[rsin]

Results files are obtained after simulating Stirred tank reactor and i would like to know the predictions of turbulence kinetic energy of the LES Smagorinsky model in the Ansys CFX 11. I can't find a procedure as LES doesn't directly calculate the kinetic energy. Please let me know if someone has an idea. Thanks

[ghorrocks]

You need to define the turbulence kinetic energy as a function of the velocity somehow. You can take time or space (or both!) averages of the velocity fields and use that to determine the averaged and fluctuating components. From the fluctuating component you can get k.

I discuss this in my PhD thesis, in the chapter where I look at the square piston engine (chapter 6 I think) - http://hdl.handle.net/2100/248

[rsin]

I agree with you.I have found in the literature a correlation which states turbulence kinetic energy as a function of the velocity as shown below

k=k+k=1/2*(-^2)

here u represents the velocity, i represents repeted index. I don't understant the difference between and^2

I have even got time average of velocity fields. but i dont know (or i can't find out) how to use that to determine the averaged and fluctuating component. Can you help with this. Thanks

[ghorrocks]

Sounds like you need to read a text book about Reynolds and Fauve averaging. It is covered by any fluid mechanics textbook which develops the basics of turbulence modelling. In fact the CFX documentation even has a basic description of it, but a good textbook will introduce it to beginners better.

But to directly answer your question - if you have calculated the average velocity field then you simply need to calculate the average of the square of the velocity and then some simple post-processing in CFD-Post and you are done.

[rsin]

after lot of serach, a very easy method was found through CFX help files.
they state that turbulent kinetic energy for LES = 1/2 * (Velocity.Trnrms^2 -Velocity.Trnavg^2)

or = 1/2 * (statistics reynolds stresses uu + ...vv + ....ww)

statistical reynolds stresses are automatically calculated for the LES/SAS-SST and DES models. While .Trnrms and .Trnavg files are transient result files that have to be turned on in the output section.

Just to save you a whole lot of time.

[Lance]

Originally Posted by rsin

after lot of serach, a very easy method was found through CFX help files.
they state that turbulent kinetic energy for LES = 1/2 * (Velocity.Trnrms^2 -Velocity.Trnavg^2)

or = 1/2 * (statistics reynolds stresses uu + ...vv + ....ww)

statistical reynolds stresses are automatically calculated for the LES/SAS-SST and DES models. While .Trnrms and .Trnavg files are transient result files that have to be turned on in the output section.

Just to save you a whole lot of time.

Is the above the whole truth? Isnt there a contribution to k from the sub-grid model as well? Anyone got an idea on how to calculate/estimate that?

[rsin]

In order to find the energy dissipation rate, it is essential to understand the way in which kinetic energy is transferred between the filtered velocity field and the residual motions. The filtered kinetic energy Average of E (x,t) is obtained by filtering the kinetic energy field E (x,t) = 1/2 * average of (U * U)
or Average of E = 1/2 * average of (U * U) (1)
It can be further decomposed as:
Average of E = Ef + kr (2)
Where Ef, the kinetic energy of the filtered velocity field, and kr the residual kinetic energy, are given by
Ef = 1/2 * average of (U ) * average of ( U)(3)
kr = 1/2 * Average of (U * U) - Average of (U) * average of (U) = 1/2*tauiiR(4)
The conservation equation for Ef is:
DEf/Dt – delta/deltaxi [ average of Uj ( 2 * mu * average of Sij – tauijr - average of p/ ro * deltaij)] = - εf - Pr(5)
where epsilonf and Pr are defined as
epsilonf = 2 * mu * average of Sij * average of Sij(6)
Pr = - tauijr * average of Sij(7)
where average of Sij is the filtered rate of strain and tauijr is the anisotropic residual-stress tensor and defined as:
tauijr = tauijR - 2/3 * kr * deltaij(8)

where deltaij , the kronecker delta, and tauijR, the residual –stress tensor, are defined as:
deltaij= 1 when i = j and =0 when i is not equal to j(9)
tauijR = Average of (Ui * Uj) - Average of (Ui) * average of (Uj)(10)

In Equation 5, terms of the left hand side represents the transport and the ones on the right hand side represents the sink terms. The first sink term – εf corresponds to the viscous dissipation directly from the filtered velocity, and at high Reynolds number with filter width much larger than the Kolmogorov scale, this term is relatively small. The second sink term - Pr, which appears as a source term ( + Pr) in the equation for kr, is the rate of production of residual kinetic energy in the equation of Ef; therefore, it represents the rate of transfer of energy from the filtered motion to the residual motions. Sometimes, it is referred as the sub-grid scale (SGS) dissipation and denoted by εs.
At high Reynolds number the filtered velocity field accounts for nearly all of the kinetic energy:
average of E is practially to E (11)
As seen above, the dominant sink for average of E is Pr, whereas that in the equation for E for two-equation models is the rate of dissipation of kinetic energy, ε; consequently:
Pr is practically equal to ε (12)
Hence,
ε is practically equal to Pr = - tauijr * average of Sij (13)
Now, both terms average of Sij and tauijr can be obtained directly from the transient results file and they need to be averaged with time.
There are two different kinds of energy dissipation rates: solved and SGS.
Solved, which is comparatively much smaller and can be neglected, is represented by the term εf, and SGS is represented by Pr, which is the dominant term and accounts for nearly all of the energy dissipation.

[Lance]

well, that's straight out of Turbulent Flows by Pope, right?
My question was if there's a way to estimate the contribution to k from the sub-grid model.

[rsin]

Hello Lance,

Yes, the equations are st out of the book by Pope and it helped me in understanding how and why k for LES = 1/2 * (Velocity.Trnrms^2 -Velocity.Trnavg^2)

or = 1/2 * (statistics reynolds stresses uu + ...vv + ....ww)

This is what i understand when i compare the equation 4 with these equations. If you think this is wrong then please do share the point of view which led you to that belief. If you find another way of calculationg k and epsilon, then plese do share it.

Thanks & Regards