A Shakhov-based Bhatnagar-Gross-Krook model for polyatomic molecules and for atomic as well as polyatomic mixtures

Abstract

The implementation of the Shakhov Bhatnagar-Gross-Krook (SBGK) method in the open-source particle code PICLas is extended for modeling of polyatomic molecules, as well as mixtures including atoms and molecules, while accounting for non-equilibrium in the internal degrees of freedom. The conservation properties of the model are shown and the model parameter for the Prandtl number is derived. In order to determine the viscosity and thermal conductivity of gas mixtures, the first approximation of the transport properties using collision integrals is employed. The model is verified with simulation test cases of a supersonic Couette flow and a hypersonic flow around a 70° blunted cone with different flow parameters and gas compositions. The results are compared to the Direct Simulation Monte Carlo (DSMC) method as well as the Ellipsoidal Statistical BGK (ESBGK) method to assess the accuracy of the model, where overall good agreement is achieved. In particular, the proposed SBGK model captures the shock in front of the 70° blunted cone more precisely than the ESBGK model.

Figures (14)

• Figure 1: Stationary translational temperature profile of the N$_2$ Couette flow.
• Figure 2: Stationary translational temperature profile of the Couette flow with Ar--He mixture.
• Figure 3: Stationary translational temperature profile of the Couette flow with $\mathrm{N_2}$--N mixture.
• Figure 4: Geometry of the $70^\circ$ blunted cone. $R_{\mathrm{b}}=25.0mm$, $R_{\mathrm{c}}=1.25mm$, $R_{\mathrm{j}}=2.08mm$, $R_{\mathrm{n}}=12.5mm$, $R_{\mathrm{s}}=6.25mm$. $S$ denotes the arc length along the surface.
• Figure 5: 70° blunted cone, Case 1: Velocity in $x$ direction (dashed) and number density (solid) along stagnation streamline using DSMC, ESBGK and proposed SBGK.