- Email: [email protected]
Concentration profiles of particle conveying using electrical charge tomography
Copyright <:> IFAC Artificial Intelligence in Real-Time Control, Kuala Lumpur, Malaysia, 1997
Concentration profiles of particle conveying using electrical chargetornography
M F Rahrnatl, R G Green2 and JAR Stone3 1. Applied Control Panel, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Skudai Campus, Locked Bag 791,80990 Johor Bahru, Johor, Malaysia [email protected] 2. School of Engineering, Sheffield Hallam University, Pond Street, Sheffield S 1 1WB, UK 3. School of Computing and Management Science, Sheffield Hallam University, Pond Street, Sheffield S 1 1WB, UK
Abstract This paper presents results for a tomographic system using an array of electrodynamic sensors. Sensitivity maps are derived for the individual sensors and then used by a back projection algorithm to calculate concentration profiles from measured sensor values. Limitations in linearity over the sensing area are reduced by applying a filter to the images. The filtered back projection algorithm is tested on both uniformly and artificially produced non-uniformly distributed solids flows. Copyright © 1998 IFAC
Electrodynamic sensors are robust, low cost and sensitive to low flow rates of dry solid material. This paper explains their use in the determination of concentration profiles within the measurement cross-section of a gravity drop conveyor.
2. The measurement system Transducers which can be used to sense the electrostatic charge carried by dry solids have applications in determining flow parameters in pneumatic conveyors, e.g. the velocity of conveyed materials [4, 12] and the solids mass flow rate [8]. Dry solids, moving through a conveyor, generate static electric charge by friction with the conveyor wall. The amplitude of this charge depends on many factors including type, shape and size of materials, humidity, etc. [10], however, in many manufacturing systems the process control provides repeatable conditions, resulting in repeatable levels of charge on the particles. Measurements are based on charge being induced in the sensors as they are passed by the flowing charged particles. These induced charges are converted to voltages, amplified to a level suitable for the data acquisition system and processed off-line.
1. Introduction Measurement of concentration profiles of dry powders flowing in pneumatic and gravity conveyors is a problem which has to be solved in order to progress to determination of volume flow rates. Present methods of concentration measurement include capacitance [9], optical [6] , gamma densitometer [11] and electrodynamic sensors, each with specific advantages and limitations. Capacitance sensors are robust, low cost and are very useful for measurement with dense phase conveying of dry powders. However they pose problems where the conveying density is below 10 % vo\.lvo\., they have a soft field mode of sensing where the shape of the electrical field depends upon the distribution of the dielectric within it and they have a large sensing volume due to the axial length of the electrodes [7].
Sensors generally consist of metal structures insulated from the walls of the conveyor. In process measurements ring electrodes are widely used and have been thoroughly investigated [11, 12]. However, they are limited in their application as they provide averaged signals relating to the concentration of the conveyed material and do not allow the determination of the concentration profile.
In comparison, optical sensors have a relatively high spatial resolution [5], but there are problems associated with keeping the optics clear of dust.
Discrete electrodynamic transducers are robust, low cost and have the potential to be used for process tomography [13] where several identical transducers (typically 8, 16 or 32) are positioned around the vessel being interrogated. These provide the data which is used to reconstruct dynamic images of the movement of the material being
Gamma densitometers are potentially very linear in their response to solids' concentration and have the advantage of use Without damaging the integrity of the conveyor. However, in order to provide high count rates the activity of the source may cause safety problems [11].
537
monitored.
The tomographic image is calculated from the measurements using a filtered back projection algorithm, which is derived from the forward problem.
In the work presented in this paper, an array of sixteen, equi-spaced, circular sensors is mounted around the circumference of the vertical flow pipe (figure I).
"
,,
3. The forward problem The forward problem determines the theoretical output of each of the sensors when the sensing area is considered to be two dimensional and contains a uniformly distributed
. ,
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charge of cr coulombs per square metre. The cross-section of the pipe is mapped onto a nine by nine rectangular array consisting of 81 pixels as shown in figure 3 below .
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Figure I. Cross-section through pipe at measurement section The solids are fed into the pipe from a hopper at a controlled rate via a rotary feeder (figure 2). Information from the sensors is collected by a proprietary data acquisition system and processed off-line to produce tomographic images of the solids concentration within the cross-section.
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Figure 3 : 9x9 rectangular array consists of 81 pixels Each sensor is considered separately and the effect on it -2
due to the uniform surface charge, cr Coulombs m , on each pixel determined. To minimise boundary problems the sensor is placed 0.5 mm outside the pipe wall. Each pixel is considered in turn. The sensitivity map is generated by calculating the charge which a chosen pixel would induce into the sensor. Calculation of the sensitivity map for sensor one is outlined below.
Figure 2. The gravity flow rig
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A typical sensor calibration graph for the flow of dry sand is showlI in figure 3.
'r : ~ :- . . .. . ....,. (x.y) ,
I.
-I
Sensitivity for 3 mm hem electrode
o IS .---.--..--:T----r----.-----.. o
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Figure 4: Sensitivity model for sensor I
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The centre of the pipe has rectangular co-ordinates (0,0). The pipe diameter is 81 mm and each pixel is 9x9 mm. The general sensitivity equation corresponding to sensor I is,
_ _~_ _~_ _~_~ 200
300
SOO
Flow role (Jr>m'oec)
Figure 3. Averaged induced voltage versus mass flow rate for 3 mm hemispherical electrode.
where (x,y) are the co-ordinates of the part of the pixel contributing to the sensor output, r is the distance of the charge to the sensor and the inverse square law is obeyed. The total in~ced charge for sensor I when to be I C m is,
538
cr
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40.5 'I
The sensitivity map for sensor I may be plotted in three dimensions (figure 6), where (x,y) represent the pipe crosssection and the z-axis the sensitivity. This shows the significant localised sensitivity of the sensor. These calculations are repeated for each of the sixteen sensors, resulting in sixteen separate sensitivity maps. These maps are then used to solve the inverse problem.
J405'-x'
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-405
-J405'-x' X
1
2
2
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However the sensitivity map requires the contribution from each pixel to be evaluated. Each pixel is identified numerically, the first number is the column number, the second is the row number starting with 11 for the top left hand pixel. Two examples of the sensitivity calculation are shown below. 4S
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Solution of the inverse problem aims to provide an image of the charge concentration distribution within the conveyor, which would result in the measured sensor outputs.
1
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-45
4. The Inverse Problem
+ (41- y)
2
4.1 Basic back projection
dy'" 0,01
A linearized back projection algorithm is used [1]. The back projection algorithm combines each sensor reading with its sensitivity map to generate the charge concentration map within the pipe which would provide these readings (assuming all particles carry the same charge). The procedure is to multiply each sensor voltage reading by its sensitivity map to produce sixteen 9x9 matrices. The corresponding individual elements from the 16 matrices are summed to produce a single matrix i.e. the concentration matrix.
This is repeated for all pixels. Complete pixels and parts of pixels outside the pipe contribute zero induced charge to the sensor and so have a sensitivity value of zero i.e. pixelll, 12,21, 81, 91, 92, 18, 19,29, 89, 98 and 99. However, pixels intersected by the pipe boundary have a contribution to the induced charge from the fraction of the pixel within the conveyor. The resulting sensitivity map for sensor 1 is shown in figure 5. o
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The theoretical concentration profile has been calculated assuming all the sensors are reading I Volt. The concentration matrix is shown in figure 7 with the relative position of the pipe mapped onto it. Figure 8 displays the result as a coloured tomogram, where colour relates to solids concentration.
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Figure 8. Theoretical image of concentration distribution obtained using the linear back projection algorithm when all sensors is I volt
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Figures 7 and 8 identify the limitation of the simple linear back projection algorithm; the low estimation of solids at the centre of the conveyor. This problem may be reduced by using a filtered back projection algorithm.
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The major limitation of the linear back projection algorithm arises due to the non-linear sensing mechanism of the electrical charge transducer. When the conveyor has a uniformly distributed solids flow the resulting concentration matrix, calculated using the linear back projection algorithm, is not uniform at 7.32 units per pixel, but shows lower values as the centre of the pipe is approached, reaching 0.77 units at the centre. However a filter can be determined, which, combined with the back projection algorithm, provides a filtered linear back projection algorithm [2). This filter provides weighting to individual pixels to provide a uniform concentration profile.
5 Results Tests were made using both plastic particles approximately 3 mm in diameter and sand with a mean diameter of 600 Il m over a range of solid flow rates. Non-linear concentration profiles were created by blocking sections of the conveyor upstream of the sensors with obstructions of know shape. A range of solid feed rates were used and the measurements were logged using a proprietary data acquisition system. The results were processed off-line using a PC with a 486 processor. The concentration profiles were determined using both linear back projection and filtered back projection algorithms.
The coefficients of the filter are obtained by assuming all the sensors have an output of 1 volt. and using these values to calculate the concentration matrix described in section 3. 1. The expected result is a uniform concentration matrix with each values of 7.32 units per pixel.
F~
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The filter matrix is obtained by taking the maximum value of 7.32 units per pixel which is then divided by each value of pixel within the pipe mapping. The resulting filter is shown in figure 9. ',yJf(UJ
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Mathematically, this filter is only applicable to full flow. Similar filters should be calculated for different flow patterns. However to be useful, this requires the flow regime or flow pattern with the conveyor to be known. Flow regimes have been identified using an array of electrodynamic sensors placed around the circumference of a conveyor [3] as shown in figure 1. A filter mask for the specific non-uniform flow of separated flow is shown in figure 10.
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6 Discussion of results The measured results obtained for uniformly distributed solids' flow, using the linearized back projection algorithm (figure 11), show concentration values are lower towards These the centre of the conveyor as predicted. measurements are improved by using the filtered back projection algorithm (figure 12). 59
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The measured concentration profiles determined for nonuniformly distributed flow show that the solids are not uniformly distributed. However by visual inspection of the solid flow, the result obtained using the simple linear back projection algorithm (figure 13) seems less representative of the shape of the flow profile being produced than that obtained using the filtered back projection algorithm (figure 14).
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In the tests, the error between the calculated concentrations and the measured flow rates had a standard deviation of 20% of calculated concentration when using the plastic beads. It is thought that the accuracy will be significantly improved by using a pneumatic conveyor rather than the gravity drop system and baffles, as the baffles may interact with the particles and modify the charge being carried by them.
0
Figure 13. Measured image of concentration distribution obtained using the linear back projection algorithm: plastic beads separated flow at a flow rate of 52 gls
7 Conclusions Tomographic images of solids concentration may be obtained using electrodynamic sensors. The non-linear field of the sensor requires that the concentration profile be calculated using a filtered back projection algorithm. As with all electrodynamic sensors, quantitative values will only be reliable and repeatable if the process being monitored is well controlled in terms of moisture content and particle size range. However, the system described in this paper provides a very low cost method for producing tomographic images of solids concentration profiles.
541
[12] Yan, Y, Byme, B, Woodhead, S, Coulthard, J, "Velocity measurement of pneumatically conveyed solids using electrodynamic sensors." Meas. Sci. Technol., Vol. 6, p 515-537, 1995b.
The system could be made to work on-line, but would require a dedicated data acquisition system and modifications to the algorithm. A processor capable of 25 Mflop should be capable of providing approximately 500 to 1000 concentration matrices per second. This paper describes a feasibility study into obtaining concentration profiles of flowing dry powders using electrodynamic sensors. Further testing with a wide range of materials and flow rates is required to determine the limitations of the measurement system.
[13] Williarns, R A and Beck, M S, Ed "Process Tomography: Principles, Techniques and Applications", Butterworth-Heinemann, 1995, \01118.
8 References [I] Abdullah, M Z, "Application of resistive electrical impedance tomography to observe hydrocycIone separator dynamics." PhD Thesis, UMIST, 1993. [2] Barber, D C and Brown, B H, "Applied potential tomography" J. Phys. E: Sci. Instrum., Vol. 17, 1984, p 723-733 . [3] Bidin, A R., Green, R G, Shackleton, M E, Taylor, R W, "Neural networks for flow regime identification with dry particulate flows." Part. Part. Syst. Charact. 10, (1993), pages 234-238. [4] Featherstone, A M, Green, R G, Shackleton, M E, "Yam velocity measurement." 1. Phys. E: Sci. Instrum., Vol. 16, 1983, P 462-464. [5] Green, R G, Horbury, N M, Abdul Rahim, R, Dickin, F J, Naylor, B D, Pridmore, T P, "Optical fibre sensors for process tomography.", Meas. Sci. Technol., Vol. 6,1995, pI699-1704. [6] Green, R G, Abdul Rahim, R, Evans, K, Dickin, F J, Naylor, B D, Pridmore, T P, "Concentration profiles in a pneumatic conveyor by optical tomography measurement." Meas. Sci. Technol., Vol. 7, 1996, p419-422. [7] Hammer, E A and Green, R G, "The spatial filtering effect of capacitance transducer electrodes." J. Phys. E: Sci. Instrum., Vol. 16,1983, p438-443 . [8] King, P.W, "Mass flow measurement of conveyed solids, by monitoring of intrinsic electrostatic noise levels." 2nd. Int. Con. on the Pneumatic Transport of Solids in Pipes, Cranfield, 1973. [9] McKee, S L, Williarns, R A, Dyakowski, T, Bell, T, Alien, T, "Solids flow imaging and attrition studies in a pneumatic conveyor." Powder Technology, Vol. 82, p 105-113, 1995. [10] Shackleton ME, "Electrodynamic sensors for process measurement." MPhil Thesis, University of Bradford, 1982. [11] Yan, Y, Byme, B, Coulthard, J, "Sensing homogeneity in mass flow rate measurement of pneumatically conveyed solids." Flow Measurement and Instrumentation, Vol. 6, No 2, p 115-119, 1995.
542
Concentration profiles of particle conveying using electrical chargetornography
M F Rahrnatl, R G Green2 and JAR Stone3 1. Applied Control Panel, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Skudai Campus, Locked Bag 791,80990 Johor Bahru, Johor, Malaysia [email protected] 2. School of Engineering, Sheffield Hallam University, Pond Street, Sheffield S 1 1WB, UK 3. School of Computing and Management Science, Sheffield Hallam University, Pond Street, Sheffield S 1 1WB, UK
Abstract This paper presents results for a tomographic system using an array of electrodynamic sensors. Sensitivity maps are derived for the individual sensors and then used by a back projection algorithm to calculate concentration profiles from measured sensor values. Limitations in linearity over the sensing area are reduced by applying a filter to the images. The filtered back projection algorithm is tested on both uniformly and artificially produced non-uniformly distributed solids flows. Copyright © 1998 IFAC
Electrodynamic sensors are robust, low cost and sensitive to low flow rates of dry solid material. This paper explains their use in the determination of concentration profiles within the measurement cross-section of a gravity drop conveyor.
2. The measurement system Transducers which can be used to sense the electrostatic charge carried by dry solids have applications in determining flow parameters in pneumatic conveyors, e.g. the velocity of conveyed materials [4, 12] and the solids mass flow rate [8]. Dry solids, moving through a conveyor, generate static electric charge by friction with the conveyor wall. The amplitude of this charge depends on many factors including type, shape and size of materials, humidity, etc. [10], however, in many manufacturing systems the process control provides repeatable conditions, resulting in repeatable levels of charge on the particles. Measurements are based on charge being induced in the sensors as they are passed by the flowing charged particles. These induced charges are converted to voltages, amplified to a level suitable for the data acquisition system and processed off-line.
1. Introduction Measurement of concentration profiles of dry powders flowing in pneumatic and gravity conveyors is a problem which has to be solved in order to progress to determination of volume flow rates. Present methods of concentration measurement include capacitance [9], optical [6] , gamma densitometer [11] and electrodynamic sensors, each with specific advantages and limitations. Capacitance sensors are robust, low cost and are very useful for measurement with dense phase conveying of dry powders. However they pose problems where the conveying density is below 10 % vo\.lvo\., they have a soft field mode of sensing where the shape of the electrical field depends upon the distribution of the dielectric within it and they have a large sensing volume due to the axial length of the electrodes [7].
Sensors generally consist of metal structures insulated from the walls of the conveyor. In process measurements ring electrodes are widely used and have been thoroughly investigated [11, 12]. However, they are limited in their application as they provide averaged signals relating to the concentration of the conveyed material and do not allow the determination of the concentration profile.
In comparison, optical sensors have a relatively high spatial resolution [5], but there are problems associated with keeping the optics clear of dust.
Discrete electrodynamic transducers are robust, low cost and have the potential to be used for process tomography [13] where several identical transducers (typically 8, 16 or 32) are positioned around the vessel being interrogated. These provide the data which is used to reconstruct dynamic images of the movement of the material being
Gamma densitometers are potentially very linear in their response to solids' concentration and have the advantage of use Without damaging the integrity of the conveyor. However, in order to provide high count rates the activity of the source may cause safety problems [11].
537
monitored.
The tomographic image is calculated from the measurements using a filtered back projection algorithm, which is derived from the forward problem.
In the work presented in this paper, an array of sixteen, equi-spaced, circular sensors is mounted around the circumference of the vertical flow pipe (figure I).
"
,,
3. The forward problem The forward problem determines the theoretical output of each of the sensors when the sensing area is considered to be two dimensional and contains a uniformly distributed
. ,
.......
.,.
charge of cr coulombs per square metre. The cross-section of the pipe is mapped onto a nine by nine rectangular array consisting of 81 pixels as shown in figure 3 below .
.. x_
•
'"
V
."
-
r---.-
~
"11
'J
\
1\
,
Figure I. Cross-section through pipe at measurement section The solids are fed into the pipe from a hopper at a controlled rate via a rotary feeder (figure 2). Information from the sensors is collected by a proprietary data acquisition system and processed off-line to produce tomographic images of the solids concentration within the cross-section.
~
l¥
l'.
Figure 3 : 9x9 rectangular array consists of 81 pixels Each sensor is considered separately and the effect on it -2
due to the uniform surface charge, cr Coulombs m , on each pixel determined. To minimise boundary problems the sensor is placed 0.5 mm outside the pipe wall. Each pixel is considered in turn. The sensitivity map is generated by calculating the charge which a chosen pixel would induce into the sensor. Calculation of the sensitivity map for sensor one is outlined below.
Figure 2. The gravity flow rig
I).,£......+ / ---l_,(o.y)
A typical sensor calibration graph for the flow of dry sand is showlI in figure 3.
'r : ~ :- . . .. . ....,. (x.y) ,
I.
-I
Sensitivity for 3 mm hem electrode
o IS .---.--..--:T----r----.-----.. o
o
o
Figure 4: Sensitivity model for sensor I
o o O~~O_~
o
l OO
The centre of the pipe has rectangular co-ordinates (0,0). The pipe diameter is 81 mm and each pixel is 9x9 mm. The general sensitivity equation corresponding to sensor I is,
_ _~_ _~_ _~_~ 200
300
SOO
Flow role (Jr>m'oec)
Figure 3. Averaged induced voltage versus mass flow rate for 3 mm hemispherical electrode.
where (x,y) are the co-ordinates of the part of the pixel contributing to the sensor output, r is the distance of the charge to the sensor and the inverse square law is obeyed. The total in~ced charge for sensor I when to be I C m is,
538
cr
is assumed
40.5 'I
The sensitivity map for sensor I may be plotted in three dimensions (figure 6), where (x,y) represent the pipe crosssection and the z-axis the sensitivity. This shows the significant localised sensitivity of the sensor. These calculations are repeated for each of the sixteen sensors, resulting in sixteen separate sensitivity maps. These maps are then used to solve the inverse problem.
J405'-x'
= Jdx.
J
-405
-J405'-x' X
1
2
2
dy'" 11.75 Coulombs
+ (41- y)
However the sensitivity map requires the contribution from each pixel to be evaluated. Each pixel is identified numerically, the first number is the column number, the second is the row number starting with 11 for the top left hand pixel. Two examples of the sensitivity calculation are shown below. 4S
Pixe/51
=
J
JdX.
31.S X
4S
-31.S
J
Pixe/59 = JdX.
2
dy", 6.20
2
+(41-y) 1 2
-40.S X
-4.S
Solution of the inverse problem aims to provide an image of the charge concentration distribution within the conveyor, which would result in the measured sensor outputs.
1
40.5
-45
4. The Inverse Problem
+ (41- y)
2
4.1 Basic back projection
dy'" 0,01
A linearized back projection algorithm is used [1]. The back projection algorithm combines each sensor reading with its sensitivity map to generate the charge concentration map within the pipe which would provide these readings (assuming all particles carry the same charge). The procedure is to multiply each sensor voltage reading by its sensitivity map to produce sixteen 9x9 matrices. The corresponding individual elements from the 16 matrices are summed to produce a single matrix i.e. the concentration matrix.
This is repeated for all pixels. Complete pixels and parts of pixels outside the pipe contribute zero induced charge to the sensor and so have a sensitivity value of zero i.e. pixelll, 12,21, 81, 91, 92, 18, 19,29, 89, 98 and 99. However, pixels intersected by the pipe boundary have a contribution to the induced charge from the fraction of the pixel within the conveyor. The resulting sensitivity map for sensor 1 is shown in figure 5. o
o
~ ora
0
~ O~
011
laD
ora ~ 0
0"
o:u
The theoretical concentration profile has been calculated assuming all the sensors are reading I Volt. The concentration matrix is shown in figure 7 with the relative position of the pipe mapped onto it. Figure 8 displays the result as a coloured tomogram, where colour relates to solids concentration.
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The major limitation of the linear back projection algorithm arises due to the non-linear sensing mechanism of the electrical charge transducer. When the conveyor has a uniformly distributed solids flow the resulting concentration matrix, calculated using the linear back projection algorithm, is not uniform at 7.32 units per pixel, but shows lower values as the centre of the pipe is approached, reaching 0.77 units at the centre. However a filter can be determined, which, combined with the back projection algorithm, provides a filtered linear back projection algorithm [2). This filter provides weighting to individual pixels to provide a uniform concentration profile.
5 Results Tests were made using both plastic particles approximately 3 mm in diameter and sand with a mean diameter of 600 Il m over a range of solid flow rates. Non-linear concentration profiles were created by blocking sections of the conveyor upstream of the sensors with obstructions of know shape. A range of solid feed rates were used and the measurements were logged using a proprietary data acquisition system. The results were processed off-line using a PC with a 486 processor. The concentration profiles were determined using both linear back projection and filtered back projection algorithms.
The coefficients of the filter are obtained by assuming all the sensors have an output of 1 volt. and using these values to calculate the concentration matrix described in section 3. 1. The expected result is a uniform concentration matrix with each values of 7.32 units per pixel.
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Mathematically, this filter is only applicable to full flow. Similar filters should be calculated for different flow patterns. However to be useful, this requires the flow regime or flow pattern with the conveyor to be known. Flow regimes have been identified using an array of electrodynamic sensors placed around the circumference of a conveyor [3] as shown in figure 1. A filter mask for the specific non-uniform flow of separated flow is shown in figure 10.
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6 Discussion of results The measured results obtained for uniformly distributed solids' flow, using the linearized back projection algorithm (figure 11), show concentration values are lower towards These the centre of the conveyor as predicted. measurements are improved by using the filtered back projection algorithm (figure 12). 59
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In the tests, the error between the calculated concentrations and the measured flow rates had a standard deviation of 20% of calculated concentration when using the plastic beads. It is thought that the accuracy will be significantly improved by using a pneumatic conveyor rather than the gravity drop system and baffles, as the baffles may interact with the particles and modify the charge being carried by them.
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Figure 13. Measured image of concentration distribution obtained using the linear back projection algorithm: plastic beads separated flow at a flow rate of 52 gls
7 Conclusions Tomographic images of solids concentration may be obtained using electrodynamic sensors. The non-linear field of the sensor requires that the concentration profile be calculated using a filtered back projection algorithm. As with all electrodynamic sensors, quantitative values will only be reliable and repeatable if the process being monitored is well controlled in terms of moisture content and particle size range. However, the system described in this paper provides a very low cost method for producing tomographic images of solids concentration profiles.
541
[12] Yan, Y, Byme, B, Woodhead, S, Coulthard, J, "Velocity measurement of pneumatically conveyed solids using electrodynamic sensors." Meas. Sci. Technol., Vol. 6, p 515-537, 1995b.
The system could be made to work on-line, but would require a dedicated data acquisition system and modifications to the algorithm. A processor capable of 25 Mflop should be capable of providing approximately 500 to 1000 concentration matrices per second. This paper describes a feasibility study into obtaining concentration profiles of flowing dry powders using electrodynamic sensors. Further testing with a wide range of materials and flow rates is required to determine the limitations of the measurement system.
[13] Williarns, R A and Beck, M S, Ed "Process Tomography: Principles, Techniques and Applications", Butterworth-Heinemann, 1995, \01118.
8 References [I] Abdullah, M Z, "Application of resistive electrical impedance tomography to observe hydrocycIone separator dynamics." PhD Thesis, UMIST, 1993. [2] Barber, D C and Brown, B H, "Applied potential tomography" J. Phys. E: Sci. Instrum., Vol. 17, 1984, p 723-733 . [3] Bidin, A R., Green, R G, Shackleton, M E, Taylor, R W, "Neural networks for flow regime identification with dry particulate flows." Part. Part. Syst. Charact. 10, (1993), pages 234-238. [4] Featherstone, A M, Green, R G, Shackleton, M E, "Yam velocity measurement." 1. Phys. E: Sci. Instrum., Vol. 16, 1983, P 462-464. [5] Green, R G, Horbury, N M, Abdul Rahim, R, Dickin, F J, Naylor, B D, Pridmore, T P, "Optical fibre sensors for process tomography.", Meas. Sci. Technol., Vol. 6,1995, pI699-1704. [6] Green, R G, Abdul Rahim, R, Evans, K, Dickin, F J, Naylor, B D, Pridmore, T P, "Concentration profiles in a pneumatic conveyor by optical tomography measurement." Meas. Sci. Technol., Vol. 7, 1996, p419-422. [7] Hammer, E A and Green, R G, "The spatial filtering effect of capacitance transducer electrodes." J. Phys. E: Sci. Instrum., Vol. 16,1983, p438-443 . [8] King, P.W, "Mass flow measurement of conveyed solids, by monitoring of intrinsic electrostatic noise levels." 2nd. Int. Con. on the Pneumatic Transport of Solids in Pipes, Cranfield, 1973. [9] McKee, S L, Williarns, R A, Dyakowski, T, Bell, T, Alien, T, "Solids flow imaging and attrition studies in a pneumatic conveyor." Powder Technology, Vol. 82, p 105-113, 1995. [10] Shackleton ME, "Electrodynamic sensors for process measurement." MPhil Thesis, University of Bradford, 1982. [11] Yan, Y, Byme, B, Coulthard, J, "Sensing homogeneity in mass flow rate measurement of pneumatically conveyed solids." Flow Measurement and Instrumentation, Vol. 6, No 2, p 115-119, 1995.
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