Fluidization of spherical versus elongated particles - experimental investigation using X-ray tomography

(cid:129) X-ray tomography applied to ﬂ uidized bed of elongated particles. (cid:129) Comparison of ﬂ uidization characteristic between spherical and elongated particles. (cid:129) Bed of elongated particles shows more turbulent ﬂ uidization behavior. (cid:129) Bed of Geldart D spherical particles remains in constant slugging regime. (cid:129) Bed of elongated particles switches between slugging and turbulent ﬂ uidization.


Introduction
Fluidized beds are irreplaceable equipment for the process industry, offering the best contact between a dispersed solid and continuous fluid phase.Fluidized beds have broad application, ranging from food-processing, waste disposal, coating, and chemical synthesis to energy production.Due to its important role in the chemical industry, fluidized beds have been the focus of numerous research in the past decades.However, a large fraction of this research focuses on a relatively smoothly bubbling fluidized beds with Geldart A or B particles.With such a versatile application of fluidized beds in industry, particles that are being fluidized can have various shapes and sizes.With the rising need to switch to more sustainable and renewable material and energy sources, fluidized beds have found an important role in biomass processing.Typical biomass particles used in the process industry, such as wood chips, pellets and straw like material are not only characterized by an elongated shape but are also of considerably larger size than powder like materials which are typically used in fluidized beds.These large elongated particles have much more complex particle-particle interactions and experience additional orientation dependent hydrodynamic forces [1,2].
Fluidized beds with non-spherical particles have become a topic of research quite recently.There is already a large number of numerical investigations of such systems [2][3][4][5][6].However, experimental studies are still quite scarce.Most experiments deal with pseudo 2D fluidized beds and are done using Particle Image Velocimetry (PIV) and/or Digital Image Analysis (DIA) [7][8][9].However, in dense fluidized beds, such methods can only give insight into the near-wall region of the bed.
To get insight into a full 3D fluidzed bed is much more challenging, and requires more advanced non-intrusive 3D experimental techniques.One possible methods is particle tracking.There are various methods of particle tracking techniques, the most famous one in fluidization is PEPT [10,11].The magnetic particle tracking technique (MPT) [12] is a novel method, that was successfully applied to fluidized beds of elongated particles [13,14].X-ray particle tracking is another method that was recently applied to investigate fluidization of binary mixtures of cylindrical and spherical particles [15,16].Particle tracking is a powerful method that gives insight into time-averaged single particle features, such as orientation, occupancy and translation and rotation velocities.
Tomographic methods like electrical capacitance tomography [17][18][19] and X-ray tomography on the other hand, can give an overall picture of gas-solids distribution.X-ray tomography was one of the first non-intrusive 3D experimental techniques applied on fluidized beds [20][21][22].Tomographic reconstruction is a unique method which is able to give insight into gas bubble size, shape and location in the fluidized bed.The bubble dynamics plays a significant role in the fluidization process as it is the main driving force for solids motion and also determines the contact surface between gas and solid phase.Therefore, understanding the bubble behavior inside a fluidized bed is crucial for determining its efficiency and for equipment optimization.So far, most of the research using X-ray tomography focused on bubbling fluidized beds.However due to the use of various types of particles, fluidzed beds can operate in different regimes like slugging and turbulent fluidization [23].This operating regime received considerably less attention compared to bubbling fluidization and most available findings are not of recent date [24][25][26][27].Recently, a few more studies on slugging behavior in small diameter columns appeared [28][29][30].However these focus only on Geldart A type powders.When it comes to Geldart D type particles, the only available models for estimating bubble properties have been developed by Baeyens and Geldart [24] and more recently by Agu et al. [31,32].Venier et al. [33] looked into slugging fluidization of different type of particles, including Geldart D type, both experimentally and numerically.However these studies are limited to high bed height to diameter ratios.
In this work we investigate the fluidization behavior of a deep bed of Geldart D particles that is expected to operate in the slugging regime by means of X-ray tomography.We will compare fluidization properties of a bed containing spherical particles to one containing elongated, spherocylindrical particles, for different gas velocities.

Experimental setup and methods
X-ray tomography (XRT) is a well established non-intrusive method for studying fluidzed beds [34][35][36][37].The main idea behind applying this method in fluidized bed investigation is to reconstruct the solid or gas fraction, based on the intensity of X-rays detected after passing trough the fluidized bed.The 2D image reconstruction for horizontal cross sections of the fluidized bed in this work is done using the simultaneous algebraic reconstruction technique (SART) as defined in [21], implemented in the ASTRA Toolbox package.This technique has already been successfully applied in the same fluidized bed vessel with other particles [38].More information about the measurement principles can be found in [21,39].

Fluidized bed and particles
In this work experiments were conducted in a perspex cylindrical column with an inner diameter of 14 cm and a height of 140 cm.The fluidized bed column is positioned inside the X-ray setup, surrounded by three X-ray sources placed at 120 °around the column, as shown in Fig. 1.Each X-ray source is paired with a detector plate positioned on the opposite side, so that the column is in-between them.The X-ray sources used in this setup were YXLON Y.TU 160-D06 tubes with a maximum voltage of 150 kV and a maximum current of 12 mA.The used voltage and current depend on the investigated material and setup and have to be chosen such that the X-ray intensity is high enough to be detected after passing trough the full bed but not exceed the upper limit of the detector after passing through an empty bed.The choice of X-ray source voltage and current used in this work is shown in Fig. 1 (b).The X-ray detector plates are Xineos-3131 with a sensitive area of × 307 mm 302 mm and a resolution of × 1548 1524 pixels.The dimen- sions of each pixel are × 198 μm 198 μm.The energy range in which the detectors can operate is from 40 kV to 120 kV.In this work we used a field of view of × 1548 100 pixels in order to do measurements at an elevated rate of 200 frames per second.
Two types of particles were considered, spherical (aspect ratio 1, AR-1) and volume equivalent spherocylinders of aspect ratio 4 (AR-4).The particles were 3D printed by means of selective laser sintering and made of alumide, a 3D printing material which is a mixture of nylon and aluminium fine powder.The obtained particles can be classified as Geldart D particles and all their properties are listed in Table 1.In all experiments, the total particle mass in the bed was kept constant at 3.3 kg.The ratios between the initial bed height and the column diameter are 1.82 and 1.85 for AR-1 and AR-4 particles, respectively, so these fluidized beds are categorized as deep beds.Deep beds of Geldart D particles are expected to operate in the slugging regime [23].

Calibration and phantom reconstruction
Image reconstruction was done using two point calibration with the empty and full bed as upper and lower limits to the signal.Separate calibration has been performed for the spherical and elongated particles.The quality of the reconstruction is tested using phantoms of known dimensions.Cylindrical phantoms of 5.2 cm and 2 cm diameter were inserted vertically in the packed bed of particles.Images of the reconstructed horizontal cross sections of the phantoms and their estimated sizes are shown in Fig. 2. The reconstructed image is presented on a × 100 100cell grid, where the gray area indicates space around the column, black color refers to areas of the bed packed with particles, while white color responds to reconstructed voids (bubbles).The estimations of the phantom sizes are accurate: in the worst case it overestimates the real size by only 6.34%.Based on the phantom reconstructions, the threshold chosen for distinguishing bubbles from a packed area of the bed is 0.09 (relative between minimum and maximum intensity value).As the particles used in this investigation are quite coarse (see Table 1), the voids presented inside the packing can also be quite large and they can lead to a distortion of the reconstructed phantom shape and overestimation of its size.This is particularly the case for the large phantom which, due to its higher contact surface with the particles around it, has a large relative overestimation of its size.The 2 cm phantom is reconstructed successfully in all cases and therefore we set it as the minimum size of the bubbles that can be reconstructed with certainty.All bubbles smaller than 2 cm will be neglected in the further analysis.

Results
In this section we present results on the average bubble diameter, average bubble velocity, waiting time distribution between the slugs and slug frequency.The measurements were done at two different heights within the bed: h low = 70 mm and h hig = 240 mm above the distributor plate.For AR-1 particles we investigated 5 different excess gas velocities: − U U mf = 0.4, 0.65, 0.9, 1.15 and 1.4 m/s.Due to the specifics of its fluidization, AR-4 particles were fluidized at only three excess gas velocities: − U U mf = 0.6, 0.9 and 1.15 m/s.At a gas ve- locity of − U U mf = 0.4 m/s, AR-4 particles were in an active chan- neling regime and there were no proper bubbles or slugs forming, while at the highest gas velocity of − U U mf = 1.4 m/s slugs of particles were lifted to the top of the column and remain stuck there, clogging the column.
As stated in Section 2.2 bubbles with an average diameter less than 2 cm are neglected in further analysis together with bubbles that are present in less than 10 frames.Measurements are done for 60 s in case of average bubble diameter and bubble velocity, while for the waiting time distribution and slug frequency measurements were run for 600 s in order to collect sufficient statistics.

Average bubble diameter
The average bubble diameter can be directly obtained from the reconstructed tomographic images.For each frame, individual bubbles are detected and their surface is calculated by summing the number of pixels that are allocated to them.A sphere-equivalent bubble diameter is calculated for each bubble and the average bubble diameter is calculated for the whole measurement.Some examples of reconstructed images and bubble visualizations are presented in Fig. 3.This is a pseudo-3D representation of reconstructed bubbles as the z-axis is a temporal and not spatial coordinate.Already from this visualizations it is clear that the fluidized beds are operating in the slugging regime.Therefore the bubble size actually refers to the slug size.
Time averaged bubble diameters for AR-1 and AR-4 particles at two heights in the bed and for different excess gas velocities are shown in Fig. 4. As the fluidized bed is operating in the slugging regime, a change   of fluid velocity does not have a considerable effect on the bubble diameter at the higher position in the bed.However it can be noticed that in all cases the average bubble diameters are smaller for the AR-4 particles than for the AR-1 particles.This can indicate that the AR-4 particles are actually slugging less and have more small and medium size bubbles.In all cases investigated, bubble diameters are larger at the higher position in the bed which is something already expected from basic theory of bubbling fluidized beds [23].However, it is surprising that the average bubble diameter at the lower height in the bed of AR-1 particles is reducing with increasing fluid velocity.
This counter-intuitive results can be explained if we look at the average number of bubbles shown in Fig. 5.It can be seen that at high position in the reactor (red crosses), the number of bubbles remains roughly the same or shows a slight increase with an increase of gas velocity.At a low position in the reactor (blue stars), for AR-1 particles it can be seen that the decrease of average bubble diameter is accompanied by a monotonous increase of number of bubbles.On the other hand Fig. 4 shows that for AR-4 particles the average bubble diameter at the low position in the bed is increasing and from Fig. 5 it can be seen that this is accompanied by a decrease in the number of bubbles.
A model for predicting the average bubble diameter for Geldart D type particles in the slugging regime, which was recently developed by Aug et al. [31], is the only one comparable with the fluidized bed investigated in this work.Even though this model was not tested for bed height to diameter ratios below 4 and for − U U mf greater than 0.4 m/s, we compare it to our experimental results for AR-1 particles in Fig. 4.This model does not depend on the height in the bed and it can be seen that it slightly overpredicts the bubble diameters, but it is still in the upper range of standard deviation at the higher position in the bed.However for AR-4 particles the model predicts fully developed slugs with diameters close to the column diameter (13.96 cm) and does not change considerably with increase of gas excess velocity, therefore it is not included in Fig. 4.
In order to get a better insight in the fluidization behavior of the considered particles, the bubble size distributions are presented in Fig. 6.The clear peak at a bubble diameter of around 13 cm indicates clear slugging behavior, knowing that the column diameter is 14 cm.It can be seen that in all cases the AR-1 particles show more extreme slugging behavior.The AR-4 particles show a much higher distribution of small and medium size bubbles compared to the AR-1 particles.The height of the peak at maximum bubble diameter is also smaller for AR-4 than AR-1 particles.At the lower position in the bed (H Low ) it can also be noted that an increase in the gas velocity leads to an increase of the number of small and medium size bubbles for AR-1 particles, however never reaching the large number of small and medium bubbles observed for AR-4 particles.In the case of AR-4 particles, the opposite is the case: an increase of the gas velocity actually reduces the number of small and medium size bubbles while increasing the number of slugs.In summary, at the lower position in the bed, the trend of the bubble size distribution with gas velocity is opposite for AR-1 and AR-4 particles, where at high gas velocity the distribution seem to approach each other.In all cases the prevalence of medium and small size bubbles is lower at the higher position in the bed.

Bubble rise velocity
The bubble rise velocity is calculated by applying a cross-correlation between the signals at the 5th and 95th rows of pixels of the measured domain.The vertical distance of 90 pixels between the two rows corresponds to a distance of 1.26 cm.This is sufficiently large to make an accurate estimate of the bubble rise velocity, yet sufficiently small to neglect changes in bubble size (i.e. they do not grow, split or coalesce) over this distance.Details of the procedure of applying a cross-correlation function for calculating the bubble rise velocity are explained in [34].[31] for spherical (AR-1) particles in a high aspect ratio bed.Fig. 5. Average number of bubbles present in the horizontal cross-sections at low ( ) and high ( ) positions in the bed, for AR-1 (---) and AR-4 (-) particles, as a function of excess gas velocity.Fig. 7 presents the bubble rise velocities for AR-1 and AR-4 particles as a function of bed height.In all cases the bubble rise velocity is larger at the higher position in the bed and it generally increases with an increase of the gas velocity.The only exception is the slightly higher bubble rise velocity observed for AR-1 particles at the lower position in the bed at an excess gas velocity of 0.4 m/s compared to that at the next excess gas velocity of 0.65 m/s.This is caused by the presence of fewer but significantly larger bubbles at the lowest gas velocity.In the case of AR-4 particles, the bubble rise velocities are considerably higher than for AR-1 particles.This is another indication that AR-4 particles are slugging less than the AR-1 particles, because large slugs have a lower rise velocity than smaller bubbles [23].

Waiting time distribution
We now investigate the waiting time, defined as the time that passes between two consecutive slugs passing trough a horizontal measurement plane.In particular, we are interested in the waiting time distribution.The signal intensity measured on one of the detector plates is averaged over a horizontal row of pixels at the height of interest.In order to consider only slugs, and neglect small and medium size bubbles, we apply a threshold on the averaged signal intensity, as shown in Fig. 8.The waiting time is calculated as the time interval between the centers of two consecutive slugs identified through the normalized signal intensity shown in the lower images of Fig. 8. Already from the signal intensities in the upper images of Fig. 8, a clear difference between AR-1 and AR-4 particles can be seen.In the case of AR-1 particles, high intensities peaks corresponding to slugs appear regularly with almost identical distance between them.In contrast, for AR-4 particles we observe a mixture of periods with high intensity peaks and periods with smaller intensity peaks, the latter of which corresponds to small and medium bubbles passing by.Similar trends are observed for other gas excess velocities (not shown).
For brevity we present the waiting time distributions for AR-1 and AR-4 particles only at the higher position in the bed h hig because we find this to be the most relevant for analyzing slugging behavior.Fig. 9 Fig. 6.Bubble size distribution for AR-1 and AR-4 particles on different excess gas velocities and low and high positions in the bed.shows quite discrete waiting time distributions for AR-1 particles.For all gas velocities there is a relatively narrow peak at a waiting time of around 1s.At the lowest gas velocity considered (Fig. 9 (a)) the main peak at 1s is followed by clear peaks at around 2, 3 and 4s.This shows that large slugs are sometimes skipped at low gas velocity, probably because a smaller slug passes by which does not overcome our threshold value for detection.With increasing the gas velocity these peaks at longer waiting times are disappearing followed by a widening of the main peak at 1s.Overall, this shows that slugs for AR-1 particles appear regularly with break of around 1s between them.Fig. 10 shows the waiting time distributions for AR-4 particles.Notice that AR-4 particle show completely different waiting time distributions than AR-1 particles.For AR-1 particles all waiting time distributions were in range from 0.5 s up to 7.5 s, with the majority of the distributions occurring in the range between 0.5 s and 2 s.For AR-4 particles, a much wider waiting time distribution can be seen, with peaks appearing at 12, 20 and even up to 60 s.Due to this large spread in waiting times, some of the figures in Fig. 10 are presented on a logarithmic scale for the waiting time.Clearly, there are long periods in the fluidization of AR-4 particles without appearance of slugs, but rather with medium and smaller size bubbles.This explains lower average bubble sizes and higher average number of bubbles appearing for AR-4 particles discussed in Section 3.1.

Slug frequency
The waiting time distribution discussed in the previous section indicate that there is a certain regularity in slug appearance.More Fig. 8. Signal intensity before and after applying threshold for (a) AR-1 and (b) AR-4 particles at h hig and − U U mf = 0.65 m/s.Fig. 9. Waiting time distribution for AR-1 particles at the higher bed height h hig and excess gas velocities − U U mf of: (a) 0.4, (b) 0.65, (c) 0.9, (d) 1.15 and (e) 1.4 m/ s. information about the frequency of slugs can be obtained from a power spectrums of the signal intensity as seen in Fig. 8.The power spectrum is calculated by applying a fast Fourier transformation with a Hanning window on the normalized signal intensity.This frequency analysis is done for the same cases as the waiting time distribution discussed in Section 3.3.
The power spectra for AR-1 particles are shown in Fig. 11.As expected, a clear peak at a frequency of 1 Hz can be observed at all gas excess velocities.The dominant frequencies that can be seen in our cases are in the same range as predicted by [24].At lower gas velocities, Fig. 11 (a) and (b) show smaller peaks at 2, 3 and 4 Hz.These peaks should be distinguished from the peaks that appear in Fig. 11 (c), but rather represent the 2nd, 3rd and 4th harmonics of the main frequency at 1 Hz.This demonstrates how regular the frequency of slug appearance actually is.With further increase of gas velocity, Fig. 11(d) and (e) shows that the main peak at 1 Hz is widening, which indicates a transition to a more turbulent fluidizing regime.Fig. 12 shows the power spectra for AR-4 particles at different gas excess velocities.It can be seen that frequency of slugs ranges predominantly between 0 and 2 Hz, however unlike the case of AR-1 particles no distinct peaks can be seen.This confirms that for AR-4 particles slugs do not appear as regularly as for AR-1 particles.The increased randomness in slug appearance indicates that the AR-4 fluidized bed is actually operating in a turbulent regime [26,40].

Discussion
In this work, we applied X-ray tomography (XRT) to investigate the differences in fluidization behavior between spherical (AR-1) and elongated (AR-4) particles.Two different bed heights were considered, together with five different excess gas velocities for spheres and three for elongated particles.As the particles used in this investigation are Geldart D particles, and the initial bed height corresponds to a deep bed, the fluidized bed was operating in a slugging regime.Even though the considered particles were volume equivalent and the initial bed heights were approximately the same, the results presented in this work Fig. 10.Waiting time distribution for AR-4 particles at the higher bed height h hig and excess gas velocities − U U mf of: (a) 0.65, (b) 0.9 and (c) 1.15 m/s.Fig. 11.spectra for appearance of slug for the AR-1 particles at the higher bed height h hig and excess gas velocities − U U mf of: (a) 0.4, (b) 0.65, (c) 0.9, (d) 1.15 and (e) 1.4 m/s.
show considerably different behavior between AR-1 and AR-4 particles.
Regarding the average bubble diameter, AR-4 particles showed lower bubble sizes than AR-1 particles for all considered cases (Fig. 4), which was accompanied by a higher average number of bubbles for the case of AR-4 particles (Fig. 5).This finding was supported by the results on the bubble size distribution, which clearly showed a higher tendency for AR-1 particles to form slugs with almost no small or medium size bubbles (Fig. 6).On the other hand, AR-4 particles showed a considerably higher distribution of medium and small size bubbles.For the average bubble rise velocity, AR-4 particles showed higher values than particles (Fig. 7).This was another indication that AR-4 particles are slugging less as smaller size bubbles have higher rise velocities than slugs [23].
The waiting time distributions between slugs and their power spectra, discussed in Sections 3.3 and 3.4 gave more insight in the periodicity and frequency of slug appearance.AR-1 particles showed a clear and narrow main peak in waiting time distribution at 1s and a corresponding dominant frequency of 1 Hz.However, the AR-4 particles waiting time distributions showed a much larger spread and the dominant peak around 1s was considerably wider than in the case of AR-1 particles.Similar behavior was noticed in the power spectra where the main frequency ranges between 1 and 2 Hz but without any clear peak of dominant frequency.This showed that once the bed of AR-1 particles is in a slugging regime, slugs appear with a quite regular frequency while AR-4 particles show much more turbulent behavior and switch between slugging and turbulent behavior [26].
Based on the results presented in this work, it can be concluded that a bed of elongated particles shows more turbulent fluidizing behavior than a bed of volume-equivalent spherical particles.With an increase of gas velocity, a slugging bed of AR-1 particles will at some point transition to turbulent fluidization [23,26].We started to see an indication of this transition in our experiments at − U U mf = 1.4 m/s.However for elongated AR-4 particles more turbulent fluidization can be already be seen at the lowest gas excess velocity studied.When fluidizing elongated particles, periodic transitions between slugging and turbulent fluidization can be observed.Elongated particles also show other specifics when it comes to fluidization, starting from channeling, different particle rotational velocities and solids circulation patterns, as discussed in [8,14].
We note that in this work we investigated non-spherical particles of a specific shape and aspect ratio, namely spherocylinders of aspect ratio 4. One may wonder what is the limit of aspect ratio and shape that still shows the qualitatively different fluidization behavior between nonspherical particles and spheres.We expect this limit will be for elongated particles around an aspect ratio of 2, because particle interlocking and hydrodynamic lift and torque start to play an important role for elongated particles with aspect ratios beyond approximately 2 [1,2].However, at this point this is speculation, and more experimental work is needed to confirm this.Applying X-ray tomography for coarse systems such as these has its limitations and challenges.Therefore we advice a certain caution when considering some of presented results.From the phantom reconstructions shown in Section 2.2 it can be seen that while the sizes of phantoms are estimated with high accuracy, the same cannot be said for their shapes.Even though we showed that small phantom with 2 cm diameter can be reconstructed with high accuracy, the high distribution of small size bubbles in Fig. 6 for AR-4 particles at low position in the bed should be interpreted with caution.Due to the higher turbulence, solid particles can be more dispersed in the gas phase and the bed shows a broader distribution of voidages, making it harder to make a clear distinction between the bubble and emulsion phases [41].Considering all the specifics and the observed different fluidization behavior of elongated particles, we emphasize the need for better understanding and further development of numerical simulations of these kinds of systems.The results presented in this work, together with our previous findings using Magnetic particle tracking (MPT) technique [14], will be valuable for future validation of simulation results.

Conclusion
The results presented in this work demonstrate clear difference in fluidization behavior between spherical and elongated particles of Geldart D type.Elongated particles show a considerably larger distribution of small and medium size bubbles compared to spherical particles which show larger average bubble diameters for all gas excess velocities and bed heights considered.In all cases, elongated particles showed larger average bubble velocities.A clear difference was also observed in the waiting time distribution between slugs.In case of spherical particles, slugs appeared with more regular waiting time than elongated particles, which demonstrated a wide distribution of waiting times.Similar behavior was observed when looking into the slug frequency where spherical particles showed a clear peak at a frequency of 1 Hz, while elongated particles had a wider spread up to 2 Hz and showed no distinct peaks.All presented results indicate that elongated particles show less slugging behaviour than spherical particles and that during fluidization they periodically switch between slugging and more turbulent fluidization.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.(a) View of the fluidized bed column between the source and the detector plate, 1-X-ray source tube, 2-Detector plate, 3-Fluidized bed column.(b) Schematic of X-ray setup (top view).

Fig. 2 .
Fig. 2. Reconstructions of different combinations of phantoms in beds of AR-1 and AR-4 particles.

Fig. 4 .
Fig. 4. Average bubble diameter for AR-1 and AR-4 particles on different excess gas velocities.Error bars indicate standard deviation of bubble diameters.The dots indicate indicate the average bubble size predicted by Aug et al.[31] for spherical (AR-1) particles in a high aspect ratio bed.

Fig. 7 .
Fig. 7. Bubble velocities for AR-1 and AR-4 particles on different gas excess velocities as a function of bed height.