Modeling of nitrogen and oxygen gas mixture with a novel diatomic kinetic model

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.