The analysis and simulation of gases expanding from sources such as rocket nozzles into vacuum, or the effects plumes from these sources create when they interact with solid surfaces, present a considerable challenge to the scientific and engineering communities. As a plume expands into vacuum, density levels, and hence collision rates, decrease rapidly by many orders of magnitude. The main difficulty lies in accurately describing a flow field extending from continuum flow at the nozzle exit, through the transition regime, and reaching free molecule behavior within a relatively short distance downstream. For thrusters, flow at the nozzle exit is usually characterized by high exit velocities and relatively high Mach numbers. Even in regions where significant intermolecular collision rates occur, relative velocity levels are low, and little thermal scattering occurs normal to the mainly radial streamlines. Such observations lead one to consider describing the expansion under certain circumstances using free molecule theory.
Under such assumptions, a model was created by solving the Boltzmann equation for a point source with a Lambertian thermal velocity distribution superimposed on a bulk, convective exit velocity. To develop this model, the collisionless Boltzmann equation had been solved for a distribution function due to a directionally constrained point source meant to describe directed flow from a nozzle exit over 2 steradians centered on the source normal. The spatial constraint may be overcome by using local conditions from a starting surface that captures the expansion of gases expanding around a nozzle lip.
One novel feature of this plume model is its transient flow capability. When considering model validation, it is difficult to recreate highly rarefied conditions using ground-based facilities due to demands for sufficient pumping capacity to eliminate the influence of vacuum chamber surface scattering on a thruster plume expansion. However, it is possible to compare limiting cases of such models to data collected during carefully executed experiments employing molecular beams and pulsed laser ablation phenomena.
Over time, ongoing validation activities such as the examples included in the previous section have led to increasing confidence in using the molecular flow plume model as a tool to describe an unusual variety of plume interaction issues, particularly for NASA Goddard Space Flight Center spacecraft missions.
This work was done by Michael Woronowicz of SGT, Inc. for Goddard Space Flight Center. GSC-17021-1