Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into in the modified lattice Boltzmann equation, which could recovery the Navier-Stokes equations, including contribution of chemical reaction, via the Chapman-Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium. The internal kinetic energies in different degrees freedoms around the detonation front do not coincide due to the fluid viscosity. They show the maximum difference at the inflexion point where the pressure has the largest spatial derivative. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.