Granular Mixer#

This example simulates the packing and mixing of particles in a mixer with a pitched-blade impeller. It is recommended to visit DEM parameters for more detailed information on the concepts and physical meanings of the parameters in Lethe-DEM.

Features#

  • Solvers: lethe-particles

  • Floating mesh

  • GMSH grids

  • Bidispersed particles (same size and properties, but different types)

Files Used in This Example#

  • Parameter file: /examples/dem/3d-granular-mixer/granular-mixer.prm

Description of the Case#

This simulation consists of two stages: packing (0-0.5 s) and mixing (0.5-5 s) of particles. There are two types of particles in this simulation (bidispersed system), that are inserted on top of each other during the packing stage. The size and properties of the two particle types are the same, we only need to define two particle types to make the visualization easier during post-processing. At \(t=0.5\) s, the pitched-blade impeller starts rotating with an angular velocity of 6 rad/s and mixes the particles.

Parameter File#

Mesh#

The background mesh (mixer body) is created using deal.II subdivided_cylinder.

subsection mesh
  set type                = dealii
  set grid type           = subdivided_cylinder
  set grid arguments      = 2 : 0.05 : 0.055
  set initial refinement  = 3
end

Lagrangian Physical Properties#

As mentioned earlier, there are two types of particles with the same size and properties.

subsection lagrangian physical properties
  set g                                   = -9.81, 0.0, 0.0
  set number of particle types            = 2
  subsection particle type 0
    set size distribution type              = uniform
    set diameter                            = 0.0015
    set number of particles                 = 23500
    set density particles                   = 1500
    set young modulus particles               = 1e6
    set poisson ratio particles             = 0.5
    set restitution coefficient particles   = 0.5
    set friction coefficient particles      = 0.5
  end
  subsection particle type 1
    set size distribution type              = uniform
    set diameter                            = 0.0015
    set number of particles                 = 23500
    set density particles                   = 1500
    set young modulus particles             = 1e6
    set poisson ratio particles             = 0.5
    set restitution coefficient particles   = 0.5
    set friction coefficient particles      = 0.5
  end
  set young modulus wall                  = 1e6
  set poisson ratio wall                  = 0.5
  set restitution coefficient wall        = 0.5
  set friction coefficient wall           = 0.5
end

Solid Objects#

In this subsection, the floating meshes are defined. We can use deal.II or Gmsh to create the floating meshes. At the moment, solid objects in Lethe have to be defined using triangular (simplex) meshes. Only triangular 2D meshes of 3D surfaces in the lethe-particles solver are presently supported. Quadrilateral 2D meshes of 3D surfaces and 1D mesh of 2D surfaces are not supported at the moment. For each floating mesh, we need to specify a translational velocity, an angular velocity, and a center of rotation. In this example, we only need an angular motion of the impeller. Note that the center of rotation of the impeller is at 0, 0, 0.

subsection solid objects
  subsection solid surfaces
    set number of solids = 1
    subsection solid object 0
      subsection mesh
        set type               = gmsh
        set file name          = pitched-blade-impeller.msh
        set simplex            = true
        set initial refinement = 0
      end

      subsection translational velocity
        set Function expression = 0 ; 0 ; 0
      end
      subsection angular velocity
        set Function expression = if(t>0.5,6,0) ; 0 ; 0
      end
      set center of rotation = 0, 0, 0
    end
  end
end

Running the Simulation#

This simulation can be launched by (in parallel mode on 8 processes):

mpirun -np 8 lethe-particles granular-mixer.prm

Warning

This example takes approximately 2 hours on 8 cores.

Results#

Animation of the granular mixing simulation:

Possibility for Extension#

The same simulation can be carried out with particles of different sizes and properties to study segregation.