> How would you define "optimum"?
That is a decision for engineers, designers, sales and marketing people to make. Computers cannot design things but they can compute optimum solutions given a few parameters to adjust and a target.
> I, for one, would be interested in leaning about BEM for this sort of thing. Mark Dodd
> at KEF has gotten some pretty excellent results and, though I've read a paper of his
> on the subject, I'd love to get some hands on with it.
I followed your suggestion to:
http://www2.kef.com/resources/conceptblade/_whitepaper/KEF_Concept_Blade_White_Paper.pdf
which, if you make allowances for the marketing, has a fair illustration of the interaction of numerical simulation and an engineer's thought processes in the section on evolving the design of the cone.
My next hop was to the commercial software (and a blast from my past):
http://www.vibroacoustics.co.uk/audio/fsaudio1.htm
although I do not recognise the name PacSys and they do not seem to have evolved much in the 30 years since I last had anything to do with their software.
> This is true, if it is even possible that way, I mean, no one has actually done it!
It is taught at undergraduate level, for example:
http://www.cmiss.org/documentation/course_notes/fembem_notes
and has been commercially available for a long time, see for an example the PAFEC link above.
> Having asked specialists in the field of modelling I have been told that if you want
> to determine the higher order mode production in a waveguide of arbitrary geometry,
> (and not just directivity), then it is necessary to calculate eigenvalue solutions to
> the wave equation, and for these to be accurate enough to be worthwhile you need to
> use a combined boundary and finite element model.
I would agree that a balanced approach would be to use finite elements for the essentially interior part of the problem coupled to boundary elements for the exterior part. Although there are extensions to classical BEM to make it more efficient for larger problems and there are extensions to classical FEM to handle getting to the far field should one be strongly attached to one or other of the methods which is often the case.
Would an engineer only be interested in the higher order modes? What about the entropy and vorticity generation around the driver and throat? This may not propagate to the far field but it is likely to influence what does, at least for high power compression drivers, but is not included in FE/BEM solution of the linear wave equation.
> In inverse problem modelling you tend to end up with a solution set rather than a
> solution, and since you are going to use a device such as a cone or dome that produces
> a wave front that is pre determined, (unless you put some sort of a phase plug in
> front of it, and then you do not get exactly the wavefront you want), you are
> restricted as to the shape of the input waveform anyway so you get more bang for your
> buck, and much less grief, solving the forward problem.
I am not sure I fully understand the parts about the predetermined wave front or set. A designer would indeed usually want a map rather than a single point in order to consider factors that were not included as part of the optimisation process which can fail and/or get stuck depending on how things are formulated. Whether an inverse method is more efficient than multiple forward methods depends on the information being sort.
I am picking up a bit of positive interest even though I am not wholly convinced there is a real world problem there to be addressed. Whatever, that would be secondary to my own personal interest which is growing a bit particularly after seeing the old PAFEC code.
That is a decision for engineers, designers, sales and marketing people to make. Computers cannot design things but they can compute optimum solutions given a few parameters to adjust and a target.
> I, for one, would be interested in leaning about BEM for this sort of thing. Mark Dodd
> at KEF has gotten some pretty excellent results and, though I've read a paper of his
> on the subject, I'd love to get some hands on with it.
I followed your suggestion to:
http://www2.kef.com/resources/conceptblade/_whitepaper/KEF_Concept_Blade_White_Paper.pdf
which, if you make allowances for the marketing, has a fair illustration of the interaction of numerical simulation and an engineer's thought processes in the section on evolving the design of the cone.
My next hop was to the commercial software (and a blast from my past):
http://www.vibroacoustics.co.uk/audio/fsaudio1.htm
although I do not recognise the name PacSys and they do not seem to have evolved much in the 30 years since I last had anything to do with their software.
> This is true, if it is even possible that way, I mean, no one has actually done it!
It is taught at undergraduate level, for example:
http://www.cmiss.org/documentation/course_notes/fembem_notes
and has been commercially available for a long time, see for an example the PAFEC link above.
> Having asked specialists in the field of modelling I have been told that if you want
> to determine the higher order mode production in a waveguide of arbitrary geometry,
> (and not just directivity), then it is necessary to calculate eigenvalue solutions to
> the wave equation, and for these to be accurate enough to be worthwhile you need to
> use a combined boundary and finite element model.
I would agree that a balanced approach would be to use finite elements for the essentially interior part of the problem coupled to boundary elements for the exterior part. Although there are extensions to classical BEM to make it more efficient for larger problems and there are extensions to classical FEM to handle getting to the far field should one be strongly attached to one or other of the methods which is often the case.
Would an engineer only be interested in the higher order modes? What about the entropy and vorticity generation around the driver and throat? This may not propagate to the far field but it is likely to influence what does, at least for high power compression drivers, but is not included in FE/BEM solution of the linear wave equation.
> In inverse problem modelling you tend to end up with a solution set rather than a
> solution, and since you are going to use a device such as a cone or dome that produces
> a wave front that is pre determined, (unless you put some sort of a phase plug in
> front of it, and then you do not get exactly the wavefront you want), you are
> restricted as to the shape of the input waveform anyway so you get more bang for your
> buck, and much less grief, solving the forward problem.
I am not sure I fully understand the parts about the predetermined wave front or set. A designer would indeed usually want a map rather than a single point in order to consider factors that were not included as part of the optimisation process which can fail and/or get stuck depending on how things are formulated. Whether an inverse method is more efficient than multiple forward methods depends on the information being sort.
I am picking up a bit of positive interest even though I am not wholly convinced there is a real world problem there to be addressed. Whatever, that would be secondary to my own personal interest which is growing a bit particularly after seeing the old PAFEC code.
I am familiar with inverse problems encountered in seismology and these are not well posed by the usual criteria and you end up having to take a core in a place where the possible solutions differ most to see what solution is the closest.
If for instance you start out with an ideal directivity pattern at some distance in front of the device and work backwards then when you come to the input wavefront there is no way your driver can produce such a wavefront, and the intervening duct cannot in anyway be realised as a single surface and must contain three dimensional scattering objects to get close to a solution, etc.
The point of all of this is that in fields such a seismology the alternative to large number crunching feats is to drill core holes down to sometimes several hundred meters on a few meter grid, so the effort is worthwhile.
In the case of the waveguide you already know what shape of intervening duct works, for a plane wave it is the o.s. contour.
In a near field device driven by a dome or a cone it is not too far from one.
It might be just that I have made the transition into the old farts club, but it seems to me it would be a lot of effort with at the end the result being you learning what you already know.
Rcw.
If for instance you start out with an ideal directivity pattern at some distance in front of the device and work backwards then when you come to the input wavefront there is no way your driver can produce such a wavefront, and the intervening duct cannot in anyway be realised as a single surface and must contain three dimensional scattering objects to get close to a solution, etc.
The point of all of this is that in fields such a seismology the alternative to large number crunching feats is to drill core holes down to sometimes several hundred meters on a few meter grid, so the effort is worthwhile.
In the case of the waveguide you already know what shape of intervening duct works, for a plane wave it is the o.s. contour.
In a near field device driven by a dome or a cone it is not too far from one.
It might be just that I have made the transition into the old farts club, but it seems to me it would be a lot of effort with at the end the result being you learning what you already know.
Rcw.
I've done the sort of inverse problem that you described - kinda!
Its in my book. What I did was to take the far field pattern that I wanted and calculated back to the mouth of a waveguide to find out what the velocity distribution should be. Then I used software to find the mouth size and shape that would give me the bandwidth and coverage that I wanted. Its an interesting study that showed me how a mouth radius would get much closer to ideal than a sharp edge.
This work was furthered on in your own country as a recent PhD thesis. He (don;t remember his name) used the same approach that I did to calculate to the mouth velocities, but then he iterated to the wavguide shape numerically to find a kind of optimum shape. Very interesting work, but he basically found that what I was already doing was pretty close to ideal. Still worth looking at however.
Its in my book. What I did was to take the far field pattern that I wanted and calculated back to the mouth of a waveguide to find out what the velocity distribution should be. Then I used software to find the mouth size and shape that would give me the bandwidth and coverage that I wanted. Its an interesting study that showed me how a mouth radius would get much closer to ideal than a sharp edge.
This work was furthered on in your own country as a recent PhD thesis. He (don;t remember his name) used the same approach that I did to calculate to the mouth velocities, but then he iterated to the wavguide shape numerically to find a kind of optimum shape. Very interesting work, but he basically found that what I was already doing was pretty close to ideal. Still worth looking at however.
> It might be just that I have made the transition into the old farts club, but
> it seems to me it would be a lot of effort with at the end the result being
> you learning what you already know.
Hmmm. I think this inverse design stuff is wandering away from my main interest but... I am not familiar with the governing equations for seismology or how the targets are introduced but I am familiar with inverse design for fluid and structural problems. Here, for example, is some code from MIT for low speed aerofoil design using inverse methods:
http://web.mit.edu/drela/Public/web/xfoil/
Development stopped a long time ago so you may have to fiddle a bit to get it to compile and run on a modern unix box. If you stick with a linear problem it is fast and efficient at generating aerofoil shapes but if you introduce a bit more realistic physics then things get more tricky when it comes to getting an answer. I would suggest that this is a reasonably general observation which tends to map well to other problems like our waveguide.
If you set things up so that the target does not necessarily match a solution then the scheme must be setup to converge on the solution that is closest. This is how schemes with nonlinear governing equations are setup. But if the governing equations are linear then much faster and more efficient schemes can be adopted.
> In the case of the waveguide you already know what shape of intervening duct
> works, for a plane wave it is the o.s. contour.
Why would one be interested in plane waves? The problem I am interested in has a tweeter and midrange in overlapping waveguides with no doubt a range of fiddly things to consider in and around the throat, the overlap and the transition to the outside of the loudspeaker box. The point of performing numerical simulations is that these non-ideal conditions that determine the limits of performance can be fully understood and systematically studied in a quantitative manner.
> it seems to me it would be a lot of effort with at the end the result being
> you learning what you already know.
Hmmm. I think this inverse design stuff is wandering away from my main interest but... I am not familiar with the governing equations for seismology or how the targets are introduced but I am familiar with inverse design for fluid and structural problems. Here, for example, is some code from MIT for low speed aerofoil design using inverse methods:
http://web.mit.edu/drela/Public/web/xfoil/
Development stopped a long time ago so you may have to fiddle a bit to get it to compile and run on a modern unix box. If you stick with a linear problem it is fast and efficient at generating aerofoil shapes but if you introduce a bit more realistic physics then things get more tricky when it comes to getting an answer. I would suggest that this is a reasonably general observation which tends to map well to other problems like our waveguide.
If you set things up so that the target does not necessarily match a solution then the scheme must be setup to converge on the solution that is closest. This is how schemes with nonlinear governing equations are setup. But if the governing equations are linear then much faster and more efficient schemes can be adopted.
> In the case of the waveguide you already know what shape of intervening duct
> works, for a plane wave it is the o.s. contour.
Why would one be interested in plane waves? The problem I am interested in has a tweeter and midrange in overlapping waveguides with no doubt a range of fiddly things to consider in and around the throat, the overlap and the transition to the outside of the loudspeaker box. The point of performing numerical simulations is that these non-ideal conditions that determine the limits of performance can be fully understood and systematically studied in a quantitative manner.
Your example of aerofoil sections reminds me of a story told to me several years ago by someone who races model aeroplanes.
In this there is much talk about magic secret aerofoil sections and so on and everybody has their favourite section that they swear by, the details of which they guard jealously from the opposition.
What they found however was that a circular arc an straight line approximation to such sections is in practice just as good.
This is because it is not possible for them to make the section accurate enough to be any more than an approximation anyway, and it is fairly easy to come up with an approximation that is closer to the ideal than the manufacturing tolerance they can achieve, and these are easier to make.
In the context of shallow wave guides when writing that article I did some head scratching and back of the envelope scribblings to get an idea how the gadgets might work.
From considerations of scattering amplitude I figured that the best wall curve for bending a plane wave at the throat into a spherical wave would be one which had a linear first derivative as every point from the throat to the point at which the final desired curvature was obtained would then have the same notional scattering, this would minimise diffraction because this is the smoothest curve that joins these two points.
If you look at the o.s. wave guide and the Peavy quadratic throat device they have curves that are very close and the Peavy case is a circular arc that meets a straight line at right angles, exactly the sort of thing I would have expected from my somewhat agricultural first thoughts, and from what Earl Geddes says Genelec had much the same idea about cones and domes.
Overall the devices in question are not that critical and from the data I have seen there seems to be a family of devices that exist between certain bounds, that work equally well, and it seems to me that that hunting for an ideal solution is something like the search for the holy grail, and about as useful.
Rcw.
In this there is much talk about magic secret aerofoil sections and so on and everybody has their favourite section that they swear by, the details of which they guard jealously from the opposition.
What they found however was that a circular arc an straight line approximation to such sections is in practice just as good.
This is because it is not possible for them to make the section accurate enough to be any more than an approximation anyway, and it is fairly easy to come up with an approximation that is closer to the ideal than the manufacturing tolerance they can achieve, and these are easier to make.
In the context of shallow wave guides when writing that article I did some head scratching and back of the envelope scribblings to get an idea how the gadgets might work.
From considerations of scattering amplitude I figured that the best wall curve for bending a plane wave at the throat into a spherical wave would be one which had a linear first derivative as every point from the throat to the point at which the final desired curvature was obtained would then have the same notional scattering, this would minimise diffraction because this is the smoothest curve that joins these two points.
If you look at the o.s. wave guide and the Peavy quadratic throat device they have curves that are very close and the Peavy case is a circular arc that meets a straight line at right angles, exactly the sort of thing I would have expected from my somewhat agricultural first thoughts, and from what Earl Geddes says Genelec had much the same idea about cones and domes.
Overall the devices in question are not that critical and from the data I have seen there seems to be a family of devices that exist between certain bounds, that work equally well, and it seems to me that that hunting for an ideal solution is something like the search for the holy grail, and about as useful.
Rcw.
The OS is exactly that curve with minimum slope change. The Peavey design has a larger slope change initially and then abruptly goes to zero. The abrupt change in second derivative will yield more diffraction and more HOM.
I do agree that chasing these things to the "n"th degree is rather pointless. Its like chasing THD from .01% to .001% in an amp when 1% has no relavence in most cases.
I do agree that chasing these things to the "n"th degree is rather pointless. Its like chasing THD from .01% to .001% in an amp when 1% has no relavence in most cases.
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