| To simulate the cluster formation in dense two-phase flow, a multi-lattice actual trajectory (MLAT) model is developed. The actual inter-particle collision and particle motion are treated by a Lagrangian trajectory model with three sets of lattices to reduce computation time. It paves a way for the simulation of dense gas-solid flow.Parameters and methods used for quantitative assessment of cluster formation in dense gas-solid flow are systematically summarized: collision frequency is used to estimate the extent of particle concentration; the standard deviation of particle volume fractions is used to assess the flow nonuniformity; correlation coefficient of the cluster patterns is defined to quantify the flow comparability; distribution of particle numbers and frequency distributions of particle volume fraction are used for flow details; the proportion of particle numbers in dense regions and the proportion of areas in dilute regions are used for special flow parts.Using the MLAT model, numerical simulation of two-dimensional dense gas-solid flow in a square domain is carried out for visualizing the process of cluster formation. Results show that the inter-particle collision and the non-uniform distribution of the gas velocity are the definitive factors for cluster formation process. Reduction of particle restitution coefficient and increase of original particle volume fraction enhance cluster formation. Particles always tend to concentrate to the areas where the gas velocity is relatively low by means of inter-particle collision.The MLAT model is used to simulate dense gas-particle flow in a vertical channel. Numerical simulations compare very well with previous simulated and experimental data: cluster formation and downward motion near the wall are successfully predicted, and time averaged particle volume fraction and velocity on a cross section show quantitative agreement with previous results. It is shown that the inter-particle collision and the gas velocity profile are the essential factors for cluster formation near the walls, and the gravitation of particles and the particle-wall collision are minor factor. Increase of width of the channel and reduction of particle diameter enhance cluster formation near the wall.A dummy particle model based on the MLAT method is developed. Compared with the simulated results by the MLAT model, the computation time is largely reduced, and the predicted particle velocity profile shows quantitative agreement and the particle distribution profile shows qualitative agreement. Therefore, it forms a foundation for the numerical simulation of large-scale dense two-phase flow under complex flow conditions. |