A three-dimensional discrete Boltzmann model for steady and unsteady detonation

Abstract

A discrete Boltzmann model (DBM) for compressible reactive flows, with a two-step reaction scheme is presented. The discrete velocity model is modified using the characteristic points of the platonic solids, which leads to excellent spatial symmetry. In the continuum limit, the reactive Navier-Stokes (NS) equations are recovered. This DBM is validated by classic one-dimensional (1D) Riemann problems and 1D detonation. The numerical results agree well with the analytical solutions. Using this model, we simulate three-dimensional (3D) detonations in a rectangular tube. The characteristic features of the 3D detonation are well captured. Two types of experimentally observed detonation modes, namely rectangular mode and diagonal mode are reproduced by the DBM. It is found that the final structures of the detonation are related to the initial perturbation and the width of the tube. The similarity between the diagonal mode and the rectangular in-phase mode is obtained. The predictions of the DBM are in excellent qualitative agreement with the previous studies. Our simulation results indicate a great potential of the DBM to simulate complex reactive flows.