Discrete-velocity simulations of high-speed flows based on binary gas mixture kinetic models

Abstract

Many high-speed flows of engineering and scientific importance involve gas mixtures. Accounting for the species diffusion in such flows is essential when strong species gradients and temperature gradients occur. The domain of possible applications includes hypersonic rarefied gases, chemical reacting flows and plasmas. Kinetic models for multicomponent gases have been considered since the original BGK model was formulated. However, BGK-derived models pose a number of difficulties, e.g. avoiding negative density and temperatures. A distinct challenge of the BGK approximation lies in the number of correct transport coefficients recovered in the continuum limit. Two new kinetic models- a Shakhov-based model and an ES-based model- were recently introduced. Both methods are capable of modelling a binary mixture of monoatomic gases and account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The main advantage is the recovery of three correct transport coefficients in the hydrodynamic limit and fixing the Prandtl number. The resulting models are implemented in a parallel multi-block discrete-velocity solver and applied to a range of test cases. This paper shows the solutions of the models for a variety of high-speed flows, obtained using the discrete-velocity method. The models are first validated against known results for normal shocks, showing good agreement for species density and temperature profiles. The models are evaluated for more demanding test cases involving flows under different conditions around a circular cylinder. A detailed comparison with DSMC results demonstrates promising results from both kinetic models.