Boundary Conditions#

In this subsection, the boundary conditions of the DEM simulation are defined. First of all, the number of boundary conditions is specified. Then for each boundary condition, its information is defined. There are five boundary types: fixed_wall, outlet, rotational (around the center), translational, and periodic. For rotational motion, rotational speed and rotational vector are required, while for translational motion, the speed should be defined in each direction. For periodic boundaries, periodic id 0, periodic id 1 and periodic direction are required.

fixed_wall is a static wall, and particles collide with these static walls upon reaching the wall. The only way to move these walls is to move the entire triangulation. If the outlet condition is chosen for a boundary, particles can leave the simulation domain via this outlet. Using rotational and translational boundary conditions, exerts imaginary rotational and translational velocities to that boundary. In other words, the boundary does not move, but the particles that have collisions with these walls receive a rotational or translational velocity from the wall. This feature is used in the rotating drum example.

In multiphysic DEM (solver type = dem_mp in the Model Parameters subsection), each wall can also be given a thermal boundary type, independently of its motion. A wall is adiabatic by default: it does not exchange heat with the particles. A wall with the temperature thermal boundary type has a temperature imposed by the user, which can vary in space and time, and it exchanges heat with the particles in contact with it via the particle-wall heat transfer model described in the theory guide.

subsection DEM boundary conditions
  # Total number of boundary motion
  set number of boundary conditions = 3

  # For each boundary condition, we need a separate subsection
  subsection boundary condition 0
    # ID of boundary
    set boundary id         = 0

    # Boundary type
    # Choices are fixed_wall|outlet|rotational|translational
    set type                = rotational

    # Rotational speed magnitude
    set rotational speed    = 2.5

    # Rotational vector
    set rotational vector   = 1, 0, 0

    # Point on rotational vector
    set point on rotational vector = 0, 0, 0

    # Thermal boundary type ("if solver type == dem_mp")
    # Choices are adiabatic|temperature
    set thermal boundary type = adiabatic

    # Temperature of the wall
    subsection wall temperature
      set Function expression = 0
    end
  end

  # OR for translational motion
  subsection boundary condition 1
    # ID of moving boundary
    set boundary id = 1

    # Motion type
    set type        = translational

    # Speed in each direction
    set speed x     = 0.15
    set speed y     = 0
    set speed z     = 0
  end

  # OR for periodic boundaries
  subsection boundary condition 2
    # Boundary type
    set type               = periodic

    # ID of principal boundary
    set periodic id 0      = 3

    # ID of associated periodic boundary
    set periodic id 1      = 2

    # Direction normal to the periodic boundary faces (x=0, y=1, z=2)
    set periodic direction = 1
end

  • The number of boundary conditions parameter defines the number of desired boundary conditions to be specified. Note that if a boundary condition type is not defined explicitly, Lethe defines it as a fixed static wall.

  • For each boundary condition, we have to define a separate subsection. In the sample parameter list above, the number of boundary conditions is equal to 3. Hence, we need to define three subsections (subsection boundary condition 0, subsection boundary condition 1 and subsection boundary condition 2`).

  • The boundary id parameter specifies the boundary ID for which the boundary condition should be applied. Periodic boundaries are an exception.

  • The type parameter specifies the type of the boundary condition. Acceptable types are: fixed_wall, outlet, rotational, translational and periodic. The default boundary condition type is fixed_wall.

  • The periodic id 0 and periodic id 1 parameters specify the periodic boundaries ID for which the periodic boundary condition should be applied. By convention, periodic id 0 should correspond to the boundary ID for which the boundary is further along the coordinate axis (this is the principal boundary).

Note

Only periodic boundaries which have co-linear normal vectors which align along an axis of the problem (e.g., x axis) are currently supported. Multiple simultaneous periodic directions are supported.

  • The periodic direction parameter specifies the perpendicular axis to a pair of periodic boundaries (0 is the x axis, 1 is the y and 2 is the z).

  • The rotational speed parameter defines the rotational speed of the specified boundary.

  • The rotational vector parameter specifies the rotational vector in x, y, and z directions.

  • The point on rotational vector parameter specifies a point x, y, z on the rotating axis.

  • The speed parameter defines the translational speed of the specified boundary.

  • The thermal boundary type parameter defines whether the boundary is adiabatic or has an imposed temperature in a multiphysic DEM simulation. Only fixed_wall, translational and rotational boundaries can have an imposed temperature, since particles cannot be in contact with outlet or periodic boundaries. The temperature thermal boundary type can only be used when the solver type is dem_mp.

  • In the subsection wall temperature, we define the imposed temperature of the boundary as a function of space and time (\(x\), \(y\), \(z\) and \(t\)). The function is evaluated at the contact point between each particle and the wall.

Note

The temperature field of a rotational or translational wall is defined in the fixed frame of reference of the background triangulation, since the grid does not move: the wall only transmits its velocity to the particles. For a temperature pattern that moves with the wall, write the function in the frame of the wall. For instance, for a wall translating at the speed \(\mathbf{v}\), use the position \(\mathbf{x} \pm \mathbf{v} t\) instead of the only \(\mathbf{x}\). This way the temperature pattern moves with the wall.

Note

The temperature of the wall is imposed, and the wall behaves like a heat reservoir of infinite heat capacity. The heat transfer rate between a particle \(i\) and the wall \(w\) is \(Q_{iw} = H_{iw} (T_w - T_i)\), where the thermal conductance \(H_{iw}\) is computed with the particle-wall model described in the theory guide. The model is the same as for the isothermal solid objects, and it uses the wall properties defined in the Lagrangian Physical Properties subsection (thermal conductivity wall, microhardness wall, etc.).