Turbulent flow frequency 1

[es335]

Hi

Is it possible to estimate the frequency of the velocity fluctuations in a turbulent flow ?

Cheers.

 

[hacksaw]

For laminar boundary layer flow (below the critical reynolds number for bluff bodies), it is given by the strouhal relation. In the critical region (the boundary layer becomes turbulent), the wake fluctuations be come increasingly turbulent and broad band. The peak frequecy approaches twice the strouhal prediction but is very random. Above the critical zone the wake agains becomes periodic at a frequency given by the strouhal relation.

In the critical zone, the vortex shedding process is three dimensional with non-stationary processes along the span of the body. Above and below it, the shedding process is more or less stationary, but can be broken up into cells.

The forces acting on the body (lift and drag components) oscillate at the strouhal frequency more or less, even in the transition zone, and inspite of the fact that the wake fluctuations have higher components.

 

[es335]

Hi and thanks.

I am not sure if I understand your answer correctly, but you are talking about the wake frequencies after a bluff body, right?
There is no bluff body in the flow. I am trying to understand the frequency dependence in a tube and right after the tube. No bluff body in the flow.
If I estimates the eddy scale and correlate the eddy velocity I can estimate the eddy frequency as f=v/L
This is however not exactly what I am looking for as this is the eddy life-time.
The frequency I am looking for is the oscillation of the flow due to turbulence (inducing eg. break-up and dispersion of flow media).

 

[hacksaw]

let me rephrase my response in the form of a question.

at what scale are you examining fluctuations? is shear flow involved, is heat input being considered, gravity effects, mach effects, single phase flow....?

 

[es335]

Well. I know that my question is not well posed, and I am not even sure that I know what I am looking for. Let me try to describe my search. I am looking for at way to calculate the frequencies of the eddies in the flow. Naturally I need to know the sizes and numbers of these eddies to know the energy distribution related to frequencies.

Eventually I am looking for a way to estimate the dispersive (eg. power in a flow that is dispersed) capability of the flow. And for that I thought that looking at frequencies would be at good starting point.

And now to your questions:
Scale: It must be them all. It is the dispersive force I am looking for.
Shear: It is only air in a tube. So not much I guess, although the tube diameter will be small. Approx. d=0.5mm
Heat: No
Gravity: No
Mach: No. Not at first. It may be considered later.
Single phase: Yes. No phase changes.

 

[hacksaw]

you need to look at the spectral energy densities. no one single frequency is involved.

 

[es335]

Thanks. I will take a closer look into that.

Do you know if it is possible to say which frequency is “the most” responsible for the dispersion (of e.g. dust) in a flow?
Is it the largest eddies, the smaller but more energy containing eddies or the smallest eddies (those responsible for viscous dissipation and those even smaller)?

Of cause the must all contribute to the dispersion, but can one pick a primary source?

 

[hacksaw]

Only in a statistical sense. As soon as you introduce particles (two phases) you have to consider that only those fluctuations comparable to and greater than the dimensions of your particles will be indicated.

There has been a lot of work done in the area.

 

[235zzzo]

Hi ES335!

I think, we can consider a cylinder as bluff body, can we?
At some moment, in a turbulent flow, there an universe of eddies, which can be characterized statistically, for instance, getting the spectral distribuition (FFT, Fast Fourier Transforms) of the velocity fluctuations, where you can identify the fundamental and the harmonic frequencies, as it was said by some earlier post, perhaps in other terms.

A big eddy happens, because a singular event occurred, somewhere in the flow, or at nearby of a surface/body element, as your cylinder. And if the flow was initially laminar, it can go through a transition phenomena, and finally, we have the turbulent flow with large eddies.

The similarity analises gives you The Strouhal Number, a dimensionless frequency, which is function of Reynolds Number. It means the frequency at which the vortices are shed into a Karman vortex street, behind a circular cylinder. You can read this in fundamental book, as "Boundary Layer Theory" by Hermann Schlichting.

Concerning the structure of the turbulent flow, this story is above all an energy process, an energy transfer with the large eddy scales develloping to the small scales again. It is a dynamic process, what we call strectching process. About the vorticity... I think you must read Tennekes or Bradshaw classic books on TURBULENCE issues. Just to re-enforce fundamental concepts.

I hope this can be some help.
Cheers.
zzzo

 

[arto]

Blevins has a lot of good stuff in his book:
Robert D. Blevins, "Flow-induced vibration," New York : Van Nostrand Reinhold, c1990. This one has good examples that make it a good "regular guy" book [i.e., not just all nerd equations] We used it for vortex shedding/Strouhal # stuff.

He's also got another one out - might be good too:
Robert D. Blevins,"Formulas for natural frequency and mode shape," Malabar, Fla. : Krieger Publishing Co., ; 2001, c2000

 

[235zzzo]

Hi ARTO

How to reach/get/buy the two books you mentioned?
Thank you.
Cheers
zzzo

 

[arto]

If you're near central Massachusetts [USA] they're in the library @ WPI.

Maybe your nearest engineering college library, or

http://www.brownbookshop.com/

has them for ~$80