Is pressure really modified pressure with 2/3k included?
 

I am trying to understand the formulation of the momentum equation in the solvers that use PISO. The divergence of the deviatoric part of the effective Reynold stress tensor is added into the left-hand implicit side of the momentum equations using divDevReff or divDevRhoReff for incompressible and compressible flow, respectively. The 2/3k delta_ij contribution to the Reynolds stress tensor has been removed since we are dealing with the deviatoric part.

Where does this 2/3 k term go? Is the pressure really a modified pressure, p + 2/3k? If that is the case, is modified pressure written to the data files or is 2/3k removed and actual pressure written to file? I know that isn't so important in incompressible flow where the gradient of pressure is all that is needed, but it is important in compressible flow.

P.S. If you well understand this subject, see my recently posted question added to the thread "Calculating divDevReff" started by jposunz. Any help would be appreciated.

Thank you,

Matt

As far as i know it is added like you wrote

I would guess that the turbulent pressure (p+2/3k) is written. I don't think if models like RANS are ( directly ) appropriate for compressible flow
Quick search on this site gave me this, maybe helpful ( edge solves compressible RANS ):
http://www.foi.se/FOI/templates/Page____4568.aspx

Hi, Matt

Your detail explantion in openfoamwiki helps me a lot to understand the code in openfoam (especially turbulence model part). I also came across the same problems as yours. one is 'dev2' inside of the divDevBeff issue and the other is modified pressure (p+2/3k) .

currently, I use incompressible pisoFoam (OF 1.7.0) so first one may affect little and it seems obvisouly 'dev2' rather than 'dev'. But second problem, I am not quite sure. based on solver itself, it seems it use only 'p' not 'p+2/3k'.

So did you figure out this issue? or Do I misunderstand something?
Thanks

Yusik

OpenFoam confirmed that 2/3 k is caculated as a part of the pressure.

http://www.openfoam.com/mantisbt/view.php?id=47

This is still confusing. If the scalar field "p" in all OpenFOAM solvers actually represent turbulent pressure (p+2/3k), then these pressures cannot be used in the equation of state. For example, the equation of state of ideal gas is

p=rho*R*T

Obviously the "p" in this equation is the actual pressure, not the turbulent pressure. However, all solvers seem ignore this issue. For instance, in the compressible solver "rhoCentralFoam", the pressure is computed from density and rPsi as follows

surfaceScalarField p_pos(rho_pos*rPsi_pos);
surfaceScalarField p_neg(rho_neg*rPsi_neg);

There is no terms involving 2/3k added.
Can anybody gives an answer? Thanks a lot.

There is a master’s thesis which gives some explanation. You can click on the following link:

http://www.diva-portal.org/smash/get...FULLTEXT01.pdf

I am also interested in how the kinetic energy term is inserted in the pressure.

Does anybody know, where we can find the implementation?

If the solver uses the Boussinesq eddy viscosity assumption, and includes the deviatoric portion of the Reynolds stress tensor into the momentum equation using divDevReff or divDevRhoRess, then the hydrostatic contribution of the Reynolds stress is incorporated in the pressure term. This happens automatically when momentum is solved, and this modified pressure (p + 2/3k) is what is written to the p field.

If anyone is unclear about this, take a look at the derivation of the momentum equation here, http://openfoamwiki.net/index.php/Bu...sinesqPisoFoam. This thread was also helpful, http://www.cfd-online.com/Forums/ope...ivdevreff.html.

Also note, the 2/3k contribution to the modified pressure is typically small. Consider what it is as compared to the dynamic pressure:

dynamic pressure = 1/2*Umean^2
turbulence intensity = u'/Umean
u'=sqrt(2/3*k), or k=3/2*u'^2

Some simple math shows that,

2/3*k = dynamic pressure * 2 * turbulence intensity^2

Since turbulence intensity typically will be between 1% and 10%, the 2/3k contribution will amount to somewhere between .02% and 2% of the dynamic pressure of the flow.

I don't think that the rhoCentralFoam solver handles the Reynolds stress in this way. So I'm not sure that it is relevant to this discussion.