The superquadric equation is typically used to mathematically describe nonspherical particles and construct particle shapes with different surface sharpness and aspect ratios.However,nonspherical elements constructed ...The superquadric equation is typically used to mathematically describe nonspherical particles and construct particle shapes with different surface sharpness and aspect ratios.However,nonspherical elements constructed using the superquadric equation are strictly convex,limiting their engineering application.In this study,a multi-superquadric model based on a superquadric equation is developed.The model combines several superquadric elements that can be used to construct concave and convex particle shapes.Four tests are performed to examine the applicability of the multi-superquadric approach.The first involves a comparison of theoretical results for a single spherocylinder impacting a flat wall.The second involves the formation of a nonspherical granular bed.The third investigates the effects of the particle shape on the hopper discharge and angle of repose.The final test evaluates the mixing behaviors of granular materials within a horizontally rotating drum.These tests demonstrate the applicability of the multi-superquadric approach to nonspherical granular systems.Furthermore,the effects of particle shape on the packing density,discharge rate,angle of repose,and Lacey mixing index are discussed.Results indicate that concave particles have a lower packing density,flow rate,and mixing rate and higher angles of repose than convex particles.Interlocking of elements becomes more pronounced for concave particles and results in local cluster structures,thereby enhancing the stability of granular systems and limiting sliding or rotation between nonspherical particles.展开更多
Non-spherical particles are widely present in industrial production,and significantly affect the macro and micro characteristics of granular materials.Although the superquadric equation can be used to construct non-sp...Non-spherical particles are widely present in industrial production,and significantly affect the macro and micro characteristics of granular materials.Although the superquadric equation can be used to construct non-spherical particles,its disadvantage is that the particle shape is geometrically symmetric and strictly convex.In this study,two composed approaches are used to describe geometrically asymmetric and concave particle shapes,including a multi-superquadric model and a poly-superquadric model.The multi-superquadric model is a combination of several superquadric elements,and can construct concave and geometrically asymmetric particle shapes.The poly-superquadric model is a combination of eight one-eighth superquadric elements,and can construct convex and geometrically asymmetric particle shapes.Both composed models are based on superquadric equations,and Newton’s iterative method is used to calculate the contact force between the elements.Furthermore,superquadric elements,multi-superquadric elements,and poly-superquadric elements are applied for the formation of complex granular beds,and the influences of particle shape on the packing fraction can be successfully captured by the proposed models.展开更多
基金This study is financially supported by the National Key Researchand Development Program of China(Grant Nos.2018YFA0605902,2016YFC1401505 and 2016YFC1402706)the National NaturalScience Foundation of China(Grant Nos.11872136 and 11772085).
文摘The superquadric equation is typically used to mathematically describe nonspherical particles and construct particle shapes with different surface sharpness and aspect ratios.However,nonspherical elements constructed using the superquadric equation are strictly convex,limiting their engineering application.In this study,a multi-superquadric model based on a superquadric equation is developed.The model combines several superquadric elements that can be used to construct concave and convex particle shapes.Four tests are performed to examine the applicability of the multi-superquadric approach.The first involves a comparison of theoretical results for a single spherocylinder impacting a flat wall.The second involves the formation of a nonspherical granular bed.The third investigates the effects of the particle shape on the hopper discharge and angle of repose.The final test evaluates the mixing behaviors of granular materials within a horizontally rotating drum.These tests demonstrate the applicability of the multi-superquadric approach to nonspherical granular systems.Furthermore,the effects of particle shape on the packing density,discharge rate,angle of repose,and Lacey mixing index are discussed.Results indicate that concave particles have a lower packing density,flow rate,and mixing rate and higher angles of repose than convex particles.Interlocking of elements becomes more pronounced for concave particles and results in local cluster structures,thereby enhancing the stability of granular systems and limiting sliding or rotation between nonspherical particles.
基金financially supported by the National Key Research and Development Program of China(Grants2018YFA0605902,2016YFC1401505,and 2016YFC1402706)the National Natural Science Foundation of China(Grants 11872136and 11772085)the Fundamental Research Funds for the Central Universities(Grants DUT19GJ206 and DUT19ZD207)。
文摘Non-spherical particles are widely present in industrial production,and significantly affect the macro and micro characteristics of granular materials.Although the superquadric equation can be used to construct non-spherical particles,its disadvantage is that the particle shape is geometrically symmetric and strictly convex.In this study,two composed approaches are used to describe geometrically asymmetric and concave particle shapes,including a multi-superquadric model and a poly-superquadric model.The multi-superquadric model is a combination of several superquadric elements,and can construct concave and geometrically asymmetric particle shapes.The poly-superquadric model is a combination of eight one-eighth superquadric elements,and can construct convex and geometrically asymmetric particle shapes.Both composed models are based on superquadric equations,and Newton’s iterative method is used to calculate the contact force between the elements.Furthermore,superquadric elements,multi-superquadric elements,and poly-superquadric elements are applied for the formation of complex granular beds,and the influences of particle shape on the packing fraction can be successfully captured by the proposed models.
