Recently,we have extended the kinetic theory of granular flow (KTGF) to include friction between the spherical particles and tested it in rectangular geometries.In this study,the extended KTGF implemented in cylindric...Recently,we have extended the kinetic theory of granular flow (KTGF) to include friction between the spherical particles and tested it in rectangular geometries.In this study,the extended KTGF implemented in cylindrical coordinates is used to model the more-commonly employed cylindrical bubbling fluidized beds.Special attention is paid to the anti-symmetric part of the velocity gradient in the solids stress tensor.For verification of the implementation,a comparison of the present model in the limit of zero friction with the original (frictionless) KTGF model was made.Subsequently,simulations of bubbling fluidized beds of inelastic particles were performed using our extended KTGF and an effective KTGF model for inelastic particles of Jenkins and Zhang.The simulation results show good agreement for the time-averaged solids volume fraction distribution and solids circulation patterns.Finally,our model is validated by predicting the individual bubble behavior in dense bubbling fluidized beds containing different granular materials in a comparison with experimental data from Verma et al.(2014).The extended KTGF leads to an improved agreement with experimental bubble data.Compared to previous work (Yang et al.,2016b,2017c),and by introducing cylindrical coordinates,the current work demonstrates that the extended KTGF improves predictions for the temporal bubble behavior of cylindrical fluidized beds.展开更多
文摘Recently,we have extended the kinetic theory of granular flow (KTGF) to include friction between the spherical particles and tested it in rectangular geometries.In this study,the extended KTGF implemented in cylindrical coordinates is used to model the more-commonly employed cylindrical bubbling fluidized beds.Special attention is paid to the anti-symmetric part of the velocity gradient in the solids stress tensor.For verification of the implementation,a comparison of the present model in the limit of zero friction with the original (frictionless) KTGF model was made.Subsequently,simulations of bubbling fluidized beds of inelastic particles were performed using our extended KTGF and an effective KTGF model for inelastic particles of Jenkins and Zhang.The simulation results show good agreement for the time-averaged solids volume fraction distribution and solids circulation patterns.Finally,our model is validated by predicting the individual bubble behavior in dense bubbling fluidized beds containing different granular materials in a comparison with experimental data from Verma et al.(2014).The extended KTGF leads to an improved agreement with experimental bubble data.Compared to previous work (Yang et al.,2016b,2017c),and by introducing cylindrical coordinates,the current work demonstrates that the extended KTGF improves predictions for the temporal bubble behavior of cylindrical fluidized beds.
