A vortex is a circular or spiral set of streamlines; a vortex core is a special type of isosurface that displays a vortex. The CFD-Post vortex core visualization tools are designed to help you identify and understand vortex regions.
The following characteristics of vortex cores will be discussed:
Note: There are several ways to insert a vortex core region:
From the menu bar, select Insert > Location > Vortex Core Region.
From the toolbar, select Location > Vortex Core Region.
Depending on the context, you may be able to perform an insert from the shortcut menu in the tree view.
The Domains setting specifies the domains where the vortex core should be found. Selected domains do not need to be contiguous.
For details, see Domains.
The Definition area is where you define the type and the strength of the vortex core.
The Method setting specifies sets of equations that detect vortices as spatial regions. Click the drop-down arrow to choose a method:
| Absolute Helicity | Absolute value of the dot product of velocity vector and vorticity vector. |
| Eigen Helicity | Dot product of vorticity and the normal of swirling plane (that is, the plane spanned by the real and imaginary parts of complex eigenvectors of velocity gradient tensor). |
| Lambda 2-Criterion | The negative values of the second eigenvalue of the symmetry square of velocity gradient tensor. Derived through the hessian of pressure. |
| Q-Criterion | The second invariant of the velocity gradient tensor. For a region with positive values, it could include regions with negative discriminants and exclude region with positive discriminants. |
| Real Eigen Helicity | Dot product of vorticity and swirling vector that is the real eigenvector of velocity gradient tensor. |
| Swirling Discriminant | The discriminant of velocity gradient tensor for complex eigenvalues. The positive values indicate existence of swirling local flow pattern. |
| Swirling Strength | The imaginary part of complex eigenvalues of velocity gradient tensor. It is positive if and only if the discriminant is positive and its value represents the strength of swirling motion around local centers. |
| Vorticity | Curl of velocity vector. |
Note: There is no recommended vortex core method; the appropriate choice of vortex core is always case-dependent.
A number of methods are based on eigen analysis in local velocity gradient tensor. The following are the related notations and equations.
For the velocity gradient tensor
 | (12–1) |
The eigenvalues of the gradient tensor satisfies
 | (12–2) |
where
 | (12–3) |
 | (12–4) |
 | (12–5) |
Now let
 | (12–6) |
 | (12–7) |
Then, if the discriminant is
 | (12–8) |
then the tensor has one real eigenvalue 
and a pair of conjugated complex eigenvalues 
That is, the tensor can be decomposed as
 | (12–9) |
We denote
 | (12–10) |
and
 | (12–11) |
Then
 | (12–12) |
 | (12–13) |
 | (12–14) |
The last one is called Swirling Strength, and represents the strength of the local swirling motion. In CFD-Post,
the magnitude of both Swirling Vector and Swirling Normal is the Swirling
Strength. The direction of the Swirling Vector is that of the real
eigenvector (
in Equation 12–19) and the direction
of the Swirling Normal is that of 
defined
in Equation 12–26.
The following relationships are useful:
 | (12–15) |
 | (12–16) |
 | (12–17) |
 | (12–18) |
Now the real eigenvector meets:
 | (12–19) |
We can calculate the real eigenvector using one of the non-zero vectors:
 | (12–20) |
 | (12–21) |
 | (12–22) |
The complex eigenvectors' real and imaginary parts meet:
 | (12–23) |
 | (12–24) |
Therefore, if
 | (12–25) |
then, 
and 
. That is, all rows of matrix A are normal to both 
and 
,
therefore they are all proportional to
 | (12–26) |
So any non-zero row vector of matrix A can be used to calculate 
.
This is useful to get the eigen-helicity 
, where 
is the vorticity vector.
On 
and 
let 
and 
Then 
and 
have all real eigen-values (
).
The region with negative of 
is used in the method
proposed by F. Hussain. By using the eigen-values and eigenvectors
of velocity gradient tensor 
, we have
 | (12–27) |
So, in the case the second eigenvalue is 
Also, we can express the tensor 
as
 | (12–28) |
Now when we look into the eigenvalues and vectors of 
, the same
should apply to 
.
Let
 | (12–29) |
Its eigenvalues meet
 | (12–30) |
where
 | (12–31) |
 | (12–32) |
 | (12–33) |
Then the three eigenvalues are:
 | (12–34) |
 | (12–35) |
 | (12–36) |
where
 | (12–37) |
 | (12–38) |
 | (12–39) |
Because 
is in the range of 
, we have 
. Therefore, the second
eigenvalue for a 3x3 symmetry tensor is 
.
The eigenvector corresponding to an eigenvalue 
can
be one of the non-zero vectors
 | (12–40) |
 | (12–41) |
 | (12–42) |
[1] Copyright © 1990. Phys. Fluid. A General Classification of Three Dimensional Flow Fields. 765-777.
[2] Copyright © 1991. AGARD Conf. Proc. CP-494. On the Footprints of Three-Dimensional Separated Vortex Flows Around Blunt Bodies.
[3] Copyright © 1995. Dept. of Aeronautics and Astronautics, MIT, Cambridge, MA. Identification of Swirling Flow in 3D Vector Fields. Tech. Report.
[4] Copyright © 1988. NASA Ames / Stanford University in Oroc. 1988 Summer Program of the Center for Turbulent Research. Eddies, Streams, and Convergence Zones in Turbulent Flows. 193-207.
[6] Copyright © 2002. Eurographics – IEEE VGTC Symposium on Visualization. A Novel Approach to Vortex Core Region Detection.
[7] Copyright © 1988. In Proc. Zoran P. Zaric Memorial International Seminar on Near Wall Turbulence. Statistical Analysis of Near-wall Structures in Turbulent Channel Flow.
[9] Copyright © 2005. Eurographics – IEEE VGTC Symposium on Visualization. Galilean Invariant Extraction and Iconic Representation of Vortex Core Lines.
[10] Copyright © 2006. Phys. Fluids 18. Eigen Helicity Density: A New Vortex Identification Scheme and its Application in Accelerated Inhomogeneous Flows.
[11] Copyright © 1996. Phys. Fluids 8. Autogeneration of Near Wall Vertical Structure in Channel Flow. 288-291.
The Level setting controls the strength of the vortex core that is displayed. The Level setting is normalized between Method types so that it is easy for you to compare the output of the different methods.
To learn how to use color to show how a variable changes through a region or just to change the color of the vortex core regions, see Color Tab.
Note: The ranges of vortex core variables are calculated by CFD-Post and will be local to the timestep (that is, the range will not be calculated across all timesteps).
To learn how to control the display of mesh lines, textures, and vortex core faces, see Render Tab.
The View tab is used for creating or applying predefined Instance Transforms for a wide variety of objects.
For details on changing the view settings, see View Tab.