A MULTIPLE TRANSLATIONAL TEMPERATURE GAS-DYNAMICS MODEL

Within shack waves, the translational motion of the gas is more energe tic 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 a re derived by solving the Boltzmann equation with a first-order Chapma n-Enskog expansion of an anisotropic velocity distribution function. T his results in a gas model with anisotropic pressure, temperature, and speed of sound. The governing equations are solved numerically for on e-dimensional steady shock waves in a Maxwellian gas. The numerical re sults are compared to those obtained using the direct simulation Monte Carlo method. The new continuum model captures many of the features o f shock waves. In particular, this paper finds that translational none quilibrium is present at all Mach numbers. For Mach numbers greater th an 1.5, the perpendicular temperature overshoots the post-shock temper ature. At the point where this temperature reaches a maximum, the mode l predicts that for any shock wave, the square of the perpendicular-di rection Mach number is one-third; this is substantiated by the DSMC re sults.