The modelling of granular flow using the particle-in-cell method

[摘要] Granular flow occurs in a broad spectrum of industrial applications thatrange from separation and mixing in the pharmaceutical industry, to grindingand crushing, blasting, stockpile construction, flow in and from hoppers,silos, bins, and conveyer belts, agriculture, mining and earthmoving.Two totally different approaches of modelling granular flow are the DiscreteElement Method (DEM) and continuum methods such as Finite ElementMethods (FEM). Continuum methods can be divided into nonpolar orclassic continuum methods and polar continuum methods. Large displacementsare usually present during granular flow which, without remeshing,cannot be solved with standard finite element methods due to severe meshdistortion. The Particle-in-Cell (PIC) method, which is a so-called meshlessmethod, eliminates this problem since all the state variables are traced bymaterial points moving through a fixed mesh.The main goal of this research was to model the flow of noncohesivegranular material in front of flat bulldozer blades and into excavator bucketsusing a continuum method. A PIC code was developed to model these processesunder plane strain conditions. A contact model was used to modelCoulomb friction between the material and the bucket/blade. Analyticalsolutions, published numerical and experimental results were used to validatethe contact model and to demonstrate the code's ability to model largedisplacements and deformations.The ability of both DEM and PIC to predict the forces acting on the bladeand bucket and the material flow patterns were demonstrated. Shear bandsthat develop during the flow of material were investigated. As part of thePIC analyses, a comparison between classic continuum and polar continuum(Cosserat) results were made. This includes mesh size and orientationdependency, flow patterns and the forces acting on the blade and thebucket.It is concluded that the interaction of buckets and blades with granularmaterials can successfully be modelled with PIC. In the cases conductedhere, the nonpolar continuum was more accurate than the polar continuum,but the polar continuum results were less dependent on the meshsize. The next step would be to apply this technology to solve industrialproblems.

[发布机构] Stellenbosch University