The simulation of the hollow cathode thruster has been broken down into 4 steps. Each step increases the level of detail of the simulation. This project deals with the simulation and visualization of step one.
In step one I am simulating the neutral flow of the particles inside of a hollow cathode thruster (HCT) and inside of a vacuum tank. The geometry of the thruster is hard coded into the program for now. I reduced the model to a neutral flow simulation, because the simulation simplifies greatly with the removal of the electric field.
When the fields are removed from the simulation the velocities of all of the particles remain constant until they hit a wall. So once the particle is injected into the simulation it moves along inside of the geometry. The algorithm that was used for the particle movement is the simplest one available known as the leap frog method:
New X Position = Old X Position + Velocity in the X Direction * Time Step
Essentially each particle jumps to its new location in the simulation. Once the particle comes in contact with a wall the velocities change and the leap frog method continues. The change in velocity is due to energy exchange with the wall and the fact that the particle must bounce back from the ball. The fraction of energy transferred between the wall and the particle is known as an accommodation coefficient and are explained in further detail in another section.
Randomness is added to the simulation in the starting location of the neutral gas in the tank and in the cathode injection of the electrons. Randomness is also added to the initial velocities and the temperatures. Each one of these are randomized using a Maxwellian distribution, which is also explained in another section.
To visualize the results from the simulation a geometric model of the hollow cathode thruster had to be created. This was done using MSC.Patran 2001, but a better method would be to use 3D Studio Max since 3D Studio Max is CAD software. Tutorials on how to generate the hollow cathode thruster are available for both of the programs.
Step two in the project is to add in the collision modeling so that the particles can bump into one another. Without the collision modeling the xenon molecules cannot ionize and the thruster becomes a simple cold gas thruster. This will be done using Bird's Direct Simulation Monte Carlo method. The other addition to the simulation in this step is to remove the hard coding of the geometry. This will allow the geometry files created using 3D Studio Max or MSC.Patran 2001 to be loaded directly into the simulation as boundary conditions. This will greatly increase the versatility of the simulation.
Step three is to add in the electric field into the simulation. This requires a quick three dimensional field solver, or faster than the one I currently have in use. The field must be solved for at every time step and is very costly in CPU time, but essential to the simulation. The electric field is what makes the thruster better than a cold gas thruster.
The last step is to extend the level of detail in the simulation to match the real thing. This step includes adding things such as the ion optics, which is the grid at the end of the thruster through which the ions pass. This step will also include a neutralizer on the outside of the thruster to reduce the number of ions returning to the grid and degrading the lifetime of the thruster.