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Is it possible to model port compression?

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as subject really, I might be blind but I haven't found good info on this so far. I am aware of rules of thumb like "keep it under x% of speed of sound" but this seems distinct from whether a particular port will compress or not.

 

if the answer is "yes, if you use akabak" then any example would be appreciated as I've never used it but have been planning to try it out :)

 

context is I'm planning on building a dual reflex bandpass sub to test out this PVL hypothesis, design details in http://www.avsforum.com/forum/155-diy-speakers-subs/2539913-ported-nf-uxl-18-build.html#post46292769in case anyone is interested

 

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Good question. I use the "rule of thumb" type modelling when I use Unibox.

 

The severity of compression is worsened with smaller surface area. Ie: smaller port/vent, easier for compression to set in.

 

I'm no expert at all. Just use good sense when designing.

 

I would like to see if there is a way to really "model" it though. The smarter guys here will know im sure.

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I found this article to be helpful:  http://www.subwoofer-builder.com/flare-testing.htm

 

Although the article mainly addresses chuffing, I believe chuffing and compression tend to coincide with one another.  I would think that once chuffing is loud enough to hear, compression is already there or is not far behind.  Of course, you may still not hear the chuffing if the content masks it, but the experiments in the article used sine waves to mostly avoid the masking problem.

 

The article suggests that larger diameter ports with greater flares can tolerate higher flow velocity before chuffing sets in.  Unfortunately, they don't address what happens with slot ports at all.  Presumably, it's not good, but maybe not so bad as to render them useless.

 

Best of luck on your design.  Unfortunately, I think port chuffing and compression are almost inevitable with ULF tuned ported and/or bandpass systems that don't have huge boxes.  The chuffing itself will very likely be more audible in the near-field, too.

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Of course it can be modeled, but it is difficult to make a model accurate enough to give useful results.

The behavior is nonlinear, mainly 2 parts are important - viscous losses along the walls, and turbulent losses where flow area changes, as it does at the exit.

The viscous part is not very difficult, the turbulent part is very difficult.

 

Then you need to find some software that can simulate the nonlinear model, and if this model also includes the rest of the speaker system, this will be quite complex. You may write your own simulator software to do it. 

 

Akabak can not simulate nonlinear systems.

But it can give you very useful information about the flow - speed, pressure.

Then you can estimate what happens, you know the size and shape of the port, and with some experience you will learn when flow speed vs port shape and size becomes a problem.

 

Flared exits behave much better, larger port area tolerates higher velocities.

 

Port compression is a significant problem at very low frequencies, and one of the reasons why even a small horn outperforms a traditional ported box.

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Ok so practically speaking we are back to rules of thumb (aka experience) as it doesn't seem amenable to modelling without being a fluid dynamics expert.

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Exactly. But a simulation - of the linear system model -  is still useful, as it will give you the velocity.

 

Then you can use the information on the page @SME linked to, to estimate performance.

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The article suggests that larger diameter ports with greater flares can tolerate higher flow velocity before chuffing sets in.  Unfortunately, they don't address what happens with slot ports at all.  Presumably, it's not good, but maybe not so bad as to render them useless.

 

Best of luck on your design.  Unfortunately, I think port chuffing and compression are almost inevitable with ULF tuned ported and/or bandpass systems that don't have huge boxes.  The chuffing itself will very likely be more audible in the near-field, too.

 

Agreed. Near field does seem to be more problematic as far as port noise goes. Ports are always one form of compromise or another. It's almost impossible to get enough vent area without impractically long ports or enclosures that are gigantic.

 

The first comment based on Collo's work does seem to hold true in my experience. The M.A.U.L. cab models with nearly 100m/s airspeeds with full K20 signal and that's a 12" port. I knew that going in but there's only so much port you can fit and the port calculator seems to indicate that it should be reasonable performing up to perhaps 40 or maybe 50m/s. I'd say it did ok based on the testing.

 

Actually there was a guy who posted over at AVS awhile back who seemed to have information indicating that perhaps a large group of small vents perform better than a single large one ultimately. Think of a port like pack of straws vs a single 4" vent as would be normal. I'd always heard that you want minimal surface area inside of the port for air friction purposes but this would be the exact opposite of that. I can't remember what thread or who the poster was but I do remember that the information he linked to did seem to be legit, but I got busy and didn't really have a chance to give it much of a look.

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Ok so practically speaking we are back to rules of thumb (aka experience) as it doesn't seem amenable to modelling without being a fluid dynamics expert.

 

 

I am way behind on the PVL / TR discussion you guys have over at AVS but it does seem like the consensus now is that particle velocity should be as high as possible. However a 1" port will always have higher velocity than a 6" vent which will have higher velocities than a 16" square horn mouth. This is opposed to the age old problem of trying to get enough vent or mouth area to avoid severe compression and noise. Also is there any thought being given to other considerations such as the total area of the high speed particles? For example a 4" port firing into the back of a couch versus a 21" driver surface area. One is a higher intensity but much more localized effect versus a more diffuse effect over a larger area.

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Also is there any thought being given to other considerations such as the total area of the high speed particles? For example a 4" port firing into the back of a couch versus a 21" driver surface area. One is a higher intensity but much more localized effect versus a more diffuse effect over a larger area.

 

I have been thinking about this in the last day or two, both with respect to port positioning (relative to the body) and how many ports to use.

 

The downside of a ported box for nearfield is the box is bigger so you can fit fewer boxes in a given seating area. The upside is they have much greater PVL so you need fewer of them to achieve a given level of TR or you can run them at a lower level (to avoid negative audible impact from the NF). Most NF subs appear to be simple sealed designs (often using an HT18 or a cheap car sub like the infinity 1260) and the 12 inch designs are commonly used in multiples, 2 per seat seems pretty common so you're looking at a bank of 8 subs spread out behind the seats. This sort of output seems to be enough to deliver plenty of TR across those seats. Therefore I've been thinking that running multiple ports (3-4 for the rear chamber, 2 for the front chamber) is a good idea so as to spread the output out across the area. I could also then more at chest height as people seem to report that this is more effective for a (lower) mid bass tune

 

I thought this might also let me play with the tune of the box a little bit (though whether that is practically useful remains to be seen).

 

The other thing I've considered is a 4th order bandpass box which comes out quite a bit smaller & still provides significant PVL through most of the range. It seems, on paper, one could use this design quite effectively if using multiple subs NF to get both the low end and the upper end. 

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came across this paper recently which goes into this area in some more detail -> http://koti.kapsi.fi/jahonen/Audio/Papers/AES_PortPaper.pdf

 

Nice find, can not remember seeing this.

 

The data in this paper shows that the relationship between port geometry and performance is very complex, and to model this for a dynamic simulation is difficult. 

 

It also shows that port compression and nonlinearities are very significant.

For very low frequencies the situation gets worse, velocity increases as frequency goes down. 

 

Build a horn instead, it will more or less solve the port compression problem.

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I am way behind on the PVL / TR discussion you guys have over at AVS but it does seem like the consensus now is that particle velocity should be as high as possible. However a 1" port will always have higher velocity than a 6" vent which will have higher velocities than a 16" square horn mouth. This is opposed to the age old problem of trying to get enough vent or mouth area to avoid severe compression and noise. Also is there any thought being given to other considerations such as the total area of the high speed particles? For example a 4" port firing into the back of a couch versus a 21" driver surface area. One is a higher intensity but much more localized effect versus a more diffuse effect over a larger area.

 

A port which is acoustically small will - which is the case for all normal reflex ports, and even bass horns - will be the same as any small point source  when you get some distance to it.

 

To be sure, I did an experiment once and measured it; a sealed box measures exactly the same as a ported.

The relationship between pressure and velocity is the same for both.

 

However, if you get close enough to the sound source, the situation will be different.

Also, if you drive the port hard enough to get very high air velocity, the nonlinear effects of the flow and flow separation will affect the situation and create something different from the small point source model.

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came across this paper recently which goes into this area in some more detail -> http://koti.kapsi.fi/jahonen/Audio/Papers/AES_PortPaper.pdf

 

Wow!  Interesting paper.  I read it all the way through.  There's some good data in there, but I'm not sure it's especially useful for modelling or design work.  I wish the different studies tied together better.  A lot of effort appears to be spent optimizing flare radius on a port that is flared across its entire length.  Most of us are lucky to be able to choose ports with flared ends.

 

Their Reynolds Number study leaves a lot to be desired.  For one thing, the Moody Diagram from which they base their argument that the output hits a wall when the flow goes turbulent, really only applies to so-called fully-developed pipe flow that is several pipe diameters away from any entrance, exit, bend, constriction, expansion or any other flow disturbance.  Only some subwoofer ports will be long enough to have a region of fully-developed flow.  The losses that grow non-linearly with output (and thus cause compression) can occur in the middle of the pipe or in part of the flare or even outside of the port.  Other experiments of their demonstrated that even a slight round-over at the entrance and exit yielded a dramatic performance improvement.  Therefore it is a shame that their Reynolds Number experiments were done on systems with hard transitions between pipe and entrance/exit.  If instead, those experiments used optimal flares at the entrance and exit, we could have gained more insight into the nature of losses in the middle of the pipe vs. elsewhere.

 

Another thing is that their Re data suggest that port velocities need to stay very low to avoid hitting a wall.  They argue on the basis of their data that there is a wall for Re somewhere between 50-100k.  Keeping Re under 50k is not easy.  For 4" tube ports, that's 7.5 m/s; 6" tubes is 5 m/s;  2" or a 1" thick slot is 15 m/s.  The Reynolds number increases with pipe diameter, so the implication if Re is in fact important is that multiple smaller tubes or slots may be better.  But let's do a reality check here, OK?  The trend in their data is that compression sets in for even lower Re with lower frequencies.  So let's look at Josh Ricci's M.A.U.L.  It's got a big honkin 12" port.  Fully-developed flow, if it exists somewhere in there will definitely be turbulent (Re >= 100000) with a port velocity of only 5 m/s, and according to the conclusion reached by looking at that data, his M.A.U.L. should hit an output wall by that point.  Correct me if I'm wrong, but I'm pretty sure 12" was pretty undersized by the usual rule-of-thumb standards.  I bet he's pushing 50 m/s or more through that thing at high drive levels.  And while there is definitely some compression, we're definitely not seeing a wall at only 5 m/s.  Right?

 

Build a horn instead, it will more or less solve the port compression problem.

 

Don't horns have their share of response non-itineraries as well?  I guess they aren't as bad, or maybe it's just that you get so much output from a horn that you're less likely to hit non-linear output levels.  The same may apply for the M.A.U.L. in practice, even though it certainly doesn't quit at 5 m/s port velocity.  :)

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A port which is acoustically small will - which is the case for all normal reflex ports, and even bass horns - will be the same as any small point source  when you get some distance to it.

 

To be sure, I did an experiment once and measured it; a sealed box measures exactly the same as a ported.

The relationship between pressure and velocity is the same for both.

 

However, if you get close enough to the sound source, the situation will be different.

Also, if you drive the port hard enough to get very high air velocity, the nonlinear effects of the flow and flow separation will affect the situation and create something different from the small point source model.

 

I'm still a major skeptic that sound intensity of the sound field in the room (without your body in it) impacts tactile feel.  In my room, I have a very obvious standing wave room resonance at around 62 Hz.  Theoretically, a standing wave has zero sound intensity.  They are also sometimes called stationary waves for a reason: no energy moves.  But I feel plenty of tactile stuff at 62 Hz or so.  My MBMs are close but not exactly near-field, and the room resonance is impossible to miss in their responses.  IIRC, I've got like a -12 dB or higher PEQ there.  The reality is that sound intensity is only zero far away from my body.  Sound intensity is actually non-zero at the interface between the air in the room and my body because my body is literally absorbing that energy.  People flesh does work fairly well as a bass trap.

 

Tactile sensation is about impedance matching, and the impedance of air is probably closer to that of the human body high pressure regions of the room.  Hence, high SPL regions of standing waves in small rooms may offer even greater tactile sensation compared to anechoic / ground-plane or near-field.

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Their Reynolds Number study leaves a lot to be desired.  For one thing, the Moody Diagram from which they base their argument that the output hits a wall when the flow goes turbulent, really only applies to so-called fully-developed pipe flow that is several pipe diameters away from any entrance, exit, bend, constriction, expansion or any other flow disturbance.  Only some subwoofer ports will be long enough to have a region of fully-developed flow.  The losses that grow non-linearly with output (and thus cause compression) can occur in the middle of the pipe or in part of the flare or even outside of the port.  Other experiments of their demonstrated that even a slight round-over at the entrance and exit yielded a dramatic performance improvement.  Therefore it is a shame that their Reynolds Number experiments were done on systems with hard transitions between pipe and entrance/exit.  If instead, those experiments used optimal flares at the entrance and exit, we could have gained more insight into the nature of losses in the middle of the pipe vs. elsewhere.

 

Another thing is that their Re data suggest that port velocities need to stay very low to avoid hitting a wall.  They argue on the basis of their data that there is a wall for Re somewhere between 50-100k.  Keeping Re under 50k is not easy.  For 4" tube ports, that's 7.5 m/s; 6" tubes is 5 m/s;  2" or a 1" thick slot is 15 m/s.  The Reynolds number increases with pipe diameter, so the implication if Re is in fact important is that multiple smaller tubes or slots may be better.  But let's do a reality check here, OK?  The trend in their data is that compression sets in for even lower Re with lower frequencies.  So let's look at Josh Ricci's M.A.U.L.  It's got a big honkin 12" port.  Fully-developed flow, if it exists somewhere in there will definitely be turbulent (Re >= 100000) with a port velocity of only 5 m/s, and according to the conclusion reached by looking at that data, his M.A.U.L. should hit an output wall by that point.  Correct me if I'm wrong, but I'm pretty sure 12" was pretty undersized by the usual rule-of-thumb standards.  I bet he's pushing 50 m/s or more through that thing at high drive levels.  And while there is definitely some compression, we're definitely not seeing a wall at only 5 m/s.  Right?

 

It's almost as if there is some factor they are missing or forgetting to include in the Reynolds number or it is not describing what we think it is. It seems to indicate that larger vent areas start to have major issues at lower velocities than smaller ones. However measurements seem to suggest that the useful core velocity limit (an output wall so to speak) is actually higher for larger vent areas not lower.

 

Correct. The M.A.U.L. design uses a roughly 12" by 40" vent and it is undersized. That's near the size of a decent subwoofer like an SVS 12" cylinder for just the vent. It's huge. Something like an 18" vent would be much better at managing the output but it just doesn't fit with the tuning involved. Almost every vented system has greatly under sized port area. The vent for the M.A.U.L.  simulated to have port velocity of almost 100m/s at maximum with a K20. Of course compression prevented it from ever reaching that type of velocities but it surely got up near 50m/s. That's not ideal by any means but the space dictated what the compromises needed to be and worked out ok. Seems to me that the larger vent area with less wall friction supports higher velocity before totally limiting but perhaps non linearity sets in earlier as compared to multiple smaller vents totaling the same area. This would be something like a 12" (730cm area) vent compared against 730, individual 1cm area vents packed into the same form as the single 12". I'm doubtful that the 1cm vents will be able to support 40-50m/s airspeeds at all and would likely be at their core limit way before that point.

 

Don't horns have their share of response non-itineraries as well?  I guess they aren't as bad, or maybe it's just that you get so much output from a horn that you're less likely to hit non-linear output levels.  The same may apply for the M.A.U.L. in practice, even though it certainly doesn't quit at 5 m/s port velocity.  :)

 

Yes they do. I believe you are fully correct that most of the time they are simply used well below their capability limitations and that is what allows them to not exhibit these things as much. Horns can and do exhibit large air velocities not to mention extremely high pressures in some cases.

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...

Don't horns have their share of response non-itineraries as well?  I guess they aren't as bad, or maybe it's just that you get so much output from a horn that you're less likely to hit non-linear output levels.  The same may apply for the M.A.U.L. in practice, even though it certainly doesn't quit at 5 m/s port velocity.  :)

 

Mouth area usually ends up so large, it is not a problem anymore.

At the throat you have a very different pressure situation, you will not get flow separation to the extent you do when a horn mouth or port radiates into free space.

 

But there will be physical limits to how loud a horn can get, and this relates to size.

Most of my horns are so small they would not perform much better with a driver with more excursion, simply due to excessive pressure and velocity levels inside the horn.

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I'm still a major skeptic that sound intensity of the sound field in the room (without your body in it) impacts tactile feel.  In my room, I have a very obvious standing wave room resonance at around 62 Hz.  Theoretically, a standing wave has zero sound intensity.  They are also sometimes called stationary waves for a reason: no energy moves.  But I feel plenty of tactile stuff at 62 Hz or so.  My MBMs are close but not exactly near-field, and the room resonance is impossible to miss in their responses.  IIRC, I've got like a -12 dB or higher PEQ there.  The reality is that sound intensity is only zero far away from my body.  Sound intensity is actually non-zero at the interface between the air in the room and my body because my body is literally absorbing that energy.  People flesh does work fairly well as a bass trap.

 

Tactile sensation is about impedance matching, and the impedance of air is probably closer to that of the human body high pressure regions of the room.  Hence, high SPL regions of standing waves in small rooms may offer even greater tactile sensation compared to anechoic / ground-plane or near-field.

 

Sound field properties does matter, a lot.

 

In the standing wave situation you have lost of velocity, and can actually have more tactile feel than audible sound, if you are in a pressure null, where the velocity is at the maximum.

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I was curious so I did some quick back of the napkin calculations.

 

Compression is maximum near 13.5Hz at about 3.8dB during the 103.8 volt sweep, which is exactly where we would expect the velocity to be the highest based on the models. By simply using the voltage applied in a simulation and allowing for 3 to 3.8dB less output from 12-16Hz after compression, it looks like the MAUL was producing about 30m/s or so during the 103.8volt sweep.The 185 volts sweep had the amplifier current limiting severely so it is hard to tell how much of the extra compression was partially the amplifier. Regardless a quick velocity estimate is a maximum of a bit above 40m/s. We don't have burst data for 13.5Hz which is the worst case scenario for velocity for the MAUL but a quick look at the maximum levels at 12.5Hz and 16Hz compared to the 103.8volt sweep results in an estimated 45m/s at 16Hz and 61m/s at 12.5Hz. I did consider the flare-it program when designing the MAUL and it suggested chuffing at 37m/s and core limit of 80m/s for a 12" pipe.

 

This is all very rough work but based on this I think it safe to say that the vent has not completely brick walled at 50-60m/s but is heavily compressing the output by 7-8dB at that point and for all practical purposes may be "there". Huge increases in input power to the drivers will continue to produce less and less output increase from the vent. Of course this is also at quite low frequencies down near 12-16Hz too so that should be considered. Yes this is accompanied by significant air noise as well. Maximum velocities in the short horn section are only an estimated 20-30m/s.

 

It might be worth a look at some other vented system tests to examine the compression behavior and guesstimated vent velocities.

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I was curious so I did some quick back of the napkin calculations.

 

Compression is maximum near 13.5Hz at about 3.8dB during the 103.8 volt sweep, which is exactly where we would expect the velocity to be the highest based on the models. By simply using the voltage applied in a simulation and allowing for 3 to 3.8dB less output from 12-16Hz after compression, it looks like the MAUL was producing about 30m/s or so during the 103.8volt sweep.The 185 volts sweep had the amplifier current limiting severely so it is hard to tell how much of the extra compression was partially the amplifier. Regardless a quick velocity estimate is a maximum of a bit above 40m/s. We don't have burst data for 13.5Hz which is the worst case scenario for velocity for the MAUL but a quick look at the maximum levels at 12.5Hz and 16Hz compared to the 103.8volt sweep results in an estimated 45m/s at 16Hz and 61m/s at 12.5Hz. I did consider the flare-it program when designing the MAUL and it suggested chuffing at 37m/s and core limit of 80m/s for a 12" pipe.

 

This is all very rough work but based on this I think it safe to say that the vent has not completely brick walled at 50-60m/s but is heavily compressing the output by 7-8dB at that point and for all practical purposes may be "there". Huge increases in input power to the drivers will continue to produce less and less output increase from the vent. Of course this is also at quite low frequencies down near 12-16Hz too so that should be considered. Yes this is accompanied by significant air noise as well. Maximum velocities in the short horn section are only an estimated 20-30m/s.

 

It might be worth a look at some other vented system tests to examine the compression behavior and guesstimated vent velocities.

 

LspCAD 5 includes an optional attempt at modeling port compression (can check a box to see with and without model).  Unfortunately it doesn't really allow a simple model of a commonly flared port.  Instead they have a model more akin to a flared vent that defines more of an hourglass shape with an effective, assumed radius greater than 1/2 the length of the port. Comparing straight ports and more significantly flared ports gives some interesting points of consideration.

 

One thing overlooked in your assumption above is that as the port compresses, the driver excursion increases.  This is seen very easily in the LspCAD models and can be estimated/correlated by comparing high level impedance sweeps around tuning, and comparing driver vs port near field measurements.  With high excursion woofers you will often see the driver picking up a good bit of the output load as excursion increases in an exponential manner due to port compression.  This actually reduces the observed output compression, so remember the port itself is even more non-linear than the total SPL compression suggests.  As with most things, the models are overly conservative and compression isn't quite as severe as suggested, but it's a lot more than none.  Long ago I recall Deon Bearden relaying on that in his testing and research most port designs start compressing anywhere past 10m/s.  That's not to say the ports aren't useful past that point, but we should understand that behavior isn't linear, just as with real drivers well before the rated Xmax.

 

The complicating factor is always the wide bandwidth, complex signal consideration.  If a component of a complex signal pushes a port into severe compression, how does this impact the rest of the complex signal being produced at the same time?  

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One thing overlooked in your assumption above is that as the port compresses, the driver excursion increases.  This is seen very easily in the LspCAD models and can be estimated/correlated by comparing high level impedance sweeps around tuning, and comparing driver vs port near field measurements.  With high excursion woofers you will often see the driver picking up a good bit of the output load as excursion increases in an exponential manner due to port compression.  This actually reduces the observed output compression, so remember the port itself is even more non-linear than the total SPL compression suggests.  As with most things, the models are overly conservative and compression isn't quite as severe as suggested, but it's a lot more than none.  Long ago I recall Deon Bearden relaying on that in his testing and research most port designs start compressing anywhere past 10m/s.  That's not to say the ports aren't useful past that point, but we should understand that behavior isn't linear, just as with real drivers well before the rated Xmax.

 

Great points. I have observed exactly that with many vented subs while testing them. I have no idea how big of a contribution it would have made in that specific case but we can probably assume that airspeeds were a bit lower than posted above. 40m/s through a 12" pipe is quite the breeze let me say. :D

 

You've got experience with passive radiators. Have you ever seen a pair of PR's appear to go out of phase with each other, when being driven very hard? I watched this happen a number of times with both the 15" and 12" TC VMP's during compression sweeps.

 

Ports are a tough compromise. It'd be easy to say simply design to stay below 10-20m/s at maximum output of the system, by using a ridiculously huge vent area and a giant air volume but that is not in the cards most of the time. Large flares become difficult to use sometimes as well. Driver design keeps moving towards higher displacement and power handling while huge amplifier power becomes cheap. Everyone wants a compact sub that also goes deep and offers high output. There's no getting around the physics behind Helmholtz resonators. Trying to juggle vent length, shape, area and pipe resonance, against a overall size that is manageable, it is often vent area that gets cut back. That's why you see 15 and 18" drivers with 3 and 4" ports or thin slot ports. PR's have advantages but also some shortcomings themselves. Cost being one and a lot of real estate on the baffle/s for them being another. Also the advantages of running them in opposed pairs make that arrangement almost a necessity. Mechanical displacement limits is another one.

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It's almost as if there is some factor they are missing or forgetting to include in the Reynolds number or it is not describing what we think it is. It seems to indicate that larger vent areas start to have major issues at lower velocities than smaller ones. However measurements seem to suggest that the useful core velocity limit (an output wall so to speak) is actually higher for larger vent areas not lower.

 

There's nothing wrong with the Reynolds number (Re).  The issue is only in how it's interpreted, which is problem specific.  The Moody Diagram was developed from empirical data of steady fluid flow in pipes.  It is most valid for fully developed flows.  My fluids textbook suggests that fully developed flow is only realized at on the order of 50 pipe diameters from the entrance or a major disturbance.  So there's the first issue with trying to relate information from this diagram to subwoofer ports:  Most subs don't have port tubes that long.  The second issue is that the flow in subs is unsteady; it oscillates.

 

With that said, we can still look at the trends in pipes and make educated guesses about what the implies for ports.  In pipes, the transition from laminar to turbulent flow happens in the 2-5k range of Re.  That's a lot less than the 50-100k "wall" reported in that article.  It suggests that subwoofer ports routinely exhibit turbulent flows at velocities that would be considered "well within normal operating range".  I think the conclusion that the sudden rise in compression is caused by laminar to turbulent flow transition is wrong.  Instead, I believe flow may be hitting a saturation point well into the turbulent flow regime, typically at some bottleneck point in the port system.  Often this will be around the entrance/exit.  The particular Re where this saturation effect occurs probably depends a lot on the design.  At the same time, there is still probably some compression that sets in after transition to turbulent flow even at much lower Re.  It's very interesting that increased driver excursion may have the effect of hiding that compression.

 

From the data in the paper and ensuing discussion, I have to say there's a lot to not like about ported systems.  :)  As a compromise, it is often an ugly one.  I know Bossobass Dave used to rail about how the frequency response of a ported system changes with output level.  It's true, and you can't really do anything to fix it like you can to reshape a sealed sub with high Fs and/or low Qtc.  The insight that port compression causes driver excursion to increase is especially concerning, being that excursion reduction is one of the biggest advantages of a ported design.  The data in the paper also illustrates that tuning frequency can shift upwards rather dramatically at high output levels as well.  These two changes (non-linear increase in excursion and upward shift in tuning frequency) made coincide with one another.

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