Numerical evaluation of novel kinetic models for binary gas mixture flows

Abstract

Most flows of practical interest consist of mixture of gases. Therefore the capability to model a gas mixture flow is important. Kinetic models for multicomponent gases have been considered since the original Bhatnagar-Gross-Krook (BGK) model was formulated. BGK-derived models pose a number of difficulties, e.g. avoiding negative density and temperature(s). A distinct challenge of the BGK approximation lies in recovering correct transport coefficients in the continuum limit. Two new kinetic models for gas mixtures: a Shakhov-based model and an Ellipsoidal-Statistical (ES)-based model, were recently introduced. Both models 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 as a result having a correct Prandtl number for the mixture. The goal of this paper is to numerically validate the two new kinetic models for a range of high-speed flows and demonstrate their capabilities and limitations. The models are first validated against known results for normal shocks, showing good agreement for species density and temperature profiles. Moreover, the importance of the Prandtl number correction is demonstrated with the evaluation of the heat flux. A parametric study demonstrates the variation in flow properties for different mass ratios between species and for different Mach numbers. Finally, the models are evaluated for the flow around a circular cylinder. A detailed comparison with Monte Carlo results demonstrates promising results from both kinetic models.

The interaction of parallel and inclined planar rarefied sonic plumes—From free molecular to continuum regime

“…In the last decade, multiscale methods have been developed which give promising results at low computational effort for simple rarefied flows, such as the unified gas kinetic scheme, 46,47 discrete unified gas kinetic scheme (DUGKS), [48][49][50] kinetic relaxation models 51,52 and the general synthetic iterative scheme. 53 Still, the simultaneously ongoing improvements of its algorithm 54 and its inherent numerical stability keep direct simulation Monte Carlo (DSMC) 55 the method of choice for accurate predictions of complex rarefied flows.…”

A discrete unified gas-kinetic scheme for multi-species rarefied flows

“…Based on the AAP model, some numerical methods have been developed, such as the discrete velocity method (DVM) [13][14][15]. In the classical DVM, like the DSMC method, the numerical mesh size and time step are limited by the molecular mean free path and relaxation time, respectively, which makes them computationally expensive for flows involving continuum or near continuum regimes.…”

An Exact Dynamic Analysis Method for Shallow Sagged Cables

“…In the model proposed in Ref. [40,41], the three transport coefficients are recovered, but it is to be improved by incorporating the correct Soret and Dufour coefficients. As to polyatomic gas mixtures [42,43] or even reactive mixtures [44,45,46], much more relaxation rates of macroscopic variable need to be recovered, like the relaxation rates of internal energy (rotational and vibrational energy).…”