It’s time to make some final choices on the engine design. Lacking time and money to build every engine design our imagination conceives, we’ve run a number of simulations. Each simulation is a thin 2D slice of an engine – much like a slice in a loaf of bread – presented with a burst of plasma. Each simulation takes about a week on an NVidia Tesla GPU and we use a combination of Processing and R to visualize the results. Sorry, we can’t share the visualizations yet as doing so would affect a patent.
Many scenarios were tried in short runs and the seven most promising were simulated in detail. Technically, an additional “null” case was also simulated. In an ion engine, the “null” case is a simple thermal expansion of the plasma without any other effects other than exit nozzle geometry. This basic thermal expansion produced much lower momentum than the 7 designs simulated. That brings up a key performance indicator of an engine: the total momentum it imparts to the spacecraft. As a pulsed design, each pulse imparts a bit of momentum. The time average of this momentum is the engine’s average force. Let’s look at the total momentum for each design choice:
Total momentum imparted by each engine design.
Interpreting this is pretty interesting. Models D and F go strongly negative, very strongly negative. This makes them unacceptable. Why? Negative momentum means movement backwards, towards the exhaust plume – an unsustainable situation. This leaves models C and E. Both converge to the same total momentum, though E converges sooner because it exhausts its plasma burst sooner.
There is another source of data to help make the choice. We can also look at the momentum on the charged plates within the engine. These plates contribute their momentum to the above totals.
Momentum due to charged plates
Model C’s charged plates have negative momentum, meaning it is gradually eroding the overall momentum gain from the engine. Model E gives the same total momentum and never backtracks on its gains, making model E the chosen design.
Now, just what can we expect from a model E engine? It creates 1.75e-9 kg m/s of momentum every 3.52e-5 seconds. From the simulation, each slice is 1e-4 meters (0.1 mm) and the total engine has 100 of these slices. The engine’s force is then (1.75e-9 / 3.52e-5) * 100 = 4.97e-5 N, or about 5 mN. A 5 mN thrust is quite reasonable, and seems quite nice in a 1 cm engine.
What affect will this engine have upon the satellite? We’ll mount the engine 2.5 cm off center of the long axis so that it’s thrust will spin the satellite. The spin rate will increase with each plasma burst and eventually get out of the noise band of gyroscope sensors. (We don’t use accelerometers to sense thrust because it is so low that we fear any accelerometer sensitive enough to detect the thrust would not survive the shock of launch.) The 750 gram TubeSat’s angular momentum vectors [Ixx, Iyy, Izz] are estimated to be [7.5938E-04, 1.3878E-03, 1.3878E-03]. This makes the angular momentum change per pulse to be (1.75e-9 * 100 * 0.025) / 1.3878E-03 = 3.15e-6 radians/second/pulse = 1.81e-4 degrees/second/pulse. So, in 5,535 pulses the satellite will have added 1 degree/second to its rotation. Its forward velocity will have also changed by ((1.75e-9 * 100) / 0.750) * 5535 = 1.29e-3 m/s. With 75 mm^3 of fuel available, we estimate 4958 degrees/second for rotation and 6.4 m/s final delta V. (Clearly, 4958 degrees/second is far too fast, but that’s another post.)
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