Please could someone tell me how to calculate the vorticity magnitude.

Thanks

Compute the curl of velocity and take the magnitude of the vector.

wx = dw/dy - dv/dz wy = du/dz - dw/dx wz = dv/dx - du/dy

w = wx(i) + wy(j) + wz(k)

vorticity magnitude = sqrt(w.w) = sqrt( wx*wx +wy*wy +wz*wz)

Could this function be defined into any cfd post.

[la7low]

|w|=||wij||

where wij is the vorticity tensor defined as the antysymmetric part of the velocity gradient tensor. Its magnitude defined by:
||wij||=sqrt(2wij*wij)
and its the same as the magnitude of the vorticity vector as defined earlier.

[Hanseny]

Originally Posted by la7low

|w|=||wij||

where wij is the vorticity tensor defined as the antysymmetric part of the velocity gradient tensor. Its magnitude defined by:
||wij||=sqrt(2wij*wij)
and its the same as the magnitude of the vorticity vector as defined earlier.

Hi,

If I define a antisymmetric matrix as:
0 x y
-x 0 z = A
-y -z 0
which is similar to Vorticity tensor, but when I calculate A*A, I got
-2*x^2-2*y^2-2*z^2 which is negative and has problem under square root. Could you please tell what causes this problem. Thank you very much.

[FMDenaro]

Originally Posted by Hanseny

Hi,

If I define a antisymmetric matrix as:
0 x y
-x 0 z = A
-y -z 0
which is similar to Vorticity tensor, but when I calculate A*A, I got
-2*x^2-2*y^2-2*z^2 which is negative and has problem under square root. Could you please tell what causes this problem. Thank you very much.

I do not understand what you did ... if you want to define a measure for a matrix, you should define some norm on that ||A||, this is not so simple.

You can define an induced norm by using a (non vanishing) vector x such that
||A.x||/||x||

[Hanseny]

Originally Posted by FMDenaro

I do not understand what you did ... if you want to define a measure for a matrix, you should define some norm on that ||A||, this is not so simple.

You can define an induced norm by using a (non vanishing) vector x such that
||A.x||/||x||

Thank you for your reply,

Now I know what is the norm of a matrix, then I still have a question:

What is the magnitude of vorticity, seems like it is not equal to the norm

of vorticity tensor. thanks again.

[FMDenaro]

Originally Posted by Hanseny

Thank you for your reply,

Now I know what is the norm of a matrix, then I still have a question:

What is the magnitude of vorticity, seems like it is not equal to the norm

of vorticity tensor. thanks again.

Indeed the vorticity vector must be extractet from the antisymmetric matrix..

[mohanty.shuvam4]

By definition, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate. In FLUENT is given by: dY-Velocity/dx minus dX-Velocity/dy.

To plot contours for this function using FLUENT go to the "Define" menu, pick "Custom Field Function". Then in the "Field Functions" drop-down box, pick "Derivatives", select "dY-Velocity/dx" from the second drop-down box, click "Select", then the "-" button, then select "dX-Velocity/dy " and click "Select".
Now choose a name for your new variable ("Vorticity-magnitude"), then click "Define".

When you go to plot contours, choose "custom field function" and then your variable will pop up there.

[LuckyTran]

I don't know why someone decided to necrobump this thread but if we're talking about Fluent...

Fluent already has a built-in field for vorticity (going back for as long as I can remember). You don't need to do all this custom field functions business. It's readily available. Just click it :4head: