Measurements of Dispersion Coefficients for FCC Particles in a Free

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Measurements of Dispersion Coefficients for FCC Particles in a Free Board Mayank Kashyap* and Dimitri Gidaspow Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616, United States ABSTRACT: Particle image velocimetry (PIV) experiments were performed noninvasively in the Illinois Institute of Technology (IIT) two-dimensional circulating fluidized bed (2-D CFB) of fluid catalytic cracking (FCC) particles to measure laminar and turbulent properties, near the front wall in the z-direction; at the center and near the right and left walls in the x-direction; and in the free board region in the y-direction. The PIV measurements were obtained simultaneously in the y- and x-axes, using a chargecoupled device (CCD) camera, with the aid of a colored rotating transparency. The instantaneous and hydrodynamic velocities were used to obtain laminar properties for particles and turbulent properties for clusters, respectively. Laminar and turbulent properties for solids conveyed anisotropy. The y-axis solids velocities, power spectral densities of hydrodynamic velocities, and granular temperatures were highest at the center in the x-direction. The mixing was on the level of particles. The y- and x-axes solids dispersion coefficients were several orders of magnitude lower than the literature values, because of the low particle velocities in the free board. However, total granular temperatures were reasonably close to the literature values.

1. INTRODUCTION The circulating fluidized beds (CFBs) are widely used in chemical, petroleum, metallurgical, process, and power industries,17 because of their ability to operate at different flow regimes, such as turbulent, fast fluidization, and dilute transport.8 They possess many advantages,9 such as excellent gassolid contacting, improved control over heat, low particle segregation and agglomeration, recirculation loop for separate operations, and ability to operate under high solids flux conditions. Nevertheless, the interactions between the gas and solid phases make the hydrodynamics of the CFB complex. Solids velocity is a main parameter in understanding the CFB, because it affects the mixing and heat and mass transfer, thus influencing the overall reaction rates in fluidized-bed reactors. The individual particle and cluster velocities can further be used to estimate the turbulent intensities of the solid phase and to estimate granular temperatures and solids dispersion coefficients. The primary challenge in measuring solids velocities is to maintain the flow characteristics during measurements. Therefore, the measurement technique should be nonintrusive. The main intrusive and nonintrusive techniques used in the literature are described in Pandey et al.3 and elsewhere as (1) particle image velocimetry (PIV),1013 (2) laser Doppler anemometry (LDA),14 (3) laser Doppler velocimetry (LDV),3,1520 (4) particle tracking velocimetry (PTV),21,22 (5) fiber optic probes,2330 (6) stroboscopic analysis,31 (7) laser fluorescence methods using tracer species,32,33 (8) radioactive particle tracer,34 (9) Pitot tube,35 (10) capacitance probe,36 (11) extraction sampling probes,3739 (12) image sensing,40 (13) video imaging,41 (14) electrostatic probes,42 (15) acoustic measurements,43 and (16) diffusing wave spectroscopy.44 Breault45 described the significance of the development of models to estimate conversion and yield of reactant species for reactors. The literature survey provided information on various correlations for the axial and radial solids and gas dispersion coefficients, and the interphase mass-transfer coefficients r 2011 American Chemical Society

between the gas and solid phases. A reasonably good knowledge of dispersion and mass-transfer coefficients is necessary in designing fluidized-bed reactors, such as gasifiers. However, the dispersion coefficients differ by at least 5 orders of magnitude in the literature, because of the differences in the hydrodynamics, locations within fluidized beds, and system geometries and properties.11,4552 Furthermore, investigators use different definitions, theories, and methods to obtain dispersion coefficients, causing differences in their values. The direction of the flow of particles also significantly affects the dispersion coefficients. For instance, Wei and Zhu53 reported that the solids dispersion coefficients are lower in the downcomer, because of the plug flow, compared to those in the riser. Jung et al.13 and Jiradilok et al.48 identified laminar dispersion coefficients due to individual particle oscillations, and turbulent dispersion coefficients due to cluster or bubble oscillations. The solids dispersion coefficient is an important parameter in designing fluidized-bed reactors, especially for reactors involving solids feedstock, such as fluidized-bed boilers for coal combustion and fluid catalytic cracking (FCC) regenerators for burning coke deposited on catalysts.54 Solids mixing in fluidized beds is usually measured using saline,35,55 ferromagnetic,56 thermal,57 radioactive,5860 carbon,61 or phosphorescent tracers.47,62,63 Nevertheless, experiments with solid tracers are difficult to perform in fluidized beds, because of the lack of continuous sampling, the need for frequent replacements, the existence of residual tracers, the transfer of heat to gas flow and column walls, safety concerns, and applications in only dilute fluidized-bed systems. Gas dispersion coefficients have been measured in the literature using tracers, such as helium, carbon dioxide, etc.6474 Received: June 2, 2010 Accepted: April 19, 2011 Revised: April 13, 2011 Published: April 19, 2011 7549

dx.doi.org/10.1021/ie1012079 | Ind. Eng. Chem. Res. 2011, 50, 7549–7565

Industrial & Engineering Chemistry Research

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Figure 1. (A) Schematic diagram and (B) photograph of the IIT two-dimensional circulating fluidized bed (2-D CFB).

This study utilized the noninvasive PIV technique near the front wall, in the dilute region, in the riser section of the Illinois Institute of Technology (IIT) two-dimensional circulating fluidized bed (2-D CFB), at three positions in the x-direction, using a colored rotating transparency, to measure y- and x-axes solids velocities. The instantaneous and hydrodynamic velocities represented movement of individual particles and clusters, respectively. The instantaneous and hydrodynamic velocities were used to determine laminar and turbulent properties, respectively. One of the main measured properties were laminar and turbulent granular temperatures. Furthermore, a novel method for the measurement of y- and x-axes laminar and turbulent solids dispersion coefficients using the autocorrelation technique is also described in this study. The mixing was on the level of particles near the wall, in the dilute region. The total granular temperatures were reasonably close to the literature. Nonetheless, solids dispersion coefficients near the wall were several orders of magnitude lower than the radially averaged literature values, because of restrictions in fluctuations in the third dimension and low solids velocities in the free board region. The y-axis and x-axis solids dispersion coefficients measured in this study were compared with the axial and radial solids dispersion coefficients in the literature, respectively. Solids volume fractions were measured using a light diode assembly.

2. MEASUREMENTS OF TURBULENT PROPERTIES 2.1. Experimental Setup. A two-dimensional circulating fluidized bed (2-D CFB) was constructed and modified at IIT, for the measurements of turbulent properties, including solids dispersion coefficients, with partial financial support from UOP and the U.S. Department of Energy. 2.2. Schematic Diagram. The PIV and light diode assembly experiments described in Kashyap75 were performed for the measurements of turbulent properties and solids volume fractions, respectively. Figure 1A shows the schematic diagram of the 2-D CFB at IIT. The inner walls of the riser section of the CFB were fabricated of 0.013-m-thick glass sheets, to avoid the FCC particles from sticking to the walls, because of electrostatics caused by abrasion. The inside dimensions of the fluidized bed were 0.305 m wide (x-direction) by 1.283 m high (y-direction) by 0.051 m deep (z-direction). The glass structure was enclosed within a 0.013-m-thick acrylic sheet framework. The downcomer section of the circulating fluidized bed was constructed of 0.013-m-thick acrylic sheets, with the inside dimensions being 0.305 m in width by 1.397 m in height by 0.051 m in depth. To support the bed of 75-μm FCC particles, fine 304 L stainless steel wire support grids 7550

dx.doi.org/10.1021/ie1012079 |Ind. Eng. Chem. Res. 2011, 50, 7549–7565


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inlet gas pipe. Then, more water was removed from the air stream by flowing air through a silica gel bed, before entering another water filter that was installed in the pipe line. Next, the air pressure was kept constant at 30 psig by a pressure regulator. Thereafter, the air flow rate into the fluidized bed was regulated by directing the air stream through a rotameter with a manual valve. The air entered the distributor of the fluidized bed at the bottom, and at the center in the x- and z-directions. Air from the top of the downcomer section of the fluidized bed was discharged to the atmosphere through an exhaust pipe. Figure 1B shows a photograph of the circulation of 75-μm FCC particles in the IIT 2-D CFB shown in Figure 1A at a low superficial gas velocity. There were formations of bubbles free of particles at the bottom of the riser, which are not clearly visible in the picture. Figure 2 shows the cluster formation (Figure 2A) and a typical bubble (Figure 2B) in the 2-D CFB. 2.3. System Properties. The particles used for the measurements of dispersion coefficients and other turbulent properties in the IIT 2-D CFB were 75-μm FCC particles, with a particle density of 1654 kg/m3. Hence, the particles fell in the category of Geldart A type particles.76 The conditioned air was used as the fluidizing gas at room temperature. Three sets of experimental data were obtained, with the system geometry and properties described in Table 1. The PIV experiments were performed in the riser section: at 0.7 m from the gas distributor in the ydirection, and near the front wall in the z-direction. The positions in the x-direction were x/X = 0 (center), 0.75 (right wall), and 0.75 (left wall) for Sets I, II, and III, respectively. The system was extremely dilute at a height of 0.7 m. The light diode assembly experiments were performed by taking the data: averaged in the z-direction, at the center in the x-direction, and at the position of the PIV experiments in the y-direction. The experiments for Sets I, II, and III were performed at a superficial gas velocity of 0.34 m/s, with air entering the riser section from the bottom of the fluidized bed. The measured z-direction averaged solids volume fraction, at the center in the x-direction, at a height of 0.7 m was 0.02.52,75 In view of the fact that the system was dilute at the point of data acquisition, this solids volume fraction was assumed to be equal at three different x-direction positions analyzed in this study and also equal near the front wall in the z-direction. The solids fluxes were obtained at the point of acquisition of PIV data using eq 3.9 in Gidaspow76 as follows: Figure 2. Typical (A) cluster and (B) bubble formation by 75-μm FCC particles in the IIT 2-D CFB.

(165 1400 mesh) were used at the bases of the riser and downcomer sections of the 2-D CFB. To allow uniform distribution of air at the inlets of the fluidized bed, two 0.318- and 0.47-m-tall gas distributors were placed below the support grids in the riser and the downcomer sections, respectively. The riser and the downcomer sections were separated horizontally by a distance of 0.305 m. An acrylic cuboid connector with openings of 0.076 m on each side was placed at an angle of 30 to the horizontal, to connect the riser and the downcomer sections at a distance of 0.076 m above the distributors. The top sections of the riser and the downcomer were connected by another acrylic cuboid connector with openings of 0.152 m on each side. The compressed air used to fluidize the FCC particles was conditioned before entering the fluidized bed. First, in an attempt to dry moisture from the air, a heating coil was used around the

W s ¼ εs F s v s

ð1Þ

where Ws was the solids flux and vs was the solids y-axis hydrodynamic velocity. The solids fluxes at the location of the PIV data acquisition were 8.5, 3.97, and 3.64 kg/(m2 3 s) in Sets I, II, and III, respectively. The time step between two frames was 3.33 102 s. The experimental data were analyzed for 025 s in Set I and for 07 s each in Sets II and III.

3. PARTICLE IMAGE VELOCIMETRY (PIV) TECHNIQUE The particle image velocimetry (PIV) technique for the measurements of solids velocities has been used in gas liquidsolid flows77,78 and in gassolid flows.1113,75,79 The PIV technique can successfully measure the particle velocities in all the three directions, using a charge-coupled device (CCD). The PIV technique is based on the principle of the scattering of light by the particles into a photographic zoom lens and 7551



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Table 1. System Geometry and Properties for PIV Measurements, Using a CCD Camera Value Geometry/Property, Symbol

Set I

Set II

Set III

Unit

2-D CFB material

acrylic/glass

acrylic/glass

acrylic/glass

riser section width, D2-D

0.3048

0.3048

0.3048

m

riser section height, H

1.283

1.283

1.283

m

riser section depth, W2-D

0.051

0.051

0.051

measuring axial distance from the bottom of riser, Hmeasurment

0.7

0.7

0.7

m

0.038 (right wall)

0.267 (left wall)

m

measuring horizontal distance from the right wall of riser, Xmeasurment (see Figure 1) 0.152 (center) measuring distance from the plane, z = 0, Zmeasurment (see Figure 1)

0.026 (front wall) 0.026 (front wall)

0.026 (front wall) m

downcomer section width, Ddowncomer cuboid connector opening, Dconecting pipe

0.305 0.076

0.305 0.076

0.305 0.076

m m

cuboid connector angle with the horizontal, Rhorizontal

30

30

30

degree

particle type

FCC

FCC

FCC

particle diameter, dp

75

75

75

μm

particle density, Fs

1654

1654

1654

kg/m3

packing fraction, εs,max

0.66

0.66

0.66

fluidizing gas

air

air

air

operating temperature, Tg gas density, Fg

298 1.2

298 1.2

298 1.2

K kg/m3

gas viscosity, μg

1.8 105

1.8 105

1.8 105

kg/(m 3 s)

terminal velocity, Ut

0.28

0.28

0.28

m/s

minimum fluidization velocity, Umf

0.003

0.003

0.003

m/s

superficial gas velocity, Ug

0.34

0.34

0.34

m/s

initial bed height, Hinitial

0.14

0.14

0.14

m

local solids flux, Ws

8.5

3.97

3.64

time step between two frames, Δt steady state for time averaging, tsteady

formation of images on a video array detector, which are then transferred to a computer for analysis. The PIV system primarily comprises a high-resolution microimage system, a light source, a motor with rotating transparency, and a data managing system. The high-resolution microimage system used in this study was a color video camera (Sony Hyper HAD CCD-IRIS/RGB, Model DXC-151A) with a CCD having a frame rate of 30 frames per second. The CCD camera had 10 electronic shutter settings and 4 gain control settings. The camera was connected to a personal computer with a camera adapter (Sony CMA-D2). The computer was installed with a microimaging board for capturing and digitizing the images, and microimaging software (Image Pro PlusTM) for the measurement and analysis of the data. Good visualization of the movement of particles required correct position and intensity of light. A fiber-optic light source (Dolan-Jenner Industries, Inc., Fiber-Lite A3200) fitted with a 150 W bulb, having aperture control, upon projection on the particles, resulted in reflected and refracted lights. The angle and position of the light beam was adjusted until the reflected light had the correct position to form good images in the form of streak lines. A three-color rotating transparency sheet, with repeated arrangement of colors of the streak lines (i.e., yellow, green, and red) was attached to a motor to consider the direction of flow of the particles (i.e., upward or downward). The comparison of the pattern of the three colors formed on the streak lines with the direction of rotation of the rotating transparency gave the direction of movement of particles in the system.

3.33 10 025

2

3.33 10 07

2

3.33 10 07

2

kg/(m2 3 s) s s

The CCD camera was calibrated separately for each set of data obtained in this study. A thin ruler or scale with numbers clearly visible was attached to the inside wall of the fluidized bed. The purpose of affixing the scale to the inside surface was to incorporate the refraction and reflection caused by the fluidizedbed walls during the actual measurements. The CCD camera was focused on the scale to read a known or calibrated length, such as 1 cm, in an empty fluidized bed. The scale was removed before taking data with the fluidized particles to avoid any obstruction to the flow by the scale. The zoom and focus of the CCD camera were then undisturbed for capturing the streaks. Only clearly visible streaks were analyzed in each frame, with a reasonable assumption that the fluctuations of particles were very close to the wall. The lengths of the streak lines were measured using the calibrated lengths. In this study, the data were taken near the inside surface of the wall of the fluidized bed without drilling a hole for the probes, against different x-direction positions with the use of intrusive probes, as described by Tartan and Gidaspow.12 The intrusive probes tend to change the flow pattern at the point of contact of particles with the probe. Besides, the flow pattern is important near the wall, as the particle velocities decrease significantly near the walls, compared to the center, giving isotropic behavior, and it can help in obtaining good boundary conditions. The data were taken at a height of 0.7 m from the bottom, which was in the dilute region. The x-direction positions of data acquisition were at the center, near the right wall, and near the left wall for Sets I, II, and III, respectively. The analysis of the streaks done manually 7552



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Figure 3. Particle image velocimetry (PIV) system.

was tedious and required high precision in the selection and analysis of as many streaks as visibly possible. Figure 3 shows a schematic diagram of the PIV measurement system at IIT, with a rotating transparency. Figure 4 shows the ideal (Figure 4A) and actual (Figure 4B) particle streak images captured by the CCD camera. The instantaneous particle velocities were measured by dividing the lengths of the streak lines by the exposure time of 1/250 s, which corresponded to the inverse of the shutter speed of the camera. Despite the fact that the PIV technique is capable of measuring particles velocities in the y-, x-, and z-axes, the velocities in this study were measured only in the y- and x-axes with a reasonable assumption that the velocities and turbulent properties in the x- and z-axes were close to each other.12 The CCD camera could be moved to the perpendicular plane to measure the velocity in the z-axis,12 but with the help of an intrusive probe. The analyses of the particle velocity in this study were done for 25 s for Set I and 7 s each for Sets II and III. Overall, 7296 particle streaks in 751 frames, 1356 particle streaks in 211 frames, and 1105 particle streaks in 211 frames were analyzed in Sets I, II, and III, respectively. Approximately 45 days were required to manually finish the tedious analysis. The typical numbers of streaks obtained in each frame were typically between 2 and 29 in Set I, and they were between 2 and 11 in Sets II and III. The exact percentage of analyzed particles in each frame was unknown. However, only the clearly visible streaks were analyzed in this study. This was done to make sure that the particles were close to the wall.

4. LIGHT DIODE ASSEMBLY A light diode assembly has been successfully used to understand the dynamics of fluidized beds by measuring solid concentrations.52,75,85,86,98 The solids volume fractions in the fluidized bed were measured by recording the voltage generated from a photovoltaic sensor upon passing a constant monochromatic light source through the fluidized bed. The Dolan-Jenner Industries, Inc., Fiber-Lite A3200 system, with a 200 W bulb, was used as the high intensity optical fiber light source. The light source provided a constant color uniform light with modulated intensity control. The light was directed through the fluidized bed, and the intensity of light was measured using a high-speed borosilicate detector (Edmunds Optics, Model NT55-338, 15 mm2). The voltage generated by the detector was inversely

Figure 4. (A) Ideal and (B) actual streak images captured by the CCD camera.

proportional to the solids volume fraction in the fluidized bed. The voltage signal was collected using a National Instruments data collection system, which was then analyzed using the LabView software. The BeerLambertBouguer law, or simply Beer’s law, was the mathematical basis for the light diode assembly technique used to analyze the experimental data for the measurement of solids volume fraction. This technique was in agreement with the concept that the transmitted light can be described as a linear function of the porosity of the system. According to Beer’s law, the intensity of the transmitted light was given as follows: I ¼ I0 expðδFlÞ

ð2Þ

where I was the intensity of the transmitted light, I0 was the intensity of incident light, δ was the attenuation coefficient, F was the bulk density of the material, and l was the path length. This method used the fact that the absorptions for light were different for the gas and solid phases. The solids volume fractions were obtained directly from the natural logarithm of intensities. From Seo and Gidaspow,99 the relationship between the intensity and the solids volume fractions could be given as follows: I ln ð3Þ ¼ ðAs Ag Þεs þ Ag I0 where As = δsFsls, Ag = δgFglg, and εs is the solids volume fraction. The coefficients in eq 3 were obtained by measuring the light intensities at known solids volume fractions, i.e., from the calibration curve obtained by measuring voltage output through an empty pipe (εs = 0) and a full pipe (εs = εs,max). The maximum solids volume fraction (or the packing fraction, εs,max) was 7553



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determined separately and experimentally, in a static bed, as εs, max ¼ ¼

ðmparticles =Fs Þ volume of particles ¼ volume of bed Vbed ðmparticles =Fs Þ 0:66 D2-D W2-D hbed

ð4Þ

where εs,max was the packing fraction of particles, mparticles was the mass of bed of particles (3.73 kg), Fs was the density of particles (1654 kg/m3), D2-D was the inner width of the riser (0.3048 m), W2-D was the inner depth of the riser (0.051 m), hbed was the height of particles in the static bed (0.22 m), and Vbed was the volume of the bed (0.003 m3). The solids volume fractions were measured at different positions along the y-direction in the fluidized bed, using the light diode assembly, and the results are presented by Kashyap and Gidaspow52 and Kashyap.75 Although the IIT 2-D CFB described in the work of Kashyap and Gidaspow52 and Kashyap75 was used as a bubbling bed without circulation and with a slightly different initial bed height, the solids volume fractions in the dilute region must have been very close to those obtained in this study. This could be supported with the fact that the fluxes at the height of 0.7 m were very low, hence, showing that the CFB was very close to the bubbling fluidized bed with an extremely dilute top. In this study, only the results obtained at a height of 0.7 m were used. Three sets of data were taken, each for the empty pipe and the pipe completely filled with particles for calibration, each time for 20 s. Voltages obtained in each set were averaged over the time for which the experiments were performed, which were further averaged over the three sets. Once the coefficients in eq 3 were obtained using this calibration method, the relationship between the voltage output and the solids volume fraction was used to obtain the time dependency of the solids volume fraction for each test run.

5. LAMINAR AND TURBULENT PROPERTIES 5.1. Particle Velocities. 5.1.1. Instantaneous Particle Velocity.

Figure 5. (A) Instantaneous and (B) hydrodynamic velocity fluctuations along the y- and x-axes for Set I (center).

instantaneous velocities in each frame, as follows:

The instantaneous particle velocities in the y- and x-axes were measured from the streak lengths and the angle made by the streaks with the vertical in each frame, as follows: cr ðp, tÞ ¼

ΔL sin R Δt

ð5Þ

ca ðp, tÞ ¼

ΔL cos R Δt

ð6Þ

where p represented any position, t was the timeframe of occurrence, ΔL was the streak length, Δt was the shutter time (or 1/shutter speed), R was the angle with the vertical, ca represented the instantaneous velocity in the y-axis, and cr was the instantaneous velocity in the x-axis. The subscripts “a” and “r” were used to show an analogy with the “axial” and “radial” directions in cylindrical coordinates, respectively. The instantaneous particle velocities were used to obtain the laminar properties, or properties of the particles. All the streak lines were simultaneously analyzed for the y- and x-axes particle instantaneous velocities in each frame. 5.1.2. Hydrodynamic Velocity. The hydrodynamic velocities due to the fluctuation of clusters rather than individual particles in the y- and x-axes were measured from the average of all the

vi ðp, tÞ ¼

1 np

np

∑ cik ðr, tÞ

k¼1

ð7Þ

where np was the number of particles in a given frame, k was the particle number in a given frame, i was the x-, y-, or z-direction, cik was the instantaneous velocity of particle k in a given frame, in direction i; vi denoted the hydrodynamic velocity in direction i, which was defined as the average value of velocities in a given frame. The hydrodynamic velocities were used to obtain the turbulent properties or properties of the clusters. A CCD camera with a speed of 30 frames per second indicated that the time increment between two frames was equal to 1/30th of a second. Figure 5 shows the fluctuations of instantaneous velocities (Figure 5A) and hydrodynamic velocities (Figure 5B) in the y- and x-axes for Set I. Detailed results for Sets II and III are given in Kashyap.75 Both the instantaneous and hydrodynamic velocities in the y-axis were positive as well as negative, thus, signifying that the solids flow was both upward and downward near the wall in the IIT 2-D CFB. However, the net effect was positive. The x-axis particle velocity fluctuations were significant in both the positive and negative directions, because of the particle movement toward the right and left walls, respectively. However, 7554



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Figure 6. Fast Fourier transform (FFT) analysis of particle hydrodynamic velocities along the y- and x-axes (fax,Set I = 0.029 Hz, frad,Set I = 0.088 Hz, fax,Set II = 0.059 Hz, frad,Set II = 0.059 Hz, fax,Set III = 0.059 Hz, frad,Set III = 0.059 Hz).

the net movement was toward the right wall. The mean y-axis instantaneous particle velocities were 0.23 m/s for Set I and 0.11 m/s each for Sets II and III. The mean x-axis instantaneous particle velocities were 0.001, 0.01, and 0.004 m/s for Sets I, II, and III, respectively. The mean y-axis hydrodynamic particle velocities were 0.26, 0.12, and 0.11 m/s for Sets I, II, and III, respectively. The mean x-axis hydrodynamic particle velocities were 0.003, 0.009, and 0.005 m/s for Sets I, II, and III, respectively. The y-axis instantaneous and hydrodynamic velocity fluctuations were highest for Set I, and they were lower and close to each other in Sets II and III. This was due to the fact that, at the x-direction center position in Set I, the particles had more freedom to move, compared to the near-side-wall positions in Sets II and III. Furthermore, the velocity fluctuations in the y-axis were higher than those in the x-axis for Sets I, II, and III due to the higher gradients of y-axis velocities caused by the turbulences or velocity fluctuations in the direction of the flow. This showed anisotropy in the system. However, the instantaneous and hydrodynamic velocities were close to each other in both the y- and x-axes for Sets I, II, and III. This shows that each frame roughly represented the entire time series, and the numbers of particles analyzed in each frame were sufficient. 5.2. Fast Fourier Transform (FFT) of Hydrodynamic Velocity. The frequency analysis of the measured hydrodynamic velocity, as a function of time, helps in understanding the motion of clusters in fluidized-bed systems. The fast Fourier transform (FFT) frequency responses for the hydrodynamic velocities in the y- and x-axes were measured using the Fourier Analysis tool in Microsoft Office Excel 2003. Figure 6 shows the FFT of the hydrodynamic velocities for Sets I, II, and III, in the y- and x-axes. The dominant frequencies were between 0.03 Hz and 0.09 Hz for the y- and x-axes hydrodynamic velocities in Sets I, II, and III. The power spectral densities for the y-axis velocities were higher than those for the x-axis velocities in Sets I, II, and III. Furthermore, the power spectral density was highest in Set I, and those in Sets II and III were similar to each other. 5.3. Instantaneous and Hydrodynamic Velocity Distribution. Figure 7A shows the instantaneous velocity distributions for all the analyzed streaks in Sets I, II, and III, in the y-axis. Figure 7B shows the instantaneous velocity distributions for all the analyzed streaks in Sets I, II, and III, in the x-axis. The y- and x-axes instantaneous velocity distributions were normal in Sets I, II, and

Figure 7. Instantaneous velocity distributions for Sets I, II, and III along (A) the y-axis and (B) the x-axis.

III, with normality maximum in Set I. This was due to the effect of only one wall in Set I, compared to that of two walls in Sets II and III. The y- and x-axes hydrodynamic velocity distributions for all the analyzed frames in Sets I, II, and III are explained in Kashyap.75 Both the y- and x-axes hydrodynamic velocity distributions were close to normal. The normal distribution was a good result, because it corroborated the first approximation for velocities in the kinetic theory of granular flow. The velocities obtained from the PIV techniques were used to obtain the laminar particle and Reynolds stresses,75 laminar and turbulent granular temperatures, and laminar and turbulent dispersion coefficients. The instantaneous velocities were used to measure the laminar properties for individual particles, whereas the hydrodynamic velocities were used to measure the turbulent properties for clusters of particles. 5.4. Granular Temperature. Gidaspow et al.11 and Jung et al.13 observed that the granular temperature is due to not only the random motion of particles, but also due to the random motion of bubbles or clusters of particles. The two types of granular temperatures are: • A “laminar” type, which is due to random oscillations of individual particles, recognized as classical granular temperature 7555



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• A “turbulent” type, which is due to the motion of bubbles or clusters of particles, and is measured or computed by the normal Reynolds stress 5.4.1. Laminar Granular Temperature. The laminar granular temperature due to the oscillation of individual particles was measured from contributions of the particle normal stresses75 in all the three directions as follows: 1 Cy Cy þ hCx Cx i þ hCz Cz i ð8Þ θlaminar, xyz ðp, tÞ ¼ 3 where θlaminar,xyz was the laminar granular temperature due to particle stresses in the x-, y-, and z-axes, Cy was the fluctuating velocity of particles in the y-axis, and ÆCyCyæ was the laminar particle stress in the y-axis. By assuming equal velocity fluctuations of particles in the x- and z-axes, the laminar granular temperature could be rewritten as 1 Cy Cy þ 2hCx Cx i ð9Þ θlaminar ðp, tÞ ¼ θlaminar, 2xy ðp, tÞ = 3 Pan et al.80 mentioned that, in two-dimensional fluidized beds, the z-axis velocity fluctuations are much smaller than those in the y- and x-axes. To check if the contributions of the velocity fluctuations in the z-axis were significant, compared to those in the x-axis in the IIT 2-D CFB, the laminar granular temperature was also measured without the z-axis component, for verification purposes, as follows: 1 Cy Cy þ hCx Cx i ð10Þ θlaminar, xy ðp, tÞ = 3 where ÆCzCzæ ≈ 0. 5.4.2. Turbulent Granular Temperature. The turbulent granular temperature due to the oscillation of bubbles or clusters of particles, was measured from contributions of the Reynolds stresses75 in all three directions as follows: 1 θturbulent, xyz ðp, tÞ ¼ ½v0y v0y þ v0x v0x þ v0z v0z 3

ð11Þ

where θturbulent,xyz was the turbulent granular temperature due to Reynolds stresses in the x, y, and z-axes, v0y was the fluctuating hydrodynamic velocity in the y-axis, and v0y v0y was the Reynolds stress in the y-axis. Similar to the laminar granular temperature, by assuming equal fluctuations of velocities of bubbles of clusters in the x- and z-axes, the turbulent granular temperature could be rewritten as follows: 1 θturbulent ðp, tÞ ¼ θturbulent, 2xy ðp, tÞ = ½v0y v0y þ 2v0x v0x 3

ð12Þ

Similar to the laminar granular temperature, the turbulent granular temperature was also measured without the z-axis component, to check the contributions of the velocity fluctuations in the z-axis, compared to those in the x-axis in the 2-D CFB, as follows: 1 θturbulent, xy ðp, tÞ = ½v0y v0y þ v0x v0x 3

ð13Þ

where v0z v0z ≈ 0. The two types of granular temperatures gave two types of mixing, i.e., one on the level of particles, represented by the laminar granular temperature, and one on the level of bubbles or clusters, represented by the turbulent granular temperature.

Figure 8. Variation of (A) laminar and turbulent granular temperatures and (B) total granular temperature, with time.

5.4.3. Total Granular Temperature. The total granular temperature was measured using the total stresses obtained from the two methods described in the work of Kashyap.75 In the first method, the total granular temperature was obtained from the “overall averaged” stresses in the y- and x-axes, which was the combined effect of laminar and Reynolds stresses. The measured Reynolds stresses are not presented in this study. However, the results are described elsewhere.75 In the second method, the total granular temperature was measured as the summation of the laminar and turbulent granular temperatures, as θtotal ¼ θlaminar þ θturbulent

ð14Þ

where θtotal was the total granular temperature. The granular temperatures were obtained from the stresses, as described earlier. Figure 8A shows the time variations of the laminar and turbulent granular temperatures for Sets I, II, and III. Figure 8B shows the variations of the total granular temperatures with time for Sets I, II, and III. Table 2 summarizes the measured granular temperatures in Sets I, II, and III. The laminar and turbulent granular temperatures for Set I were 7.5 103 and 6.7 103 m2/s2, respectively. The laminar and turbulent granular temperatures for Set II were 4.2 103 and 2.5 103 m2/s2, respectively. 7556



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obtained by considering velocity fluctuations only in the y- and x-axes were very close to those obtained by velocity fluctuations in all the three directions. This shows that the contributions in both the x- and z-axes were significantly lower than those in the y-axis. The difference was highest at the center along the

The laminar and turbulent granular temperatures for Set III were 2.2 103 and 1.2 103 m2/s2, respectively. Hence, the granular temperatures due to the oscillations of particles were larger than those due to the oscillations of clusters, showing that mixing was on the level of particles, rather than on the level of clusters. Table 2 also shows that the granular temperatures Table 2. Measured Laminar and Turbulent Granular Temperatures Granular Temperature (m2/s2) Set

Laminar

Turbulent

Considering Velocity Fluctuations in the x-, y-, and z-Axes I II III

7.5 103

6.7 103

4.2 10

3

2.5 103

2.2 10

3

1.2 103

Considering Velocity Fluctuations Only in the x- and y-Axes I II III

6.5 103

5.6 103

3

2.4 103

3

1.2 103

3.8 10

2.1 10

Figure 9. Distribution of granular temperature in the x-direction.

Table 3. Comparison of Instantaneous and Hydrodynamic Velocities, and Laminar and Turbulent Granular Temperatures, at Time Intervals of 025 s and 05 s for Set I, and 07 s and 05 s for Sets II and III Set I Laminar Property (Unit)

Direction

25 s

5s

instantaneous velocity (m/s)

y-axis

0.232

0.22

instantaneous velocity (m/s)

x-axis

0.001

0.001

Turbulent 25 s

5s

hydrodynamic velocity (m/s)

y-axis

0.257

0.248


x-axis

0.003

0.002

0.007

0.007

granular temperature (m2/s2)

0.008

0.009

Total (Summation)

Total (Overall Average)

25 s

5s

25 s

5s

0.014

0.016

0.013

0.015

Set II Laminar Property (Unit)

Direction

7s

5s

instantaneous velocity (m/s) instantaneous velocity (m/s)

y-axis x-axis

0.105 0.01

0.103 0.01

Turbulent 7s

5s

0.114


y-axis

0.117


x-axis

0.009

0.01

0.003

0.002


0.004

0.005

Total (Summation)


7s

5s

7s

5s

0.007

0.007

0.007

0.007

Set III Laminar Property (Unit)

Direction

7s

5s

instantaneous velocity (m/s) instantaneous velocity (m/s)

y-axis x-axis

0.11 0.004

0.11 0.003

Turbulent 7s

5s


y-axis

0.11

0.1


x-axis

0.005

0.004

0.001

0.001


0.002

0.003

7557

Total (Summation)


7s

5s

7s

5s

0.003

0.004

0.003

0.004



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Figure 10. Effect of superficial gas velocity on total granular temperature, using data from this study, Tartan and Gidaspow,12 Jung et al.,13 Jiradilok et al.,48 Gidaspow and Huilin,79 Campbell and Wang,81 Cody et al.,82 Polashenski and Chen,83,84 Driscoll and Gidaspow,85 and Kashyap et al.86

Figure 11. Effect of solids velocity on total granular temperature, using data from this study, Tartan and Gidaspow12 and Jung et al.13

x-direction in Set I. This shows that the velocity fluctuations in the z-axis were most significant at the center along the x-direction. Nevertheless, the exact values of the velocity fluctuations in the z-axis can be measured with intrusion caused by a probe, which was earlier used by Tartan and Gidaspow.12 Table 3 summarizes the particle and cluster velocities, and laminar and turbulent granular temperatures, at the time intervals of 025 s and 05 s for Set I, and 07 s and 05 s for Sets II and III. The velocities in the y-axis were higher than those in the x-axis for Sets I, II, and III, because of the higher gradient of the y-axis

velocity than that of the x-axis velocity caused by the turbulences or velocity fluctuations in the direction of the flow. Hence, the anisotropy was prevalent in the fluidized bed system used in this study. The granular temperatures and other properties described in Table 3 did not change significantly between the two time intervals for each set. This shows that the time interval of 7 s used for time averaging in Sets II and III was sufficient to obtain steady-state results, and the time interval of 25 s in Set I was not necessary. 7558



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Table 4. Measured Solids Dispersion Coefficients in the y- and x-Axes, Using the Autocorrelation Method Solids Dispersion Coefficient (m2/s) y-axis

x-axis Set I

1.94 104

laminar

6.51 105

4

turbulent

1.6 10

laminar

2.2 104

3.8 105

Set II 1.55 105

4

turbulent

1.48 10

laminar

3.3 104

5.63 106

Set III 1.86 10

turbulent

4.62 106

4

2.29 106

The total granular temperatures obtained using the two methods described earlier showed slight differences in their values. However, these differences were not significant enough to say that insufficient numbers of particles were analyzed per frame in this study. Figure 9 shows the distribution of laminar, turbulent, and total granular temperatures, along the x-direction. The granular temperatures were highest at the center along the x-direction in Set I, because of greater freedom for particle movement without the effect of the walls. The granular temperatures were low in Sets II and III, because of the restrictions in the movement of particles caused by the wall. There was an asymmetry between the two walls, because of the effect of one inlet at the bottom. Figure 10 shows the effect of the superficial gas velocity on total granular temperature, when compared with the literature. The measured granular temperatures for Geldart A type particles in this study were in reasonable agreement with literature values. The granular temperatures of the 10-nm the particles were several orders of magnitude higher than those for larger particles, at the same superficial gas velocities. These high granular temperatures of the nanoparticles were due to their random motion caused by the collision with air molecules as in the case of Brownian motion, rather than just caused by shear, as is the case in the granular flow of conventional particles. The effect of the solids velocity on the total granular temperature is shown in Figure 11. The solids velocity (vs), under steadystate conditions, was calculated from the superficial gas velocity (Ug) and the terminal velocity of particles (Ut), using the following relations given on page 51 in the work of Gidaspow:76 v s ¼ Ug Ut Ut ¼

Ut ¼

dp2 ðFs Fg Þg

for Ret e 2

18μg

0:153dp1:14 g0:71 ðFs Fg Þ0:71

Ut ¼ 1:74

0:29 μ0:43 g Fg

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gdp ðFs Fg Þ Fg

ð15Þ ð16Þ

for 2 < Ret < 1000 ð17Þ

for 1000 < Ret < 250 000 ð18Þ

Figure 12. Distribution of (A) y-axis and (B) x-axis solids dispersion coefficients in the x-direction.

The results from this study (Ret ≈ 1.44) were compared with those presented by Tartan and Gidaspow76 for Ret ≈ 140 and Jung et al.13 for Ret ≈ 0.38. The solids velocities computed using eqs 1518 were different from those measured using the PIV technique (Table 3). The reason for the difference was that the computed velocities were independent of position within the fluidized bed, whereas the PIV measurements were positiondependent. The measured total granular temperatures were low in this study, because of the low solids velocities. As expected, the total granular temperature increased with the solids velocity. 5.5. Dispersion Coefficient. Jiradilok et al.48 defined two types of dispersion coefficients, which are related to two types of granular temperatures, as follows: • A “laminar”-type dispersion coefficient, measured or computed by laminar granular temperature due to random oscillations of individual particles • A “turbulent”-type dispersion coefficient, measured or computed by the normal Reynolds stress, caused by the motion of bubbles or clusters The dispersion coefficient measured using the autocorrelation method75 was the product of the variance of the fluctuating velocity, either instantaneous or hydrodynamic, and the 7559



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Figure 13. Effect of superficial gas velocity on the y-axis solids dispersion coefficient, using data obtained in this study, Gidaspow et al.,11 Du et al.,47 Jiradilok et al.48,50 Avidan and Yerushalmi,56 Wei et al.,62,88 and Thiel and Potter.87

Lagrangian integral time scale, as follows:94 DiðlaminarÞ ¼ Ci Ci TL

ð19Þ

DiðturbulentÞ ¼ v0i v0i TL

ð20Þ

where Di(laminar) was the laminar dispersion coefficient in idirection, Di(turbulent) was the turbulent dispersion coefficient in i-direction, Ci Ci was the root-mean-square of the fluctuating instantaneous velocity, v0i v0i was the root-mean-square of the fluctuating hydrodynamic velocity, TL was the Lagrangian integral time scale for the particle or cluster motion

(defined R¥ R¥ 0 0 02 as TL ¼ 0 RL ði, τÞdτ ¼ 0 v ðtÞv ðt þ τÞ=v dτ), C was the time-dependent Lagrangian instantaneous fluctuating velocity, v0 was the time-dependent Lagrangian hydrodynamic fluctuating velocity, t was the time of occurrence of frame, τ was the frame rate, and RL(i,τ) was the autocorrelation coefficient for the turbulent dispersion coefficient (RL ði, τÞ ¼ v0 ðtÞv0 ðt þ τÞ =v02 ). In this study, the velocity fluctuations were measured at a particular location, rather than tracking particles at various locations. In other words, the Eulerian framework was utilized in this study, where any property varied with respect to a fixed position. Hence, the Lagrangian integral time had to be converted to Eulerian integral time. Hay and Pasquill95 related the Lagrangian and Eulerian turbulence characteristics by a coefficient, βHP, as follows:4850 TL ¼ βHP TE

ð21Þ

where TE was the Eulerian integral time for the gas or particle motion and βHP was the Hay and Pasquill coefficient. Hinze94 reported that, to estimate the magnitude of the dispersion coefficient, the Lagrangian turbulence characteristics could be converted to Eulerian turbulence characteristics by equating the two as follows: TL TE

ð22Þ

Note that the Lagrangian integral time scale could not be measured for the analysis of instantaneous velocities, because the frame rate (τ) could not be defined for each particle velocity, in each frame. Otherwise stated, the Lagrangian integral time scale could only be defined for a frame, not for a particle. In view of the difficulties in defining the Lagrangian integral time scale for particle fluctuations, another assumption was used in the measurement of the laminar dispersion coefficient, as follows: TLðlaminarÞ TLðturbulentÞ

ð23Þ

where TL(laminar) was the Lagrangian integral time for particles and TL(turbulent) was the Lagrangian integral time for clusters. This assumption was reasonable, since the time-averaged instantaneous and hydrodynamic velocities were similar to each other. However, the differences between the laminar and Reynolds stresses caused differences between the laminar and turbulent dispersion coefficients. Hence, in the autocorrelation method, the dispersion coefficient is a function of the normal particle or Reynolds stress and the Lagrangian or Eulerian integral time scale. Breault et al.96 mentioned that the time period for which the analysis for the dispersion coefficient is done should be at least 10 times the Lagrangian integral time scale.97 In this study, the Lagrangian integral time scales for the x- and y-axes velocity fluctuations were

Measurements of Dispersion Coefficients for FCC Particles in a Free

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