A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, an...A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method （DEM） simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.展开更多
Few studies have investigated scale-up of the residence-time distribution （RTD） of particles in bubbling fluidized beds （BFBs） with continuous particle flow. Two approaches were investigated in this study： first,...Few studies have investigated scale-up of the residence-time distribution （RTD） of particles in bubbling fluidized beds （BFBs） with continuous particle flow. Two approaches were investigated in this study： first, using well-known scaling laws that require changes in particle properties and gas velocity; second, using a simple approach keeping the same particles and gas velocity for different beds. Our theoretical analysis indicates it is possible to obtain similar RTDs in different BFBs with scaling laws if the plug-flow residence time （tpiug） is changed as m^0.5, where m is the scaling ratio of the bed; however, neither approach can ensure similar RTDs if tplug is kept invariant. To investigate RTD variations using two approaches without changing tplug, we performed experiments in three BFBs. The derivatives dE（θ）/dθ （where E（θ） is the dimensionless RTD density function and θ is the dimensionless time） in the early stage of the RTDs always varied with m 1, which was attributed to the fact that the particle movement in the early stage were mainly subject to dispersion. Using the simple approach, we obtained similar RTDs by separately treating the RTDs in the early and post-stages. This approach guarantees RTD similarity and provides basic rules for designing BFBs.展开更多
基金The National Science Foundation of China(No.51276036,51306035)the Fundamental Research Funds for the Central Universities(No.KYLX_0114)
文摘A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method （DEM） simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.
文摘Few studies have investigated scale-up of the residence-time distribution （RTD） of particles in bubbling fluidized beds （BFBs） with continuous particle flow. Two approaches were investigated in this study： first, using well-known scaling laws that require changes in particle properties and gas velocity; second, using a simple approach keeping the same particles and gas velocity for different beds. Our theoretical analysis indicates it is possible to obtain similar RTDs in different BFBs with scaling laws if the plug-flow residence time （tpiug） is changed as m^0.5, where m is the scaling ratio of the bed; however, neither approach can ensure similar RTDs if tplug is kept invariant. To investigate RTD variations using two approaches without changing tplug, we performed experiments in three BFBs. The derivatives dE（θ）/dθ （where E（θ） is the dimensionless RTD density function and θ is the dimensionless time） in the early stage of the RTDs always varied with m 1, which was attributed to the fact that the particle movement in the early stage were mainly subject to dispersion. Using the simple approach, we obtained similar RTDs by separately treating the RTDs in the early and post-stages. This approach guarantees RTD similarity and provides basic rules for designing BFBs.
