Theoretical and numerical studies of plume flows in vacuum chambers

This thesis consists of three parts: a study of facility effects on the background flow in large vacuum chambers; an analytical study of free molecular flows out of exits with different shape representing thruster plumes; and particle simulations of plasma plume flows from a cluster of Hall thrusters.; The first part of this thesis discusses the facility effects on large vacuum chambers, which is quite important to the Electric Propulsion (EP) community. Based on the fact that the background flows in large vacuum chambers equipped with cryogenic pumps are free molecular, five models are proposed to study the average background pressure and flow velocity and their relation to several facility effects, such as pump sticking coefficient, pump size, wall and pump temperatures, and chamber sidewall length. The analysis are based on the mass flow rates into and out of the chamber, the fluxes along two directions and various number density relations at various stations such as chamber ends and vacuum pumps.; The second part of the thesis develops several sets of analytical solutions to free molecular flows out of exits with different shapes. It is demonstrated that the plasma plume flows expanding into vacuum can be studied analytically as a combination of several free molecular flows, if the electric field and collision effects are omitted. There exists a unique relation of velocity and positions.; The last part of the thesis presents several three-dimensional particle simulations of plasma plume flows from a cluster of Hall thrusters. A detailed electron fluid model is used to solve important electron properties such as plasma potential and electron temperature. A finite element solver is developed to solve the equations of the electron properties on unstructured meshes. Several important implementation issues are discussed and one significant finding is that the class of particle-to-node weighting schemes based on areas or volumes on an unstructured mesh is inaccurate. This problem is not obvious if the Boltzmann relation is used to determine the plasma potential: however, if the detailed electron model is used to calculate the plasma potential, especially when ionization effects are included in the simulation, then the class of allocation schemes yields invalid results. The other significant treatment that distinguishes these simulations is that background static particles representing the backpressure are assigned velocities sampled from a distribution that takes into consideration the facilities effects. (Abstract shortened by UMI.)...