Utility computable modeling of a Boltzmann model equation for bimolecular chemical reactions and numerical application

Abstract

A Boltzmann model equation (kinetic model) involving the chemical reaction of a multicomponent gaseous mixture is derived based on Groppi's work [“A Bhatnagar–Gross–Krook-type approach for chemically reacting gas mixtures,” Phys. Fluids 16, 4273 (2004)], in which the relaxation parameters of elastic collision frequency for rigid elastic spheres are obtained based on the collision term, and the pivotal collision frequency of the chemical reaction is deduced from the chemical reaction rate that is determined by the direct simulation Monte Carlo (DSMC) method. This kinetic model is shown to be conservative, and the H theorem for an endothermic reaction is proven. In the framework of the gas-kinetic unified algorithm, the discrete velocity method, finite volume method, and implicit scheme are applied to solve the proposed kinetic model by introducing a suitable boundary condition at the wall surface. For hypersonic flows around a cylinder, the proposed kinetic model and the corresponding numerical methods are verified for both endothermic and exothermic reactions by comparison of the model's results with results from the DSMC method. The different influences of endothermic and exothermic reactions are also given. Finally, the proposed kinetic model is also used to simulate an exothermic reaction-driven flow in a square cavity.