# how to plot Q criterion in fluent

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 July 13, 2005, 10:06 how to plot Q criterion in fluent #1 anindya Guest   Posts: n/a Can anyone suggest how I can plot Q criterion in fluent to visualize the coherent structures? Thanks for your help. Anindya randolph likes this.

 July 21, 2005, 08:02 Re: how to plot Q criterion in fluent #2 said Guest   Posts: n/a hi anindya, you certainly have the definition of that q criterion which is based on velocity gradient. Fluent do not provide it directly,i mean you have to compose it from computed velocity gradient as a custom field function. for that: define>custom field function and type the name of the criterion "q" for example. you will be then able to visualize the q value on a specified surface on the contour panel... if you want to create an animation of an iso-q surface for example you also have to create an isosurface, hope it helps. best regards Said

 July 22, 2005, 13:33 Re: how to plot Q criterion in fluent #3 anindya Guest   Posts: n/a Thanks a lot for your message. I have already created that custom field function Q. So when I create iso-surfaces, do I create iso surfaces of Q ( say specific values of Q) and then plot Q on those Q iso-surfaces? Or do I plot Q on iso-surfaces of low pressure, vorticity-maginitude, etc? Anindya

 July 24, 2005, 14:06 Re: how to plot Q criterion in fluent #4 Helper Guest   Posts: n/a Fortunately, you don't have to use UDF. Here's a simpler way of visualizing the iso-contours of the second-invariant. You can use the custom field funtion capbility in FLUENT. First you define the second-invariant of deformation tensor with Q = 0.5(W*W - S*S) where W is the vorticity magnitude (you can find it under the "Velocity" menu) and S is the mean rate-of-strain (you can find it under "Derivatives" menu). Once you defined Q, you can generate iso-surfaces of Q for several positive values. jiez, soheil_r7, randolph and 2 others like this.

 July 24, 2005, 23:57 Re: how to plot Q criterion in fluent #5 anindya Guest   Posts: n/a Thanks a lot for your help. Anindya

March 20, 2011, 16:51
Q expressed with scalars or tensors...
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Quote:
 Originally Posted by Helper ;122608 Fortunately, you don't have to use UDF. Here's a simpler way of visualizing the iso-contours of the second-invariant. You can use the custom field funtion capbility in FLUENT. First you define the second-invariant of deformation tensor with Q = 0.5(W*W - S*S) where W is the vorticity magnitude (you can find it under the "Velocity" menu) and S is the mean rate-of-strain (you can find it under "Derivatives" menu). Once you defined Q, you can generate iso-surfaces of Q for several positive values.

Hi Guys,

should not it be the following:
Q=0.25*(W*W - S*S)
???

As the mean rate-of-strain (scalar) is defined as:
S=(2Sij*Sij)^0.5
and similarly the vorticity magnitude (scalar):
W=(2Wij*Wij)^0.5
with Sij being the mean rate of strain tensor and with Wij the mean vorticity tensor (besides, Sij=symmetric, while Wij=antisymmetric part of mean velocity gradient tensor).
Finally the second invariant of velocity grad tensor is defined as:
Q=0.5*(Wij*Wij - Sij*Sij). So I think Q should be: Q=0.25*(W*W - S*S). Is that right?

Besides, this formula of Q is only valid for incompressible flows, more precisely for flows with divergence free velocity field so that divUj=0 <=> Sii=0 !

Thanks!

Last edited by la7low; March 22, 2011 at 20:31.

 May 10, 2011, 05:26 Q expressed with scalars or tensors #7 New Member   Dipanjay Join Date: May 2011 Posts: 1 Rep Power: 0 Hi la7low, I completely agree with you. Cheers..

 October 22, 2012, 08:37 Q criterion Reference #8 New Member   Mohamed Ashar Join Date: Feb 2011 Posts: 13 Rep Power: 15 Hi la7low, Could you please give the reference, from where you have taken this Q criterion. Thanks Last edited by ashar_md2001; October 22, 2012 at 08:52.

February 13, 2016, 01:03
Q criterion
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Subhasish Mitra
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Quote:
 Originally Posted by ashar_md2001 Hi la7low, Could you please give the reference, from where you have taken this Q criterion. Thanks
Q criterion was proposed by Jeong & Hussain (1995), J.Fluid Mech., vol.285, pp.69-94.
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 February 23, 2016, 09:16 Different definitions in Fluent and CFD-Post #10 New Member   C. Meraner Join Date: Dec 2012 Posts: 1 Rep Power: 0 According to "F.R. Menter, Best Practice: Scale-Resolving Simulations in ANSYS CFD, Version 2.00, November 2015" it is: "[...] for historic reasons 0.5 in ANSYS Fluent and 0.25 in ANSYS CFD-Post". However, I don't know how it is in ANSYS CFX.

February 24, 2016, 17:15
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Quote:
 Originally Posted by subha_meter Q criterion was proposed by Jeong & Hussain (1995), J.Fluid Mech., vol.285, pp.69-94.
My apology for a correction required in the earlier post. Below are the actual references for the three useful criteria often used for detecting vortex:

1. Q criterion: positive second invariant of velocity gradient tensor

HUNT,J . C. R., WRAY, A.A., & MOIN, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report CTR-S88, p. 193.

2. Discriminant (DELTA) criterion: complex eigenvalues of velocity gradient tensor

CHONG, M.S., PERRY, A.E. & CANTWELL, B. J. 1990 A general classification of three-dimensional flow field. Phys. Fluids A 2, 765.

3. Lambda 2 criterion: negative second eigenvalue of the S^2 + W^2 tensor where S = strain rate tensor (symmetric part of velocity gradient tensor) and W = vorticity tensor (antisymmetric part of velocity gradient tensor)

Jeong & Hussain (1995), J.Fluid Mech., vol.285, pp.69-94.
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 August 19, 2016, 15:10 plot in 2-D #12 New Member   amir Join Date: Sep 2014 Posts: 7 Rep Power: 11 How can we plot Q criterion, Discriminant (DELTA) criterion, and Lambda 2 criterion in a 2D plane. what is an important plot to draw?

 April 9, 2017, 06:38 #13 Super Moderator   Sijal Join Date: Mar 2009 Location: Islamabad Posts: 4,553 Blog Entries: 6 Rep Power: 54 This reference may be helpful for defining different vortex detection criteria in 2d http://aip.scitation.org/doi/10.1063/1.4927647 Mike Navak likes this.

September 26, 2017, 11:57
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Quote:
 Originally Posted by la7low Hi Guys, should not it be the following: Q=0.25*(W*W - S*S) ??? As the mean rate-of-strain (scalar) is defined as: S=(2Sij*Sij)^0.5 and similarly the vorticity magnitude (scalar): W=(2Wij*Wij)^0.5 with Sij being the mean rate of strain tensor and with Wij the mean vorticity tensor (besides, Sij=symmetric, while Wij=antisymmetric part of mean velocity gradient tensor). Finally the second invariant of velocity grad tensor is defined as: Q=0.5*(Wij*Wij - Sij*Sij). So I think Q should be: Q=0.25*(W*W - S*S). Is that right? Besides, this formula of Q is only valid for incompressible flows, more precisely for flows with divergence free velocity field so that divUj=0 <=> Sii=0 ! Thanks!
The constant does not really matter for visualization.

Ps: If I am not wrong, I remember is due to some historical reason to use 0.5 and 0.25 in Fluent