Hi to all,
As it is known that the root mean square of the turbulent velocity fluctuation can be calculated in RANS as follows (if the turbulent kinetic energy k is known );
u'=(2k/3)^0.5
I am doing simulation in OpenFOAM using one equation eddy viscosity model under the framework of impilicit LES and i want to calculated the rms of turbulent velocity for this LES model.
I would like to ask that is there any expression in LES like indicated in RANS to calculate it ?
Thank you.
Kindly Check this post it could be of some help to you.
http://www.cfd-online.com/Forums/openfoam-solving/112913-utilities-post-average-turbulence-fields-create-turbulence-fields-les.html
Regards,
Rahul
generally, the LES solution is unsteady, therefore to define a steady average field the LES solution is sampled and averaged in space and time. Once computed the statistical steady velocity, you can compute the fluctuation by its definition
As written by Filippo, LES is instantaneous and the RMS values (at every mesh point) are calculated by using the time-averaging the quantities (i.e mean u,v and u*u,u*v components), which were taken as average for a long period of time, much longer than the relevant problem time scales (turbulent time scale, flow-through time scale).
The idea is that after "enough" time have passed, the time averaging converges to the mean values of many different realizations of the same flow. Then, by using these values the RMS can be calculated by simple mathematical expressions (i.e SQRT(-) and similarly the rest)
I just forgot to mention a litte issue...statistics in LES are performed on a filtered field, say V_bar. Therefore when you compute the time-averaged field this is slight different from the field considered in RANS approach.
How this two field can be efficiently compared is still an open issue
I would add to Zvi's and Filippo's answers that in case the statistics of subgrid-scale , sgs,velocity fluctuations are needed, they can be evaluated directly from the sgs model. Loosely, eddy viscosity is related to sqrt(TKE) and TKE (turbulent kinetic energy) has a sense of squared sgs velocity fluctuations. LES studies often show resolved plus sgs statistics.
cheers
Piotr
Thank you very much to all for kind answers.
As far as I understood from the answers, is it possible to represent the turbulent velocity fluctuation (U') in LES as follows:
U(t)=Umean+U'
U'=(|U(t)-Umean|)^0.5+(2k/3)^0.5
where first part represents the sgs velocity fluctuation whereas second part shows the resolved part...
just to avoid misunderstanding...
Assume v(x,t) is the pointwise velocity field. Now the RANS decomposition is
v(x,t) = v_mean(x) +v'(x,t)
being v_mean(x)= the statistical averaging, while the LES decomposition is
v(x,t) = v_fil(x,t) +v''(x,t)
being v_fil(x,t)=G*v(x,t) the filtered field. You see that the two fluctuation fields are different by definition.
If you perform the statistical averaging on the LES velocity you get
= (x)
then
v_fil(x,t) - (x) = v'''(x,t).
In conclusion, you get three formal different definitions of fluctuation field. Only the latter can be explicitly computed from the LES solution, the other being modelled.
I see that is quite tedious using so much symbolism but this way you can distinguish better RANS and LES fluctuations...
This statement cannot be correct due to dimensional arguments:
|U-Umean|^0.5 doesn't have the same dimensions as U' or k^0.5
I got the notion that you were referring to the Reynold-Stress terms, i.e u'u', u'v', etc, not the actual unresolved velocity components.
Note that (2/3)*K is the isotropic part of the Reynolds stress model. If you want to approximate the fluctuating velocity, based on you LES model, than you can use the square-root of each diagonal term of the Reynolds Stress Tensor (u'u',v'v',w'w') based on the value the model gives you (with Bousinnesq-based model, you will need the eddy-viscosity and the strain-rate tensor).
u'u' = 2/3*K - 2*eddy_visc*S11 = 2/3*K - eddy_visc*2*dU/dx
v'v' = 2/3*K - 2*eddy_visc*S22 = 2/3*K - eddy_visc*2*dV/dy
...
But pay attention that this will give you an *approximation to the magnitude* of the velocity component - not it's direction!
Can you explain why are you looking for the actual velocity components?
Hi again,
Dear Filippo, thanks so much for your explanation. Now, it is almost clear to imagine the LES and RANS equations.
Dear Zvi, thank you for kind explanation. It is really informative. I am doing cavitating turbulent flow analysis inside of fuel injector nozzle both experimental and numerical. I have measured turbulent flow data from experiment and carried out simulation with LES model. So, i would like to compare both results. That is why i am looking for the turbulent velocity values.
Thank you
Barış,
The actual velocity field is very sensitive to initial conditions and BC, which is the reason why we work with expected values and correlations, rather than instantaneous values. If you are tying to match instantaneous velocities from an experiment with those from the simulation, I would doubt that you will need the SGS velocities, due to their magnitude in comparison with the resolved scales - and also since they don't have to actually conform with your *specific* "realization" of the simulation
As the same can you help me to find Cp rms (Coefficient of pressure ),
Hai,
I am using Fluent, my problem is environmental wind flow over a building, I want to find a rms values of pressure. who can help me to sort out my problem.
There is nothing of different from the computation of rms of a velocity component
Thank you Filipo..,,
But i want to make it in ANSYS Fluent Calculator as a variable.
Please help me to sort out
https://www.researchgate.net/post/How_to_find_Cd_rms_and_Cl_rms_in_ANSYS_fluent
https://caefn.com/openfoam/reynolds-stress
hi you should go to above site...
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