Confusing results open-closed duct acoustics harmonic analysis simulation

Numerical methods and mathematical models of Elmer
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msui
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Joined: 15 Feb 2011, 13:59

Confusing results open-closed duct acoustics harmonic analysis simulation

Post by msui »

For design activities on duct noise control I am trying to set up a frequency scanning simulation of air duct acoustics in Elmer. Through this very helpful tutorial of CrocoDuck I learnt how to do that for a rigid walled room. However I am considering a duct which is open on one side and therefore the standard boundary condition of zero wave flux at that side of the duct air volume does not apply.
Because a considerable portion of the opening is blocked by the radiator and I would like to study the frequency spectrum up to wave lengths of only 1 to 2 times the duct diameter, I assume the plane wave impedance to be invalid at that boundary. See attached drawing for duct geometry used here:
OpenClosedDuct.png
OpenClosedDuct.png (15.46 KiB) Viewed 2457 times
To model the open connection of pressure waves with the air outside the duct, I couple an additional air space to the duct to form a mesh domain and hope to allow for meaningful wave solutions. Regarding the radially outward motion of the waves which will hit the boundary of the additional air space at almost right angles, assignment of the plane wave impedance to that boundary seems justified.
In one of the first iterations of simulation development I managed to achieve credible results for the sound pressure level over the considered frequencies using a mesh in 3D of a mirror halve of the duct with additional air space.
SPL_old_mesh_fine_4100Hz_direct.png
iteration 2
(252.69 KiB) Not downloaded yet
As you can see from the ParaView screenshot above the VTU solution contains a clear pattern of nodes and antinodes in the sound pressure amplitude in the interior of the duct. In the line plot sound pressure level is graphed as a function of source frequency (+10 Hz for each successive solution index). Note that in this damping less simulation the sound pressure level of the peak valleys increases with frequency.
Moving on with modifications to the mesh for an adjusted source size and position I ended up with rather confusing results.
SPL_third_mesh_3360Hz_direct.png
iteration 1
(79.12 KiB) Not downloaded yet
Again you see a surface plot of sound pressure level of the obtained VTU solution with next to that a line plot of sound pressure level on the duct central axis as a function of source frequency (+10 Hz for each successive solution index). However no clear pattern of nodes and antinodes in the sound pressure amplitude in the interior of the duct can be distinguished. Instead of that the source seems radiating into the extended air space only and the sound pressure level on the duct central axis keeps showing up antiresonances for increasing frequency.

After the obvious checks and double checks in solver input file and mesh definition file (IDs of boundary conditions, solver settings, mesh element type etc…) I am left in confusion.
What could have gone wrong in this last iteration of my simulation development? I would be happy to hear your suggestions. Please find the Elmer mesh + solver input + solver log files of the first iteration in iteration1.zip and those of the second in iteration2.zip.
kevinarden
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by kevinarden »

I used ElmerGrid to mirror iteration2 model to also make it a half cylinder, and the results look more like iteration1.

There are BCs on the planes, so whatever the "do nothing" BC is appears to influence the result when going from a half cylinder to a 1/4 cylinder.
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results.png
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CrocoDuck
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by CrocoDuck »

Hi there! I am glad my tutorial was helpful for you!

I cannot quite comment on the issue about the iterations, but I have a comment about this:
msui wrote: 27 May 2021, 12:52 Because a considerable portion of the opening is blocked by the radiator and I would like to study the frequency spectrum up to wave lengths of only 1 to 2 times the duct diameter, I assume the plane wave impedance to be invalid at that boundary. See attached drawing for duct geometry used here:
The plane wave outlet boundary condition is not very realistic because the layer of air at the mouth of the pipe, in the approximation of wavelength much bigger than the pipe radius, is vibrating as a radiating piston. If you have Fundamental of Acoustics by Kinsler and Frey, 4th Edition, you can read about this at page 272-273.

From equation 10.2.14 the termination impedance for an unflanged pipe, already converted for use in Elmer (if I did it properly), reads:

c * (1/4 (ka)^2 + j 0.6 ka) (Equation 10.2.14 from Fundamentals of Acoustics)

with k the wavenumber, j the imaginary unit and a the pipe radius. This holds for wavelength much bigger than the radius. At higher wavelength the air at the mouth of the pipe will break, in the sense that it will not oscillate any more as a lumped piston, yielding to more complex radiation.

To understand how the impedance for Elmer is obtained, see page 286-297 of Fundamentals of Acoustics, equation 10.9.3. Then, remember that Elmer wants specific acoustic impedance divided by density (if I remember correctly). I invite you to double check my result as I just did it quickly.

If you are interested in going beyond the large wavelength approximation, you might want to look at equation 7.5.11, page 186.
CrocoDuck
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by CrocoDuck »

Hi again,

Sorry, I completely misunderstood your problem somehow, despite there being a very clear diagram. You are right, at the open end you should not use the plane wave outlet condition, but not the piston one either. There are perhaps formulas for the radiation impedance of an anular radiator, if your problem is that of a cylindrical pipe with a cylindrical driver at the open end. I will look into my books. Otherwise, I do not see fundamentally wrong things with your strategy, except that it will lead to higher computational costs.
CrocoDuck
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by CrocoDuck »

Hi there!

I took at look at your study. I think there are a couple of issues.

Plane Wave Outlet:

Code: Select all

Boundary Condition 3
  Target Boundaries(1) = 3 
  Name = "nrbc"
  Wave impedance 1 = Real MATC "343*p"
  Wave impedance 2 = 0
End
This is wrong. If you look at the Elmer Models Manual you will see that the physical dimensions of Z (the impedance according to this solver definition) are not those of a specific acoustic impedance (density by velocity) but simply those of a velocity. This means that you need to divide any specific acoustic impedance by the density of the medium to have the correct value for use with the Elmer Solver. This means that your `Wave Impedance 1` keyword should simply read 343. I touch upon this in this episode of my series. Note that you can simply use the keyword `Plane Wave BC = True`.

Also, I see that no condition is assigned to boundary 7. I am not sure how the solver handles this. If you are modelling a quarter of the tube with the aim of modelling the whole thing, I think a periodic boundary condition needs to be applied here. I have never attempted this so maybe more expert users can weight in.

I was able to find the radiation impedance for a baffled ring radiator at page 329 of Formulas of Acoustics. It is a massive expression and It seems to me your tube is not flanged, so it would not apply to this problem really. It is perhaps more straightforward to follow your approach with a radiating volume terminated by a plane wave outlet.

I gave it a quick stab with a few frequencies, I can see the modal patterns. Below the 500 Hz solution. See also my case linked below. Note the use of p-elements as well.

Image

Link to case

In short: I think that boundary 7 needs to be handled with a periodic boundary condition, or you can just model the whole system. Also, if for some frequency your source just so happen to be at a node than the tube will not be excited, so there might be physical solutions with little to no action inside the tube (and hence also outside of it too I would guess).
msui
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by msui »

Hi Kevinarden, CrocoDuck,

Thnx for your informative replies. I guess correct use of periodic/symmetry BCs is indeed key to my problem. Moreover good to keep in mind the plane wave BC assumes units of velocity and not of density times velocity!
To save memory I need to keep using a divided geometry part for the mesh size not to get to large. I am trying now with a pure axially symmetric version of the problem where I can skip the third dimension completely. Would one of you know which BC to put on the symmetry axis of the duct?
kevinarden
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by kevinarden »

This may be an example to review using the axial symmetric coordinate system.

https://github.com/ElmerCSC/elmerfem/bl ... eWavesAxis

I think the model should be in the XY plane and the axis of symmetry is Z.

I believe that having it defined as axial symmetric case means that you do not have to define a BC in the symmetry axis.
raback
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by raback »

Hi

I had time to have a look at this thread. Some comments

1) The natural BCs (do nothing) should be fine for symmetry. Even for double symmetry.
2) The asymmetry of the mesh may break the symmetry a little if the solution is sensitive to mesh quality. This may be particularly true for resonance.
3) For constant matc expressions use rather $ to save time. So "Density = $p" rather than "Density = Real MATC "p"". Saves a lot of time. MATC goes string->number->string->number for all integration points which costs a lot.
4) The "impedance" should not include density, it is just velocity at the outlet (as written in documentation). This may be unorthodox and is due to the way it is coded long ago. Rather use "Plane Wave BC = True", as suggested, if in doubt. I added this keyword to documentation just.
5) There is a consistency test "HelmholtzPlaneWaves" that ensures that plane waves stay as plane waves with this outlet BC (does not visualized well due to high order nodal elements).
6) You might want to use quadratic elements for accuracy. Either nodal or p:2.
7) Axially symmetric case is indeed a good idea. Look at the test case "HelmholtzPlaneWavesAxis".

Have fun!

-Peter
CrocoDuck
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Re: Confusing results open-closed duct acoustics harmonic analysis simulation

Post by CrocoDuck »

raback wrote: 02 Jun 2021, 11:23 Hi

I had time to have a look at this thread. Some comments

1) The natural BCs (do nothing) should be fine for symmetry. Even for double symmetry.
2) The asymmetry of the mesh may break the symmetry a little if the solution is sensitive to mesh quality. This may be particularly true for resonance.
3) For constant matc expressions use rather $ to save time. So "Density = $p" rather than "Density = Real MATC "p"". Saves a lot of time. MATC goes string->number->string->number for all integration points which costs a lot.
4) The "impedance" should not include density, it is just velocity at the outlet (as written in documentation). This may be unorthodox and is due to the way it is coded long ago. Rather use "Plane Wave BC = True", as suggested, if in doubt. I added this keyword to documentation just.
5) There is a consistency test "HelmholtzPlaneWaves" that ensures that plane waves stay as plane waves with this outlet BC (does not visualized well due to high order nodal elements).
6) You might want to use quadratic elements for accuracy. Either nodal or p:2.
7) Axially symmetric case is indeed a good idea. Look at the test case "HelmholtzPlaneWavesAxis".

Have fun!

-Peter
Oh there's quite a number of useful tricks there. Can't wait to try those, thanks!
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