Direct simulation Monte Carlo study of rotational nonequilibrium in shock wave and spherical expansion of nitrogen using classical trajectory calculations

Abstract

The rotational nonequilibrium in a normal shock wave and in a steady spherical expansion is studied for nitrogen using the direct simulation Monte Carlo method coupled with classical trajectory calculations. The intermolecular potential for nitrogen is taken as an accurate potential energy surface constructed by van der Avoird et al. [J. Chem. Phys. 84, 1629 (1986)] and readjusted by Cappelletti et al. [Mol. Phys. 93, 485 (1998)]. The shock wave results are compared with the rotational distribution and the number density and rotational temperature profiles measured by Robben and Talbot [Phys. Fluids 9, 653 (1966)]. The agreement is generally good except at extremely low upstream temperatures, where the classical-mechanical treatment may be inadequate. The spherical expansion results are compared with the rotational distribution and the number density and rotational temperature profiles measured by Marrone [Phys. Fluids 10, 521 (1967)] and Coe et al. [Phys. Fluids 23, 706 (1980)] along the axis of a low density free jet expansion. It is shown that the rotational distribution gradually departs from a Boltzmann distribution farther downstream with an overpopulation in the higher rotational levels, in good agreement with the measured spectral data except near the orifice, where the spherical source expansion analogy may be inapplicable. The rotational temperature obtained by a Boltzmann fit at the low rotational levels or defined as the mean rotational energy agrees satisfactorily, except near the orifice, with the experimental rotational temperatures determined from the spectral data.