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Proceedings Paper

Algorithm for studying inversion in gas dynamic systems
Author(s): T. E. Horton
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Paper Abstract

Solutions of the binary master equations for the state populations in an expanding gas are facilitated by the use of a flow similarity variable. This similarity variable accounts for the density and velocity variation associated with a gas dynamic expansion and can be expressed as a function of the local Mach number, the stagnation conditions, and a nozzle geometry parameter. With the similarity variable, the master equations are transformed into a form which is independent of the nozzle shape and similar to those for a non-flow system. This simplification facilitates both numerical solutions and closed form approximations for populations in nozzle flow. With solutions in terms of the similarity variable the design conditions leading to a population inversion can be presented as a simple algorithm. An illustration is presented for a wedge nozzle expansion. The conditions for inversion are determined by the expansion Mach number at a stagnation pressure. With the algorithm these conditions for a range of nozzle sizes are presented as an inversion criteria curve.

Paper Details

Date Published: 4 May 1993
PDF: 4 pages
Proc. SPIE 1810, 9th International Symposium on Gas Flow and Chemical Lasers, (4 May 1993); doi: 10.1117/12.144657
Show Author Affiliations
T. E. Horton, Univ. of Mississippi (United States)

Published in SPIE Proceedings Vol. 1810:
9th International Symposium on Gas Flow and Chemical Lasers
Costas Fotakis; Costas Kalpouzos; Theodore G. Papazoglou, Editor(s)

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