| Popis: |
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. |
