GENERAL PARTICLE TRACKING ALGORITHM
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Sources of Information :
•
Phoenics Lecture: GENTRA
•
Workshop: GENTRA
•
GENTRA user guide: (html) or (PDF)
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Coupling of the Interfacial Force
to the Continuous Phase
Introduction
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• The Gentra algorithm applies to low concentration (one
way coupling) and, at most, two way coupling.
• This section describes a simple one-way coupling where
the solids concentration is too low that it does not interfere
to the continuous fluid flow field.
Simple Theory
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• The Technical Report 211 brings, in detail, all theoretical
content of particle tracking including its implementation on
the CFD routine.
• For a fully account one must go to TR 211.
• The following slides brings, in a concise form, a simple
theory for isothermal particles.
Simple Theory
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• The particle velocity equation stems from Newton’s 2nd law:
EXTERNAL FORCES


1
p
 p CD U  U p U  U p    p    g  P
dt
2
PRESSURE
dU p
DRAG
BUOYANCY
Particle Acceleration
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• The particle acceleration is better written as:
D
 D
1
  U  Eg  P   U p

 
dt
p
 p
 p
dU p
B
A
Ap
1
D  CD U  U p
;
2

 p   
E
  
 p 
• and the vector equation can be represented in a general
form as:
dU p
dt
 A  BU p
Particle Velocity
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• Notice that vector A and the scalar B are known from the
continuous phase flow when one follows the particle
(Lagrangian concept).
dUp
dt
 A  t   B  t  Up
• The equation above has an analytical solution for Up which,
expressed as function of the time step becomes:
At
 Bt
 Bt
U p  t  t  
1

e

U
t
e


p 
B t 
Particle Trajectory
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• The particle trajectory and its time history are determined
integrating the particle velocity at each time step.
t t
S

t
Up dt
Particle Trajectory
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• The particle trajectory and its time history are determined
integrating the particle velocity at each time step.
t t
S

t
Up dt
Particle Initial Conditions
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• To get the particle’s velocity and position is necessary to
declare:
–the (X,Y,Z) particle position
– the (U,V,W) particle initial velocity,
–the particle size and density and finally,
–the particle mass flow rate / frequency delivered by the emission point.
• Notice that for that particular point the these particle features
can not change in time.
•This information is transmitted to phoenics in a separate file,
usually embedded inside q1 file (it will seen shortly).
The Particle Frequency
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• Every particle emission spot delivers particles at a
constant mass flow rate (kg/s). These particles parcels will
describe the particle trajectory as shown on the figure
bellow
• The particle frequency, , for each particle’s parcels is
evaluated by the ratio
Mass Flow Rate

Particle Mass
The Particle Concentration
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• The volumetric concentration of particles, C, within a
specific grid volume VG is defined by the ratio between the
volume of particles within the cell by the volume of the
cell:
grid
Vol.
k=1
k=2
n
C
    t 
k 1
k
k
CELL
k
k – parcel of particles
Vk – volume of particle on parcel k
k – particle freq. of parcel k
tk – residence time of parcel k in the cell
Vcell – is the cell volume
The Particle Momentum Source
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• It is the law of action and reaction. If the continuous fluid
acts on the particle accelerating or decelerating therefore
a force with the same magnitude but opposite direction
will act on the continuous phase.
•The source of momentum Smom (N/m3) which appears on
the continuous phase momentum eq. is equal to the rate of
change of particle momentum as each particle parcel
traverses a cell
Smom
 n
   k  p U p d3p
6 k 1 


 t t 

 p U p d
3
p

t 
k – parcel of particles
k – particle freq. of parcel k
Uk – particle vel. of parcel k within the cell

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MAIN LIMITATIONS
•In BFC cases, cyclic boundaries must be physically coincident.
•Particle-particle interactions such as collision or coalescence are
not considered.
•Although GENTRA can calculate and display the volume fraction
occupied by the particles, it is not taken into account by the gas
phase.
•Turbulence modulation - the damping of gas phase turbulence
due to the presence of particles - is not considered.
•GENTRA cannot perform simulations on multi-block meshes, or
meshes with fine-grid embedding.
• In polar coordinates RINNER has to be zero. Annular domains
still can be built setting REINNER=0 and blocking cells.
WORKSHOP - GENTRA
Flow of solid particles over a backward facing step
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•This workshop shows the user how to set up a simple case
which simulates the 2d turbulent flow of solid particles over a
backward facing step.
0.76
0.11
0.04
0.15
•Air, laden with solid particles, enters a 2d plane channel with a
velocity of 13 m/s. The total channel width is 0.1143m and the
length of the channel is 0.762m. The step is 0.1524m long by
0.0381m high. Turbulence is represented by means of the
standard k-e model with equilibrium wall functions.
• Load single phase flow Q1, case 300. Change for 500 iterations
and turn-off ASCII output. Run case for reference .
The work shop
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•Go to Help/POLIS/Tutorials/Multi-phase Flow/Gentra. Open
CHAM’s workshop.
• At Menu/Model/Lagrangian Particle Tracking – ACTIVATE model.
The work shop 1)Particle Type
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• Select the Isothermal particles.
The work shop 1) Isothermal Particle Settings
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•Drag Coefficient, Buoyancy, Pressure & Stochastic Model
Isothermal particles.
workshop 2) Boundary Conditions for Particles
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workshop 2) Boundary Conditions for Particles INLET
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• An inlet-data file has to be written with the particles
properties.
•It can be done externally or inside the Q1 file.
workshop 2) Boundary Conditions for Particles INLET
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• Inlet data file sample to the workshop (isothermal
particles). Start typing after the 3rd column.
• MASSFLO means mass flow rate kg/s
workshop 2) Boundary Conditions for Particles OUTLET
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• The inlet and outlet patches have names starting with GX,
do not forget the change the names.
workshop 3) Numerical Controls
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• For time definitions see section 2.8, page 25 of TR211.
workshop 4) I/O
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workshop 4) Output variables
• MONX, MONY,MONZ are the external forces acting on the
particles and its negative value are the source terms acting
on the continous phase flow.
• GHIS has the history of the particle or the displacement of
the particle as a function of time
• Files h001, h002 etc are the history files for each track
• Files t001, t002 etc are the trajectory files for each track
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workshop 5) Visualizing particles trajectories
•The particle trajectories are displayed in VR Viewer by using the
MACRO file written by EARTH. Click on 'Macro' and then enter
'GHIS' as the name of the macro file to run. Click 'OK' to close
the dialog and plot the particle paths will be displayed
automatically on the screen.
•HISTORY READ
filename m n filename is the name of the history file. All tracks
are read unless;
if m is present, it is the track to be read
if n is present, all tracks in the range m-n are read
Flow Simulation (1)
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•Buoyancy OFF
•Pressure Gradient OFF
•Stochastic Model OFF
• Particle size and density 10 μm & 1500 kg/m3
• Mass flow rate 5e-05 kg/s
Flow Simulation (2)
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•Buoyancy OFF
•Pressure Gradient OFF
•Stochastic Model ON
• Particle size and density 10 μm & 1500 kg/m3
Flow Simulation (3)
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•Buoyancy ON
•Pressure Gradient ON
•Stochastic Model ON
• Particle size and density 10 μm & 1500 kg/m3
Flow Simulation (4)
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•Buoyancy ON
•Pressure Gradient ON
•Stochastic Model ON
• Particle size and density 100 μm & 1500 kg/m3
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END