Rarefaction effect analysis of supersonic flows based on reduced Boltzmann equations

Rarefaction effect on supersonic flow fields in the transition from near continuum to near free-molecule flow is analyzed numerically. The model Boltzmann equations, which are derived from the transformations of reduced distribution function and discrete velocity ordinate together, are solved through using an implicit flux-corrected second-order upwind TVD (total variation diminishing) scheme. Gas molecule diffuse reflection model is implemented on the wall. For five cases, namely that Knudsen numbers are 0.001, 0.01, 0.1, 1.0 and 10 respectively, the argon gas flows around a two-dimensional cylinder are simulated numerically, and different wave systems and wake structures are investigated. The calculated total drag coefficients can agree qualitatively well with the experimental data. Flow details obtained by employing Shakov kinetic model for collision term are a little better than by modified BGK model. Rarefaction effect tends to make supersonic flows move smoothly, and to enlarge the influence domain of cylinder.