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*Corresponding author. Fax: 47 22 06 7350; e-mail: davoudt@chem.

sintef.no.

Chemical Engineering Science 54 (1999) 2113}2122

Dynamics of #uidized-bed reactors. Development and application of a new multi-"ber optical probe

Davoud Tayebi*, Hallvard F. Svendsen, Arne Grislinga s, Thor Mejdell,Kjetil Johannessen

Department of Chemical Engineering, Norwegian University of Science and Technology, NTNU, N-7034 Trondheim, Norway

STATOIL Research Centre, Trondheim, Norway

SINTEF Applied Chemistry, Trondheim, Norway

SINTEF Electronics & Cybernetics, Trondheim, Norway

Abstract

There seems to be no method available to measure all parameters of interests in multiphase #ow systems with high solids

concentration and with reasonable accuracy. Parameters include, local particle velocity vectors, solids volume fractions and bubble

rise velocity, size, frequency and volume fraction. In this study a novel method based on a "ber optical technique and tracer particles

has been developed for simultaneous measurements of the mentioned local #ow properties in highly concentrated multiphase #ow

systems such as gas}solid #uidized bed reactors. A particle present in the measuring volume in front of the probe is marked with

a #uorescent dye. A light source illuminates the particles and the detecting "bres receive re#ected light from uncoated particles and

#uorescent light from the tracer particle. Using optical "lters, the #uorescent light can be distinguished and together with a small

fraction of background light from uncoated particles can be used for the determination of local #ow properties. The method gives the

possibility for simultaneous measurement of the local movement of a single tracer particle, local bubble properties and the local solidsvolume fractions in di! erent positions in the bed. 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Particle velocity; Bubble properties; Solids volume fraction; Tracer particles; Fiber optics; Fluidized beds

1. Introduction

Fluidized bed- and circulating #uidized-bed reactors

are used in many areas in the process industry, especially

in the oil and petrochemical industries. There are still

many uncertainties in the design, operation and scale up

of such reactors, particularly when the movement and

circulation of solids is concerned. In these systems the

local values of solids volume fraction may range from

0 to approximately 60 vol.%. For better understanding

of the #ow properties, behaviour and for fundamental

modelling of these multiphase systems, it is of prime

importance to know the details of the #ow. The local

velocities of both phases and the local distribution of

solids volume fraction are particularly important. Also

any phenomenological model developed in this area re-

quire empirical data. The reliability, accuracy and quality

of these models therefore depend on the accuracy of the

employed measurement techniques.

Pressure measurements have long been used in #uidiz-

ation studies. The time-averaged values of the pressure

measurements at di! erent locations in the bed give quali-

tative information of the bed behaviour (Glicksmann

et al., 1993; Marzocchella et al., 1997).

For suspensions with a solid volume fraction greater

than a few percent the optical depth is of the order a few

particle diameters. As a result, techniques such as visual-

ization or Laser}Doppler velocimetry are impractical

under such conditions (Arastoopour and Yang, 1992;

Horio and Kuroki, 1994).

Electroresistivity techniques are sensitive to the cha-nges in the e! ective dielectric properties. The e! ective

properties of arbitrary powders which are a! ected by

0009-2509/99/$} see front matter 1999 Elsevier Science Ltd. All rights reserved.

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humidity, temperature, and particle shapes may be di$-

cult to establish (Louge and Opie, 1990).

The main limitations of capacitance tomography tech-

niques are the poor resolution and the blurring of void-

age boundaries. In addition comes the uncertainties

prevalent in all tomographic techniques, relating to the

deconvolution of the current measurements. False im-

ages may also occur, especially when there are more thantwo objects within the same imaging "eld (Halow and

Nicoletti, 1992; Williams and Beck, 1995). The major

disadvantage of X-ray, -ray and C¹ scanners is thetime-averaged nature of the measurements, which limits

the usefulness of these techniques in process diagnostic

applications (Azzi et al., 1991, Yates and Cheesman, 1992;

Kumar et al., 1997).

The overall #ux of solids circulation in high-velocity

systems may be determined by collecting the total #ow

over a period of time and measuring each phase separ-

ately by means of sampling probes. In #uidized beds,

particle motion appear in di! erent directions. It is neces-

sary to collect solids from various positions with the

probe opening in di! erent directions at separate time

periods. Time averaging is therefore necessary (Rhodes

and Laussmann, 1992; Werther et al., 1993).

The particle-tracking techniques such as CARPT

(Computerized Automated Particle Tracking) or PEPT

(Positron Emission Particle Tracking) are limited to

the use of a de"ned particle. In a #uidized bed, par-

ticles are distributed over a certain range of sizes, and

generally may have non-spherical form. Therefore, the

tracer particle will at best represent only a narrowfraction of the bed particles. The implementation of

the above techniques require many detectors and much

calibration works. The experiments may also be of

long duration. (Lin et al., 1985; Sannvs, 1997; Simons

et al., 1993).

Many investigators have attempted to measure local

solids motion and volume fractions in dense suspensions

using optical "bre sensors. Optical "bre probes are

simple, yield high signal-transmission-to-noise ratios,

and create a minimum disturbance to the #ow. The

sensors used are either based on forward light scattering

between emission and detection "bres separated by

a short distance, or on backscattering onto an optical

"bre system. Forward scattering is limited to relatively

low solids volume fractions and also is considered to

disturb the #ow structure more than the backscattering

method. It is therefore impractical for dense systems

(Okhi and Shirai, 1976; Hartge et al., 1989). Because

backscattering sensors are simpler and less intrusive, they

have received wider attention, see Oki et al. (1975)

Lischer and Louge (1992) and Cocco et al. (1995).

In the measurement of particle velocities with "bre

optical probes, almost all detection systems apply twoparallel sensors placed at a certain distance. This design

can determine the magnitude of the velocity vector in one

dimension. As shown in this paper, the values obtained

by such a method can be misleading.

As discussed brie#y above, and according to the de-

tailed review of the measurement techniques by Tayebi

(1998), to the knowledge of the authors there is presently

no method available to determine all the parameters of

interests in multiphase systems with high solids concen-

tration with a reasonable accuracy.Any successful technique for measuring the above-

mentioned parameters, particularly solids movement

has to combine the ability to work over a wide range

of solids concentrations and particle sizes. It requires

also minimum disturbance of the #ow structure and

robustness under harsh conditions. A successful design of

optical probes can ful"l the necessary conditions, and

this work is therefore based on the application of this

technique.

2. Measuring principle

The local motion of a single particle in gas}solid #ow

can be determined using two parallel optical "bres separ-

ated by a known distance as light detectors. For a su$-

ciently high light sampling frequency the movement of

a self-lighting particle in front of the probe may be

detected as two bell-shaped curves separated in time.

One component of the particle velocity vector, u

can be

obtained by dividing the distance between the sensors,

x, by the measured time delay, t.

;"

x

t . (1)

This measuring principle is directly applicable only in

very dilute gas}solid #ows. In #uidized beds, especially in

the dense region, the above technique can only be applied

by using tracer particles. These tracer particles should

have exactly the same physical properties as the other

particles in the bed apart from the radiation properties.

This can be achieved by a #uorescent dye impregnation

of the tracer particles to be. Only one tracer particle at

a time should be present in the measuring volume. It is

then possible to distinguish between the radiation from

the main particles and that from the tracer particle. The

re#ected light from uncoated particles in the bed and the

#uorescent light from the tracer particle may be separ-

ated using a proper optical "lter combination. Fig. 1

illustrates this method whereby the obtained signals from

the passing tracer particle are similar to those from

a system with only one single particle.

A two-dimensional picture of the tracer particle move-

ment in front of the probe can be obtained by arranging

a number of detectors in a certain geometrical con"gura-tion. Knowing the relative positions of the detectors,

the local particle velocity vector in two dimensions is

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Fig. 2. Schematic illustration of the in#uence of illumination and "bre viewing angle on the e! ective distance, l

, relative to the geometric distance l.

(A) the end surface plane is not perpendicular to the "bre axis (B) The illumination light placed between receiving "bres (C) external illumination; (D)

uniform illumination. The distribution of illuminating light, I

is schematicaly illustrated in the right-hand side of each "gure.

Fig. 1. Schematic illustration for velocity measurement of a passing

single #uorescent dye impregnated tracer particle in the presence of

other uncoated particles using two parallel optical "bres as detectors.

The re#ected light from uncoated particles is blocked and only the

#uorescent light from the tracer particle is recorded.

Fig. 3. Optical "bres con"guration and details of the probe tip design.

The external steel cover keeps the sapphire window "xed in front of the

probe.

obtained by a simultaneous treatment of the time-series

signals from all detectors.

3. Probe design

The probe is made as small as possible with a sharp

edge and smooth face to reduce the distortion of the #ow.In #uidized beds where the particle movement may occur

in all directions, a circular design of the probe tip is an

optimal solution. For velocity measurements usually two

or more detectors/probes are required. Using separate

probes will disturb the #ow and create probe interfer-

ence. This can be avoided by embedding all detectors in

the same probe.

For particle velocity measurements an important fac-

tor is determination of the e + ective distance between two

sensors. Consider a particle passing in front of two paral-

lel detecting "bres separated by a known distance. If the

moving path of the particle is parallel to the end face of

the "bres, the in-line component of its velocity can be

determined from Eq. (1). Maximum light intensity is

obtained when the particle has the shortest distance to

the "ber end centre. The distance between two light

maxima is the e + ective distance, l

which in some cases

can be di! erent from the geometric distance, l, (Patrose

and Caram, 1982). The e! ective distance, l, is seen to be

a function of the viewing angle of the receiving "bres and

the nature of illumination at the measuring site, see

Fig. 2.To overcome the above problems, uniform illumina-

tion should be applied with both central and surrounding

light emitting "bres as shown in Figs. 2D and 3. A thin

glass window in front of the probe covers the blind spots

and together with the right "ber con"guration ensures

optimum illumination/detection uniformity.

Fig. 3 shows the "ber arrangement and details of the

probe tip. Thirty seven equal diameter plastic "bres are

"xed by epoxy glue in a specially made steel pipe with

a hexagonal shaped inner wall. Seven of the "bres are

selected as detectors while the other 30 are used as

emitters. The geometrical con"guration of "bers is such

that six of the detecting "bres are positioned at the

corners of an inner hexagon and one in the centre of the

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Fig. 4. (A) Schematic diagram of the light spectral assembly. (B) The light spectra from spent FCC particles coated with #uorescent dye and used as

tracer particles in this study, no optical "lter present.

probe. Each detector is surrounded by six emitters ensur-

ing symmetric and &&uniform'' light illumination of the

measuring site. The end face of the "bres are polished by

a multi procedure operation using ultra "ne sand papers.

The tip of the probe is smoothed and protected by a thin

sapphire window with a thickness of 0.5 mm and dia-

meter of about 2.5 mm. The distances and angles between

all detecting "bres were measured by microscopy andimage processing.

4. Tracer particles

When tracer particles are used to represent the #ow of

particles, their physical properties must be close to the

other particles in the bed. As tracer particles, one may use

a size fraction, or only one size of particles with the same

physical properties as the bed particles. Movement of

particles with other physical properties than the particles

in the bed can be measured using a small fraction of these

particles as tracer.

When tracer particles are made by #uorescent dye

impregnation as in this work, the weight of the dye is

negligible. The physical properties of the tracer particles

are then almost unchanged. In a #uidized bed a tracer

particle is always surrounded by and collides with other

particles. The #uorescent dye should not be lost or trans-

ferred to other uncoated neighbouring particles, but "xed

to the tracer particles both physically and chemically.

In this study "ve batches of spent #uidized cracking

catalyst (FCC) particles with the size distribution, shapeand density as the bed particles were coated with di! er-

ent #uorescent dyes. Two batches were impregnated by

Molecular Probes Inc., USA and three batches by SIN-

TEF Applied Chemistry, Norway. The #uorescence e$-

ciency and light spectra of all "ve tracer groups were

analysed by exposing them to the same laser source with

constant output power and wavelength (488}514 nm).

The analysis were carried out using a light spectrometer

(MCS UV-NIR 190}1015 nm, ZEISS), Fig. 4A. The spec-

trum of the chosen dye is shown in Fig. 4B. The dye-

impregnated tracer particles can easily be deactivated by

exposure to low concentrated ozone.

5. Particle velocity vector

When a group of particles passes the probe, a tracer

particle in the measuring volume will be detected by up

to seven detectors. The number of detecting sensors de-

pends on the local particle concentration in front of the

probe and the tracer particle path. The local particle

velocity vector in two dimensions is then obtained by

simultaneous data treatment of the time series signals

from all detectors.

Fig. 5 shows a small section of a time series measure-

ment conducted in a 7 cm ID bed of SiC particles. In thisexample the sampling frequency was set to 20 kHz per

detector. As shown in this "gure, the signals from the

passing tracer particles and the background signals from

uncoated particles are clearly distinguishable. A thre-

shold can be set as indicated by the dashed line.

The velocity vector determination for a passing tracer

particle is based on the maximum points of the signals

from the individual detectors. The projected distances

between the detecting "bres for each individual case are

calculated based on the measured maximum intensities,

the order of detection, and the geometrical positions of

the sensors in the probe.Fig. 6 illustrates a particle passing two sensors with

a "xed distance, X. In both cases (A) and (B), the magni-

tude of the particle velocity vector, u

and its angle of

direction, are determined by

u"

Xcos

t "

x

t . (2)


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Fig. 5. A section of a time-series measurement conducted in a laboratory #uidized-bed reactor of uncoated SiC particles and #uorescent dye

impregnated spent FCC tracer particles. The measurements are carried out at the centre of a 7 cm ID bed and axial height of h"160 mm above thegas distributor with a super"cial gas velocity of 0.065 m/s.

Fig. 6. Schematic illustration of the determination of the particle velo-

city vector based on the e! ective distance, x: (A) the particle passes inbetween two sensors, (B) the particle passes the detecting "bres without

passing in between them.Fig. 7. Signals from various detectors during the passage of a tracer

particle in front of the probe The particle has a straight moving path,

u"0.41 m/s and "3503.

Here, x is the projected distance between the sensors

and t is the measured time delay between detected

signals. Eq. (2) has two unknown variables and one

additional equation is required for calculation of u

and

. Therefore, successful signals from at least three de-tectors are needed for determination of the velocity vec-

tor. It should be emphasized that the velocity vector

determined in this way represents an averaged velocity

across the probe head. Since the probe diameter is

2.5 mm, this is considered to be a local velocity and

determined as a straight vector.

Fig. 7 shows an example of the signals received from

a tracer particle passing the probe. In this case the par-

ticle has an average speed of 0.41 m/s and a moving

direction angle of about 3503 relative to the main direc-

tion of the probe. It has been observed "rst by detectornumber 5, with a maximum signal intensity at point (a),

then detector number 6, with a maximum signal intensity

at point (b). Detector number 1 has also seen the tracer

particle, but since it is far from it, the signal level is much

lower than the others. Finally, the tracer particle has

been observed by detector number 7, with a maximum

signal intensity at point (d). The maximum intensities

may indicate in-plane distances to the detectors, but will

be strongly in#uenced by the distance from the probe

surface. Therefore, only the time sequences of maxima,

denoted by a}d in Fig. 7 are used for velocity determina-

tion. These correspond to the shortest distances to the

detectors in the probe tip plane as depicted in Fig. 6.

6. Local particle volume fraction

The probe was calibrated experimentally in two ex-

treme cases, "rst in a dark and particle-free space and


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Fig. 8. The probe calibration curves viewing a single #uorescent tracer

particle: (A) In a dark and particle-free space; (B) In an expanded bed of

SiC particles.

Fig. 9. Characteristic curve of coaxial sensors when a glass window is

used to cover the dark region. The re#ected light intensity decreases

from its maximum with increasing distance from the outer surface of the

glass window.

then in a &&uniformly'' expanded #uidized bed of uncoated

SiC particles using a speci"c tracer particle. A single

average-size tracer particle was "xed at the end of an

adjustable steel wire placed in a dark and particle-free

space. The optical probe was "xed on the opposite side of

the wire in the same horizontal and vertical plane. The

particle was then moved away gradually and the received

signal intensity was recorded, Fig. 8A.

The probe was also calibrated in a &&uniformly'' ex-

panded bed of uncoated SiC particles by the same pro-

cedure as described above, see Fig. 8B.Based on the above calibration results it is possible to

de"ne the limits of the measuring volume. As shown in

Fig. 8A, at a distance of 1.5 mm the signal intensity

reaches 0.1 V, corresponding to the background signal

level, see Fig. 5. This may be interpreted as the outer limit

of the measuring volume. Any tracer particle further

away will be practically undetectable regardless of local

particle concentration. The maximum depth of the

measuring volume at minimum #uidization velocity is

about 0.5 mm, as shown in Fig. 8B. Since the #uorescent

tracer particles applied in this study have a wide size

distribution, a lower signal intensity is obtained from

particles smaller than the average-size tracer particle

used in the calibrations. The measuring depth will there-

fore, be limited to between about 0.3 and 1.5 mm, de-

pending on the local particle concentration and the size

of the passing tracer particle.

As shown in Fig. 5 the re#ected light from the un-

coated particles passing through the long-pass "lter gives

a visible background signal. Using a proper calibration

function, this background signal can be used to deter-

mine the local particle concentration.

The design of the probe is such that each sensor can beconsidered as a separate coaxial sensor giving a max-

imum uniform illumination intensity, see Fig. 2D and

Reh and Li (1991). One of the advantages of this design is

that the characteristic curve of the sensor will be similar

to that of a single emitting/detecting "bre as shown in

Fig. 9. As shown in this "gure, the signal contribution

from the blind spot region of a coaxial "bre arrangement

is blocked by a glass window. This design can be used for

local solids volume fraction measurements with the ad-

vantages of having a more uniformly distributed emitting

light over the entire measuring cross-section and having

several detectors in the probe.

For the measurement of local solids volume fractions,

one of the major di$culties with optical probes in gen-

eral, and the re#ection type in particular, is that they arevery di$cult to calibrate experimentally, especially in

gaseous suspensions (Mastuno et al., 1988; Tung et al.,

1988; Hartge et al., 1989; Lischer and Louge, 1992; Amos

et al., 1996). Various methods have been used for calib-

ration of single "bre emitting/detecting probes. Despite

all attempts, no exact and accurate method or function is

available for the entire range of concentrations. However,

reasonable results have been reported using the empirical

correlation given by Eq. (3) in gas}solid suspensions

(Hartge et al., 1989; Werther et al., 1993; Rensner and

Werther, 1993; Werther and Hage, 1996).

;!;"aC

. (3)

Here, ; is the measured voltage and ;

is the voltage at

C"0. To use this correlation for SiC particles, the

coe$cients a and k need to be determined. According to

the theoretical model (Rensner and Werther, 1993), the

exponent k depends mainly on the size distribution of

particles whereas the factor a depends mainly on the

refractive index of the #uid and on the optical properties

of the particles. Thus, in a gas}solid system the numerical

value for k will be the same as in the liquid}solid system.k"0.57 was chosen based on the calibration data given

by (Werther et al., 1993) and a"0.094 for the gas}solid


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Fig. 10. Schematic illustration of detected signals by two sensors in the

probe from the passage of a bubble.

Fig. 11. The calculated particle velocity based on ) r versus themeasured particle velocity by the probe.

system was obtained from Eq. (3) by measurements of the

voltage ; in a "xed bed and at C"0, respectively.

7. Bubbles

As discussed earlier, when the signal level in a mea-

sured time series is lower than a certain value, a bubble is

identi"ed. By simultaneous treatment of all time series

from various detectors the bubble rise velocity can be

determined. This is done based on the time delays be-

tween detected signals from various sensors during the

passage of a bubble as illustrated in Fig. 10. The rise

velocity at the front and tail may be measured separately

based on the measured time delays ¹

and ¹

.

In a bubbling #uidized bed, bubbles are mainly risingupward along the bed as vertical axis. Therefore, the time

delay between signals from sensors placed in the same

horizontal level are close to zero. The e! ective distances

between these detectors are also zero and the resulting

velocity will be in"nite. Therefore, only signals from

detectors with di! erent axial positions are compared

with each other assuming the bubble motion to be verti-

cal. Bubble chord length is determined from the average

value of the rising velocities and their average passage

time by

l"u N )¹ . (4)

The size of bubbles are determined from the measured

chord length (Chan et al., 1987)

d N"1.43 u

)¹

. (5)

The bubble frequency is obtained from the number of

identi"ed bubbles per time unit.

8. Tests and veri5cations

In order to verify the accuracy of the velocity measure-ments, one average-size tracer particle was "xed on

a rotating disk. The particle was positioned at a certain

radius by means of a microscope. The rotation frequency

of the disk, , could be adjusted with high accuracy. Theparticle velocity was then determined based on its posi-

tion on the disk and the rotation frequency. The data

presented in Fig. 11 shows a comparison between the

measured particle velocities and the corresponding

values determined by means of r.The probe tip was positioned at various distances and

di! erent angles relative to the particle. The velocity de-

termination accuracy was always better than $0.5%.

9. Particle velocity vectors

The probe was applied in a transparent laboratory#uidized bed reactor with 7 cm ID with air at ambient

temperature as the gas phase, SiC particles as the solid

phase and dye impregnated FCC particles as tracers. An

example of the time-series measurements is presented in

Fig. 5.

Tracer particle velocity vectors in two dimensions were

measured at various radial and axial positions in the bed.

The measurements were carried out at three di! erent

super"cial gas velocities of 0.140, 0.065 and 0.035 m/s

respectively. Fig. 12 shows the variations in particle

velocity vectors in the bed at u"0.065 m/s. All the

measurements were made under the same conditions,

including optical properties, ampli"cation of the signals

and sampling rate of 20 000}25 000 scans/s/detector. The

sampling time was set to 60 s in all cases.

Each "gure shows the measured velocity vectors in two

dimensions at di! erent radial positions but at the same

axial level. The vertical axis of the probe is indicated in

the "gures with an arrow in the x-direction and is parallel

to the column vertical axis. The arrows in the "gures

represent the velocity vectors of each successfully mea-

sured individual passing tracer particle. The magnitude

and direction of the resultant velocity vector (u and )for each time-series measurement is given beside the

corresponding "gures. As shown in the "gures, due to the


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Fig. 12. Tracer particle velocity vectors at h"160 mm and u"0.065 m/s.

Fig. 13 Resultant particle velocity vectors measured in a bed of SiCparticles at the axial height of h"160 mm and various radial positions

with u"0.065 m/s.

rapid variations in moving direction, the value of theresultant velocity vector is often smaller than the magni-

tude of the instantaneous velocity vectors. In some cases

this averaged value is almost zero.

In order to study the repeatability of the results,

a number of measurements were repeated and good

agreement was obtained,$5% in resultant velocity and

$3% in moving directions.

Based on the resultant velocity vectors of tracer par-

ticles at various radial positions and axial heights at

constant super"cial gas velocity, the radial particle velo-

city pro"les were determined. An example of these pro-

"les is illustrated in Fig. 13. As shown in this "gure the

net particle #ow is upward in the core region and down-

ward close to the wall. The particle motion is also seen to

be non-symmetrical, but downward motion is seen close

to the wall on both sides.

Detailed and valuable information can be obtained by

studying the distribution of the particle velocity vectors.

Fig. 14 shows the detailed study of the particle measure-

ments made in the centre of the bed at axial height

h"160 mm and super"cial gas velocity of 0.065 m/s. In

Fig. 14A the tracer particle vectors in two dimensions are

shown. Fig. 14B shows the particle velocity magnitudefrequency spectrum and Fig. 14C shows the frequency of

particles moving directions. The values represented in the

frequency distributions are normalized with respect to

the values obtained from the total number of measured

tracer particles and shows the percentage of the total

measured tracer particles having a certain speed (the

magnitude of velocity vectors) and moving direction. As

shown in Fig. 14 the passing tracer particles move mainly

upward. Almost all particles have a speed greater than

0.06 m/s. Their moving directions appear within!90}903 with respect to the vertical axis. The net velo-

city vector was 0.115 m/s.


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Fig. 14. Tracer particle velocity vectors measured at h"160 mm and u"0.14 m/s. (A) presentation in polar coordinates illustrating the magnitude

and direction of the velocity vectors; (B) the frequency distribution of the velocity magnitude; (C) the frequency distribution of the velocity vectors

directions. From !90 to #90 denotes upward #ow. Zero is parallel to the main bed axis.

10. Conclusions

A method for simultaneous measurements of local

particle velocity vector, bubble properties and solids vol-

ume fraction based on the application of a "bre optical

technique and #uorescent tracer particles has been suc-

cessfully developed. The optical "bre probe has an outer

diameter of 2.5 mm. Its measuring depth is of order

0.3}1.5 mm depending on the local solids concentration.

The probe was successfully calibrated in two extremecases, including, a particle-free dark space and a &&uni-

form'' expanded bed of SiC particles. The calibration

curves were used to estimate the outer limits of the probe

measuring volume. These data were also used to "t the

calibration function of (Hartge et al., 1989) for determina-

tion of local solids volume fractions.

The accuracy of the measured velocity vectors by the

probe were tested by the application of a single tracer

particle "xed at a certain radius on a rotating disk at

known rotation frequency. The results obtained by the

probe were in very good agreement with the calculated

ones, ($0.5%).

The method is independent of the physical properties

of the tracer particles such as size distribution, density,

and shape. The technique is also independent of the local

solids volume fractions in the range of 0}60 vol.%, but is

mainly designed for highly concentrated #ow systems.

A software program for simultaneous treatment of the

signals from all detectors has been developed. The pro-

gram calculates the tracer particle velocity vectors in two

dimensions based on successfully detected signals from at

least three sensors and the order of detection. It deter-

mines the bubble rise velocity based on measured timedelays at the front of the bubble. The bubble sizes are

determined based on the measured duration times and

the rise velocity. Bubble frequencies are determined from

the number of successfully measured bubbles.

The local solids volume fractions were determined

based on the background signals from uncoated particles

in the measuring volume.

The particle moving directions in the bed found to be

rapidly changing and are by no means parallel to the

column vertical axis. Thus, measurements of particle

velocity based on only two parallel detectors separated

with a certain distance as used by many investigators,may often lead to misleading results.

Notation

a coe$cient in the calibration function (Eq. (3))

C

solids volume fraction, Vol.%

d

averaged bubble diameter, m

h axial height from gas distributor in the bed, m

k exponent in the calibration function (Eq. (3))

I

incident light intensity, mW

l

bubble chord length, m

l

e! ective distance between detectors, m

l

geometric distance between detectors, m

r radius from the centre of the rotating disk, m

r

radial position in the bed, m

¹

averaged bubble passing time, s

u N

averaged bubble rise velocity, m/s

u

particle velocity, m/s

u

averaged (resultant) particle velocity, m/s

u

in-line component of the particle velocity, m/s

u

super"cial gas velocity, m/s

; measured signal intensity, V;

measured signal intensity at C"0, V

X distance between detectors in the probe, m


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x projected distance between detectors, m

t measured time delay, s

¹

measured time delay at front of the bubble, s

¹

measured time delay at tail of the bubble, s

Greek letters

direction angle of the velocity vector rotation frequency, s

References

Amos, G., Rhodes, M.J., & Benkreira, H. (1996). Calculation of optic

"bre calibration curves for the measurement of solids volume frac-

tions in multiphase #ows. Powder ¹echnol., 88, 107}121.

Arastoopour, H., & Yang, Y. (1992). Experimental studies on dilute gas

and cohesive particle #ow behavior using Laser Doppler Anemo-

meter. In O.E. Potter, & D.J. Nicklin (Eds.), Fluidization vol.

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