Example 15 : Rotation in Box

This example performs a three-dimensional discrete element method simulation of rotation of a box. We insert 4000 particles (diameter = 1 mm), and rotate the box for 5 s. The box rotates around the x axis and the rotation speed is 1 rad/s.

# --------------------------------------------------
# Simulation and IO Control
#---------------------------------------------------
subsection simulation control
  set time step                 			 = 1e-5
  set time end       					 = 5
  set log frequency				         = 1000
  set output frequency            			 = 1000
end

In the model parameters section, particle-particle and particle-wall broad and fine search frequencies are defined. We also define the particle contact search size (neighborhood threshold), contact forces and integration methods. The contact detection method is dynamic, and it needs dynamic contact search size coefficient (a safety factor for dynamic contact search). The rolling resistance torque model is constant_resistance, and velocity_verlet is chosen as the integration method.

# --------------------------------------------------
# Model parameters
#---------------------------------------------------
subsection model parameters
  set contact detection method 		   		 = dynamic
  set dynamic contact search size coefficient	 	 = 0.9
  set neighborhood threshold				 = 1.3
  set particle particle contact force method             = pp_nonlinear
  set particle wall contact force method                 = pw_nonlinear
  set rolling resistance torque method			 = constant_resistance
  set integration method				 = velocity_verlet
end

In the physical properties section, the physical properties of particles and walls, including diameter and density of particles, Young's modulus, Poisson's ratios, restitution coefficients, friction and rolling frictions of particle and wall are specified. The gravitational acceleration is also set in this section. Diameter of particles in this example is 1 mm. Total number of particles in this example is 4000.

#---------------------------------------------------
# Physical Properties
#---------------------------------------------------
subsection physical properties
    set gx            		 			= 0.0
    set gy            		 			= 0.0
    set gz						= -9.81
    set number of particle types	                = 1
    	subsection particle type 0
		set size distribution type		= uniform
    		set diameter            	 	= 0.001
    		set number				= 4000
    		set density particles  	 		= 1000
    		set young modulus particles         	= 1000000
    		set poisson ratio particles          	= 0.3
    		set restitution coefficient particles	= 0.3
    		set friction coefficient particles      = 0.1
    		set rolling friction particles         	= 0.05
	end
    set young modulus wall            			= 1000000
    set poisson ratio wall            			= 0.3
    set restitution coefficient wall           		= 0.3
    set friction coefficient wall         		= 0.1
    set rolling friction wall         	      	  	= 0.05
end

Next, we define the insertion properties, which are insertion method, inserted number of particles at each insertion step, insertion frequency, insertion domain and other information regarding the initial positions of particles inside the insertion domain.

#---------------------------------------------------
# Insertion Info
#---------------------------------------------------
subsection insertion info
    set insertion method				= non_uniform
    set inserted number of particles at each time step  = 4000
    set insertion frequency            		 	= 2000000
    set insertion box minimum x            	 	= -0.019
    set insertion box minimum y            	        = -0.019
    set insertion box minimum z            	        = -0.01
    set insertion box maximum x            	        = 0.019
    set insertion box maximum y           	 	= 0.019
    set insertion box maximum z            	        = 0.019
    set insertion distance threshold			= 1.5
    set insertion random number range			= 0.2
    set insertion random number seed			= 19
end

We use a dealii hyper_cube for creating a box. The edge length of the cube is 0.02 m.

#---------------------------------------------------
# Mesh
#---------------------------------------------------
subsection mesh
    set type                 				= dealii
    set grid type            				= hyper_cube
    set grid arguments       				= -0.02 : 0.02 : false
    set initial refinement   				= 3
end

We define a rotational motion of the grid around the x axis. Note that values 0, 1 and 2 for the grid rotational axis mean rotational motion around x, y and z axis, respectively. The rotational speed is 1 rad/s.

#---------------------------------------------------
# Grid Motion
#---------------------------------------------------
subsection grid motion
    set motion type                 			= rotational
    set grid rotational speed            		= 1
    set grid rotational axis		            	= 0
end

dem_3d solver simulates this example.

Watch the animation of this simulation: