Trying to understand the limitations of Helmholtz resonators in LF absorption

[Delrin]

All I can say is to copy what the calculations publishers said:



Whether I call the above a paper of a book is irrelevant. The only other sources cited are below, which are not directly related to resonators.

What you are saying is correct for the "Helmholtz Calculator", but I have been referring to the "Multi-Layer Absorber Calculator". The latter appears to be more comprehensive and includes updated model options.

The screen shots I showed above are for the "Multi-Layer Absorber Calculator" section. From what I have learned so far, I would not recommend using the "Helmholtz Calculator" section (although this does seem an obvious place to look given that we're talking about Helmholtz absorbers).

I am not saying the web site is perfect, and it would certainly be nice if they provided more guidance relating to the different calculators provided. However, the site designers have gone to the effort of providing the (seemingly) more modern "Multi-Layer" calculator and Andy Mac Door has gone to the trouble of researching these options and sharing in detail what has (apparently) worked for him on YouTube.

Thanks for pointing this out, as it's important to be clear that I have been referring specifically to this calculator.

Here are links to the full text of Komatsu, Ingard papers and the Allard book. The Ingard paper looks like a really nice overview (from 1953!) of the nuts and bolts of acoustic resonators. Among other things in Ingard: "Nonlinear effects on the absorption and resonance frequency are also included, and a discussion of the onset of turbulence is presented."

Hopefully there is enough math in Ingard for you sarumbear ! That treatment is clearly way more rigorous than anything in Cox & D'Antonio.

 

[sarumbear]

The screen shots I showed above are for the "Multi-Layer Absorber Calculator" section. From what I have learned so far, I would not recommend using the "Helmholtz Calculator" section (although this does seem an obvious place to look given that we're talking about Helmholtz absorbers).

You said it. I was commenting as expected on the subject matter. What you you recommend or not is your prerogative.

Hopefully there is enough math in Ingard for you sarumbear ! That treatment is clearly way more rigorous than anything in Cox & D'Antonio.

You have not shown any math on what you are suggesting other than linking references. That is not how scientists work. I'm surprised that you do not know that being an educator.

 

[Delrin]

You said it. I was commenting as expected on the subject matter. What you you recommend or not is your prerogative.


You have not shown any math on what you are suggesting other than linking references. That is not how scientists work. I'm surprised that you do not know that being an educator.

A scientist will know a good source when they see it. I can digest the material easily enough to understand that it's a much more solid basis for the simulations presented than other references I have seen. I have no worries that I can apply this information to develop a more rigorous understanding of the questions which interest me, and will do so in due course. That is how scientists work.

A scientist will also have no problem admitting that they would not have found the reference if it weren't for a guy on YouTube wearing a funny hat.

I will respectfully ask that we focus further discussion in this thread on the scientific and technical aspects of acoustic resonators, and not on the personal qualities or qualifications of other forum members.

 

[Holmz]

… treatment also needs to cover a large surface area. So when people are buying something like a few units of a product you see below to work at 50 Hz, there's no surprise it wont't do much.
...

^B.S. !^

I can use a single 750 ml resonator and the sound definitely changes as the resonator volume increases.
But going from 1 resonator bottle to 3 of them is not as good.

 

[Delrin]

^B.S. !^

I can use a single 750 ml resonator and the sound definitely changes as the resonator volume increases.
But going from 1 resonator bottle to 3 of them is not as good.

Measurements or it didn't happen . I know this is annoying to some people, but there are just too many anecdotal claims on this topic in my view.

 

[Holmz]

Measurements or it didn't happen . I know this is annoying to some people, but there are just too many anecdotal claims on this topic in my view.

Would you believe it with a picture of the empty wine bottle?

 

[Delrin]

Would you believe it with a picture of the empty wine bottle?

You might have missed it, as this thread has become rather long and my posts are admittedly verbose, but I have tested bottles and they are fantastic resonators (all of the physical characteristics of resonance are easily demonstrated). It's just that, in my experience, a few bottles placed in a modal pressure peak have negligible effect on the room acoustics at the main listening position.

The initial posts in this thread focused on how perforated MDF panels with a particular hole geometry failed to exhibit the anticipated impedance effects at resonance (attributed to turbulence around the sharp hole edges). Bottles are better due to the flared neck geometry. With enough bottles at the right frequency, in the right locations and with the appropriate damping, it seems very likely that you could influence the room acoustics (not to mention have one heck of a party emptying the bottles).

 

[Delrin]

^B.S. !^

I can use a single 750 ml resonator and the sound definitely changes as the resonator volume increases.
But going from 1 resonator bottle to 3 of them is not as good.

Ok I am way too slow... now I get the joke, which is subtle but hilarious . Sorry for the gratuitous lecture on wine bottles and measurements - my bad!

 

[sarumbear]

I have no worries that I can apply this information to develop a more rigorous understanding of the questions which interest me, and will do so in due course.

I wish you luck and hopefully read about your progress.

I will respectfully ask that we focus further discussion in this thread on the scientific and technical aspects of acoustic resonators, and not on the personal qualities or qualifications of other forum members.

I said nothing personal to you as I do not know you. How can someone say something personal to an avatar positive or negative?

I do however repeat that I disagree that your approach is not "scientific" as you label it. You show no mathematical explanation of your tests. Without math science doesn't exist. When I mean math, I mean formulas that relate directly to the design you are talking about, not what some researcher used to explain their own design on a paper or book.

If you use math to explain your experiments you don't have to keep changing the design like you showed us earlier. If you define your model mathematically you will know what change will cause what effect and can simulate it. If you want to get "your head around the Helmholtz resonator," simulation is the shortest way.

Post a summary of a design that you think may work, add the related formulas (use your students to build a calculator even) and see if the ASR community are willing to build and test it.

 

[Delrin]

I wish you luck and hopefully read about your progress.


I said nothing personal to you as I do not know you. How can someone say something personal to an avatar positive or negative?

I do however repeat that I disagree that your approach is not "scientific" as you label it. You show no mathematical explanation of your tests. Without math science doesn't exist. When I mean math, I mean formulas that relate directly to the design you are talking about, not what some researcher used to explain their own design on a paper or book.

If you use math to explain your experiments you don't have to keep changing the design like you showed us earlier. If you define your model mathematically you will know what change will cause what effect and can simulate it. If you want to get "your head around the Helmholtz resonator," simulation is the shortest way.

Post a summary of a design that you think may work, add the related formulas (use your students to build a calculator even) and see if the ASR community are willing to build and test it.

Hi Sarumbear,

A scientist understands that applying math without a solid grasp of the underlying concepts is pointless.

Math is like computers in this respect: if you put garbage in, then you will get garbage out.

A scientist also freely admits when they don't understand something, and tries to learn about it if they think it's important or interesting. A scientist does not worry about looking silly, or pretend that they understand something when they do not.

A scientist understands that different scientists will approach the same problem in different ways, and that there is usually something valuable to be learned from the alternate approaches.

Scientists frequently cite peer reviewed articles as a practical shorthand to support claims made in a discussion, and understand that there are limitations and risks in this approach.

It would be premature for me to introduce math into this discussion, because I don't feel I understand the underlying physical concepts well enough. I am still trying to learn about these, and "shopping around" for the math that offers the best insight and predictive value. I will be happy to share what I learn, and to learn from others who have something to contribute.

I will close in pointing out that students who can slog through reams of math without making a procedural error are a dime a dozen. The subset of these students who develop a strong intuitive grasp of the concepts being expressed through the math is much smaller. As educators we are always happy if we can cultivate more of the latter.

 

[Delrin]

I do however repeat that I disagree that your approach is not "scientific" as you label it.

To be honest, I don't think I ever said my approach was "scientific" and have no need to brand it as such. Some problem-solving techniques may or may not be borrowed from science, engineering, or from plain common sense.

Don't get me wrong - I think there is merit in much of what you suggest. I will try and post a summary of the math I've already done, and where I think it went off the rails.

 

[sarumbear]

Perhaps I should formalize some ground rules for what I will call "the Helmholtz Open Science Challenge".

To be honest, I don't think I every said my approach was "scientific" and have no need to brand it as such.

 

[Delrin]

Sarumbear you are conflating some initial tests that I made in the past with a set of aspirational recommendations that I posted in regards to how future tests might be carried out and reported. It is evident that my initial tests did not meet all of the guidelines that were subsequently laid out, and indeed if I could already do this it would be kind of pointless to post the "challenge".

I make no claim that the tests I posted early in this thread are scientific, not that it really matters.

In regards to the "Challenge", I have no problem attaching the word "Science" as these are evidentiary and reporting standards that correspond closely to what is currently practiced in science. Whether the "standards" are met using math, stick drawings, physical models, computational models, or whatever is completely beside the point.

 

[Delrin]

Anything that requires simulation of a physical phenomena I suggest using Wolfram Mathematica.

Here is what Wolfram gives as an example. Imagine what can be done by using a custom front end and using the actual architectural model of the room that the builders used to build it.

Just ping Wolfram support, they are pretty responsive. May require an add-on or have changed files and you need to point elsewhere.

I didn't hear back from Wolfram yet, but you are right Don that it's a path issue.

On MacOS, the "Support Files" referenced in some of the acoustics examples are installed inside of Mathematica's "application bundle":

/Applications/Mathematica.app/Contents/SystemFiles/Components/PDEModels/SupportFiles

The code in the "Eigenfrequencies of a Room" example looks for SupportFiles under

/Library/Wolfram/Documentation/13.2/en-us/Documentation/

a directory which exists, but is not the location for SupportFiles on a MacOS installation. Editing the code to point to the correct path fixes the problem. Annoyingly, when built-in examples are loaded in Mathematica, the "Save As..." option seems to be disabled (I can understand "Save" being disabled so you don't overwrite internal documentation). I just made a copy of the notebook and it works great after fixing the path.

To be clear, the notebook mentioned above models room modes by numerically solving the Helmholtz equation within an arbitrarily defined surface envelope. This gives a more general solution than the simpler analytical approach that can be easily applied with rectangular geometry. The PDE approach allows modelling complex room shapes and furniture etc (the tutorial includes a nice comparison between analytical and numerical results - there's not much difference at low frequencies even with furniture).

There is a different example notebook that models a Helmholtz resonator using the same basic approach (there don't seem to be any glitches in this notebook, which does not require external support files). Note that the "Helmholtz Equation" provides a general description of wave phenomena among other things, and is not specific to Helmholtz resonators. It is a powerful approach and it's helpful to know that Mathematica has such relevant examples. There is also an example of an automotive muffler (which imports an stl file from the correct path).

It would not be difficult to model interactions between one or more Helmholtz resonators and a room, which I gather is what sarumbear has done.

Hopefully this workaround will be helpful if anyone tries experimenting with this on a Mac. Files inside the application bundle do not show up in a normal system search on MacOS, so are harder to find. I have no idea if the paths resolve correctly on Windows or Linux versions of Mathematica.

Thanks again to sarumbear for pointing out these tutorials.

 

[Delrin]

So after further experimentation with Mathematica I was able to get some initial visualizations of the room modes in the space where I have been doing my measurements (known to have a bad acoustic geometry). I use Autodesk Fusion 360 for a lot of stuff at work, and it was pretty easy to make a fairly accurate model of my room envelope that included the main features like window recesses, a door alcove, and a bulkhead. Using a laser measure I was able to get the room dimensions to within a couple of millimetres.

Fusion allows you to export .stl files, so I was able to generate a drop-in replacement for the room envelope used in the built-in Mathematica tutorial. I found I got a good result using "Medium" export quality for the .stl file, whereas "High" quality resulted in very long execution times in Mathematica for little gain in quality.

Other than that, everything worked and the modal maps and frequencies look plausible:



Here you can see the fundamental length and width modes calculated using the PDE solution as well as the equivalent modes using analytic equations for a cuboid of the same major dimensions (ignore the skewed aspect ratio in the cuboid results - it's rendered in a slightly different way).

The asymmetries of the room create some interesting patterns in the modes that are evidently not going to be predicted by the analytic cuboid approximation. I'll do some SPL measurements to see if the relative pressure levels in different room corners correspond to the simulations. The simulation also shows, not surprisingly, that the length and width modes differ by a few Hz (probably not significant for absorption but it makes sense). For the cuboid, the length and width modes are identical (other than being rotated by 90 degrees) since the main room envelope is very close to square (and modelled as such in the analytic calculation).

Now that I have something basic working, I will try and drill into the details to make sure all the assumptions are valid for my case (not to mention add some furniture). Then I can try adding some simple Helmholtz cavities at various locations to gauge the effect. Being able to generate the models with Fusion will be a huge help, as it's a very user friendly parametric CAD program. One could also likely do this in Sketchup.

For what it's worth, the main room dimensions are 12' x 12' with 7' ceiling (neglecting door alcove, windows, and bulkhead). I am aware that this is pretty much a textbook example of bad room geometry, but it was never intended to be a critical listening space. The badness of it actually makes for an interesting challenge in terms of acoustic treatment (and it's very well soundproofed due to past use as a workshop and music practice space). Here's a rendering of the room:



So yet again I will thank @sarumbear for recommending Mathematica!

 

[Delrin]

I wanted to mention a couple of caveats related to the simulation approach described above. This is a departure from the thread's topic of understanding Helmholtz resonators, but the simulation concepts are relevant and might be of interest should others wish to experiment with this.

One thing is that the simulations apply a "hard boundary condition" which means that all the walls are treated as being perfectly reflective. This is reasonable for a "naked" room, but would be unrealistic if - for example - there is carpet on the floor (the effect of carpet is probably negligible for the low modal frequencies discussed here, but would have an impact at higher frequencies). So simulations like this are a great starting point to visualize the modal pressure distributions in a room before any other treatment (or contents with absorbent surfaces) are added. There are other types of boundary condition available in Mathematica, which presumably can help in adding absorbent surfaces to the model.

Another thing to watch out for is that the numerical solution can give unexpected results for a perfectly cuboid room in which two dimensions are equal (this is not a problem for the analytic solution of room modes from basic geometry). This is easy to demonstrate by running Mathematica's example code on a simplified model of my room in which the length and width are exactly equal at 3.6576 metres (∼12 feet):



The image above shows Mathematica's PDE solution for the length mode, which is clearly distorted since the pressure gradient should be perfectly aligned with the room's length axis (the code is taken verbatim from Mathematica's example - only the room model was changed). This is happening because the length and width modes must have exactly the same frequencies, which leads to something called "degenerate eigenstates". The numerical solution relies on having distinct "eigenvalues" (the frequencies) that are related with distinct "eigenfunctions" (the modal pressure distributions). If there is an ambiguity, then the solver will output an arbitrary linear combination of the two degenerate room modes which is probably not what you want (even though this is perfectly possible in the physical world for systems exhibiting various types of symmetry - like the room, which has a rotational symmetry about its central vertical axis).

I found that increasing the density of the simulation mesh could make the distortion go away, but then it would come back intermittently under further increases in mesh density (which makes sense because this doesn't change the underlying degeneracy). The bottom line is that results using simplified geometry for perfectly square rooms are likely to give unexpected results (on top of other the other limitations one would normally expect in such a simplification).

This issue goes away if there is even a small departure from perfect rotational symmetry, such as would typically be present in a more realistic room simulation like the one I posted earlier. Changing the length of my simplified cuboid room by only one cm (with the width and all other code unchanged) gives the following (correct) result:



It might seem silly to worry about numerical errors in such a clearly oversimplified model of a room, but simplified models can be a good starting point for experimentation (or debugging) and the issues arising from (rotational) room symmetry can make the simulation code look "broken" when it's not. To be clear, we are not talking about left/right symmetry etc but the fact that the room model is identical if you rotate it by 90 degrees.

 

[Delrin]

I adapted Mathematica's Helmholtz Resonator tutorial example to the geometry I used earlier with flared ABS pipe sections.

I just used a measuring tape and calibers to quickly note the dimensions within the nearest millimetre (actual precision is probably more like 2mm).

It came out pretty well - the simulated resonance frequency of 44Hz (without damping) was within a couple of Hz of what I measured before in REW for the 4.5" neck length.





This simulation makes use of the axial symmetry of the resonator, so the geometry is specified entirely in terms of its longitudinal cross section (as seen in the SPL map). Note that the first "pipe resonance" just under 200Hz is also correctly modelled.

With a few modifications, the script should work with an arbitrary resonator geometry imported from an stl file. Of course this simulation just gives the resonance frequency and doesn't really provide any information about impedance or absorption...

 

[Delrin]

Managed to get it working using a 3D CAD model instead of 2D drawing primitives:



The predicted resonance frequency is the same, at 44Hz, and the frequency response plot is identical to that obtained using the 2D drawing and axial symmetry. Scaling of the SPL map is arbitrary, but the overall distribution is the same.

 

[Delrin]

I used Mathematica to solve the wave equation for the box resonator that I tested at the beginning of this thread, for both a single "cell" and the full array:



The calculated resonance frequency was 47.8 Hz for the single cell and 48.4 for the "array" that I actually built. The frequency response plots are indistinguishable, apart from an arbitrary scale factor:



Interestingly, the ∼48 Hz resonance is in pretty good agreement with the result computed using the the www.acousticmodelling.com calculator, using either the "Layered Absorber" or "Helmholtz Calculator" options:



The agreement isn't terribly surprising, as computing the resonance frequency of an empty resonator is the "easy part" but it's good to see that these very different approaches give such consistent results. The harder part is predicting the specific impact on room acoustics in the real world, which would usually involve addition of a porous absorber and modelling the interaction with room modes.

One respect in which all of these modelling approaches fail, for this specific example, is that they can't predict the non-linear vortex formation that was demonstrated earlier for this geometry (and which causes the acoustic effect to deviate from the model).

The experimentally determined resonance frequency for the large box with 1/4" holes was a bit lower than the model predictions, at around 40Hz (based on candle flame deflections). This is not surprising because the non-linear turbulence effects are not modelled and will change the effective hole/neck parameters. In the case of my "flared tube" resonator, the PDE modelling agreed pretty much exactly with the frequency response measured in REW.

I also want to dig deeper into some of the excellent old papers by Ingard, but it's been busy at work and I haven't had the time. The Acoustics book by Allard also seems to have a much deeper coverage of resonant absorbers than Cox & D'Antonio, so I'm hoping to go through that as well.

 

[Delrin]

One interesting point about the PDE solutions described above is that the resonance frequency is determined by finding the lowest frequency at which there is a local maximum in the computed cavity pressure (in Pa). Helmholtz resonance occurs at the frequency when the inertial resistance of the air mass in the neck just starts to exceed the compressive resistance of air in the cavity. It makes sense then that the pressure is maximal at resonance, because there will be less air compression at higher frequencies where the inertial resistance of air in the neck becomes dominant.

There can be pipe resonances at higher frequencies, but in general the Helmholtz resonance will be lower than all of these due to the different resonance mechanism.