Particle Motion near the Wall of a Fluidized Bed at Elevated Pressure

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Ind. Eng. Chem. Res. 2004, 43, 5562-5570

Particle Motion near the Wall of a Fluidized Bed at Elevated Pressure Igor Sidorenko, Art Yew Looi, and Martin Rhodes* CRC for Clean Power from Lignite, Department of Chemical Engineering, Monash University, Victoria 3800, Australia

The influence of operating pressure on the motion of particles near the fluidized-bed wall surface was studied for Geldart group A and B particles using luminescent pigment as bed solids in a vessel of diameter 146 mm. A pulse of bright light transmitted from outside the pressure vessel via fiber optics was used to illuminate a 7-mm-diameter region of the bed particles adjacent to a transparent vessel wall. Digital image analysis of the motion of the illuminated region of bed particles and its decay in luminosity permitted the determination of the influence of pressure on a particle exchange frequency in the direction perpendicular to the wall surface, the mean particle residence time at the wall, and the velocity of bed solids adjacent to the wall. These findings are related to the observations of the effect of pressure on bed-to-surface heat transfer in fluidized beds reported by other workers. 1. Introduction One of the attractive features of bubbling fluidized beds from a design viewpoint is their excellent heattransfer properties. Gas-to-particle heat transfer is normally very efficient because of the high surface area of the particulate phase. More interesting is heat transfer between the bed material and solid surfaces such as walls or immersed surfaces. Since the 1970s, considerable attention has been given to research in the field of fluidized-bed combustion and gasification of solid fuels at elevated pressure. The operating conditions of combustion boilers and reaction chambers of gasifiers involve high bed temperatures (1023-1173 K) and increased fluidizing gas pressures (up to 2 MPa). Under these conditions, heat transfer between a surface and a fluidized bed has a rather complex conductiveconvective-radiative character1 and is presented as a sum of three independent components: particle convective, gas convective, and radiative.2 The main factors in the heat transfer between a surface and a fluidized bed are the movement of particles close to the surface and their residence time at the surface. According to Botterill,2 the good heat-transfer properties of fluidized beds are the result of the high heat capacity of bed particles and their mobility. At temperatures below 873 K, when the radiative heat-transfer component is negligible, the particles in the bulk of the fluidized bed exchange heat by gas-phase conduction and stay in the bulk of the bed long enough to reach the same temperature as their neighboring particles. When some of the particles are swept into close proximity with the heat-transfer surface, there is a high local temperature gradient between the surface and the particles. The longer the particles stay at the surface, the more their temperature approaches the surface temperature, which leads to a reduction in the local temperature gradient and the effective rate of heat * To whom correspondence should be addressed: Martin Rhodes, Department of Chemical Engineering, Monash University, VIC 3800, Australia. Tel.: Int ++61-3-9905-3445. Fax: ++61-3-9905-5686. E-mail: [email protected].

transfer. The highest rates of heat transfer between a surface and a fluidized bed are obtained, therefore, when there is rapid exchange of material between the heattransfer region and the bulk of the bed, i.e., when particle residence times at the surface are very short. However, it is common for vertical surfaces to become covered by the downward return flow of solids. In 1953, Toomey and Johnstone (in ref 2) described the now wellknown appearance of particle motion close to the wall, in which there is upward flow of particles through the center of the column induced by bubbles and comparatively slow downward flow at the wall. In general, material adjacent to the wall is only occasionally disturbed by rising bubbles and slugs that penetrate to the wall. According to Borodulya et al.,1 one of the most wellknown empirical correlations for calculating the maximum bed-to-surface heat-transfer coefficient h was proposed by Baskakov and Panov,3 and it predicts a strong dependence of the conductive component on pressure. However, this fact was not confirmed by extensive experimental studies.4 Several researchers studied the influence of pressure on convective heat transfer between fluidized beds and surfaces (e.g., refs 5-12). Convective heat transfer in fluidized beds of fine particles is not expected to change much with pressure, as was, in fact, observed by Xavier et al.11 and Barreto et al.5 Convective heat transfer can be characterized by a dimensionless parameter, the Nusselt number. To describe heat-transfer experiments under different conditions, Borodulya et al.1 analyzed the results available in the literature and proposed a relation that combines the Nusselt number at maximum conductive-convective heat transfer (hgc + hpc), the Galileo number Ga, and the Prandtl number Pr

() ()

Numax ) 0.4Ga0.16

Fp Fg

0.14

cp cg

0.3

+ 0.0013Ga0.63 Pr (1)

where cp and cg are the specific heat capacities of particles and gas, respectively.

10.1021/ie030777b CCC: $27.50 © 2004 American Chemical Society Published on Web 04/23/2004

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According to Borodulya et al.,1 eq 1 is valid for particles in the size range from 100 µm to 4 mm and the operating pressure range from atmospheric to 10 MPa. The exponents of the Galileo number and the density ratio in eq 1 are almost equal, and the dependence of the particle convective heat-transfer coefficient on pressure is very weak. Because the gas convective heat-transfer coefficient is proportional to the square root of gas density, fluidization at elevated pressures is expected to enhance this component. Experimental confirmation of higher heat-transfer coefficients in pressurized fluidized beds of coarse particles can indeed be found in the literature (e.g., refs 7, 8, 11, and 13). The experimental data presented by Borodulya et al.13 show that the effect of pressure increases with particle size. A pressure increase from 1100 to 8100 kPa resulted in a 29% increase in the maximum heat-transfer coefficient for 126-µm sand particles, a 110% increase for 1.22-mm sand particles, and a 140% increase for 3.1mm glass ballotini. For particles less than 500 µm, the effect of pressure on the bed-to-surface heat transfer is considered to be negligible.2,14 However, according to Molerus and Wirth,9 heat transfer clearly depends on pressure within the range of particle sizes from 50 µm to 1 mm, and the influence of particle motion on heat transfer should manifest itself in a similar pressure dependence. Here, we present the results of a study of the influence of operating pressure on the motion of particles near the fluidized-bed wall surface for Geldart group A and B particles using luminescent pigment as bed solids in a vessel of 146-mm diameter. The results are analyzed, and the implications for heat-transfer modeling are considered. 2. Experimental Method The process and instrumentation diagram of the pressurized fluidized bed used in this study of the effects of pressure on fluidization is given elsewhere.15 The pressure vessel, capable of operating at pressures up to 2600 kPa, was 2.38 m high and was equipped with five glass observation ports. The fluidized-bed vessel was 146 mm in diameter, had transparent walls of Perspex, and was inserted into the pressure vessel and positioned vertically. Fluidizing gas for the experiments was supplied either from a building compressed air supply or from dedicated nitrogen and compressed air cylinders and metered by variable-area flow meters. The variable-area flow meters had an accuracy class 1.6, according to German Standard VDI/VDE 3513 Part 2, and were properly compensated for differences in gas properties at different operating pressures and temperatures. The operating pressure in the fluidized bed was set with a back-pressure control valve. The experimental facility was of an open circuit type so the same gas was used for pressurizing the system and for fluidizing the solids. The apparatus was pressurized to the desired operating pressure before the fluidizing gas flow rate was adjusted to a desired value. With transparent side walls of the fluidized-bed column, direct observation of the motion of particles along the wall was possible through one of the pressure vessel’s observation windows. Experimental observation of the motion of particles near the wall surface was

Figure 1. Experimental setup for studying particle motion along the wall.

based on the pulsed-light method described by Molerus and Wirth.9 The motion of particles at the wall surface was visualized by using particles of a luminescent pigment as bed solids. Six kilograms of the original luminescent pigment Lumilux (pigment A), with a Sauter mean diameter of 62 µm, was used for charging the fluidized bed in the series of experiments with a Geldart A material. To study the particle motion in a bed filled with a Geldart B material, 6 kg of the agglomerated pigment (pigment B), with a Sauter mean diameter of 234 µm, was used. A well-known method of measuring the dependence of the bed pressure drop on the superficial gas velocity was used to establish the experimental values of the minimum fluidization velocity. For pigment A, the minimum fluidization velocity was 0.003 m/s and independent of pressure. For pigment B, the minimum fluidization velocity decreased from 0.112 m/s at atmospheric pressure to 0.103 m/s at 1300 kPa. A pulse of bright light from a conventional photoflash with an adaptor was transmitted from outside the pressure vessel via a specially made fiber-optic light guide. The flash illuminated a 7-mm-diameter spot of the luminescent bed material adjacent to a transparent fluidized-bed vessel wall inside the pressure vessel. After illumination, the spot, consisting of a cluster of particles, showed an afterglow for several seconds. The fiber-optic light guide was positioned in such way that the illuminated spot was at approximately mid-height of the bed level and could be clearly seen through one of the observation windows (Figure 1). A digital video camera was mounted in front of the window and covered with some lightproof fabric. All of the remaining observation windows were blocked so that it was completely dark inside and only the illuminated spot on the black background was visible through the camera viewfinder. Under packed-bed conditions, the illuminated spot was still visible after 3 min. When the bed was fluidized, the illuminated spot shifted along the wall surface while its shape deformed and its luminosity decreased. However, the illuminated particles stayed in close proximity as a cluster, and the spot remained a single identifiable object until it disappeared from the field of view. When an image disappeared from view, it could be assumed that, depending on the gas velocity, the image either moved out of the camera view or its brightness diminished.

5564 Ind. Eng. Chem. Res., Vol. 43, No. 18, 2004

Experiments were carried out at different gas velocities up to 15 times the minimum fluidization velocity under various pressure conditions. The pressure range was from atmospheric to 2100 kPa for experiments with pigment A and up to 1600 kPa for experiments with the agglomerated pigment B. However, because of the relatively high material density and the gas supply limitations, it was not possible to fluidize pigment B at velocities well above the minimum fluidization velocity at operating pressures higher than 800 kPa. At the predetermined operating pressure and gas velocity, an experiment proper consisted of illuminating a small cluster of particles with the photoflash and filming the spot until it disappeared. At each gas velocity, at least 10 separate flashes were recorded, and the fate of each illuminated spot was analyzed separately using image analysis techniques. 3. Data Analysis The images of the illuminated spot were captured by a digital video camera at a rate of 25 frames per second. Digital videos were downloaded onto a dedicated computer and edited in order to extract separate frames and organize them in stacks for each light pulse. Image analysis was then carried out to quantify the statistics of particle movement near the wall surface. Each pixel of the image was characterized by its X and Y coordinates and luminosity, expressed in dimensionless form on a grayscale, where 0 is black and 255 is white. From filming a reference ruler in daylight, it was determined that, on the linear scale, each pixel was equal to 0.25 mm. Under packed-bed conditions, it was observed that the cluster of illuminated particles remained visible as an unmoving spot decreasing in intensity with time. The initial step in digital data analysis involved discrimination of illuminated spots from the rest of the bed material. In general, the procedure for this image identification involves examination of the histogram of grayscale values for a normal image consisting of both illuminated spot and dark background. Because the lighting conditions were uniform and the image contrast was quite high, accurate detection of the image boundary was possible using the global thresholding method.16 As a result, it was found that applying a grayscale threshold (Lthreshold) of 60 accurately characterized illuminated spots while they were visible. On each frame, the following data for the illuminated spot were obtained: image area; mean, maximum, and minimum luminosity within the image threshold; and X-Y coordinates of the center of gravity of the image. More than 160 000 files were processed, and the results were organized for separate light pulses at each gas velocity. Further statistical analysis was performed using special software, where for each gas velocity data from 10 to 14 flashes were averaged and plotted and nonlinear regression was applied. Because the detection of clusters depended on their visibility, it could be possible that the disappearance of images resulted from loss of material luminosity with time or possibly from the mixing of clusters. A simple analysis showed that the light source had enough power to sufficiently illuminate a spot and the material had sufficient luminosity that the illuminated object could still be observed by the end of each test. The effect of particle motion in a fluidized bed on cluster maximum luminosity compared to that in a

Figure 2. Decay of maximum image luminosity on a grayscale in a packed bed of pigment A compared to fluidized bed at atmospheric pressure (fluidization gas velocity U ) 0.012 m/s).

packed bed is illustrated in Figure 2. In both cases, the luminosity decay was found to be exponential in time; however, the rate of decay was much higher in the fluidized bed. It was found that the motionless illuminated spot in the packed bed was clearly visible for at least 100 s (2500 frames), and some afterglow could be distinguished on the dark background even after 3 min. In comparison, the experiments showed that, in a fluidized bed, the illuminated spot always became invisible in less than 4 s (100 frames). On the basis of such a large difference between the natural material luminosity decay and the luminosity loss during fluidization, it was assumed that the luminosity decay during fluidization is caused only by the fact that the illuminated cluster particles move away from the wall and are replaced by dark particles. Although the natural material luminosity decay with time for agglomerated pigment B was less than that for the original pigment, it was still much greater than the image luminosity decay during the fluidization experiments. 4. Particle Motion at Similar Fluidizing Velocities Some influence of operating pressure on pigment A particle motion near the fluidized-bed wall can be illustrated through the results of experiments carried out at similar fluidization velocities at different pressures. The gas fluidization velocity in the following examples equals approximately 5 times the minimum fluidization velocity. As can be seen in Figures 3-7, the illuminated spot shifts down along the wall surface while its shape deforms and luminosity decreases. These images (Figures 3-7) were produced by superimposing all of the separate frames during the image lifetime, and they show the motions of the illuminated clusters of particles along the wall surface. These images are typical, and similar observations were made under different operating conditions. Some qualitative conclusions emerge from the visual analysis of these results. For example, in these videos, the direction of motion of the illuminated clusters of particles was observed to be downward, as expected.


Figure 3. Image trajectory for pigment A at atmospheric pressure and a gas velocity of 0.012 m/s (actual size).

Figure 8. Difference between mean image luminosities on a grayscale for pigment A at different operating pressures and similar fluidization velocities. Figure 4. Image trajectory for pigment A at 500 kPa and a gas velocity of 0.011 m/s (actual size).

Figure 5. Image trajectory for pigment A at 1100 kPa and a gas velocity of 0.011 m/s (actual size).

downward in close proximity to the wall and only a small number of particles are replaced by particles coming from within the bed. At higher operating pressures, the motion behavior appears to change. Although the clusters also move downward, they do not disappear below the camera view. The brightness of the clusters decreases much more quickly, and it appears that the lateral mixing becomes predominant and the illuminated particles move inside the bed. With increasing pressure, this behavior becomes stronger (Figures 4-7). In an attempt to quantify these observations, the decay of mean luminosity of the illuminated clusters at different pressures and similar gas velocities for pigment A is presented in Figure 8. In all cases, the luminosity decay was found to be exponential in time. A number of linear and nonlinear regression models were tested, and it was found that an exponential decay model17,18 predicted the experimental data very well. The following equation was used for the decay model

L - Lthreshold ) (L0 - Lthreshold) exp(-kt) Figure 6. Image trajectory for pigment A at 1500 kPa and a gas velocity of 0.011 m/s (actual size).

Figure 7. Image trajectory for pigment A at 2000 kPa and a gas velocity of 0.011 m/s (actual size).

As can be seen in Figure 3, at ambient conditions, the illuminated cluster travels down along the wall and disappears from the camera view. Its brightness decreases slightly, but the image is expected to be visible at the wall for some time after it disappears below the camera view. It seems that, under the given experimental conditions, the majority of cluster particles move

(2)

where the function of luminosity on a grayscale (L) starts at an initial level of span (L0 - Lthreshold) above a constant plateau (Lthreshold) and decays with time (t) to the plateau (Lthreshold) at a rate constant (k). The value of the plateau (Lthreshold) was determined by the threshold applied to the images during the processing. One of the characteristic parameters of an exponential decay model is the half-life, which is the time it takes for the parameter (L), or image luminosity, to drop by one-half. In the case presented in Figure 8, the half-life decreased from 0.62 s at atmospheric pressure to 0.11 s at 2000 kPa. For comparison, the half-life of the natural luminosity decay of pigment A established in the packed bed was 41.84 s. 5. Particle Motion at Similar Fluidizing Velocities 5.1. Analysis of Experimental Data. As illustrated above (Figure 2), the increased rate of decay in luminosity in a fluidized bed, compared to that in a packed bed, is attributed to the fact that the originally illuminated


particles move away from the wall during the fluidization process and are replaced by particles coming from the rest of the bed. Using the rules for conditional probability, Molerus and Wirth9 deduced an equation for the exchange frequency of particles, f, perpendicular to a solid surface. It was postulated that the probability, W(t), that a particle in contact with the wall at time t ) 0 moves inside the fluidized bed is proportional to the time interval ∆t, i.e., equivalent to f∆t. Using the initial condition when W(0) ) 1, Molerus and Wirth9 obtained the following equation:

W(t) ) exp(-ft)

(3)

This equation indicates that the luminosity decay L, related to the initial brightness L0, directly corresponds to the constant slope of the curve and the parameter f can be determined by plotting ln(L/L0) versus time:

( )

ln

L ) -ft L0

(4)

Figure 9. Mean time between pigment A particle illumination and departure from the wall versus gas velocity at various operating pressures.

Using the area of the original illuminated spot and the particle size, the initial number of the illuminated particles next to the bed wall, np0, can be estimated from the following relationship

np0

πD02 πdp2 ) (1 - ) 4 4

(5)

where dp is the mean particle diameter, D0 is the diameter of the illuminated spot, and is bed voidage. According to Molerus and Wirth,9 the illuminated spot diameter D0 is equivalent to the fiber-optic diameter, which is true only if the fiber optic is positioned perpendicular to the wall surface right against it. However, positioned in this way, the fiber optic would completely block the original illuminated spot, so that filming and further image analysis of the original spot would not be possible. For clear view in this study, the 3-mm-diameter fiber optic did not touch the wall surface and was positioned at a slight angle in such way that, in a packed bed, the diameter of the initial illuminated spot was 7 mm. Using eq 5 and experimentally obtained values of the bed voidage at the initial conditions, the original number of illuminated particles was estimated to be around 6375 for pigment A and around 260 for pigment B. Because the luminosity decay in a fluidized bed is caused by the motion of particles, Molerus and Wirth9 estimated the number of particles in an image with luminosity L from L/np ) L0/np0 as follows:

np ) (1 - )

( )( ) D0 dp

2

L L0

(6)

In this study, using the image threshold value of 60 and eq 6, the final number of particles left at the wall can be estimated at 21 for pigment A and just 1 for pigment B. Comparing eq 2 to eq 4 shows that the rate constant k determined above corresponds to the particle exchange frequency f defined by Molerus and Wirth.9 5.2. Mean Residence Times of Particles at the Wall. The mean residence time of illuminated particles near the wall was deduced by Molerus and Wirth9 as

Figure 10. Mean time between pigment B particle illumination and departure from the wall versus gas velocity at various operating pressures.

the reciprocal of the particle exchange frequency f. The mean residence time τ, established in this work as the reciprocal of rate constant k, is shown in Figure 9 for pigment A and in Figure 10 for pigment B. For pigment A, as can be seen in Figure 9, mean residence times measured close to the wall decrease with increasing gas velocity in the range 3-10Umf and become practically independent of gas velocity in vigorously bubbling fluidized bed. The values of the mean residence time settle at below 0.1 s, which means that, during the experiments, the illuminated images disappeared within only three frames on video and could not be measured with higher accuracy. Considering the experimental error of (0.04 s, it is not possible to establish any significant effect of pressure on particle residence times at the wall. As previously mentioned, the highest rates of heat transfer between a surface and a fluidized bed are obtained when the particle residence times at the surface are very short. Therefore, from Figure 9, it can be estimated that the typical mean residence times measured close to the wall at maximum heat transfer


are practically independent of pressure and approximately equal to 0.1 s. This result, however, does not agree well with the experimental data presented by Molerus and Wirth,9 who observed the following mean residence times of illuminated particles with a size of 50 µm at vertical solid surfaces in a fluidized bed at maximum heat transfer: 1.28 s at 100 kPa, 0.35 s at 500 kPa, 0.52 s at 1000 kPa, and 0.45 s at 2000 kPa. Contrary to their claim that the heat transfer clearly depends on pressure and expectations of a similar pressure dependence on particle motion, there is no clear trend in their data, but the magnitude is considerably higher than the values measured in the present work. For pigment B, the investigated range of superficial gas velocities was much narrower and did not exceed 2Umf at atmospheric pressure. As was found with pigment A, mean residence times measured close to the wall for pigment B were found to decrease with increasing gas velocity (Figure 10). Again, no significant effect of pressure on the particle residence times at the wall can be observed in the somewhat limited range of experimental pressures and velocities. However, absolute residence time values are again lower than those observed by Molerus and Wirth9 for a similarly sized material. In their work, it is not clear how the illuminated image was distinguished from the background. If they applied linear regression to the luminosity decay curve, plotted in semilog coordinates for the whole image grayscale (0-255), as opposed to the nonlinear regression for only the visible image threshold presented here, then that could possibly produce different results. 5.3. Relating Contact Time to Heat Transfer. In practice, it is common for fluidized beds to contain fixed surfaces to extract heat. For fluidized-bed combustion, the important heat-transfer surfaces are vertical and horizontal heat-transfer tubes immersed in the bed. By using internal cooling tubes, a large total heat-transfer surface can be obtained. The effect of pressure on heat transfer from the bed to the immersed horizontal tube was investigated by Olsson and Almstedt,10 who found a significant increase in the heat-transfer coefficient with increasing operating pressure. One way of evaluating the impact of the observed mean particle residence times at the wall is to use them in conjunction with the cluster renewal model developed for bubbling fluidized beds by Mickley and Fairbanks.19 According to this model, it was found that, for the particle convective heat-transfer component hpc, the following equation holds20

δ 1 ) + hpc λg

x

πτ λpFpcp

(7)

where δ equals the distance between the illuminated particles and the wall; λg is the gas thermal conductivity of this gap; τ is the time during which particles are moving in contact with the wall before moving into the bulk of the bed; and λp, Fp, and cp are the thermal conductivity, density, and specific heat capacity of the particles, respectively. The only gas-related parameter in eq 7, the gas thermal conductivity λg, is independent of pressure for the ideal (perfect) gas. For real gases, however, the gas thermal conductivity is a rather complex function of pressure and temperature, and usually increases with

an increase in either pressure or temperature.21 Ignoring the effect of the gas gap, the particle convective heattransfer component hpc is proportional to τ0.5. For Geldart A solids, Figure 9 shows that, at superficial gas velocities below 0.015 m/s, the mean residence times slightly decrease with pressure, and therefore, the particle convective heat-transfer component is expected to increase slightly with elevated pressure. However, with a further increase in gas velocity, the mean residence times reach a minimum value and are not influenced by pressure. Thus, the particle convective heat-transfer coefficient should also reach a maximum in a bubbling bed that must be dependent only on particle physical properties and not on operating pressure or superficial gas velocity, provided a certain gas velocity is exceeded. This observation of the effect of pressure is in line with findings of other workers2,5,11,22 who did not observe much variation in the particle convective heat transfer for small particles at pressures above atmospheric. According to Borodulya et al.,1 the weak dependence of the conductive-convective heat-transfer coefficient on pressure in fluidized beds of small (less than 1 mm) particles is a well-known experimental fact, although some researchers would probably disagree.9 The present work forms part of a larger program in which the operation of a pressurized steam-fluidizedbed dryer was studied. The program included a study of the influence of operating pressure on fluidized-bedwall heat transfer. A comprehensive account of this work can be found in Looi et al.23 Analysis of these results24 shows that the particles on the heat-transfer surface are at thermal equilibrium with the heat source such that the mechanism of heat removal is left to the wall-to-gas route. Consequently, any further increase in the gas velocity from the incipient conditions would raise the wall-to-bed heat-transfer coefficient. This phenomenon remains prevalent for ratios between the Reynolds and Archimedes numbers of Re/Ar < 0.002, at which point particle mobility from the heated wall becomes significant. When the fluidized bed becomes vigorously bubbling, i.e., Re/Ar > 0.002, there is no further increment in the heat-transfer coefficient for systems with Ar > 100. This observation shows that, when the Ar value is sufficiently high, the buoyancy effect dominates over the inertial effect. This leads to the tendency of particles to migrate radially away from the heat-transfer wall. These heat-transfer results are consistent with the observations made in the study of particle motion reported here, namely, that there is minimal bubbling effect such that very little particle migration occurs on the heat-transfer wall when the superficial gas velocity is low. As the gas velocity is increased, the particle migration from the heat-transfer wall becomes more rapid and hence results in a greater wall-to-bed heat-transfer rate. 6. Particle Motion Velocity 6.1. Observation of Particle Motion Parallel to the Wall. Solids motion in bubbling fluidized beds is driven by bubbles, which carry particles upward in their drifts and wakes. This upward flow of solids is balanced by a downward solids flow that occurs in regions where there are no bubbles. Previously presented images (Figures 3-7) represent the summations of separate frames during the image lifetimes and show typical trajectories of the illuminated


Figure 11. Particle motion velocity in the vertical direction versus superficial gas velocity at various operating pressures for pigment A.

clusters of particles along the wall surface. Similar observations were made under different operating conditions. As expected, the predominant direction of movement of the illuminated image along the wall was downward. On each frame, the X-Y coordinates of the center of gravity of the illuminated image were also obtained. For each image, the variation of the center of gravity in the vertical and horizontal directions with time was plotted and analyzed. Visual analysis of all plots representing image motion in the vertical direction (downward) and in the horizontal direction (sideways) at various operating conditions showed that the axial movement was approximately linear. Initial X0-Y0 coordinates correspond to the center of gravity of the original image at the time of light impulse t ) 0, and the final Xn-Yn coordinates describe the center of gravity of the disappearing image at the time equal to the mean residence time t ) τ. The distance travelled by the image during the mean residence time was established as (Xn - X0) in the horizontal direction and as (Yn - Y0) in the vertical direction. Axial particle motion velocities were obtained for each light impulse at various operating conditions by dividing these distances by the corresponding mean residence time. Resulting velocities were then averaged according to the operating conditions and plotted. 6.2. Axial Particle Motion Velocity at Elevated Pressures. Vertical Velocity. The main direction of the illuminated spot movement was downward, and the vertical image velocity is plotted in Figure 11 for pigment A and in Figure 12 for pigment B. For pigment A, the particle migration velocities Uy along the wall in the vertical direction were oriented downward and reached a maximum value of about 0.08 m/s at atmospheric pressure. At operating pressures above 500 kPa, the particle migration velocities Uy along the wall in the vertical direction are much lower than those obtained at ambient conditions. Some trend for the vertical motion velocity to decrease with increasing operating pressure can be observed in Figure 11. Similar results can also be qualitatively estimated from the image trajectories presented in Figures 3-7. For pigment B, the particle motion velocities Uy along the wall in the vertical direction were also oriented downward and reached a maximum value of only about

Figure 12. Particle motion velocity in the vertical direction versus superficial gas velocity at various operating pressures for pigment B.

Figure 13. Particle motion velocity in the horizontal direction versus superficial gas velocity at various operating pressures for pigment A.

0.004 m/s at atmospheric pressure. Within the studied range, no effect of pressure on the vertical particle motion velocity could be established (Figure 12). Horizontal Velocity. Because the predominant movement of the illuminated image was downward, the particle motion velocity in the horizontal direction was much smaller for pigment A (presented in Figure 13 on the same scale as Figure 11) and practically nonexistent for pigment B. This observation is in line with the experimental results of Bellgardt and Werther,25 who found at ambient conditions in a large fluidized bed that vertical solids mixing was at least 1 order of magnitude higher than lateral mixing. In a bubbling fluidized bed with pigment A as the bed material, some apparently random horizontal deviation off the vertical axis was observed while the illuminated image shifted downward. As shown in Figure 13, in general, lateral particle migration velocities Ux lower than 0.01 m/s were measured. Although small by itself, the horizontal movement of the illuminated cluster at operating pressures above 700 kPa was less obvious than at ambient conditions.


7. Conclusions Major factors in the heat transfer between a wall and a fluidized bed are the movement of particles close to the wall and their residence time at the wall. Experimental measurement of particle motion in a bubbling fluidized bed can provide a better understanding of wallto-bed heat transfer. The influence of operating pressure, up to 2100 kPa, on the motion of Geldart A and B particles near the fluidized-bed-wall surface was studied using luminescent pigment as bed solids. Digital image analysis was applied to the experimental data with the aim of quantifying the statistics of particle motion near the wall. Image analysis of the movement of the illuminated cluster of particles gave its statistically determined axial velocities along the surface, and the decay in luminosity defined the particle exchange frequency in the direction perpendicular to the wall surface. For both Geldart A and B solids, no significant effect of pressure on particle residence times at the wall within the vigorously bubbling fluidized bed was established. This observation is in line with findings of other researchers who observed minimal variation in the particle convective heat transfer for small particles at pressures above atmospheric. Solids motion in bubbling fluidized beds is driven by bubbles, which carry particles upward in their drifts and wakes. This upward flow of solids is balanced by a downward solids flow that occurs in regions where there are no bubbles. As expected, the predominant direction of movement of the illuminated image along the wall was downward. For Geldart A solids, the particle migration velocities along the wall in the vertical direction were much lower at operating pressures above 500 kPa than at ambient conditions. For Geldart B solids, within the pressure range and narrow range of gas velocities studied, no pressure effect on the vertical particle motion velocity was established. Acknowledgment We gratefully acknowledge the financial support received for this research from the CRC for Clean Power from Lignite, which is established under the Australian Government’s Cooperative Research Centres Scheme. Nomenclature Ar ) Archimedes number cg ) specific heat capacity of the gas cp ) particle specific heat capacity dp ) mean particle diameter D0 ) diameter of the illuminated spot f ) particle exchange frequency (eq 3) Ga ) Galileo number hgc ) particle conductive heat-transfer coefficient hpc ) particle convective heat-transfer coefficient k ) rate constant (eq 2) L ) luminosity on a grayscale Lthreshold ) threshold level of luminosity on a grayscale L0 ) initial level of luminosity on a grayscale np ) number of the illuminated particles np0 ) initial number of illuminated particles (eq 5) Nu ) Nusselt number Pr ) Prandtl number Re ) Reynolds number t ) time Umf ) superficial gas velocity at incipient fluidization

Uv ) particle motion velocity along the wall in the vertical direction W(t) ) probability that a particle is in contact with the wall at time t (eq 3) W(0) ) probability that a particle is in contact with the wall at time t ) 0 (eq 3) X ) x coordinate of the center of gravity of the illuminated image (section 6.1) Y ) y coordinate of the center of gravity of the illuminated image (section 6.1) ) bed voidage δ ) distance between illuminated particles and the wall λg ) gas thermal conductivity of the gap δ τ ) time during which particles are moving in contact with the wall λp ) thermal conductivity of the particles Fp ) particle density λg ) gas thermal conductivity

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Received for review October 16, 2003 Revised manuscript received February 18, 2004 Accepted February 26, 2004 IE030777B

Particle Motion near the Wall of a Fluidized Bed at Elevated Pressure

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