turbulence velocity part II
 

Hi all.

Sorry for this repeating the question, but maybe if I explain the problem somewhat better, some might be tempted to try to answer :)

How can I determine the maximum velocity (the fluctuating turbulent part) in a flow that I estimate to have a turbulence intensity of 50% ?

I cannot see by looking at the definition of the intensity how I with the intensity and a mean velocity can calculate the fluctuating velocities.

Any help is appreciated and please let me know if you need the problem elaborated.

Cheers.

Re: turbulence velocity part II
 

hello, yes u need to explain ur problem more since this field is new. ur explanation should cover what are u trying to do and what is ur exact problem and comercial package u r using to solve ur problem thank

Re: turbulence velocity part II
 

In my opinion... First of all you have a big turb intensity, which very probably go outside the validity range for most turbulence models. (by the way, which model are you using?). In the modeling, they generally assume small disturbancy from the averaged speed. It does not seem to be your case.

Even if youhad a small intensity, like 5%, you would have trouble trying to find an exact maximum value, since it is a stochastic process (or at least it is treated as such).

But I think a rough order estimation is to think

delta U = sqrt(2*q/3); where q is the turbulence intensity = 50% * Umean

so that, Umax = Umean + delta U

Does it help? Good luck. Luiz

Re: turbulence velocity part II
 

hello, try this

Knight, D., ``Improved Calculation of High Speed Inlet Flows. Part II: Results'', AIAA Journal, 19, February 1981, pp.172-179.

Re: turbulence velocity part II
 

Hey. Thank you for your time.

Oh. I'm sorry. This is not a question of CFD. I know that this is a CFD forum, but there are so many people in here that also has a great knowledge in fluid mechanics – and my question is a fluid mechanics question. I have also seen several other questions regarding F.M. and I assumed that since F.M. is the foundation of CFD it would be ok.

I am trying to estimate the turbulent velocities in at flow, downstream of a blower. I have estimated the intensity to be 50% (but this number might be wrong – I do not have a solid background for this estimate).

A word on intensity: I have read two definitions, and cannot see how they can be the same ( =one of them is wrong) I is the intensity and u_mean the mean area flow velocity. 1) I=sqrt(2/3*k)/u_mean; where k=0.5*u^2_mean 2) I=u'/u_mean; where u' is the turbulent deviation from the u_mean. It seems however more likely that I remember wrong and that u' should be a u'_mean i.e. a mean turbulent deviation from the u_mean

And what I am looking for is a rough estimate of the distribution of the velocities in the turbulent flow (e.g. max velocities u') for an analytic approach.

Re: turbulence velocity part II
 

Ups. Sorry. I ment that the u' should be a square u'^2_mean (sqrt(u'^2)_mean) to make sence to me, and not just u'_mean whitch is zero.

Re: turbulence velocity part II
 

Hi

The two definitions appear to be quite similar :

1) I=sqrt(2/3*k)/U_mean <=> I=sqrt((u'^2+v'^2+w'^2)/3)/U_mean

2) I=sqrt(u'^2)/U_mean

the first one is the true one, with an average over the 3 directions (to use with for instance ``free'' turbulence which is almost isotropic), as the second one is a simplification that has to be used for strongly inhomogeneous flow where one fluctuation is larger than the two others (for instance flows with wall effects like channel flow)

For a turbulent process, you can assume that the distribution is Gaussian (though the study of the non-gausian effects in turbulence is a very hot topic)

Hope this helps

Best regards

Re: turbulence velocity part II
 

...and because the distribution is Gaussian all you can get is an estimate of how 'often' high velocities occurs. I'm sure there are statistics equations that can relate a mean and a standard deviation to the probablity of witnessing a specific value. I however don't know them ;)

An LES or DNS model would give you much more information. Having said that it would be eaiser to stick a hwa downstream of the blower and measure speed vs. time looking for the high velocity peaks.

Re: turbulence velocity part II
 

k = 1/2 * [u_iu_i]

where [ ] is for mean value, and where there is a sommation over i. Thus both definitions are valid if the turbulence is supposed to be isotropic :

[u_1u_1] = [u_2u_2] = [u_3u_3]

so,

[u_iu_i] = 3 [u_1u_1] = 3 [uu]

then

k = 3/2 [uu]

For Luiz contribution : I am not so sure that there is an intensity limitation for turbulence modeling. How could a wake can be modelised if it is true...

Re: turbulence velocity part II
 

You're right. They are the same - haven't seen that. Thanks.

Ok, I will assume a gaussian distribution and from here I will calculate the maximum for my estimation.

Thanks all.

Re: turbulence velocity part II
 

Hi (again)

This might be very case-specific, but is it possible to give a quantitative guess on the standard dev. in the gaussian dist.?

Re: turbulence velocity part II : Sylvain
 

Something bothers me.

Suppose a 2D case. If u1=5m/s and u2=5m/s, then the resultant velocity would be 7.07m/s. Right?

Why is it the directional velocities (u1, u2) one shall use in calculating k? Why not the resulting velocity? This velocity is the one the fluid package has, and not fist 5m/s in one direction, and the 5m/s in another direction.

If I had to calculate k, it would be like this: k=1/2*[u_iu_i]/n, where n is the number of dimensions. But this is apparently not correct. Can anyone explain that to me please.

In advance, thanks. And have a nice weekend.