LES evaluation help needed
4 Attachment(s)
Dear all,
I try to get some experience in LES and need some help. My setup is a simple straight pipe of 4m length and 1m diameter. Periodic bc with a mass flow rate of 0.044 kg/s is applied, which results (for air) in a velocity of about 0.07 m/s and thereby Re(pipe)=4800. y+=0.9 nearly everywhere, with y=6mm. I have a z and x of about 30mm, thus x+=z+=5. Attachment 19017 Initialization with RANS, then switched to LES (SmagorinskyLilly) with some disturbances from the terminal (as described in the Fluent manual). I set the timestep to something save dt=0.15s, time to cross one cell should be about 0.5s. Also solution methods are set as recommended in the manual. Now, from yesterday to today the simualtion ran and I got some first results. zvelocity: Attachment 19020 yvelocity: Attachment 19019 xvelocity: Attachment 19018 1) Simulation time is 261s, so the fluid traveled nearly four times through the entire pipe, which is a bit too less, I guess. (?) 2) I would like to let some monitor run during the simulation with some good predictor for convergency. Any ideas? What about a volume integral of vorticity magnitude? 3) Now, I want to check for numerical stability by means of grid size, time step,... What would be good for a judgement of that? Just the velocity profile? 4) Also I was wondering of a Re=4800 pipe is "turbulent enough" to see something in an LES at all. 5) Is there any other good way to see, if my simulation is actually a real LES (and not some VLES with a too large grid), then just do the grid / time step  independence study? 
1) compute the volumeaveraged kinetic energy and follow its timeevolution. You must reach first a statistically steady state
2) Then, you have to save several samples of your fields, the sampling frequency can be for example any 1 nondimensional timeunit. 3) For each sample, compute statistics, that is averaged velocity profiles, rms, spectra 4) compute the average of the statistics then show us the results ... you can find the reference LES solutions in the AGARD report of some years ago 
Dear Filippo, thanks for your fast reply.
With "kinetic energy" you mean the kinetic energy of the resolved scales, right? I have to do this with a custom field function "0.5 * v * v * rho"? All the other points of your post... this is to verify the statistics, correct? Wouldn't it be (nearly) equivalent to show the grid independence? 
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Yes, compute the resolved kinetic energy and plot versus the time so that you can check for the statistical equilibrium. Statistics are the only relevant result you can use to validate LES, indeed for implicit filtering such as the approach used in Fluent, you don't have a grid independence as in RANS. Actually by refining the grid your solutions will tend asintotically to the DNS one... 
Of course you are right, my bad. But for the time step size I could do that, right?

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what do you mean? simply compute first your nondimensional time step and then save the files each N timesteps, such that N*dt = 1. Save at least 15 samples 
Sorry, I ment, I can double / half the time step size to see if any relevant parameter changes.

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As I understand it, for a given grid, there should be independence of LES statistics for small time step sizes. Thus, when I decrease my time step, hopefully results won't change... Right now I think I am "on the safe site" with dt=0.15s because dz/v = 0.5s.

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yes, for a fixed spatial grid and vanishing dt, you reach an independence in the solution, say v(x,t;Delta), but this solution will change when you refine your spatial grid since Delta depends implicitly on the mesh size. Therefore, the general rule in LES is to use a dt such that you resolve all relevant time scales (a sort of a DNS in time). Otherwise, you implicitly are doing a timespace filtering and your sgs model should take into account also for the unresolved timescales. But this is a different history ... 
Alright, that was what I ment. I wanted to change dt just to see, if it is already small enough!

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Is this really the relevant timescale? I don't think so, because the needed timescale should depend on the grid size.

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are you talking about the cfl condition? first, the numerical stability condition involves also the diffusive scale in a complicate manner that depends on the discretization... then, you must use a dt smaller than that estimated from the convective condition, such that in the computational cell the characteristic diffusive time is of the same order of your computational timestep. This is equivalent to guarantee a DNS resolution in time. 
Sorry, but I still don't get your point. :o
Now, there is some time scale needed for DNS. For LES the grid is coarser and the fastes eddies get modeled  so the required time step gets larger. The degree of modeling depends on the size of the grid. That makes the time step of the LES grid size dependent. 
> 1) Simulation time is 261s, so the fluid traveled nearly four times through
> the entire pipe, which is a bit too less, I guess. (?) It depends on the type of flow. For example, accelerating flows tend to settle quickly whereas diffusing flows can take a long time to settle. Given the short length then yes 4 pass throughs will not be enough. > 2) I would like to let some monitor run during the simulation with some > good predictor for convergency. Any ideas? What about a volume > integral of vorticity magnitude? It isn't clear from your description quite what is fixed and what floats. If the mass flow adjusts to balance the stresses and an imposed pressure drop then the mass flow itself is a simple and reasonable monitor. If the mass flow is fixed and the stresses adjust then you could use those to monitor for equilibrium. The energy in the turbulent motion is also a common measure. > 3) Now, I want to check for numerical stability by means of grid size, > time step,... What would be good for a judgement of that? Just the > velocity profile? The Peclet and diffusion numbers in the three grid directions and every cell is the usual means of monitoring flow stability and choosing a suitable time step and possibly regridding for more complex flows. During the settling down phase there is often a bit of a bang requiring the time step to be reduced if the convection and/or diffusion is explicitly treated. > 4) Also I was wondering of a Re=4800 pipe is "turbulent enough" to see > something in an LES at all. LES is usually a high Reynolds number model. If you have a low Reynolds number flow then a turbulence model should not be used. Simply perform an unsteady laminar simulation. > 5) Is there any other good way to see, if my simulation is actually a real > LES (and not some VLES with a too large grid), then just do the grid / > time step  independence study? There is no need to perform a simulation at all. The Reynolds number of the flow tells you. If you insist on performing a simulation then a "proper" LES needs to resolve all the large scale motion from the largest strongly anisoptropic energy containing scales down to a scale which is reasonably isotropic but still well above the scales dissipating energy directly to heat. Evaluating the work done against the viscous stresses, the LES model stresses and the energy in the resolved motion should indicate if the required assumptions about the turbulent motion are being met. 
From a book of Sagaut:
We follow the common interpretation of LES as result of an evolution equation with spatially reduced resolution, and thus we focus on the analysis of errors due to spatial discretizations and spatial filtering. This implies that the timestep size chosen for time integration is always sufficiently small so that error contributions from temporal discretization and temporal filtering (if applied) are negligible as compared to spatial error contributions. From now on this will will be tacitly assumed. That means that your dt should be formally at level of the Kolmogorov timescale to ensure it does not produce filtering effects (or, form a numerical point of view, a timecontribution of the local truncation error) 
So it's recommened to take the worst case (=smallest) time step to ensure that it is actually small enough. Ok, but if you double it afterwards and compare the results you can learn for future simulations what might be small enough...

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