Markov-Chain-Based Statistic Model for Predicting Particle Movement in Circulating Fluidized Bed Risers

To increase the calculation speed of the computational fluid dynamics (CFD)-based simulation for the gas–solid flow in fluidized beds, a Markov chain model (MCM) was developed to simulate the particle movement in a two-dimensional (2D) circulating fluidized bed (CFB) riser. As a statistic model, the MCM takes the results obtained from a CFD–discrete element method (DEM) as samples for calculating transition probability matrixes of particle movement. The transition probability matrixes can be directly used to describe the macroscopic regularities of particle movement and further used to simulate the particle motion combined with the Monte Carlo method. Particle distribution snapshots, residence time distribution (RTD), and mixing obtained from both MCM and CFD-DEM are compared. The results indicate that the MCM offers a computational speed that is approximately 100 times faster than that of the CFD-DEM. The discrepancy in the mean particle residence time, as computed by the two models, is under 2%. Furthermore, the MCM provides an accurate depiction of time-averaged particle motion. In sum, the MCM can well describe the time-averaged particle mixing compared to the CFD-DEM.