Re: turbulent flow and frequency
- From: ari <ari.karjalainen@xxxxxxxxxxxx>
- Date: Sat, 01 Apr 2006 11:12:51 +0300
My comments below.
Olin Perry Norton wrote:
abhi.menon@xxxxxxxxx wrote:Good questions. Haven't got experience with liquids but probably act similarily than gases, at least if the case "purely" turbulent.
I am trying to determine the properties of the sound generated byWhat is the fluid? Is it liquid or gas? What is the velocity?
turbulent flow.
_____ ________
|___________|
----> ____________--->
____| |_________
Suppose the fluid flows through the above system in the direction of
the arrow, there is going to be turbulence caused due to the variation
in the diameter of the tube. I need to know what the sound spectra
generated is going to be and what it is dependent on(could be the
diameter's/ velocity/ some property of the fluid like the viscosity)
If the above figure is not clear, look at the one below
_____ ________
|___________|
---->____________--->
____| |_________
An other question is, are the end acoustically semi-infinite? Or are there to be expected reflections (other than in the middle pipe/duct)?
There is plenty of this kind of articles for broadband noise. The noise correlates with pressure drop. Authors (among others)for duct systems Gordon, Munjal, Nelson, Oldham D. J., Ukpoho A. U., Waddington D. C.. Both in books and in scientific papers. Even "Woods (the fan company): Practical guide to noise control" might be enough. The limitation in that they consider only one discontinuity (to my knowledge).
If I were trying to solve this problem, I would (in order of preference):
1. Try to find some published experimental data for a similar situation.
Your situation resembles the flow through an orifice plate, a venturi,
and also a partially opened valve. (Try Googling combinations of
terms like flow, noise, orifice, valve, constriction, expansion,
restriction, etc.)
You should be able to find some data on the noise produced by thisThese ( and other)expansion have bee studied in connection to narrow band noise and theory gets easily pretty heavy. Basically there is (potential) flow instability which developes into a "bigger" instability. This is usually explained by a feed back system (Rockwell D., Naudascher E., Review – Selfsustaining oscillations of flow past cavities, Journal of Fluids Engineering, vol 100 (June 1978), pp. 152-165). Feedback can be caused by "geometry", acoustic and/or structural resonances.
type of flow restriction. If you're lucky, you might even find some
empirical equations and correlations you can use.
Chapter 5 of this publication:
http://www.grc.nasa.gov/WWW/AcousticalTest/Documents/PDF/Reduced_Noise_Gas_Flow_Design_Guide_6.pdf
has a good discussion of noise produced by orifices, venturis, and partially opened valves,
and has some equations you can use.
Most of the noise seems to come from the downstream section, where
the flow expands and creates a "constrained jet".
Theoretically these phenomena appear (at least) in laminar-turbulent transition around Re 10^5 but are found in "fully turbulent" flows as well. For theories you can start with classic one found e.g. in Schlichting, Boundary layer theory, Springer Verlag, Saksa, 2000 and Further developed by Michalke. Or then you can take an other approach Doak P. E., Acoustic, thermal and turbulent energy density and linear momentum density relationships and fluxes in fluctuating fluid flows, Proceeding of the 8th International Congress on Acoustics, Contributed papers, Vol II, s. 532. (hope tihs is correct)
BR,
ari
www.machineryacoustics.fi
PS I would expect much help from Lighthill, I would prefer vorticy theories. Unless flow velocities are high.
2. Build it and measure the noise produced.
3. Try to predict noise spectrum analytically. (Note I listed this one in last place.)
Prediction of turbulent flows is a difficult subject. The simplest prediction methods
try to predict averaged velocities and pressures. However, noise is a product
of the unsteadiness of the flow, so most people nowadays use "large eddy
simulation" to predict the fluctuations in the flow. For example:
http://www.iag.uni-stuttgart.de/Euromech-467/Proceedings/Gloerfelt.pdf
If you go with 1 or 2, you will want to use dimensionless numbers:
Reynolds number,
Strouhal number,
Mach number (maybe),
Cavitation number (maybe).
I would scale the sound pressure level with the dynamic
pressure of the flow (one half the density times the velocity
squared). The sound frequency should scale according to
the Strouhal number.
.
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