Computational Fluid Dynamics applied to Waveguide optimization

[thadman]

Just some thoughts,

I remember reading one of Dr. Geddes' articles, wherein he discusses higher order modes. He concludes that HOMs are linear, however their audibility is level dependent and is non-linear.

Geddes, Le'Cleach, and others have discussed waveguide optimization on this forum. However, I'm not sure if their simulations include the full compressible flow of newtonian fluids equations (ie Navier-Stokes) or simply the progression of the pressure wave.

The reason I ask...

Waveguides contribute significant sound pressure levels, INTENSE levels...even at appreciable distances. I believe that is one of their main attributes. At a point in time (before it reaches your ears), all of that energy is abruptly compressed into the throat and then forced to abruptly expand. I would expect vortices and eddies to form at the boundaries (ie turbulence) under such circumstances, which is VERY level dependent (ie highly non-linear, chaotic). I would also expect this fact to lead to a gross error in simulations which do not include it, other than low levels (laminar flow).

Perhaps (significant?) turbulence in the throat is another reason horns may *sound good* at low levels (laminar flow) and *harsh* at high levels (turbulent flow).

Just thinking out loud...

Best Regards,
Thadman

[skeptic43]

I'd be willing to bet major speaker companies are doing CFD modelling already.

Not so easy for the average DIY'r, unless, of course, he/she has the background and access to sophisticated software and advanced computer hardware to crunch the numbers.

[John Sheerin]

I'm a bit rusty on my fluid flow theory and haven't done any cfd in a few years, but I don't think this would be the cause of any effect you would see in high frequency horns. The air molecules are moving very small distances, bunching up and spreading out. But I think to say they're flowing anywhere is a bit of a stretch. On the other hand in bass reflex ports, that is a more appropriate way to look at things if you're interested in high output levels and reducing compression effects. JBL as well as some others applied CFD to this area in some AES papers. The thing to remember is that the air is flowing both ways through the port which complicates things when searching for a good solution.

As I remember, the main effect of high sound pressures in the throat of horns is due to local increases in the density of the air leading to changes in the speed of sound. This can cause sine waves to change to triangle waves. I believe Tom Danley posted about this, possibly at the AA HE forum, possibly in relation to acoustic levitation. He might have posted some SPL values where this started occurring.

[catapult]

Originally Posted by thadman

Waveguides contribute significant sound pressure levels, INTENSE levels...even at appreciable distances.

The pressures are really quite small compared to those experienced by, for example, an airplane wing. 120 dB is only about .003 psi. As I recall from my basic aerodynamics courses, you are pretty safe treating air like an incompressible fluid as long as the flow velocity is well below the speed of sound.

[Theo404]

PA Systems

air has a non-linear relationship between pressure and volume, so adiabatic compression and rarefaction can only approximate a linear function over a very limited range.

A sensible upper limit for throat acoustic power is around 6-10mW/mm², meaning that a 25mm (1") throat should not be subjected to more than 3-5W.

[thadman]

Originally Posted by skeptic43

I'd be willing to bet major speaker companies are doing CFD modelling already.

An excellent assumption. However, I have not seen it discussed on this forum.

Originally Posted by John Sheerin

As I remember, the main effect of high sound pressures in the throat of horns is due to local increases in the density of the air leading to changes in the speed of sound. This can cause sine waves to change to triangle waves. I believe Tom Danley posted about this, possibly at the AA HE forum, possibly in relation to acoustic levitation. He might have posted some SPL values where this started occurring.

Interesting

Originally Posted by catapult

The pressures are really quite small compared to those experienced by, for example, an airplane wing. 120 dB is only about .003 psi.

I understand the pressures will be low. However, I believe the CD is a unique case.

The compression driver rapidly accelerates the fluid creating a pressure wave. The phase plug-throat-waveguide abruptly compresses the pressure wave into a very small area and then abruptly expands it, possibly leading to high fluid velocity in the throat. However, although excursion may be small, it possess tremendous acceleration.

The mass of air (ie molecules) within the waveguide (coupled to the diaphragm) oscillates. This requires that the fluid flow over the boundaries of the waveguide. My thinking was that the tremendous acceleration (instantaneous velocity) of the fluid may lead to a high Reynolds number (ie turbulence), which may disjoint the boundary fluid layer and form vortices and eddies. This effect may be pronounced at high levels and may be absent at low levels (laminar flow).

Originally Posted by catapult

As I recall from my basic aerodynamics courses, you are pretty safe treating air like an incompressible fluid as long as the flow velocity is well below the speed of sound.

I believe turbulence is observed (ie chuffing) in ports at >20m/s. Wouldn't this be significantly lower than the speed of sound?

[thadman]

With regards to psychoacoustics...

Beyond 20ms, energy is processed as separate from the initial transient. It is perceived as ambient and is often preferred by listeners. However, it was observed that if the energy is much closer in time (<1ms) to the initial transient, a significant degradation in sound quality is observed.

I believe this is because pressure waves naturally encounter obstacles in nature. We have evolved to process the initial transient separate from the obstacles effects. However, if the obstacle is very close, we may not be able to make such a distinction and the initial transient is smeared. I believe the throat of the compression driver will contribute effects very close in time to the initial transient.

I'm aware that pressure waves are refracted through temperature gradients. Perhaps similar effects will be observed as a pressure wave passes through turbulence. I would expect the forces to be reactive.

[catapult]

Originally Posted by thadman

I believe turbulence is observed (ie chuffing) in ports at >20m/s. Wouldn't this be significantly lower than the speed of sound?

Turbulence can be defined for an incompressible fluid too -- water has turbulence when it flows over a rock. Just doing it in my head, the max peak velocity in the throat of a 1" waveguide would be something on the order of 4 m/s or 1% of the speed of sound so I don't think you'd need to get too fancy figuring out how it reacts to the horn shape.

Of course you could use way too much power and make it sound bad if you wanted to but the whole point of a Geddes-style waveguide vs. a traditional horn is sound quality, not max SPL.

About Tom's levitation experiments, as I recall he was looking at 160+ dB SPL levels to get things to float and I'm sure that causes all kinds of audio nasties.

[thadman]

With regards to foam placed within the waveguide,

I'm aware that Geddes considers it simply as a resistive element for mathematical simplicity. However, due to its highly complex microstructure, I believe it may have other effects which may not be easily ignored.

I have access to several journal articles through my Universities research library. Numerical simulations which agreed most with experimental results modeled it as a *bed*. The fluid is forced through the windows of the foam between the ligaments. This rapid compression and expansion has several effects beyond a simple resistance. The foam structure at the surface can result in disruption of the boundary layer (ie turbulence).

I'm not aware of any experiments which could determine turbulence in the throat, other than numerically.

[thadman]

Originally Posted by catapult

Turbulence can be defined for an incompressible fluid too -- water has turbulence when it flows over a rock. Just doing it in my head, the max peak velocity in the throat of a 1" waveguide would be something on the order of 4 m/s or 1% of the speed of sound so I don't think you'd need to get too fancy figuring out how it reacts to the horn shape.

How did you determine the max peak velocity in the throat?

Have you considered the channels within the phase plug as a possible source of turbulence?

I have looked through Geddes' phase-plug patent application. All of his examples force the fluid through incredibly small ducts before expanding into the throat.