Abstract:
How to investigate high-speed reactive flows effectively is an important open issue in the fields of aerospace, energy, and power engineering, etc. For this purpose, a simplified discrete Boltzmann model (DBM) is proposed for supersonic compressible reactive flows. Based on the kinetic method, this model uses a unified discrete Boltzmann equation to describe the evolution of reactive flows. The chemical reaction is naturally coupled with multi-physics fields through the reaction term on the right-hand side of the discrete Boltzmann equation. A two-dimensional nine-velocity model is proposed with the velocities divided into three groups, and the speed of each group is independently adjustable. To describe extra degrees of freedom corresponding to molecular rotation and/or oscillation, three groups of independently adjustable parameters are employed to describe the internal energies in extra degrees of freedom. Therefore, DBM is suitable for reactive flows with adjustable specific heat ratios. In addition, both the equilibrium discrete distribution functions and reaction terms satisfy nine independent moment relations, and their expressions can be obtained by the matrix inversion method. Through Chapman-Enskog multiscale analysis, it is proved that DBM not only can recover the reactive Euler equations in the continuum limit, but also has the capability of describing some thermodynamic nonequilibrium behaviors. Finally, three benchmarks, including the homogeneous reaction, Sod tube, and detonation wave, are employed to verify and validate DBM. It turns out that results of DBM agree well with theoretical solutions.