Observed Mixing Behavior of Single Particles in a Bubbling Fluidized

Article pubs.acs.org/IECR

Observed Mixing Behavior of Single Particles in a Bubbling Fluidized Bed of Higher-Density Particles Jack Halow,*,† Kerri Holsopple, and Benjamin Crawshaw Waynesburg University, 51 West College Street, Waynesburg, Pennsylvania 15370

Stuart Daw and Charles Finney Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 ABSTRACT: We report experimental observations of the dynamic behavior of single, magnetically tagged 3−4 mm particles varying in density from 0.55 g/cm3 to 1.2 g/cm3 as they migrate freely in a bubbling air-fluidized bed of 177−250 μm glass beads of 2.5 g/cm3 density over a range of air flows. The densities of the tracer particles (made by imbedding small magnets in wooden particles) were chosen to span a range typical for many biomass materials and exhibited both segregated and well-mixed behavior. Using high-speed measurements from externally mounted magnetic probes, we were able to reconstruct three-dimensional spatial and temporal information about the tracers’ trajectories over periods of five minutes. Based on this information, we describe general trends in how the tracers moved and redistributed themselves as functions of their density, fluidization air flow, and the overall concentration of low density particles present. One key finding was that the time average vertical probability distribution of the tracer particles locations is consistent with a Weibull distribution. The effective Weibull parameters appear to vary systematically with the degree of fluidization and particle density. Also, we observed that temporal autocorrelations in the vertical position of the tracer particles vary systematically with fluidization intensity and reveal important information about the dominant bed circulation time scales. Our results suggest that it may be possible to develop relatively simple statistical models or correlations for describing the spatial distribution and circulation of mm sized particles in bubbling beds of this type. Such tools should be useful for simulating some types of fluidized biomass processing and for validating kinetic-theory models of fluidized bed systems.

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INTRODUCTION AND BACKGROUND While fluidized beds have been extensively studied for many applications, the detailed hydrodynamics and mixing patterns in systems with disparate types of bed particles are still not fully understood. A number of biomass gasification and pyrolysis processes now being considered employ a bubbling bed of sand-like particles in which particles of biomass are suspended. At steady state, the biomass particles usually constitute only a small fraction of the bed so that the dynamics involve a few coarse, less-dense particles circulating in a finer, denser medium. Our objective in this study is to experimentally measure the trajectories of such particles over time with sufficient resolution to better understand the statistics of their behavior and possible approaches for modeling and/or correlating spatiotemporal features. It is widely recognized that solids mixing in bubbling fluidized beds is induced by the motion of rising bubbles.1 Rising bubbles push solids outward, causing radial and angular mixing. Solids are also carried upward in bubble wakes, contributing to large-scale axial solids motion. Overall mass continuity requires solids not attached to bubble wakes to move downward to balance the upward flow. Portions of the bubble wakes are frequently shed, adding to the complexity of the axial and radial solids dispersion. When there are solids of different density and/or size present, the net effect of all of these mixing processes can lead to segregation of the different solids into distinct spatial zones. Many previous studies2−12 have examined © 2012 American Chemical Society

binary as well as continuous distributions for segregation tendencies. A recent overview of fluid bed segregation13 summarizes this work and points out that there is still no clear understanding of the details of this process. It is not our intention here to study particle segregation in a general sense, but rather to consider the special case where most of the bubbling bed is composed of smaller, denser particles and the particle of interest is larger and less dense. This is often the situation in fluidized beds used for processing biomass. Different experimental techniques have been used to observe solids motion and mixing. Visual observations (including photography and videography)14,15 have been employed in optically accessible beds. Typically these methods rely on beds specially designed for optical access (e.g., two-dimensional (2D) beds) or in-bed optical probes, both of which can modify the dynamics of interest. The potential for disturbing the particle dynamics is also true for high speed pressure and heat transfer probes16,17 that are inserted into the bed itself. More recently, capacitance,18 X-ray,19 and magnetic resonance imaging (MRI) have been used to resolve three-dimensional (3D) dynamic density variations in the flow field with remarkably high resolution. While these nonintrusive imaging Received: Revised: Accepted: Published: 14566

June 12, 2012 September 17, 2012 October 10, 2012 October 10, 2012 dx.doi.org/10.1021/ie301517w | Ind. Eng. Chem. Res. 2012, 51, 14566−14576

Industrial & Engineering Chemistry Research

Article

particles to align their magnetic axes with Earth’s magnetic field like a compass needle. Proper positioning of the probes around the bed can take advantage of this tendency, which simplifies the data analysis. Figure 1 shows the bed in its support stand

methods can eliminate potential flow field distortions, they do not readily lend themselves to tracking the motion of individual particles. They also require highly specialized, expensive equipment and considerable operating expertise. Two other nonintrusive techniques have been developed to directly track the motion of individual particles in fluidized beds. The first, usually referred to as computer aided radioactive particle tracking (CARPT),19 employs gamma emitting radioactive tracers embedded in single particles with external gamma detectors to follow the tracer motion. The second, positron emission tomography (PET),19 is similar to CARPT, except that it is based on a different type of radioactive isotope that emits correlated pairs of γ-rays. Both of these methods allow direct measurement of tracer particle trajectories, but like the nonintrusive imaging approaches, they require expensive and specialized equipment and considerable operating expertise. They also require access to short-lived radioactive isotopes and involve concomitant safety issues. We recently developed and reported a particle tracking method that uses small embedded magnets in particles and sensitive, external, fast-response magnetic sensors20 to track the motion of single particles in fluidized beds. While this method can only be used on beds constructed from nonmagnetic materials and the magnetic sensor signals must still be deconvolved with special algorithms, this method has many advantages in terms of safety, complexity, and cost compared to other nonintrusive particle tracking methods such as CARPT, PET, X-ray, and NMR. The only similar tracking study we have found in the literature uses a large metal coated tracer in a bed with an imposed magnetic field, such as a metal detector, to follow the tracer motion.21 In this study, we employed our magnetic tracking method to observe the motion of single simulated particles of biomass in a bubbling fluidized sand bed. This measurement provided detailed information on the 3D location of the tracer particle as it migrated through the bed for periods of several minutes. As far as we are aware, this is the first time such detailed statistics have been acquired for a single particle trajectory under these conditions. Some examples of the trajectory data obtained in our experiments are presented as 3-D “dot clouds” where each point represents a measured position and as vertical position versus time graphs. All of the vertical data was analyzed to develop time averaged frequency distributions and also fitted to Weibull probability distributions. Finally, the temporal aspects of the data were examined by autocorrelation methods. The results should be useful for incorporation into process models to predict bed performance and validating first principles models.

Figure 1. 55 mm fluidized bed with external magnetic sensor probes.

and the probes positioned around the bed in the north, south, east, and west directions. We also collected high-definition slow-motion videos of the bed surface to observe the state of fluidization and appearances of the tracer particle at the top of the bed. These recordings were made with a Sony model HDRXR150 high definition video camera in slow motion (1/4 normal speed). The bed consisted of a 55-mm-diameter by 600-mm-long glass tube attached to a plastic PVC collar assembly that housed the distributor and plenum. The distributor consisted of a 1.27 cm thick ultrahigh density porous polyethylene plate with 50 μm pores. The grid was sealed in place with a silicone sealant. The bed rested on a plate, and its position adjusted with sets of moveable positioning rods at the top and the bottom of the bed. Air exiting the bed was exhausted to a lab hood. The probes were mounted on an acrylic sheet that could be positioned vertically. Our experimental system configuration is shown in Figure 2. A standard oil-free 200-psig shop air compressor with a 15 gal air tank and two additional air tanks (11 gallons each) for added capacitance supplied the air. After passing through a filter and pressure regulator, the air was metered with a Cole-Parmer precision mass flow meter and bubbled through a tank containing distilled water to humidify the air. Flexible clear plastic tubing was used upstream of the humidification tank. Rigid polyethylene tubing was used downstream of the humidifying tank to the inlet of the bed to avoid any possible effect of tubing flexing with the pressure pulsations that can occur in fluidized beds. Simulated biomass particles were created by embedding 1.6 mm (1/16 in.) long by 1.6 mm diameter cylindrical grade N52 neodymium magnets in either balsa wood or bass wood 3 to 4 mm cylinders. The magnets have a density of approximately 7.4 g/cm3, while the balsa wood density is variable depending on the particular piece of wood of from about 0.05 to 0.2 g/cm3. The density of bass wood is also variable, with usual values in the range 0.5−0.6 g/cm3. The composite particle densities are thus between the densities of the wood and magnet material. For the experiments reported here, we used tracer particles with

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EXPERIMENTAL EQUIPMENT The experimental results summarized here were obtained using our previously reported20 magnetic particle tracking method applied to a 55 mm cylindrical glass bed fluidized with air at ambient conditions. Briefly, this low-cost tracking method makes it possible to follow the motion of a single, magnetically tagged particle while avoiding any concerns with exposure to radiation. The tracer particles contain embedded neodymium magnets. Magneto-resistive detectors continuously measure the strength of the tracer’s magnetic field from multiple locations outside of the bed. The algorithm for interpreting the signals takes advantage of the tendency of the strongly magnetized 14567

dx.doi.org/10.1021/ie301517w | Ind. Eng. Chem. Res. 2012, 51, 14566−14576


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Figure 2. Schematic of the experimental fluidized bed system.

fluidization velocity remeasured at the end of the experimental runs. No significant changes were observed. We maintained a slumped height to diameter ratio of 1 in this study. This material fluidized to form a bubbling bed (bubbles at the surface) with U/Umf of up to about 4. At velocities above this, the bed appeared to be turbulent without distinct bubbles. Before beginning each set of experiments, the bed was vertically aligned and the orientation of the four probes adjusted to ensure that they were aligned along north, south, east, and west axes. The bed particles were then poured into the bed, and the bed was fluidized to fluff it. The probe elevation was adjusted to 10 cm above the grid, which would place the probes above the bed level at the maximum velocity. Then, fluidizing air was introduced at the desired rate. Immediately before each test, the magnetic field probes were initially zeroed to offset Earth’s magnetic field. After data acquisition was initiated, a single simulated biomass particle was dropped into the bed. Signals from the probes were recorded over a 5-min period at a rate of 200 samples/s. The three-dimensional position of the tracer particle at each time was determined by postprocessing the recorded signals using the previously reported algorithm.22 For each tracer particle, fluidization velocity was varied between 1.1 to 6 times the minimum fluidization velocities. Typically, data was acquired for 5 or 6 different air flows for each tracer. The first 20 s of each recorded set of magnetic signals were discarded to remove initial transients associated with the tracer particle introduction.

densities of 0.55−1.2 g/cm3, spanning the range of many woody biomass materials. Figure 3 is a photograph of a typical 4 mm balsa tracer.

Figure 3. Typical 4 mm simulated biomass tracer particle.

Data logging was achieved with a National Instruments data acquisition module (USB 6210). This interface provides 16 bit sampling. Labview signal express was used to collect and record the data.

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EXPERIMENTAL PROCEDURE Results discussed here were obtained from a bed of 177 to 250 μm highly spherical glass beads with a weight mean diameter of 205 μm, density of 2.5 g/cm3, and an experimentally measured minimum fluidization velocity of 6.5 cm/s. Figure 4 is a micrograph of the bed material. To check for possible attrition, the bed was periodically reweighed and the minimum

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RESULTS AND DISCUSSION Initial tests were performed over a range of tracer densities of from 0.55 up to 2.5 g/cm3 (the particle density of the bed material). We found that tracers with densities much greater than 1.2 g/cm3 would simply settle to the bottom and remained there without being appreciably entrained into the bed, even at high fluidization velocities. It was decided to do detailed tests on five tracer densities of 0.55, 0.76, 0.89, 1.1, and 1.2 g/cm3. Visual observations and magnetic tracking data revealed that, depending on density and fluidizing velocity, the tracer particles could exhibit flotsam-like, jetsam-like, and well-mixed behavior. The heavier tracers (1.1 and 1.2 g/cm3) tended to reside near the bottom of the bed at lower velocities, while the lower density tracers (0.55 and 0.76 g/cm3) tended to migrate toward the top. The intermediate density tracer (0.89 g/cm3) tended to mix relatively uniformly at all velocities. Over short time scales, the individual particle trajectories were quite complex, as illustrated in Figure 5. Here, we observe

Figure 4. Glass beads used as bed material. 14568



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Figure 5. Pick up and segregation of a 1.1 g/cm3 tracer in a bed fluidized at 2 Umf.

Figure 7. Light tracer in a bed fluidized at 1.5 Umf.

the vertical position (left) and a three-dimensional trajectory followed by a 1.1 g/cm3 tracer over a 6 s time span while the bed was fluidized at twice the minimum fluidization. This particle was initially segregated near the bottom and then was picked up presumably by a bubble and carried up into the bed. The particle position oscillated briefly and then descended downward in several steps. It is possible to get a more global sense of the regions visited by the tracer particles by considering much longer time spans. Figures 6−11 illustrate examples of the “dot clouds” constructed by plotting the measured positions for two different density tracers over a 5 min period. These 3D clouds are depicted from both top and side views at three different air flows. X and Y are the horizontal coordinates, and Z is the vertical coordinate. In Figures 6, 7 and 8 we can see that the

Figure 8. Light tracer in a bed fluidized at 3 Umf.

Figure 9. Heavy tracer (1.2 g/cm3) in a bed fluidized at 2.0 Umf.

bubbles. The cone shapes seen in several of these figures suggest the tracers were settling in the central region of the bed. Visual observation of the bed surface showed that bubbles there erupt in an annular region around the bed axis but rarely along the axis itself. The axis region appears to be emulsion phase and occasionally, if the tracer appeared on the surface, it would migrate toward this central region and be drawn down with the descending emulsion. This agrees with the cone shaped dot clouds if we realize that, lower in the beds, bubbles would be smaller and the tracer would be able to appear over a wider region. Our bed had an L/D of approximately one and was not

Figure 6. Light tracer (0.76 g/cm3) in a bed fluidized at 1.2 Umf.

lighter (0.76 g/cm3) tracer tended to segregate near the central area of the bed surface at the lowest velocity and mix more uniformly at higher velocities. In Figures 9, 10, and 11, we observe that the heavier (1.2 g/cm3) tracer segregated near the bottom at a low air flow and mix more uniformly at higher fluidizing velocities. Even at the higher velocities, the heavier tracer tended to segregate between pickups by the forming 14569



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resulted in top segregation of the tracer all of the time. At 1.3 Umf, limited mixing occurred but the tracer tended to reside mostly near the bed surface. As the velocity increased beyond this point, mixing into deeper levels of the bed occurred. At a fluidization level of about 3 Umf, mixing was effectively uniform. The 0.89 g/cm3 tracer seemed to circulate through the bed even at the lowest velocity, although circulation rate was slower at the lower rates of fluidization. Figure 13 shows this. At 3 Umf the tracer was well mixed. In general, the denser 1.2 g/cm3 tracer particle tended to segregate downward to near but not on the distributor. At fluidization velocities below 2.1 Umf, this tracer sank to a location slightly above the distributor and remained there. At an air flow of 2.1 Umf, the heavy tracer particle circulated briefly after being introduced but then settled again near the distributor. At a flow of 3 Umf, the heavy tracer was repeatedly lifted by bubbles from the region near the distributor. After each lifting event, the tracer then settled back toward the grid region, where it again was lifted by rising bubbles. In this repeated sinking and rising, the tracer trajectory appeared to reflect the large scale solids circulation cell generated by the bubbles. The data suggests the area immediately above the grid is a region of bubble formation and rapid coalescence, which prevents the tracer from actually settling on the grid. We speculate that this lifting effect may be a function of the size of the distributor openings, and thus, it would be interesting in future studies to see how heavy tracers behave on distributors with different hole sizes and spacings relative to the tracer particle size. Statistical Analysis. To quantify the global statistics of the tracer trajectories, we divided the possible vertical positions into 40 bins over the 10 cm height to calculate the frequency of appearance of the tracer at various positions. Each bin width was 0.25 cm. The counts were normalized by dividing each bin count by the total number of counts, yielding the fraction of the time that the tracer spent in each bin. The frequency distributions for three tracers at various velocities are shown in Figures 15−17. Figure 15 is for a tracer with a density of 0.76 g/cm3. At the lowest velocity of 1.2 Umf, The tracer remained

Figure 10. Heavy tracer in a bed fluidized at 2.5 Umf.

Figure 11. Heavy tracer in a bed fluidized at 3 Umf.

deep enough to accommodate complete coalescence into a central bubble channel. We performed a more quantitative analysis of the tracer trajectories by considering just the vertical coordinate of the tracer particles over time, as depicted in Figures 12−14 for three different density tracers at two fluidization velocities. For the 0.76 g/cm3 tracer, fluidization velocities below 1.3 Umf

Figure 12. Example time series of the vertical position of the 0.76 g/cm3 tracer at two fluidization rates. 14570



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Figure 13. Vertical position of the 0.89 g/cm3 tracer.

Figure 14. Vertical position of the 1.2 g/cm3 tracer.

Figure 15. Frequency distribution with vertical position of a 0.76 g/ cm3 tracer.

Figure 16. Frequency distribution with vertical position of a 0.89 g/ cm3 tracer.

segregated at the top of the bed. At 1.5 Umf, the tracer mixed into the bed but not uniformly . As the fluidizing velocity increased, its vertical probability distribution became more uniform. In Figure 16, for the 0.89 g/cm3 tracer, the vertical position has a wider distribution for the lowest velocities but seems to be biased toward the lower portion of the bed at the lowest

velocities of 1.1 and 1.2 Umf with the peak shifting upward in the bed as the velocity increases. For the densest tracer, 1.2 g/cm3, the bottom segregation tendency is obvious over the entire fluidization range. Increasing the fluidization velocity increased the likelihood that the heavy tracer would be lifted upward by rising bubbles, thereby increasing the probability that it would be found at any moment at some higher location in the bed. 14571



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Figure 17. Frequency distribution with vertical position of a 1.2 g/cm3 tracer.

Figure 19. Weibull shape parameter variation with fluidizing velocity.

We found empirically that it was possible to describe the vertical probability distributions of all the tracers (heavy, medium, and light density) in terms of a Weibull distribution. This is a commonly used non-Gaussian distribution that is expressed by the following probability density function: f (z ) =

k−1 k k ⎛⎜ z ⎞⎟ e−(z / α) α⎝α⎠

(1)

The parameter k is a shape factor that relates to the asymmetry of the distribution function, and the parameter α is a scaling factor that relates how rapidly the probability changes with the z-axis. Both parameters and the z coordinate must be positive. Figure 18 illustrates an example of how well the observed vertical probability distributions can be fitted by the Weibull

Figure 20. Weibull scale parameter variation with fluidization velocity.

further air flow increases lead to a slight re-segregation tendency, which corresponds to a slight rise in the shape parameter. Likewise, the rising value of the fitted shape parameter for denser the 1.1 and 1.2 g/cm3 tracers at lower velocities reflects the decreasing bottom segregation tendency with increasing flow. The shape parameter variation for the intermediate density tracer appears to follow an intermediate trend with air flow. The fitted scale parameter decreases from high values at low velocities, as shown in Figure 20 for all of the different tracer densities. In simple terms, this shift in scaling appears to correspond mainly to the expansion of the bed with increasing fluidization velocity with some additional effect of the tracer density. Bed Composition Effects. The observations reported were all made with a single low-density tracer particle in the bed of higher-density glass particles. In many applications (e.g., biomass processing beds), there are typically more that just one low-density particle, although the low-density particles may still only constitute a small fraction of the total bed. To investigate the effect of having additional low-density particles on the tracer particle behavior, we prepared a quantity of biomass-like particles from a hardwood dow rod that was cut and shaped to be similar in size and density to the 0.76 g/cm3 balsa tracer. These additional low-density particles did not contain magnets and were not tracked, but their presence still potentially affected the fluidization dynamics. The tracer behavior was then studied at light-particle volume concentrations up to 10% at fluidizing velocities of 2, 4, and 6 Umf. We observed a modest broadening of the distribution at the higher concentrations, and the effect was more pronounced at low velocities. At air velocities >2 Umf, there was little effect.

Figure 18. Comparison of a fitted Weibull distribution with the observed vertical position frequency distribution for a 0.89 g/cm3 tracer fluidized at 1.5 times Umf.

distribution. The correlation coefficient in this case was over 0.99. In all cases the correlation coefficients were above 0.9 with only a few cases (highly segregated) being less han 0.95. The best fit Weibull parameters systematically vary with fluidizing velocity and density, as illustrated in Figures 19 and 20. In Figure 19, we plot the fitted shape parameter as a function of the fluidization velocity and tracer density. The curves that go up at low velocities correspond to the tracers that segregate at the top of the bed, while the curves that go down at low velocities are the one that segregate at the bottom of the bed. The decrease in the shape parameter with velocity for the 0.55 and 0.76 g/cm3 tracers at very low air flows reflects the initial increase in mixing as the tracers penetrate deeper into the bed with increased bubbling. At around 2 Umf, the mixing of the lighter tracers apparently reaches a maximum, and 14572



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We speculate that the enhanced tracer mixing at low air flows resulted from an increase in the fluidization intensity associated with the higher concentration of low-density particles. Figures 21−23 illustrate the frequency distributions for these experiments.

n

AC(τ ) =

∑ t=0

(z(t ) − μ)(z(t + τ ) − μ) nσ 2

(2)

where AC = autocorrelation function for particle position n = number of lagged point pairs in time series t = time index z(t) = measured position at time t z(t + τ) = measured position at time t + τ μ = mean value of z(t) σ = standard deviation of z(t) τ = time lag Consistent with this definition, the autocorrelation function of the particle position represents the average cross correlation between successive axial locations of the particle separated by different time intervals. Thus, peaks in the autocorrelation function indicate periodic tendencies in the particle position; that is, they reveal time scales at which the particle is more likely to return to the same axial location. Note that, for zero time lag (τ = 0), one should always obtain AC = 1, because no matter what location the tracer particle is in, it will correlate perfectly with itself. However, for any other time delay, the autocorrelation function of real processes will either oscillate (when the process is strongly periodic) or it will decay rapidly toward zero as the time lag increases (when the process is stochastic). As we explain in the following, the tracer behavior in our experiments exhibited different degrees of both oscillations and decay. The autocorrelation function and Fourier power spectrum are direct transforms of each other,22 so it is also possible to observe these periodic time scales using the power spectrum. However, we have empirically found that it is easier to identify the periodic time scales in the tracer particle motion using the autocorrelation function due to the inherent broadening of the power spectrum, which tends to obscure peaks in the frequency domain. This broadening is a natural result of the inherent complexity in the particle motion, which involves translation in three spatial directions as well as features of both deterministic chaos and high dimensional noise.23,24 The effect of this complex motion is to cause visible periodicities in the axial position that decay over time (effectively resulting in a loss of ‘memory’ in the axial particle position). Thus, while it is possible to predict the probability that the particle will return to a certain axial position with some confidence over relatively short times, this predictability decays with time. The autocorrelation function for the vertical location of the 0.76 g/cm3 particle at eight different fluidization velocities is illustrated in Figure 24. To facilitate comparison in this stacked format, the autocorrelation axes of the various plots (which would normally overlap) have been shifted vertically. The autocorrelation function scales have also been expanded or contracted in order to more consistently resolve the shape and time locations of the peaks. We observe that, for air flows near minimum fluidization, the autocorrelation function decays only over very long times since the tagged particle moves very slowly. That is, the slow movement of the particle means that is likely to be found near the same location for long times. On the other hand, as air flow is increased above twice Umf, the autocorrelation function in Figure 24 exhibits decaying oscillations at relatively short time scales. The location of the first oscillation peak reflects a characteristic circulation time scale, in which the particle is likely to return to previously

Figure 21. Biomass concentration effect at 2 Umf.



Temporal Features in Tagged Particle Trajectories. In addition to analysis of the time averaged spatial location of the magnetically tagged particles, our measurements of the trajectories reveal interesting temporal features. More specifically, we found that temporal features such as the autocorrelation time scales in the tracer particle position appear to provide quantitative indicators of overall solids movement in the bubbling bed. In the following discussion, we use the autocorrelation function according to its standard definition22 applied to the measured vertical position of the tagged particle: 14573



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Figure 24. Autocorrelation analysis for time series data of the 0.76 g/cm3 tracer.

Figure 25. Autocorrelation analysis for time series data of the 1.2 g/cm3 tracer.

they involve dominant time scales that can be used to characterize their regularity and persistence. Because the lighter particles tend to act similar to flotsam and the heavier particles similar to jetsam, the actual domains they each traverse are different, as indicated by the statistical distributions of their spatial locations. One other interesting observation along this line is that the intensity of the dominant circulation processes appeared to reach a maximum at some intermediate fluidization velocity (which appeared to vary some among the different density tagged particles). At air flows near minimum fluidization, no obvious circulation was present. At the highest flows (near the expected transition point between the bubbling and turbulent regimes), it appeared that the tagged particle had a more complicated motion that diminished the likelihood of periodic visitation to the same location. This suggests that it might be possible to use the tagged particle trajectory behavior as a way to quantitatively discriminate the transition between fluidization regimes.

occupied levels. As explained, the visibility of this periodicity gradually diminishes at longer time scales because the particle motion is inherently higher dimensional and unstable. At a fluidization velocity of about 4.0, the visible periodicity in the autocorrelation function appears to reach its strongest level. At still higher air flows, the behavior of the autocorrelation function becomes more complex and the strength of the periodicity is less pronounced. The average period decreases from about 2.2 s at 1.5 U/Umf to about 0.75 at 4 Umf and remains there at 5 and 6 U/Umf. Similar general trends were observed for the tracer particles with densities of 0.53 and 0.89 g/cm3. The heavier 1.1 and 1.2 g/cm3 tracers that segregated at the bottom show a much longer time scale. Figure 25 shows the data for the 1.2 g/cm3 tracer. The dominant time scale begins at about 12 s and increases to around 17 s at 6 U/Umf. We propose that the autocorrelation patterns are consistent with the development of circulation cells that cause the tagged particle to be repeatedly cycled in the vertical direction. The motion of these cells is complex and not precisely periodic, but 14574



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Figure 26. Five-run reproducibility test spatial comparison.

Reproducibility of Data. Reproducibility is obviously a concern in acquiring experimental data, particularly with a new technique and new ways of representing the data, as we are presenting here. It is especially important if the data is to be used in and for validating predictions of theoretical models such as multiphase kinetic theory and discrete particle models. To test our tracer measurement reproducibility, we replicated a five minute long experiment five times. The experiments were with the 0.76 g/cm3 tracer operating the bed at 2.5 times Umf. Directly comparing trajectories would be of little value because it would be difficult or impossible to find identical initial conditions within the bed to begin a trajectory comparison even though the overall conditions were the same. A statistical comparison is however possible and more appropriate. Normalized frequency distributions of the vertical tracer position were calculated for each of the five experiments. They are shown in Figure 26 along with a curve for the average of the five. We see the agreement is quite good. The average standard deviation for the five runs is 0.00125 and a maximum of 0.0034 around the peak. Three-sigma would therefore be about 0.004 for the average and about 0.01 at the maximum. A comparison of the autocorrelations for the five tests is shown in Figure 27. The first maximum represents a

characteristic circulation time but diverges after this as slight differences from the finite nature of the runs grow with time. Both the frequency and autocorrelation plots illustrate a reasonable level of reproducibility in the experiments.

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SUMMARY

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AUTHOR INFORMATION

In this study, we have shown that magnetic particle tracking can provide highly detailed spatiotemporal information about the motion of single low-density particles in bubbling fluidized beds. For the range of particle properties, bed compositions, and fluidization rates studied, we observed that a two-parameter Weibull distribution function can be used to represent the time average spatial distribution of the low-density particle under top-segregating, bottom-segregating, and well-mixed conditions. The Weibull parameters varied systematically as functions of tracer particle density and fluidization air flow. It also appears that temporal autocorrelations in the vertical position of the tracked particle can be used to infer changes in global solids circulation. The observed trends imply that it might be possible to develop relatively simple correlations and statistical models to describe the mixing of larger, lower-density particles in beds of smaller, higher-density particles. We expect that data of this type should be useful for validating phenomenological and kinetic-theory models of fluidized bed systems, including fluidized beds used for processing biomass.

Corresponding Author

*E-mail: [email protected]. Present Address †

Separation Design Group, Waynesburg, Pennsylvania

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

The work reported here was sponsored by a contractor of the United States Government under Contract No. DEAC0500OR22725 with the United States Department of Energy.

Figure 27. Five run reproducibility test temporal comparison. 14575



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(23) Moon, F. C. Chaotic and Fractal Dynamics; John Wiley and Sons: New York, 1992; pp 55−58. (24) Daw, C. S.; Finney, C. E. A.; Vasudevan, M.; van Goor, N. A.; Nguyen, K.; Bruns, D. D.; Kostelich, E. J.; Grebogi, C.; Ott, E.; Yorke, J. A. Phys. Rev. Lett. 1995, 75, 2308−2311.

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