Heterogeneous detonation in gas-particle mixtures with full pattern flows: Numerical model, method, and verification

In practical engineering applications, heterogeneous detonation in gas-combustible particle mixtures often involves distinct flow regimes, including dilute, dense, dense-to-dilute transition patterns. This study aims to develop a numerical model and method suitable for heterogeneous detonation simulation of gas-particle systems with full pattern flows. First, based on the Eulerian-Lagrangian framework that is more consistent with particle dynamics, a numerical model for gas-particle detonation with four-way coupling of gas-particle and particle-particle interactions is established. For the gas phase, the governing equations are constructed on continuous Eulerian meshes, accounting for the effects of particle combustion, volume fraction, and interphase coupling. The dispersed particle phase is modeled in Lagrangian coordinates, with collisions among particles in the cloud resolved via a coarse-grained discrete element model. Particularly, the effect of mass transfer caused by particle combustion on the interphase momentum and energy coupling is carefully considered. Afterwards, a multiphase HLL/HLLC solver with high-order reconstruction scheme is employed to discretize the nozzling terms and convective fluxes of gas equations. To quickly solve for temperatures of the gas and particles (considering phase transition latent heat and realistic heat capacity), an efficient algorithm based on the Newtonian iterative method is proposed. To ensure the fidelity of two-phase interaction simulations in strong discontinuity and dense particle flow scenarios, an improved interphase coupling strategy with second-order accuracy is developed. Finally, a series of numerical verification and validation tests are conducted, covering key sub-models, interphase coupling algorithms, inert gas-particle flows and heterogeneous detonation across various flow patterns. Comparisons with theoretical solutions and experimental data demonstrate that the proposed numerical models and methods can accurately predict interphase coupling, shock interaction with particle clouds of different volume loadings, characteristic parameters of dilute heterogeneous detonation, and evolution of two-phase detonation in dense conditions.