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Tracing the motion of a large object in a fluidized bed using electrical capacitance tomography
Flow Measurement and Instrumentation 33 (2013) 1–9
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Tracing the motion of a large object in a fluidized bed using electrical capacitance tomography Cai Rong-rong, Zhang Yan-guon, Li Qing-hai, Meng Ai-hong Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
art ic l e i nf o
a b s t r a c t
Article history: Received 18 November 2012 Received in revised form 7 April 2013 Accepted 24 April 2013 Available online 9 May 2013
An innovative method using electrical capacitance tomography (ECT) to trace a large object's motion on an air distributor in a fluidized bed is described here. The method fills the large object to be traced with a high permittivity material, and then a recalibration process is applied to reduce the nonlinearity caused by the large permittivity difference between the tracer particle and other fine particles in the measurement zone. The local dynamic threshold selection method is performed on the reconstructed image to locate the tracer particle's position. Static simulations and dynamic experiments testify that tracer particles with a diameter of one ninth of the measured cross-section and a fluidization velocity v/vcr≤4.2 can be accurately located and traced. Employing this method to trace the motion of a spherical object in a bed shows that the fluidization velocity significantly influences the directional motion of a large, heavy object on an inclined air distributor. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Electrical capacitance tomography (ECT) Fluidized bed Tracing Dense zone Recalibration
1. Introduction Fluidized bed reactors have been used for a variety of applications at many scales, ranging from small chemical reactors to large coal combustors. Examples of their application include thermal conversion of solid fuels, drying processes, and pneumatic conveying. In some cases, the presence of large objects, such as catalysts, fuel particles (large solid waste, biomass particle etc.) or agglomerates, in a bed of fine particles is required or occurs during fluidization. The motion pattern of large objects may thus prove to be a key factor in the performance of these beds. Extensive work has been carried out to analyze the motion of large objects immersed in a fluidized bed. Several researchers have studied the sinking and rising processes of large objects in 2-D and 3-D beds [1–6]. These researchers focused on the mixing and segregation processes of binary or ternary mixtures and found that the hydrodynamic behavior of the particles was strongly influenced by the difference in the properties of the particles, especially the density, shape and size. In addition, some researchers tried to trace a single large object's trajectory during fluidization to directly understand its motion pattern [7–10]. However, most of these studies concentrated on the large objects with a low density and the vertical motion in the dilute zone rather than on the motion of heavy, large objects near the air distributor. This is
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Corresponding author. Tel.: +86 10 62783373. E-mail address: [email protected] (Y.-g. Zhang).
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partly due to the lack of reliable experimental methods to observe the particles' motions in the dense zone of the bed. In the visual observation of 3-D beds, it is typically impossible to trace the motion of individual large objects because of shielding by the surrounding neighbors in the dense zone. Recently, positron emission particle tracking (PEPT) and computer-aided radioactive particle tracking (CAPRT) have been used to obtain detailed information on the motion of particles in a fluidized bed [11–13]. These techniques use positron cameras to detect the pairs of back-to-back γ-rays arising from the annihilation of the emitted positrons. The positron-emitting tracers are normally labeled by the radionuclides 18F, 61Cu and 66Ga. A location algorithm is used to calculate the tracer location. Both of the methods allow direct measurement of particle trajectories; however, they require high-cost, specialized equipment and sound operating expertise. Also reported was magnetic particle tracking (MPT), which utilizes less expensive Hall-effect sensors instead of the expensive γ-ray detectors to trace neodymium magnets to continuously locate the position of a single tracer particle over time [14]. This technique also has certain limitations, including the complexity and limited range of the tracer's bipolar magnetic field. All of the described measurement techniques collect information about the particle's movement from signals arising from the interaction between the tracer and the external sensor. Zhang et al. proposed a new tracing concept, which would enable the particles to sense and record by themselves and send this information to the user [15]. They encapsulated a micro 3-D acceleration sensor into a tracer particle to sense the force
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a w, v (X,Y)
Nomenclature db C K S V E P v m
mean fine particle diameter capacitance between the electrodes material permittivity sensitivity map voltage electric field intensity element area fluidization velocity adjustment coefficient
threshold weight factor position of the tracer particle
Subscripts ab nor re cr
information of the particle. The method was validated to be feasible by free fall and was used to detect phase structure. However, because of the existence of the sensor, it is difficult to simulate particles in wide size or density ranges. Also the accuracy in locating the position from the force information remains in doubt. Other non-intrusive imaging methods, such as magnetic resonance imaging (MRI), X-ray tomography (XRT), electrical resistance tomography (ERT) and electrical capacitance tomography (ECT) are widely used for the analysis of solid motion in a fluidized bed. Among these techniques, ECT is considered to be the most available tomographic technique because of its high-speed capability, low construction cost, high safety and suitability for either small or large vessels. A review of the available fluidization literature with the application of the ECT system has shown that previous studies have mainly concentrated on the observation of flow patterns [16,17], measurement of particle concentrations [18– 20], or measurement of particle velocities [21,22]. Because of the technique's low resolution, it has not been used to measure the motion of individual particles. In this paper, the use of ECT to trace a large object's motion on an inclined air distributor in a fluidized bed was investigated. Special treatment was applied to the large tracing particle to enhance the permittivity difference between the particle and the bed materials. Recalibration was applied to reduce the nonlinearity caused by the large permittivity difference in the measurement zone. Image subtraction and the local dynamic threshold selection method were used to locate the particle's position. The method described here will widen the ECT application range and become a practical and simple technology in particle tracing.
2. Experiment lab and materials The experiment was carried out in a cold conventional fluidized bed with a 0.24 0.28 m2 cross-section and a height of 1.8 m. A 51 inclined air distributor made of plexiglass was placed 0.6 m above the bottom of the cuboid at its lower side. 194 Orientation air cups were evenly distributed on the plate, oriented towards the plate's downward direction. The opening ratio was 5.68%. Air was introduced to the bottom of the bed from a vortex fan after passing through a rotameter and a valve.
absolute (capacitance) normalized (capacitance) recalibration critical
To obtain a large permittivity difference, polypropylene particles with a relative permittivity of 1.5 were chosen as the bed material. Following a sieving process, the bed material's size was limited to particles in the range of 0.6–1 mm, and the mean particle diameter was calculated according to the surface to −1 volume ratio as db ¼ ðΣ m i ¼ 1 ðxi =dbi ÞÞ . The particle density was 3 756 kg/m , and the particles therefore belong to Geldart Group B. The large tracer particle was made by filling a box with different high permittivity materials, according to practical simulation requires. The box's shape and size were determined by a thin outer box, and its density was varied by changing the ratio of the inner materials. Some large tracer particles was created in this experiment, and their characteristics are given in Table 1.
3. ECT system and recalibration The ECT system consisted of an electrical capacitance sensor unit, a data acquisition module (PTL300E-SP-G ECT) and a personal computer equipped with custom communication hardware. The capacitance sensor unit was composed of 12 measurement electrodes, each with an axial length of 5.0 cm, and 2 axial electrodes, each 6.0 cm high. Details of the electrodes' sizes can be found in Fig. 1. The air distributor sensor was arranged outside of the cuboid bed, so that the bottom edge of the measurement electrode was as high as the lower edge of the air distributor. This arrangement ensured that the inclined air distributor partly lay in the measurement zone, and any large tracer particle in the dense zone was detected, as shown in Fig. 2. All of the electrodes were connected to the PC through a data acquisition module, which had a capturing rate of 50 frames/s. The Landweber image reconstruction algorithm [23] was employed to derive the image from the capacitance data. Because of the large tracer particle's much higher permittivity, its position could be found in the reconstruction image. Prior to data recording, the system requires calibration. Unlike traditional ECT application in a gas–solid fluidized bed, there are three materials with different permittivities in the measurement zone: air, bed materials and a large tracer particle. Originally, a twopoint calibration was taken at two extreme cases: zero for the lower permittivity materials (air usually) in the bed and one for the higher permittivity material, and then the measured capacitance data was
Table 1 The properties of the large tracer particles. Shape
Size (cm)
Density (g/cm3)
Material
Sphere
D¼ 3 D¼ 4 D¼ 5
0.90 0.87 0.83
Shell: plastic; Filling: acid polymethylene methyl acrylate
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3
Fig. 1. Experimental setup and arrangement of ECT sensor.
Fig. 2. The position of the air distributor and electrodes.
linearly normalized. However, the relationship between the material permittivity change in the bed and the capacitance change among any two electrodes is nonlinear, as shown in Fig. 3. This behavior was especially noticeable in this experiment, as the permittivity of the large tracing particle is several times larger than that of the bed materials, which aggravates the nonlinearity and may cause serious errors. Therefore, recalibration was performed in this work to reduce the nonlinearity. Five different materials, with relative permittivities ranging from 1 to 8 were filled into the bed, and their absolute capacitance data were recorded. Then, a quadratic curve was used to fit these data to obtain a calibration curve C¼ f(K) as shown by the solid line in Fig. 4, which is suitable for the specific measurement zone and the electrode arrangement. C is the capacitance between the electrodes, and K is the material permittivity. With this information, before every measurement, only two
points of absolute capacitance must be measured by filling the bed with air (low permittivity) and bed material (relatively high permittivity). The calibration curve C ¼f(K), was stretched to fit these two points, and then a new calibration curve was produced, as shown by the bold dashed line in Fig. 4. The normalized capacitances calculated from absolute capacitances with or without recalibration were shown in Table 2. A tracer particle was placed in the corner of the measurement zone near electrode 12. Clearly, the normalized capacitance with recalibration can be as much as 10% different from the original two-point calibration when there exists extremely high permittivity zone. Therefore, recalibration can effectively reduce the nonlinearity in normalization, especially if the difference in permittivity between materials in the measurement zone is large. The normalized capacitance may be greater than 1; however, this does not affect the tracing result.
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4. Method validation 4.1. Validation of ECT tracing by static simulation As illustrated in Fig. 2, the measurement zone has an obstacle– air distributor. This is another difference from traditional applications, in which there is only air between the electrodes when no materials are present. To determine the influence of the plate on the measurement, static simulations with or without the air distributor plate in the measurement zone were performed using the Comsol software. One geometric model was based on the actual experimental configuration and electrode design pattern shown Fig. 2. The inclined air distribution plate was made of
380 360
C/pF
340 320 300 280
value linerization fit curve
260 240
1
2
3
4
5
6
7
8
K Fig. 3. Capacitance between adjacent electrodes when filled with different permittivity materials.
550 two point calibratin curve
500 450 C/pF
recalibration curve 400 350 300
C = f (K)
where Si,j is the sensitivity map between electrode i and electrode j, Ei is the electric field distribution when electrode i is excited by voltage Vi, and P(x,y) is the element area. The existence of the air distributor has the greatest influence on the sensitivity map of opposite electrodes if there is any influence; therefore, only the sensitivity maps of opposite electrodes are compared here, as shown in Fig. 5. This figure shows that the shapes and values of the sensitivity map in the two cases are very similar to each other, which means that the existence of the air distributor plate has little influence on the sensitivity map in this experimental configuration (air distributor with an inclined angle of 51, thickness of 1 cm, relative permittivity of 3.75). Next, a spherical particle with a diameter of 4 cm and a relative permittivity of 15 was placed in the center or corner of the bed, on the air distributor. The other part of the measurement zone was filled with bed materials with a relative permittivity of 1.5. The inter-electrode capacitances were calculated by the finite element method (FEM) using Comsol, and then the calibration method described in Section 3 was used to calibrate and normalize the capacitance data. Finally, Landweber algorithms and the sensitivity map calculated above were applied to reconstruct the image. As shown in Fig. 6, the spherical particle's position can be accurately and easily recognized. More simulations verify that if the permittivity of the tracer particle is more than ten times greater than that of the surrounding materials, the particle's position can be located when its size is one tenth of the measurement zone's diameter in a static simulation. Moreover, a particle near the wall is more easily recognized than one in the center. The key to tracing a particle is accurately and in a timely manner locating its position; that means that only the relative value of pixel permittivity in the measurement zone is of concern. Because of the higher permittivity of the tracer particle, it is believed that the pixels with high permittivity in the reconstructed image indicate where tracer particle is located. The distribution of the permittivity value in the reconstructed image does not correspond to the material concentration in the measurement zone. Therefore, a normalized capacitance larger than 1 and a pixel value in the reconstructed image larger than 1 are accurate. 4.2. Validation of ECT tracing by experiment
250 200
plexiglass, with a thickness of 1 cm and a relatively permittivity of 3.75. The other geometric model included no plate. The sensitivity map is an important factor that influences the ECT reconstruction result. Therefore, the sensitivity maps in the above two cases were first calculated and compared. Five different cross-sections alone electrode heights were used to calculate each section's electric fields, and then the electric fields were averaged as the measurement zone's electric fields. Finally, the sensitivity map was calculated according to the following equation: Z Ei ðx; yÞ Ej ðx; yÞ Si;j ðx; yÞ ¼ − dx dy ð1Þ Vi Vj pðx;yÞ
1
2
3
4
5
6
7
8
K Fig. 4. Recalibration process.
Static simulation reveals that it is feasible to locate a large object's position in a static bed when its size is one tenth of the measurement cross-section's diameter. However, in actual gas–solid fluidization, the bed material distribution is uneven in the dense zone near the air distributor; in addition, the distribution fluctuates irregularly with
Table 2 The normalized capacitances from with or without recalibration. Electrode pairs
C1,2
C1,3
C1,4
C1,5
C1,6
C1,7
C1,8
C1,9
C1,10
C1,11
C1,12
C_ab (Ff) C_nor C_nor_r
352.40 0.601 0.598
42.86 0.526 0.520
24.04 0.544 0.539
14.86 0.429 0.423
10.85 0.440 0.435
10.14 0.603 0.601
11.20 0.553 0.549
16.06 0.568 0.56
28.44 0.641 0.640
52.86 0.934 0.934
397.42 1.658 1.831
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C1,6
y
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Fig. 5. Sensitivity maps with or without an air distributor. (1) With air distributor. (2) Without air distributor.
Fig. 6. Static simulation result. (1) Particle in the center. (2) Particle in the corner.
time. Also, ECT has a soft field effect, meaning that the permittivity change in any region of the measured zone will affect the entire result. For example, if the bed materials suddenly agglomerate in the center of the bed, then only the pixel permittivity in that region is correspondingly higher. However, in the reconstruction image, all pixel permittivity in the measurement zone will be higher, and the closer from the center the location is, the greater the effect will be. Therefore, a change in the bed materials' distribution with space and time will interfere in the determination of the tracer particle's position. For this reason, the following experiments were performed to study this effect, and some measurements were obtained to reduce the effect.
4.2.1. Experimental verification method A spherical particle with a diameter of 3, 4 or 5 cm and relative permittivity of 15 was fixed at the end of a plastic hollow rod, and the rod was then inserted at the top of the bed to place the tracer particle in a different position on the air distributor during fluidization. A coordinate system was set at the top of the bed to accurately determine the large tracing particle's coordinates. Seven different positions (1 (−120,100); 2 (−120,0); 3 (0,100); 4 (120,−100);
5 (120,0); 6 (70,−60); 7 (0,0)) were chosen in this experiment, as shown in Fig. 7. The fluidization velocity was set as v/vcr ¼3.0–4.6 (vcr ¼0.27 m/s). To reduce the influence of the bed materials' distribution on the measurements, the following experimental procedures and data post-processing methods were used. (1) Capacitance data were captured for 5 min at a rate of 50 frames/s when there was no large particle in the fluidized bed. The image was reconstructed as described in Section 4.1, and then the total 15,000 frames of image were averaged as the background image. (2) The tracer particle was fixed at a certain position on the air distributor, and capacitance data were captured for 5 min at rate of 50 frames/s. The image was reconstructed as described in Section 4.1, and then each successive five images were averaged as the measurement image. In this step, the sampling frequency was 10 Hz. (3) The measurement image obtained in (2) was subtracted from the background image to obtain the difference image. Then dynamic threshold segmentation method was used on the difference images to obtain a contour map of the large tracer particle.
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where a is the threshold, and m is the adjustment coefficient. In the experiment, we choose a2 as the following formula: a ¼ 0:8 K ðT_20%Þ_ave
ð3Þ
where K(T_20%)_ave averages the top 20 pixel permittivity value.
Fig. 7. The position of tracer particle.
Fig. 8. Different region in measurement zone.
The background image shows the overall bed material distribution in a gas–solid fluidized bed of mono-sized particles under a specific operating condition. When a large tracer particle is placed in the bed, the overall fluidization state in the bed is disturbed to some extent. However, the size of tracer particle is small compared to the bed diameter, so the distribution of bed materials in the dense zone when the tracer particle is present has some similarity to the case without the tracer particle under the same operating condition. Therefore, subtracting the background image from the measurement image made the tracer particle with high permittivity more significant. More importantly, image subtraction reduced the influence of the existence of the high permittivity region caused by fine particle agglomeration when locating the large tracer particle. The local dynamic threshold is another method used in data processing. ‘Dynamic’ means each difference image chooses its own threshold according to the image information. ‘Local’ means each region of one difference image chooses its own threshold. Because of the soft field, ECT is more sensitive near the bed wall (near the electrode) than in the center. That means if one tracer particle is placed in a different position on the air distributor, it is blurrier and more difficult to recognize than when it is in the center of the bed. Therefore, if one threshold is chosen to be the whole difference image, it may be difficult, even impossible, to find the large particle's contour map when it is located in the center. To solve this problem, the measured cross-section was divided into three regions (see Fig. 8), and different thresholds over the different regions were taken as formula, 8 > < a1 ¼ m1 a 1 o m1 a2 ¼ a ð2Þ > : a ¼ m a 0om o1 3 2 2
4.2.2. Verification results Figs. 9–12 show the tracing results when tracer particles were placed in different positions at different fluidization velocities. As can be seen from Fig. 9, when the tracer particle is in the corner or near the bed, at positions labeled 1–5 in Fig. 7, the particle's position from the measurement image at any fluidization velocity can be directly located. However, when the tracer particle is far away from the bed wall, at positions labeled 6 and 7 in Fig. 7, its position cannot be distinguished from the measurement image. More experiments show that only a tracer particle in region 1 (see Fig. 8) can be clearly located from the measurement image. Fig. 10 demonstrates the time series of different images at a velocity v/vcr ¼3.0. Although the measured outline of the tracer particle changes from time to time because of the background disturbance caused by the bed materials' fluidization, its position is correct, and its center is stable. Fig. 11 displays the time series of different images at a velocity v/vcr ¼4.6. Figs. 10 and 11, it is seen that, with the increase of velocity, the accuracy and stability to locate the position of the tracer particle decreases. Because the fluidization becomes more intense with an increase in the velocity, the background disturbance is enhanced. When the disturbance increases to a certain extent, the tracer particle's significance in the difference image is weakened, and its position obtained from the threshold segmentation method may deviate. When the velocity increases to a high value, the concentration of the bed material near the air distributor decreases, and therefore, the tracing results will improve. However, that investigation was not a part of this study plan. Satisfactory tracing results can be obtained when v/vcr≤4.2, even when the tracer particle is in the center of the measurement zone. As shown in Fig. 12, with a decrease in the tracer particle size, the accuracy of locating its position decreases. It is difficult to determine the particle's position when the particle size is too small, and wrong information will be obtained. In these experiments, only particles with diameters larger than 3 cm, approximately one ninth of the measured cross-section, can be located reliably when v/vcr ¼4.2. From the above analysis, the accuracy and stability in locating the tracer particle's position improve when the fluidization velocity is decreased or the particle size is increased. The larger the tracer particle is, the higher the velocity that can be chosen. Also, the permittivity difference between the tracer particle and the bed material has a vital influence on the tracing result. For a particular configuration and application, a reasonable choice of parameters can achieve a good result.
5. Tracing an object's trajectory In this section, ECT combined with the described postprocessing methods were employed to trace the motion of a spherical particle with a diameter of 4 cm on an inclined air distributor. The tracer particle was dropped vertically from the upper part of the bed, fell on the high side of the air distributor, and then slipped, scrolled or bounced in the bed. Fig. 13 displays the tracer particle's position at different times at v/vcr ¼4.0. Clearly, the particle does not move directly to the low side of the air distributor; instead, it moves alternately in the middle of the bed and then finally stays in the corner of the bed, on the low side of the air distributor. To obtain the particle's trajectory, the geometric
R. Cai et al. / Flow Measurement and Instrumentation 33 (2013) 1–9
Fig. 9. Measurement image when the tracer particle is placed in different zones (v/vcr ¼ 4.6, D ¼4 cm).
Fig. 10. Time series of different image (tracer particle at position 7, v/vcr ¼ 3.0, D¼ 4 cm ).
Fig. 11. Time series of different image (tracer particle at position 7, v/vcr ¼ 4.6, D¼ 4 cm).
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Fig. 12. Different images of different size particles (position 7, v/vcr ¼ 3.6).
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Fig. 13. Time series of image (tracer particle in bed, v/vcr ¼4.0, D ¼ 4 cm 0–11 s).
center of the particle in the difference image was considered as the tracer particle's position, which can be calculated as formula
6. Conclusions
(
Results demonstrate that ECT, combined with the tracing concept and image processing techniques, is capable of tracing the motion of a large object on an inclined air distributor in a fluidized bed. For the bed configuration, particle properties and operating conditions studied in this work, satisfactory tracing results can be obtained when the permittivity of the tracer particle is more than ten times higher than the surrounding fine particles, and when the object's size is not smaller than one ninth of the measured cross-section and the fluidization velocity v/vcr is less than 4.2. Moreover, by changing the tracer particle's size, density, shape and surface characteristics, the technique can be adapted to different requirements in various applications. More experience with the techniques show that the accuracy and stability for locating the tracer particle's position improve when the fluidization velocity is decreased, the particle size is increased, or the particle is placed near the electrodes. Particles
X ¼ Σwi xi ;
Σwi ¼ 1
Y ¼ Σvi yi ;
Σvi ¼ 1
ð4Þ
where xi, yi is the pixel coordinate of the particle location in the image, and wi, vi is the weight factor, with pixels at the edge having a lower weight. The tracer particle trajectories at different velocities are shown in Fig. 14 and 15. Not all large tracer particles will move to the lower side of the air distributor. If the fluidization velocity is low, the particle may reach dynamic equilibrium in the bed and never move to the lower side of the air distributor. When the fluidization velocity is increased, the directional movement from the higher side to the lower side of the air distributor becomes apparent, although there are many repeated processes and uncertain paths.
R. Cai et al. / Flow Measurement and Instrumentation 33 (2013) 1–9
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Acknowledgments
tracing particle trajectory
The financial support from National Basic Research Program of China is gratefully acknowledged (973 Program, No. 2011CB201502).
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Fig. 14. Tracer particle trajectory (v/vcr ¼4.0, 0–12 s).
tracing particle trajectory 100
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Fig. 15. Tracer particle trajectory (v/vcr ¼ 2.4, 0–354 s).
with a diameter one ninth of the measured section near or in the corner of the bed wall can be directly located from the measurement image at any fluidization velocity, but when the particle is in the middle of bed, it can only be located from the difference image at a velocity v/vcr≤4.2. The performance of this approach will be improved if a higher permittivity material, such as water, is chosen to be encapsulated in the large tracer particle or if a higher resolution ECT system is applied. This approach is expected to become a practical and simple technology in the study of solid behavior in bubbling or slugging bed or in any multiphase system in which the motion of an irregular large object is important.
[1] Lim KS, Agarwal PK. Circulatory motion of a large and lighter sphere in a bubbling fluidized bed of smaller and heavier particles. Chemical Engineering Science 1994;49:421–4. [2] Zhang Y, Jin B, Zhong W. Experimental investigation on mixing and segregation behavior of biomass particle in fluidized bed. Chemical Engineering and Processing 2009;48:745–54. [3] Rees AC, Davidson JF, Hayhurst AN. The rise of a buoyant sphere in a gas fluidized bed. Chemical Engineering Science 2005;60:1143–53. [4] Hoffmann AC, Janssen LP, Prins J. Particle segregation in fluidized binary mixtures. Chemical Engineering Science 1993;48:1583–92. [5] Formisani B, Girimonte R, Longo T. The fluidization process of binary mixtures of solids: development of the approach based on the fluidization velocity interval. Powder Technology 2008;185:97–108. [6] Formisani B, De Cristofaro G, Girimonte R. A fundamental approach to the phenomenology of fluidization of size segregating binary mixtures of solids. Chemical Engineering Science 2001;56:109–19. [7] Weinell CE, Dam-Johansen K, Johnsson JE. Single-particle behavior in circulating fluidized beds. Powder Technology 1997;92:241–52. [8] Wei L, Wang G, Hao L, Zhao Y. Moving behavior of an object in gas-solid fluidized beds, J. Journal of China University of Mining and Technology 2005;15:7–11. [9] Sanderson J, Rhodes M. Hydrodynamic similarity of solids motion and mixing in bubbling fluidized beds. AIChE Journal 2003;49:2317–27. [10] Soria-Verdugo A, García-Hernando N, Almendros-Ibánez JA, Ruiz-Rivas U. Motion of a large object in a bubbling fluidized bed with a rotating distributor. Chemical Engineering and Processing 2011;50:859–68. [11] Hoffmann AC, Dechsiri C, van deWiel F, Dehling HG. PET investigation of a fluidized particle: spatial and temporal resolution and short term motion. Measurement Science and Technology 2005;16:851–8. [12] Parker DJ, Fan XF. Positron emission particle tracking—application and labeling techniques. Particuology 2008;6:16–23. [13] Stein M, Ding YL, Seville JPK, Parker DJ. Solids motion in bubbling gas fluidized beds. Chemical Engineering Science 2000;55:5291–300. [14] Patterson EE, Halow J. Innovative method using magnetic particle tracking to measure solids circulation in a spounted fluidized bed. Industrial & Engineering Chemistry Research 2010;49:5037–43. [15] Zhang Q, Huang C, Jiang D, Wei X, Qian Z, Wei F. Particle Measurement Sensor for in situ determination of phase structure of fluidized bed. Particuology 2009;7:175–82. [16] Dyakowski T, Luke SP, Ostrowski KL, Williams RA. On-line monitoring of dense phase flow using real time dielectric imaging. Powder Technology 1999;104: 287–95. [17] Warsito W, Fan LS. Dynamics of spiral bubble plume motion in the entrance region of bubble columns and three-phase fluidized beds using 3D ECT. Chemical Engineering Science 2005;60:6073–84. [18] Zhao T, Takei M, Masaki K, Ogiso Ryoji, Nakao Koji, Uchiura Akira. Flow Measurement and Instrumentation 2007;18:268–76. [19] Kuhn FT, Schouten JC, Mudde RF, van den Bleek CM, Scarlett B. Analysis of chaos in fluidization using electrical capacitance tomography. Measurement Science and Technology 1996;7:361–8. [20] Niedostatkiewicz M, Tejchman J, Grudzien K, Chaniecki Z. Application of ECT to solid concentration measurements during granular flow in a rectangular model silo. Chemical Engineering Research and Design 2010;88:1037–48. [21] Datta U, Dyakowski T, Mylvaganama S. Estimation of particulate velocity components in pneumatic transport using pixel based correlation with dual plane ECT. Chemical Engineering Journal 2007;130:87–99. [22] Liu S, Chen Q, Wang HG, Jiang F, Ismail I, Yang WQ. Electrical capacitance tomography for gas-solid flow measurement for circulating fluidized beds. Flow Measurement and Instrumentation 2005;16:135–44. [23] Landweber L. An iteration formula for fredholm integral equations of the first kind. American Journal of Mathematics 1951;73:615–24.
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Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Tracing the motion of a large object in a fluidized bed using electrical capacitance tomography Cai Rong-rong, Zhang Yan-guon, Li Qing-hai, Meng Ai-hong Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
art ic l e i nf o
a b s t r a c t
Article history: Received 18 November 2012 Received in revised form 7 April 2013 Accepted 24 April 2013 Available online 9 May 2013
An innovative method using electrical capacitance tomography (ECT) to trace a large object's motion on an air distributor in a fluidized bed is described here. The method fills the large object to be traced with a high permittivity material, and then a recalibration process is applied to reduce the nonlinearity caused by the large permittivity difference between the tracer particle and other fine particles in the measurement zone. The local dynamic threshold selection method is performed on the reconstructed image to locate the tracer particle's position. Static simulations and dynamic experiments testify that tracer particles with a diameter of one ninth of the measured cross-section and a fluidization velocity v/vcr≤4.2 can be accurately located and traced. Employing this method to trace the motion of a spherical object in a bed shows that the fluidization velocity significantly influences the directional motion of a large, heavy object on an inclined air distributor. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Electrical capacitance tomography (ECT) Fluidized bed Tracing Dense zone Recalibration
1. Introduction Fluidized bed reactors have been used for a variety of applications at many scales, ranging from small chemical reactors to large coal combustors. Examples of their application include thermal conversion of solid fuels, drying processes, and pneumatic conveying. In some cases, the presence of large objects, such as catalysts, fuel particles (large solid waste, biomass particle etc.) or agglomerates, in a bed of fine particles is required or occurs during fluidization. The motion pattern of large objects may thus prove to be a key factor in the performance of these beds. Extensive work has been carried out to analyze the motion of large objects immersed in a fluidized bed. Several researchers have studied the sinking and rising processes of large objects in 2-D and 3-D beds [1–6]. These researchers focused on the mixing and segregation processes of binary or ternary mixtures and found that the hydrodynamic behavior of the particles was strongly influenced by the difference in the properties of the particles, especially the density, shape and size. In addition, some researchers tried to trace a single large object's trajectory during fluidization to directly understand its motion pattern [7–10]. However, most of these studies concentrated on the large objects with a low density and the vertical motion in the dilute zone rather than on the motion of heavy, large objects near the air distributor. This is
n
Corresponding author. Tel.: +86 10 62783373. E-mail address: [email protected] (Y.-g. Zhang).
0955-5986/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.flowmeasinst.2013.04.009
partly due to the lack of reliable experimental methods to observe the particles' motions in the dense zone of the bed. In the visual observation of 3-D beds, it is typically impossible to trace the motion of individual large objects because of shielding by the surrounding neighbors in the dense zone. Recently, positron emission particle tracking (PEPT) and computer-aided radioactive particle tracking (CAPRT) have been used to obtain detailed information on the motion of particles in a fluidized bed [11–13]. These techniques use positron cameras to detect the pairs of back-to-back γ-rays arising from the annihilation of the emitted positrons. The positron-emitting tracers are normally labeled by the radionuclides 18F, 61Cu and 66Ga. A location algorithm is used to calculate the tracer location. Both of the methods allow direct measurement of particle trajectories; however, they require high-cost, specialized equipment and sound operating expertise. Also reported was magnetic particle tracking (MPT), which utilizes less expensive Hall-effect sensors instead of the expensive γ-ray detectors to trace neodymium magnets to continuously locate the position of a single tracer particle over time [14]. This technique also has certain limitations, including the complexity and limited range of the tracer's bipolar magnetic field. All of the described measurement techniques collect information about the particle's movement from signals arising from the interaction between the tracer and the external sensor. Zhang et al. proposed a new tracing concept, which would enable the particles to sense and record by themselves and send this information to the user [15]. They encapsulated a micro 3-D acceleration sensor into a tracer particle to sense the force
2
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a w, v (X,Y)
Nomenclature db C K S V E P v m
mean fine particle diameter capacitance between the electrodes material permittivity sensitivity map voltage electric field intensity element area fluidization velocity adjustment coefficient
threshold weight factor position of the tracer particle
Subscripts ab nor re cr
information of the particle. The method was validated to be feasible by free fall and was used to detect phase structure. However, because of the existence of the sensor, it is difficult to simulate particles in wide size or density ranges. Also the accuracy in locating the position from the force information remains in doubt. Other non-intrusive imaging methods, such as magnetic resonance imaging (MRI), X-ray tomography (XRT), electrical resistance tomography (ERT) and electrical capacitance tomography (ECT) are widely used for the analysis of solid motion in a fluidized bed. Among these techniques, ECT is considered to be the most available tomographic technique because of its high-speed capability, low construction cost, high safety and suitability for either small or large vessels. A review of the available fluidization literature with the application of the ECT system has shown that previous studies have mainly concentrated on the observation of flow patterns [16,17], measurement of particle concentrations [18– 20], or measurement of particle velocities [21,22]. Because of the technique's low resolution, it has not been used to measure the motion of individual particles. In this paper, the use of ECT to trace a large object's motion on an inclined air distributor in a fluidized bed was investigated. Special treatment was applied to the large tracing particle to enhance the permittivity difference between the particle and the bed materials. Recalibration was applied to reduce the nonlinearity caused by the large permittivity difference in the measurement zone. Image subtraction and the local dynamic threshold selection method were used to locate the particle's position. The method described here will widen the ECT application range and become a practical and simple technology in particle tracing.
2. Experiment lab and materials The experiment was carried out in a cold conventional fluidized bed with a 0.24 0.28 m2 cross-section and a height of 1.8 m. A 51 inclined air distributor made of plexiglass was placed 0.6 m above the bottom of the cuboid at its lower side. 194 Orientation air cups were evenly distributed on the plate, oriented towards the plate's downward direction. The opening ratio was 5.68%. Air was introduced to the bottom of the bed from a vortex fan after passing through a rotameter and a valve.
absolute (capacitance) normalized (capacitance) recalibration critical
To obtain a large permittivity difference, polypropylene particles with a relative permittivity of 1.5 were chosen as the bed material. Following a sieving process, the bed material's size was limited to particles in the range of 0.6–1 mm, and the mean particle diameter was calculated according to the surface to −1 volume ratio as db ¼ ðΣ m i ¼ 1 ðxi =dbi ÞÞ . The particle density was 3 756 kg/m , and the particles therefore belong to Geldart Group B. The large tracer particle was made by filling a box with different high permittivity materials, according to practical simulation requires. The box's shape and size were determined by a thin outer box, and its density was varied by changing the ratio of the inner materials. Some large tracer particles was created in this experiment, and their characteristics are given in Table 1.
3. ECT system and recalibration The ECT system consisted of an electrical capacitance sensor unit, a data acquisition module (PTL300E-SP-G ECT) and a personal computer equipped with custom communication hardware. The capacitance sensor unit was composed of 12 measurement electrodes, each with an axial length of 5.0 cm, and 2 axial electrodes, each 6.0 cm high. Details of the electrodes' sizes can be found in Fig. 1. The air distributor sensor was arranged outside of the cuboid bed, so that the bottom edge of the measurement electrode was as high as the lower edge of the air distributor. This arrangement ensured that the inclined air distributor partly lay in the measurement zone, and any large tracer particle in the dense zone was detected, as shown in Fig. 2. All of the electrodes were connected to the PC through a data acquisition module, which had a capturing rate of 50 frames/s. The Landweber image reconstruction algorithm [23] was employed to derive the image from the capacitance data. Because of the large tracer particle's much higher permittivity, its position could be found in the reconstruction image. Prior to data recording, the system requires calibration. Unlike traditional ECT application in a gas–solid fluidized bed, there are three materials with different permittivities in the measurement zone: air, bed materials and a large tracer particle. Originally, a twopoint calibration was taken at two extreme cases: zero for the lower permittivity materials (air usually) in the bed and one for the higher permittivity material, and then the measured capacitance data was
Table 1 The properties of the large tracer particles. Shape
Size (cm)
Density (g/cm3)
Material
Sphere
D¼ 3 D¼ 4 D¼ 5
0.90 0.87 0.83
Shell: plastic; Filling: acid polymethylene methyl acrylate
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3
Fig. 1. Experimental setup and arrangement of ECT sensor.
Fig. 2. The position of the air distributor and electrodes.
linearly normalized. However, the relationship between the material permittivity change in the bed and the capacitance change among any two electrodes is nonlinear, as shown in Fig. 3. This behavior was especially noticeable in this experiment, as the permittivity of the large tracing particle is several times larger than that of the bed materials, which aggravates the nonlinearity and may cause serious errors. Therefore, recalibration was performed in this work to reduce the nonlinearity. Five different materials, with relative permittivities ranging from 1 to 8 were filled into the bed, and their absolute capacitance data were recorded. Then, a quadratic curve was used to fit these data to obtain a calibration curve C¼ f(K) as shown by the solid line in Fig. 4, which is suitable for the specific measurement zone and the electrode arrangement. C is the capacitance between the electrodes, and K is the material permittivity. With this information, before every measurement, only two
points of absolute capacitance must be measured by filling the bed with air (low permittivity) and bed material (relatively high permittivity). The calibration curve C ¼f(K), was stretched to fit these two points, and then a new calibration curve was produced, as shown by the bold dashed line in Fig. 4. The normalized capacitances calculated from absolute capacitances with or without recalibration were shown in Table 2. A tracer particle was placed in the corner of the measurement zone near electrode 12. Clearly, the normalized capacitance with recalibration can be as much as 10% different from the original two-point calibration when there exists extremely high permittivity zone. Therefore, recalibration can effectively reduce the nonlinearity in normalization, especially if the difference in permittivity between materials in the measurement zone is large. The normalized capacitance may be greater than 1; however, this does not affect the tracing result.
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4. Method validation 4.1. Validation of ECT tracing by static simulation As illustrated in Fig. 2, the measurement zone has an obstacle– air distributor. This is another difference from traditional applications, in which there is only air between the electrodes when no materials are present. To determine the influence of the plate on the measurement, static simulations with or without the air distributor plate in the measurement zone were performed using the Comsol software. One geometric model was based on the actual experimental configuration and electrode design pattern shown Fig. 2. The inclined air distribution plate was made of
380 360
C/pF
340 320 300 280
value linerization fit curve
260 240
1
2
3
4
5
6
7
8
K Fig. 3. Capacitance between adjacent electrodes when filled with different permittivity materials.
550 two point calibratin curve
500 450 C/pF
recalibration curve 400 350 300
C = f (K)
where Si,j is the sensitivity map between electrode i and electrode j, Ei is the electric field distribution when electrode i is excited by voltage Vi, and P(x,y) is the element area. The existence of the air distributor has the greatest influence on the sensitivity map of opposite electrodes if there is any influence; therefore, only the sensitivity maps of opposite electrodes are compared here, as shown in Fig. 5. This figure shows that the shapes and values of the sensitivity map in the two cases are very similar to each other, which means that the existence of the air distributor plate has little influence on the sensitivity map in this experimental configuration (air distributor with an inclined angle of 51, thickness of 1 cm, relative permittivity of 3.75). Next, a spherical particle with a diameter of 4 cm and a relative permittivity of 15 was placed in the center or corner of the bed, on the air distributor. The other part of the measurement zone was filled with bed materials with a relative permittivity of 1.5. The inter-electrode capacitances were calculated by the finite element method (FEM) using Comsol, and then the calibration method described in Section 3 was used to calibrate and normalize the capacitance data. Finally, Landweber algorithms and the sensitivity map calculated above were applied to reconstruct the image. As shown in Fig. 6, the spherical particle's position can be accurately and easily recognized. More simulations verify that if the permittivity of the tracer particle is more than ten times greater than that of the surrounding materials, the particle's position can be located when its size is one tenth of the measurement zone's diameter in a static simulation. Moreover, a particle near the wall is more easily recognized than one in the center. The key to tracing a particle is accurately and in a timely manner locating its position; that means that only the relative value of pixel permittivity in the measurement zone is of concern. Because of the higher permittivity of the tracer particle, it is believed that the pixels with high permittivity in the reconstructed image indicate where tracer particle is located. The distribution of the permittivity value in the reconstructed image does not correspond to the material concentration in the measurement zone. Therefore, a normalized capacitance larger than 1 and a pixel value in the reconstructed image larger than 1 are accurate. 4.2. Validation of ECT tracing by experiment
250 200
plexiglass, with a thickness of 1 cm and a relatively permittivity of 3.75. The other geometric model included no plate. The sensitivity map is an important factor that influences the ECT reconstruction result. Therefore, the sensitivity maps in the above two cases were first calculated and compared. Five different cross-sections alone electrode heights were used to calculate each section's electric fields, and then the electric fields were averaged as the measurement zone's electric fields. Finally, the sensitivity map was calculated according to the following equation: Z Ei ðx; yÞ Ej ðx; yÞ Si;j ðx; yÞ ¼ − dx dy ð1Þ Vi Vj pðx;yÞ
1
2
3
4
5
6
7
8
K Fig. 4. Recalibration process.
Static simulation reveals that it is feasible to locate a large object's position in a static bed when its size is one tenth of the measurement cross-section's diameter. However, in actual gas–solid fluidization, the bed material distribution is uneven in the dense zone near the air distributor; in addition, the distribution fluctuates irregularly with
Table 2 The normalized capacitances from with or without recalibration. Electrode pairs
C1,2
C1,3
C1,4
C1,5
C1,6
C1,7
C1,8
C1,9
C1,10
C1,11
C1,12
C_ab (Ff) C_nor C_nor_r
352.40 0.601 0.598
42.86 0.526 0.520
24.04 0.544 0.539
14.86 0.429 0.423
10.85 0.440 0.435
10.14 0.603 0.601
11.20 0.553 0.549
16.06 0.568 0.56
28.44 0.641 0.640
52.86 0.934 0.934
397.42 1.658 1.831
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C1,6
y
-100
0
100 x
C1,7
y
0.01
0.008
0.008
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0.004
0.006
100 y
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0 x
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Fig. 5. Sensitivity maps with or without an air distributor. (1) With air distributor. (2) Without air distributor.
Fig. 6. Static simulation result. (1) Particle in the center. (2) Particle in the corner.
time. Also, ECT has a soft field effect, meaning that the permittivity change in any region of the measured zone will affect the entire result. For example, if the bed materials suddenly agglomerate in the center of the bed, then only the pixel permittivity in that region is correspondingly higher. However, in the reconstruction image, all pixel permittivity in the measurement zone will be higher, and the closer from the center the location is, the greater the effect will be. Therefore, a change in the bed materials' distribution with space and time will interfere in the determination of the tracer particle's position. For this reason, the following experiments were performed to study this effect, and some measurements were obtained to reduce the effect.
4.2.1. Experimental verification method A spherical particle with a diameter of 3, 4 or 5 cm and relative permittivity of 15 was fixed at the end of a plastic hollow rod, and the rod was then inserted at the top of the bed to place the tracer particle in a different position on the air distributor during fluidization. A coordinate system was set at the top of the bed to accurately determine the large tracing particle's coordinates. Seven different positions (1 (−120,100); 2 (−120,0); 3 (0,100); 4 (120,−100);
5 (120,0); 6 (70,−60); 7 (0,0)) were chosen in this experiment, as shown in Fig. 7. The fluidization velocity was set as v/vcr ¼3.0–4.6 (vcr ¼0.27 m/s). To reduce the influence of the bed materials' distribution on the measurements, the following experimental procedures and data post-processing methods were used. (1) Capacitance data were captured for 5 min at a rate of 50 frames/s when there was no large particle in the fluidized bed. The image was reconstructed as described in Section 4.1, and then the total 15,000 frames of image were averaged as the background image. (2) The tracer particle was fixed at a certain position on the air distributor, and capacitance data were captured for 5 min at rate of 50 frames/s. The image was reconstructed as described in Section 4.1, and then each successive five images were averaged as the measurement image. In this step, the sampling frequency was 10 Hz. (3) The measurement image obtained in (2) was subtracted from the background image to obtain the difference image. Then dynamic threshold segmentation method was used on the difference images to obtain a contour map of the large tracer particle.
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where a is the threshold, and m is the adjustment coefficient. In the experiment, we choose a2 as the following formula: a ¼ 0:8 K ðT_20%Þ_ave
ð3Þ
where K(T_20%)_ave averages the top 20 pixel permittivity value.
Fig. 7. The position of tracer particle.
Fig. 8. Different region in measurement zone.
The background image shows the overall bed material distribution in a gas–solid fluidized bed of mono-sized particles under a specific operating condition. When a large tracer particle is placed in the bed, the overall fluidization state in the bed is disturbed to some extent. However, the size of tracer particle is small compared to the bed diameter, so the distribution of bed materials in the dense zone when the tracer particle is present has some similarity to the case without the tracer particle under the same operating condition. Therefore, subtracting the background image from the measurement image made the tracer particle with high permittivity more significant. More importantly, image subtraction reduced the influence of the existence of the high permittivity region caused by fine particle agglomeration when locating the large tracer particle. The local dynamic threshold is another method used in data processing. ‘Dynamic’ means each difference image chooses its own threshold according to the image information. ‘Local’ means each region of one difference image chooses its own threshold. Because of the soft field, ECT is more sensitive near the bed wall (near the electrode) than in the center. That means if one tracer particle is placed in a different position on the air distributor, it is blurrier and more difficult to recognize than when it is in the center of the bed. Therefore, if one threshold is chosen to be the whole difference image, it may be difficult, even impossible, to find the large particle's contour map when it is located in the center. To solve this problem, the measured cross-section was divided into three regions (see Fig. 8), and different thresholds over the different regions were taken as formula, 8 > < a1 ¼ m1 a 1 o m1 a2 ¼ a ð2Þ > : a ¼ m a 0om o1 3 2 2
4.2.2. Verification results Figs. 9–12 show the tracing results when tracer particles were placed in different positions at different fluidization velocities. As can be seen from Fig. 9, when the tracer particle is in the corner or near the bed, at positions labeled 1–5 in Fig. 7, the particle's position from the measurement image at any fluidization velocity can be directly located. However, when the tracer particle is far away from the bed wall, at positions labeled 6 and 7 in Fig. 7, its position cannot be distinguished from the measurement image. More experiments show that only a tracer particle in region 1 (see Fig. 8) can be clearly located from the measurement image. Fig. 10 demonstrates the time series of different images at a velocity v/vcr ¼3.0. Although the measured outline of the tracer particle changes from time to time because of the background disturbance caused by the bed materials' fluidization, its position is correct, and its center is stable. Fig. 11 displays the time series of different images at a velocity v/vcr ¼4.6. Figs. 10 and 11, it is seen that, with the increase of velocity, the accuracy and stability to locate the position of the tracer particle decreases. Because the fluidization becomes more intense with an increase in the velocity, the background disturbance is enhanced. When the disturbance increases to a certain extent, the tracer particle's significance in the difference image is weakened, and its position obtained from the threshold segmentation method may deviate. When the velocity increases to a high value, the concentration of the bed material near the air distributor decreases, and therefore, the tracing results will improve. However, that investigation was not a part of this study plan. Satisfactory tracing results can be obtained when v/vcr≤4.2, even when the tracer particle is in the center of the measurement zone. As shown in Fig. 12, with a decrease in the tracer particle size, the accuracy of locating its position decreases. It is difficult to determine the particle's position when the particle size is too small, and wrong information will be obtained. In these experiments, only particles with diameters larger than 3 cm, approximately one ninth of the measured cross-section, can be located reliably when v/vcr ¼4.2. From the above analysis, the accuracy and stability in locating the tracer particle's position improve when the fluidization velocity is decreased or the particle size is increased. The larger the tracer particle is, the higher the velocity that can be chosen. Also, the permittivity difference between the tracer particle and the bed material has a vital influence on the tracing result. For a particular configuration and application, a reasonable choice of parameters can achieve a good result.
5. Tracing an object's trajectory In this section, ECT combined with the described postprocessing methods were employed to trace the motion of a spherical particle with a diameter of 4 cm on an inclined air distributor. The tracer particle was dropped vertically from the upper part of the bed, fell on the high side of the air distributor, and then slipped, scrolled or bounced in the bed. Fig. 13 displays the tracer particle's position at different times at v/vcr ¼4.0. Clearly, the particle does not move directly to the low side of the air distributor; instead, it moves alternately in the middle of the bed and then finally stays in the corner of the bed, on the low side of the air distributor. To obtain the particle's trajectory, the geometric
R. Cai et al. / Flow Measurement and Instrumentation 33 (2013) 1–9
Fig. 9. Measurement image when the tracer particle is placed in different zones (v/vcr ¼ 4.6, D ¼4 cm).
Fig. 10. Time series of different image (tracer particle at position 7, v/vcr ¼ 3.0, D¼ 4 cm ).
Fig. 11. Time series of different image (tracer particle at position 7, v/vcr ¼ 4.6, D¼ 4 cm).
7
8
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Fig. 12. Different images of different size particles (position 7, v/vcr ¼ 3.6).
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Fig. 13. Time series of image (tracer particle in bed, v/vcr ¼4.0, D ¼ 4 cm 0–11 s).
center of the particle in the difference image was considered as the tracer particle's position, which can be calculated as formula
6. Conclusions
(
Results demonstrate that ECT, combined with the tracing concept and image processing techniques, is capable of tracing the motion of a large object on an inclined air distributor in a fluidized bed. For the bed configuration, particle properties and operating conditions studied in this work, satisfactory tracing results can be obtained when the permittivity of the tracer particle is more than ten times higher than the surrounding fine particles, and when the object's size is not smaller than one ninth of the measured cross-section and the fluidization velocity v/vcr is less than 4.2. Moreover, by changing the tracer particle's size, density, shape and surface characteristics, the technique can be adapted to different requirements in various applications. More experience with the techniques show that the accuracy and stability for locating the tracer particle's position improve when the fluidization velocity is decreased, the particle size is increased, or the particle is placed near the electrodes. Particles
X ¼ Σwi xi ;
Σwi ¼ 1
Y ¼ Σvi yi ;
Σvi ¼ 1
ð4Þ
where xi, yi is the pixel coordinate of the particle location in the image, and wi, vi is the weight factor, with pixels at the edge having a lower weight. The tracer particle trajectories at different velocities are shown in Fig. 14 and 15. Not all large tracer particles will move to the lower side of the air distributor. If the fluidization velocity is low, the particle may reach dynamic equilibrium in the bed and never move to the lower side of the air distributor. When the fluidization velocity is increased, the directional movement from the higher side to the lower side of the air distributor becomes apparent, although there are many repeated processes and uncertain paths.
R. Cai et al. / Flow Measurement and Instrumentation 33 (2013) 1–9
9
Acknowledgments
tracing particle trajectory
The financial support from National Basic Research Program of China is gratefully acknowledged (973 Program, No. 2011CB201502).
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Fig. 14. Tracer particle trajectory (v/vcr ¼4.0, 0–12 s).
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Fig. 15. Tracer particle trajectory (v/vcr ¼ 2.4, 0–354 s).
with a diameter one ninth of the measured section near or in the corner of the bed wall can be directly located from the measurement image at any fluidization velocity, but when the particle is in the middle of bed, it can only be located from the difference image at a velocity v/vcr≤4.2. The performance of this approach will be improved if a higher permittivity material, such as water, is chosen to be encapsulated in the large tracer particle or if a higher resolution ECT system is applied. This approach is expected to become a practical and simple technology in the study of solid behavior in bubbling or slugging bed or in any multiphase system in which the motion of an irregular large object is important.
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