Abstract

Numerical simulations of granular flows based on the Distinct Element Method (DEM) commonly use spherical particles for ease of contact mechanics calculations and for having fast contact searching algorithms. However, for irregularly shaped particles, rotation is not only affected by friction but also by mechanical interlocking (Cleary, 2010). Only tangential forces lead to the rotation of spherical particles, whereas for irregularly shaped particles, rotation can be as a result of both normal and tangential contact forces (Favier et al., 2001). Mechanical interlocking of irrregularly shaped particles can be simulated in DEM by (i) limiting the rolling friction of spherical particles (Morgan, 2004), (ii) using overlapping spheres (Favier et al., 2001), (iii) using polyhydra (Potapov and Campbell, 1997). The first two method have been critically evaluated for the flow of corn seeds and spray-dried powders. A comparison is made of the estimated solid fraction and the tangential and radial velocity distributions of the particles from DEM and those measured experimentally. The shapes of the corn seeds and spray-dried powders have been captured using X-Ray micro tomography, and ASG2013 software has been used to generate the coordinates of the overlapping spheres. It is shown that the approximation of particle shape is only critical for dense shearing flows. The use of polyhydra enables particle fracture to be simulated more realistically, but necessitates implementation of fracture mechanics to be predictive. In this paper the results of our evaluations are reported.

Abstract

The aim of this work is to present a new procedure for modelling industrial processes
that involve granular material flows, using a numerical model based on the Particle
Finite Element Method (PFEM). The numerical results herein presented show
the potential of this methodology when applied to different branches of industry.
Due to the phenomenological richness exhibited by granular materials, the present
work will exclusively focus on the modelling of cohesionless dense granular flows.

The numerical model is based on a continuum approach in the framework of
large-deformation plasticity theory. For the constitutive model, the yield function is
defined in the stress space by a Drucker-Prager yield surface characterized by two
constitutive parameters, the cohesion and the internal friction coefficient, and
equipped with a non-associative deviatoric flow rule. This plastic flow condition is
considered nearly incompressible, so the proposal is integrated in a u- p mixed
formulation with a stabilization of the pressure term via the Polynomial Pressure
Projection (PPP). In order to characterize the non-linear dependency on the shear
rate when flowing a visco-plastic regularization is proposed.

The numerical integration is developed within the Impl-Ex technique, which increases
the robustness and reduces the iteration number, compared with a typical
implicit integration scheme. The spatial discretization is addressed within the
framework of the PFEM which allows treating the large deformations and motions
associated to granular flows with minimal distortion of the involved finite element
meshes. Since the Delaunay triangulation and the reconnection process minimize
such distortion but do not ensure its elimination, a dynamic particle discretization of
the domain is proposed, regularizing, in this manner, the smoothness and particle
density of the mesh. Likewise, it is proposed a method that ensures conservation of
material or Lagrangian surfaces by means of a boundary constraint, avoiding in this
way, the geometric definition of the boundary through the classic -shape method.

For modelling the interaction between the confinement boundaries and granular
material, it is advocated for a method, based on the Contact Domain Method (CDM)
that allows coupling of both domains in terms of an intermediate region connecting
the potential contact surfaces by a domain of the same dimension than the contacting
bodies. The constitutive model for the contact domain is posed similarly to that for
the granular material, defining a correct representation of the wall friction angle.
In order to validate the numerical model, a comparison between experimental
results of the spreading of a granular mass on a horizontal plane tests, and finite
element predictions, is carried out. These sets of examples allow us validating the
model according to the prediction of the different kinematics conditions of granular
materials while spreading – from a stagnant condition, while the material is at rest,
to a transition to a granular flow, and back to a deposit profile.

The potential of the numerical method for the solution and optimization of industrial
granular flows problems is achieved by focusing on two specific industrial
applications in mining industry and pellet manufacturing: the silo discharge and the
calculation of the power draw in tumbling mills. Both examples are representative
when dealing with granular flows due to the presence of variations on the granular
material mechanical response.

Abstract

The main objective of this work lies in the development of a variational implicit Material Point Method (MPM), implemented in the open source Kratos Multiphysics framework. The ability of the MPM technique to solve large displacement and large deformation problems is widely recognised and its use ranges over many problems in industrial and civil engineering. In the current work the continuum based implicit MPM is applied to engineering applications, where granular material flow is involved.

For the resolution of the length and time scale of these particular problems, both continuum and discrete models are typically used. Even if discrete techniques predict more feasible results, nowadays, their use is limited to the investigation of element tests of particles, or to the simulation of reduced systems, not allowing to make important decisions in the analysis and design of granular processes. Some advantages of MPM over discrete methods are tested, such as, the ability to simulate granular flow at the large scale with acceptable computational cost and the capability to get information of stress and strain state in a more straightforward way.

The focus of this paper is a comparative study between an irreducible and a mixed formulation, both implemented in the MPM code, to assess the improvement in accuracy and reliability of the numerical results when the latter formulation is adopted.