Three-dimensional multiple-relaxation-time discrete Boltzmann model of compressible reactive flows with nonequilibrium effects

Based on the kinetic theory, a three-dimensional multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for nonequilibrium compressible reactive flows where both the Prandtl number and specific heat ratio are freely adjustable. There are 30 kinetic moments of the discrete distribution functions, and an efficient three-dimensional thirty-velocity model is utilized. Through the Chapman–Enskog analysis, the reactive Navier–Stokes equations can be recovered from the DBM. Unlike existing lattice Boltzmann models for reactive flows, the hydrodynamic and thermodynamic fields are fully coupled in the DBM to simulate combustion in subsonic, supersonic, and potentially hypersonic flows. In addition, both hydrodynamic and thermodynamic nonequilibrium effects can be obtained and quantified handily in the evolution of the discrete Boltzmann equation. Several well-known benchmarks are adopted to validate the model, including chemical reactions in the free falling process, thermal Couette flow, one-dimensional steady or unsteady detonation, and a three-dimensional spherical explosion in an enclosed cube. It is shown that the proposed DBM has the capability to simulate both subsonic and supersonic fluid flows with or without chemical reactions.