Modeling Steady-State Gas Expansion from a Spherical Surface Into a Vacuum

Abstract

The direct statistical modeling method is used to study spherically-symmetric gas expansion into a vacuum, following evaporation or injection from a spherical surface, over the Knudsen number range from 10−5 to ∞. It is established that, as in the case of cylindrically-symmetric expansion, the sonic transition at Kn < 10−2 occurs at a distance from the source surface far exceeding the thickness of the zone of initial nonequilibrium relaxation. As the Knudsen number decreases, the number of molecular free paths between this zone and the M = 1 surface increases, i.e., the sonic surface is established in the continuum gas flow. With reference to the example of transonic region analysis, it is shown that the description of the flow with local Knudsen numbers Knl < 10−2 by numerical solution of the complete Navier-Stokes equations is in good agreement with the solution of the Boltzmann equation by the direct statistical modeling method. The conservatism of the relative values of the flow parameters at the M = l surface at low Kn makes it possible to suggest this surface as a flow boundary in formulating the problem and calculating the radial expansion of a viscous gas within the framework of the Navier-Stokes equations.