# How can I use Q-criterion to visualize vortex?

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 March 5, 2011, 03:31 How can I use Q-criterion to visualize vortex? #1 Member   Edison Join Date: Mar 2009 Posts: 40 Rep Power: 9 I am simulating incompressible boundary layer transition flow. I separate the flow velocity (u, v, w) into a base flow part (U, V, W) and a disturbance part (u’ ,v’ ,w’,). I use the below equations to calculate Q (second invariant of velocity gradient tensor): Ω= (0.5*{dudy}-0.5*{dvdx})**2+(0.5*{dudz}-0.5*{dwdx})**2+ (0.5*{dvdx}-0.5*{dudy})**2+(0.5*{dvdz}-0.5*{dwdy})**2+ (0.5*{dwdx}-0.5*{dudz})**2+(0.5*{dwdy}-0.5*{dvdz})**2 S={dudx}**2+(0.5*{dvdx}+0.5*{dudy})**2+(0.5*{dwdx} +0.5*{dudz})**2+ (0.5*{dvdx}+0.5*{dudy})**2+{dvdy}**2+(0.5*{dwdy}+0 .5*{dvdz})**2 + (0.5*{dwdx}+0.5*{dudz})**2+(0.5*{dwdy}+0.5*{dvdz}) **2+{dwdz}**2 Q=0.5*(Ω-S) My questions are: (1) In the calculation of velocity gradient tensor, should I use the total flow or disturbance flow quantities? (2) I have tried both in (1), but the values of dudx is around 1.0e2 pre second in the transition region and the final Q is around 1.0e5 or larger. Are these values normal? In the papers I read, Q are usually closed to zero about 1.0e-2. (3) I am using very coarse grid in my simulation (820*80*16 for streamwise, wall-normal and spanwise direction) and I cannot see vortical structures, for example, a ring at the tip and two long legs at the tail as the papers. Is that because of my resolution? Thank you in advance.

 March 5, 2011, 04:57 #2 Member   Join Date: Apr 2010 Location: Pisa / Italy Posts: 60 Rep Power: 8 Hi, I can't understand your notation very well, sorry, but i usually write Q=0.5*(Ω^2-S^2) where Ω is the vorticity magnitude and S the mean strain rate (absolute quantities) I use the normalized Q-criterion, so the range is -1

 March 6, 2011, 03:31 #3 Member   Edison Join Date: Mar 2009 Posts: 40 Rep Power: 9 Thanks a lot. After normalization the result looks better.

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