Upon reading a bit more, I’ve noticed that sources mention using an elliptical mirror-which reflects waves from one focus to the other-instead of a parabola. This appears to mostly work, and I’ve looked into getting an elliptical chamber fabricated. The magnitude of the rarefaction behind the wavefront worries me a bit for some applications, but everything will change as more details are included.

The chamber will be open a bit before the focus so the waves can be applied to objects. The cords for the spark gap will go in the narrower hole in the back. I plan on doing more detailed simulation work before finalizing the chamber design and putting in an order.

So, as a sanity check I decided to simulate focusing the wave from an underwater arc. The simulation setup is very simplified-a cell is chosen to have 10X the pressure of the surrounding cells in a parabolic geometry. I’ve tried modeling this with cavitatingFoam and sonicFoam. sonicFoam only models the equation of state for gases which is not ideal.

And it looks like this will not work because of the different times to the focal point for different paths. This would not be a problem with an acoustic lens, so I will be working more on that instead.

The polymesh format used by OpenFOAM requires that for a polyhedron’s face, the points are listed in order definining the circumference of a face, and such that the normal (from the right hand rule) is to the cell with a higher index or outside of the domain. It has been inconvenient to construct and maintain the correct point ordering, so I have switched to doing it in post. It took a while to think of a good algorithm so I’m writing it down. This requires some level of ‘niceness’ to the face but that’s true of CFD in general too.

The first point in an unordered list can be used unchanged. A vector normal to the plane the points roughly lie on (faces can be skew) can be calculated with the cross product of the vectors between one point and any other two points. The rest of the points can be sorted by the angle from the first point to their projection into the normal plane.

For example, given 5 points indexed 0-4, the 0th point will not change. A normal vector to the plane can be calculated with 3-0 cross 3-2 or any other pair. The center of mass of the face is just the average coordinate of {0…4}. The points can be sorted by the angle from their projection into the plane to 0 through the center of mass.

The current was destroying the mechanical relay I was using, but a friend gave me some SKT 55/06D Thyristors. After a small trigger charge (~V, ~100mA) thyristors act as diodes, so they can be used as switches which stay open until the current through them stops and they reset. These are rated up to 700V, which gives roughly half the stored energy that the capacitor is capable of. The steady state current limit is only ~100 but the surge current is rated to 1300A, so they should be fine for this application. I’ve been concerned about the difference in shot quality, especially with wasted energy by the arcing on the relay, so I thought I would compare the two.

To measure current in the main line, I made a Rogowski coil. Changing currents induce a voltage in the coil, which can be measured in the usual manner. I tried calibrating the readings to the output of a signal generator, which gave a reading of 1.5E-6V/AHz. Unfortunately I was only able to calibrate it at higher frequencies, greater than 1MHz, as otherwise the signal was too small with the test current I could produce. The output voltage should correspond to dI/dt, but in this case it also had a phase lag of ~pi/2 behind that. Also the output was nonlinear in frequency, increasing faster than linearly above 5MHz. Obviously, this could be done better, and there are proper ways to compensate for the inductance of the coil and so on. There is also an amusing tradeoff, which is that without too much more efficiency, the coil would reach voltages beyond what is safe to probe with my oscilloscope, while with the efficiency currently, the voltages are low enough it is hard to test.

Below are three measurements of voltage on the coil and on the main line, two for the relay and one for the thyristor. The thyristor has much more consistent shots.

In all cases, which the swtich closes there is a momentary current increase seen on the Rogowski coil (hard to see). Then comes a ~0.5 ms period of roughly constant voltage, before the saltwater breaks down. I assume that the water in the gap heats up during this period. After this, the current spikes as resistance of the spark gap drops to around zero, and the resistance of the system is set by the 1 Ohm current limiting resistor. Finally, at around 150V the current is extinguished.

In terms of diagnostics, it would be nice to get a peizoelectric pressure sensor, but I am also concerned about difficulties due to frequency response with something like that.

The color also appears to change depending on the shot power, so I believe it would be interesting to look at spectra. I got a diffraction grating but haven’t taken any data.

I have realized that a better way to deposit energy into the water would be to limit the current with an inductor instead of a resistor, and hook up my other thyristor across the capactitor reverse to the starting polarization. This would allow the current to flow in the loop longer, dissipated only by the spark gap and the voltage drop across the thyristors. I’m not sure this would be better for pressure waves/shock wave generation, as the initial breakdown might be the main contributor for that. The speed of sound in water is ~1km/s, so during the ms discharge of the capacitor sound has had the time to travel a full meter, which is much larger than the system. The time for the initial breakdown is 1us, giving 1mm, about the size of the spark gap. This is very rough logic-it may be that the slower timescale is fine if enough power is delivered.

While arcs are cool on their own, I’m interested in using them for hydroacoustics. One of the ways to treat kidney stones uses focused ultrasound to break the stone while inside the patients body, and some of the devices use underwater spark gaps for the wave source. Electrohydrolic forming uses the pressure waves to force metal into molds. I doubt this is possible, but it would be really neat to be able to have shock sintering of materials with this sort of setup.

Lenses for sound work the same way light lenses work, with refraction according to Snells law. Unlike light, where lens materials have slower speed of transmission than air, most lens materials will have faster speeds of sound than water, so the geometry of converging and diverging lenses are reversed. The ratio of reflected to transmitted power is given by the difference in impedances, and shortly, plastics should mostly allow sound to be transmitted, making them useful as lenses, while metals mostly reflect sound, making them suitable for mirrors.

I’ve been playing with underwater arcs recently. This will be more of a photodump than a writeup. I’m using a 1kV capacitor with ~600J stored energy. I’m also using saltwater because the breakdown voltage is lower.