A multiple translational temperature gas dynamics model

Within shock waves, the translational motion of the gas is more energetic in the direction perpendicular to the shock than in the direction parallel to the shock. To represent this translational nonequilibrium, new continuum conservation equations are developed. These equations are derived by solving the Boltzmann equation with a first-order Chapman-Enskog expansion of an anisotropic velocity distribution function. This results in a gas model with anisotropic pressure, temperature, and speed of sound. The governing equations are solved numerically for one-dimensional steady shock waves in a Maxwellian gas. The numerical results are compared to those obtained using the direct simulation Monte Carlo method. The new continuum model captures many of the features of shock waves. In particular, this paper finds that translational nonequilibrium is present at all Mach numbers. For Mach numbers greater than 1.5, the perpendicular temperature overshoots the post-shock temperature. At the point where this temperature reaches a maximum, the model predicts that for any shock wave, the square of the perpendicular-direction Mach number is one-third; this is substantiated by the DSMC results.