Radio active particle tracking implemnetation

Radioactive Particle Tracking (RPT)
Gas
Liquid
Gas
Detector
In RPT, the motion of a tracer particle
designed to be the marker of the phase whose
velocity is to be mapped, is tracked
The tracer particle is normally a gamma ray
emitter
The particle is made neutrally buoyant for
tracking liquid phase, and for tracking granular
solids, the size, shape and density of the tracer
particle is matched to that of the granular
material
 An array of detector is placed around the
vessel to record the photon counts
 The first level processing yields the
Lagrangian position time series of the tracer
particle
 Secondary processing leads to Eulerian
mean velocities, moments of velocity
fluctuations , and other flow quantities

Photon counts time series
Lagrangian
position time
series
Lagrangian velocity time
series
Eulerian
grid
Eulerian
velocity
i
,
j
,
k
i
,
j
+
1
,
k
r, θ i, j, k
i, j, k+1
i, j, k+2
r, z
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 0.2 0.4 0.6 0.8 1
r/R [-]
z=25 cm
z=15 cm
z=7.5 cm
Mean
Axial
Velocity
of
Solid
[m/s]

Steps in RPT
RPT
Calibration Photon counting and
data collection
Reconstruction
Experimental
(direct
measurement at
all possible
position in the
column)
Monte Carlo based
(numerical)
Velocity reconstruction
(time differentiation of
two successive position)
Post processing of
instantaneous
fluctuations
(Hardware)
(Hardware)
(Software)
(Software)

Flow chart of Radioactive Particle Tracking
(RPT)
(Limtrakul et al. (2005))
RPT Experiments (counts from
detector)
Instantaneous Position of the
Particle
Instantaneous velocity (time
differentiation of two
successive position)
Ensemble Average Velocity
Fluctuating Velocity
Reynolds stress
Reconstruction
Algorithm
Calibration (Distance count
map)
Root Mean Square Velocity
Kinetic Energy
i
,
j
,
k
i
,
j
,
k
+
1
r, θ
r, z
i, j, k
i, j, k+1
i, j, k+2
Eulerian grid
1 2 3 .... N
q
v v v v
v
N
  


Quantities Calculated from RPT
Experimental data
Instantaneous Velocity
Ensemble average velocity
Fluctuating velocity component
RMS velocity
Stress
Fluctuating kinetic energy per unit volume
z
z
v
t



( , , )
,
1
1
( , , ) ( , , )
( , , )
N i j k
q q n
n
v i j k v i j k
N i j k 
  
'
( , , ) ( , , ) ( , , )
q q q
v i j k v i j k v i j k
   
'2
RMS
q q
v v
    
' '
( , , ) ( , , )
qs p q s
v i j k v i j k
 
  
'2 '2 '2
1
[ ]
2
p r z
KE v v v


        

Hardware Needed to Perform RPT
Experiment
• Radioactive Source
(gamma ray source)
• Scintillation Detector
(used for photon collection)
• Multi Input Data Acquisition System (MIDAS)
(used for photon acquisition )
• Data Acquisition Machine (PC)
(used for storage of data)

Detector Functioning
Detector
Crystal
Photo
Multiplier
Tube
Multi
Channel
Analyzer
Photocathode Anode
 ray
Signal BNC cable
High Voltage
Supply cable

Number
of
Photons
in
given
energy
bin
Counted Photon Energy
Photopeak
Flow Chart of Data Acquisition System
γ ray Photo
Multiplier Tube
Pre amplifier
High
Voltage
Amplifier
Single Channel
Analyzer
To Data
Acquisition
Detector Crystal (NaI (Tl))
Multi Input Data
Acquisition System
(MIDAS)

Radio active particle tracking implemnetation

0
400
800
1200
1600
0 200 400 600 800 1000 1200
Counts
Distance from Detector Centre(mm)
Detector 12
Distance Count Map from ‘in-situ’
Experimental Calibration

Photon Detection
Tracer particle releases
photons at solid angle of 4π.
Only a small fraction of
released photons are incident
on the detector crystal.
If the photon is capable of
penetrating through the
detector, it does not
contribute to counts.
Photons that are absorbed by
the detector crystal are
considered as a counts.
Photon fronts
Detector

L
ρ
α

min

cri
m
ax
X
Z
ρ
X
ma
x

mi
n
Solid Angle Subtended by the Tracer Particle at
the detector for Different Particle Locations
When tracer particle is placed
out side the detector disk
When tracer particle is placed
within the detector disk


L
L

h


L
L
h

h L

h
L
L
Top entrance bottom exit Top entrance lateral exit
Lateral entrance, bottom exit Lateral entrance lateral exit
Possible Cases By Which Photon Can Travel In
Detector

 
 
 
 












 d
d
l
r
n
r
D
N
j
j
j
abs 

 exp
1
exp
.
1
3








abs
abs
A
A
T
C


1
Photon Count Rate:
Absolute Efficiency of Detector:
Monte Carlo Simulation

Count
Vs
Distance
0
50
100
150
200
250
300
350
400
450
500
-600
-400
-200
0
200
400
600
Distance
(in
mm)
Count
Count
Vs
Distance
0
50
100
150
200
250
300
350
400
450
500
-600
-400
-200
0
200
400
600
Distance
(in
mm)
Count
Count
Vs
Distance
0
50
100
150
200
250
300
350
400
450
500
-600
-400
-200
0
200
400
600
Distance
(in
mm)
Count
Line Spread Response Function (LSRF) from
Monte Carlo Program

0
200
400
600
800
1000
0 10 20 30 40 50 60
Distance from Detector Axis, cm
Photon
Counts
Effective field of view
Area Spread Response Function (ASRF) from
Monte Carlo Program

RPT Performance Parameters
Roy, Larachi, Al-Dahhan and Dudukovic (2002), Appl. Radiat. & Isotopes, 56, 485-503.
r
C
C
Sr



1
Sensitivity:
C
r
c
r




Resolution:
- measure of ability of detector(s)
to record a change in tracer
particle location
- measure of uncertainty in locating
tracer particle
Wish:
- highest sensitivity, i.e., high S
- highest resolution, i.e., low s
   



N
i i
T z
y
x
z
y
x 1
2
2
,
,
1
,
,
1


   



N
i
i
T z
y
x
S
z
y
x
S
1
2
2
,
,
,
,
For a combination of detectors:

Effect of Number of Detectors in Same Plane
Increase in Resolution ~ No Improvement
in Resolution
Increase in Sensitivity
Resolution Sensitivity
mm mm-1

Effect of Multiple Detectors at Different
Axis Number of detector used = 6
1
3
5
2
4
6
Front View
140
mm
140
mm
3
1,
5
2,6
4
Top View
Detectors
Resolution
Sensitivity
mm mm-1

Reported Position Reconstruction
Algorithms
• Weighted least squares algorithm
• Monte Carlo algorithm
• Neural network based reconstruction
• Cross correlation algorithm

Weighted Least Square Method
• In this method a distance count map is created by
placing the particle at different known locations.
• This step is called ‘calibration’.
Distance Count Map
0
200
400
600
800
1000
0 10 20 30 40 50 60
Distance from Detector Axis, cm
Photon
Counts

• Then the counts recorded during calibration is
fitted in a polynomial equation and distance from
each detector is calculated.
Where
ri is the distance of tracer particle from the ith
detector
Ii is the intensity recorded at the ith
detector.
and a0, a1, a2 are constants.
2
1 2
1 1
.....
i oi i i
i i
r a a a
I I
   
   
   
   
• ri and Ii is calculated form distance count map. Like, for
detector 9 at 10 cm distance, 1200 counts is recorded on
detector.

• Then actual RPT experiment is performed.
• Now the co-ordinate of tracer particle is calculated by
estimating by least squares method:
1 1 1
| | (| | | | | |) | | | | | |
T T
b X W X X W Z
  

Where:
b= co-ordinate of the tracer particle.
Z= experimentally measured distance.
X= hardware constant depend upon the co-ordinates of the
centre of the detector.
W= Weighting function
2
1
1
2
1
0
| |
1
0
N
W



 
 
 
 
      
 
 
 
 
 
 
Z, X and W can
be represented
as:

m
i i
r
 
1 1 1
2 2 2
1 2 2 2
1 2 2 2
| |
1 2 2 2
N N N
x y z
x y z
X
x y z
  
 
 
  
 

 
       
 
  
 
2 2 2 2
1 1 1 1
2 2 2 2
2 2 2 2
2 2 2 2
( )
( )
| |
( )
( )
N N N N
r x y z
r x y z
Z
r x y z
 
  
 
  
 

 
        
 
  
 
 
Where-
xi, yi, zi are the co-ordinates of the ith
detector.

Fine Grids
Coarse
Grid
Iterative Grid Refinement
Estimate the neighborhood in an
iterative manner matching the
“predicted” counts and the
measured counts…

2D Reconstruction with Monte Carlo
Algorithm
-- Reconstructed points
-- actual points

3D Reconstruction with Monte Carlo
Algorithm
Actual results
Reconstructed result

0 100 200
100
200
300
400
500
600
700
800
x (mm)
z
(mm)
0 100 200
100
200
300
400
500
600
700
800
x (mm)
z
(mm)
0 100 200
100
200
300
400
500
600
700
800
x (mm)
z
(mm)
0 100 200
0
100
200
300
400
500
600
700
800
x (mm0
z
(mm)
Reconstruction of Particle Trajectories
0-6 sec 0-12 sec 0-18 sec 0-30 sec

-150
-100
-50
0
50
100
150
0 50 100 150 200 250 300 350 400
Vz
(mm/s)
Time (s)
-150
-100
-50
0
50
100
150
0 50 100 150 200 250 300 350 400
Vy
(mm/s)
Time (s)
-150
-100
-50
0
50
100
150
0 50 100 150 200 250 300 350 400
Vy
(mm/s)
Time (s)

Total occurrences in the cell (nr=4) = 1238
-50 -25 0 25 50
0
50
100
150
-50 -25 0 25 50
0
50
100
150
Axial Velocity (cm/s)
Azimuthal Velocity (cm/s)
Radial Velocity (cm/s)
-50 -25 0 25 50
0
50
100
150
Frequency
Frequenc
y
Frequenc
y
Middle (r=3.29 cm)
-50 -25 0 25 50
0
50
100
150
Radial Velocity (cm/s)
-50 -25 0 25 50
0
50
100
150
-50 -25 0 25 50
0
50
100
150
Frequency
Frequency
Frequency
Axis (r=0.047 cm)
-50 -25 0 25 50
0
50
100
150
-50 -25 0 25 50
0
50
100
150
-50 -25 0 25 50
0
50
100
150
Frequency
Frequenc
y
Frequenc
y
Wall (r=6.13 cm)

Quantities Calculated from RPT
Experimental data
Ensemble average velocity
Fluctuating velocity component
RMS velocity
Stress
Fluctuating kinetic energy per unit volume
z
z
v
t



( , , )
,
1
1
( , , ) ( , , )
( , , )
N i j k
q q n
n
v i j k v i j k
N i j k 
  
'
( , , ) ( , , ) ( , , )
q q q
v i j k v i j k v i j k
   
'2
RMS
q q
v v
    
' '
( , , ) ( , , )
qs p q s
v i j k v i j k
 
  
'2 '2 '2
1
[ ]
2
p r z
KE v v v


        
Photon counts time series
Lagrangian
position time
series
Lagrangian velocity time
series
Eulerian
grid
Eulerian
velocity
i
,
j
,
k
i
,
j
+
1
,
k
r, θ i, j, k
i, j, k+1
i, j, k+2
r, z
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 0.2 0.4 0.6 0.8 1
r/R [-]
z=25 cm
z=15 cm
z=7.5 cm
Mean
Axial
Velocity
of
Solid
[m/s]

Solids Mean Velocity
i
,
j
,
k
i
,
j
+
1
,
k
r, θ
i, j, k
i, j, k+1
i, j, k+2
r, z
-40
-20
0
20
40
60
80
0 0.2 0.4 0.6 0.8 1
r/R [-]
z/H = 0.06
z/H = 0.19
z/H = 0.46
Ug = 1.12 m/s
Mean
Axial
Velocity
of
Glass
[cm/s]
-20
-10
0
10
20
30
40
50
0 0.2 0.4 0.6 0.8 1
r/R [-]
z/H=0.1
z/H=0.3
z/H=0.5
Mean
Radial
Velocity
of
glass[cm/s]
Ug= 1.12 m/s

Radio active particle tracking implemnetation

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