## General Mechanical

#### Simulating acoustic propagation in an elliptic resonator.

• Suidakl
Subscriber

Hello, I'm not sure if this category is appropriate for my discussion.

But actually I'm a master student currently doing a master thesis of photoacoustic sensor design.

So the idea is the following, by choosing carefully the parameters of the ellipse (the length a and c),

we create an ultrasound spherical wave (100 kHz) at the first focal point F, and because of the particular elliptic property which is as follows : MF + MF' = 2a (where F is whatever the point you want on the ellipse curve), we can deduce that every acoustics waves that are gonna hit the wall are also gonna end up in phase at the opposite focal point F' with the forward propagating wave if you choose a suitable a and c (so a and b) in such a way that 2a-2c = lambda (acoustic wavelength).

Actually I've already tried it out in reality. I mean I designed the ellipse on Autodesk Inventor and I printed it out in 3D. To generate the ultrasound I inserted a Quartz Tuning Fork at the first focal point, and to detect it I inserted an other quartz tuning fork at the opposite focal point (both inserting in with a very small opening) connected to a preamplifier circuit to increase the output signal. With a 10V sinusoidal input function I get out a signal of 200 mV magnitude at the other tuning fork and of course at the same frequency.

However I would also like to validate the acoustic theory with a simulation. I've never used Ansys before and I've just downloaded the student version. I tried to simulate it with my 3D ellipse with thickness and a tiny sphere at the first focal point to modelize the ultrasound source. And I also created the soustracted volume to modelize the air inside. I tried to mesh it but apparently it's not working. And I'm a bit lost with the boundary conditions. The tutorials on youtube are not really helping.

Is it possible to simulate it without ACT? Any help/advises to push me onto good tracks for fulfilling this simulation ??

• peteroznewman
Subscriber

Hello Suidaki,

ANSYS 19.1 has a significant acoustics capability, without the ACT, which you don't have access to as a Student. There are systems in the toolbox, such as Harmonic Acoustics that would be useful.

Your problem will be the node and element limit of 32,000 elements or nodes of the Student license when you try to build the 3D model.

Here is the "back of the envelope" calculation to scope out the problem.

What is the maximum frequency, f, of ultrasound you want to use? You say 100 kHz.

The speed of sound, c,  in air is about 343 m/s.

Let's calculate the wavelength of a 100 kHz sound in air:  lambda = c/f  = 343/1e5 = 0.00343 m or 3.43 mm.

At least 6 quadratic elements are needed along one wavelength to adequately represent the wave. That means the maximum element size in the model would be 0.5 mm for 1 kHz. If you take a 10 mm cube of air, and mesh it with 0.5 mm elements, you end up with > 35,000 nodes. With the Student license, the limit on nodes or elements is 32,000 before it will not solve.

Does your institution have a Research license of ANSYS, which has no node limit, that you can use?

Regards,

Peter

P.S. This discussion should get moved out of Fluid Dynamics, since this type of Acoustics computation is in the Mechanical domain (though there is an acoustics capability in Fluent for turbulent flow).

• Karthik R

Hello,

As per Peter's advice, I am moving this discussion to the 'Structural Mechanics' thread. I hope this helps you find the answer you're looking for.

Thank you.

Best Regards,

Karthik

• sk_cheah
Subscriber

I tried to simulate it with my 3D ellipse with thickness and a tiny sphere at the first focal point to modelize the ultrasound source. And I also created the soustracted volume to modelize the air inside. I tried to mesh it but apparently it's not working.

I believe you only need to mesh the air volume of the ellipse.

And I'm a bit lost with the boundary conditions. The tutorials on youtube are not really helping.Is it possible to simulate it without ACT? Any help/advises to push me onto good tracks for fulfilling this simulation ??

You could use a monopole inside the model to represent the source. By default, the natural boundary condition in acoustics corresponds to rigid wall.

Take a look at the Internoise 2014 workshop material and "software" at the link here. It is a bit dated but is a good resource beyond the help manual.

Kind regards,
Jason

• Suidakl
Subscriber

Hello !

Thank you for all of your responses.

Unfortunately I don't have Ansys license so I will try to follow your tips and apply them over a very small ellipse just to highlight the phenomenon.

Nicolas