CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > Main CFD Forum

HELP - stream function from the velocity field

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Display Modes
Old   January 22, 1999, 05:38
Default HELP - stream function from the velocity field
  #1
Fred
Guest
 
Posts: n/a
Could anyone please help me with the following problem

I have some solutions to the 2D driven cavity problem, where the solutions have been obtained using primitive variables. I would like to be able to plot contours of stream function, but as I only have the u and v velocity fields, I would need to derive the stream function from this.

Does anyone out there know how to do this? If so, your help would be much appreciated.

Many thanks.
  Reply With Quote

Old   January 22, 1999, 06:00
Default Re: HELP - stream function from the velocity field
  #2
Roland Bender
Guest
 
Posts: n/a
Hi in my diploma work i had the same problem. You can get the streamfunktion by a integrating over the velocity-field.

I think you can find the formular in a fluid dynamics book. Then you must transform the integration into a summation.

  Reply With Quote

Old   January 22, 1999, 06:15
Default Re: HELP - stream function from the velocity field
  #3
Essemiani
Guest
 
Posts: n/a
you can calculate that by preapearing a subroutine , where for every cell position you caculate the derivate of the stream function U=d (ksi)/dy and V= d ( ksi)/dx , by using a finite difference method you can get the value of the variation of the stream function at the bondaries of your cell.

Generate this for your whole volume

good luck
  Reply With Quote

Old   January 22, 1999, 20:46
Default Re: HELP - stream function from the velocity field
  #4
Duane Baker
Guest
 
Posts: n/a
A quick correction:

caculate the derivate of the stream function U=d (ksi)/dy and V= d ( ksi)/dx

should read:

caculate the derivative of the stream function U=d (ksi)/dy and V= - d ( ksi)/dx

but this is going the wrong way. The question is how to go from velocity to stream function NOT the other way. The guy from Stuttgart has the right idea this means that one has to integrate!!

  Reply With Quote

Old   January 23, 1999, 12:03
Default Re: HELP - stream function from the velocity field
  #5
Michael Song
Guest
 
Posts: n/a
I believe Essemiani is also right. A PDE can be either integrated or finite-differenced for a solution. I guess the latter is preferable for a general problem. Hope you agree with me.

Michael
  Reply With Quote

Old   January 25, 1999, 04:07
Default Re: HELP - stream function from the velocity field
  #6
Christoph Lund
Guest
 
Posts: n/a
Simple.

Set u=d(Psi)/d(y) and v=-d(Psi)/d(x), where Psi is supposed to be the stream function. Take the definition of the vorticity, omega=d(u)/d(y)-d(v)/d(x) and express u and v in this equation using the stream function. This will give you a poisson equation for the stream function,

div grad (Psi) = d^2(Psi)/dx^2+d^2(Psi)/dy^2 = omega,

which can easily be solved by any method you like. Applying this equation to your driven cavity problem you should use Psi=0 on all boundaries, even on the upper (or whatever) moving plate.

For some reference data you could check Sohn, J.L., Int.J.for Num. Meth. in Fluids, 8, (1988), 14469-1490.

Chris.
  Reply With Quote

Old   January 25, 1999, 11:50
Default Re: HELP - stream function from the velocity field
  #7
John C. Chien
Guest
 
Posts: n/a
Ah! A long trip from the primitive-variable-approach back to the stream-function-vorticity-approach. It is an acceptable approach. For the direct-line-integration-approach, the derived stream-function value may not be unique, depending on the direction of integration ( you can integrate the definition in either x- or y-direction). Most of the time, the particle trajectory method is used for the primitive-variable-approach to obtain the streamline information. This is because neither stream-function nor vorticity is used directly in the formulation. And the vorticity calculation has to be defined through out the flow field and boundary consistently.
  Reply With Quote

Old   January 26, 1999, 03:47
Default Re: HELP - stream function from the velocity field
  #8
Christoph Lund
Guest
 
Posts: n/a
Hi John,

in what way do you think will your response to my response to fred's original question be of any help to fred ?

With the incompressibility constraint satisfied only in the mean I can for a given velocity field - at least for the driven cavity problem in question - not think of any other method as simple as the one described.

If you have a (concrete) better suggestion I am of course interested to hear about it.
  Reply With Quote

Old   January 26, 1999, 08:02
Default Re: HELP - stream function from the velocity field
  #9
Ronan Laffan
Guest
 
Posts: n/a
For a particle trajectory method, how do you decide where to 'start' each streamline? I am looking at a similar problem with a triangular mesh and primitive variables.

Ronan
  Reply With Quote

Old   January 26, 1999, 13:35
Default Re: HELP - stream function from the velocity field
  #10
John C. Chien
Guest
 
Posts: n/a
When I answer a question, normally, I don't have any particular person in mind. But rather the issues related to the original question. The practical answer to the original question first: the field approach of solving the stream-function equation with the vorticity source term derived from the U,V velocity field is the nature selection. Because this will eliminate the uniqueness issue associated with the directional integration of the velocity component to obtain the streamfunction. This does not mean that the direct integration is not practical. When you have fine mesh solution, the error will be small. Therefore, if you have fine mesh solution, you can do it either way. Otherwise, I would say, the field approach is a more formal solution. Now that I have answered the original question, I'd like to expand it a little more in this primitive-variable-stream-function-vorticity loop. Suppose that we derive the vorticity from the velocity components field and obtain the stream-function from stream-function field equation with vorticity source term, then ask a question: " Will the derived vorticity function still follow the vorticity governing equation ?" If it does not satisfy the vorticity equation, then " Is the derived streamfunction still valid ?"
  Reply With Quote

Old   January 26, 1999, 13:58
Default Re: HELP - stream function from the velocity field
  #11
John C. Chien
Guest
 
Posts: n/a
Based on my experience with the commercial CFD codes and post-processors, I normally pick a point a couple of points aways from the wall and several points away from the inlet to start the trajectory tracing to begin with. Once I have some general picture of the flow field, I then move to other neighboring points ( skipping a point is a good idea).Once the general flow pattern ( or separation regions) is defined, I can move into the specific region and start a trajectory tracing process there. You will get better pictures when you are dealing with fine mesh solutions. In 3-D simulation, trajectory tracing is extremely important, because there is no replacement for it yet. It is a great tool for viscous flows. So, if you have not used this tool before, you are encouraged to check it out. It will help you a great deal in your CFD career.
  Reply With Quote

Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
stream function boundary condition for cylinder with slots on it sara2115 Main CFD Forum 1 May 18, 2011 09:50
problems after decomposing for running alessio.nz OpenFOAM 5 April 20, 2011 08:44
mean, variance and covariance statistics of any field function on any part. Subhadeep STAR-CCM+ 8 February 18, 2010 18:19
Version 15 on Mac OS X gschaider OpenFOAM Installation 120 December 2, 2009 11:23
fixed velocity field Glen CFX 3 August 28, 2006 12:17


All times are GMT -4. The time now is 08:56.