
|It may take some time for the '''iterations''' to stop.
  
 
|-
 
|-
| 06:40
+
| 06:45
 
|The '''Iterations''' running will stop at the end of the time step. To visualize the results, let us open the '''paraView''' window. To do this, in the terminal, type "paraFoam" and press '''Enter'''. This will open the '''paraView''' window.
 
|The '''Iterations''' running will stop at the end of the time step. To visualize the results, let us open the '''paraView''' window. To do this, in the terminal, type "paraFoam" and press '''Enter'''. This will open the '''paraView''' window.
  
 
|-
 
|-
| 06:57
+
| 07:02
 
| On the left hand side, in the '''Object Inspector''' menu, click on '''Apply'''. You can see the '''lid driven cavity''' geometry. A common visualization is '''surface plots'''.  
 
| On the left hand side, in the '''Object Inspector''' menu, click on '''Apply'''. You can see the '''lid driven cavity''' geometry. A common visualization is '''surface plots'''.  
  
 
|-
 
|-
| 07:09
+
| 07:14
 
|Change the '''display''' to '''Surface''' in the column and from the drop-down menu change from '''solid color''' to 'U'. You can see the initial condition of velocity.
 
|Change the '''display''' to '''Surface''' in the column and from the drop-down menu change from '''solid color''' to 'U'. You can see the initial condition of velocity.
  
 
|-
 
|-
| 07:22
+
| 07:27
 
| Now on the top of the paraView window, you can see the '''VCR control'''. Click on the '''play''' button.  
 
| Now on the top of the paraView window, you can see the '''VCR control'''. Click on the '''play''' button.  
 
You can see the motion of the fluid inside the '''cavity'''.
 
You can see the motion of the fluid inside the '''cavity'''.
  
 
|-
 
|-
| 07:34
+
| 07:39
 
|You can also toggle on the '''color legend''' from the left hand side top of '''paraView''' '''active variable control''' menu. Click on it. you can see the '''color legend'''.
 
|You can also toggle on the '''color legend''' from the left hand side top of '''paraView''' '''active variable control''' menu. Click on it. you can see the '''color legend'''.
  
 
|-
 
|-
| 07:46
+
| 07:51
 
|Now, to visualize the '''stream lines''', on the top of the menu bar of '''paraView''' go to '''Filters > Common > Stream Tracers'''. Click on it.
 
|Now, to visualize the '''stream lines''', on the top of the menu bar of '''paraView''' go to '''Filters > Common > Stream Tracers'''. Click on it.
  
 
|-
 
|-
| 07:58
+
| 08:03
 
| On the left hand side of the '''Object inspector''' menu, you can see '''Apply'''. Click on it. You can see the '''stream lines''' at the center of the '''lid driven cavity'''.
 
| On the left hand side of the '''Object inspector''' menu, you can see '''Apply'''. Click on it. You can see the '''stream lines''' at the center of the '''lid driven cavity'''.
  
 
|-
 
|-
| 08:10
+
| 08:15
 
|You can also change the orientation in which the stream lines are viewed. To do this , scroll down.  
 
|You can also change the orientation in which the stream lines are viewed. To do this , scroll down.  
 
You can see the ''' Seed Type'''.
 
You can see the ''' Seed Type'''.
  
 
|-
 
|-
| 08:21
+
| 08:26
 
|Let me shift this to the right. Change from''' Point Source''' to '''Line Source'''.
 
|Let me shift this to the right. Change from''' Point Source''' to '''Line Source'''.
  
 
|-
 
|-
| 08:27
+
| 08:37
 
| You can see the X, Y and Z axes which are visible. Select any one of these axes in which you would like to view the '''stream lines'''.
 
| You can see the X, Y and Z axes which are visible. Select any one of these axes in which you would like to view the '''stream lines'''.
  
 
|-
 
|-
| 08:36
+
| 08:41
 
|I will select the Y axis and click '''Apply'''. You can see the '''streamlines''' along the Y axis.
 
|I will select the Y axis and click '''Apply'''. You can see the '''streamlines''' along the Y axis.
  
 
|-
 
|-
| 08:44
+
| 08:49
 
|Similarly, you can select the X axis and plot the '''streamlines''' along the X axis. Now delete this.
 
|Similarly, you can select the X axis and plot the '''streamlines''' along the X axis. Now delete this.
  
 
|-
 
|-
| 08:53
+
| 08:58
 
| You can also plot the velocity along the x and y axes using '''plot over line'''. To do this, go to '''Filters > Data Analysis > Plot over line'''.
 
| You can also plot the velocity along the x and y axes using '''plot over line'''. To do this, go to '''Filters > Data Analysis > Plot over line'''.
  
 
|-
 
|-
| 09:06
+
| 09:11
 
|Save the data as''' .(dot) csv''' file. From file menu, click on '''Save Data'''.
 
|Save the data as''' .(dot) csv''' file. From file menu, click on '''Save Data'''.
  
 
|-
 
|-
| 09:13
+
| 09:18
 
| You can plot this data in '''LibreOffice spreadsheet '''or any other '''plotting''' software of your choice. Now, let me switch back to the slides.
 
| You can plot this data in '''LibreOffice spreadsheet '''or any other '''plotting''' software of your choice. Now, let me switch back to the slides.
  
 
|-
 
|-
| 09:23
+
| 09:28
 
|The results obtained can be '''validated''' by using results of '''Ghia et.al''' for Reynolds Number Re = 10000.
 
|The results obtained can be '''validated''' by using results of '''Ghia et.al''' for Reynolds Number Re = 10000.
  
 
|-
 
|-
| 09:32
+
| 09:37
 
| That's all we have in this tutorial. Let us summarize.
 
| That's all we have in this tutorial. Let us summarize.
  
 
|-
 
|-
| 09:34
+
| 09:39
 
|'''Turbulent Flow in a Lid Driven Cavity''' and '''plotting streamlines '''in''' paraView'''. This brings us to the end of the tutorial.
 
|'''Turbulent Flow in a Lid Driven Cavity''' and '''plotting streamlines '''in''' paraView'''. This brings us to the end of the tutorial.
  
 
|-
 
|-
| 09:44
+
| 09:49
 
| As an assignment- modify the '''grid size''' of the cavity. Change it to (100 100 1) and visualize the results in '''paraview''' using '''streamlines'''.
 
| As an assignment- modify the '''grid size''' of the cavity. Change it to (100 100 1) and visualize the results in '''paraview''' using '''streamlines'''.
  
 
|-
 
|-
| 09:55
+
| 10:00
 
| Watch the video available at this URL:
 
| Watch the video available at this URL:
 
http://spoken-tutorial.org/What_is_a_Spoken_Tutorial.
 
http://spoken-tutorial.org/What_is_a_Spoken_Tutorial.
Line 233: Line 237:
  
 
|-
 
|-
| 10:05
+
| 10:10
 
| The Spoken Tutorial Project team
 
| The Spoken Tutorial Project team
  
Line 241: Line 245:
  
 
|-
 
|-
| 10:20
+
| 10:45
 
| '''Spoken Tutorial''' project is a part of '''Talk to a Teacher''' project. It is supported by the National Mission on Education through ICT, MHRD, Government of India.
 
| '''Spoken Tutorial''' project is a part of '''Talk to a Teacher''' project. It is supported by the National Mission on Education through ICT, MHRD, Government of India.
  
 
|-
 
|-
| 10:30
+
| 10:55
 
|More information on this mission is available at the following URL: http://spoken-tutorial.org/NMEICT-Intro
 
|More information on this mission is available at the following URL: http://spoken-tutorial.org/NMEICT-Intro
  
 
|-
 
|-
| 10:34
+
| 10:59
 
| The script is contributed by Shekhar Mishra and Chaitanya talnikar. This is Rahul Joshi from '''IIT Bombay''', signing off. Thanks for joining.
 
| The script is contributed by Shekhar Mishra and Chaitanya talnikar. This is Rahul Joshi from '''IIT Bombay''', signing off. Thanks for joining.
  
 
|}
 
|}

Latest revision as of 15:34, 11 April 2019

Time Narration
00:01 Hello and welcome to the spoken tutorial on modelling Turbulent flow in a Lid Driven Cavity using OpenFOAM.
00:09 In this tutorial, I will show you: Solving turbulent case in OpenFOAM Plotting streamlines in Paraview.
00:20 To record this tutorial, I am using: Linux operating system Ubuntu version 12.04 OpenFoam version 2.1.1 Paraview version 3.12.0
00:33 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.
00:38 To practice this tutorial, you should have some basic knowledge of Turbulence modelling, knowledge of how to solve flow in a Lid driven cavity.
00:48 If not so, please refer to the relevant tutorial on our website.
00:55 This problem is identical in geometry and boundary conditions to the 'Lid Driven Cavity' problem discussed in the basic level tutorial.
01:04 Please make a note this problem is already set up in'pisoFoam' solver in OpenFoam directory.
01:12 The boundary conditions are the Lid velocity U =1 m/s. We are solving this for a Reynolds number Re =10000.
01:25 We are using a transient solver for in-compressible, turbulent flow of Newtonian fluids called as pisoFoam.
01:34 Now, let us open the terminal window by pressing Ctrl+Atl+t keys together.
01:42 In the terminal window, type "run" and press Enter. Now type cd space tutorials and press Enter. Now, type cd space incompressible and press Enter.
02:04 Now, type cd space pisoFoam (note that F here is capital ) and press Enter.
02:15 Now type "ls" and press Enter. In this, you will see two folders "les" and "ras".

Our problem setup is inside "ras" folder which is called as reynolds average stress.

02:31 Our folder name is cavity. Now type cd space ras and press Enter. Now type "ls" and press Enter.
02:44 You can see the cavity folder. Let me clear this off. Now type cd space cavity and press Enter. Now type "ls" and press Enter.
03:02 You can see three folders 0, constant and system. The initial conditions are specified within the files in the '0' (zero) directory.
03:13 Let us take a look at the files in the '0' directory.
03:17 To do this, in the command terminal, type cd space 0 and press Enter. Now type "ls" and press Enter.
03:27 You can see the files named as epsilon, k, nut, nutilda, p, R and U.
03:35 These files are to be kept as default until the inlet parameters don't change. If any changes are to be done please refer to the tutorial
03:46 on Simulating flow in a channel using OpenFoam to calculate these values.
03:52 Now type cd space dot dot (..) and press Enter. Let me clear this off. Let us open the constant folder. To do this, type cd space constant and press Enter. Now type "ls" and press Enter.
04:13 In this, you will see the polyMesh folder containing the geometry of the case inside blockMeshDict and the fluid properties.
04:24 In this case, you will see two more files other than transportProperties named as RASProperties and turbulenceProperties.
04:34 Let us open these two files.
04:37 In the terminal, type gedit (space) RASProperties and press Enter. Let me drag this to the capture area.
04:54 Scroll down. RASProperties contains the Reynolds average stress model for this case which is kept as kepsilon close this.
05:08 Now in the command terminal, type gedit (space) turbulentproperties and press Enter.
05:20 Scroll down. simulation Type model for this case is kept as RASModel. Close this.
05:30 Now let us open the transportProperties model. To do this, in the terminal, type gedit space transportProperties and press Enter.
05:41 The transportModel we are using here is Newtonian and Viscosity is kept as 1 e raise to -4. Close this.
05:51 We are not changing the geometry in this case. So, we need not go inside the polyMesh folder and look at the blockMeshDict file.
05:59 It can be kept as it is. In the terminal, type cd space (dot dot) .. and press Enter. We will keep the system folder default as there are no changes inside it.
06:13 Now we are done with the setup. We can mesh the geometry. To do this, in the terminal window, type "blockMesh" and press Enter. Meshing has been done.
06:27 Now we can run the solver. To do this, in the terminal, type "pisoFoam" and press Enter. The iterations running can be seen in the terminal window.
06:39 It may take some time for the iterations to stop.
06:45 The Iterations running will stop at the end of the time step. To visualize the results, let us open the paraView window. To do this, in the terminal, type "paraFoam" and press Enter. This will open the paraView window.
07:02 On the left hand side, in the Object Inspector menu, click on Apply. You can see the lid driven cavity geometry. A common visualization is surface plots.
07:14 Change the display to Surface in the column and from the drop-down menu change from solid color to 'U'. You can see the initial condition of velocity.
07:27 Now on the top of the paraView window, you can see the VCR control. Click on the play button.

You can see the motion of the fluid inside the cavity.

07:39 You can also toggle on the color legend from the left hand side top of paraView active variable control menu. Click on it. you can see the color legend.
07:51 Now, to visualize the stream lines, on the top of the menu bar of paraView go to Filters > Common > Stream Tracers. Click on it.
08:03 On the left hand side of the Object inspector menu, you can see Apply. Click on it. You can see the stream lines at the center of the lid driven cavity.
08:15 You can also change the orientation in which the stream lines are viewed. To do this , scroll down.

You can see the Seed Type.

08:26 Let me shift this to the right. Change from Point Source to Line Source.
08:37 You can see the X, Y and Z axes which are visible. Select any one of these axes in which you would like to view the stream lines.
08:41 I will select the Y axis and click Apply. You can see the streamlines along the Y axis.
08:49 Similarly, you can select the X axis and plot the streamlines along the X axis. Now delete this.
08:58 You can also plot the velocity along the x and y axes using plot over line. To do this, go to Filters > Data Analysis > Plot over line.
09:11 Save the data as .(dot) csv file. From file menu, click on Save Data.
09:18 You can plot this data in LibreOffice spreadsheet or any other plotting software of your choice. Now, let me switch back to the slides.
09:28 The results obtained can be validated by using results of Ghia et.al for Reynolds Number Re = 10000.
09:37 That's all we have in this tutorial. Let us summarize.
09:39 Turbulent Flow in a Lid Driven Cavity and plotting streamlines in paraView. This brings us to the end of the tutorial.
09:49 As an assignment- modify the grid size of the cavity. Change it to (100 100 1) and visualize the results in paraview using streamlines.
10:00 Watch the video available at this URL:

http://spoken-tutorial.org/What_is_a_Spoken_Tutorial. It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it.

10:10 The Spoken Tutorial Project team

Conducts workshops using spoken tutorials. Gives certificates to those who pass an online test.

For more details, please write to: contact@spoken-tutorial.org

10:45 Spoken Tutorial project is a part of Talk to a Teacher project. It is supported by the National Mission on Education through ICT, MHRD, Government of India.
10:55 More information on this mission is available at the following URL: http://spoken-tutorial.org/NMEICT-Intro
10:59 The script is contributed by Shekhar Mishra and Chaitanya talnikar. This is Rahul Joshi from IIT Bombay, signing off. Thanks for joining.

Contributors and Content Editors

DeepaVedartham, PoojaMoolya, Pratik kamble, Sandhya.np14