![Photon counts time series
Lagrangian
position time
series
Lagrangian velocity time
series
Eulerian
grid
Eulerian
velocity
i
,
j
,
k
i
,
j
+
1
,
k
r, ¦È 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]](https://image.slidesharecdn.com/moocsrpt-240920193134-ebe16987/85/Radio-active-particle-tracking-implemnetation-2-320.jpg){kind=tracking}
![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
?
?
? ? ? ? ? ? ? ? ?](https://image.slidesharecdn.com/moocsrpt-240920193134-ebe16987/85/Radio-active-particle-tracking-implemnetation-5-320.jpg){kind=tracking}
![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
?
?
? ? ? ? ? ? ? ? ?
Photon counts time series
Lagrangian
position time
series
Lagrangian velocity time
series
Eulerian
grid
Eulerian
velocity
i
,
j
,
k
i
,
j
+
1
,
k
r, ¦È 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]](https://image.slidesharecdn.com/moocsrpt-240920193134-ebe16987/85/Radio-active-particle-tracking-implemnetation-35-320.jpg){kind=tracking}
![Solids Mean Velocity
i
,
j
,
k
i
,
j
+
1
,
k
r, ¦È
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](https://image.slidesharecdn.com/moocsrpt-240920193134-ebe16987/85/Radio-active-particle-tracking-implemnetation-36-320.jpg){kind=tracking}
Radio active particle tracking implemnetation
- 1. 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
- 2. Photon counts time series Lagrangian position time series Lagrangian velocity time series Eulerian grid Eulerian velocity i , j , k i , j + 1 , k r, ¦È 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]
- 3. 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)
- 4. 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, ¦È 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 ? ? ? ?
- 5. 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 ? ? ? ? ? ? ? ? ? ? ?
- 6. 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)
- 7. Detector Functioning Detector Crystal Photo Multiplier Tube Multi Channel Analyzer Photocathode Anode ? ray Signal BNC cable High Voltage Supply cable
- 8. Number of Photons in given energy bin Counted Photon Energy Photopeak Flow Chart of Data Acquisition System ¦Ã 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)
- 11. 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
- 12. Photon Detection ?Tracer particle releases photons at solid angle of 4¦Ð. ?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
- 13. L ¦Ñ ¦Á ? min ? cri ?m ax X Z ¦Ñ 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
- 15. ? 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
- 16. ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 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
- 17. 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
- 18. 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
- 19. 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:
- 20. Effect of Number of Detectors in Same Plane Increase in Resolution ~ No Improvement in Resolution Increase in Sensitivity Resolution Sensitivity mm mm-1
- 21. 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
- 22. 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)
- 23. Reported Position Reconstruction Algorithms ? Weighted least squares algorithm ? Monte Carlo algorithm ? Neural network based reconstruction ? Cross correlation algorithm
- 24. 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
- 25. ? 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.
- 26. ? 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:
- 27. 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.
- 28. ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 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
- 29. Fine Grids Coarse Grid Iterative Grid Refinement Estimate the neighborhood in an iterative manner matching the ¡°predicted¡± counts and the measured counts¡
- 30. 2D Reconstruction with Monte Carlo Algorithm -- Reconstructed points -- actual points
- 31. 3D Reconstruction with Monte Carlo Algorithm Actual results Reconstructed result
- 32. 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
- 33. -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) Instantaneous Velocity
- 34. 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) Total occurrences in the cell (nr=1) = 1104 -50 -25 0 25 50 0 50 100 150 Radial Velocity (cm/s) -50 -25 0 25 50 0 50 100 150 Azimuthal Velocity (cm/s) -50 -25 0 25 50 0 50 100 150 Axial Velocity (cm/s) Frequency Frequency Frequency Axis (r=0.047 cm) -50 -25 0 25 50 0 50 100 150 Total occurrences in the cell (nr=7) = 1333 -50 -25 0 25 50 0 50 100 150 Azimuthal Velocity (cm/s) -50 -25 0 25 50 0 50 100 150 Frequency Axial Velocity (cm/s) Frequenc y Frequenc y Wall (r=6.13 cm) Instantaneous Velocity
- 35. 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 ? ? ? ? ? ? ? ? ? ? ? Photon counts time series Lagrangian position time series Lagrangian velocity time series Eulerian grid Eulerian velocity i , j , k i , j + 1 , k r, ¦È 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]
- 36. Solids Mean Velocity i , j , k i , j + 1 , k r, ¦È 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