A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is ...A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid modeling method, dynamic equations of the system, which include all states（before, during, and after the collision）are obtained. Simulation results of a concrete example are compared with the results obtained from two other models： a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.展开更多
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
基金supported by the National Natural Science Foundation of China(Grants 11272155,11132007,and11502113)the 333 Project of Jiangsu Province in China(Grant BRA2011172)the Fundamental Research Funds for Central Universities(Grant 30920130112009)
文摘A flexible beam with large overall rotating motion impacting with a rigid slope is studied in this paper. The tangential friction force caused by the oblique impact is analyzed. The tangential motion of the system is divided into a stick state and a slip state. The contact constraint model and Coulomb friction model are used respectively to deal with the two states. Based on this hybrid modeling method, dynamic equations of the system, which include all states（before, during, and after the collision）are obtained. Simulation results of a concrete example are compared with the results obtained from two other models： a nontangential friction model and a modified Coulomb model. Differences in the results from the three models are discussed. The tangential friction force cannot be ignored when an oblique impact occurs. In addition, the results obtained from the model proposed in this paper are more consistent with real movement.
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.
