looks close to perfect
it's hard to imagine there will be many more appropriate phase plugs to give this idea the best chance of success. The ND4015 series suggests at least some of the design choices decisions concerning the throat. The vanes can come close to the ends of some or all of the phase plug terminations.
There are several other decisions that come to mind, some of which have been mentioned. These all look hard to me.
Above 10kHz, the radially-symmetric diaphragm modes are going to come through. I wouldn't know whether it's better to blend some of the rings at the throat (one or two vanes) or keep them all separate.
It will take judgement to decide how much to thicken the vanes as they extend outward, and at what rate.
I can't see how to decide the length of the vanes. For a pure OS, I wonder about ending the vanes on a sphere (or oblate sphere) at the mouth, i.e., the middle vane should be longest. I've no intuition what will happen or what to do with an OSSE type guide - I'm thinking of all your roll-back trials, and can't start to imagine how to fit all that together.
Ken
it's hard to imagine there will be many more appropriate phase plugs to give this idea the best chance of success. The ND4015 series suggests at least some of the design choices decisions concerning the throat. The vanes can come close to the ends of some or all of the phase plug terminations.
There are several other decisions that come to mind, some of which have been mentioned. These all look hard to me.
Above 10kHz, the radially-symmetric diaphragm modes are going to come through. I wouldn't know whether it's better to blend some of the rings at the throat (one or two vanes) or keep them all separate.
It will take judgement to decide how much to thicken the vanes as they extend outward, and at what rate.
I can't see how to decide the length of the vanes. For a pure OS, I wonder about ending the vanes on a sphere (or oblate sphere) at the mouth, i.e., the middle vane should be longest. I've no intuition what will happen or what to do with an OSSE type guide - I'm thinking of all your roll-back trials, and can't start to imagine how to fit all that together.
Ken
For those of you who want to try simulating, here is a way to generate the contours in Fusion360
There is a addon called Equation Driven Curve. It can be used to draw the OS contours with the help of a few predefined user parameters.
The equation in Fusion style: sqrt(( sin(a) ^ 2 / sin(a0) ^ 2 ) * k ^ 2 * r0 ^ 2 + t ^ 2 * tan(a) ^ 2) - ( sin(a) / sin(a0) ) * r0 * ( k - 1 )
I multiply the S parameter to get the offset curves (in my case by 0.2, 0.4, 0.6 and 0.8)
There is a addon called Equation Driven Curve. It can be used to draw the OS contours with the help of a few predefined user parameters.
The equation in Fusion style: sqrt(( sin(a) ^ 2 / sin(a0) ^ 2 ) * k ^ 2 * r0 ^ 2 + t ^ 2 * tan(a) ^ 2) - ( sin(a) / sin(a0) ) * r0 * ( k - 1 )
I multiply the S parameter to get the offset curves (in my case by 0.2, 0.4, 0.6 and 0.8)
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Why do you think the vanes will need thickening at all? My understanding is that the thinner the better and that there's nothing better that one could do about it (?).
Regarding the extension towards the mouth, I think it will only work as long as the wall contour really follows the OS profile, which is also why I wouldn't extend the vanes more than about 1/4 - 1/3 of the profile. Then it's not an OS anymore.
Anyway, BEM simulations should answer us all these question soon.
ends
By thickening, I meant a little, for stability. The vanes should be thin at the throat, I wonder if the optimum is to have them thin there and thicken - only enough for stability, if at all - farther down the waveguide where small deviations from the "ideal" are less problematic.
I look forward to seeing some BEM results - if the vanes can be that short it would be convenient and allow them to be kept thin.
Ken
By thickening, I meant a little, for stability. The vanes should be thin at the throat, I wonder if the optimum is to have them thin there and thicken - only enough for stability, if at all - farther down the waveguide where small deviations from the "ideal" are less problematic.
I look forward to seeing some BEM results - if the vanes can be that short it would be convenient and allow them to be kept thin.
Ken
Being conical-like, the vanes should be very stable and not need thickness for support.
The issue not being addressed is termination. As usual, the waveguide and vanes must be terminated. If this is not done properly then diffract6ion will occur. I think that the vanes should go out to the point where the OS contour is deviated to supply the flare. If they go any further then the vanes won't be normal to the wavefront and there will be diffraction at the termination.
I would use a single vane to start as multiple vanes only make the situation more complex with no apparent advantage.
The issue not being addressed is termination. As usual, the waveguide and vanes must be terminated. If this is not done properly then diffract6ion will occur. I think that the vanes should go out to the point where the OS contour is deviated to supply the flare. If they go any further then the vanes won't be normal to the wavefront and there will be diffraction at the termination.
I would use a single vane to start as multiple vanes only make the situation more complex with no apparent advantage.
I already printed some on a FDM 3D printer just for a test and don't worry much about stability (this was PLA, 0.4 mm thickness, it's actually printed just as one spiral). But it needs an additional coating as it's not 100% airtight (I suppose it should be).
If epoxy coated I think it will be quite stable.
- But perhaps it shouldn't be airtight, I don't know. What if it was perforated?
If epoxy coated I think it will be quite stable.
- But perhaps it shouldn't be airtight, I don't know. What if it was perforated?
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I suspect that it would would as well or better. 0th mode waves won't see a pressure differential. HOMs will. They could get damped instead of just reflecting.
So everything went quite esoteric lately, wow! I don't have anything to contribute to the multi cell coaxial story. Patrick: Though it is neat to print the foam permanently into the waveguide, it does not sound wise. It will be impossible to replace it and cleaning it from dust could only be done in a big ultra sonic cleaner. In any case: if the foam could be printed, it should be a seperate piece.
Now, I want to share my impressions with the idea to add a slotted throat. In the end, I could not really break through the brick wall that is at 15k. When Source.Shape = 2 is set, it does look very much better, but as noone knows whether this mode or Source.Shape = 1 represents actual HF behaviour, it does not seem to give a lot. Attached 4 graphs, first two in mode 2, HF peak with the unslotted, slotted shines, second two in mode 1, HF with unslotted look better than slotted in mode 2. I went to the extremes of Slot.Length = n*cos(2*p)^n, tried more than four slots (times*p) and made them wider, still a 15k brickwall, more or less. I could not figure how to make them very long but not widen, so that they would reach deep into the termination, but that is all I have missed. Until there is some other idea, I think I will go for an axisymmetric device.
The only thing that I could see is that the -1 and -6 dB lines seem to behave differently if you compare the first and last (best looking) graphs.
Now, I want to share my impressions with the idea to add a slotted throat. In the end, I could not really break through the brick wall that is at 15k. When Source.Shape = 2 is set, it does look very much better, but as noone knows whether this mode or Source.Shape = 1 represents actual HF behaviour, it does not seem to give a lot. Attached 4 graphs, first two in mode 2, HF peak with the unslotted, slotted shines, second two in mode 1, HF with unslotted look better than slotted in mode 2. I went to the extremes of Slot.Length = n*cos(2*p)^n, tried more than four slots (times*p) and made them wider, still a 15k brickwall, more or less. I could not figure how to make them very long but not widen, so that they would reach deep into the termination, but that is all I have missed. Until there is some other idea, I think I will go for an axisymmetric device.
The only thing that I could see is that the -1 and -6 dB lines seem to behave differently if you compare the first and last (best looking) graphs.
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I was thinking about printing vanes into a wave guide or horn, the foam basically provides too much obstruction to the sound for my ears.
So 
I have implemented all the above discussed functionality into Ath, including export of the contours into ripple tank. After the very first attempts, this is what I was initially worried about - dividing the waveguide into several "discrete" channels simply won't sum smoothly at the exit of the vanes. So far I was not able to obtain a significantly better result than without the vanes.
I have implemented all the above discussed functionality into Ath, including export of the contours into ripple tank. After the very first attempts, this is what I was initially worried about - dividing the waveguide into several "discrete" channels simply won't sum smoothly at the exit of the vanes. So far I was not able to obtain a significantly better result than without the vanes.
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Anyway, it's fascinating to watch - here's a sample Ripple Tank code (Ripple Tank Simulation)
Code:
$ 3 2000 125 0 0 728 0.00037463
S 2 251 837 251 1163 0 0.01637368881118881 0 10.000178395549446 99.9998652719957 1 0
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