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.
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 [...]