[CeesH]

Dear all,

I'm running a large eddy simulation of a mixing tank. (smaroginksy subgrid model)
The results show a heavily underestimated value of epsilon in the domain, when calculating e = [v + v_t]*S^2 . When calculating the impeller power number based the dissipation, the result is about a factor 2-3 lower than the power number based on impeller torque (dissipation gives around 2.2 for a Rushton turbine, vs. 5.5-6 for the impeller torque). Testing my epsilon determination and integration script on a RANS simulation, the results are just fine.

Now, because we run at relatively high Re, the wall resolution is a bit shabby (y^+ of 10-20 typically). So, one hypothesis is that this leads to underestimation of energy dissipation in the bulk. But if that is the case, should the torque power number not be much lower, too?

Does anyone have any ideas on the possible cause of the underestimation? Could it be wall resolution? and why is the impeller torque still of the right order then?

Thanks in advance!
Cees

[FMDenaro]

Originally Posted by CeesH

Dear all,

I'm running a large eddy simulation of a mixing tank. (smaroginksy subgrid model)
The results show a heavily underestimated value of epsilon in the domain, when calculating e = [v + v_t]*S^2 . When calculating the impeller power number based the dissipation, the result is about a factor 2-3 lower than the power number based on impeller torque (dissipation gives around 2.2 for a Rushton turbine, vs. 5.5-6 for the impeller torque). Testing my epsilon determination and integration script on a RANS simulation, the results are just fine.

Now, because we run at relatively high Re, the wall resolution is a bit shabby (y^+ of 10-20 typically). So, one hypothesis is that this leads to underestimation of energy dissipation in the bulk. But if that is the case, should the torque power number not be much lower, too?

Does anyone have any ideas on the possible cause of the underestimation? Could it be wall resolution? and why is the impeller torque still of the right order then?

Thanks in advance!
Cees

I never worked on your flow problem but I suggest to do a mesh refinement analysis to check its influence.
Then:
1) did you reached an energy equilibrium in your LES solution?
2) how many sample did you use for the statistics?

[CeesH]

Thank you for your reply Filippo,

Considering the statistics: The here reported power numbers are based on a single realization; monitoring them over time shows some variations naturally, but the difference between the power calculated from torque (on either rotor or stator), and the power dissipation in the volume, is always much bigger than these variations.

Statistics for the dissipation rate epsilon have been acquired over 8 impeller revolutions. Although this is a bit low to truly conclude the statistics have converged, all major trends are surely captured, and a consistent underestimation of 50-60% is observed when comparing LES to k-epsilon results for the same domain (and a local underestimation of experimental results by a factor 3-4). I am quite confident these are no statistical flukes.

Regarding the energy equilibrium; I have only judged the power input from torque on the impeller, and power dissipation from epsilon. These two are absolutely not in agreement. Is this what you mean, or are you referring to another measure? I am rather new to LES, so if you have any suggestions for other checks related to power equilibrium, I am more than happy to learn.

I have conducted further mesh refinement, but to reach a y^+ of approx. 1 takes a quite fine mesh for these cases, with the computational resources at hand, it will take a while before I have sufficient results to analyze. Alternatively, I am considering Detached Eddy Simulation or Wall-Modeled LES. I've seen some work yielding quite good results in stirred tanks with DES; I haven't seen any application of WMLES for such cases. Do you think a mesh with y^+ around 10-20 is sufficiently fine for the application of WMLES?

Thanks again!
Cees

[FMDenaro]

Considering the energy equilibrium, I mean the case where production and dissipation of kinetic energy are statistically balanced

[CeesH]

The turbulent kinetic energy levels are properly captured by the simulation, and I see no changes of them in time (aside from of course the typical noise and periodicities, but no accumulation over the longer time) - so on that level it seems the TKE budget is closed.

Also calculating the production of subgrid TKE from <T_ij S_ij> yields the same result as calculating energy dissipation - but I guess that has to because both refer to the turbulent viscosity in their definition.

but I'm not sure if that is what you mean. Are you referring to the above, or to the RANS-based calculation of the production term? (-u_i u_j dU_i/dx_j)? I haven't found time to implement the calculation of the latter yet...

[FMDenaro]

did you already check your LES code in a controlled case such as the channel flow problem? If yes, did you find the same behaviour?

[CeesH]

I didn't do that, but I did the LES using FLUENT so I hope the code itself is fine I did check my post-processing on RANS cases, and did find proper values of epsilon there.

[FMDenaro]

Originally Posted by CeesH

I didn't do that, but I did the LES using FLUENT so I hope the code itself is fine I did check my post-processing on RANS cases, and did find proper values of epsilon there.

well, try that, you will find interesting things

[CeesH]

Thank you for the suggestion, will do!

[sharonyue]

Hi Cees,

The power number calculated by the TE dissipation rate and by the torque may be different. For my cases, the predictions from the torque is always the better. You can also see this underestimation from many literatures (e.g., Handbook of mixing and other papers in journals).

However, I see some literature says the power number prediction from LES is much better, which is controversy to your results. I am wondering that how is your results now? Does it get better?

Best,

[normanp]

Hi Cees,

I know this post is old, but I was wondering if you have any further thoughts or insights about this?

I have also seen a similar situation in external aerodynamics simulations of bluff body simulations. If you integrate the dissipation rate throughout the domain, you should get close to the drag*V_inf. This is the case for RANS simulations, but DDES is underpredicting by a factor of 2-3. To me it seems strange that there is not good mechanical energy balance. All I can think is that maybe a lot of energy is being dissipated by the numerical scheme?


I did find a reference for what sharonyue was talking about above here:


'Predicting the energy dissipation rate in a mechanically stirred tank'


https://publications.csiro.au/rpr/do...55171&dsid=DS4

From the article:

'A DES simulation was also carried out as an alternative to
RANS turbulence modelling. Only 70% of power input
was found here from integration of the dissipation rates,
suggesting a need for higher mesh resolution'