Gas mixtures are important for many practical applications. Extending kinetic model equations of the Bhatnagar-Gross-Krook (BGK) type from a single-species gas to a multi-species gas mixture presents a number of significant challenges. First, obtaining the correct species diffusions, viscous stresses as well as heat conduction in the continuum limit requires a careful design of the collision terms in the kinetic equations. Secondly, the derived model collision terms need to guarantee positivity of the macroscopic fields. In the present work, two new kinetic models are introduced and compared: an approach based on the Shakhov kinetic model and an approach involving an anisotropic Gaussian equilibrium function. The two new models are capable of modelling a binary mixture of monoatomic gases, with updated definitions for the relaxation parameters and target species velocities and temperature. Both methods account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The key contribution of the models is the exact recovery of the Fick, Newton and Fourier laws in the continuum limit, while preserving positive temperature fields and crucial properties of the Boltzmann equation. The profile of a normal shock wave is inspected under various flow conditions to numerically validate the two models. The results show improvement upon comparison with a model, which has two correct transport coefficients, and demonstrate the ability to reliably model inert gas mixtures.
Practical applications involve flows that often have more than one constituent. Therefore, the capability to model a gas mixture flow is important. Extending kinetic model equations of the Bhatnagar–Gross–Krook type from a single-species gas to multi-species gas mixtures presents a number of important challenges. This challenge is further pronounced when diatomic gas mixtures are considered due to the addition of internal energy modes. In this paper, a novel diatomic binary mixture model with separate translational, rotational, and vibrational temperatures is derived. The species drift-velocity and diffusion are considered by introducing separate species velocities and accounting for their relationship. The derivation is detailed as a logical build-up with a multi-step approach from a diatomic model for a single gas, known in the literature. Transport properties are obtained through the Chapman–Enskog type expansion. The diatomic mixture model is numerically evaluated for a gas mixture of nitrogen and oxygen. The model is validated against Monte Carlo results for normal shocks, showing good agreement for species density and temperature profiles. A parametric study demonstrates the variation in flow properties for different Mach numbers, vibrational collision numbers, and concentrations. Interesting results for the mixture properties are shown when the physics of the flow is discussed in greater detail. The effect of the different levels of vibrational excitation in the different species emphasizes the importance of modeling the flow as a mixture. The newly introduced diatomic gas mixture model demonstrates promising computational results for relevant applications.
The formulation of computationally efficient methods describing gas mixtures at kinetic level suitable for demanding aerospace applications presents significant challenges. In this work, we contribute a gas-kinetic scheme for binary gas mixtures in which the kinetic model is capable of recovering, in the continuum limit, the correct heat transfer, mixture viscosity as well as species diffusion. The model accounts for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The main goal is to derive a numerically
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.
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