Computation of 1-D shock structure in a gas in rotational non-equilibrium using a new set of simplified Burnett equations

Abstract

This paper describes the computations of hypersonic shock wave structure in a gas in rotational non-equilibrium using a newly developed simplified set of Burnett equations designated as Simplified Conventional Burnett (SCB) equations. Since the original formulation by Burnett, a number of variations to the original Burnett equations have been proposed and the differences among these variants and their merits/shortcomings have been described in the literature. A new variant is created based on the conventional Burnett equations for hypersonic flows by neglecting terms that are inversely proportional to the Mach number. This simplified set of conventional Burnett equations is linearly stable for small disturbances in contrast to the conventional Burnett equations which suffer from Bobylev instability. To simulate the rotational non-equilibrium effect in a diatomic gas, both the Navier-Stokes (NS) and the SCB equations are modified by including a rotational non-equilibrium relaxation model. The flow variables (density, translational and rotational temperature) in a typical 1-D shock at different Mach numbers (1.2, 5, and 10) in Nitrogen are computed using the SCB and NS equations and are compared with the DSMC results. SCB calculations are in close agreement with the DSMC results at high Mach numbers.