Computation of rarefied hypersonic flows using modified form of conventional Burnett equations

This paper describes the computations of hypersonic flows in a diatomic gas in rotational nonequilibrium using a newly developed simplified set of Burnett equations designated as simplified conventional Burnett 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 basedon the conventional Burnett equations for hypersonic flowsby neglecting higher-order terms that are inversely proportional to the Mach number. This set of simplified conventional Burnett equations is linearly stable for small disturbancesin contrasttothe conventional Burnett equations that suffer from Bobylev instability. To simulate the rotational nonequilibrium effect in a diatomic gas, both the Navier-Stokes and the simplified conventional Burnett equations are modified by including a rotational nonequilibrium relaxation model. The flow variables (densityandtranslational and rotational temperature) for one-dimensional shock structure, flow pastatwo-dimensional cylinder, and an axisymmetric bicone in nitrogen are computed using both the simplified conventional Burnett and Navier-Stokes equations in the continuum-transition regime and are compared with the direct simulation Monte Carlo results. Simplified conventional Burnett calculations are in close agreement with the direct simulation Monte Carlo results at high Mach numbers.