Wednesday, October 8, 2014

New Set-Up at Stanford Plasma Physics Lab

I started at Stanford as a freshman last fall, and amongst the tumult of beginning college, I was able to navigate my way into an internship at the Stanford Plasma Physics Lab (the SPPL, check them out here). I spent 10 weeks this past summer working in the lab, and one of the several things I did there was build a new experimental apparatus for continuing my high school water explosion project. My work there is far from finished, and I have yet to take data from the new apparatus I set up, but I thought it was about time to let you guys know what I've been up to!

My favorite part about working at the SPPL has been getting to talk with other bright, interested scientists and engineers about water explosions and the eyebrow-raising papers that have been published on them. In particular, my conversations with Professor Mark Cappelli, the head researcher for the SPPL, have been very helpful in shaping my experimental design. Cappelli is an expert in applied plasma physics, and has worked extensively with Hall-effect thrusters, surface plasmons, and coaxial plasma accelerators, among other technologies. He has offered much guidance in crafting my experiment design since I first approached him about studying water arc explosions in his lab last spring.

From my conversations with him about the nature of the water explosions and the resources available to the lab, I decided to pursue a different method for measuring the water explosions' energies: bomb calorimetry. Instead of the projectile-based methods for measuring explosion energy that Graneau et al. used in their experiments (Graneau et al., 2000), I opted to make more precise energy measurements by setting off the explosions in an insulated, closed calorimeter and measuring how much energy the explosions deposit to the water as heat.

To produce the explosions, I used the capacitor banks and discharge circuit Professor Cappelli had set up for his high-current coaxial plasma gun. I worked with Keith Loebner and Ben Wang, two of Cappelli’s PhD students, to modify the system’s charging power supply, triggered spark gap switches, and safety interlocks to be compatible with my calorimeter.

One of the SPPL's four 52 uF, 20 kV capacitor banks. So far, I've just been using one of the four 14 uF caps shown here
My experiment is simple in principle: measure the energy going in to the chamber as electricity, measure the energy released from the explosion, and compare the two. I will measure the electrical energy delivered to the water as I did before: by monitoring the voltage across and the current through the chamber over the duration of the pulse event.

Measuring the energy released by the explosion will be more difficult. I currently have two different strategies for making this measurement.

Method 1: Closed Calorimeter
The first, and simplest, approach is to monitor the temperature of the water in the calorimeter over the duration of the explosion event. If the calorimeter is sufficiently well insulated, eventually all the various forms of energy (kinetic, thermal, chemical, etc.) released by the explosion will appear in the water as heat, and the water’s temperature will increase correspondingly over time. With this temperature-vs-time measurement, some heat loss modeling and a careful calibration of the chamber-water-system’s heat capacity, I can calculate the explosion’s energy straightforwardly.


The water explosion calorimeter, as of August 2014.

View of the inner chamber, with electrodes visible

I designed and machined the calorimeter myself in the lab’s machine shop. The brass piece mounted through the top permits thermistor and thermocouple measurements of the water’s temperature while still allowing the chamber to hold pressure.

Method 2: shock wave time-of-flight measurements
I may also be able to calculate the energy released in the water explosion indirectly by measuring the speed of the shockwave the explosion produces. In the late 1940s, Geoffrey Taylor derived an elegant expression for the energy released in an intense explosion involving only the shock front’s speed, the surrounding medium’s density, and the surrounding medium’s specific heat ratio (Taylor, 1950; Sedov, 1959). Taylor used his equations to calculate the energy released in the first atomic explosion in New Mexico based on images of the shock wave it created. I'm hoping to use Taylor's equations similarly, but on a water explosion instead of an atomic bomb.

Unfortunately, Taylor’s method relies on a self-similar solution to the fluid equations that is valid only for an ideal gas, and not for a medium like water without a polytropic equation of state. Last summer I attempted to reconcile Taylor’s methods with a couple different equations of state for water. I was able to make some progress, but it is unclear if my approach will pan out in the end.

To measure the shock wave’s speed in water, I will use either a high-speed Schlieren camera or an array of lasers and photodetectors to image the density gradient produced by the shock.

It is also possible that the shock wave will propagate out through the water and calorimeter and into the surrounding air. I could then use an array of microphones or other pressure transducers to measure the shock wave’s speed in air and apply Taylor’s methods directly. The hurdle with this approach is understanding the shock front’s behavior as it transitions between different media.

I will attempt to implement Method 2 only if Method 1 does not satisfactorily yield the desired energy measurements.

I've applied for one of Stanford's $1500 undergraduate research grants to support my continued work on my water explosion project throughout the school year. At the time of my writing this, I have yet to hear back from on high whether or not my application has been accepted. If I get the money, I'll be able to start working in the lab again within the end of the year. If not, I might have to wait until next summer to start up work on the project again. Either way, you'll be hearing back from me before too long!

Before I sign off, I'll leave you with a few other pictures of things around the lab this summer.

My initial prototype of the calorimeter. As you can see, I didn't make the walls quite thick enough. These water explosions are forces to be reckoned with!

My prototype of the thermistor amplifier circuit for measuring the temperature of the water in the calorimeter.
My ad-hoc power supply control unit and discharge triggering circuit

As an end note, I'd like to acknowledge a number of people at the SPPL whose help was invaluable this summer. Thanks to Keith Loebner and Ben Wang for their guidance and supervision, Mike Carter for his tutelage in the machine shop, and Mark Cappelli for his thoughtful feedback and discussions.

References:
Graneau, P., Graneau, N., Hathaway, G., & Hull, R. (2000). Arc-liberated chemical energy exceeds electrical input energy. Journal of Plasma Physics63, 115-128.

Sedov, L. (1959). Similarity and Dimensional Methods in Mechanics. Academic Press. New York, NY.
Taylor, G. (1950). The formation of a blast wave by a very intense explosion: I. Theoretical discussion. Proceedings of the Royal Society of London, 159-174.

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