If anybody is still interested in fiber, air, models in a duct ...

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Reading some more, I am wondering how acoustic impedance and possibly other damping characteristics will vary with linear density of fibers and volume density of application. It seems that lots of lower priced products use fibers of larger diameter. Once I asked for a finer fibers, it had to be special ordered. Even on special order, the fiber diameters seemed much larger than the sample I provided which came from a pillow.
 
The flow past a fiber causes a force and the fiber, not being perfectly rigid, has to deflect.
It could be.
But the only example of that are the measurements of R. A. Robinson in his Ph. D. Thesis (with Marshall Leach).
RAR uses the same technique as MJK, but with a TL filled of fiberglass (brrrrrr !).
RAR makes his own model (purely mechanical, translated into electrical: there you see the Leach "hand"). This model too is completely "out of the mainstream". It's made for fiberglass and it is hardly adaptable to other fibers.
It seems working better than standard, "rigid", models.
With those I get:
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(2.6 kg/m3)
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(5.2 kg/m3)
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(7.9 kg/m3)
"Rigid" models loose completely the resonance that is quite evident at 40 / 50 / 70 Hz, and the fit is not so satisfactory.
Are those measurements correct ? I don't know.
Is the fit "good enough" to predict the SPL (what we hear ...) from the line ? I don't know.
 
soongsc
Once I asked for a finer fibers, it had to be special ordered.
Dacron Hollofil II is quite easy to find in the States (Amazon.com: Dupont ® Dacron Hollofil II Standard Pillows (2 Standard Pillows): Kitchen & Dining). You pay (a lot !) for pillows that then you destroy, but, at the end, you have something whose characteristics are well known (and "good enough" for a TL).
BAF and AcoustaStuf are interesting material, but I don't have any measurement on then (apart the usual generic statements).
Again on fiberglass: how can I be sure that the fiberglass I buy in the store near me has the same fiber diameter as the one used by RAR ?
 
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Heh, my enclosure supplier suggested I use US$3 pillows from which my original samples were from. :D My question was what kind of pain he would be willing to go through to measure within 10% for each speaker. :eek: But I will review the models to gain more understanding. Thank you!

I also noticed that the more course fibers were stiffer. Of course fiberglass is also quite stiff, but it does not seem to expand to fill, so this might also effect measurement data. In once set of speaker, I stuffed fibers in trying to distribute it as good as I could, but the sound was compressed. Then I just tore the fiber sheet into small pieces so that they could be spread out more evenly, this then made the sound more relaxed.
 
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Reading some more, I am wondering how acoustic impedance and possibly other damping characteristics will vary with linear density of fibers and volume density of application. It seems that lots of lower priced products use fibers of larger diameter. Once I asked for a finer fibers, it had to be special ordered. Even on special order, the fiber diameters seemed much larger than the sample I provided which came from a pillow.
I am not sure whether I presented the above clearly or not.
By linear density, I mean the actual material density of the fiber, not the suffing density term normally used. By volume density, I mean how much physical volume is accupied by the fiber. When the fiber has low linear density, it will occupy more volume for the same stuffing density.

Another aspect that would be very important is the finess of fiber constructed of the same material. This will also effect the acoustic impedance at different frequencies.

All the models seem to address stuffing density.
 
The fiber models I'm using rely on the flow resistivity. There is (commonly) another model, the Johnson-Champoux-Allard that relies on more parameters which require specialized measurement tools.
The JCA model is (best) suitable when you have some specific material, of which you don't change the (apparent) density when you use it (look, e.g., at fiberform, just another PET composite, that come in well defined densities).
I don't use it because I want to do just the opposite: control the density.
The other model I'm using is Bies-Hansen that gives you the flow resistivity as a function of the fiber diameter and the (apparent) density.
This is why I don't use porosity, which in turn would require the bulk density of the material.
 
I wish I had the math skills, but I can only rely on inuition and test articles. My gut feeling is that the fibers used should to have some desireable properties:
1. They need to be able to compress and expand well to allow better control of volume density. Volume density would be related with resistive nature of the stuffing.
2. The fibers should be as fine as possible. More fibers per cross section will create more resistance.
3. They need to have low linear density. This will make the fibers more easy to be moved by soundwaves/airflow such that irregular fiber movement can create additional resistance for less suffing density.

Do you have any links to information on the JCA model? I have just searched...
"the Johnson-Champoux-Allard model which supposes a motionless frame, they may yield wrong parameters when this condition is not satisfied."

This site is also interesting:
http://apmr.matelys.com/index.html
 
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Hi teodorom,:)
*
I guess you’ve already read DR Putlands thesis?

http://grputland.com/files/thes.pdf
*
If not I,m looking forward for your eventual comment(s) on Putland's take on 'fiber absolute velocity' in : Chapter 7.1.1.

Do you agree with with Putlands approximation to neglect any:

/(b) a second damping force proportional to the “absolute” velocity of
the fiber, and
(c) an elastic restoring force proportional to the displacement of the fiber
from the equilibrium position./

...for...

/(a) a damping force proportional to the relative velocity between the
fiber and the air,/
?

//7.1.1 Discussion of approximations; review of literature
A quantity called complex density was derived and used by Leach in his 1989 paper on fiber-filled enclosures [30]. Leach’s application is simpler than the present one in that it does not involve the finite-difference method; the complex density expression is substituted into a conventional low-frequency model of an undamped enclosure.

But Leach’s expression for complex density is more complicated than the one to be derived here. His equation (21), which describes the motion of the fiber, includes three force terms, namely

(a) a damping force proportional to the relative velocity between the
fiber and the air,
(b) a second damping force proportional to the “absolute” velocity of
the fiber, and
(c) an elastic restoring force proportional to the displacement of the fiber
from the equilibrium position.

Leach’s analysis assumes that forces (b) and (c) are uncoupled, i.e. independent of the motion of adjacent fibers or even adjacent parts of the same filament.
This is unrealistic given that both forces are internal to the fiber and arise from non-uniformity in the motion of the fiber (which causes deformation) rather than the motion itself.
In Leach’s defense, it should be noted that the distinction between motion and deformation is not critical in his analysis because the two quantities may
be assumed to be proportional; the entire volume of the fiber-filled box is modeled as a single volume element, with the fiber constrained to be stationary at the boundary.

But in the general finite-difference volume element, no such constraint applies, so that deformation and displacement must not be confused.
If deformation and displacement are proportional, as Leach may have assumed, then velocity is proportional to strain rate, which in turn may be proportional to internal viscous forces.
But one would not expect such forces to be significant when compared with elastic forces, especially in a brittle material such as glass.
Moreover, frictional forces caused by fibers sliding over adjacent fibers are not proportional to velocity, - absolute or relative. Hence one must question Leach’s treatment of force (b) even for his own purposes.
One may be tempted to neglect forces (b) and (c) solely because of lack of realism.
But it is preferable to show that these forces are negligible compared with (a), the air drag. The following argument proceeds in two steps, suggesting that (b) is less significant than (c), which in turn is negligible compared with (a).
Force (b) comprises viscous forces within each filament, plus friction due to
fibers sliding over fibers. The internal viscous forces are expected to be smaller than elastic forces, as already stated. Concerning friction, the fibers are excited by a common airflow and therefore tend to move together with minimal sliding.
If sliding is neglected, the only kind of frictional force is static friction, which is non-dissipative and serves only to transmit the elastic force (c) through the fiber network.//

b
 
Since we are discussing of that: IF ANYBODY KNOWS ANY PAPER ON "MOVING FIBERS" (please don't point me out the usual Bradley and Auspurger papers), A PAPER WITH MEASUREMENTS, PLEASE TELL ME !!!

This site is also interesting:
[URL]http://apmr.matelys.com/index.html[/URL]

At the bottom of the page is a history chart related with research of various material.

http://apmr.matelys.com/pages/AcousticalPorousMediaHistory.jpg

Continuing some search...

Hmm, I am wondering whether periodical "Applied Acoustics" is a good source of such information or not.
Such as http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1S-3WCSYKP-2&_user=10&_coverDate=06%2F30%2F1996&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1444463620&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=85d6b10a3abbcfb5376990d68ee5d2de&searchtype=a
 
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"For a wave with frequency 100 Hz in glass wool of density 30 kg/m3, the attenuation of a layer of thickness 0.20 m is 4 dB if the fibers move, and 12 dB if they do not move."
This density seems higher than what I have used in the past. Just a quick browse through the paper, it seems the material is placed against a wall rather than in a duct where the waves propogate through. I think this will be different because porous material work more effeciently where the velocity is highest, whereas when placed against the wall, the velocity is lowest.
 
This is true, but the low frequency attenuation improves when most damping material is at a certain distance from the wall. Normally these are measured for wall treatment products. I guess I need to look into the paper a bit more to see if there is anything applicable to speakers.

Thank you for the information.

I've always wished there were some software that will allow users to define the suffing distribution and simulate it.
 
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