ACCURACY OF THE BURNETT EQUATIONS FOR HYPERSONIC REAL-GAS FLOWS

The Burnett equations have long been proposed as an alternative to the Navier-Stokes equations for flows exhibiting translational nonequilibrium. However, Burnett solutions for hypersonic flows have until recently been unattainable. Burnett solutions of normal shock-wave structure are presented for four gases: two purely theoretical gases, Maxwellian and hard-sphere, and two real gases, argon and nitrogen. For the theoretical gases, solutions are obtained for Mach numbers from 1.1 to 50, and, for the real gases, solutions range from Mach 1.1 to Mach 11. These Burnett solutions are compared with Direct Simulation Monte Carlo (DSMC) solutions, with Navier-Stokes solutions, and, for the real gases, with experimental data. Experimental data and DSMC solutions represent the assumed correct solution, while Burnett and Navier-Stokes solutions represent continuum approximations. For the three monatomic gases, Burnett solutions are significantly more accurate than Navier-Stokes solutions. For nitrogen, fundamentally different solutions are obtained since rotational nonequilibrium must be included. For this diatomic case, the Burnett solutions also are more accurate than the Navier-Stokes solutions, however, best agreement between DSMC, experiment, and Burnett require different values of rotational collision number in the DSMC and Burnett simulations. The Burnett equations thus represent a significant improvement over Navier-Stokes equations for flows exhibiting translational nonequilibrium.