2 way waveguide speaker build ABEC modelling

[andy19191]

It is good to see more numerical simulations and I will follow your progress with interest.

Originally Posted by fluid

The size of the elements is also important to make the model accurate and realistic to higher frequencies. The simulation above was done with elements between 5mm at the driver through to 10mm at the mouth. This seems to be a good compromise between time and accuracy.

For acoustic BEM simulations the constraints on element size don't work quite like that. They have something like a Nyquist criteria of two elements per wavelength and if violated will produce nonsensical random garbage. Below this hard limit increasing the element density will increase accuracy. A common rule of thumb used by commercial codes is 6 elements per wavelength but this is more for higher order elements.

ABEC uses flat zero-order elements which are the least accurate requiring higher numbers of elements to achieve a given level of accuracy but they are relatively easy to program and require the least computer resources per element. Generally where you will need to increase resolution in order to reasonably specify the problem with flat triangles are things like the tweeter surrounds and lips. For example, it is well known that diffraction from a non-recessed tweeter will create small but audible differences. This requires resolving with flat triangles if the simulation is to be accurate.

[fluid]

Thanks for following along BEM is a very useful tool and ABEC/ AKABAK is the most accessible to the diyer. There isn't a huge amount of guidance on it's use so I thought I would try and shed some light on what little I have been able to do so far.

According to the ABEC help file the Edge length should be at a minimum 1/2 x C / Mesh Frequency, which I have taken to be half the speed of sound divided by the highest frequency of interest. Which for the 12KHz in my sims works out to be 14.3mm. Which is why I have stuck to 10mm as the maximum on the front baffle and that seems to have been sufficient. The waveguide goes down to 5mm at the driver (throat) end as without sufficient resolution there the waveguide contour is not preserved.

So I think your comments are a more informed expansion but not really at odds with what I said?

[andy19191]

Originally Posted by fluid

According to the ABEC help file the Edge length should be at a minimum 1/2 x C / Mesh Frequency, which I have taken to be half the speed of sound divided by the highest frequency of interest. Which for the 12KHz in my sims works out to be 14.3mm. Which is why I have stuck to 10mm as the maximum on the front baffle and that seems to have been sufficient. The waveguide goes down to 5mm at the driver (throat) end as without sufficient resolution there the waveguide contour is not preserved.

So I think your comments are a more informed expansion but not really at odds with what I said?

The limit on mesh size quoted in the ABEC manual is to avoid predicting garbage it is not the limit required to reduce the discretization errors to an acceptable level for a reliable simulation. I was trying to point out that your current simulations will contain significant discretization errors. Perhaps this doesn't matter too much at this stage when trying to get on top of things but if it all comes together and the simulations start to look useful then it will become more important.

[wesayso]

You don't think they look useful already?

[fluid]

Originally Posted by andy19191

I was trying to point out that your current simulations will contain significant discretization errors. Perhaps this doesn't matter too much at this stage when trying to get on top of things but if it all comes together and the simulations start to look useful then it will become more important.

It's good to have this pointed out as an issue. Can you can offer a way to tell what the problems might be and how much greater resolution will be needed to make them non significant?

I would like to make the simulations as realistic as possible but I am already approaching a point of diminishing returns with resolution in ABEC. With the code you are used to you can probably just use whatever resolution you need and use a faster computer to crunch through it.

In my experience with ABEC beyond 4,000 elements the solve time gets out of hand quickly and 10,000 elements seems to be a practical limit before there will never be a solution found in a realistic time frame. My laptop is faster than my server but I don't like to leave it on overnight that often so it tends to be used for less than 2 hour sims. I have no other need for a monster workstation and I'm not convinced it would be a solution even if I had one.

If I expand the model to cover a complete baffle and woofer (which is in the works) then I am limited to half symmetry and the problem gets twice as bad.

I personally think the simulations are quite useful as they are, I have had the benefit of seeing more of them in various different stages to know that these current ones look much more acceptable.

There have been a few constructions made already where the results from ABEC at similar resolution to this matched reality well enough which gives me hope I'm not chasing ghosts.

[DonVK]

Originally Posted by fluid

Don recreated the CAD files and meshes and ran a simulation showing much improvement. He used a flat interface instead of the one created from Ath and made it so that every waveguide and baffle vertex were aligned with each other. The vertical edge is rounded so the vertical looks smoother than the horizontal.

Originally Posted by fluid

I wanted to try and get a similar result using my own CAD process. I spent a lot of time getting Rhino to Duplicate the mesh edge as a polyline where there was a point at every vertex. I was able to export that as a DXF and import it into Fusion to cut my baffle. Fusion still joins all the straight lines into one so it was no different to using the STL to BRep.

Hi Fluid, its moving along nicely. The VCAD import looks like a useful tool for DI.

One thing that should be mentioned is that you are using Fusion and I am using FreeCad for the CAD work. FreeCad can easily capture the horn mouth outline to create a polyline wire with exactly all the edges and vertices. Your Fusion flow is merging multiple straight lines to form a single longer line (missing intermediate vertices). There may be someone familiar with Fusion that knows how to avoid this merge and preserve the polyline.

[DonVK]

Originally Posted by mabat

I see there's a lot of struggle you are going through with these models...

Depends on the tool flow used. FreeCad appears to be easier than Fusion (I use FreeCad). Since the parts are meshed at different times the only way to transfer the vertices position is by capturing the exact mouth wire (polyline).

Originally Posted by mabat

I've read this many times (about the flat interface) but it still doesn't make any sense to me. The whole purpose of the extruded interface is to avoid too sharp angles between boundaries at the mouth egde, i.e. too narrow spaces - this is even recommended by the ABEC author and I can see the point in that. Otherwise the shape of the interface should be just irrelevant.

This also depends. A horn mounted in an IB must raise the subdomain mouth interface because the mouth is in the IB. ABEC's author gives examples of both horns with flat mouth interface (finite baffle) and raised mouth interface (IB mount). In my models, the horn's subdomain ends at the horn mouth apex. When the horn's subdomain is solved it should only include the horn (hence flat mouth@apex). The wavefront in free space, just outside the horn mouth, might be effected by something on the outside (ie. finite baffle). So you don't want this near mouth area solved before finding what's actually near it. I try to keep the physical boundary and subdomain interface boundary consistent.

Originally Posted by mabat

Yeah, the nice thing about using the Gmsh library (when used alone) is that it aligns all edges automatically - you just don't have to care about that. It "simply" creates all the vertices from defined geometry and mesh densities (at each control point) and joints them into one cohesive structure.

That is a key goal, you don't require the same resolution everywhere (ie. back of the case). It's also why it's so important to exactly capture the existing meshed component's (horn mouth) vertices. It allows subsequent meshing of cad files to properly align to those pre-existing vertices.

[DonVK]

Originally Posted by andy19191

The limit on mesh size quoted in the ABEC manual is to avoid predicting garbage it is not the limit required to reduce the discretization errors to an acceptable level for a reliable simulation. I was trying to point out that your current simulations will contain significant discretization errors. Perhaps this doesn't matter too much at this stage when trying to get on top of things but if it all comes together and the simulations start to look useful then it will become more important.

I use the general ABEC guidelines as a start for items especially near the drive source. Then you can look at your results to see if they are well behaved or just disintegrate beyond some frequency. If there's a problem you'll probably re-mesh a bit finer to see if you're improving things. This is what @fluid has done. At some point it looks well behaved and you call it done.

How would you know when the mesh is fine enough to have an acceptable level of discretization errors. ? Since these are entire speakers, it's not really practical to use the same resolution everywhere.

[fluid]

Originally Posted by DonVK

Hi Fluid, its moving along nicely. The VCAD import looks like a useful tool for DI.

One thing that should be mentioned is that you are using Fusion and I am using FreeCad for the CAD work. FreeCad can easily capture the horn mouth outline to create a polyline wire with exactly all the edges and vertices. Your Fusion flow is merging multiple straight lines to form a single longer line (missing intermediate vertices). There may be someone familiar with Fusion that knows how to avoid this merge and preserve the polyline.

Thanks for your input Don, without your help I think I would have put this in the too hard box and moved on

There are no controls in the extrude command that allow the polyline to remain. Using another command might be able to accomplish that but I think maybe not. If anyone has any suggestions I am open to try them.

Originally Posted by DonVK

Depends on the tool flow used. FreeCad appears to be easier than Fusion (I use FreeCad). Since the parts are meshed at different times the only way to transfer the vertices position is by capturing the exact mouth wire (polyline).

I am still convinced in this circumstance that it does not matter if the baffle and interface are meshed purely at 10mm as this forces the vertices to the correct points. I appreciate that this will not work in every situation and the principal is an important one to be aware of.

Fusion does capture the exact outline through the mesh to BRep conversion it just refuses to keep the single line cuts where they form a straight line with the extrude command. So if that could be solved Fusion would be very easy.

CAD programs are so different in terminology and layout that once you've learned one learning another can be frustrating.

[mabat]

Originally Posted by DonVK

... When the horn's subdomain is solved it should only include the horn (hence flat mouth@apex). The wavefront in free space, just outside the horn mouth, might be effected by something on the outside (ie. finite baffle). So you don't want this near mouth area solved before finding what's actually near it. I try to keep the physical boundary and subdomain interface boundary consistent.

This is the point we seem to disagree on. I don't think the above is true. I just see no reason for that. Boundaries of subdomain interfaces (or the number of subdomains used) are really arbitrary, there are no physical constraints like that. Everything should get solved the same no matter the shape(s). The only constraint in the case of an IB is that everything in the exterior domain must be in front of the plane, that's about all. (What's still not completely clear to me is whether it can be exactly in the plane or not - to be on the safe side I make each element to be on the positive coordinates but I'm not sure it is really necessary.)