Title: “Acoustic black holes in airfoils”
 
NRC Postdoctoral Fellow, Acoustics Division, Code 7165,
U S Naval Research Laboratory
4555 Overlook Ave SW,
Washington, DC 20375
 
Caleb F. Sieck – caleb.sieck@nrl.navy.mil
Matthew D. Guild – matthew.guild@nrl.navy.mil
Charles A. Rohde – charles.rohde@nrl.navy.mil
Acoustics Division, Code 7165,
U S Naval Research Laboratory
4555 Overlook Ave SW,
Washington, DC 20375
 
Popular version of paper 2aSA9 – “Incorporating acoustic black holes in hydrofoils”
Presented at 11.30 am on December 3, 2019
178th ASA Meeting, San Diego, California.
 
Most of us who have flown in an airplane can recall how bumpy it gets when there is ‘turbulence’. It is scary to watch wings bend the way they do, even though they are designed to withstand such bumps. However, as one can imagine, these vibrations are not desirable and affect the aircraft’s longevity and performance. When we slice an aircraft wing somewhere in between (as highlighted in the sketch below), we find that it has a unique shape, called an ‘airfoil’. This is the shape that makes the plane fly, and also, as a result, bears the brunt of turbulent air and those vibrations.
 
 
In 1988, Mironov pointed out that vibrations that strike on one end of a beam may never make it through if the other end is tapered gradually enough all the way down to a ‘zero thickness’. In other words, those vibrations get trapped or absorbed inside forever – also known as the ‘acoustic black hole’ effect. In reality, since it isn’t possible to make an edge have zero thickness, scientists have figured out that sticking some damping material near the edge (similar to foam or rubber on furniture feet) works almost as well.
 
In this study, we explore a way this effect could help reduce those airfoil vibrations. For the airplane, only the shape on the outside of the airfoil matters, not the inside. We take advantage of this fact and show that it is possible to design an airfoil with these black holes inside, without changing either the outside shape or the total weight.
 
Shown below are three of the designs that we tested. We fix the mass of the structure and damping that we use, and redistribute them between the three cases. The first case has uniformly spread structure and damping, to represent a ‘standard’ design. We’re basically trying to improve on this. The second case has a single black hole inside along with appropriate damping, while the third case has three.
 
 
We use some of the latest in 3d printing technology to create these complex designs. For testing them, we vibrate all three airfoils on their front edge in the same way and measure how vibrations move through the airfoil length all the way to the back edge. Shown below are the vibration levels that we measured at the rear edge over three frequency ranges. Note, lower the vibration, the better.
 
When compared with the uniform case, the sample with one black hole does 10-15% in the low and mid frequency ranges, and ~30% better in the high frequency range. The three-black hole case does almost similar (~1% worse in fact) for the low frequency range, but performs 50-65% better for higher frequencies. These results are promising and motivate us to expand our research in this direction.
 
Work sponsored by the Office of Naval Research.
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