Rotational Temperature in an Underexpanded Jet

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Abstract
The axial rotational temperature distribution in an underexpanded nitrogen jet emitted from a sonic orifice has been investigated. The expansion is from room temperature and the gas possesses negligible vibrational energy. The observed difference between the rotational temperature measured with an electronbeam probe and the isentropic value can be described by a rotational relaxation analysis. The governing flow equations were integrated numerically by the classical fourth-order Runge-Kutta method. The rotational relaxation time developed by Lordi using Wang Chang and Uhlenbeck's formal kinetic theory and Parker's molecular model was employed. Both the easy and difficult energy transfer cases were investigated and the easy case was shown to underestimate nonequilibrium affects. The numerical solutions were very sensitive to the separation between the repulsive force centers, for both energy transfer cases. The rotational temperature distributions obtained in this study are in general agreement with existing experimental data for nitrogen.