Quadratic Products of RS
 

Hi all,

I’m working on turbulent heat flux implementation to a commercial CFD package.
I need a full form of the turbulent heat flux (please see the attached pic) that includes quadratic products of Reynolds Stresses. I’m little confused though. Can someone direct me to a source for this or show me how the full form of this looks like?

Many thanks.

From what source have you taken this expression? The turbulent heat flux is something that stems from the unresolved convective flux of internal energy.

Its high order generalized gradient diffusion hypothesis. The picture were cropped out when uploading for some reason. The complete form;

uT = C * (tau/k) * uiuk * ukuj * ( dT/dxj )

tau: time scale, k: turbulent kinetic energy

Ok, the equation makes now sense. The general vector expression should look like this



C*(tau/k) [(u'u')_bar . (u'u')_bar] . Grad T_bar


and the result is a vector but in terms of unresolved velocity, then a model should be introduced. But you should provide the reference.

Thanks for your interest Filippo!

The paper is "Analysis of Turbulent Scalar Flux Models for a
Discrete Hole Film Cooling Flow". Please follow the link as it may be open access: https://core.ac.uk/download/pdf/33664453.pdf