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Engineering

Procedía Engineering 102 (2015) 841 - 849 =

www.elsevier.com/locate/procedia

The 7th World Congress on Particle Technology (WCPT7)

Estimation of particle rotation in fluidized beds by means of PTV

Thomas Hagemeiera, Andreas Bucka*, Evangelos Tsotsasa

aThermal Process Engineering, NaWiTec, Otto-von-Guericke University Magdeburg, D-39106, Germany

Abstract

Fluidized bed granulation is a widely used process to produce pharmaceuticals, food and fertilizer. The achievable product quality, for example the uniformity of the formed layer or the size of the agglomerates, inherently depends on the particle dynamics in the bed. Generally, the solid phase velocity field is used to determine characteristic particle times (turn-over and residence time) in different zones of a spray fluidized bed. This information can be acquired using particle image velocimetry (PIV) together with digital image analysis (DIA) as for example in Börner et al. (2011, 2013). In order to derive certain quantities, such as particle mass flow rates, the measurement results are averaged in space and time, which is directly associated with a loss of information. However, an alternative is available when using the Lagrangian particle description (particle trajectories and local particle velocities) in terms of particle tracking velocimetry (PTV). Particle velocities are estimated on the basis of identifying individual particles, leading to exact particle mass flow rates. There are known shortcomings with this method for dense particulate flows, in particular ambiguities during particle identification. These problems have been fixed to a certain extent, for example using colored tracer particles (Natarajan et al. 1995, Bendicks et al., 2011) or recognition of flow pattern (Capart et al., 2002). The former approach yields a low resolution, but ensures reasonable results for particle velocities and associated trajectories. Additionally, it is possible to obtain information concerning the particle rotation, when using traces with an adequate color pattern (e.g. Zimmermann et al., 2011). Therefore, we used half-page blackened tracer particles in order to estimate particle velocities and particle rotation simultaneously and unambiguously within 2D-fluidized bed. Solid mass flow rates and particle residence times can be derived from the local particle velocities. At the same time, the observation of discontinuous particle tracks together with the quantification of the particle rotation can be used to foster the insight and understanding of particle-particle contact and the associated momentum transfer in dense gas-solid multiphase flows. Eventually, we can obtain local particle collision rates and corresponding changes of normal and angular momentum of individual tracer pairs.

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS)

CrossMar]

Corresponding author. Tel.:+86-13808694306; fax: +64 6 3505241. E-mail address: Andreas.Bueck@ovgu.de

1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selection and peer-review under responsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS) doi:10.1016/j.proeng.2015.01.202

Keywords: particle rotation, 2D-fluidized bed, colored tracer, particle tracking velocimetry

1. Motivation and fundamentals

The knowledge of individual particle and particle cluster velocities in granular systems is essential for the model based description of particulate processes. For instance, the classical two-compartment modeling approach of granulation processes relies on particle velocities. Information for residence times in and solid mass fluxes between two characteristic zones, where spraying and drying take place, are to be determined on the basis of particle velocities. Therefore, an exact quantification of particle velocities within the process chamber is of enormous value to modern macroscopic modeling approaches.

There are many ways how to gather information concerning particle velocities in fluidized beds (Bhusarapu et al. 2006). Diversity of measurement devices is available to acquire particles velocities, for instance fiber optical probe (FOP), laser-Doppler velocimetry (LDV) or particle image velocimetry (PIV), as summarized by Werther (1999). Each has its advantages and shortcomings. In this communication we present an approach to apply particle tracking velocimetry (PTV) to dense particulate flow in a pseudo two-dimensional fluidized bed. Up to now, the PTV technique has been applied to measure particle velocities in vibrated beds, Couette flows in shear cells, rotating drums or during hopper discharge. All these contributions considerably improved PTV in the field of granular flows. However, to the best of our knowledge, it has not been applied to the complex flows in fluidized beds, where densely packed particle clusters exist together with loose particles in large gas bubbles at the same time. Even higher complexity arises from opposing particle trajectories, inter-particle and particle-wall collisions. Those aspects have not been captured with other measurement devices for larger particle systems. Moreover, the particle system has been seeded with half-page blackened tracer particles to estimate the rotational behavior together with translational particle motion.

Nomenclature

Latin symbols

d particle diameter m

fr frame rate Hz

m mass kg

sf scale factor pixel/mm

v particle velocity m/s

A area m2

I12 image 1 and 1 -

R rotation matrix -

Sij Voronoi star i,j -

Tgran granular temperature m2/s2

Greek letters

£ volume fraction -

0 rotation angle o

p density kg/m3

a standard deviation of particle velocity m/s

w angular velocity s

Subscripts

p particle

s solid

x, y, z x-, y- and z-coordinate

I Interrogation

2. Experimental setup and processing algorithms

2.1. Experimental facility

The experimental investigations of this study have been realized on a 2D fluidized bed apparatus of 300 x 20 x 1000 mm3 in width; depth and height (see Fig. 1). Optical access is provided by a transparent front made of shatterproof glass, while the side walls are made of aluminum. To prevent abrasion, the glass was covered with a thin plastic film. For monitoring purpose, several thermo couples and pressure sensors are connected to the process chamber. The air flow is generated from an in-house compressed air supply in combination with a mass flow controller. Homogenous gas dispersion is realized using a sintered metal plate distributor of 3 mm thickness and a mean pore size of 100 ^im.

300 mm

shatterproof glass (front/back)

aluminum side walls

sintered metal

mass flow controller 20 mm;

air flow

Fig. 1 Schematic drawing of the 2D laboratory fluidized bed chamber with mountings and dimensions, the red box indicates the field of view

The particle system within the rectangular process chamber consists of spherical y-Al2O3 particles with a diameter of dp = 3 mm. The particle density is pp = 1300 kg/m3 and the minimum fluidization velocity is umf = 0.98 m/s. The static bed height was measured at 11.5 cm which corresponds to a total solid mass of ms = 0.466 kg. Additionally, 1% by weight of half-page blackened tracer particles has been used to seed the two-phase flow. For this study, a single fluidization velocity of 2umf was employed to fluidize the particle system.

The PTV measurements have been carried out using a high-speed CCD camera with a chip size of 1024 x 1024 pixel. Due to requirements concerning the spatial resolution for the PTV approach, as explained later on, only a section of 8.4 x 8.4 cm2 bounded to the right wall was observed during the experiments. The field of view ranged from 13.1 to 21.5 cm above the gas distributor plate and was illuminated by two halogen lamps, each with 400 W electrical power.

2.2. Particle tracking velocimetry with Voronoi-Imaging

Particle tracking velocimetry is an image-based measurement technique to quantify velocities in the field of fluid mechanics, in particular of liquid flows. However, there are also some contributions describing the PTV measurements in particulate multiphase flows which generally cause certain challenges for the application of PTV. The highly dense nature of fluidized bed flows, the strong fluctuating particle motions with discontinuous path lines and the sharp velocity gradients require adaptations of the methodology (Capart et al., 2002). Obviously, the system has to yield optical access for the high-speed imaging process, including high intensity illumination. Therefore, the application of the PTV approach is restricted to pseudo-2D configurations, where the particle dynamics are assumed to be constant over the depth of the flat fluidized bed process chamber. Moreover, the high particle density leads to correspondence problems within the tracking algorithm. In order to avoid wrong results, particles need to be identifiable, which was achieved in this study by employing a specific imaging method, where the particles are not only segmented, but a certain type of bed structure was identified. Based on the Voronoi-diagram, a net of connection lines between neighboring particles can be constructed which yields specific pattern of the particle bed and ensures particle assignment with high accuracy even for dense particle systems (Capart et al., 2002).

Particle tracking based on the Voronoi imaging method assumes that pattern formed by the particles within the fluidized bed are existent over a certain period of time. The Voronoi-diagram is a fragmentation of an area, here the image taken with the high-speed camera, into a number of polygons. Each polygonal area is located around a centroid with the restriction, that all Euclidean points within a polygon are closer to its centroid than to any other centroid. The connection of one centroid with all neighboring centroids is called Voronoi star and plays a key role in the evaluation procedure. The method can be applied to 2D and 3D, although limitations to near-wall regions come with dense particle packing. Stereoscopic images can be obtained either by using one camera which captures two perspectives in one image through a complex mirror arrangement or by two synchronized cameras (Spinewine et al., (2003). The three-dimensional approach enables the investigation of all three velocity components as well as the estimation of volumetric solid concentration. This requires special treatment to resolve particle positions and overcome occlusion effects. Furthermore, PTV-Voronoi methods have been applied to observe the granular flow in rotating drums or to analyze particle motion in dam-break situations and in every case, the coupled approach showed superior capabilities compared to other optical methods.

2.3. PTV-Voronoi-Algorithm

The PTV-Voronoi algorithm in our study consists of the following steps, which are carried out in sequential manner:

• Particle segmentation,

• Particle assignment using Voronoi cell matching and

• Filter operation

• Further post-processing.

In advance, all raw images are corrected for intensity inhomogeneity via subtracting a background image. In contrast to other segmentation approaches, we are not using gray level thresholding or gradient to identify individual particles. Particles are identified by correlating a sample particle image with every raw image of the actual series. The sample particle image is a manually chosen image section of the first image in a corresponding image sequence. It is bounded that way that the sample particle is captured completely in the image, but most of the background is excluded. The particle image is of the size of 39 x 39 pixel. This ensures the complete enclosure of the sample particle since the overall scale factor obtained by geometrical calibration is sf = 12.12 pixel/mm. Based on standard calibration tools, image distortion was corrected and each particle is resolved with approximately 36 pixel per diameter. This is more than usually needed for individual particle segmentation. However, the estimation of the color pattern on the tracer particles requires better spatial resolution.

Individual particles are recognized by cross-correlating the sample image with raw image which provides pixel-wise correlation coefficients. Correlation peaks are assigned to particle centroids, using a standard peak-finder. The threshold value for the correlation coefficient has been set to 0.61. This threshold value ensures reasonable particle

detection in terms of number of detected particles and quality. At the end of the segmentation step, the particle center x- and y-positions are stored for further use in the tracking step.

The particle tracking is carried out by identifying one and the same particle in two subsequent images. To overcome the correspondence problem, the Voronoi method has been applied. It yields certain advantages based on geometrical, kinematic and computational properties of the Voronoi diagrams (Capart et al. 2002). The processing always runs with two consecutive images, in the following called I1 and I2. The whole algorithm is introduced in the following through a stepwise description of each individual step, which are additionally visualized in Fig. 2

— 3 nearest neighbor distances -- Voronoi star of centroid Su in I

- - Voronoi stars of corresponding

nearest neighbors (Sj i_3) in l2

' S -S

Fig. 2 Voronoi-diagram and processing steps including Voronoi tessellations for two consecutive time steps, nearest neighbor search and

evaluation of Voronoi star matching

The generation of Voronoi tessellations for both images is based on previously detected particle centroids. The resulting polygons are stable in terms of shape and neighbors over several time steps, what can be verified in Fig. 4. This step is carried out only once for two consecutive images. Each of the following steps is carried out for every individual particle found in I1. For each centroid in I1, the distance to all centroids in I2 is calculated and the three nearest neighbors are identified based on minimum distance. The Voronoi cell properties are only compared for the nearest neighbors, to identify the best match for each centroid of I1 in I2. Most import quantity of the Voronoi cells for this algorithm is represented by the Voronoi stars S. These connections of a centroid with all its neighboring centroids, are computed for the three nearest neighbors (called Sj, 1-3), as well as for the centroid in I1 (called S, 1). In order to evaluate the matching, the stars are translated, so that their centroids coincide. Furthermore, the minimum distances of each extremity of S, 1 to the nearest extremities of Sj, 1-3 are calculated and stored in a vector for each cell. This is possible irrespectively of the number of branches of the individual stars. Then, the median values of the vectors yield information about the quality of the matching. The minimal median corresponds to the best match and assigns to each particle in I1 the respective particle in I2. Finally, the displacement between two corresponding centroids in I1 and I2 can be measured and the particle velocity can be computed, combining the displacement with the frame rate fr, which has been used during the image acquisition process.

Additional filter operations have been applied to exclude double allocation of particles to the same particles in the next image and to avoid unrealistic particle velocities. Double allocations of particles might occur in the case of degeneration of Voronoi cells. If a particle in I2 is assigned two times, an additional evaluation of the Voronoi stars is carried out (steps 4 and 5 of the Voronoi algorithm). Once again, the minimum median value decides which particle centroid in I1 is assigned to the centroid in I2, while the other is deleted from the list of assignments. To preclude unrealistic particle velocities, we defined the maximum allowed particle displacement to one particle

diameter per time step. This is a reasonable restriction based on the information given by manually tracked colored tracer particles. They never moved farther than this maximum value, even in case of fast particle motion within rising bubbles.

2.4. Estimation of particle rotation

The estimation of particle rotation is limited to tracer particles (1% by weight) which have been added to the particle system. Specialty of these tracer particles is the coloring which covers only one half of the spherical particles. Minor imperfections can be found along the perimeter, where small color streaks extend towards the half which is otherwise completely white. However, these imperfections improve the estimation of the particle rotation when particles change the orientation without visibly moving the color front. The particle orientation at different time steps yields the information about the particle rotation, where the spatial resolution is decisive for the accuracy of the orientation measurement. This can be seen in Fig. 3 where a time series of 20 images of a rotating particle is shown. The particle is contrasted as red circle against the background and the inner of this circle shows the changing orientation of the particle. In the first image, the particle side view can be seen with the color front almost centered. In the following images, the uncolored particle side advances within the field of view and finally fills the whole projection area.

Fig. 3 Image series of a rotating tracer particle. The exemplary series runs over 20 time-steps (from upper left image ti to lower right image t2o).

The time-step size is 0.001 s, corresponding to a frame rate of 1000 fps. The red circles mark the approximated circumference of the particle,

while the inner region shows the changing particle orientation.

Following Zimmermann et al. (2011), three parameters are required to describe the particle rotation according to the Euler's rotation theorem. It describes the particle orientation in terms of transforming the reference coordinate system (shown in Fig. 1) into a particle coordinate system. The Tait-Bryan convention is then used to describe the particle rotation by three elementary rotations corresponding to Euler angles dx, dy and Qz. Hence, the orthogonal rotation matrix R is used to fully describe the rotation.

R{dx,0y A )=Rx{dx)Ry [dyR fa) (1)

Estimating the displacement of the color front in the images of Fig. 3 yields two Euler angles (dz and 0x). The value for dz can be obtained from the displacement of the intersection points of the color front with the

circumference in x-direction. Similar, the value 6x for can be obtained from the displacement of the intersection points in z-direction. Since there are always two intersection points, the averaged displacement value is used to calculate the corresponding angle.

When the white or blackened particle side faces the camera frontal, an estimation of the rotation around the third axis is not possible unless the imperfections along the color front can be used to approximate the third Euler angle 6y. Finally, the corresponding angular velocity w of a particle is then given by

sin d.,

0 cos 0x - sin 0x cos 0y 0 sin 0x cos 0x cos 0y

However, all rotation evaluation processes are subject to limitations, as there is more than one solution (triplet) how a specific particle orientation could be achieved. In our estimations, the order of rotation is always first z-, then x- and finally y-direction associated to the respective elementary rotations Rz(Oz), Rx(Ox) and Ry(0y). Thus, the rotation matrix reads as R(Ox,Oy,Oz)=Ry(Oy)Rx(Ox)Rz(Oz).

3. Results and discussion

Applying the PTV-Voronoi algorithm, the individual particle trajectories have been obtained which are the Lagrangian representations of the particle translations. Exemplary results for particle trajectories are presented in Fig. 4, together with initial and final particle positions in the raw images. The length of each trajectory is limited to 20 time steps to improve readability and colored with local particle velocity magnitude. The total time shown in Fig. 4 is 0.02 s corresponding to the frame rate of 1 kHz.

Particles® t=t>001 s

200 4M 605 eco IOOO Horizontal direction [pixel]

Particles @ l*0.019s

200 JCO em see 1000 oooo

Horizontal direction |ptxol]

Fig. 4 Particle positions in two raw images including one tracer particle and its trajectory marked in red (left), individual particle trajectories over

20 time-steps, as obtained by PTV-Voronoi algorithm (right).

The tracer particle which was chosen to represent particle rotation is encircled in red in the two raw images shown in Fig. 4. It moves within a rising gas bubble, where the trajectory is drawn as dotted red line in the lower raw image of Fig. 4. At the same time, it rotates without any contact to other particles. In cases where particles contact the front wall, a rolling motion can be observed, where the rotation axis is normal to the particle trajectory. The

rolling motion was observed for a majority of tracer particles and thus, illustrates the significant influence of the wall on the particle dynamics for this flat fluidized bed configuration. However, the chosen tracer particle rotates in opposite direction and thus, cannot be rolling along the front wall.

In the following, both, the tracer particle translation velocity and angular velocity are shown in Fig. 5. The translation velocity is given in terms of x- and z-velocity components, which are assigned to the reference coordinate system specified before. The horizontal velocity component vx appears to be almost constant, while the vertical velocity component v. slightly decreases over the 20 time steps evaluated here.

time step [s] time step [s]

Fig. 5 Tracer particle translation velocity (left) and particle angular velocity (right).

The particle rotation was evaluated on the basis of the moving color front. It vanishes after 15 time steps and no further particle rotation could be observed, as can be visually verified from the last 5 images in Fig. 3. Consequently, the rotation angles become zero. Before, the rotation angles 6z and 6x scatter between 1° and 3°. In total the rotation around the z- and x-axis sum up to values of approximately 22°, each. From our estimates, the rotation around the third axis appears to be insignificant within the investigated time frame. The corresponding angular velocity is presented in the right plot of Fig. 5. It shows some scattering for both angular velocity components around a mean value of 20 rad/s. Certainly, the scattering is caused by both, changing angular velocity and measurement uncertainty, with respect to identifying the color front and the intersection points. Nevertheless, a reasonable value for the angular velocity can be obtained simultaneously with the particle trajectory.

4. Conclusions

In this paper, we reported the application of particle tracking velocimetry to estimate not only individual particle velocities but also particle rotation. The particle tracking approach has been adapted using the Voronoi method to be able to assign particles in dense two-phase flow situations, for instance in fluidized beds. Contrary to previous applications of particle imaging techniques, individual particles have been tracked in large number under fluctuating flow conditions of a bubbling fluidized bed. Coupling high-speed imaging, with an innovative segmentation approach and the Voronoi algorithm, particle velocities can be acquired in densely packed bed regions as well as in dilute regions of rising bubbles. The different particle dynamics, which are usually found in rising bubbles or densely packed bed, can be captured, regardless of the direction of particle motion or velocity magnitude.

Furthermore, we manually estimated the rotation of tracer particles which have been half-page blackened. Therefore, the combined information of particle trajectory and particle angular velocity has been reported, exemplarily. An automated evaluation of the particle orientation was not possible due to individual coloring imperfections. Future work will focus on an automated approach for particle orientation evaluation, similar to Zimmermann et al. (2011), together with an improved color texture of the particles. This will eventually lead to quantitative characterization of particle dynamics in terms of individual trajectories and particle rotation which can foster the insight and understanding of particle-particle contact and the associated momentum transfer in dense gassolid multiphase flows.

Acknowledgements

The authors gratefully acknowledge the funding of this work by the German Federal Ministry of Science and Education (BMBF) as part of the InnoProfile-Transfer project NaWiTec (03IPT701X). Moreover, we thank Christian Knopf for supporting the experimental work.

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