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# 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 drum.
* **20000** particles with **4 mm** diameter, at the rate of 20000 particles/s for 1 sec.
<html>
<body>
<div align="center"><b>
a view of the tote-blender while rotating
</div></b>
<div align="center">
<img src="sample sample sample sample", width=700px>
</div>
</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.
<div align="center">
in <b>caseSetup/particleInsertion</b> file
</div>
```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;
// box for positioning particles
box
{
// lower corner point of the box
min (-0.06 -0.06 0.08);
// upper corner point of the box
max (0.06 0.06 0.18);
}
```
## 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
{
enterGate
{
// type of wall
type planeWall;
// coords of wall
p1 (-0.05 -0.05 0.3);
p2 (-0.05 0.05 0.3);
p3 ( 0.05 0.05 0.3);
p4 (0.05 -0.05 0.3);
// material of wall
material prop1;
// motion component name
motion rotAxis;
}
cylinderinlet
{
// 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 rotAxis;
}
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 rotAxis;
}
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 rotAxis;
}
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 rotAxis;
}
/*
This is a plane wall at the exit of silo
*/
cylinderoutlet
{
// 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 rotAxis;
}
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 rotAxis;
}
}
```
### 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++
rotatingAxisMotionInfo
{
rotAxis
{
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 3; // rotation speed (rad/s)
}
}
```
## 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.

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/* -------------------------------*- C++ -*--------------------------------- *\
| phasicFlow File |
| copyright: www.cemf.ir |
\* ------------------------------------------------------------------------- */
objectName interaction;
objectType dicrionary;
/* ------------------------------------------------------------------------- */
// 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);
}
contactSearch
{
// method for broad search particle-particle
method NBS;
// method for broad search particle-wall
wallMapping cellMapping;
NBSInfo
{
// each 20 timesteps, update neighbor list
updateFrequency 20;
// bounding box size to particle diameter (max)
sizeRatio 1.1;
}
cellMappingInfo
{
// each 20 timesteps, update neighbor list
updateFrequency 20;
// bounding box for particle-wall search (> 0.5)
cellExtent 0.7;
}
}

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/* -------------------------------*- C++ -*--------------------------------- *\
| phasicFlow File |
| copyright: www.cemf.ir |
\* ------------------------------------------------------------------------- */
objectName particleInsertion;
objectType dicrionary;
/* ------------------------------------------------------------------------- */
// is insertion active?
active no;
// not implemented for yes
collisionCheck No;

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/* -------------------------------*- C++ -*--------------------------------- *\
| phasicFlow File |
| copyright: www.cemf.ir |
\* ------------------------------------------------------------------------- */
objectName sphereDict;
objectType sphereShape;
/* ------------------------------------------------------------------------- */
// names of shapes
names (sphere1);
// diameter of shapes (m)
diameters (0.004);
// material names for shapes
materials (prop1);

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#!/bin/sh
cd ${0%/*} || exit 1 # Run from this directory
ls | grep -P "^(([0-9]+\.?[0-9]*)|(\.[0-9]+))$" | xargs -d"\n" rm -rf
rm -rf VTK
#------------------------------------------------------------------------------

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#!/bin/sh
cd ${0%/*} || exit 1 # Run from this directory
echo "\n<--------------------------------------------------------------------->"
echo "1) Creating particles"
echo "<--------------------------------------------------------------------->\n"
particlesPhasicFlow
echo "\n<--------------------------------------------------------------------->"
echo "2) Creating geometry"
echo "<--------------------------------------------------------------------->\n"
geometryPhasicFlow
echo "\n<--------------------------------------------------------------------->"
echo "3) Running the case"
echo "<--------------------------------------------------------------------->\n"
sphereGranFlow
#------------------------------------------------------------------------------

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/* -------------------------------*- C++ -*--------------------------------- *\
| phasicFlow File |
| copyright: www.cemf.ir |
\* ------------------------------------------------------------------------- */
objectName geometryDict;
objectType dictionary;
/* ------------------------------------------------------------------------- */
// motion model: rotating object around an axis
motionModel rotatingAxisMotion;
surfaces
{
enterGate
{
// type of wall
type planeWall;
// coords of wall
p1 (-0.05 -0.05 0.3);
p2 (-0.05 0.05 0.3);
p3 ( 0.05 0.05 0.3);
p4 (0.05 -0.05 0.3);
// material of wall
material prop1;
// motion component name
motion rotAxis;
}
cylinderinlet
{
// 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 rotAxis;
}
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 rotAxis;
}
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 rotAxis;
}
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 rotAxis;
}
/*
This is a plane wall at the exit of silo
*/
cylinderoutlet
{
// 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 rotAxis;
}
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 rotAxis;
}
}
// information for rotatingAxisMotion motion model
rotatingAxisMotionInfo
{
rotAxis
{
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 3; // rotation speed (rad/s)
}
}

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/* -------------------------------*- C++ -*--------------------------------- *\
| phasicFlow File |
| copyright: www.cemf.ir |
\* ------------------------------------------------------------------------- */
objectName particlesDict;
objectType dictionary;
/* ------------------------------------------------------------------------- */
setFields
{
/*
Default value for fields defined for particles
These fields should always be defined for simulations with
spherical particles.
*/
defaultValue
{
// linear velocity (m/s)
velocity realx3 (0 0 0);
// linear acceleration (m/s2)
acceleration realx3 (0 0 0);
// rotational velocity (rad/s)
rotVelocity realx3 (0 0 0);
// name of the particle shape
shapeName word sphere1;
}
selectors
{}
}
// 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;
// box for positioning particles
box
{
// lower corner point of the box
min (-0.06 -0.06 0.08);
// upper corner point of the box
max (0.06 0.06 0.18);
}
positionOrderedInfo
{
// minimum space between centers of particles
diameter 0.004;
// number of particles in the simulation
numPoints 20000;
// axis order for filling the space with particles
axisOrder (z y x);
}
}

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/* -------------------------------*- C++ -*--------------------------------- *\
| phasicFlow File |
| copyright: www.cemf.ir |
\* ------------------------------------------------------------------------- */
objectName settingsDict;
objectType dictionary;;
/*---------------------------------------------------------------------------*/
run toteBlender;
// time step for integration (s)
dt 0.00001;
// start time for simulation
startTime 0;
// end time for simulation
endTime 10;
// time interval for saving the simulation
saveInterval 0.1;
// maximum number of digits for time folder
timePrecision 6;
// gravity vector (m/s2)
g (0 0 -9.8);
/* Simulation domain */
/* every particles that goes outside this domain is deleted. */
domain
{
min (-0.5 -0.5 -0.5);
max (0.5 0.5 0.5);
}
// integration method
integrationMethod AdamsBashforth2;
// report timers?
timersReport Yes;
// time interval for reporting timers
timersReportInterval 0.01;