Numerical Simulation of Three-Dimensional Augmented Burnett Equations for Hypersonic Flow

Abstract

For computation of hypersonic e owe elds about space vehicles in low Earth orbits, where the local Knudsen numbers Kn lie in the continuum-transition regime, a set of extended three-dimensional hydrodynamic equations is required that is more accurate than the Navier ‐Stokes equations and computationally more efe cient than the direct simulation Monte Carlo (DSMC) computations. The three-dimensional augmented Burnett equations are derived from the Chapman ‐Enskog expansion of the Boltzmann equation to O(Kn 2) and adding the augmented terms (linear third-order super Burnett terms with coefe cients determined from linearized stability analysis to ensure stability of the augmented Burnett equations to small wavelength disturbances ). The three-dimensional augmentedBurnettequationsareappliedtocomputethehypersonicblunt-bodye owsforvariousrangeofKnudsen numbers (0:0884 < ‐ Kn < ‐ 0:227) and Mach numbers (10 < ‐ M < ‐ 25:3). The computational results are compared with the Navier ‐Stokes solutions, the existing augmented Burnett solutions, and the available DSMC results. The comparisons show that the difference between the Navier ‐Stokes and the augmented Burnett solutions is very small (less than 3% for the shock layer thickness ) at Knudsen numbers less than 0.01; the difference becomes signie cant as the Knudsen number increases. The comparisons also show that the augmented Burnett solutions are signie cantly closer to the DSMC results for the temperature distributions in the continuum-transition regime than the Navier ‐Stokes calculations.