Column Number Density Expressions Through M = 0 and M = 1 Point Source Plumes Along Any Straight Path

Providers of payloads carried aboard the International Space Station must conduct analyses to demonstrate that any planned gaseous venting events generate no more than a certain level of material that may interfere with optical measurements from other experiments or payloads located nearby. This requirement is expressed in terms of a maximum column number density (CND). Depending on the level of rarefaction, such venting may be characterized by effusion for low flow rates, or by a sonic distribution at higher levels. Since the relative locations of other sensitive payloads are often unknown because they may refer to future projects, this requirement becomes a search for the maximum CND along any path.In another application, certain astronomical observations make use of CND to estimate light attenuation from a distant star through gaseous plumes, such as the Fermi Bubbles emanating from the vicinity of the black hole at the center of our Milky Way galaxy, in order to infer the amount of material being expelled via those plumes.This paper presents analytical CND expressions developed for general straight paths based upon a free molecule point source model for steady effusive flow and for a distribution fitted to model flows from a sonic orifice. Among other things, in this Mach number range it is demonstrated that the maximum CND from a distant location occurs along the path parallel to the source plane that intersects the plume axis. For effusive flows this value is exactly twice the CND found along the ray originating from that point of intersection and extending to infinity along the plumes axis. For sonic plumes this ratio is reduced to about 43.