# PhasicFlow: Problem Definition

Problem Definition

The problem is to simulate a double pedestal tote blender with the diameter 0.03 m and 0.1 m respectively, the length 0.3 m, rotating at 28 rpm. This blender is filled with 20000 Particles. The timestep for integration is 0.00001 s. There is one type of Particle in this blender that are being inserted during simulation to fill the blender.

- 20000 particles with 4 mm diameter, at the rate of 20000 particles/s for 1 sec. َAfter settling particles, this blender starts to rotate at t=**1s**.

<html> <body>

a view of the tote-blender while rotating
<img src="sample sample sample sample", width=700px>

</body> </html>

# Setting up the Case

As it has been explained in the previous cases, the simulation case setup is based on text-based scripts. Here, the simulation case setup are sotred in two folders: `caseSetup`, `setting`. (see the above folders). Unlike the previous cases, this case does not have the `stl` file. and the geometry is described in the `geometryDict` file.

## Defining particles

Then in the `caseSetup/sphereShape` the diameter and the material name of the particles are defined.
{C++}
// names of shapes
names (sphere1);
// diameter of shapes (m)
diameters (0.004);
// material names for shapes
materials (prop1);

## Particle Insertion

In this case we have a region for ordering particles. These particles are placed in this blender. For example the script for the inserted particles is shown below.
in caseSetup/particleInsertion file
{C++}
// positions particles
positionParticles
{
// ordered positioning
method positionOrdered;
// maximum number of particles in the simulation
maxNumberOfParticles 40000;
// perform initial sorting based on morton code?
mortonSorting Yes;
// cylinder for positioning particles
cylinder
{
// Coordinates of top cylinderRegion (m,m,m)
p1 (0.05 0.0 0.12);
p2 (0.05 0.0 0.22);
// radius of cylinder
radius 0.066;
}
positionOrderedInfo
{
// minimum space between centers of particles
diameter 0.003;
// number of particles in the simulation
numPoints 20000;
// axis order for filling the space with particles
axisOrder (z y x);
}
}

## Interaction between particles

In `caseSetup/interaction` file, material names and properties and interaction parameters are defined: interaction between the particles of rotating drum. Since we are defining 1 material for simulation, the interaction matrix is 1x1 (interactions are symetric).
{C++}
// a list of materials names
materials (prop1);
// density of materials [kg/m3]
densities (1000.0);
contactListType sortedContactList;
model
{
contactForceModel nonLinearNonLimited;
rollingFrictionModel normal;
/*
Property (prop1-prop1);
*/
// Young modulus [Pa]
Yeff (1.0e6);
// Shear modulus [Pa]
Geff (0.8e6);
// Poisson's ratio [-]
nu (0.25);
// coefficient of normal restitution
en (0.7);
// coefficient of tangential restitution
et (1.0);
// dynamic friction
mu (0.3);
// rolling friction
mur (0.1);
}

## Settings

### Geometry

In the `settings/geometryDict` file, the geometry and axis of rotation is defined for the drum. The geometry is composed of a cylinder inlet and outlet, cone shell top and down, a cylinder shell and enter and exit Gate.
{C++}
surfaces
{
topGate
topGate
{
// type of wall
type cylinderWall;
// begin point of cylinder axis
p1 (0.0 0.0 0.299);
// end point of cylinder axis
p2 (0.0 0.0 0.3);
// radius at p1
radius1 0.03;
// radius at p2
radius2 0.0001;
// material of wall
material solidProperty;
// motion component name
motion axisOfRotation;
}
topCylinder
{
// type of the wall
type cylinderWall;
// begin point of cylinder axis
p1 (0.0 0.0 0.28);
// end point of cylinder axis
p2 (0.0 0.0 0.3);
// radius at p1
radius1 0.03;
// radius at p2
radius2 0.03;
// number of divisions
resolution 36;
// material name of this wall
material prop1;
// motion component name
motion axisOfRotation;
}
coneShelltop
{
// type of the wall
type cylinderWall;
// begin point of cylinder axis
p1 (0.0 0.0 0.2);
// end point of cylinder axis
p2 (0.0 0.0 0.28);
// radius at p1
radius1 0.1;
// radius at p2
radius2 0.03;
// number of divisions
resolution 36;
// material name of this wall
material prop1;
// motion component name
motion axisOfRotation;
}
cylinderShell
{
// type of the wall
type cylinderWall;
// begin point of cylinder axis
p1 (0.0 0.0 0.1);
// end point of cylinder axis
p2 (0.0 0.0 0.2);
// radius at p1
radius1 0.1;
// radius at p2
radius2 0.1;
// number of divisions
resolution 36;
// material name of this wall
material prop1;
// motion component name
motion axisOfRotation;
}
coneShelldown
{
// type of the wall
type cylinderWall;
// begin point of cylinder axis
p1 (0.0 0.0 0.02);
// end point of cylinder axis
p2 (0.0 0.0 0.1);
// radius at p1
radius1 0.03;
// radius at p2
radius2 0.1;
// number of divisions
resolution 36;
// material name of this wall
material prop1;
// motion component name
motion axisOfRotation;
}
/*
This is a plane wall at the exit of silo
*/
bottomCylinder
{
// type of the wall
type cylinderWall;
// begin point of cylinder axis
p1 (0.0 0.0 0.0);
// end point of cylinder axis
p2 (0.0 0.0 0.02);
// radius at p1
radius1 0.03;
// radius at p2
radius2 0.03;
// number of divisions
resolution 36;
// material name of this wall
material prop1;
// motion component name
motion axisOfRotation;
}
exitGate
{
type planeWall;
p1 (-0.05 -0.05 0);
p2 (-0.05 0.05 0);
p3 ( 0.05 0.05 0);
p4 (0.05 -0.05 0);
material prop1;
motion axisOfRotation;
}
}

### Rotating Axis Info

In this part of `geometryDict` the information of rotating axis and speed of rotation are defined. Unlike the previous cases, the rotation of this blender starts at time=**0 s**.
{C++}
// information for rotatingAxisMotion motion model
rotatingAxisMotionInfo
{
axisOfRotation
{
p1 (-0.1 0.0 0.15); // first point for the axis of rotation
p2 (0.1 0.0 0.15); // second point for the axis of rotation
omega 1.5708; // rotation speed ==> 15 rad/s
// Start time of Geometry Rotating (s)
startTime 1;
// End time of Geometry Rotating (s)
endTime 9.5;
}
}

## Performing Simulation

To perform simulations, enter the following commands one after another in the terminal.
Enter `$ particlesPhasicFlow` command to create the initial fields for particles.
Enter `$ geometryPhasicFlow` command to create the Geometry.
At last, enter `$ sphereGranFlow` command to start the simulation.
After finishing the simulation, you can use `$ pFlowtoVTK` to convert the results into vtk format storred in ./VTK folder.