Abstract
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.
Highlights
Most practical applications include flows involving gas mixtures, and in the vast majority of cases, these are not noble gases
Unlike atoms, are known to have rotational and vibrational DoFs. These extra degrees of freedom and the corresponding flow-field variables associated with the internal DoFs differ for each species in a diatomic gas mixture, which makes the modeling of a mixture of gases with internal degrees of freedom a complex task
The focus of this section is on the novel diatomic mixture model, while the properties and Navier– Stokes equations of models we used to build-up to it are summarized in Appendixes A–C
Summary
Most practical applications include flows involving gas mixtures, and in the vast majority of cases, these are not noble gases. A recent model, introduced by Klingenberg, Pirner, and Puppo,[32] is capable of modeling a binary gas mixture with internal degrees of freedom It demonstrates an extension from a single-species diatomic model,[33] which has a separate rotational relaxation applied to the macroscopic variables rather than the RHS of the governing equation. The other ES-based models for polyatomic gas mixtures have been detailed with a particular focus on chemically reactive gases.[34–36] These models do not model the internal energy in detail, e.g., with a multi-relaxation collision term or separate translational, rotational, and vibrational variables. It follows that a kinetic model for a binary mixture of diatomic gases, with separate translational, rotational, and vibrational temperatures for each species with accurate modeling of species diffusion effects, has not yet been demonstrated and numerically evaluated in the literature Providing such a detailed model derivation and numerical evaluation forms the main novelty of the present work.
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