Focused Acoustic Shock Wave Device for Generating High Pressures

[BrandonBerchtold]

TL;DR Summary

What level of pressure magnification could a device such as the one shown in "Diagram.png" be capable of generating. Are there examples of similar devices, and if so, what sort of pressure magnification are they capable of?

I am trying to come up with a design for a device that can generate very high and very brief waves of pressure directed at a 1 mm diameter target (shown as "E" in "Diagram.PNG") housed in a steel support structure "D". The idea is to accelerate hammer "A" towards anvil "B" in a vacuum tube. The hammer and anvil are both made of steel. Over the course of a couple microseconds, the anvil will stop the hammer while at the same time creating a sharp longitudinal pressure wave in the water directed towards the acoustic lens "C". The acoustic lens is made of steel and should focus the pressure waves to a point at the center of target "E". The steel would be precision ground in order to minimize aberrations in the lens surfaces.

Question: If the lens has a diameter of 100 mm, the pressure wave generated by the anvil has a peak pressure of 1 MPa, and the lens geometry is ground perfect to within a few microns of error, what sort of pressure magnification could be expected?

If the pressure wave is focused to a circle on the target with a diameter of 1 mm, would the pressure magnification be 10,000 times since the area difference between the target and the lens is 10,000X? Is the pressure wave peak pressure able to simply build up like that after being focused or will it become less sharp (i.e. spread out more in direction of travel) and have a peak pressure much less that 10,000 times the original pressure?

"Wave Spike.png" and "Focused Acoustic Lens.jpg" are similar examples of what I'd like to achieve, but in a different medium and scale."Wave Spike.png" []
"Focused Acoustic Lens" [https://discovery.kaust.edu.sa/en/article/235/focus-on-acoustic-lenses]

 

[Baluncore]

If the pressure wave is focused to a circle on the target with a diameter of 1 mm, would the pressure magnification be 10,000 times since the area difference between the target and the lens is 10,000X?

You must calculate based on the energy focus, not the pressure or the displacement.
I would expect pressure and proportional displacement, to both increase by a factor of only 100, making 10,000 times the energy density.

There is the problem of impedance matching the impulse in the water into the target. Target amplitude will be a function of acoustic impedance mismatch between water and target.

When the hammer hits the anvil, some energy will be reflected from the anvil-water interface back to the hammer. Again, that is a transmission line matching problem. The dimensions of the hammer and anvil will colour the spectrum of the transmitted energy.

If you used a narrow-band ultrasonic frequency you could use a quarter wave transformer coating on the lens. But for a broad-band impulse you need to match the acoustic impedance of the lens material to the water. While doing that you need to have a difference in velocity capable of making a lens.

Without a gas being heated by a pressure wave there can be no shock wave. Only a bandwidth limited step impulse can propagate in the water.