Collision numbers in expanding conical nozzle flow fields

The cumulative elastic collision number has been calculated for the supersonic region of isentropic, continuum conical nozzle flow fields for gaseous species characterized by the specific heat ratios Gamma = 5/3, 7/5, and 9/7. The cumulative collision number was determined as a function of Mach number and axial distance parameter Cap x tan 0, the latter specialized to the nozzle half-angles 0 = 5, 10.5, and 15 deg. The calculations were extended to study the effects of the type of intermolecular potential interaction on the cumulative collision number. Specifically, the interaction potentials investigated included the attractive inverse -r6, the Lennard-Jones 12:6, the Stockmayer and Krieger 12:6:3 potentials, and the hard-sphere interaction. The results have been presented in nondimensional form in terms of the characteristic well-depth energies and ranges of the intermolecular potentials, and the range of the nondimensional reservoir temperature studied was 2 < t0 < 10, which corresponds to the range of approximately 200 to 1000 K for typical nonpolar molecular species. The results obtained for the inverse -r potential using a close-encounter collision model allowed simple scaling of the results with reservoir temperature which was not possible for the two- and three-term potentials. Quantitative comparisons of the results are presented.