Stabilization of the Burnett equations and application to hypersonicflows

Abstract

Numerical solutions of the Burnett for hypersonic flow at high altitudes in the continuum transitional regime were not possible except for some one-dimensional flows. It is shown from both analytical investigation and numerical computations that the Burnett are unstable to disturbances of small wavelengths. This fundamental instability arises in numerical computations when the grid spacing is less than the order of a mean free path and precludes Burnett flowfield computations above a certain maximum altitude for any given aerospace vehicle. A new set of termed the augmented Burnett equations has been developed and shown to be stable both by a linearized stability analysis and by direct numerical computations for one-dimensional and plane-two-dimensional flows. The latter represents the first known Burnett solutions for two-dimensional hypersonic flow over blunt leading edges. The comparison of these solutions with the conventional Navier-Stokes solutions reveals that the difference is small in low-altitude low-speed flows but significant in high-altitude hypersonic flows.