Thank you, that helps a lot. In the meantime, I build the speaker. But due to the weather, I have only been able to take indoor measurements so far, which are difficult to compare with the simulation.
With 24Hz the lower cut-off frequency is slightly higher than in the simulation. Since the slope is extremely steep, I don't quite understand it yet. I'm using the Behringer A800 amp which should not be the limiting factor here. The same with the minidsp 2x4HD as source.
@AndyGR42 you're welcome. That was fast to actually physically build it 🙂
The VLF slope should be very shallow -6dB/octave according to the simulation. If yours is steep, then could it be something else in the system (amp, mic, dsp) that has issues in the 24Hz range?, or maybe a reflection null? I'm assuming this measurement is nearfield ground plane.
The VLF slope should be very shallow -6dB/octave according to the simulation. If yours is steep, then could it be something else in the system (amp, mic, dsp) that has issues in the 24Hz range?, or maybe a reflection null? I'm assuming this measurement is nearfield ground plane.
@DonVK: Exactly, measurement is nearfield. My current suspicion lies with the minidsp UMIK-1. Or a combination of several parts in the chain.
But I'm fully ok with the result. Even if it is “only” 24 Hz, the sound is very good and meets my expectations. The level is also more than sufficient, especially as I have only installed one system so far. There will be two in the final setup.
The enclosure is back in my shop for the finish. The MDF shell is the smaller part of the effort. 🙂 I think it will take another 2-3 weeks for veneer and painting. I hope that the weather will also be better by then and allow a measurement outside the room.
But I'm fully ok with the result. Even if it is “only” 24 Hz, the sound is very good and meets my expectations. The level is also more than sufficient, especially as I have only installed one system so far. There will be two in the final setup.
The enclosure is back in my shop for the finish. The MDF shell is the smaller part of the effort. 🙂 I think it will take another 2-3 weeks for veneer and painting. I hope that the weather will also be better by then and allow a measurement outside the room.
Hi,
My name is Hugo Hermansson, I'm currently conducting my masters thesis in mechanical engineering at Lunds University in Sweden. For my thesis, I'm investigating the possibilities to utilize simulation software to give a better understanding of how a microphone port of specific dimensions affects the sound reaching a MEMS- or a EC - Microphone.
I've seen papers utilizing Comsol Acoustics, I'll attach a link for an example. https://www.edn.com/acoustic-design-for-mems-microphones/
Would something similar be possible to construct in BEM or in LEM?
Any ideas or general thoughts would be highly appreciated!
Best,
Hugo
My name is Hugo Hermansson, I'm currently conducting my masters thesis in mechanical engineering at Lunds University in Sweden. For my thesis, I'm investigating the possibilities to utilize simulation software to give a better understanding of how a microphone port of specific dimensions affects the sound reaching a MEMS- or a EC - Microphone.
I've seen papers utilizing Comsol Acoustics, I'll attach a link for an example. https://www.edn.com/acoustic-design-for-mems-microphones/
Would something similar be possible to construct in BEM or in LEM?
Any ideas or general thoughts would be highly appreciated!
Best,
Hugo
@hugoherman I was curious about how Akabak BEM would work when things get very small. An air molecule is 3.4nm, so plenty to fill the tube. I used a 2.5mmx1.5mm chamber and a 4mmxR0.25 tube. I drove the membrane (red) at constant velocity of 0.1m/s to see if the system worked as a Helmholtz resonator. Sure enough,.. it works. The Akabak files are attached if you wanted to investigate. The drawing (STEP) was done in FreeCad and mesh by GMSH.
Attachments
@DonVK Thank you for the reply!
Interesting approach, I've mainly used Akabak's own 3d modelling tools in order to make the calculations faster. How come you did put the the driver inside the Helmholtz? What I've found to work is to put a pressure source outside of the opening of the "bottle" and then have a measurement point inside, see attached file🙂
Interesting approach, I've mainly used Akabak's own 3d modelling tools in order to make the calculations faster. How come you did put the the driver inside the Helmholtz? What I've found to work is to put a pressure source outside of the opening of the "bottle" and then have a measurement point inside, see attached file🙂
@hugoherman , You're welcome, and thanks for the project file. The example I provided was just my experiment to see if the model worked for very small geometries. This is the smallest thing I've ever tried to simulate in Akabak. There should be reciprocity whether its excited internal or external.
Yes for your specific application I would also use the external pressure source to excite the resonator, and measure at the mic plane. The Akabak primitives are OK if your design actually matches the shapes available. The solve times are based on what symmetry is used (circular is fastest) and #elements. I just looked at the paper you referenced and built something like that shape in FreeCad because it was convenient for me and it solved quickly.
Yes for your specific application I would also use the external pressure source to excite the resonator, and measure at the mic plane. The Akabak primitives are OK if your design actually matches the shapes available. The solve times are based on what symmetry is used (circular is fastest) and #elements. I just looked at the paper you referenced and built something like that shape in FreeCad because it was convenient for me and it solved quickly.
Hi,
I’m currently exploring the capabilities of Akabak for microphone simulations and came across an interesting observation regarding cylindrical Helmholtz resonators. I’ve noticed a small difference in the calculated resonance frequency depending on how the internal and external volumes are defined.
Specifically, I’ve been comparing two modeling scenarios:
Thanks in advance!
I’m currently exploring the capabilities of Akabak for microphone simulations and came across an interesting observation regarding cylindrical Helmholtz resonators. I’ve noticed a small difference in the calculated resonance frequency depending on how the internal and external volumes are defined.
Specifically, I’ve been comparing two modeling scenarios:
- Scenario 1: Only the internal volume is defined with inward-pointing normals.
- Scenario 2: Both the internal volume and corresponding external walls (placed as exterior boundaries) are defined (See figure).
- Volume: r = 0.2m, L = 0.4m
- Neck: r = 0.025m, L = 0.05m
- ~56Hz for Scenario 1
- ~52Hz for Scenario 2
Thanks in advance!
The linear acoustics equation is derived from the full Navier-Stokes equations governing fluid flow by introducing some large assumptions in order to reduce 5 equations down to 2 (or 1 higher order one). This can be reasonable when the only thing of significance going on in the fluid are acoustics waves. In the case of a Helmholtz resonator there is a largely incompressible slug of air oscillating in the neck with the air flow pattern flowing in being quite different to that flowing out, friction on the walls may be significant, turbulence may form, etc... Much of this sort of thing has been discarded in deriving the linear acoustics equation. It can be included by using a CAA (Computaional AeroAcoustics) code instead of a linear acoustics BEM code.
In addition BEM codes tend to have numerical errors associated with thin shapes, including internal cavities in external simulations, and a few other things. Partitioning the domain (don't know if you have done this?) is a way to overcome some of these numerical issues but at the cost of approximating the solution further.
Linear acoustic BEM can often produce something plausible for a Helmholtz resonator but it won't produce accurate results because too much relevant physics has been discarded by the modelling assumptions.
What theory is used to predict the resonance frequency?
How fine is the grid relative to that required to get essentially grid independent results?
In addition BEM codes tend to have numerical errors associated with thin shapes, including internal cavities in external simulations, and a few other things. Partitioning the domain (don't know if you have done this?) is a way to overcome some of these numerical issues but at the cost of approximating the solution further.
Linear acoustic BEM can often produce something plausible for a Helmholtz resonator but it won't produce accurate results because too much relevant physics has been discarded by the modelling assumptions.
What theory is used to predict the resonance frequency?
How fine is the grid relative to that required to get essentially grid independent results?
There are a few factors to consider in comparing the models. Overall the global mesh freq should be specified otherwise it may not be consistent between the models compared. The tuned freq depends on the effective air mass of the tube which includes the port exit air mass and this depends on the termination (flare) and the surrounding boundary coupling. Sometimes a port correction factor is used based on port cross section, termination shape (flare) and boundaries. Since only discrete sample freq are solved some care is needed in selecting the number of samples and freq range (PPO) to find any peak accurately.
Model 1 has only internal surfaces and port exit (subdomain interface) but no external surfaces. To make this model more accurate include an IB at the port exit. This is a "hole in the wall" for perfect 2Pi radiation space, and there will only be an n-Pi to 2Pi boundary transition.
Model 2 has both internal and external surfaces (good). The port exit has zero surface area (coincident tubes, no baffle) so there is an abrupt transition to 4Pi space. The baffle step will be around 6dB between 2Pi and 4Pi radiation space. The transition is affected by boundary surface area, location, radiator size and wavelength. This is a "tube hanging in 4Pi freespace". The actual tuning freq will be somewhere between V1a and V1b depending on the actual boundary area and port flare.
I've included the models I used and this link for some PortTuningExperiments .
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@andy19191
Thanks for your thoughts on the approach. I get where you're coming from regarding the simplifications in the linear acoustics model. Yes, it does overlook things like turbulence and friction, but for the purposes of getting a quick, reasonable estimate of the resonance frequency, I thought it was a good starting point.
For the resonance frequency, I used the standard equation for Helmholtz resonators:
It gives a solid first-pass result, and while it doesn’t include all the nuances of the flow, I felt it was accurate enough for this context. (L being effective length).
On the grid resolution, I made sure the mesh was refined enough to resolve the acoustic wavelengths properly—around 5-10 grid points per wavelength. I did some checks to make sure it was close to grid-independent, and it seems like further refinement didn’t change much.
Thanks for your thoughts on the approach. I get where you're coming from regarding the simplifications in the linear acoustics model. Yes, it does overlook things like turbulence and friction, but for the purposes of getting a quick, reasonable estimate of the resonance frequency, I thought it was a good starting point.
For the resonance frequency, I used the standard equation for Helmholtz resonators:
It gives a solid first-pass result, and while it doesn’t include all the nuances of the flow, I felt it was accurate enough for this context. (L being effective length).
On the grid resolution, I made sure the mesh was refined enough to resolve the acoustic wavelengths properly—around 5-10 grid points per wavelength. I did some checks to make sure it was close to grid-independent, and it seems like further refinement didn’t change much.
12% looks a reasonable error to me given the missing physics w.r.t. the flowfield assumed by the linear wave equation. You can get a feel for this to some extent by considering potential and rotational flow into and out of a hole. Your error is in the ballpark of the "end corrections" that get applied to try to compensate for the missing physics in your formula.
6 elements per wavelength is a rule of thumb for BEM schemes that use conventional reasonably accurate elements. Akabak I believe (never used it) uses zeroth order elements (sidesteps a number of numerical issues) with a flat planar geometry when integrating in space over an element. Resolution will need watching particularly in regions where the geometry various sharply. But 10 elements per wavelength looks a reasonable place to start to me.
If you are coupling various domains I would suggest moving the coupling surfaces around to get a feel for the size of the approximation they are introducing. For example move the coupling at the mouth into the port perhaps a diameter or two so that the changing conditions around the mouth are reasonably resolved.
6 elements per wavelength is a rule of thumb for BEM schemes that use conventional reasonably accurate elements. Akabak I believe (never used it) uses zeroth order elements (sidesteps a number of numerical issues) with a flat planar geometry when integrating in space over an element. Resolution will need watching particularly in regions where the geometry various sharply. But 10 elements per wavelength looks a reasonable place to start to me.
If you are coupling various domains I would suggest moving the coupling surfaces around to get a feel for the size of the approximation they are introducing. For example move the coupling at the mouth into the port perhaps a diameter or two so that the changing conditions around the mouth are reasonably resolved.
The previous link to experimental results was to show how differences in configuration can shift the resonance freq.
Lets repeat Helmholtz's experiment using the same configuration that he used. I used a sphere blended into a cylinder. I've used a R229mm sphere to match the volume of the previous cylinder merged with a 100mm X 100mm exit port.
Lets repeat Helmholtz's experiment using the same configuration that he used. I used a sphere blended into a cylinder. I've used a R229mm sphere to match the volume of the previous cylinder merged with a 100mm X 100mm exit port.
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@andy19191 Thanks for the tips!
I’m curious, do you think there’s a way to account for thermoviscous losses in the model? Maybe by adding impedance to the interior surfaces?
I know FEM is typically used for these simulations, but I’d like to see how close I can get to real-world results using BEM and LEM.
Thanks!
I’m curious, do you think there’s a way to account for thermoviscous losses in the model? Maybe by adding impedance to the interior surfaces?
I know FEM is typically used for these simulations, but I’d like to see how close I can get to real-world results using BEM and LEM.
Thanks!
Kludging has it's place with 0D design methods like the lumped element model because they don't capture physical details only large broad lumps of physics. With 3D design methods that do capture physical details (usually the primary reason for making the extra effort) then physically incorrect kludging may improve some aspect that is not captured by the physics in the model but this will come at the cost of degrading what the model is capturing. For example, one may consider softening the impedance of port walls in order to add some damping to the low frequency incompressible Helmholtz resonance. However, some manufacturers soften the port walls in order to damp the unwanted compressible resonances at higher frequencies in the port. These resonances are likely to be fairly well captured by a BEM code and are useful to a speaker designer. The introduction of unphysical damping will almost certainly degrade this aspect of the simulation. If you soften the walls of the cabinet to introduce damping then, as anyone that played with room acoustics is aware, soft walls change the resonant frequency away from what a tape measure and the speed of sound would suggest.
The most reliable approach with detailed 3D simulations is to understand what physics is captured and what physics is not and then account for what is not separately. This is less the case with more strongly approximated 0D lumped simulations. Also if the 3D simulations are being performed for non-engineering purposes such as marketing then kludging to get an answer you want can sometimes be reasonable given reliability, consistency, repeatability, etc... is less relevant.