Simulating a small rotating drum

Problem definition

The problem is to simulate a rotating drum with the diameter 0.24 m and the length 0.1 m rotating at 11.6 rpm. It is filled with 30,000 4-mm spherical particles. The timestep for integration is 0.00001 s.

a view of rotating drum

Setting up the case

PhasicFlow simulation case setup is based on the text-based scripts that we provide in two folders located in the simulation case folder: settings and caseSetup (You can find the case setup files in the above folders. All the commands should be entered in the terminal while the current working directory is the simulation case folder (at the top of the caseSetup and settings).

Creating particles

Open the file settings/particlesDict. Two dictionaries, positionParticles and setFields position particles and set the field values for the particles. In dictionary positionParticles, the positioning method is positionOrdered, which position particles in order in the space defined by box. box space is defined by two corner points min and max. In dictionary positionOrderedInfo, numPoints defines number of particles; diameter, the distance between two adjacent particles, and axisOrder defines the axis order for filling the space by particles.

in settings/particlesDict file
{C++}
positionParticles
{
method positionOrdered; // ordered positioning
maxNumberOfParticles 40000; // maximum number of particles in the simulation
mortonSorting Yes; // perform initial sorting based on morton code?
box // box for positioning particles
{
min (-0.08 -0.08 0.015); // lower corner point of the box
max ( 0.08 0.08 0.098); // upper corner point of the box
}
positionOrderedInfo
{
diameter 0.004; // minimum space between centers of particles
numPoints 30000; // number of particles in the simulation
axisOrder (z y x); // axis order for filling the space with particles
}
}

In dictionary setFields, dictionary defaultValue defines the initial value for particle fields (here, velocity, acceleration, rotVelocity, and shapeName). Note that shapeName field should be consistent with the name of shape that you later set for shapes (here one shape with name sphere1).

in settings/particlesDict file
{C++}
setFields
{
defaultValue
{
velocity realx3 (0 0 0); // linear velocity (m/s)
acceleration realx3 (0 0 0); // linear acceleration (m/s2)
rotVelocity realx3 (0 0 0); // rotational velocity (rad/s)
shapeName word sphere1; // name of the particle shape
}
selectors
{}
}

Enter the following command in the terminal to create the particles and store them in 0 folder.

> particlesPhasicFlow

Creating geometry

In file settings/geometryDict , you can provide information for creating geometry. Each simulation should have a motionModel that defines a model for moving the surfaces in the simulation. rotatingAxisMotion model defines a fixed axis which rotates around itself. The dictionary rotAxis defines an motion component with p1 and p2 as the end points of the axis and omega as the rotation speed in rad/s. You can define more than one motion component in a simulation.

in settings/geometryDict file
{C++}
motionModel rotatingAxisMotion;
.
.
.
rotatingAxisMotionInfo
{
rotAxis
{
p1 (0.0 0.0 0.0); // first point for the axis of rotation
p2 (0.0 0.0 1.0); // second point for the axis of rotation
omega 1.214; // rotation speed (rad/s)
}
}

In the dictionary surfaces you can define all the surfaces (walls) in the simulation. Two main options are available: built-in geometries in PhasicFlow, and providing surfaces with stl file. Here we use built-in geometries. In cylinder dictionary, a cylindrical shell with end radii, radius1 and radius2, axis end points p1 and p2, material name prop1, motion component rotAxis is defined. resolution sets number of division for the cylinder shell. wall1 and wall2 define two plane walls at two ends of cylindrical shell with coplanar corner points p1, p2, p3, and p4, material name prop1 and motion component rotAxis.

in settings/geometryDict file
{C++}
surfaces
{
cylinder
{
type cylinderWall; // type of the wall
p1 (0.0 0.0 0.0); // begin point of cylinder axis
p2 (0.0 0.0 0.1); // end point of cylinder axis
radius1 0.12; // radius at p1
radius2 0.12; // radius at p2
resolution 24; // number of divisions
material prop1; // material name of this wall
motion rotAxis; // motion component name
}
wall1
{
type planeWall; // type of the wall
p1 (-0.12 -0.12 0.0); // first point of the wall
p2 ( 0.12 -0.12 0.0); // second point
p3 ( 0.12 0.12 0.0); // third point
p4 (-0.12 0.12 0.0); // fourth point
material prop1; // material name of the wall
motion rotAxis; // motion component name
}
wall2
{
type planeWall;
p1 (-0.12 -0.12 0.1);
p2 ( 0.12 -0.12 0.1);
p3 ( 0.12 0.12 0.1);
p4 (-0.12 0.12 0.1);
material prop1;
motion rotAxis;
}
}

Enter the following command in the terminal to create the geometry and store it in 0/geometry folder.

> geometryPhasicFlow

Defining properties and interactions

In the file caseSetup/interaction , you find properties of materials. materials defines a list of material names in the simulation and densities sets the corresponding density of each material name. model dictionary defines the interaction model for particle-particle and particle-wall interactions. contactForceModel selects the model for mechanical contacts (here nonlinear model with limited tangential displacement) and rollingFrictionModel selects the model for calculating rolling friction. Other required prosperities should be defined in this dictionary.

in caseSetup/interaction file
{C++}
materials (prop1); // a list of materials names
densities (1000.0); // density of materials [kg/m3]
.
.
.
model
{
contactForceModel nonLinearNonLimited;
rollingFrictionModel normal;
Yeff (1.0e6); // Young modulus [Pa]
Geff (0.8e6); // Shear modulus [Pa]
nu (0.25); // Poisson's ratio [-]
en (0.7); // coefficient of normal restitution
et (1.0); // coefficient of tangential restitution
mu (0.3); // dynamic friction
mur (0.1); // rolling friction
}

Dictionary contactSearch sets the methods for particle-particle and particle-wall contact search. method specifies the algorithm for finding neighbor list for particle-particle contacts and wallMapping shows how particles are mapped onto walls for finding neighbor list for particle-wall contacts. updateFrequency sets the frequency for updating neighbor list and sizeRatio sets the size of enlarged cells (with respect to particle diameter) for finding neighbor list. Larger sizeRatio include more particles in the neighbor list and you require to update it less frequent.

in caseSetup/interaction file
{C++}
contactSearch
{
method NBS; // method for broad search particle-particle
wallMapping cellsSimple; // method for broad search particle-wall
NBSInfo
{
updateFrequency 20; // each 20 timesteps, update neighbor list
sizeRatio 1.1; // bounding box size to particle diameter (max)
}
cellsSimpleInfo
{
updateFrequency 20; // each 20 timesteps, update neighbor list
cellExtent 0.7; // bounding box for particle-wall search (> 0.5)
}
}

In the file caseSetup/sphereShape, you can define a list of names for shapes (shapeName in particle field), a list of diameters for shapes and their properties names.

in caseSetup/sphereShape file
{C++}
names (sphere1); // names of shapes
diameters (0.004); // diameter of shapes
materials (prop1); // material names for shapes

Other settings for the simulation can be set in file settings/settingsDict. The dictionary domain defines the a rectangular bounding box with two corner points for the simulation. Each particle that gets out of this box, will be deleted automatically.

in settings/settingsDict file
{C++}
dt 0.00001; // time step for integration (s)
startTime 0; // start time for simulation
endTime 10; // end time for simulation
saveInterval 0.1; // time interval for saving the simulation
timePrecision 6; // maximum number of digits for time folder
g (0 -9.8 0); // gravity vector (m/s2)
domain
{
min (-0.12 -0.12 0);
max (0.12 0.12 0.11);
}
integrationMethod AdamsBashforth2; // integration method

Running the case

The solver for this simulation is sphereGranFlow. Enter the following command in the terminal. Depending on the computational power, it may take a few minutes to a few hours to complete.

> sphereGranFlow

Post processing

After finishing the simulation, you can render the results in Paraview. To convert the results to VTK format, just enter the following command in the terminal. This will converts all the results (particles and geometry) to VTK format and store them in folder VTK/.

> pFlowToVTK