Chemical Engineering Science 65 (2010) 5447–5454

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Experimental study on solids concentration distribution in atwo-dimensional circulating fluidized bed

Jing Xu, J.-X Zhu n

Particle Technology Research Centre, Department of Chemical & Biochemical Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9

a r t i c l e i n f o

Article history:

Received 19 January 2010

Received in revised form

7 July 2010

Accepted 20 July 2010Available online 27 July 2010

Keywords:

Fluidization

Hydrodynamics

2-D CFB

Riser geometry

Scale-up

Solids holdup

09/$ - see front matter & 2010 Elsevier Ltd. A

016/j.ces.2010.07.015

esponding author. Tel.: +1 519 661 3807; fax

ail addresses: jzhu@uwo.ca, zhu@uwo.ca (J.-X

a b s t r a c t

The axial and lateral solids holdup profiles in a 2-D circulating fluidized bed (CFB) were measured with

an optical fibre probe under a wide range of operating conditions. The CFB is 7.6 m in height and has a

19�114 mm2 narrow cross-section riser. The results showed that the operating conditions influence

the flow structure significantly and control the flow in the same manner as that in cylindrical risers. The

solids had lower concentrations at the riser centre than the near wall region. Compared with data from

cylindrical columns, the axial and lateral profiles of solids holdup in 2-D riser had a similar pattern in

shape, but were more uniform. The geometry of the riser was found to be an important factor that

affects the solids distribution due to differences in terms of the perimeter per unit cross-sectional area

and the wall-to-centre distance. To some extent, the two-dimensional and three-dimensional risers are

more comparable under fast fluidization conditions. Generally, the solids distributions along the axial

and the lateral directions in 2-D riser were dissimilar to those in cylindrical risers, while the main

differences have been discussed in the current study.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Circulating fluidized bed (CFB) reactors have been used for awide range of industrial applications over the past 50 years.Hydrodynamics of gas–solid two-phase flow, which often dictatesmass transfer, heat transfer, gas and solids residence timedistribution and mixing, as well as extent of chemical reaction,plays a crucial role in defining the performance and applicationsof CFB reactors. This has led to a significant number of scientificstudies focused on the behavior of gas–solid two-phase flows inrisers of different sizes and shapes, operated under a variety ofconditions. Axial and radial voidage distributions (Bai et al., 1996,1992; Zhu et al., 1997; Bi et al., 1993; Liu et al., 2003a), gas andparticle velocity profiles (Yang et al., 1991; Parssinen and Zhu,2001a), differential pressure profiles (Schlichthaerle and Werther,1999; Bi, 2007), and gas–solids mixing (Mostoufi and Chaouki,2001) as well have been investigated. However, some issues suchas the influence of particle properties, gas–solids contact, solidssegregation, the size and velocity of clusters and the developmentof clusters are still unclear.

The solids concentration, particle velocity, and the correspond-ing solids flux are considered as the main parameters ofcharacterizing the two phase hydrodynamic flow structures. Moststudies on solids distribution were conducted by measuring the

ll rights reserved.

: +1 519 850 2441.

. Zhu).

axial profiles of pressure gradient. Although this method isreliable and easy to apply, it is too basic and incapable ofobtaining local solids concentration and other quantities. Reflec-tive-type optical fibre probe, a type of intrusive technique,overcomes these drawbacks and has been shown to be aneffective tool in measuring the local solids holdup and particlevelocity in the riser by a number of researchers (Liu et al., 2003a,2003b; Parssinen and Zhu, 2001a, 2001b; Zhang et al., 1998;Issangya et al., 1999). These probes, whose tips may be eithersingle- or multi-fibre type, emit light to illuminate a small volumeof particles passing by the probe tips and detect the reflectedlight intensity with electrical impulses output. They are goodfor local properties, effective under a wide range of condi-tions, and applicable for most powder types in both gas andliquid media measurements. Additionally, they are nearly freefrom interference of extreme temperatures, humidity, electro-statics and electromagnetic fields, etc. (Zhang et al., 1998).

Measurements with optical fibre probes provide local solidsconcentration and particle velocity to the data can be used toobtain overall profiles by integrating the local values. However,the measuring volume at the probe tip is limited and decreases asthe solids concentration increases. It is difficult to obtain particlevelocity components in directions other than the vertical. Inaddition, the probe’s intrusion into the column causes disturbanceto the flow field, the amount of which can be barely quantified.Optical fibre probes can be made small in size, which makes theirflow interference less than that caused by most other types ofintrusive probes.

Windbox

Bag filter

Downer

19 m

m

114 mm

Steam

Air

Cyclone

Riser

Fig. 1. Narrow rectangular circulating fluidized bed unit.

0.75 inch (19 mm)Face wall

4.5 inch (114 mm)

Side wall

J. Xu, J.-X Zhu / Chemical Engineering Science 65 (2010) 5447–54545448

Visualization technique is a type of method that can providevaluable information on the governing mechanisms of solidsmixing and cluster development. It presents instantaneousmapping of solids distribution and particle velocity inside theriser. The technique not only focuses on the local values (Arenaet al., 1989), but also on the global quantities in the whole riser.However, due to the non-planar structure of three-dimensionalcolumns, it is difficult to view through the walls and toreconstruct a three-dimensional flow structure by analyzingtwo-dimensional images. Narrow rectangular transparent riserscircumvent this problem since they have two planar walls thateffectively ‘‘cut a slice’’ from the three-dimensional flow field toshow much clearer two-dimensional images. Also, the depth-to-width ratio of the riser is so small that the flow along the depthdirection can be ignored. It has been proved to be especially usefulas a means of qualitatively measuring the flow structure (Pallaresand Johnsson, 2006; Park et al., 2002; Arena et al., 1989). The flowproperties, such as solids concentration, particle velocity andcluster development, can be visually observed and photographedto derive both qualitative and quantitative details.

To some extent, the rectangular riser can be considered as atwo-dimensional column; since the width is considerably largerthan the depth, and the fluidized particles are confined in thenarrow gap between two flat transparent walls, which is usuallyin the range of 10–25 mm (Grace and Baeyens, 1986). However,there are some differences between the rectangular two-dimen-sional and the conventional three-dimensional fluidized beds. Thedifferences arising mainly from bubble properties have been wellstudied (Gera and Gautam, 1995; Zhou et al., 2007; Almendros-Ibanez et al., 2006; Fan, 1990). Most of the previous studies wereconducted in the 3-D cylindrical risers; some researchers havealso studied the flow structure in CFB riser of square cross-section.Zhou et al. (1994) used an optical fibre particle concentrationmeasuring system to carry out the voidage profiles and particlevelocity profiles in a square riser. They found that a core-annulusflow structure also existed in the circulating fluidized bed riser ofsquare cross-section. Though numerous investigations have beencarried out in 3-D risers, very few studies have been conducted intwo-dimensional fluidized beds under fast fluidization conditionsfor the gas velocities higher than 3 m/s (Bi et al., 1993).

A great number of previous investigations have been con-ducted on the hydrodynamics of circulating fluidized bedsystems. However, very few studies have investigated the effectof particle properties on the flow pattern in CFB risers. The currentproject aims at a comprehensive understanding of the effect ofparticle properties, including particle size and density, on the flowstructure through measurements with both an intrusive opticalfibre probe and a non-intrusive high-speed video camera. Thus,the narrow rectangular CFB risers offer in addition an opportunityto compare the two measurement techniques. Knowing the flowpatterns in this rectangular CFB and comparing it with three-dimensional bed results facilitate systematic understanding of theinfluences of particle properties. This study investigates the solidsconcentration measured by optical fibre probes in a rectangularCFB system, compares with the results in three-dimensionalcolumns, and discusses the influences of column geometry to theflow pattern as well.

(51 mm)

2.0 inch

Fig. 2. Schematic of the cross-section of the rectangular riser and the equivalent

cylindrical riser.

2. Experimental apparatus

The rectangular CFB system was designed and set up as shownin Fig. 1. The riser is 7.6 m with a rectangular cross-section, whichis 19�114 mm2 (0.75 in�4.5 in) and is equal to a 2-in-diametercylindrical riser column in cross-sectional area (see Fig. 2).Besides the riser, a storage vessel with 203 mm (8 in) i.d. and

1.5 m height is placed on top of a 38�203 mm2 (1.5 in�8 in)narrow rectangular downcomer, which is 6.9 m tall. A smallstream of air is introduced into the bottom of the downcomer toaerate the returning particles. FCC particles with a Sauter meandiameter of 67 mm and a particle density of 1884 kg/m3 wereused. The total solids inventory was approximately 70 kg, whichwas equivalent to the weight of 5 m solids in the downcomer. Theprimary air at ambient temperature and pressure was supplied tothe windbox located at the riser bottom, with a small stream of

0.00 0.05 0.10 0.15 0.20 0.250

1

2

3

4

5

6

7

100/5.0

150/3.5

150/5.0

200/3.5

200/5.0

200/8.0

Hei

ght f

rom

the

riser

bot

tom

, (m

)

Solids holdup, (-)

Gs (kg/m2s)/Ug(m/s)

Fig. 3. Axial solids holdup profile.

J. Xu, J.-X Zhu / Chemical Engineering Science 65 (2010) 5447–5454 5449

steam merged in to control the relative humidity of the gas fedinto the riser to be between 70% and 80%. This is considered as theoptimal value required to avoid misleading effects due toelectrostatic forces (Park et al., 2002). The gas fed into the riserwas monitored by a rotameter and a thermo-hygrometer. Thesolids circulation rate was measured by a device located in thestorage vessel at the top of the downcomer and dividesthe column into two halves with a central vertical plate. Twohalf butterfly valves are fixed at the top and the bottom of thetwo-half sections. By appropriately flipping the top valve to be 451to one half column, all the falling particles are induced to passthrough the other half column, which is sealed by the bottomvalve. Thus, all the particles are collected in one half column andincrease the packed bed height with time elapsing. A 20 cmdistance from the closed valve is marked with a line. Once theparticles’ bed surface passes the line, the accumulative time isrecorded. The solids circulation rate can then be obtainedknowing the time period for solids accumulation and the solidspacked volume.

The local solids concentrations were measured with a multi-fibre optical probe, PV6, developed by Institute of ProcessEngineering, Chinese Academy of Sciences. The 3.8 mm diameterprobe tip consists of two bundles of optical fibres, which arearranged precisely in a vertical line. Each of the bundles hasapproximately 8000 fibres, which have a uniform diameter of15 mm. Within the bundle, the fibres for light emitting andreceiving are in stagger alignment. The active area, where thefibres are located, is approximately 1�1 mm2. The optical probewas calibrated so that the solids concentration could be calculatedfrom the output voltage signal. Particle velocity was determinedthrough cross correlation. Details of the calibration process andvelocity calculation were elaborated in precursor’s works (Liuet al., 2003b; Zhang et al., 1998).

The solids concentrations were measured in the middle of theriser at 6 axial levels at H¼1.27, 2.29, 3.30, 4.32, 5.33 and 6.35 m,and 9 lateral locations at y/Y¼�0.98, �0.75, �0.50, �0.25, 0,0.25, 0.50, 0.75 and 0.98 on each axial level. Here, y/Y is thedimensionless distance from the riser axis and H is the heightfrom the riser distributor. In these experiments, the superficial gasvelocity and solids circulation rate were in the range 3.5–8 m/sand 50–200 kg/m2 s, respectively.

3. Results and discussion

The solids suspension in the 2-D riser was observed to bedilute with particles moving faster in the central region while amuch denser suspension with slower particles moving in thewall area. Almost all particles moved upward although some sliddownward at the side walls at high solids flux operating condi-tions. No solids buildup or solids downflow was observed on thefront and back faces. Qualitatively, this flow behavior in the 2-Driser seemed to resemble that observed in cylindrical CFB risers.Therefore, a 2-D riser can be an approximate representation of adiametral slice of a cylindrical riser.

3.1. Axial solids holdup profile

On each level, the cross-sectional average of solids holdupswas derived by averaging the local solids holdups measured at 9lateral positions. Fig. 3 compares the axial profiles of the meansolids holdups under different operating conditions. According toprevious studies (Bai et al., 1992; Adanez et al., 1994; Yan, 2004;Qi et al., 2008), three sections can be identified along the axialdirection in a CFB riser: a dense section at the bottom, a transitionsection in the middle and an upper dilute section. Issangya et al.,

(1999) using a 0.76 m diameter, found that the dense phase startsfrom the bottom of the riser when the solids circulation rateexceeds about 75 kg/m2 s under the superficial gas velocity of6.0 m/s. However, in this study there was no distinct densesection at the riser bottom until the solids circulation rate reached200 kg/m2 s, and there was also no significant inflection betweenthe transition regime in the middle and the upper dilute sections.Therefore, in the riser of the current study, the axial profiles weremore uniform in the whole riser. This may be attributed to thesmall column with 2-in-equivalent diameter that resulted infaster development of the axial flow. Furthermore, the largerperimeter per unit cross-sectional area of the riser might be themain reason for the faster flow development in the smallerdiameter riser (Grace, 1996; Yan et al., 2005). The details of theeffect of this factor on the flow are discussed in Section 3.3. Theinfluence from the operating condition was as expected, whereincreasing solids circulation rate increased the cross-sectionalaverage of solids holdup on each level and resulted in a steeperaxial distribution of solids holdup. As superficial gas velocityvaried from 3.5 to 8 m/s, the solids holdup increased, but nosignificant change of the shapes of the holdup profiles wasobserved.

3.2. Lateral solids holdup profile

Fig. 4 shows the lateral solids holdup profiles under differentoperating conditions at five axial levels. As studied by the otherresearchers, the lateral distribution of solids concentrationshowed a parabolic shape, which was relatively lower in the

-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.000.0

0.1

0.2

0.0

0.1

0.2

0.0

0.1

0.2

0.0

0.1

0.2

0.0

0.1

0.2

0.3

Sol

ids

hold

up (-

)

Lateral position y/Y (-)

Z = 1.27 m

Z = 2.29 m

Z = 3.30 m

Z = 5.33 m

Z = 6.34 m

3.55.08.0

Gs = 200 kg/m2.s

Ug (m/s)

Fig. 4. The influence of superficial gas velocity on the lateral solids holdup

distribution.

0.0

0.1

0.2

0.0

0.1

0.2

0.0

0.1

0.2

0.0-1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00

0.1

0.2

0.0

0.1

0.2

0.3

H = 3.30 m

H = 2.29 m

H = 5.33 m

Solid

s hol

dup

(-)

Lateral position y/Y (-)

H = 1.27 m

H = 6.34 m

50 100 200Ug = 5.0 m/s

Gs(kg/m2⋅s)

Fig. 5. The influence of solids circulation rate on the lateral solids holdup

distribution.

J. Xu, J.-X Zhu / Chemical Engineering Science 65 (2010) 5447–54545450

centre of the riser and higher near the side walls. Under thesame operating condition, the near-wall solids concentration atthe lower section of the riser was higher than that at theupper section, and presented steeper curves. Reducing super-ficial gas velocity, Ug, led to an increased solids concentration andan increased concentration gradient. Moreover, Ug influencedthe solids concentration not only in the close-to-wall region butalso in the centre of the riser. For example, as shown in Fig. 4,when the superficial gas velocity increased from 3.5 to 8 m/s, theaverage solids holdup decreased in the centre region on eachlongitudinal level and dropped more significantly in the wall area.The solids distributed less uniformly at the lower superficial gasvelocity. The influence of Ug played important roles in changingsolids distribution along the lateral and axial direction.

Fig. 5 shows the impact of the solids circulation rate, Gs,on the lateral distribution of solids holdup. Increasing solidscirculation rate (or solids flux) resulted in a higher average solidsconcentration with a less uniform profile. Under high solids fluxconditions, the effects of the walls are more confined to the nearwall region, generating an increased concentration gradient.Lower Gs made the solids holdup distribution more even withlower local concentration at each lateral position. Moreover,under the same Gs, the solids holdup distribution became moreuniform as the axial height increased.

3.3. Comparison between different risers

3.3.1. Geometries and dimensions of different risers

‘‘Two-dimensional’’ columns are considered as an effectiveway of viewing the flow patterns in a rectangular cross-section

where the width is considerably greater than the depth. There are,however, quantitative differences between two- and three-dimensional fluidized beds (Grace and Baeyens, 1986). It is ofgreat importance to understand these differences for the futureinvestigation of particle properties in this experimental appara-tus. Any comparison between the results obtained from therectangular riser and other researchers’ data must be based on thesame reference basis.

Table 1 shows the dimensions of the current riser and someother CFB risers reported in the literature. Compared to the riserused in this study, riser Nos. 3 and 5 are 3 and 8 in (0.076 and0.203 m) diameter cylindrical risers investigated by Yan (2004)and Qi et al. (2008), respectively. Riser No. 2 is an imaginativecolumn that has a 2-in-equivalent diameter calculated accordingto the equation for transfer of area, De ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffi4Ar=p

p. The cross-

sectional area of the current 2-D riser is equivalent to the 2-in-diameter cylindrical column, but has a much larger perimeter perunit cross-section (see Fig. 2). For the four cylindrical columns, asthe diameter increases, the specific surface area decreases,indicating less surface area is in contact with the particles andmore particles may be present on the same wall surface.

3.3.2. Axial and lateral profile of solids holdups

Two typical conditions were selected to compare the profilesof solids holdup in the narrow rectangular riser and in thecylindrical risers studied by the other researchers. It was assumedthat the hydrodynamic flow conditions were symmetrical overthe column cross-section, although this assumption was notnecessarily valid in the entrance region near the distributor and

Table 1Dimensions of risers.

No. Riser name Riser geometry Dr (in) Area equivalent diameter

De ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffi4Ar=p

p(in)

Perimeter per unit cross-sectional

area PA (in/in2)

1 Current riser Rectangular 0.75�4.5 2 3.1

2 Equivalent riser Cylindrical 2 2 2

3 Yan (2004) Cylindrical 3 3 1.3

4 Qi’s (2008) Cylindrical 4 4 1.0

5 Yan (2004) Cylindrical 8 8 0.5

0.000.0 0.2 0.4 0.6 0.8 1.0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Solid

s hol

dup,

(-)

Dr(inch) This study Yan, 2004 Qi, 2008 Yan, 2004 Anticipated

Lateral position y/Y, (-)

--------

H(m) Ug(m/s) Gs(kg/m3.s)23

84

2

5.335.90

5.846.34

NA

5.05.55.55.55.5

100100

100108

100

Fig. 6. Comparison of lateral/radial solids holdup profiles of different bed column

structure. 0.000.0 0.2 0.4 0.6 0.8 1.0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Wall region

This study Yan, 2004 Qi, 2008 Anticipated

Solid

s hol

dup,

(-)

Lateral position y/Y, (-)

Centre region

2-D CFB

Equivalent 3-D CFB

y/Y =0.75

-------

Dr(inch) H(m) Ug(m/s) Gs(kg/m3.s)

2342

5.335.906.34NA

5.05.55.55.5

200200201200

Fig. 7. Comparison of lateral/radial solids holdup profiles of different bed column

structure.

J. Xu, J.-X Zhu / Chemical Engineering Science 65 (2010) 5447–5454 5451

exit region. Figs. 6 and 7 show the lateral profiles of solids holdupin the developed region of the five risers listed in Table 1. Underboth operating conditions, the distribution curves of solids holdupwere concave parabolas: low in the centre of columns and highclose to the wall. For cylindrical risers Nos. 3–5, the local averagesolids concentration increased with increase in riser diameter.At the same solids circulation rate and superficial gas velocity, thesolids holdups in the centre region, where y/Yo0.5, were com-parable, but quite different near the walls. In Fig. 6, the solidsconcentration close to the walls of the 8-in riser was significantlyhigher than that in the smaller risers, while the 4-in riser has aslightly higher concentration than the 3-in one. Yan (2004) statedthat the scale-up effect is that the radial profiles of solidsconcentration of a large riser increase more sharply towards thewall than in a small riser. According to this conclusion, moreover,since in the centre of cylindrical risers the solids concentrationsare nearly the same (see Figs. 6 and 7), the profile of solids holdupfor riser No. 2, which has a 2 in diameter, is anticipated as thedash line shown in Fig. 7. The lateral solids distribution of thecurrent rectangular riser with an equivalent diameter of 2 in wasmuch flatter compared with that of the 2 in cylindrical riser,especially under higher solids flux conditions, as Fig. 7 shows. Thesolids holdup of the rectangular riser was higher than that ofcylindrical risers in the centre region but relatively lower closer tothe wall.

It appears from the results that two effects exist. One is thescale-up effect and the other is the influence of the column shape.The scale-up effect, according to the bed diameter, decreasesthe solids concentration as the bed diameter decreases, with therate of concentration decrease declining from the wall to thecentre. Consequently, the solids holdup in the rectangular riser is

supposed to be lower than that in the larger risers in each lateralposition and decreases more sharply from the wall to the centre.However, the dash lines in Figs. 6 and 7 predicted by the rule ofthe scale-up effect are incapable of predicting the solids holdupprofile in the rectangular riser with 2-in-equivalent diameter.Therefore, the effect of riser structure impacts the solids holdup ina different way from the scale-up effect, flattening the lateraldistribution of solids concentration by increasing the solidsholdup in the column centre while reducing it close to the wall.

Fig. 8 shows the comparison of typical axial profiles of solidsholdup and the corresponding lateral profiles for Nos.1, 3 and 5risers with 2-in-equivalent, 3-in and 8-in diameter, respectively.The operating conditions for the 3-in and 8-in diameter riserswere Ug¼5.5 m/s and Gs¼100 kg/m2s, and Ug¼5.0 m/s andGs¼100 kg/m2s for the 2-in-equivalent diameter riser. The axialsolids holdup profiles were slightly higher in the bottom sectionsthan that in the upper sections. The two small risers had a lowercross-sectional average of solids holdup than larger risers at eachaxial location. In conformity with the axial profiles of solidsholdup, the lateral distribution of solids concentrations wasdecreasing longitudinally from the riser bottom to its top andmore uniform in the upper sections. Comparing among the threerisers, it can be found that the solids holdups and their near-wallgradients increased with riser size, at each longitudinal level.Fig. 8 also shows that the 2-in-equivalent diameter riser hadmuch more uniform lateral profiles of solids holdup than thethree-dimensional risers. In the centre region, these profiles were

0.00 0.25 0.50 0.75 1.000.000.050.100.150.200.250.000.050.100.150.200.250.000.050.100.150.200.250.000.050.100.150.200.250.30

Lateral position, (r/R)

H = 1.27m

H = 2.29m

H = 4.32m

H = 6.35m

Solid

s hol

dup,

(-)

0.00 0.25 0.50 0.75 1.000.000.050.100.150.200.250.000.050.100.150.200.250.000.050.100.150.200.250.000.050.100.150.200.250.30

H = 1.53m

Solid

s hol

dup,

(-)

Radial position, (r/R)

H = 2.73m

H = 3.96m

H = 5.90m

0.00 0.25 0.50 0.75 1.000.000.050.100.150.200.250.000.050.100.150.200.250.000.050.100.150.200.250.000.050.100.150.200.250.30

H = 1.47mSo

lids h

oldu

p, (-

)

Radial position, (r/R)

H = 2.69m

H = 3.91m

H = 5.84m

0.00 0.05 0.10 0.150

2

4

6

8

10

De = 2 inch Dr = 3 inch Dr = 8 inch

Hei

ght f

rom

the

riser

bot

tom

, (m

)

Solids holdup, (-)

De = 2 inchGs = 100 kg/m2sUg = 5.0 m/s

Dr = 3 inchGs = 100 kg/m2sUg = 5.5 m/s

Dr = 8 inchGs = 100 kg/m2sUg = 5.5 m/s

Fig. 8. Comparison of axial and radial solids holdup distributions in different size riser.

J. Xu, J.-X Zhu / Chemical Engineering Science 65 (2010) 5447–54545452

higher than those in the 3-in riser and even in the 8-in riser, whilemuch lower in the close-to-wall region.

The causes for this unusual distribution of solids holdup in thecurrent 2-D riser are summarized into two effects: scale-up effectand the column shape effect. The perimeter per unit cross-sectional area (PA) is an important factor contributing significantlyto the two effects mentioned above and mainly affects the solidsdistribution on the surface wall. In larger columns, there will becomparatively less wall surface area available for the particlesbuildup and more particles move slowly, downwards, or stag-nantly to accumulate on the wall surface to increase wallcoverage. Consequently, the cross-sectional average of solidsholdup is higher as the riser size increases even under the samesolids circulation rate. This also agrees with the axial and lateralprofiles of solids holdup. From Table 1, it can be seen that PA for2-in-equivalent diameter, 3-in and 8-in risers are 3.1, 1.3 and0.5 in/in2, respectively. As such, the area of the wall surface perunit sectional area is much greater in current narrow rectangularriser than in 8-in cylindrical riser. Thus, with specified solidscirculation rate and gas velocity, the axial solids holdup increaseswith riser size, so does the lateral solids holdup. As a result, theperimeter per unit cross-sectional area is the main reason for thelow solids accumulation on the wall and the reduction ofthe solids holdup closer to the wall in the 2-D riser.

From the other aspect, the distance between the wall and theriser centre also plays an important role in determining thedistribution of solids holdup, especially in the centre region ofthe riser. The average velocity of the gas is related with thedistance between the wall and the centre. Due to the wall friction,a boundary layer forms near the walls, where the gas velocity isslower than that in the centre. Yan (2004) also stated that, underthe same superficial gas velocity and solids circulation rate, thegreater the distance between the wall and the centre, the biggerthe difference between the gas speeds in these two regions. For

the rectangular column, the two face walls are so close to eachother that there is no significant difference between the gasvelocities near the face walls and in the centre. Following the gas,the particles near the face walls move as fast as those in thecentre. As a result, the solids tend not to cling to the face walls butto distribute uniformly along the depth direction. For the sidewalls, though they are farther from the wall to the centre of thecolumn, their area is so small that the amount of contactingparticles is small as well. Therefore, the rectangular geometryleads to a uniform distribution of the solids concentration in theriser column along the width direction.

3.3.3. One-dimensional slip velocity

Slip velocity, defined as Uslip¼Ug�Vp, reflects the interactionbetween gas and solids and is a main factor influencing masstransfer, momentum transfer and chemical reactions. One-dimensional slip velocity equals the cross-sectional average ofthe slip velocity, defined as the average gas velocity Ug/(1�es),minus the average particle velocity Gs/(esrs). It has been foundthat the one-dimensional slip velocity, which is considered as anessential design parameter, is caused by clustering, and is anindicator of the degree of particle aggregation and flow develop-ment. So, comparisons of one-dimensional slip velocities betweendifferent risers are important for an in-depth understanding of theeffects of riser geometry (Yan et al., 2005; Yang et al., 1992, 1993).

Fig. 9 shows the one-dimensional slip velocity in current rect-angular riser and in the 3- and 8-in risers under different operat-ing conditions. It was found that the one-dimensional slip velocitywas comparatively high at the riser bottom and decreasesgradually towards the top of the riser for all three risers. Highergas velocity resulted in higher slip velocity, while Gs does not havesignificant effects.

0

2

4

6

8

10

0

2

4

6

8

10

00 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9

2

4

6

8

10

0

2

4

6

8

10

100/5.5100/8.0200/5.5

Dr=3 inch

Gs(kg/m2s) /Ug (m/s)

De=2 inch100/5.0150/5.0200/5.0200/8.0

100/5.5100/8.0

Dr=8 inch

One

-dim

ensi

onal

slip

vel

ocity

, (m

/s)

Height from the riser bottom, (m)

De= 2 inch 100/5.0

Dr = 3 inch 100/5.5Dr= 8 inch 100/5.5

Fig. 9. Profiles of one-dimensional slip velocity for three risers.

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Fig. 9 shows the one-dimensional slip velocity decreased alongthe height with different slopes, which reflected the flow develop-ment along the risers. It is also shown that higher slip velocity isencountered in the larger diameter riser. As mentioned above, in thelarger riser, the cross-sectional solids holdup is higher since moreparticles accumulate on the surface walls, which increases thetendency of solids aggregation. As a result, larger and more frequentsolids aggregations decrease the effective drag between the gas andthe particles, and generate higher slip velocity. It is observed that theshapes of the slip velocity profiles for rectangular riser and thecylindrical risers are similar. However, the decreasing section of slipvelocity in the current rectangular riser was shorter than in 3- and 8-in risers, which means the flow development is faster in 2-in-equivalent diameter riser. Also observed is that the slip velocity inthe current riser is smaller than in the other two risers, implying lessaggregation in the riser of the current study.

4. Conclusions

Solids distribution was studied in a rectangular riser operatedunder a wide range of conditions. Both axial and lateral profiles ofsolids holdup show that the operating conditions play importantroles in influencing the flow structure, and control the flowproperties in the rectangular riser in the same way as that incylindrical risers: increasing Ug and reducing Gs result in a lowersolids holdup. The solids concentration profile, within the rangeof this study, remains low at the riser centre throughout thewhole riser compared with the solids holdup in the wall region.Comparing the rectangular riser with the other cylindricalcolumns, it is found that the general shapes of the axial andlateral profile of solids holdup in rectangular riser are quitesimilar to that in cylindrical risers, but more uniform. It isconcluded that the geometry of the riser is a factor that affects thesolids distribution due to differences in terms of the perimeter perunit cross-sectional area and the distance from the wall to thecentre. These two factors result in the more uniform lateral and

axial distributions of solids holdup in the rectangular riser thanthose in three-dimensional cylindrical risers. It is reasonable tostudy the scale-up effect by comparing the perimeter per unitcross-sectional area between different risers. The larger PA valueresults in lower solids holdup on the side walls and less particlesaggregation in a rectangular riser. The distance between the facewalls and the centre of the rectangular riser is a factorcontributing to the uniform solids distribution along the depthdirection and is the main reason for the higher solids holdup inthe centre. To some extent, the two-dimensional and three-dimensional risers are more comparable under fast fluidizationconditions since the factors from bubbles have been lessened.Generally, the solids distributions along the axial and the lateraldirections in rectangular riser are different from those in cylind-rical risers, with the main differences having been discussed inthis paper. Therefore, it is reasonable to investigate the effects ofparticle properties on the hydrodynamics of gas–solid flows in theCFB using a rectangular riser.

Nomenclature

Ar cross-section area of riser (m2 or in2)De area equivalent riser diameter (m or in)Dr riser diameter (m or in)Gs solids circulation rate (kg/m2 s)H height from the riser bottom (m)PA perimeter per unit cross-sectional area (m/m2 or in/in2)r lateral distance from riser axis (m)R radius of riser (m)Ug superficial gas velocity (m/s)Uslip slip velocity (m/s)Vp particle velocity (m/s)y lateral distance from riser axis (m)Y lateral distance between riser axis and wall (m)es local solids holdup (dimensionless)rs particle density (kg/m3)

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