So to change (refine?) the question - Can a 180 degree waveguide (boundary extension) add length to a horn? I don't think so, but diffraction effects might make it appear that way. (Insert horn flush mounted into wall argument again.)
Looking forward to seeing evidence either way, but for now xrk's sim seems pretty compelling in showing that adding diffraction to the sim gets us pretty close and a few tweaks to the rear chamber, flare and mouth in that sim would probably get even closer.
Looking forward to seeing evidence either way, but for now xrk's sim seems pretty compelling in showing that adding diffraction to the sim gets us pretty close and a few tweaks to the rear chamber, flare and mouth in that sim would probably get even closer.
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Every kind of openening exiting a flat surface will have some kind of bubble. The size of the bubble is dependent on the crosssection area of the horn.
The difference is how you modify and create this boundary effect, to either maximize it or make it smaller. Compare with the waterflow around a hull. A blunt shipping container being pulled through the water will create a huge wave from the large flat front. The same amounta and weight of steel shaped like long slender hull will barle make a visiable wake at the same speed.
I don't do computational fluid dynamics in my head before breakfast (must have some coffee first) so excuse the over simplified drawing presented here.
I hope this explains how i believe it works, better then my poor technical "swinglish".
Cheers,
Johannes
The difference is how you modify and create this boundary effect, to either maximize it or make it smaller. Compare with the waterflow around a hull. A blunt shipping container being pulled through the water will create a huge wave from the large flat front. The same amounta and weight of steel shaped like long slender hull will barle make a visiable wake at the same speed.
I don't do computational fluid dynamics in my head before breakfast (must have some coffee first) so excuse the over simplified drawing presented here.
I hope this explains how i believe it works, better then my poor technical "swinglish".
Cheers,
Johannes
A large wall boundary around a sharp edged orifice (like the BC415) will produce what is called a "sudden expansion" flow in fluid mechanics. This type of flow is characterized by a large vortical recirculation donut around the jet exiting the orifice. The sudden expansion flow expands rapidly vs a straight walled jet into a boundary-less free space where the jet flow entrains (pulls) the surrounding flow as it exits and is narrower and goes farther before spreading due to normal viscous dissipation associated with boundary layer formed between the jet flow and quiescent air around the jet.
Acoustically, I think the sudden expansion will have lower frequency resonances associated with the larger scale vortex. The flow expands at a faster rate and in all cases with higher SPL's will likely be turbulent. In which case, neither the HR or AkAbak models which are solving a simplified wave equation rather than the full time dependent viscous Navier-Stokes equations, can capture. So I think as TD says, some manual "correction" factors will need to be applied. However, if one were to use a 3d time dependent flow solver (like what is used for aerospace flows in rocket nozzles), the simulation just will not capture all the nuances. Given that AkAbak is a 1d lumped element model, it does a surprisingly good job to get us "almost" there to the solution.
Acoustically, I think the sudden expansion will have lower frequency resonances associated with the larger scale vortex. The flow expands at a faster rate and in all cases with higher SPL's will likely be turbulent. In which case, neither the HR or AkAbak models which are solving a simplified wave equation rather than the full time dependent viscous Navier-Stokes equations, can capture. So I think as TD says, some manual "correction" factors will need to be applied. However, if one were to use a 3d time dependent flow solver (like what is used for aerospace flows in rocket nozzles), the simulation just will not capture all the nuances. Given that AkAbak is a 1d lumped element model, it does a surprisingly good job to get us "almost" there to the solution.
This is very close to the definition of diffraction. Change "bubble" to "wave" and it is the definition of diffraction.
"Diffraction - the process by which a beam of light or other system of waves is spread out as a result of passing through a narrow aperture or across an edge, typically accompanied by interference between the wave forms produced."
Circlomanen's boat analogy is also a diffraction effect.
Fluid mechanics is certainly not my area, but the velocity out of a horn mouth is usually far too low to create much (if any) vortex or turbulence.
Considering the fact that Akabak does not calculate the bubble some manual correction factors can be applied to account for it but that's not unique to this design and no one has mentioned the need to do this before to get a pretty accurate result with other designs. You would have to manually correct EVERY design you ever enter into Akabak that has a port or mouth. And as I mentioned, the difference is so small I've never even noticed it between Hornresp and Akabak with the same sim.
Anyway, all that is required to sort this out is someone with a measurement mic and a horn that has accurate plans to sim from. Put up some boundary extensions, take some accurate measurements and we'll see if there's anything other than diffraction going on.
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Bubble
This bubble talk, it seems to me, is what End Correction is about. As "regular" horns generally are more efficient, the EC would be less of a concern than with other designs, such as Reflex ones, i would expect.
However the majority of TH's designs i've seen published etc, don't have large mouths to match the outside air load. Therefore i would have though that EC would need to be taken more into consideration ?
This bubble talk, it seems to me, is what End Correction is about. As "regular" horns generally are more efficient, the EC would be less of a concern than with other designs, such as Reflex ones, i would expect.
However the majority of TH's designs i've seen published etc, don't have large mouths to match the outside air load. Therefore i would have though that EC would need to be taken more into consideration ?
It's not just the velocity, it depends on characteristic size of the flow feature. In this case, the orifice diameter. I probably mentioned this elsewhere but it is the Reynolds number which is the ratio of momentum forces over viscous forces.
Velocity at mouth at max SPL is U=18 m/s. Dia of mouth is D=0.8m. Kinematic viscosity of air is nu=10^-5m^2/sec.
Re=U*D/nu
Re=18*0.8/10^-5=1.44x10^6
1.44 Million is the Re number, a number greater than 2000 is generally start of turbulence onset. Number over 100,000 is strong turbulence.
Let's say we only play to 125dB max SPL (12 volts drive) the velocity is 2.7 m/sec. Re number is still 216,000 - way turbulent.
The power of non-dimensional scaling lets one analyze the regime of a problem very quickly without any hand waving.
I don't speak math so I can't comment on any of it but I'm not hand waving. I rely on software to overcome my lack of math skills.
Flare It was developed by real world testing and measurements and it's been found to be pretty accurate. Flare It wasn't developed to work with a mouth this large but it will still crunch the numbers. It reports that for a .8m diameter exit with no flare, chuffing occurs at 330 m/s at 35 hz. I know that chuffing is massive turbulence, and turbulence starts long before chuffing but still... 330 m/s.
Compare that with a port with .1m diameter exit with no flare, and it's 7 m/s chuffing onset. If 18 m/s coming out a .8m diameter horn mouth is "way turbulent" and creates a large vortical recirculation donut that amount of turbulence should be readily audible, and smaller ports would be so turbulent they wouldn't work at all. I don't think you can have 1.44 million Re without very audible chuffing.
Flare It was developed by real world testing and measurements and it's been found to be pretty accurate. Flare It wasn't developed to work with a mouth this large but it will still crunch the numbers. It reports that for a .8m diameter exit with no flare, chuffing occurs at 330 m/s at 35 hz. I know that chuffing is massive turbulence, and turbulence starts long before chuffing but still... 330 m/s.
Compare that with a port with .1m diameter exit with no flare, and it's 7 m/s chuffing onset. If 18 m/s coming out a .8m diameter horn mouth is "way turbulent" and creates a large vortical recirculation donut that amount of turbulence should be readily audible, and smaller ports would be so turbulent they wouldn't work at all. I don't think you can have 1.44 million Re without very audible chuffing.
An externally hosted image should be here but it was not working when we last tested it.
Chuffing and turbulence are different things. You can have turbulent flow without chuffing. Turbulent flow is the norm in most fluids laminar is very limited in scope and much care is required to maintain laminar flow. The flow in your AC furnace duct is turbulent, probably doesn't chuff. Turbulent flow is flow that is not laminar. Laminar means it flows in flat straight layers without vortical structures or recirculation. Laminar flow only exists for very small flow diameters or highly viscous flows like molasses. Guy, you are very good with modeling horns and HR so I can't imagine you are not good at math - especially an equation with three terms and only involving a product and division.
Btw, 330 m/sec is close to sonic or the speed of sound - flow cannot go faster than that without an expanding nozzle (like a rocket) - it is choked at Mach number. Generally flows near Mach 1 are extremely turbulent and I would imagine chuffing would be a problem. I think this just says for a large dia you need to flow close to sonic before chuffing is an issue. So that is good, this sub doesn't have issues with chuffing at the mouth. However there are smaller dia passages inside that may be prone to chuffing.
Having a recirculation zone (vortical structure) around the mouth jet is not a bad thing - think of how low of a velocity is produced by someone's mouth blowing smoke rings from cigarettes. That is turbulent flow with a vortex. No chuffing there.
Btw, 330 m/sec is close to sonic or the speed of sound - flow cannot go faster than that without an expanding nozzle (like a rocket) - it is choked at Mach number. Generally flows near Mach 1 are extremely turbulent and I would imagine chuffing would be a problem. I think this just says for a large dia you need to flow close to sonic before chuffing is an issue. So that is good, this sub doesn't have issues with chuffing at the mouth. However there are smaller dia passages inside that may be prone to chuffing.
Having a recirculation zone (vortical structure) around the mouth jet is not a bad thing - think of how low of a velocity is produced by someone's mouth blowing smoke rings from cigarettes. That is turbulent flow with a vortex. No chuffing there.
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This paper is all about velocity, vortexes, Reynolds number and compression. http://koti.kapsi.fi/jahonen/Audio/Papers/AES_PortPaper.pdf I'm familiar with all this stuff, just not the equations.
The subwoofer measured here is quite different than the one we are talking about, but the picture below from that paper shows that Re of more than about 50000 completely chokes the port and it no longer functions as a port. You are talking about 1.5 million Re from an 18 m/s horn mouth. This doesn't seem right especially when scaled up for the much larger horn mouth which should have much lower Re at the mouth than this regular ported sub. 1.5 million Re seems a couple decimal points off.
I can't theorize in math, and further theory isn't going to help much. We need an accurate sim and measurement of a real horn with boundary extensions to see what's happening.
The subwoofer measured here is quite different than the one we are talking about, but the picture below from that paper shows that Re of more than about 50000 completely chokes the port and it no longer functions as a port. You are talking about 1.5 million Re from an 18 m/s horn mouth. This doesn't seem right especially when scaled up for the much larger horn mouth which should have much lower Re at the mouth than this regular ported sub. 1.5 million Re seems a couple decimal points off.
I can't theorize in math, and further theory isn't going to help much. We need an accurate sim and measurement of a real horn with boundary extensions to see what's happening.
An externally hosted image should be here but it was not working when we last tested it.
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I was using rounded off hip pocket numbers. If you use the exact value of kinematic viscosity of air at 1 atm and 20C it is 1.5x10^-5m^2/sec.
Re=U x D / nu
Re=18m/sec x 0.18m / 1.5x10^-5 m^2/sec
Re=960,000.
If you look at the plot you showed and take the curves out asymptotically down - they probably extend to about 100,000 Re.
But Re and choked flow are not the same. Choked flow depends on velocity being equal to speed of sound or 340 m/sec. You can have smaller duct with smaller Re choked while bigger duct has bigger Re and not choked.
Re scale directly with dia so a bigger duct has higher Re for same velocity.
I really don't know what you are arguing about. I don't see any the problem with a large 18m/sec flow from a 0.8m dia duct with an Re of 1 million being a problem. That big duct won't choke until it reaches 340 m/s - or close to the chugging limit your flare program gave.
What's the problem ? You think it can't be called turbulent because it doesn't chug according to your program?
Look at this example: flow out the back of a passenger aircraft jet engine. The flow is of order 300 m/sec and the duct is about 0.8 m in dia. It is not choked and it does not chug (that would cause instabilities and shut he engine down), and it is certainly turbulent and has killer jet noise.
High Re, high turbulence, loud, not chugging.
Re=U x D / nu
Re=18m/sec x 0.18m / 1.5x10^-5 m^2/sec
Re=960,000.
If you look at the plot you showed and take the curves out asymptotically down - they probably extend to about 100,000 Re.
But Re and choked flow are not the same. Choked flow depends on velocity being equal to speed of sound or 340 m/sec. You can have smaller duct with smaller Re choked while bigger duct has bigger Re and not choked.
Re scale directly with dia so a bigger duct has higher Re for same velocity.
I really don't know what you are arguing about. I don't see any the problem with a large 18m/sec flow from a 0.8m dia duct with an Re of 1 million being a problem. That big duct won't choke until it reaches 340 m/s - or close to the chugging limit your flare program gave.
What's the problem ? You think it can't be called turbulent because it doesn't chug according to your program?
Look at this example: flow out the back of a passenger aircraft jet engine. The flow is of order 300 m/sec and the duct is about 0.8 m in dia. It is not choked and it does not chug (that would cause instabilities and shut he engine down), and it is certainly turbulent and has killer jet noise.
High Re, high turbulence, loud, not chugging.
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The sharp edge at the mouth will "trip" the flow near the edge and create the vortical recirculation donut , but the air closer to the center of the port will flow more laminar or straight. The vortical recirculation donut will shape the wave like an extended horn-section outside of the box, effectively create an larger horn then the box itself.
If the mouth did not have that sharp constriction edge creating the vortical recirculation donut, the horn would have the normal 60% of horn-mouth diameter bubble. Of course the horn has to have an expansion-rate that "sees" the outside vortical recirculation donut as a continuation of the horn.
If the mouth did not have that sharp constriction edge creating the vortical recirculation donut, the horn would have the normal 60% of horn-mouth diameter bubble. Of course the horn has to have an expansion-rate that "sees" the outside vortical recirculation donut as a continuation of the horn.
Yes you are correct and that's where I was wrong. From memory I thought it was the other way around - lower Re for larger hydraulic diameter. I found an online calculator and got roughly the same Re you did. So I was wrong about that for sure and it is turbulent.
Still not so sure turbulence is going to add horn length; still pretty sure diffraction is the key here. But that's it, I'm way out of my area with fluid mechanics math and this can all be solved pretty easily one way or the other with an accurate sim and measurement.
Nobody has a sim, a horn, a couple of pieces of scrap wood and a measurement mic? I don't have a mic or I already would have done it.
This is a nice theory, a horn flare built literally out of (vortexes of) air.
Consider this. Even with my limited math skills I can see that velocity is a factor in Reynolds number. If the bubble depends on turbulence to contain it in a virtual flare, tuning would change depending on how much power was applied because the vortex would change. A woofer tester tests at tiny fractions of a watt and there would be very little turbulence but you could also test at high power with other devices. If what you are saying is true it would have different tuning at different power levels.
The one constant thing on the outside of the box is the boundary and it's diffraction.
I know that if you aim the output of a bass horn into the corner and floor junction (1/2pi space) the corner acts an as extended mouth to the horn and you get both gain and extension of bass. A flat wall or large baffle is sort of like this but relies on this mythical bubble to get gain and extension. I have a PPSL bandpass sub that I could put behind a large cardboard baffle to see if there is an effect on bass extension. Will have to wait for when I have some time to get in the speaker lab again.
Which is EXACTLY why I built a Tapped-Tapered Quarter Wave Tube (Pipe) as my home theater sub.
Positive flare TH = efficiency, large enclosure, reverse speaker mounting.
Straight flare TH = ease of build, medium enclosure, standard speaker mounting.
Negative flare TH = bandwidth, small enclosure, standard speaker mounting.
Great information in this thread fellas! I should have went to the lecture yesterday at Ohio State University's Wexner Center on Music & Math instead watching the Dallas Cowboys get blown out at a sports bar.
Science Sundays Upcoming Talks | Arts and Sciences
The "bubble" is not mythical, it can be measured. The large baffle is to some extent part of the path length (varying in length since the baffle is square, not round), and as such lowers Fb (Fc) slightly, but it's primary function is boundary control. Because the boundary adds a lot of directivity, with multiple cabinets it is possible to increase sensitivity to a level that would appear to exceed 100% efficiency if one does not consider that the on axis sensitivity of the BC is specifically higher because the off axis level is lower. No law of conservation of energy is broken, power response is equal, but "putting it where you want it" makes a huge difference in impact there.
As far as your previous question regarding unwrapping the phase response of your sims, I don't know how to do it in Ackabak. In Hornresp (at least in the V.29 version I still use) there is a panel under "Tools" while in the "Phase Response" Window called "Standard Wrapped Phase" which features an "Offset Delay Correction" slider.
If the Offset Delay Correction is set to the proper length/time, (as needed for aligning a front loaded top cabinet to a folded horn's path length) the phase "unwraps".
For instance, the LAB(Live Audio Board)Horn, Tom Danley's dual 12" FLH design that led to the development of the Lab 12" it uses, has around 315 degrees of phase "wrap" in the pass band of 35-100 Hz. If 14.5ms Offset Delay Correction is applied (as it can be in a FFT based measurement system that can measure acoustic phase), the phase response only deviates from "0" by 45 degrees through the same pass band- just like in "real life".
Apply the proper offset delay correction to your sim, if the frequency, impedance, phase response and cabinet enclosure volume match the actual measured response of a real cabinet you are attempting to emulate, you can be reasonably confident that the sim matches reality. To match reality, a BC sim will require inclusion of some factors that are not normally employed in FLH sims to get the proper response.
DSL's TH spec sheets include frequency, phase, and impedance response curves, the few available BC spec sheets no longer include impedance response curves
.DSLs measurements are truncated at the point where frequency and phase response are in a reasonably flat range, above that line of demarcation, they rapidly deviate from flat as can be seen in independent test results.
Art
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I'm pretty sure that "mythical" statement was just a friendly poke at me in response to my insisting that the bubble is not going to help in a sim, diffraction is. I don't think anyone questions the existence of the bubble.
Again, this paragraph is pretty close to the definition of diffraction.
It will require the inclusion of diffraction.
I'm pretty sure you guys are getting sick of me saying the word "diffraction". So let's stop talking theory and get some measurements of a boundary enhanced flh to study. We'll find out pretty fast if diffraction gets all (or at least most) of the way there.
FLH measurements will require a reduced mouth exit area (aperture) as well as an enlarged boundary to measure the effects of the diffraction making the "bubble" fill the boundary.
I'll be eagerly awaiting your measurements and sim revisions
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