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Profiles of particle velocity and solids fraction in a high-density riser
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Powder Technology 100 (1998) 183-189
Profiles of particle velocity and solids fraction in a high-density riser Fei Wei *, Hongfei Lin, Yi Cheng, Zhanwen Wang, Yong Jin Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
Received 4 December 1997; received in revised form 6 May 1998
Abstract
Radial profiles of particle velocity and solids fraction in a high density circulating fluidized bed (HDCFB) at average cross-sectional solids fraction up to 0.21 were measured by an improved optical fiber laser doppler velocimeter and an optical fiber density sensor. The axial development of these radial profiles and the influence of operating conditions on the profiles were examined. The results showed that similar radial profiles of solids fraction exist in the HDCFB. The following Boltzman function can correlate well the solids fraction profile: ( 1 - 8) / ( 1 - e) = 2.2 - (2) / ( 1 + exp( 10' r/R - 7.665) ). The radial profiles of particle velocity in HDCFB can also be described by the Boltzman function, that is, (Vp)/(Ug) = (2.7)/( 1 +exp( 1 0 - r / R - 1 0 . : g o ) - 0.2). The Boltzman profiles of particle velocity in the high density operating regime was different with the parabolic shape operating in dilute phase regime. The local particle fluctuation velocity in the center of the riser increases with average solids concentration, while the fluctuation velocity decreases sharply as the radial position near the wall. © 1998 Elsevier Science S.A. All rights reserved. Keywords: High density; Circulating fluidized bed; Particle velocity; Solids fraction
I. I n t r o d u c t i o n
Gas-solids circulating fluidized beds (CFBs) have been widely used in many process industries as chemical reactors. A high-density CFB (HDCFB) is one in which the solids circulation rate reaches a saturated state and a dense region exists at the bottom region of the riser [ 9 ]. At the high density operating regime, the 'S' shape axial voidage profile can be found in the riser. It can be operated at much higher average solids concentration than that of conventional CFB. Its high bed density, high heat and mass transfer rate and large throughput of solids will enlarge the applications of HDCFB reactors to many chemical processes with moderate and slow reactions [7]. Furthermore, many commercial applications of CFB require high bed density to adapt to their special needs. Although numerous studies have been performed in the past on CFBs, the studies were focused on the low density CFB, corresponding to the operating conditions of coal combustion and alumina calcination. Studies on the hydrodynamics of CFB at relative high solids concentration and high solids flux are clearly lagging behind the industry need [ 1 ]. Recently, our research on the radial profiles of solids mass * Corresponding author. Tel.: +86-10-6278-5464; Fax: +86-10-62770304; E-mail: [email protected]
flUX in HDCFB, showed that the profiles can be divided into three regimes according to the shape of the profiles [7]. Due to the very complex hydrodynamics of the systems, sigmficant difficulties are encountered in measuring local fluid mechanic properties in a dense gas-solid suspension. An advance in local hydrodynamics measurement such as nonintrusive measurement of particle velocity, gas velocity and slip velocity as well as local solids fraction in a high-density riser is critical for understanding and developing predictive models for gas-solid flow, especially when direct comparison between dense phase and dilute phase is made. The laser doppler velocimeter (LDV) is an advanced nonintnlsive measuring method for particle velocity and turbulent intensity. The particle velocity profiles in the dilute phase of the riser have been studied by Tsuji and Morikawa [4] using the LDV. They reported a parabolic shape profile with high particle velocities at the center of the riser. This profile has since been observed by others (e.g., Refs. [6,8] ). Unfortunately, this technique can only be used in the low solids fraction (solids fraction < 0.01, which depends on traversing length). As been pointed out by Soo et al. [ 3 ], measurements of particle velocity and turbulent intensity by the LDV in a dense gas-solid suspension have been hampered by the appearance of more than one particle in the collecting volume of the beams. Furthermore, it is difficult for a laser beam to penetrate the dense suspension in a non-intrusive way [ 6,8 ].
0032-5910/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PIIS0032-5910(98)00139-9
184
F. Wei et al. / Powder Technology I00 (1998) 183-189
Application of the LDV to a dense suspension remains undeveloped. In this study, an improvement has been made on the LDV which make it possible to measure local particle velocity at average solids fraction up to 0.21. In addition, detailed measurements of local solids fraction by an optical fiber density sensor will be presented in a 186 mm i.d. pilot scale CFB unit for several operating conditions in order to gain a better understanding of the hydrodynamic behaviors in the dense phase of the riser.
2. Experimental 2.1. Apparatus Main air F~rge air
A schematic diagram of the apparatus used in the experiments is shown in Fig. 1. The system consists of a riser (8 m in height and 186 mm in diameter), a downcomer (276 mm in diameter), a device for solids circulation rate measurement and gas/solids separation devices (including a rapid gas/ solids separator and a cyclone). All experiments were carded out at ambient temperature and pressure with air and FCC catalyst (d o = 54/zm, pp = 1398 kg/m3). The twelve radial positions ( r / R : 0, 0.215, 0.323, 0.430, 0.538, 0.645, 0.753, 0.807, 0.860, 0.914, 0.968, 1) and the six axial elevations: 1.5, 2.2, 2.5, 2.9, 5.1, 6.2 m above the gas distributor of the riser were chosen in measuring local particle velocity. Superficial gas velocity ranges from 2.3 to 6.2 m/s, average solids circulation rate is from 18 to 200 k g / m 2 s. 2.2. Particle velocity measurement
A backward scattering optical fiber LDV system (system 9100-8 model of TSI) was used to determine the local particle velocity. The laser source was 2 W Argon-Ion with a 15 m optical fiber. Table 1 shows the dimensions of the measuring volume. The LDV is an advanced tool for measuring particle velocity in a non-intrusive way at sufficiently dilute suspension. In the past, the LDV has only been able to measure gas and particle velocity at solids fraction less than 0.015 [4]. At dense gas solids suspension, there are two main problems in the measurement: ( 1 ) measurement of the velocity and intensity by the LDV has been hampered by the appearance of more than one particle in the collecting volume of the beams [4] ; and (2) the intensity of the laser beam and its scattered light decay in an exponential way with its penetration distance into the dense gas solids suspension, which worsens the signal-to-noise ratio of Doppler signal. For the first problem, the limitation of measurement largely depends on the measuring volume, V, and the number of particles in each cubic millimeter, Np. For the FCC particle, the average particle size is 54 I~m, and the measuring volume of the LDV is as small as the volume of three FCC particles. That is, the probability of finding one and only one particle
Fig. 1. Schematic diagram of experimental apparatus.
Table 1 Dimensionsof the measuringvolume Height of the measuring volume, de 2 (mm)
Width of the measuring volume, dm (mm)
Lengthof the measuring volume,Lm (mm)
The measuring volume, V ( mm3)
0.03
0.03
0.5l
2.5 X 10 - 4
in the measuring volume reaches the greatest value at the condition: V. Np = 1 or 1 - e = 0.33 for the FCC particle. In other words, for solids fraction less than 0.33 in the riser, there is no concern about more than one particle in the measuring volume. For the latter problem, reducing the distance between the measuring window and measuring volume will exponentially increase the intensity of the laser reaching the measuring volume as well as the scattering light in the measuring window as shown in Fig. 2. That will largely improve the signal to noise ratio of the LDV signal and make it possible to measure particle velocity in dense gas-solids suspension. Our LDV system is a backward scattering type, as shown in Fig. 2. Reducing the penetration distance of the laser beam in the dense suspension also reduces the penetration distance of scattered light and hence exponentially increases the intensity of the scattered light at the same time. The major improvements in out LDV system are shown in Fig. 2 and Table 2. The improw~d probe reduces the distance between the measuring volume and measuring window to 2 mm which cause Rccciv© ,~ transmit lens
old measuring window
new measuring window
La.~l
Fig. 2. Configurationof LDV measuringprobe.
F. Wei et al, / Powder Technology 100 (.!998) 183-189 Table 2 Dimension of the old and new probe Probe
Length of the probe L (mm)
Diameter of measuring window d (ram)
Distance between measuring window to measuring volume X (mm)
Old New
40 58
10 5
20 2
a disturbance of the flow field by the measuring window. In order to reduce this undesirable effect, the cross-sectional area of the measuring window is only one fourth of its original size. With this improvement, the new LDV system can measure the particle velocity at average solids fraction up to 0.21.
2.3. Solids fraction measurement The optical fiber density probe is the same as the one used by Tung et al. [5]. An improvement has been made to increase the stability of the instrument and to prevent any disturbance caused by the photomultiplier tube (PMT), as shown in Fig. 3. A double light legs system, a reference leg and a measuring leg, is used to reduce the effects of any PMT instability. Data acquisition system records the reference and measuring light signals from two PMT detectors at the same time. The ratio of the two signals, N, is chosen as the measured density signal. This improvement guarantees the deviation of the signal under 0.1% within 5 h. The measured density signal has a nonlinear relationship with local solids fraction. The following exponential function was used as the calibration function:
185
averaged bed voidage, the parameters of the calibration function can be determined by putting Eq. (1) into Eq. (2) and using the nonlinear regression method. The validation of Eq. ( 1 ) can be checked by the standard deviation of the measured average bed voidage and the predicted one by Eq. (2). It was found that Eq. (1) agrees well with the measured cross-sectionally averaged solids fraction in the range from 0.05 to 0.35. Details of the optical fiber density probe and probe calibration method have been reported elsewhere [ 5 ].
2.4. Validation of the measurement In order to check the validation of the improved LDV system, the radial profile of gas velocity in the empty riser was measured with the new probe using a very fine particle as tracer, as shown in Fig. 4. The measured velocity fits the 1/7 power law (the solids curve) perfectly showing that the improved LDV can precisely measure the gas velocity in a gas phase tube. Fig. 4 also shows the radial profiles of particle velocity in a very dilute phase by using both the improved probe and the old one. It can be seen that the measured particle velocities in the dilute phase by the two probes are almost the same. The average error for the two probes is less than 3%, which shows that the improved new probe has little influence on the flow field. To provide a check with respect to the measured radial profiles of particle velocity as well as solids fraction in dense suspension, the solids circulation rate Gs* calculated from Eq. (3) has been compared with the solids circulation rate G~ measured by measuring tank. R
1 - e = A . e x p ( N.B)
I
(1) G~*=
At the same time, the measured local solids fraction must meet the following cross-sectional mass balance of the riser: R
1 f 1- ~= _-S-L-712(1-e)Tr.r.dr 7rR J
(2)
0
Each experimental set measures the radial density signal profile and pressure gradient at the measuring plane. With a series of experimental sets under the different cross-sectional
"/TR 2
• 0
0
where 1 - e is the measured solids fraction. Fig. 5 shows the comparison between G~ measured by the measuring tank and G~* calculated by Eq. (3). It can be seen that the error is less than 5%. That is to say, the measured particle velocity and solids, fraction profiles are correct. 1.40
0.80
0.60 t~ l-e (m)
0.40
I
0.20
~
L.
Riserl
0.00
ql It
"; , "F'.'", 3,180.~06 n~ ~abe ./|
'
0.01 0.20 0.40 0.60 0.80 1.00 r/R
Fig. 3. Schematic diagram of double legs density sensor.
Fig. 4. Comp~u'ison the measured V~ between the new and old probe.
F. Wei et al. /Powder Technology100 (1998) 183-189
186 2O0
,
i
I
160 E
Fig. 7 shows the reduced solids fraction, the ratio of local solids fraction to cross-sectional average solids fraction plotted against r/R. The profiles of solids fraction under various operating conditions in the high density riser is unchanged. A similar radial profile of solids fraction can clearly be seen in the riser. Analysis of the experimental data measured at gas velocities from 2.0 to 10.5 m / s and solids flux from 30 to 180 k g / m 2 s shows that the radial profiles of the measured density are only a function of the cross-section averaged solids fraction and are not directly related to gas velocity and solids circulation rate no matter whether the measured plane is in the dense phase or in the dilute phase of the riser. The following Boltzman function can correlate the experimental data well:
,'"'"'""'.,..,... i
,
'
i
',
I
i ....
120
O
40 O0
40
80 Gs(exp),
120 160 kgt(n~ s)
200
Fig. 5. ComparisonbetweenG, calculatedby gp and measuredone. 0.20 0.15 0.10 0.05
1-e 2 -- =2.20.68< ~<0.95 1-e 1+exp(10.r/R-7.665)
S'00] Ug=3-ZSm/s
.=o~
[[ 6 0 0 ~ Gs =98" . . . . . . .
Thirty-five sets of experimental data at various gas velocities, solids circulation rates and measuring heights were used with the Mardquart non-linear parameter estimation method. Figs. 6 and 7 plot the comparison between the measured solids fraction (points) with the correlation predictions (curves). It is found that predictions of Eq. (4) shows good agreement with experimental data for a rather wide bed voidage range. The correlation strictly obeys the mass balance in Eq. (2). The average standard deviation is 8.3%.
z 0.20 "0 ~ 0.~ ~ 0.6O ~ 2.00 . . . . . . . .
11.40 0.20 0.~
0.70
0.0 0.2 0.4 0.6 0.8 1.0 r/R
(4)
0.80 0.90 1.0O Bed voidage
Fig. 6. Solids fractionprofilesat differentaxialpositions.
3.2. Axial development of the radial velocity profiles 3. R e s u l t s a n d d i s c u s s i o n
The axial development of the radial particle velocity profiles under the same operating conditions is shown in Fig. 8. In order to compare the shape of the particle velocity profiles under different operating conditions, Vp/Ug was plotted as a function of r/R. The local particle velocity has a maximum value at the axis and a rather flatter radial distribution near the center region. At the radial position around 0.4< r~ R<0.85, the particle velocity has a very steep velocity decrease as the radial position shifts towards the wall. When r/R is larger than 0.85, the particle flows downward. The flatter velocity zones in the axis and wall areas correspond to
3.1. Radial profiles of solids fraction in HDCFB Fig. 6 plots the radial solids fraction profiles at different axial positions. The three profiles show the difference between dense phase and dilute phase at the same superficial gas velocity and solids circulation rate. With the increase of cross-sectional bed density, the axial solids fraction distribution becomes non-uniform. The profiles of radial solids fraction between the dilute phase and the dense phase of the riser are similar. 2.5
,? -.
2.0
2.5
I
"/. ,?2o1.5
i
1.5
i
1,0
v
0.5
~
1
i
1
,
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.0
0.0 0.0
0.2
r/R
(a) Ug=4.57m/s Gs = 132kg/m2s H[m] : • 6.26 03.92 &2.31 E
0.6
0.4
0.8
#R
(b) Gs=120kg/m2s H=3.92m Ug[m/s]:A 3.44
O4.11
• 4.63
: • 0. 957 • 0. 934 • 0.760 ¢ : • 0.755 • 0. 779 • 0. 894 Fig. 7. Similarprofilesof solids fractionin HDCFB.
1.0
187
F. Wei et al. / Powder Technology 100 (1998) 183-189
3.0
(a)
3.0
(b)
2.~ 2.0
2.0
1.5 ~1.0
1.5
~1.0
0.5 0.0
0.0 i -0.5
0.0
'
I
0.2
~
I
,
I 0.6
0.4
i • 0.8
-0.5 0.0
•
~).957 I
0.2
,
5.1
I
,
0.4
• I
i
0.6
0.8
1.0
r/R
dR
Fig. 8. Radialprofilesof particlevelocityalongaxial position. the core and annulus region, and the steep velocity zone corresponds to the transition of the two regions. The shapes of these profiles are similar. As the elevation of the measuring plane moves from the bottom to the top of the riser, the average solids fraction changes from 0.211 to 0.04. The maximum and minimum particle velocities near the axis and near the wall region of the riser are unchanged. The area of low particle velocity region near the wall enlarges as the average solids fraction increases or axial elevation decreases. The downward particle flow exists in the measured elevations of the high density riser. The local solids fraction near the wall region of the riser increases linearly with average solids fraction, which thickens the annulus downflow region and shifts the downflow or low velocity region toward the core region. The shape of the particle velocity profile in an HDCFB changes little with changing average solids fraction, which reflects that the interaction of gas solids flow reaches its stable stage in the highdensity operating regime.
3.3. Influence of operation conditions on the radial profiles The influence of solids circulation rate, Gs, on the radial profiles of particle velocity is shown in Fig. 9. A clear change of the shape of radial Vp profiles occurs when the solids circulation rate reaches the saturated state in the riser and a dense region exists in the bottom of the riser (Gs = 47 kg/m 2 s at Ug=2.33 m/s, or G~= 167 kg/m 2 s at Ug=6.1 m/s). When Gs is lower than 47 kg/m 2 s at a superficial velocity of 2.33 m/s, the riser is in the dilute phase operating regime as shown by the dashed line and the particle velocity near the core region decreases with decreasing G~. On the contrary, the particle velocity near the wall increases with decreasing Gs. The particle velocity profile changes to a parabolic shape. At the same time, the particle velocity at the axis decreases from 2.5 times of superficial gas velocity to about 1.5 times. That is the radial particle velocity profile reported by Bader et al. [2] and Wang et al. [6]. Further decrease in solids
3.0
Ug = 2.33 m/$ H =2.9m
~
2.9AI
2.01
0,5
• •
47.6 0.o95 ~
40.6 0.033 4,51 0,002
\
•
~
~. ~
~
I
[ ", |
0.0
-0.50.0
0.2
0.4
r/R
0.6
0.8
1.0
Fig. 9. Influenceof G~on particlevelocityprofile. circulation rate causes the particle velocity profile to approach its extreme form: the 1/7 power law, which can only be obtained in the very dilute phase system. Fig. 10 shows the influence of superficial gas velocity on the ~radial particle velocity profile at the same solids circulation rate of 47 kg/m 2 s. At the superficial gas velocity of 2.34 m/s and G~=47 kg/m 2 s, the riser is in the high density regime, and the profiles of particle velocity can be described by the Boltzman function as shown by the solid line in Fig. 10. With increasing superficial gas velocity, the riser turns to the dilute phase operating regime, and the profiles change back to the parabolic shape, as shown by the dashed line in Fig. 10. At high superficial gas velocity of 6.13 m/s, when Gs reaches the high-density operating regime, the profile changes back to the Boltzman distribution again, as shown by dae solid line in Fig. 10. All of the 20 sets of our radial particle velocity profiles in HDCFB show that the following Boltzman function describes the profiles well: Vp/Ug=(Vmax-Vmin)/( l + e x p { ( r / R - X o ) / D x } + Vmin)
(5)
F. Wei et al. /Powder Technology100 (1998) 183-189
188 3.01
2.0 o) >
1.0-
.
u~ G6
.~ • 0.0 - X -O.E
0.0
-\
rn/s kg/rn2s '
3.22 47 0.975 4.25 47 0.984 6.13 167 0.923 ,
I
0.2
,
I
0.4
~',
~
,
:
"~lt
\
i
i
0.6
0.8
1.0 r/R Fig. 10. Effectof U~on particle velocity.
Twenty sets of experimental particle velocity profiles at various gas velocities, solids circulation rates and measuring heights were used with the Mardquart nonlinear parameter estimation method to obtain the parameters in the Boltzman function. Vmax, Vmi, are the initial and final value of the function, they unchanged by the operating conditions and have about the same value as Vo/Ug at the axis and wall of the riser. The regression result shows that Vm,, = 2.5, V m i n = - - 0.2. Xo stands for the center of the Boltzman function. It determines the radial position at which the radial gradient of the velocity profiles passes through zero. Xo can be expressed as a function of the average voidage as follows: X0=2.5 -
2 l+exp(20. ~-21.8)
X
(6)
D~ stands for the width of the Boltzman function. It represents the width of the particle velocity between steep change range. The regression result shows that Dx = 0.1, which is a constant parameter in our experimental conditions. The correlation of Vp/U~ can be expressed as follows: W= 2.7 -0.2 U~ l + e x p ( l O . r / R - l O . X o )
tuation w,qocity profile is shown in Figs. 11 and 12. In the bottom of the riser where the average solids concentration is the highest, the fluctuation velocity at the axis reaches the highest value and has a rather flatter distribution along the radial direction in the center region. At r/R = 0.6, the fluctuation velocity has a steep decrease at the radial position towards the wall, although the local solids fraction is high near the wall. At the center region of the riser, the fluctuation velocity decreases with increasing the elevation of the riser or decreasing average solids fraction. The fluctuation velocity near the wall region is controlled by the distance to the wall. When the solids concentration is high, there exists a rather flatter profile in the center region and then a steep decrease towards the wall. The particle fluctuation velocity near the wall region is close to zero. The steep decreasing fluctuation velocity region enlarges as solids concentration increases. The decrease in particle fluctuation velocity near the wall reflects the existence of a bulk annulus dense solids downward flow. The turbulence of the dense region is much lower than that of the core region. The same trend also shows up in the results of Yang et al. [8] and Tsuji and Morikawa [4] for dilute gas solids suspension, although the fluctuation magnitude reported by them was lower than that from our study.
"~>" 2.[ ®
• 0,0
X,
Ug=6.09 m/s Gs=167 kg/rn' s
X
,
0958
5.1
:9631
6'21
0.2
0.0
0.4
~Y
~11(
,
0.6
,
~
0.8
1.0
r/R
Fig. 11. Particle fluctuationvelocityprofiles. (7)
Figs. ( 8 ) - ( 1 0 ) plot the comparison between the measured solids fraction with the correlation predictions. The solid curves represent predictions of Eq. (6) which show good agreement with experimental data. It must be pointed out that the correlation for Vp and the solids fraction only approximately obeys the mass balance of Eq. (3). The error of correlation within our experimental conditions is about 10%.
2.0
@
•
1.*,
1.0
3.4. Fluctuation of particle velocity in HDCFB 0.5 In the present study, the fluctuation of local particle velocity is also investigated. The root mean square (RMS) fluctuation of particle velocity reflects the turbulence of the local suspension flow, which represents the turbulent energy and is a key parameter in modeling of the riser. The RMS fluc-
•
0.0 0.0
4.25 0.984 1
I
I
I
0.2
0.4
0.6
0.8
1.0 dR Fig. 12. Effectof Ugon particle fluctuationvelocityprofiles.
F. Wei et al. / Powder Technology 100 (1998) 183-189
The high solids concentration, low particle velocity and low fluctuation of particle velocity near the wall region of the high density riser may cause the lateral solids and gas mixing decrease, which brings many disadvantages to use high density risers as reactors. In the reactor, the high solids concentration means high reaction rate, which requires high heat and mass transfer rate and extensive lateral gas and solids mixing. While the low values of particle velocity and fluctuation velocity in the dense region mean the heat and mass transfer rate may be very low. That causes the radial non-uniform of temperature and/or reactants/products concentrations in the high density riser. This may be the reason why downflow dense region has small heat transfer rate in the CFB boilers as reported by many investigators. More studies in the future should be focused on the method to improve radial concentration and velocity uniformity in the high density riser in order to put this reactor in to commercial use. At the same time, transfer and lateral mixing behaviours studies are also needed to show the influence of this non-uniformity on the reactions.
189
5. Nomenclature
A B
Parameter of the calibration in Eq. ( 1) Parameter of the calibration in Eq. ( 1) Width of the Boltzman function G~ Solids circulation rate measured by measuring tank (kg/m z s) Average solids flux calculated by Eq. (3) (kg/m 2 s) Gs • N Ratio of the Intensity of the reflection light to the reference light N~ Number of particles in 1 mm 3 F Radial position (m) R Radius of riser (m) Superficial gas velocity (m/s) Measuring volume (mm 3) V Vm~× The initial value of Boltzman function Vmio The final value of Boltzman function v. Local particle velocity (m/s) xo the zero point of Boltzman function Local voidage Pp Particle density (kg/m 3) Cross-sectional average bed voidage
4. Conclusions Acknowledgements
An improved LDV successfully measures local particle velocity and particle velocity fluctuation in a high density riser with solids fraction up to 0.21. The profiles of particle velocity are influenced by the operating regime of the riser as well as the superficial gas velocity. The local solids fraction is proportional to the cross-sectional averaged solids fraction. The radial profiles of solids fraction and particle velocity can be correlated very well by the Boltzman function. Radial profiles of the particle velocity, the particle fluctuation velocity and solids fraction in an HDCFB can be divided into the following parts. ( 1) Core region (r/R < 0.4): high particle velocity, high particle fluctuation velocity and low solids fraction, the velocity, fluctuation velocity and solids fraction vary little with radial position. (2) Steep velocity region (0.4 < r/R <0.85): which is a transition region from core to annulus, particle velocity and solids fraction undergo large radial changes in this region. (3) Annulus region (r/R>0.85): Particle velocity is slowly downward moving and changes little with operating conditions and radial position. Particle velocity fluctuation decreases markedly on reducing the distance to the wall. The solids fraction reaches its highest value and changes little with radial position.
This work is supported by the Chinese National Natural Science Foundation under contract number of 29725613 and Tsinghua University Foundation. References [ 1] H.T. Bi, J.X. Zhu, AIChE J. 39 (1993) 1272-1280. [2] R. Bader, J. Findlay, T.M. Knowlton, Gas/Solid Flow Patterns in a 30.5 cm Diameter Circulating Fluidized Bed, in: P. Basu, J.F. Large (Eds.), Circulating Fluidized Bed Technology II, Pergamon, 1988, p. 123. 13 ] S.L. Son, Slaughter, J.G. Plumpe, Particulate Science and Technology 12 (1994) 1. [4] Y. Tsuji, Y. Morikawa, J. Fluid Mech. 120 (1982) 385-4092. 15] Y. Tung, J. Li, M. Kwauk, Radial Voidage Profile in a Fast Fluidized Bed, Fluidization '88: Science and Technology, Science Press, Beijing, 1988. [6] Z.W. Wang, D.R. Bai, Y. Jin, Powder Technol. 70 (1992) 271. [7] F. Wei, F. Lu, Y. Jin, Z. Yu, Powder Technol. 92 (1997) 243. [ 8 ] Y.L. Yang, Y. Jin, Z.Q. Yu, J.X. Zhu, H.T. Bi, Local slip behavior in the circulating fluidized bed, AIChE Symp. Ser. 89 (296) (1993) 8190. [9] J. Li, Y. Tung, M. Kwauk, Method of Energy Minimization in MultiScale Modeling of Particle-Fluid Two-Phase Flow, in: P. Basu, J.F. Large (Eds.), Circulating Fluidized Bed Technology II, Pergamon, Toronto, pp. 89-103.
ltll
Powder Technology 100 (1998) 183-189
Profiles of particle velocity and solids fraction in a high-density riser Fei Wei *, Hongfei Lin, Yi Cheng, Zhanwen Wang, Yong Jin Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
Received 4 December 1997; received in revised form 6 May 1998
Abstract
Radial profiles of particle velocity and solids fraction in a high density circulating fluidized bed (HDCFB) at average cross-sectional solids fraction up to 0.21 were measured by an improved optical fiber laser doppler velocimeter and an optical fiber density sensor. The axial development of these radial profiles and the influence of operating conditions on the profiles were examined. The results showed that similar radial profiles of solids fraction exist in the HDCFB. The following Boltzman function can correlate well the solids fraction profile: ( 1 - 8) / ( 1 - e) = 2.2 - (2) / ( 1 + exp( 10' r/R - 7.665) ). The radial profiles of particle velocity in HDCFB can also be described by the Boltzman function, that is, (Vp)/(Ug) = (2.7)/( 1 +exp( 1 0 - r / R - 1 0 . : g o ) - 0.2). The Boltzman profiles of particle velocity in the high density operating regime was different with the parabolic shape operating in dilute phase regime. The local particle fluctuation velocity in the center of the riser increases with average solids concentration, while the fluctuation velocity decreases sharply as the radial position near the wall. © 1998 Elsevier Science S.A. All rights reserved. Keywords: High density; Circulating fluidized bed; Particle velocity; Solids fraction
I. I n t r o d u c t i o n
Gas-solids circulating fluidized beds (CFBs) have been widely used in many process industries as chemical reactors. A high-density CFB (HDCFB) is one in which the solids circulation rate reaches a saturated state and a dense region exists at the bottom region of the riser [ 9 ]. At the high density operating regime, the 'S' shape axial voidage profile can be found in the riser. It can be operated at much higher average solids concentration than that of conventional CFB. Its high bed density, high heat and mass transfer rate and large throughput of solids will enlarge the applications of HDCFB reactors to many chemical processes with moderate and slow reactions [7]. Furthermore, many commercial applications of CFB require high bed density to adapt to their special needs. Although numerous studies have been performed in the past on CFBs, the studies were focused on the low density CFB, corresponding to the operating conditions of coal combustion and alumina calcination. Studies on the hydrodynamics of CFB at relative high solids concentration and high solids flux are clearly lagging behind the industry need [ 1 ]. Recently, our research on the radial profiles of solids mass * Corresponding author. Tel.: +86-10-6278-5464; Fax: +86-10-62770304; E-mail: [email protected]
flUX in HDCFB, showed that the profiles can be divided into three regimes according to the shape of the profiles [7]. Due to the very complex hydrodynamics of the systems, sigmficant difficulties are encountered in measuring local fluid mechanic properties in a dense gas-solid suspension. An advance in local hydrodynamics measurement such as nonintrusive measurement of particle velocity, gas velocity and slip velocity as well as local solids fraction in a high-density riser is critical for understanding and developing predictive models for gas-solid flow, especially when direct comparison between dense phase and dilute phase is made. The laser doppler velocimeter (LDV) is an advanced nonintnlsive measuring method for particle velocity and turbulent intensity. The particle velocity profiles in the dilute phase of the riser have been studied by Tsuji and Morikawa [4] using the LDV. They reported a parabolic shape profile with high particle velocities at the center of the riser. This profile has since been observed by others (e.g., Refs. [6,8] ). Unfortunately, this technique can only be used in the low solids fraction (solids fraction < 0.01, which depends on traversing length). As been pointed out by Soo et al. [ 3 ], measurements of particle velocity and turbulent intensity by the LDV in a dense gas-solid suspension have been hampered by the appearance of more than one particle in the collecting volume of the beams. Furthermore, it is difficult for a laser beam to penetrate the dense suspension in a non-intrusive way [ 6,8 ].
0032-5910/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PIIS0032-5910(98)00139-9
184
F. Wei et al. / Powder Technology I00 (1998) 183-189
Application of the LDV to a dense suspension remains undeveloped. In this study, an improvement has been made on the LDV which make it possible to measure local particle velocity at average solids fraction up to 0.21. In addition, detailed measurements of local solids fraction by an optical fiber density sensor will be presented in a 186 mm i.d. pilot scale CFB unit for several operating conditions in order to gain a better understanding of the hydrodynamic behaviors in the dense phase of the riser.
2. Experimental 2.1. Apparatus Main air F~rge air
A schematic diagram of the apparatus used in the experiments is shown in Fig. 1. The system consists of a riser (8 m in height and 186 mm in diameter), a downcomer (276 mm in diameter), a device for solids circulation rate measurement and gas/solids separation devices (including a rapid gas/ solids separator and a cyclone). All experiments were carded out at ambient temperature and pressure with air and FCC catalyst (d o = 54/zm, pp = 1398 kg/m3). The twelve radial positions ( r / R : 0, 0.215, 0.323, 0.430, 0.538, 0.645, 0.753, 0.807, 0.860, 0.914, 0.968, 1) and the six axial elevations: 1.5, 2.2, 2.5, 2.9, 5.1, 6.2 m above the gas distributor of the riser were chosen in measuring local particle velocity. Superficial gas velocity ranges from 2.3 to 6.2 m/s, average solids circulation rate is from 18 to 200 k g / m 2 s. 2.2. Particle velocity measurement
A backward scattering optical fiber LDV system (system 9100-8 model of TSI) was used to determine the local particle velocity. The laser source was 2 W Argon-Ion with a 15 m optical fiber. Table 1 shows the dimensions of the measuring volume. The LDV is an advanced tool for measuring particle velocity in a non-intrusive way at sufficiently dilute suspension. In the past, the LDV has only been able to measure gas and particle velocity at solids fraction less than 0.015 [4]. At dense gas solids suspension, there are two main problems in the measurement: ( 1 ) measurement of the velocity and intensity by the LDV has been hampered by the appearance of more than one particle in the collecting volume of the beams [4] ; and (2) the intensity of the laser beam and its scattered light decay in an exponential way with its penetration distance into the dense gas solids suspension, which worsens the signal-to-noise ratio of Doppler signal. For the first problem, the limitation of measurement largely depends on the measuring volume, V, and the number of particles in each cubic millimeter, Np. For the FCC particle, the average particle size is 54 I~m, and the measuring volume of the LDV is as small as the volume of three FCC particles. That is, the probability of finding one and only one particle
Fig. 1. Schematic diagram of experimental apparatus.
Table 1 Dimensionsof the measuringvolume Height of the measuring volume, de 2 (mm)
Width of the measuring volume, dm (mm)
Lengthof the measuring volume,Lm (mm)
The measuring volume, V ( mm3)
0.03
0.03
0.5l
2.5 X 10 - 4
in the measuring volume reaches the greatest value at the condition: V. Np = 1 or 1 - e = 0.33 for the FCC particle. In other words, for solids fraction less than 0.33 in the riser, there is no concern about more than one particle in the measuring volume. For the latter problem, reducing the distance between the measuring window and measuring volume will exponentially increase the intensity of the laser reaching the measuring volume as well as the scattering light in the measuring window as shown in Fig. 2. That will largely improve the signal to noise ratio of the LDV signal and make it possible to measure particle velocity in dense gas-solids suspension. Our LDV system is a backward scattering type, as shown in Fig. 2. Reducing the penetration distance of the laser beam in the dense suspension also reduces the penetration distance of scattered light and hence exponentially increases the intensity of the scattered light at the same time. The major improvements in out LDV system are shown in Fig. 2 and Table 2. The improw~d probe reduces the distance between the measuring volume and measuring window to 2 mm which cause Rccciv© ,~ transmit lens
old measuring window
new measuring window
La.~l
Fig. 2. Configurationof LDV measuringprobe.
F. Wei et al, / Powder Technology 100 (.!998) 183-189 Table 2 Dimension of the old and new probe Probe
Length of the probe L (mm)
Diameter of measuring window d (ram)
Distance between measuring window to measuring volume X (mm)
Old New
40 58
10 5
20 2
a disturbance of the flow field by the measuring window. In order to reduce this undesirable effect, the cross-sectional area of the measuring window is only one fourth of its original size. With this improvement, the new LDV system can measure the particle velocity at average solids fraction up to 0.21.
2.3. Solids fraction measurement The optical fiber density probe is the same as the one used by Tung et al. [5]. An improvement has been made to increase the stability of the instrument and to prevent any disturbance caused by the photomultiplier tube (PMT), as shown in Fig. 3. A double light legs system, a reference leg and a measuring leg, is used to reduce the effects of any PMT instability. Data acquisition system records the reference and measuring light signals from two PMT detectors at the same time. The ratio of the two signals, N, is chosen as the measured density signal. This improvement guarantees the deviation of the signal under 0.1% within 5 h. The measured density signal has a nonlinear relationship with local solids fraction. The following exponential function was used as the calibration function:
185
averaged bed voidage, the parameters of the calibration function can be determined by putting Eq. (1) into Eq. (2) and using the nonlinear regression method. The validation of Eq. ( 1 ) can be checked by the standard deviation of the measured average bed voidage and the predicted one by Eq. (2). It was found that Eq. (1) agrees well with the measured cross-sectionally averaged solids fraction in the range from 0.05 to 0.35. Details of the optical fiber density probe and probe calibration method have been reported elsewhere [ 5 ].
2.4. Validation of the measurement In order to check the validation of the improved LDV system, the radial profile of gas velocity in the empty riser was measured with the new probe using a very fine particle as tracer, as shown in Fig. 4. The measured velocity fits the 1/7 power law (the solids curve) perfectly showing that the improved LDV can precisely measure the gas velocity in a gas phase tube. Fig. 4 also shows the radial profiles of particle velocity in a very dilute phase by using both the improved probe and the old one. It can be seen that the measured particle velocities in the dilute phase by the two probes are almost the same. The average error for the two probes is less than 3%, which shows that the improved new probe has little influence on the flow field. To provide a check with respect to the measured radial profiles of particle velocity as well as solids fraction in dense suspension, the solids circulation rate Gs* calculated from Eq. (3) has been compared with the solids circulation rate G~ measured by measuring tank. R
1 - e = A . e x p ( N.B)
I
(1) G~*=
At the same time, the measured local solids fraction must meet the following cross-sectional mass balance of the riser: R
1 f 1- ~= _-S-L-712(1-e)Tr.r.dr 7rR J
(2)
0
Each experimental set measures the radial density signal profile and pressure gradient at the measuring plane. With a series of experimental sets under the different cross-sectional
"/TR 2
• 0
0
where 1 - e is the measured solids fraction. Fig. 5 shows the comparison between G~ measured by the measuring tank and G~* calculated by Eq. (3). It can be seen that the error is less than 5%. That is to say, the measured particle velocity and solids, fraction profiles are correct. 1.40
0.80
0.60 t~ l-e (m)
0.40
I
0.20
~
L.
Riserl
0.00
ql It
"; , "F'.'", 3,180.~06 n~ ~abe ./|
'
0.01 0.20 0.40 0.60 0.80 1.00 r/R
Fig. 3. Schematic diagram of double legs density sensor.
Fig. 4. Comp~u'ison the measured V~ between the new and old probe.
F. Wei et al. /Powder Technology100 (1998) 183-189
186 2O0
,
i
I
160 E
Fig. 7 shows the reduced solids fraction, the ratio of local solids fraction to cross-sectional average solids fraction plotted against r/R. The profiles of solids fraction under various operating conditions in the high density riser is unchanged. A similar radial profile of solids fraction can clearly be seen in the riser. Analysis of the experimental data measured at gas velocities from 2.0 to 10.5 m / s and solids flux from 30 to 180 k g / m 2 s shows that the radial profiles of the measured density are only a function of the cross-section averaged solids fraction and are not directly related to gas velocity and solids circulation rate no matter whether the measured plane is in the dense phase or in the dilute phase of the riser. The following Boltzman function can correlate the experimental data well:
,'"'"'""'.,..,... i
,
'
i
',
I
i ....
120
O
40 O0
40
80 Gs(exp),
120 160 kgt(n~ s)
200
Fig. 5. ComparisonbetweenG, calculatedby gp and measuredone. 0.20 0.15 0.10 0.05
1-e 2 -- =2.20.68< ~<0.95 1-e 1+exp(10.r/R-7.665)
S'00] Ug=3-ZSm/s
.=o~
[[ 6 0 0 ~ Gs =98" . . . . . . .
Thirty-five sets of experimental data at various gas velocities, solids circulation rates and measuring heights were used with the Mardquart non-linear parameter estimation method. Figs. 6 and 7 plot the comparison between the measured solids fraction (points) with the correlation predictions (curves). It is found that predictions of Eq. (4) shows good agreement with experimental data for a rather wide bed voidage range. The correlation strictly obeys the mass balance in Eq. (2). The average standard deviation is 8.3%.
z 0.20 "0 ~ 0.~ ~ 0.6O ~ 2.00 . . . . . . . .
11.40 0.20 0.~
0.70
0.0 0.2 0.4 0.6 0.8 1.0 r/R
(4)
0.80 0.90 1.0O Bed voidage
Fig. 6. Solids fractionprofilesat differentaxialpositions.
3.2. Axial development of the radial velocity profiles 3. R e s u l t s a n d d i s c u s s i o n
The axial development of the radial particle velocity profiles under the same operating conditions is shown in Fig. 8. In order to compare the shape of the particle velocity profiles under different operating conditions, Vp/Ug was plotted as a function of r/R. The local particle velocity has a maximum value at the axis and a rather flatter radial distribution near the center region. At the radial position around 0.4< r~ R<0.85, the particle velocity has a very steep velocity decrease as the radial position shifts towards the wall. When r/R is larger than 0.85, the particle flows downward. The flatter velocity zones in the axis and wall areas correspond to
3.1. Radial profiles of solids fraction in HDCFB Fig. 6 plots the radial solids fraction profiles at different axial positions. The three profiles show the difference between dense phase and dilute phase at the same superficial gas velocity and solids circulation rate. With the increase of cross-sectional bed density, the axial solids fraction distribution becomes non-uniform. The profiles of radial solids fraction between the dilute phase and the dense phase of the riser are similar. 2.5
,? -.
2.0
2.5
I
"/. ,?2o1.5
i
1.5
i
1,0
v
0.5
~
1
i
1
,
0.5
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.0
0.0 0.0
0.2
r/R
(a) Ug=4.57m/s Gs = 132kg/m2s H[m] : • 6.26 03.92 &2.31 E
0.6
0.4
0.8
#R
(b) Gs=120kg/m2s H=3.92m Ug[m/s]:A 3.44
O4.11
• 4.63
: • 0. 957 • 0. 934 • 0.760 ¢ : • 0.755 • 0. 779 • 0. 894 Fig. 7. Similarprofilesof solids fractionin HDCFB.
1.0
187
F. Wei et al. / Powder Technology 100 (1998) 183-189
3.0
(a)
3.0
(b)
2.~ 2.0
2.0
1.5 ~1.0
1.5
~1.0
0.5 0.0
0.0 i -0.5
0.0
'
I
0.2
~
I
,
I 0.6
0.4
i • 0.8
-0.5 0.0
•
~).957 I
0.2
,
5.1
I
,
0.4
• I
i
0.6
0.8
1.0
r/R
dR
Fig. 8. Radialprofilesof particlevelocityalongaxial position. the core and annulus region, and the steep velocity zone corresponds to the transition of the two regions. The shapes of these profiles are similar. As the elevation of the measuring plane moves from the bottom to the top of the riser, the average solids fraction changes from 0.211 to 0.04. The maximum and minimum particle velocities near the axis and near the wall region of the riser are unchanged. The area of low particle velocity region near the wall enlarges as the average solids fraction increases or axial elevation decreases. The downward particle flow exists in the measured elevations of the high density riser. The local solids fraction near the wall region of the riser increases linearly with average solids fraction, which thickens the annulus downflow region and shifts the downflow or low velocity region toward the core region. The shape of the particle velocity profile in an HDCFB changes little with changing average solids fraction, which reflects that the interaction of gas solids flow reaches its stable stage in the highdensity operating regime.
3.3. Influence of operation conditions on the radial profiles The influence of solids circulation rate, Gs, on the radial profiles of particle velocity is shown in Fig. 9. A clear change of the shape of radial Vp profiles occurs when the solids circulation rate reaches the saturated state in the riser and a dense region exists in the bottom of the riser (Gs = 47 kg/m 2 s at Ug=2.33 m/s, or G~= 167 kg/m 2 s at Ug=6.1 m/s). When Gs is lower than 47 kg/m 2 s at a superficial velocity of 2.33 m/s, the riser is in the dilute phase operating regime as shown by the dashed line and the particle velocity near the core region decreases with decreasing G~. On the contrary, the particle velocity near the wall increases with decreasing Gs. The particle velocity profile changes to a parabolic shape. At the same time, the particle velocity at the axis decreases from 2.5 times of superficial gas velocity to about 1.5 times. That is the radial particle velocity profile reported by Bader et al. [2] and Wang et al. [6]. Further decrease in solids
3.0
Ug = 2.33 m/$ H =2.9m
~
2.9AI
2.01
0,5
• •
47.6 0.o95 ~
40.6 0.033 4,51 0,002
\
•
~
~. ~
~
I
[ ", |
0.0
-0.50.0
0.2
0.4
r/R
0.6
0.8
1.0
Fig. 9. Influenceof G~on particlevelocityprofile. circulation rate causes the particle velocity profile to approach its extreme form: the 1/7 power law, which can only be obtained in the very dilute phase system. Fig. 10 shows the influence of superficial gas velocity on the ~radial particle velocity profile at the same solids circulation rate of 47 kg/m 2 s. At the superficial gas velocity of 2.34 m/s and G~=47 kg/m 2 s, the riser is in the high density regime, and the profiles of particle velocity can be described by the Boltzman function as shown by the solid line in Fig. 10. With increasing superficial gas velocity, the riser turns to the dilute phase operating regime, and the profiles change back to the parabolic shape, as shown by the dashed line in Fig. 10. At high superficial gas velocity of 6.13 m/s, when Gs reaches the high-density operating regime, the profile changes back to the Boltzman distribution again, as shown by dae solid line in Fig. 10. All of the 20 sets of our radial particle velocity profiles in HDCFB show that the following Boltzman function describes the profiles well: Vp/Ug=(Vmax-Vmin)/( l + e x p { ( r / R - X o ) / D x } + Vmin)
(5)
F. Wei et al. /Powder Technology100 (1998) 183-189
188 3.01
2.0 o) >
1.0-
.
u~ G6
.~ • 0.0 - X -O.E
0.0
-\
rn/s kg/rn2s '
3.22 47 0.975 4.25 47 0.984 6.13 167 0.923 ,
I
0.2
,
I
0.4
~',
~
,
:
"~lt
\
i
i
0.6
0.8
1.0 r/R Fig. 10. Effectof U~on particle velocity.
Twenty sets of experimental particle velocity profiles at various gas velocities, solids circulation rates and measuring heights were used with the Mardquart nonlinear parameter estimation method to obtain the parameters in the Boltzman function. Vmax, Vmi, are the initial and final value of the function, they unchanged by the operating conditions and have about the same value as Vo/Ug at the axis and wall of the riser. The regression result shows that Vm,, = 2.5, V m i n = - - 0.2. Xo stands for the center of the Boltzman function. It determines the radial position at which the radial gradient of the velocity profiles passes through zero. Xo can be expressed as a function of the average voidage as follows: X0=2.5 -
2 l+exp(20. ~-21.8)
X
(6)
D~ stands for the width of the Boltzman function. It represents the width of the particle velocity between steep change range. The regression result shows that Dx = 0.1, which is a constant parameter in our experimental conditions. The correlation of Vp/U~ can be expressed as follows: W= 2.7 -0.2 U~ l + e x p ( l O . r / R - l O . X o )
tuation w,qocity profile is shown in Figs. 11 and 12. In the bottom of the riser where the average solids concentration is the highest, the fluctuation velocity at the axis reaches the highest value and has a rather flatter distribution along the radial direction in the center region. At r/R = 0.6, the fluctuation velocity has a steep decrease at the radial position towards the wall, although the local solids fraction is high near the wall. At the center region of the riser, the fluctuation velocity decreases with increasing the elevation of the riser or decreasing average solids fraction. The fluctuation velocity near the wall region is controlled by the distance to the wall. When the solids concentration is high, there exists a rather flatter profile in the center region and then a steep decrease towards the wall. The particle fluctuation velocity near the wall region is close to zero. The steep decreasing fluctuation velocity region enlarges as solids concentration increases. The decrease in particle fluctuation velocity near the wall reflects the existence of a bulk annulus dense solids downward flow. The turbulence of the dense region is much lower than that of the core region. The same trend also shows up in the results of Yang et al. [8] and Tsuji and Morikawa [4] for dilute gas solids suspension, although the fluctuation magnitude reported by them was lower than that from our study.
"~>" 2.[ ®
• 0,0
X,
Ug=6.09 m/s Gs=167 kg/rn' s
X
,
0958
5.1
:9631
6'21
0.2
0.0
0.4
~Y
~11(
,
0.6
,
~
0.8
1.0
r/R
Fig. 11. Particle fluctuationvelocityprofiles. (7)
Figs. ( 8 ) - ( 1 0 ) plot the comparison between the measured solids fraction with the correlation predictions. The solid curves represent predictions of Eq. (6) which show good agreement with experimental data. It must be pointed out that the correlation for Vp and the solids fraction only approximately obeys the mass balance of Eq. (3). The error of correlation within our experimental conditions is about 10%.
2.0
@
•
1.*,
1.0
3.4. Fluctuation of particle velocity in HDCFB 0.5 In the present study, the fluctuation of local particle velocity is also investigated. The root mean square (RMS) fluctuation of particle velocity reflects the turbulence of the local suspension flow, which represents the turbulent energy and is a key parameter in modeling of the riser. The RMS fluc-
•
0.0 0.0
4.25 0.984 1
I
I
I
0.2
0.4
0.6
0.8
1.0 dR Fig. 12. Effectof Ugon particle fluctuationvelocityprofiles.
F. Wei et al. / Powder Technology 100 (1998) 183-189
The high solids concentration, low particle velocity and low fluctuation of particle velocity near the wall region of the high density riser may cause the lateral solids and gas mixing decrease, which brings many disadvantages to use high density risers as reactors. In the reactor, the high solids concentration means high reaction rate, which requires high heat and mass transfer rate and extensive lateral gas and solids mixing. While the low values of particle velocity and fluctuation velocity in the dense region mean the heat and mass transfer rate may be very low. That causes the radial non-uniform of temperature and/or reactants/products concentrations in the high density riser. This may be the reason why downflow dense region has small heat transfer rate in the CFB boilers as reported by many investigators. More studies in the future should be focused on the method to improve radial concentration and velocity uniformity in the high density riser in order to put this reactor in to commercial use. At the same time, transfer and lateral mixing behaviours studies are also needed to show the influence of this non-uniformity on the reactions.
189
5. Nomenclature
A B
Parameter of the calibration in Eq. ( 1) Parameter of the calibration in Eq. ( 1) Width of the Boltzman function G~ Solids circulation rate measured by measuring tank (kg/m z s) Average solids flux calculated by Eq. (3) (kg/m 2 s) Gs • N Ratio of the Intensity of the reflection light to the reference light N~ Number of particles in 1 mm 3 F Radial position (m) R Radius of riser (m) Superficial gas velocity (m/s) Measuring volume (mm 3) V Vm~× The initial value of Boltzman function Vmio The final value of Boltzman function v. Local particle velocity (m/s) xo the zero point of Boltzman function Local voidage Pp Particle density (kg/m 3) Cross-sectional average bed voidage
4. Conclusions Acknowledgements
An improved LDV successfully measures local particle velocity and particle velocity fluctuation in a high density riser with solids fraction up to 0.21. The profiles of particle velocity are influenced by the operating regime of the riser as well as the superficial gas velocity. The local solids fraction is proportional to the cross-sectional averaged solids fraction. The radial profiles of solids fraction and particle velocity can be correlated very well by the Boltzman function. Radial profiles of the particle velocity, the particle fluctuation velocity and solids fraction in an HDCFB can be divided into the following parts. ( 1) Core region (r/R < 0.4): high particle velocity, high particle fluctuation velocity and low solids fraction, the velocity, fluctuation velocity and solids fraction vary little with radial position. (2) Steep velocity region (0.4 < r/R <0.85): which is a transition region from core to annulus, particle velocity and solids fraction undergo large radial changes in this region. (3) Annulus region (r/R>0.85): Particle velocity is slowly downward moving and changes little with operating conditions and radial position. Particle velocity fluctuation decreases markedly on reducing the distance to the wall. The solids fraction reaches its highest value and changes little with radial position.
This work is supported by the Chinese National Natural Science Foundation under contract number of 29725613 and Tsinghua University Foundation. References [ 1] H.T. Bi, J.X. Zhu, AIChE J. 39 (1993) 1272-1280. [2] R. Bader, J. Findlay, T.M. Knowlton, Gas/Solid Flow Patterns in a 30.5 cm Diameter Circulating Fluidized Bed, in: P. Basu, J.F. Large (Eds.), Circulating Fluidized Bed Technology II, Pergamon, 1988, p. 123. 13 ] S.L. Son, Slaughter, J.G. Plumpe, Particulate Science and Technology 12 (1994) 1. [4] Y. Tsuji, Y. Morikawa, J. Fluid Mech. 120 (1982) 385-4092. 15] Y. Tung, J. Li, M. Kwauk, Radial Voidage Profile in a Fast Fluidized Bed, Fluidization '88: Science and Technology, Science Press, Beijing, 1988. [6] Z.W. Wang, D.R. Bai, Y. Jin, Powder Technol. 70 (1992) 271. [7] F. Wei, F. Lu, Y. Jin, Z. Yu, Powder Technol. 92 (1997) 243. [ 8 ] Y.L. Yang, Y. Jin, Z.Q. Yu, J.X. Zhu, H.T. Bi, Local slip behavior in the circulating fluidized bed, AIChE Symp. Ser. 89 (296) (1993) 8190. [9] J. Li, Y. Tung, M. Kwauk, Method of Energy Minimization in MultiScale Modeling of Particle-Fluid Two-Phase Flow, in: P. Basu, J.F. Large (Eds.), Circulating Fluidized Bed Technology II, Pergamon, Toronto, pp. 89-103.