Comparison of continuum and particle simulations of expanding rarefied flows

Comparisons of Navier-Stokes solutions and particle simulations for a simple two-dimensional model problem at a succession of altitudes are performed in order to assess the importance of rarefaction effects on the base flow region. In addition, an attempt is made to include 'Burnett-type' extensions to the Navier-Stokes constitutive relations. The model geometry consists of a simple blunted wedge with a 0.425 meter nose radius, a 70 deg cone half angle, a 1.7 meter base length, and a rounded shoulder. The working gas is monatomic with a molecular weight and viscosity similar to air and was chosen to focus the study on the continuum and particle methodologies rather than the implementation of thermo-chemical modeling. Three cases are investigated, all at Mach 29, with densities corresponding to altitudes of 92 km, 99 km, and 105 km. At the lowest altitude, Navier-Stokes solutions agree well with particle simulations. At the higher altitudes, the Navier-Stokes equations become less accurate. In particular, the Navier-Stokes equations and particle method predict substantially different flow turning angle in the wake near the after body. Attempts to achieve steady continuum solutions including 'Burnett-type' terms failed. Further research is required to determine whether the boundary conditions, the equations themselves, or other unknown causes led to this failure.