Lattice Boltzmann Models of Xe, Xe+, Xe++, e- Flow Through Ion Thruster Optics
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The lattice-Boltzmann method (LBM) is applied to modeling the flow in electric propulsion (EP) systems such as ion thrusters. Specifically investigated are issues that affect thruster operation like the back-flow of ions that can erode the optics and reduce engine life. Historically, the transport of mass, momentum, energy, subatomic particles, etc. and the complex multi-scale physics involved, have been modeled using Direct Simulation Monte Carlo (DSMC). While DSMC has achieved great success in EP models, its connection to Boltzmann s equation for the molecular velocity distribution function and recent developments in LBM suggest an alternate mesoscale model using LBM. To model an EP system with LBM, the Boltzmann equation is coupled with an electric field as tf + -f + q(E/m)-f = Q(f, f),E = -,02= e ffd - rho;0 where is the electrostatic potential that yields the electric field E, m is the mass of a molecule, q is the associated charge, and rho;0 is the charge density due to oppositely charged species that are not necessarily explicitly simulated. The typical EP number densities imply Knudsen numbers (Kn) that can be lower than the Kn 0.1 limit of the usual LBM but not necessarily near the optics. Also, EP systems have been modeled with Q(f, f) = 0 i.e., no collision as in a collision-less plasma driven by the electric field, and linear BGK-type collisions for large numbers of particles. This same linear form occurs in a model of charge exchange collision (CEX) between beam ions and neutral gas that can produce slow ions that can impact thruster grid surfaces. The linear collisions may be modeled via Q(f, f) = (n, T)(f0 - f) where (n, T) = 4nkT/irm and T = m(< v2> - < v >2)/3k These forms are amenable to modeling with LBM. The simulations are compared to similar DSMC and experimental results Copyright 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
