Lambda-2 criterion

SonyCFD · May 23, 2012, 20:41

Thanks,
I will try it and get back to you.
Cheers,
Sony

upal_arif · May 24, 2012, 01:51

Hi,

I am looking for a freelancer to simulate supersonic flow through C-D nozzle by fluent 6.2.16

Please contact upal_arif@yahoo.com

Quote:

Originally Posted by sbaffini

Dear saeedi,

the lambda 2 criterion simply concerns the definition of the scalar lambda2 and how turbulent structures can be visualized by proper isosurfaces of lambda2 (like for the Q criterion). Hence, the real difference with the scalar Q is how you compute the scalar lambda2.

This is defined as the second (in magnitude) eigenvalue of the matrix:

$S_{ik} S_{kj} + \Omega_{ik} \Omega_{kj}$

where:

$S_{ij} = \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}\right)$

$\Omega_{ij} = \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} - \frac{\partial u_j}{\partial x_i}\right)$

This requires the construction of the characteristic cubic equation and its resolution in order to obtain lambda2 (that is, lambda2 is the second solution of the cubic characteristic equation).

For coherent structures the matrix above can be related to the opposite of the pressure Hessian matrix. As this matrix is real and symmetric, it has two positive eigenvalues when the pressure is at minimum. As a consequence, the matrix above has two negative eigenvalues and lambda2 is certainly negative (for coherent structures). How much negative you have to pick its isosurfaces is (for what i understand) related to the visual appealing of your images (like for the Q criterion)

I still have to seriously use and check it (so it comes without any warranty) but, some time ago, i made a routine for the computation of lambda2 in Fluent (you find it attached). It is very rudimental but i remember it did the job. Also, it is basically C so you can clearly adapt the core part to your needs (Fluent related parts are very understandable also for non-Fluent users)

Once you got lambda2, you just need to pick some negative isosurface and you're done

Hope it helps

magicbretzel · August 3, 2012, 15:20

Hello,

If I can save some time to the people who downloaded the lambda2.c, there is a small error in the definitionof p, (which has a huge impact on the output, of course)...
Instead of p=b/(3.0*a);

One should read p= -b/(3.0*a);

Hope this can be helpful to someone !

sbaffini · August 3, 2012, 15:38

I knew there was something wrong with it (can't say i didn't write it clear

) but i lost my reference on the cubic equation and put it aside. Thank you very much for your attention, it will help me.

brunntho · May 6, 2013, 05:48

Hi all,

I've just implemented both criteria, Lambda2 and the Q-criterion. However the two methods yield almost the same result, which lead me to the questions:

In which cases the Q-criterion perform better than the lambda2 criterion?
What exactly differs them?

My data set under consideration is a measurement and contains noise. Both methods are sensitive of the gradient computation of the vector field.

Considering noise in data, can we make a statement about which methods works best for measured data sets?

Thank you for your feedback

sbaffini · May 6, 2013, 06:50

The following reference should answer some of your questions:

http://www.aero.polimi.it/~quadrio/papers/1999-ejmb.pdf

brunntho · May 6, 2013, 07:00

Hi,

thank you, in fact most of my questions can be answered with your reference.

bests,
brunntho

August 3, 2012, 15:20	Small error in the code	#23
magicbretzel New Member Guillaume Beardsell Join Date: Aug 2012 Posts: 1 Rep Power: 0	Hello, If I can save some time to the people who downloaded the lambda2.c, there is a small error in the definitionof p, (which has a huge impact on the output, of course)... Instead of p=b/(3.0a); One should read p= -b/(3.0a); Hope this can be helpful to someone !

May 6, 2013, 05:48		#25
brunntho New Member Tom Join Date: May 2013 Posts: 2 Rep Power: 0	Hi all, I've just implemented both criteria, Lambda2 and the Q-criterion. However the two methods yield almost the same result, which lead me to the questions: In which cases the Q-criterion perform better than the lambda2 criterion? What exactly differs them? My data set under consideration is a measurement and contains noise. Both methods are sensitive of the gradient computation of the vector field. Considering noise in data, can we make a statement about which methods works best for measured data sets? Thank you for your feedback

Thread Tools
Show Printable Version Email this Page
Display Modes
Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
problem with Min/max rho	tH3f0rC3	OpenFOAM	7	February 23, 2013 05:37
Lamda 2 criterion for vortex identification	Aindya	FLUENT	4	June 7, 2011 03:51
question to courant criterion	tH3f0rC3	OpenFOAM	6	May 16, 2011 04:32
convergence criterion	Dominique	FLUENT	5	November 24, 2006 02:36
Convergence criterion	Moose	Main CFD Forum	5	June 9, 2005 20:39

May 23, 2012, 20:41		#21
SonyCFD New Member Sony Join Date: May 2010 Posts: 9 Rep Power: 4	Thanks, I will try it and get back to you. Cheers, Sony

August 3, 2012, 15:38		#24
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 252 Rep Power: 12	I knew there was something wrong with it (can't say i didn't write it clear ) but i lost my reference on the cubic equation and put it aside. Thank you very much for your attention, it will help me.

May 6, 2013, 06:50		#26
sbaffini Senior Member Paolo Lampitella Join Date: Mar 2009 Location: Italy Posts: 252 Rep Power: 12	The following reference should answer some of your questions: http://www.aero.polimi.it/~quadrio/papers/1999-ejmb.pdf

May 6, 2013, 07:00		#27
brunntho New Member Tom Join Date: May 2013 Posts: 2 Rep Power: 0	Hi, thank you, in fact most of my questions can be answered with your reference. bests, brunntho