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### Generating visible waves from an acoustic waveguide

Posted: 30 Mar 2021, 22:05
Hi all;
This is a topic switch from the "Helmholts equation errors" post.

I decided to switch to a Navier Stokes solver for my acoustic waveguide analysis. I am trying to produce an analysis that shows the propagation of the acoustic wave fronts from an hyperbolic acoustic waveguide. I need to accomplish two things. First I need to determine the acoustic pattern vs frequency. Second I need to look for any anomalies within the throat of the waveguide that would "color" the sound that the waveguidthee produces. A third possibility is to determine the efficiency increase of a tweeter attached to the waveguide. This third project is a long term project with a not very high priority.

Presently the solver time steps through the analysis satisfactorily but the files are all the same and are nearly blank. I have attached the .sif file, a .unv file for someone that wishes to recreate the analysis and a .png file of a paraview screen shot of the end of an analysis.

I suspect that there is something wrong with the Driver BC but am not sure. Any help will be sincerely appreciated.

Gary R.

### Re: Generating visible waves from an acoustic waveguide

Posted: 30 Mar 2021, 22:40
Based on your mesh, and the BC velocity equation, the inlet is 20 meters wide, the velocity is -116.6 meters/sec, and the viscosity is 1.98E-5 kg/m-s. This would result in turbulent flow well beyond the capability of the standard stokes, equation. The mesh is much to course to even approach a converged solution with those inputs.

### Re: Generating visible waves from an acoustic waveguide

Posted: 30 Mar 2021, 23:54
Hi

As said in the previous thread, I would not recommend using N-S for pressure vawes. It will exhaust your computer capacity if you try to capture pressure waves with that. Rather use "Wave Equation" which is Ch. 14 in Models Manual. It is meant for transient waves. With a suitable ansatz this results to the Helmholtz equation.

We have sometimes just tested to solve pressure waves with N-S. You need compressible material law and bubble stabilization to even have a shot at the problem. Incompressible material law (default) cannot resolve pressure waves since they would travel at infinite speed.

-Peter

### Re: Generating visible waves from an acoustic waveguide

Posted: 01 Apr 2021, 06:44
Hi all;

OK. So the Navair Stokes equation is a bad idea. I had to try I one more time. Stubborn I guess. I worry that the Helmholtz equation assumes non compressible conditions which may not be true at higher power levels, especially in the throat. Kevins remark about the size of the throat worries me. The throat size is actually 1.5 inches. I thought I used consistent MKS units throughout. As far as the fineness of the mesh goes, I ran the .unv file through gmsh and split the mesh twice before using. Sorry I didn't mention that sooner.

I found a problem similar to what I am trying to do at:

I am attaching the sif file from the above and also the my present efforts. There are some differences that I do not understand - like the extra equation that shows up. I think Peter remarked that the ResultOutput solver was done in the background.

My models manual is from 2019 and needs to be updated. I found the Wave Equation section and also the Large Amplitude Air Waves. I need to read these. I just downloaded the latest manual and am going to read it before I go any further with this project.

I must be a colossal pain at this point and apologize. I've a degree in applied math but am having a hard time getting my arms around Elmer.

Gary R

### Re: Generating visible waves from an acoustic waveguide

Posted: 01 Apr 2021, 12:06
Hi

The case by "ben qui" at youtube was using the standard Helmholtz equation. There are several minimal tests on this with the distro. This is just the scaled up problem with a nice geometry. The sif files are though almost the same.

Yes, at high pressure values the equation will become nonlinear. Also if you have very small channels the viscous and thermal boundary layers may have to be considered. But Helmholtz is really the place to start. When we collaborated with Nokia on these models years ago that was the case even then. Helmholtz is not incompressible, it is derived precisely for material with linear pressure-density relationship.

-Peter

### Re: Generating visible waves from an acoustic waveguide

Posted: 01 Apr 2021, 12:21
Based on the units of your constants and material, length should be meter. You can scale the length units in the sif file.

Simulation
coordinate scaling = 0.001
End

### Re: Generating visible waves from an acoustic waveguide

Posted: 01 Apr 2021, 13:00
You also only reference one of the boundaries in the baffle, is that the intent?

### Re: Generating visible waves from an acoustic waveguide

Posted: 01 Apr 2021, 14:28
The mesh doesn't converge well over 3000 HZ but at 350 Hz, video and files in the github.
https://github.com/mrkearden/waveguide

### Re: Generating visible waves from an acoustic waveguide

Posted: 01 Apr 2021, 16:57
Hi

Note that if you want to present the wave somewhat accurately you need perhaps ~10 elements for each wave. If you have 3000 Hz your wavelength is ~10 cm. So your element size should not be larger than 0.01 m anywhere. Using quadratic elements is also advicable.

With these choices unfortunately the solution of the linear system becomes rather difficult for large wave numbers.

-Peter

### Re: Generating visible waves from an acoustic waveguide

Posted: 02 Apr 2021, 21:57
I am somewhat confused about the dimensions of the problem. I set FreeCAD to meter/Kg/second but entered my dimensions in millimetres. It is my understanding that FreeCAD outputs everything in mm. I assumed that because all constants in Elmer are in M/K/S units that my problem would scale properly. Per Kevin, this does not seem to be the case. The mouth of the waveguide should be 50.8 mm radius (0.75 inches). I scaled the problem by 0.001 but am not sure what the size really is at this point. Please comment.

Could someone send me a paraview file or a screen shot of their results. I'm attaching mine. I'm not sure anymore what I should be getting for output. The the screen shot is for the Helmholtz equation at 1000Hz.

Gary R