Study of granular flow in silo based on electrical capacitance tomography and optical imaging

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Study of granular flow in silo based on electrical capacitance tomography and optical imaging K. Grudzień, Z. Chaniecki, L. Babout

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Institute of Applied Computer Science, Lodz University of Technology, Stefanowskiego 18/22, 90-924 Lodz, Poland

A R T I C L E I N F O

A B S T R A C T

Keywords: Silo discharging Asymmetric flow Electrical capacitance tomography CMOS camera Boundary detection

This paper presents a comparison between optical images and two different modalities of electrical capacitance tomography (ECT), namely an off-the-shelf ECT system and a model one combining an inductance (L) - capacitance (C) - resistance (R) meter with a multiplexer. This comparison was performed to analyse the degree of measurement accuracy and to estimate the spatial resolution of the ECT systems. In this case, the detection of the position of flow boundaries during silo discharging and its translation when discharging changes from concentric to eccentric were investigated. A versatile rectangular silo model was used to generate different types of funnel flow of rice material, which was designated as the most adapted granular material to create both optical and electrical permittivity contrasts between stagnant and flowing zones. When a high temporal resolution is not requested, the model ECT system reduces the measurement error of flow boundary detection between 3% and 9% when compared with optical measurements. Moreover, the system is able to capture boundary translation of about 5% of the silo bin width, which is below the assumed spatial resolution of standard commercial ECT systems.

1. Introduction Storage solutions like hoppers or silos have major use in a various range of industrial applications, such as agriculture, pharmaceutical industry or even in nuclear engineering (pebble bed reactor). Their purpose is two-fold: to store materials – usually granular materials – and to discharge them with a controlled speed for further usage (e.g. drug dosage, power generation). The geometry of the structure and the initial packing of the granular materials have strong effects on the type of flow (e.g. mass flow, semi-mass flow of funnel flow) and on the discharging rate [1,2]. Moreover, silos with asymmetric design or inclined walls have also been designed for discharging set-up efficiency, leading to so-called eccentric discharging. It is known that such a flow type generates strong normal pressure at the silo wall that can have a direct impact on the structure integrity during servicing [3–5]. Therefore, the biggest challenge for researchers and engineers is to define the best silo design that meets with flow specifications for given granular material and application. This has often induced the development of solid numerical simulations, usually based on discrete element method (DEM) [6–8] or finite element methods (FEM) [9–11] that can predict the structure and behavior of the silo during exploitation. Moreover, measurement techniques have also been adapted to monitor online material behavior during filling, storing and emptying processes.

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As far as experimental measurement is concerned, recent studies involving tomography technology take into consideration two different modalities: X-ray tomography and electrical capacitance tomography (ECT). While the former have shown its potential to quantitatively characterize structural changes occurring during mass and funnel flows [12–14] due to its high spatial resolution capabilities, the latter one has shown its usefulness in investigating rapid changes revealed during dynamic phenomena such as shear zone presence during mass flow [13,15,16] due to its good temporal resolution. In recent years, the technique has shown its usefulness to investigate industrial processes such as moisture ingress in cement-based materials, fluidized beds, liquid/gas separation or chemical process conveyors [17–20], with the upstream usage of 3D ECT sensor layouts [18,19,21,22], and downstream usage of advanced data processing strategies for flow identification and monitoring [21,23–25]. However, its main drawback, which is a spatial resolution limitation due to the non-linear nature of the electrical field and the reduced number of measurements imposed by the limited number of electrodes, reduces significantly its appealing tomography nature and development beyond Technology Readiness Level TRL 6–7 (demonstration in high-fidelity lab / operational environment). There has been a growing consideration to avoid the image reconstruction step (which is time consuming if based on complex nonlinear mathematical approaches and may lead to images that are prone

Corresponding author. E-mail address: [email protected] (L. Babout).

https://doi.org/10.1016/j.flowmeasinst.2017.11.001 Received 1 February 2017; Received in revised form 20 September 2017; Accepted 6 November 2017 0955-5986/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Grudzien, K., Flow Measurement and Instrumentation (2017), http://dx.doi.org/10.1016/j.flowmeasinst.2017.11.001

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right hopper sheet to a given value to be in contact with the right edge of the silo bin. One plane of 12 electrodes was fixed on the outside of the bin part of the silo, 2 cm above the bin-hopper boundary (Fig. 1c-d). The electrodes were made of copper adhesive and of size 5.5 cm by 6.5 cm on the front and back sizes and 7.25 cm by 6.5 cm on the side, leaving in both cases an electrode interspace of 0.5 cm. In order to reduce electrical noise, the electrodes were surrounded by ring and flat radial guards electrodes, all connected to the ground. Moreover, electrodes were connected to the bottom ring guard electrode with insulation resistance of 1 MΩ to avoid electric charge build-up on the capacitance electrodes during discharging experiments. The electrodes were connected sequentially to two different electrical tomography setups, which are shown in Fig. 1a:

to interpretation issues) and focuses only on analyzing raw signals to study dynamic processes, as mentioned in [25–27]. However, in the current study, since the gravitational process can be controlled without losing its important dynamic characteristics such as concentration changes between stagnant and flowing zones during funnel flow, it was decided to evaluate the level of accuracy of ECT image reconstruction to determine flowing zone boundaries and its evolution with respect to the hopper configuration (i.e. symmetric/asymmetric setting). In order to investigate the influence of the hopper parameters mentioned above, authors have realized the need of designing a versatile experimental silo system that enables to control key parameters such as outlet width, hopper angle and orientation of bin part. In such matter, changes from concentric funnel flow to eccentric mass flow or avalanche-like flow can be possible. Such silo design as well as preliminary results of concentration changes in concentric/eccentric funnel flow measured using ECT have already been presented in [28]. Particularly, a good imaging contrast was found between so-called stagnant and flowing zones. However, the study has revealed some doubts concerning the interpretation of the results that may be related to either ECT measurements carried out with a LCR meter or experimental conditions linked with the silo discharging process. Therefore, new experimental consideration has been thought to better conclude about the discharging processes based on ECT data. The main aim of the paper is to compare the results recorded simultaneously between the ECT systems and a digital camera, the latter being considered here as a reference measurement system since it is frequently used for gravitational flow experiments in the case of rectangular cross-sectioned systems [29–31]. This comparison allows to identify the capability of ECT systems to capture changes at the level of flow boundaries related to silo settings, especially the positioning of the outlet and hopper angles mentioned above. The structure of the paper is the following. Firstly, experimental setup is presented, which highlights the experimental silo stand as well as the measurement techniques. Secondly, the experimental results section presents and discusses the comparison between the quantitative results gathered by a digital camera and the ECT systems to attest the level of accuracy of the latter technique for the detection of the stagnant zone boundaries. In that matter, tests have been carried out for concentric and eccentric funnel flow regimes in order to see if ECT measurements can detect the difference of stagnant zone localization for these different flowing setups. The paper ends with the conclusion and perspectives of work.

• Commercial ECT system from ECT instruments Ltd. • Agilent E4980A Precision LCR meter connected to home-made 1

multiplexer to simulate real capacitance tomography system, named hereinafter referred to as the model ECT system.

The first system follows a traditional ECT design based on AC-based capacitance measuring circuit with high-frequency sinusoidal excitation and phase-sensitive demodulation [32]. This circuit can measure the change in capacitance as small as 0.0001 pF and it can acquire image data at 140 frames per second from a 12-electrode sensor. In the present case, measurements were acquired at a frequency of 60 Hz. The second system that couples a multiplexer with a LCR meter was intended to reconstruct permittivity maps based on real capacitance measurements. The multiplexer is based on the Arduino® technology. However, because of the time needed to switch between pairs of electrodes in the multiplexer this model ECT system cannot work in realtime mode. This implies that the investigated process is stopped, which hinders the use of the model ECT system for many dynamic applications, such as plug/slug flow or fluidized beds. The system integrates 5 ms between two consecutive measurements for stabilisation issues. Moreover, in the case under consideration, averaging of three measurements was done for each electrode pair. However, in the case of gravitational flow in silo, the process can be stopped without creating strong concentration changes. It can be possible to increase measurement acquisition speed of LCR meter at the expense of reducing the measurement accuracy. In this investigation the LCR meter was used as the reference tool, so the accuracy of the measurements was more important than the acquisition speed. Last but not least, ECT-based results are compared with the ones obtained from Basler acA2040-180kc colour camera with the CMOSIS CMV4000 CMOS (Complementary Metal-Oxide Semiconductor) sensor that has the size of 11.3 mm × 11.3 mm (pixel size 5.5 µm × 5.5 µm) and an array size of 2046×2046 pixels. A slow acquisition rate of 2 frames/s was chosen to better emphasize concentration changes and facilitate flow boundary detection, which will be explained in Section 3.2

2. Materials 2.1. Experimental stand The main view of the experimental silo stand is shown in Fig. 1a. Firstly, one can see the versatile silo that was designed for the purpose of the paper (detailed view on Fig. 1b). The inner rectangular cross section of the bin is of size Wb=24 cm (width) by Bb=15 cm (breadth). The structure is made of 0.5 cm thick polystyrene sheet. One can see on Fig. 1b that the positioning and angle control of the oblique hopper sheets are managed by means of two metallic rods on each side. Moreover, both parts can slide to control the outlet width, in order to adapt to the mean grain size of the granular bed and control the discharge velocity. The front and back sheets of the bin are longer than the side sheets and are inserted in slits so as the whole structure can adapt to the different heights of the silo when the hopper angle is changed from funnel flow to mass flow set-ups. In any case, the bin height Hb is 35 cm. With such a device, a wide range of discharging modes can be studied, from concentric funnel flow to eccentric mass flow. This is simply achieved by: (1) translating the outlet horizontally left to right, keeping its width constant, (2) changing the angle of the left hopper sheet to a given value, (3) translating vertically the silo bin to be in contact with the left hopper sheet and (4) changing the angle of the

2.2. Studied material At the beginning of this work, no particular material was targeted. Previous ECT studies used polystyrene pellets (PP) or quartz sand to investigate solids flow in pneumatic conveyors or silos [15,16,33,34]. Both present adapted electrical properties for ECT investigation, i.e. low dielectric constant. However, other materials were also considered for this study, mainly driven by size considerations. Indeed, while PP is relatively large in size (7–8 mm average diameter), quartz sand is small (d50=0.8 mm) and difficult to handle with current versatile silo design. 1 An electronic equipment that measures inductance (L), capacitance (C) and resistance (R) of an electronic component.

2

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Fig. 1. (a) General view of the experimental stand showing versatile silo with rectangular bin crosssection equipped with 12 electrodes sensor layer, commercial ECT system, LRC meter connected to multiplexer and CMOS digital camera. (b) Zoom on silo model with eccentric setup. (c-d) zoom on electrode layer and connections.

of electrodes. Active electrode was set as electrode #1 and measurements were performed for pairs: C12, C13,…, C78. The presented values depict difference between full sensor and empty sensor. One can see that rice presents higher level of measurements changes, while Seramis™, which is a highly porous material, presents the lowest capacitance changes. Table 1 collects results for average value of capacitance between adjacent electrodes and opposite electrodes. The difference between adjacent and opposite measurements value is obvious from ECT tomography point of view – higher sensitivity for wall sensor area than in the centre of sensor. One can also notice that measurements were done in a dry environment, which is indicated by the fact that the moisture contents measured using a grain moisture meter (Benetech® GM640) were all below 10%. Based on the presented results, the most convenient material for the current ECT measurement study is rice (dielectric constant: 3.5), which characterizes the highest range measurement values between empty and full sensor configurations. Each change of local rice concentration during silo discharging should generate the highest measured capacitance changes.

The granular material selection concentrated mainly on whole grains (rice and sorghum) and glass particles (glass sphere and grit), all presenting a similar size (2–5 mm). The best candidate for the present work was selected based on its capacitance response to electrical signal. Fig. 2 presents results of capacitance measurements for five different materials. The measurements were conducted using an 8-electrode cylindrical sensor (inner diameter 7 cm) connected to the LCR meter presented above. Plots show capacitance distribution for one set of pairs

Table 1 Average measurements for opposite and adjacent pair of electrodes.

Fig. 2. Pair capacitance profile for 5 selected granular materials with electrode #1 active in the case of an 8-electrode cylindrical sensor.

3

Material

Moisture content [%]

Opposite electrodes [fF]

Adjacent electrodes [fF]

Seramis™ Glass grit Glass sphere Sorghum grain Rice

9.2 – – 7.5 7.5

24.73 67.79 75.57 119.23 138.02

204.36 480.84 536.93 697.15 792.24

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3. Data handling From the moment ECT measurements are recorded, two important steps are performed, as far as data handling is concerned, i.e. image reconstruction and image processing. These are explained in the next subsections. 3.1. ECT image reconstruction The Image reconstruction procedure allows to obtain image of dielectric permittivity distribution in the sensor space. Numerous methods for ECT image reconstructions are described in literature [35–37]. As far as the paper is concerned, linear back projection (LBP) algorithm and Landweber iteration techniques were considered. In a nutshell, LBP method is based on the linearization of the normalized forward problem. Applying Taylor series and neglecting terms of order higher than 2 allow to write:

g = STC

(1)

where: ST – normalized sensitivity matrix; C – normalized measurements vector; g – reconstructed image In Landweber method the reconstructed image is obtained using the following iterative process:

gk +1 = gk − αS T (Sgk − C )

(2)

where gk is the reconstructed image in the k-th step, α is a relaxation factor and S is normalized sensitivity matrix. LBP algorithm belongs to direct reconstruction methods and provides an image in a very short time but with limited quality. The Landweber algorithm, which is regarded as the most reliable iterative algorithm by many researchers, modifies image in each iteration step in order to generally obtain better quality of reconstruction. Its advantage in comparison to direct methods (including LBP) is more significantly visible when high contrast of material distribution in the measurement area occurs [38,39], e.g. homogeneous phantom located in empty space or when liquid/gas flow is observed. Key elements for the Landweber method are the choices of α and the number of iterations [40–43]. Previous works have shown that the number of iterations depends on the electrical properties of the object to be investigated and the relative image error, which is a direct effect of solving the ill-posed problem, follows a so-called semi-convergence profile [44]. In other words, the relative image error will reach a minimum before divergence occurs as the number of iterations increases. On the other hand, small values of α reduce the algorithm speed but allow better convergence, while the iterative reconstruction process may diverge with larger values. While testing different values of α range < 0.01, 0.9 > and the number of iterations range < 5, 500 > were analysed to select the best result in terms of image reconstruction quality. In the case of gravitational flow of rice, the best results that fulfilled the calculation convergence were obtained for α=0.02 with 200 iterations for both ECT measurement systems. For example, a lack of convergence was observed for α ten times larger than the value selected with the same number of iterations, resulting in reconstructed images with artefacts. The common element for different reconstruction methods is the numerical analysis of the electrical field distribution inside the sensor space in order to find the sensitivity matrix. This can be done using Finite Element Method techniques [36]. Fig. 3 presents examples of obtained sensitivity maps, which are interpreted as sensitivity measurement area for single pair of electrodes. The scale on the images is the same in order to confirm that the sensitivity is higher for each pair of adjacent electrodes. The sensitivity maps provide information about

Fig. 3. Sensitivity map for chosen pair of electrodes a) adjacent electrodes C7–8, b) electrodes on the same silo wall C4–6 c) opposite electrodes C5–10 defined in Fig. 1c.

the area where permittivity changes have influence on capacitance measurement. Each pixel has an assigned value, which depicts the level of influence on the measurement. 3.2. Image processing One of the most important aims of this study is the comparison between ECT measurements and CMOS camera measurements to evaluate the accuracy of the former, in the case of asymmetric funnel flow. A quantitative analysis is foreseen, which implies to explain the chosen methodology to compare both measurement techniques. Firstly, one needs to keep in mind that, because the CMOS camera only reveal flow characteristics at the silo surface, the comparison with ECT measurements only considers boundaries of the reconstructed cross-section. Secondly, the region of interest for the CMOS camera to make the comparison between the two measurements contains a hidden zone of the flow corresponding to the ECT sensor layer that needs to be deduced from the flow boundary profile viewed above and below. This has been 4

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Fig. 4. Image processing and analysis strategy to estimate flow boundary characteristics from CMOS camera images. (a) Original image from sequence after equalization (case of symmetric flow). (b) Absolute difference between successive image (c) 0-entropy map (with scale). (d) Chan-Vese active contour (red). (d) Selected stagnant-flow boundary portions (red) and corresponding polynomial fits (blue). The horizontal dashed line indicates where the funnel boundary positions are calculated from polynomial fit for future comparison with ECTbased width calculations.

Fig. 4c, where one can see the funnel zone that is better revealed after local entropy calculation that uses a square neighbourhood of size 5×5 around each image pixel (mirroring is applied for pixels with neighbourhood exceeding image boundaries). In the next step, segmentation needs to be performed to further extract the boundaries between the stagnant and flow zones (hereinafter referred to as stagnant-flow boundaries). In the case of flowing zone segmentation, the Chan-Vese active contour [46,47] has been privileged with respect to classical segmentation, e.g. thresholding, region growing or inter-class variance algorithm such as the Otsu method, because of its local propagation nature and robustness to detect edges of objects, even in noisy image environments. In a nutshell, the algorithm is based on the level set method to implicitly represent the segmentation boundary that solves an energy minimization problem. The method is robust for initialization and evolves depending on the number of iterations N and a factor μ that influences the smoothness vs. correctness of the object contour. The application of the Chan-Vese active contour method for the segmentation of the flowing zone in CMOS camera images is shown in Fig. 4d, for N=1000, μ=1 for the top part of the flow and N=1000, μ=0.5 for the bottom part. One can visually notice a satisfying segmentation of the flowing zone. Finally, the last step consists in interpolating the stagnant-flow boundaries so as to estimate the position of the boundary in the middle of the hidden part corresponding to the ECT sensor area. Two

retrieved as follows, as illustrated by Fig. 4. One can see that even after a few seconds of silo discharging, the shape of the free upper surface reveals that funnel flow occurs in the presented symmetric case, but one can barely see the presence of the funnel flow or stagnant zone on Fig. 4a. However, the presence of the flow zone, both for its top and bottom parts not hidden by the sensor layer, is well revealed after the image processing strategy presented below has been applied, as shown in Fig. 4c. It is based on the enhancement method already presented in [12] in the case of the sequence of X-ray radiography images. Firstly, a Hadamard (pixel-to-pixel operation) absolute difference between successive images in the recorded sequence of optical images is performed. Such operation, which is illustrated in Fig. 4b, is done to discriminate parts of the image where intensity changes are very small (e.g. around the silo area, in the area defined by the ECT sensor and, more importantly, in the stagnant zone) from the area where intensity changes are large, i.e. in the flowing zone. Secondly, a contrast enhancement is applied. Considering the fact that the movement of rice grains induce local intensity changes where movement occurs, it is suggested that the local 0-entropy parameter should be used to better reveal the flowing zone. This parameter, which is commonly used to characterize textured images [45], works as an indicator to localize perturbation in images. Smooth regions will have a low entropy value while regions with larger intensity fluctuations will have a higher entropy value, like in the flowing zone. This is verified in 5

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permittivity bounds. During gravitational flow of rice, the changes of packing density are observed in a very narrow range of the normalized permittivity data, i.e. in the < 0.9, 1.1 > interval. Therefore, in Fig. 5(c-d) and Fig. 6(c-d), g0 and g1 were set to 0.9 and 1, respectively. Last but not least, in each presented case, the Landweber method is set with 200 iterations and a relaxation factor α=0.02, as mentioned in Section 3.1. As one can see, the results with the model ECT system, which uses LRC meter, are better by far than for the commercial ECT system, as far as image contrast and object delineation are concerned. However this observation is obvious. The acquisition time for LCR is much longer than for the commercial ECT system, which has a positive impact on the corresponding image quality. This element is visible qualitatively by visual inspection of the reconstructed images (e.g. comparison between Fig. 5a and Fig. 6a), but also by looking at the intensity range, that can be defined as the ratio max(g)/min(g). This is summarised in Table 2, where one can see that the intensity range is wider for the model ECT system than for the commercial one. This suggests that smaller changes for commercial ECT measurements should be interpreted as significant changes in granular concentration, while area and position of funnel in both cases are very similar. Another important conclusion from Table 2 is that this intensity range coefficient is larger for images reconstructed using the Landweber iteration method. It seems clear, that the iterative method tends to increase intensity gradient in reconstructed images. However, one can notice, by looking at Fig. 5b-d and Fig. 6b-d, that the boundary between the lower and higher permittivity regions has a concave shape after Landweber reconstruction. However, in the case of image reconstruction with LBP, the boundary rather has a linear or convex shape, which is in agreement with observations of funnel flow in rectangular silo [12]. Therefore, this comparison reveals that the model ECT system and the LBP image reconstruction are better adapted for the comparison with CMOS camera images, even though they do not represent standard experimental conditions, especially from the hardware side.

estimations were proposed: linear connection or polynomial fit. While the former considers connecting flow curve extremities of top and bottom boundaries to calculate intermediary position, the latter interpolates the two unconnected curves (either representing the left or right stagnant-flow boundary) with a polynomial function (usually of order 3), depending on the error minimization. Note that choosing such interpolation is conformed with previous observation that showed that the profile of the stagnant-flow boundary gradually changes from sigmoidal to linear shape as the granular material flows down [12]. For simplicity, the extremities of the stagnant-flow boundaries are manually selected from the flowing zone boundaries. Fig. 4e shows the interpolation of the selected boundaries using a polynomial fit of order 3. The fit has a good accuracy with a coefficient of determination R2=0.977 for the left stagnant-flow boundary and R2=0.991 for the right one. Afterwards, it is trivial to estimate the funnel width and position w.r.t. the left edge of the silo at the middle of the hidden part, as marked by the horizontal dashed line in Fig. 4e. As far as ECT reconstructed images are concerned, Chan-Vese active contour was also applied to segment areas with lowest conductivity, that is to say areas that correspond to flowing zone. Also, N=1000 and μ=0.5 have been used for the segmentation. 4. Results and discussion As it has been mentioned in the introduction, it is widely agreed to characterise an ECT system with respect to its temporal resolution, which means its ability to capture changes in process between successive frames. Because of the non-linearity of the electrical field within the sensor area and the ill-posedness of the inverse problem to be solved in order to reconstruct images, it is a challenging task to estimate the spatial resolution in reconstructed ECT images, which is non uniform across the sensing area (i.e. larger close to the walls than in the centre). Reinecke et al. has pointed out [48] that the average spatial resolution of ECT is about 10–15% of the sensor diameter. In this particular work, the spatial resolution is not evaluated directly, but the study focuses on estimating the level of accuracy that the ECT system can achieve w.r.t. CMOS camera images to detect boundary positions and also its potential to capture changes for different flowing conditions. More specifically, by changing the outlet position and hopper angles, one can change the type of flow, from concentric to eccentric silo discharging. In the case of funnel flow, this can be intuitively interpreted as a translation of the stagnant-flow boundary that should be of a similar order of magnitude as the translation of the outlet. Different silo discharging setups have been thought to achieve the different goals mentioned above. One concentric case with both hopper plates oriented at 20° from the horizontal axis, which has been presented in the previous section, was tested (hereinafter referred to as H20-20), while two eccentric situations were analysed: left plate at α1=20° and right plate oriented at α2=30° (H20-30) or at α2=40° (H20-40). The two eccentric situations correspond to a successive translation of the outlet to the right by 2 cm.

4.2. Measurement comparison Once the interpolation of the hidden parts of the flow boundaries are done, they can be compared with the results obtained using ECTbased measurements. The reader shall recall that in both cases, active contour was used to automatically retrieve stagnant/flow zone boundaries. The previous section has shown that the results gathered with the model ECT system, which connects a LCR meter to a multiplexer, is more accurate than the selected commercial ECT system. Also, the Landweber reconstruction method does not deliver a much stronger delineation of the assumed stagnant-flow boundary compared with LBP. Therefore, the model ECT system is taken into consideration in this section for the comparison with CMOS camera results, and the LBP image reconstruction is retained. These results, at this stage, are presented in the form of reconstructed images, for the three types of hopper configurations mentioned above, at one discharging time. The results are presented in Fig. 7. Always, the bottom of the upper free surface of the granular bed is above the top of the sensor layer when ECT measurements are recorded. This is to make sure that the sensor area is always filled with granular material. Moreover, all permittivity maps correspond to ECT measurements recorded after the silo outlet has been closed. The ECT wires of the front electrodes are also visible, especially in Fig. 7c, but do not hinder the qualitative result comparison. One can see on Fig. 7a, which shows the case H20-20, that the symmetric stagnant-flow boundaries estimated from the CMOS camera do match relatively well with the boundaries detected using the ECT reconstructed images. Still, the latter overestimates the optical measurements. At that stage, the comparison can only be done along the long edges of the permittivity map, since they correspond to the front side of the silo bin facing the camera. However, one can see that the

4.1. ECT image reconstruction comparison The comparison between LBP and Landweber iteration was conducted for concentric and eccentric flow conditions. Figs. 5 and 6 present examples of reconstructed permittivity distributions of H20-40 case for the model and commercial ECT systems, respectively. Figures also show distributions with permittivity cut-off, defined as follows:

P [g (i)] =

0,if g (i) < g0 ⎧ ⎪ g (i), if g0 ≤ g (i) ≤ g1 , ⎨ ⎪ 1,if g (i) > g1 ⎩

(3)

where i depicts the value of the i-th pixel and g0 and g1 are low and high 6

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Fig. 5. Image reconstruction in the case H20-40 for the model ECT system. (a) LBP, (b) Landweber (200 iterations, relaxation factor 0.02). (c-d) correspond to (a-b) respectively, but after low and high reconstructed permittivity cut-offs ((i.e. g < 0.9 or g > 1).

ECT image gives another level of information about the shape of the flowing zone, being in the present case not purely concentric, since the flow zone orientation seems oblique. After verification, this was attributed to experimental configurations of the positioning of the hopper sheets. The above observations can also be extended for the two other scenarios, i.e. H20-30 (Fig. 7b) and H2-40 (Fig. 7c). One can see that the asymmetric nature of the flows is captured and the boundary localisations do also match well between the two modalities. Moreover, both modalities capture the disappearance of the right stagnant-flow boundary in the case of H20-40 (left boundary on the figure due to mirroring of the image display, as explained in the figure caption). Still, the shape of the flow zone is not realistic and is attributed to the illposedness of the permittivity estimations based on the LBP reconstruction. A quantitative comparison of the flow boundary detection at the silo front side is shown in Table 3. This compares the stagnant-flow boundary (left/right side) between interpolated positions in CMOS camera images and the retrieved boundary positions at the edge of the sensing area in ECT images. The measurement line corresponds to the intersection between optical and ECT images in Fig. 7. In the case of the ECT images, only the ones of the model system are used, since they present a larger contrast for the chosen data scaling. The estimated error δ between the two modalities is expressed as follows:

δ=

bCMOS − bECT W

Table 2 Summary of permittivity ratio/intensity range for three different silo configurations, two different ECT systems and reconstruction methods.

H20–20 H20–30 H20–40

LCR ECT LCR ECT LCR ECT

Landweber

LBP

1,48 1,36 1,37 1,17 1,54 1,12

1,43 1,33 1,33 1,15 1,50 1,10

Fig. 7a) and W is the full width of the silo bin (i.e. 25 cm). Since ECT provides cross-sectional images, bECT is an average of the flow boundary in the z-axis. Since this average value corresponds intuitively to halfheight of the sensing area, bCMOS is interpolated at that position, as already mentioned in Section 3.2. One can see that the δ values confirm the observations from the figure above, where the maximal error is of the order of 9% (H20-30 case), which corresponds to around 2 cm position mismatch. Generally, this table also confirms that ECT measurements overestimate optical measurements, as far as flowing zone width is concerned. This statement obviously assumes that optical measurements are closer to the real case, even if one should keep in mind that measurement error is also introduced due to the interpolation of the boundary curve. One can also notice that the outlet translation of 2 cm, which traduces the change from H20-20 to H20-30, creates a nonuniform stagnant-flow boundaries translation captured by optical images, which is larger on the right side (i.e. around 2 cm) than on the left side (i.e. about 0.6 cm). Interestingly, the range of the displacement

(4)

where bCMOS and bECT are the calculated left or right stagnant-flow boundary position w.r.t. the left size of the silo bin (as illustrated in

Fig. 6. Image reconstruction in the case H20-40 for the commercial ECT system. (a) LBP, (b) Landweber (200 iterations, relaxation factor 0.02). (c-d) correspond to (a-b) respectively, but after low and high reconstructed permittivity cut-off s((i.e. g < 0.9 or g > 1).

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Fig. 7. Comparison of flow zone boundary detection between CMOS camera images and model ECT for three hopper configurations. (a) H20-20, (b) H20-30 and (c) H20-40. Images are presented in such a way as if the reader stands in the back of the versatile silo, the CMOS camera being on the opposite side. The silo shape is drawn for clarity.

system is able to detect changes that are at least of the centimetre range. This can be considered as an evaluation of a spatial resolution of the order of 5% of the bin width. The above results are promising for future exploratory work using ECT modality that could focus, for instance, on evaluating the true level of concentration changes occurring during silo discharging. This also confirms that the choice of using an LCR meter for better object detection when processes can be paused or for non-destructive testing. Of course, there is a strong limitation to use the proposed method during dynamic process with unsteady state, e.g. bubble column, slug/plug flow or fluidized bed. However, one can think of using the model ECT system in the case of inline separation where the originating vortex, even being unsteady, could time by time be scanned using the proposed modality to better extract its geometrical properties. One may also consider using both ECT modalities in situations where the model ECT system could be used to rescale commercial ECT data. Comparisons shown in Section 4.1 suggest that small changes for commercial ECT measurements should be interpreted as significant changes in granular

Table 3 Quantitative comparison of flow boundary calculation after segmentation using active contour method for both CMOS camera and model ECT images. Values taken from left side of silo bin. Values in bracket correspond to error parameter δ. Model ECT

CMOS CAMERA

Case

H20–20 H20–30 H20–40

LEFT BOUNDARY

RIGHT BOUNDARY

LEFT BOUNDARY

RIGHT BOUNDARY

(CM)

(CM)

(CM)

(CM)

8,5 9.07 14.2

17 18,96 –

7,65 (0.033) 8.48 (0.023) 12,95 (0.05)

18,3 (0.053) 21.3 (0.09) –

is also captured by the model ECT system in a similar order of magnitude. Indeed, after reconstructing the image with the LBP method and applying automatic segmentation using the Chan-Vese active contour method, the difference of the left boundary position is about 0.8 cm while for the right boundary it is about 3 cm. Therefore, the model ECT 8

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concentration. These could be compensated by the measurements from the model ECT system. However, this would involve a new approach, either during raw data calibration or during image reconstruction. Last but not least, more advanced image reconstruction methods could be used to increase the image quality, such as non-linear methods combined with complete sensor model proposed by Banasiak et al. [36].

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5. Conclusion

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The following conclusions can be drawn from the present study:

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1. The versatile rectangular silo system is an interesting tool to generate and control different types of funnel flow in order to test the potential of non-destructive techniques to characterise gravitational processes. 2. ECT measurements have been confronted with digital images from CMOS camera, taken in this work as reference measurements. Especially, a simple but effective image processing method based on active contour and polynomial interpolation has been used to facilitate the extraction of the flow boundary and its position estimation in the bin area hidden by the ECT sensor layer. 3. Results show a good agreement between the calculations of the flow boundaries between the two modalities, with a relative error being lower than 10% in the worst case. The model ECT system is more reliable for such comparison than the commercial ECT system, mainly due to longer data acquisition time. A spatial resolution at the silo wall of around 1 cm, which corresponds to around 5% of the bin width, has been estimated. However, the model ECT system can only be used for static measurements or steady state processes because of its low temporal resolution. 4. Qualitative and quantitative image analyses confirm the well-known fact that the use of a single measurement method is not always reliable. An excellent example is the asymmetry in the visualized flow inside the silo bin, which cannot be discovered while using optical images but is revealed by non-invasive tomographic methods. 5. Work is in progress to carry out the comparison between optical images and the commercial ECT system that includes data from the model ECT system as prior knowledge. Moreover, another challenge concerns the estimation of the concentration changes during silo emptying process.

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Acknowledgments

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The authors would like to thank G. Budzińska from Lodz University of Technology for providing language help.

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