Learning Forum

[kasparek1]

Hello

I am trying to perform harmonic acoustic analysis which simulates experiment inside the impedance tube. I chose Delany-Bazley model for porous specimen, but the problem is that I dont know the value of Fluid Resistivity. What I do know is Absorption Coefficient of the material from the experiment which I performed on real impedance tube. So I wanted to try to "fit" these results to the results from the ANSYS and find the right values of Fluid Resistivity this way and so replicate the experiment I performed.

The problem is that I found out that Fluid Resistivity has minimal influence on Absoprtion Coefficient. For example:

Fluid Resistivity: 10 000 kg/s*m^3 --> Absorption Coefficient at 500 Hz = 0,1

Fluid Resistivity: 100 000 kg/s*m^3 --> Absorption Coefficient at 500 Hz = 0,12

The material used in this case is polymer foam AIREX T92 200 (density = 210 kg/m^3, speed of sound = 1050 m/s), but results with other materials are similar - still minimal impact of Fluid Resistivity on Absorption Coefficient.

I even tried to evaluate SPL along the tube, find the maximum and minimum of SPL and calculate the Absorption Coefficient according to ISO 10534-1 norm, but still, the Fluid Resistivity has such a small influence on SPL inside the tube.

Mesh is fine enough.

Can please anybody explain me how is it possible that the most important property of sound-absorbing material has such a small influence on sound absorption?

Thank in advance

K.

[Ashish Khemka]

Please see if the following link helps:

Flow resistivity estimation from practical absorption coefficients of fibrous absorbers - ScienceDirect

Regards Ashish Khemka

[kasparek1]

Thanks for the paper. It can help with finding value of flow resistivity, but it still doesn't answer me why does it have such a small impact to absorption coefficient.

Thank you anyway
Have a nice day
K.

[Sheldon Imaoka]

Please refer to the Theory Reference in the Mechanical APDL documentation. Specifically, in Section 8.3.5.2.2. "Delany-Bazley and Miki Models", you will see the equations, and the term is (f/sigma), where sigma is the fluid resistivity. So this depends a lot on the frequency of excitation since we are taking the ratio (f/sigma). Note in the bottom of that section, it lists the working range for the Delany-Bazley model for 0.01 < (f/sigma) < 1. Is your (f/sigma) ratio beyond that proposed working range?
Regards Sheldon

[kasparek1]

thank you for your kind reply.
I know that this model depends on frequency of acoustic signal. The range of my analysis is 500-2000 Hz with 150 Hz steps, Fluid Resistivity is 30 000 kg/s*m^3. So the (f/sigma) range of this analysis is between 0,017 and 0,07 which means that delany-bazley model should work. Unfortunetaly It doesn't look like it works, because the peak-to-peak value (which has main influence on absorption coefficient according to ISO 10534-1 norm) of SPL inside the impedance tube is still too big and increasing Fluid Resistivity (while im still in range where DB model should work) doesn't help.
I tried to make a simple model to see if these models work. The model consists of two tubes filled with air and there is an absoprtion specimen between them. There is an excitation at one end and radiation boudnary at the second end. My goal was to evaluate the SPL behind the specimen (in an outlet tube) while I change the Fluid Resistivity of the specimen. The value of SPL in the outlet tube got lower any time I increased Fluid Resistivity (and other way around), which means that the model works fine. Unfortunately it doesn't look like working in case of closed impedance tube, which is my problem.
If you have any ideas why, please let me know.

Have a nice day
K

[Sheldon Imaoka]

For your boundary conditions, did you put a radiation boundary on both ends of the open impedance tube (including excitation end)? Likewise, for the closed impedance tube, did you specify the radiation boundary condition on the same location as the excitation? Also, how did you specify excitation - was it acoustic pressure or velocity?
You don't want to put excitation as pressure constraint since you would be prescribing total pressure, not incident pressure, so use excitation like mass source or surface velocity instead, as those methods are not constraining the total pressure to a specific value. Also, you need an absorption boundary condition like radiation boundary condition in the excitation, too. This is so that any reflected waves do not bounce back. If you do not put a radiation boundary condition at the excitation location, then reflected waves will continue to bounce back since the reflected waves will hit a 'rigid wall' at the excitation location.
Regards Sheldon

[kasparek1]

In the case of closed impedance tube (model that simulates experiment I performed on real impedance tube) I set excitation as Surface Velocity and on the same face I set Radiation Boundary, just as you descirbed. The other end is reflecting waves back.
In the case of open tube (one for testing absorption models) I put excitation on one end (as a Surface Velocity) and Radiation Boundary on both ends.
Have a nice day
K.

[Sheldon Imaoka]

How are you calculating the absorption coefficient?
Regards Sheldon

[kasparek1]

I calculate absorption coefficient according to ISO 10534-1 norm. This norm defines process of experiment with an impedance tube. According to this norm, you have to find first (starting as near to specimen as possible) minimum and following maximum of SPL inside the tube. After that you are able to calculate absorption coefficient with following formula:
where α is absorption coefficient of specimen inside the tube and ΔL is difference between minimum and following maximum of SPL inside the tube.
Have a nice day K.

[Sheldon Imaoka]

Thanks for your response.
The wavelength for 500-2000 Hz is between ~0.7m and ~0.2m for air. From your original post, it seemed that you were looking at 500 Hz. What is the length of your model? Is it about the length of the wavelength? If it is too short, that may be causing the problem. For higher frequencies, do you get better correlation, or is the correlation bad for all frequencies (500 - 2000 Hz)?
Also, just curious, but what is the thickness of the region of the absorption material? Do you have more than 1 element through the thickness of the absorption material?
Lastly, what kind of results do you get if you put a lower fluid resistivity, such as 1,000 kg / s * m^3? Do you see expected results? In your original post, the value of 100,000 is quite high (and outside range of applicability for Delany-Bazley model), so to examine the results of fluid resistivity, comparing values of 30,000 with 10,000 and 1,000 at 500 Hz (use a single frequency for testing) may be better to understand the response.
Regards Sheldon

[kasparek1]

thank you for reply and for trying to find the problem in my analysis.
To answer all your questions:
1. the length of the tube is circa 2.5 meters. So even the wave with the lowest frequency (the longest wave) is still short enough to be captured by this geometry. I dont have problem with positions of maximum and minimum of SPL inside the tube, these are fitted very well, the difference between ansys results and experimental results are not bigger than few milimeters. The only problem are values of SPL minimum. The value of SPL maximum depends mainly on the source magnitude, which I measured and it fits lets say kinda fine. The problem is with the sharp fall of SPL in the minimum -> see picture below.
The problem is not dependent on frequency, it occurs in every frequency I performed experiment for and performed ansys analysis for (which is 500 - 2000 Hz with 150 Hz steps). The diffenrence between experiment and ansys data is sometimes lower, and sometimes higher, but it is still there in every frequency and it doesn't look like its frequency dependent.
2. The thickness of absopriton material is different with every material, but it goes from 10 mm to 40 mm. In every case I have at least 5 elements through specimen thickness.
3. When I have put low fluid resistivity (1000 kg/sm^3 as you suggest for example), the problem unfortunately still occurs. It occurs even if I turn off the Delany-Bazley completely or even when I tried the Miki model. I tried to change all the material charatecteristics of the specimen material and even of the air inside the tube, but none of them seem to have influence on this sharp falls of SPL in its minimum (of course speed of sound and density has influence, but I cant put unrealistic values). The highest value I tried (100 000 kg/sm^3) was of course just out of curiosity. I just wanted to find which material property has influence on this behavior.
Thank you and have a nice day K.

[Sheldon Imaoka]

Thanks for your explanation.
If I understand correctly, with the closed tube case, you have standing waves. So if you have a standing wave, you get a point of zero pressure - your node may not be exactly zero, but that is why the SPL dips so much. For example, plot pressure (not SPL), and you should see +/- peak and a point of zero pressure.
I'm not familiar with ISO 10534-1, but maybe the equation and measuring method is not suitable for a numerical model? Numerically, if you have a standing wave, you'll get a point of zero pressure. (Open tube does not have standing wave, so you should see constant SPL for an open tube case, for example.)
Regards Sheldon