Hello,

How can I calculate (estimate) the turbulent dissipation rate and the turbulent kinetic energy in an LES?

Let's say you calculate velocities u, v and w in your *closed* computational domain.

The kinetic energy is simply

KE = 1/2 * (u*u + v*v + w*w)

KE can be calculated as the calculation progresses.

At the end of the calculation, you can Reynolds decompose your velocity field into averages and fluctuations,

u = uBar + u'; v = vBar + v'; w = wBar + w';

and find the turbulent kinetic energy,

TKE = 1/2 * (u'*u' + v'*v' + w'*w')

Note that TKE from an LES cannot be compared with those from experiments or DNS.

To calculate dissipation, simply calculate the time rate of change of KE. For a closed computational domain, this is the sum of the SGS dissipation, numerical dissipation and viscous dissipation. To find the contribution of each component to the total dissipation, either evaluate each term separately, or if that is not an option (e.g. in a commercial code), simply turn off viscosity / SGS models to calculate the dissipation terms separately.

For domains with inflow and outflows, a little more work is needed. You have to keep track of the flux of KE, TKE, etc. I hope you get the general idea.

"Note that TKE from an LES cannot be compared with those from experiments or DNS."

Why? how do you compare them?

TKE is the kinetic energy associated with all the turbulent eddies of the flow. In an LES, small eddies are not explicitly represented in the calculation, only their effect on the large scales is accounted for.

Hence, with the lack of small scale information, the LES TKE (in time / frequency / wavenumber spaces) will lack the completeness of a true DNS or a sophisticated experiment. For this reason it does not suffice to make a direct comparison between LES and experiments.

If you would like to know how to successfully compare (i.e. validate) LES calculations with experiments, that is a whole new area of discussion.

Thank you for u r answer. Could you then please give some hints on how to compare LES and experimetal results?

Dear Sir, I wish to express sincere thanx for providing explaination in simple words. However, would you kindly clarify the follwing. 1. Does "closed" system mean a computational domain with No-slip wall boundaries on its all 8 sides? OR a closed system is a GRID CELL you are talking about? 2. Kindly teach how to "Reynolds decompose your velocity field into averages and fluctuations"? From the time loop, I have calculated u,v,w but how to decompose them into average and fluctuating componants? Regards..