Hi all; The inlet velocity BC for LES should have some stochastic components or some random perturbations. Why is that so? and How is it expressed mathematically? Any references or papers are also good. Thanks.

Because LES is the real thing, turbulent eddies represented directly on your grid (except for the smaller ones). Not doing anything at the inlet means you are just hoping that some numerical errors will be enough to destabilise the steady state flow you are imposing at the inlet. This is a big gamble, very code dependant. You should impose random fluctuations on top of your mean velocity profile, on all 3 components with a magnitude up to about 10% of the mean velocity, as these tend to die out before they organise as vortices.

Hmm. There is still a problem - if you introduce random fluctuations, the effective length-scale would be the mesh size, i.e. epsilon would be very high. Surely, some sort of a "Stanford trick" needs to be performed, i.e. take a turbulent channel flow with proper Re number and feed in into the inlet plane by plane, to provide the inlet condition. My problems with this are: - it's not general. For example, it assumes that the inlet condition is fully developed, which may not be the coince - it's a real pain: I've no time to do a channel flow for every new LES case

So, what I would like is a better way of getting organised turbulence with a given length-scale without doing another calculation. Any ideas?

Hi,

You may have a look at this recent JCP article :

M. Klein, A. Sadiki and J. Janicka, "A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations", JCP 186(2), pages 652-665, 2003.

I use myself a somehow similar though far more crude approach for LES (space filter + time correlation), and it results fluctuations that are less damped than simple non-correlated white noise (see AIAA 2003-0068 for some details).

Best regards

Dear Dr. Jasak; Can you please give me a bit more explanation on how the effective length would be the mesh size in case i introduce random fluctuations? What if i impose periodic conditions on the inlet, take the average of the velocity and assume that this average value is a seed then add to each velocity component in each control volume a random number (say between certain limits) based on the average of the velocity? I guess fl**nt does something like this. Any justifications? I need to formulate it mathematically. Peace be with you.

Peace be with you too, Son!

(Sorry, this really made me laugh - I once had a Jesuit teacher whom I fondly remember...)

Well, the integral lenth-scale is obtained from a two-point correlation (for details look at Hinze or other source on turbulence) and measures the size of an energy-containing vortex. When you add a random fluctuation onto it, there's no correlation at all, ie. there are no vortices at the inlet. What you've basically added is lots of very small "vortices" (having no correlation, I can only assume that the energy-containing vortex is the size of the cell and that's why I cannot see it). Small vortices = high epsilon and an early death, well before larger turbulent structures are formed. Wouldn't it be better to put some "real" turbulent structure at the inlet

There's lots of people doing this kind of thing and assuming that the simulation has got enough uninteresting space at the inlet to develop turbulence from the noise you put in before it gets to the interesting part, which in fact is not so bad.

Finally, it's the other tow guys who are really big guns in LES and I would definitely have a look at the papers mentioned in the previous posting.

Hi,

Probably you can use something like Kinematic Simulations for generating random velocity fluctuations at the inflow. You can then prescribe the energy spectrum or in other words the length scale of the fluctuations. Thus you can impose disturbances with a long length scale which develop much faster to real turbulence than just random noise at the inflow. The inflow conditions are also divergence free which is not true for just random fluctuations. A disadvantage is that you can only specify homogeneous inflow conditions.

Tom

Why is it said that random fluctuations at the inlet are damped out in the first cell or so? Is it simply because there are no correlations?

[Komon]

hey,

bringing this topic from the ashes I have a problem with imposing fluctuations. But instead of putting velocity fluctuations on the inlet I'd like to impose them on whole domain. Namely, I'm trying to run LES simulation of a periodic channel flow with which I'd like to get results for turbulent (in)flow that will be used in other simulations. I've noticed that there are some simulations that impose fluctuations on the mean velocity profile in whole domain (namely Lund et al, 1998 mentions this)...but I haven't noticed that they use periodic bc (again, Lund uses semi implicit periodic conditions). Neither have I seen how these fluctuations are described. The only recommendation I got was to use 10% amplitude of mean velocity. So I'd like to ask if anyone can give some advice/further info on my intention-is it ok to make such simulations, what kind of fluctuations should I use....basically what to look for.

As for the moment, I'm using sinusoidal set of fluctuations (2-4 frequencies of fluctuations are used) imposed on the prescribed average velocity in the domain. but these just level out after a certain time and flow becomes laminar.

thanks for the answers and all the best

[FMDenaro]

Originally Posted by Komon

hey,

bringing this topic from the ashes I have a problem with imposing fluctuations. But instead of putting velocity fluctuations on the inlet I'd like to impose them on whole domain. Namely, I'm trying to run LES simulation of a periodic channel flow with which I'd like to get results for turbulent (in)flow that will be used in other simulations. I've noticed that there are some simulations that impose fluctuations on the mean velocity profile in whole domain (namely Lund et al, 1998 mentions this)...but I haven't noticed that they use periodic bc (again, Lund uses semi implicit periodic conditions). Neither have I seen how these fluctuations are described. The only recommendation I got was to use 10% amplitude of mean velocity. So I'd like to ask if anyone can give some advice/further info on my intention-is it ok to make such simulations, what kind of fluctuations should I use....basically what to look for.

As for the moment, I'm using sinusoidal set of fluctuations (2-4 frequencies of fluctuations are used) imposed on the prescribed average velocity in the domain. but these just level out after a certain time and flow becomes laminar.

thanks for the answers and all the best

I don't understand what you want to set ... if you perform the periodic channel flow just have to store the velocity in a plane and use them as inflow...

[Komon]

well, the intention is to use LES simulations of periodic channel flow to obtain developed turbulent flow. this will be then recorded at a certain plane and this data will be used as inflow b.c. for DNS or LES of more complex geometry. now...I have only the channel in which I preset some average velocity. as you know-doing this, the flow remains laminar although the reynolds could be well in the turbulent region. I've seen in some articles and even here on CFD online that you can impose some fluctuations on the initial velocity profile, which then lead you to the developed turbulent flow case. I just don't know what kind of fluctuations should I impose.....the only thing I seem to get is that they should have amplitude 10% of the mean flow velocity and they can be even unphysical.....so my question is-what fluctuations should I use, does anyone have some recommendations...or-does anyone have any other suggestion, comment on the method I'm proposing.

[FMDenaro]

Originally Posted by Komon

well, the intention is to use LES simulations of periodic channel flow to obtain developed turbulent flow. this will be then recorded at a certain plane and this data will be used as inflow b.c. for DNS or LES of more complex geometry. now...I have only the channel in which I preset some average velocity. as you know-doing this, the flow remains laminar although the reynolds could be well in the turbulent region. I've seen in some articles and even here on CFD online that you can impose some fluctuations on the initial velocity profile, which then lead you to the developed turbulent flow case. I just don't know what kind of fluctuations should I impose.....the only thing I seem to get is that they should have amplitude 10% of the mean flow velocity and they can be even unphysical.....so my question is-what fluctuations should I use, does anyone have some recommendations...or-does anyone have any other suggestion, comment on the method I'm proposing.

... why the flow should remain laminar? it will develop turbulence even for the presence of a small perturbation (e.g. the numerical error). Furthermore, any arbitrary initial perturbation in the velocity field can be used because you have to wait that the numerical transient is finished and, when the energy equilibrium is developed, you can start storing the velocity.

[Komon]

well, I thought the same about the flow developing on its own...but it just gets to the point where it has the shape of a turbulent velocity profile, no fluctuations of velocity. it remains like this, the only thing that changes is the boundary layer thickness. btw, I hope that it is clear that the flow is periodic in the flow direction.

[FMDenaro]

What about the value of Re_tau?
To accelerate the developent You can set a small perturbation on the 3 velocity components, even forcing some wavenumbers

[Komon]

I've just implemented the equation to tell me what Re_tau I'm at actually and it seems to be a bit lower than I expected it to be.

what I'm doing to impose some perturbations is, as I said-using some sinusoidal functions added to the mean velocity (sinusoidal change over x,y,z). I can add whole set of such fluctuations...they do not change the average velocity in the domain...their aplitude is 10% of the mean velocity....but up to now, they always returned back to laminar flow....but as I said, the Re_tau is a bit lower than I've thought that it is....so I'll try to increase this now.

[sbaffini]

In my experience with Fluent, using a logarithmic mean velocity profile (Reichardt actually) with random fluctuations generated by a simple logistic map is sufficient to obtain a transition to the real turbulence. Still, you have to use a non dissipative scheme and will have to wait some time.

If you want a more drastic approach, you don't actually need the small scale perturbations as much as the most unstable modes, which usually have much larger wavelength. I remember a M.Sc. Thesis comparing StarCCM with OpenFOAM where this approach was clearly shown. Still, there should be several works on this or using this. Roughly, you could try using a high power law profile (e.g., y^4 or y^6) modulated by a lateral meandering (e.g., sin(kx)).

A general method to provide well correlated velocity fluctuations is the following one:

https://www.google.it/#q=MDSRFG+inflow+LES

which is applicable in space, time, or both. There is also a recent related JCP article but i can't find it at the moment