a comparison of flow dynamics and flow structure in a riser and a downer

Research Article

A Comparison of Flow Dynamics and FlowStructure in a Riser and a Downer

Flow development and flow dynamics were systematically investigated using localsolids concentration measurements in a pair consisting of a downer (0.1 m I.D.,9.3 m high) and a riser of the same diameter (0.1 m I.D., 15.1 m high). Both sta-tistical and chaos analysis were employed. Values for the Kolmogorov entropy(K), correlation dimension (D), and Hurst exponent (H) were estimated fromtime series of solids concentration measurements. Axial distributions of chaosparameters were more complex in the downer than those in the riser, especiallyin the entrance section. Flow in the downer was more uniform with a flatter corein all the radial profiles of chaos parameters. The radial profiles of K varied signif-icantly with increasing axial levels due to different clustering behavior in the wallregion of the downer. In both the riser and the downer, anti-persistent flow in thecore region and persistent flow behavior near the wall were identified from theprofiles of H. Different flow behavior in the region close to the wall in the downerand riser was characterized from the combination of the three chaos parameters.Relationships between chaos parameters and local time-averaged solids holdup inthe core and wall regions of the developed sections in both the downer and riserwere also analyzed.

Keywords: Circulating fluidized beds, Flow behavior, Reactors, Riser

Received: September 15, 2006; revised: December 18, 2006; accepted: January 3, 2007

DOI: 10.1002/ceat.200600281

1 Introduction

Cocurrent upflow circulating fluidized bed reactors (CFB ri-sers) have been extensively investigated [1, 2]. Riser reactorshave many industrial applications including fluid catalyticcracking, calcinations, Fischer-Tropsch synthesis and combus-tion. CFB risers have many advantages over conventionalbubbling and turbulent fluidized bed reactors, such as highgas-solids contact efficiency and reduced axial dispersion [3].However, CFB riser reactors still have some shortcomings,such as severe solids backmixing and significant clustering andnonuniform axial and radial solids distributions, thus reducingthe gas-solids contact efficiency and reaction selectivity. Thesedisadvantages can be reduced in the downer reactor [4].Downer reactors have been shown to provide shorter resi-

dence times, less backmixing, more uniform gas-solids flow,and less solids aggregations compared to riser reactors [4].These properties meet the requirements of specific reactions,such as fluid catalytic cracking (FCC). Hydrodynamics in

downer reactors have been studied with many research paperspublished as summarized by Zhang [5]. A comparison of thehydrodynamics in the riser and in the downer has been carriedout to investigate their differences and similarities [3, 6]. How-ever, only statistical analysis was used in the study of Zhang etal. [3] and very limited operating conditions of low solids flux(Gs < 50 kg/m2/s) were performed in the study of [6]. Transi-ent flow behavior over a large range of operating conditionsmust be compared to fully understand the flow dynamics andflow structures in the riser and the downer1).Chaos analysis has been applied in CFB risers since early

1990’s [7]. As reviewed by van den Bleek et al. [8], chaos is auseful tool for the investigation of multi-phase flow behaviorin fluidized bed systems, e.g., regime transition, characteriza-tion of flow behavior, scale-up, chaos control, and chaos moni-toring.In this study, solids concentration signals measured in a ri-

ser-downer system were analyzed using both statistical andchaos analyses to compare the flow dynamics and the flowstructures in the riser and the downer.

� 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com

B. Wu1

J.-X. Zhu1

L. Briens1

1Department of Chemical andBiochemical Engineering, TheUniversity of Western Ontario,London, Canada.

–Correspondence: J.-X. Zhu ([email protected]), Department of Chemicaland Biochemical Engineering, The University of Western Ontario,London, Ontario, Canada N6A 5B9.

–1) List of symbols at the end of the paper.

448 Chem. Eng. Technol. 2007, 30, No. 4, 448–459

2 Experimental Setup

The riser-downer unit consisted of a 9.3 m high downer and a15.1 m high riser of the same I.D. of 0.1 m (see Fig. 1). It wasdesigned to incorporate both the riser and the downer in thesame experimental operation. The column was made of plexi-glass. Compared with the experimental setups used by manyother researchers, both the riser and the downer columns weremuch longer, and therefore, permitted the gas-solids flow tohave a longer distance for particle acceleration and for radialflow development. The gas distributor at the riser bottom in-cluded a perforated plate and a bundle of nozzles, with37 tubes of 0.8 mm I.D. uniformly installed on the perforatedplate. The perforated plate allowed auxiliary gas to fluidize thesolids from the storage tank while the nozzles allowed the maingas to carry the solids upwards in the riser.During operation, solids from the storage tank were first fed

to riser bottom above the riser distributor, where they werefluidized by the auxiliary gas through the perforated plate, andthey were then carried up the riser by the main gas throughthe nozzles to the riser primary cyclone installed at the top ofthe downer. After the separation of solids from the gas with anefficiency greater than 99%, the remaining solids in the gas

were further captured in the secondary and tertiary cyclones.Fine particles were finally retained in a baghouse filter, and thegas was exhausted. There was a distributor at the downer topand below the dipleg of the riser primary cyclone. The solidsabove the distributor were maintained at minimum fluidiza-tion by downer distributor air. Solids then fell down into thedowner column through 31 vertically positioned (with trian-gular pitch) brass tubes (10.7 mm I.D., 12.7 mm O.D. andlength 0.36 m). The gas distributor was a plate with 31 holes(16.7 mm I.D.), located below the solids distributor fluidizedbed, but 50.8 mm above the bottom exit of the solids feedtubes. Those 31 holes were arranged in the same pattern as the31 brass tubes in the solids distributor so that the downer flui-dizing gas was distributed through the 2 mm gap between theair holes and the brass tubes. At the downer exit, the solidsand gas were separated in a fast separator, with the solids en-tering the storage tank and the gas flowing to another second-ary cyclone. Finally, the solids were recycled to the riser bot-tom from the storage tank, through a butterfly valve located inthe inclined feeding pipe. The tertiary cyclone was shared withgas from the two secondary cyclones. In addition, aerationports were also installed on the cyclone diplegs, the storagetank and the inclined feeding pipe to assist the flow of solids.


Downerdistributor air

(0.1 m i.d./9.30 m)

Cyclone and

Solids flowcontrol valve

Secondary cyclones

Tertiary cyclone

(0.1 m i.d./15.1 m)

Downer

downer distributor

Riser distributor air

Storage tank

Measuring vessel

Fast separator

Diverter

Riser main air

Air out

Riser

Auxiliary fluidization

air distribution grid

Distributor shell

(0.2 m i.d.)

Auxiliaryfluidizationair

Solids feed tubes(10.7 mm i.d.)

56.3 deg

Seal plate

Downer gas-solids distributor

Downermain air

Downermain air

Riser main air

Auxiliaryfluidizationair

Riser gas distributor(8 mm i.d.)

Seal plate

Auxiliary fluidization

air distribution grid

Riser

Distributor shell

(0.2 m i.d.)

Riser gas-solids distributor

Figure 1. Schematic diagram of the riser-downer system.

Chem. Eng. Technol. 2007, 30, No. 4, 448–459 Circulating fluidized beds 449

Air from a blower was used as the fluidization gas, and thegas flow rate was measured by an orifice meter. FCC catalystwith mean diameter of 67 lm and particle density of1500 kg/m3 was used in this study. Electrostatics were mini-mized by introducing a small stream of steam into the mainair pipeline to obtain a relative humidity of 70–80%. The sol-ids concentration was measured using an optical fiber probe ateight axial positions along the riser (0.95, 2.59, 4.51, 6.34, 8.16,10, 12.28, and 14.08 m) and downer column (0.02, 0.51, 1.20,2.11, 4.40, 6.23, 8.06, and 9.15 m) and at 11 radial positions(r/R= 0.0, 0.158, 0.382, 0.498, 0.59, 0.67, 0.741, 0.806, 0.866,0.922, and 0.975). The measurement volume of the opticalprobe was very small, so that the flow dynamics were micro-scopic and local; and any disturbance to the flow was minimal.More details about the probe and the riser-downer system canbe found in Zhang et al. [3, 9]. The solids circulation rate wascontrolled by a butterfly valve and measured by diverting thesolids from the downer to a measurement tank for a given pe-riod of time. All experiments were conducted at ambient tem-perature and pressure. The true solids concentration was con-verted from the original voltage time series using a calibrationequation [9]. Fluctuations in the solids concentration weremeasured at a frequency (f) of 970 Hz and a time length of30 s. The data were filtered at a low-pass frequency of 250 Hzbased on power spectrum analysis.Five operating conditions were tested in each of the riser

and the downer with superficial gas velocities, Ug, in therange of 3.5–10 m/s and solids fluxes, Gs, in the range of50–200 kg/m2/s. The experimental data has previously beenused to study the average solids flow behavior [3, 5] and statis-tical behavior [10].

3 Chaos Method

Kolmogorov entropy, K, reflects the information loss rate andpredictability into the future and was estimated using the max-imum likelihood method [11]. The correlation dimension, D,is another frequently used chaos parameter, reflecting the com-plexity of the attractor in the phase space and the dynamicaldegree of freedom. The correlation dimension was estimatedusing the method proposed by Grassberger and Procaccia [12].An embedding window was used with length estimated fromthe dominant cycle time using V statistics [13]. The embed-ding dimension, m, was at least 18 in the calculation of thecorrelation dimension according to Takens [14]. Hurst [15]developed the rescaled range analysis to study reservoir storagein the Great lakes of the Nile River Basin. The Hurst exponent,H, was used to characterize the fluctuations of the time series:0 £H<0.5 indicates anti-persistence, H=0.5 indicates randombehavior, and 0.5 <H £1 indicates persistence. The Kolmogor-ov entropy, correlation dimension and Hurst exponent wereestimated for each time series of local solids concentrationmeasurements to characterize the solids flow behavior. For adetailed mathematical definition of these chaos parametersand the calculation method, please refer to the references citedin this section.

4 Results and Discussion

4.1 Axial Flow Development in the Riser and theDowner

Axial flow development in the riser-downer system has beenstudied using the cross-sectional average solids concentrationand particle velocity [3]. To examine the axial flow develop-ment at various radial positions, axial profiles of es at 3 radialpositions at Gs of 100 kg/m2/s and Ug of ca. 3.6 m/s, are shownin Fig. 2. The axial flow development was faster in the core re-gion than near the wall in both the riser and the downer. Inthe core region, the length of the solids acceleration (LOA) wascomparable in the riser and the downer. In the wall region, theLOA in the downer was clearly shorter than that in the riserdue to high es in the wall region of the riser. The solids concen-tration in the downer was generally much lower than that inthe riser under comparable conditions.

Fig. 3 shows the axial profiles of chaos parameters in the ri-ser and the downer. K varied more significantly along the axisin the downer than in the riser due to dilute and fast flow inthe downer. However, the distances required for K to becomerelatively constant were similar except near to the wall(r/R= 0.866) in the two units, where K decreased along the axissimilar to the time-averaged solids holdup profiles. K in thewall region of the downer was much higher than that in thewall region of the riser, which was opposite to the time-aver-aged solids holdup. In the wall region of the downer, the for-mation and breakage of clusters was more frequent than in thewall region of the riser. Clustering behavior decreased alongthe axial direction in the development region of the downer asthe solids concentration decreased. In the wall region of the ri-ser, solids tended to form large clusters, especially in the bot-tom section of the riser, where es was very high. The solids flow


2 4 6 8 10 12 140.00

0.02

0.04

0.06

0.08

Gs=100 kg/m

2/s

Ug=3.5 (riser) or 3.7 m/s (downer)

Tim

e-a

ve

rag

ed s

olid

s h

old

up,

ε s (

-)

Axial distance from the riser or downer entrance, h (m)

Downer, r/R=0.0

Downer, r/R=0.741

Downer, r/R=0.866

Riser, r/R=0.0

Riser, r/R=0.741

Riser, r/R=0.866

Figure 2. Axial flow development in the riser and the downerusing time-averaged solids concentrations at Gs of 100 kg/m2/sand Ug of around 3.6 m/s (data from Zhang et al. [3]).

450 B. Wu et al. Chem. Eng. Technol. 2007, 30, No. 4, 448–459

was more regular with relatively low K, and K slightly in-creased along the axis of the riser in the bottom section of thewall region. The solids flow in the bottom zone of CFB riserswas reported to resemble a bubbling/turbulent bed [16–22].This study confirmed the previous statement with relativelylow K in the bottom section of the riser. The values of K in thecore region of the riser were comparable to those in the coreregion of the downer, indicating similar complex flow behaviorof dispersed particles in the riser and the downer. Very inter-mittent flow behavior of clusters and particles in the entrancesection of the downer resulted in relatively high K. An exit ef-fect in the riser could be found with relatively low es and highK at around 14 m due to freer and dilute flow at the exit of theriser. No exit effect was found in the downer.Axial profiles of D were similar to that of K except near the

wall of the development section. There was strong cyclic be-havior due to large clusters in the wall region of the develop-ment section (see Fig. 4) which caused more structured behav-ior in the time series, and therefore low D. The local flowbehavior of clusters was generally more regular than for dis-persed particles [6, 21], since dispersed particles flow morefreely and intermittently, and therefore, are more chaotic. Ahigh K generally corresponded to a low H, so that trends inprofiles of H were opposite to those of K. In summary, in gen-eral the trends of the profiles of the chaos parameters fluctu-ated more than those of time-averaged solids concentrationand may reflect the time-dependent dynamic behavior.

4.2 Radial Flow Dynamics and Flow Structures in theRiser and the Downer

Radial profiles of time-averaged solids concentration, Kolmo-gorov entropy, correlation dimension and Hurst exponents atfour selected axial levels of the riser and the downer are shownin Figs. 5–8. There was a flat core in both the riser and thedowner. The solids concentration increased sharply near thewall and formed a local maximum exactly at the wall in theriser, Fig. 5. A dense annular region with a peak at r/R atca. 0.85 existed in the downer at values of h of 2.112 and6.227 m, and radial flow structures varied significantly alongthe axis of the downer. More details about the radial profiles ofsolids concentrations can be found in [3].Profiles of K (see Fig. 6) generally had a flat core with very

high K and decreasing K at the wall except in the entrance sec-tion (h=0.512 and h= 2.112 m) of the downer, and a flat corein the downer indicating relatively uniform flow. Correspond-ing to the peak of es in the annulus of the downer at a h valueof 2.112 m, K reached a local maximum due to very intermit-tent flow behavior of clusters with different sizes and dispersedparticles. This observation has not been reported in a downerreactor before. High K could also be found closer to the en-trance at a h value of 0.512 m in the wall region of the downerdue to very intermittent flow of clusters. Such intermittentflow is mainly due to the distributor effect, where intermittentstreams of solids are fed into the downer surrounded by areasprimarily occupied by gas. In the riser, there was a core regionwith relatively high K due to the flow of dispersed particles.


2 4 6 8 10 12 140

100

200

300

400

500 (a) Komogorov entropy

K (

bit/s

)


Downer, r/R=0.0

Downer, r/R=0.741

Downer, r/R=0.866

Riser, r/R=0.0

Riser, r/R=0.741

Riser, r/R=0.866

2 4 6 8 10 12 14 16

4

6

8

10(b) Correlation dimension

Co

rre

latio

n D

ime

nsio

n, D

(-)


2 4 6 8 10 12 14 160.40

0.45

0.50

0.55

0.60

0.65

0.70(c) Hurst exponent

Hurs

t e

xpo

ne

nt, H

(-)


Figure 3. Axial flow development examined by K, D, and H at Gs

of 100 kg/m2/s andUg of ca. 3.6 m/s in the riser and the downer.


The value of K kept decreasing towards the wall due to moreregular flow behavior of large clusters in the annulus and wallregion of the riser. Corresponding to the highest es at the wallof the riser (see Fig. 5) K reached a minimum exactly at thewall. In the riser, solids flowed against gravity and tended toform large clusters in the wall region in order to consume lessenergy during transportation, and therefore, the cycling behav-ior in the time series was enhanced and the flow was less inter-mittent.The shapes of the radial profiles of D (see Fig. 7) under dif-

ferent operating conditions were similar at different axial levelsin the riser and the downer except at a h value of 0.512 m inthe downer, as were profiles of H (see Fig. 8). A flatter core inthe profiles of D and H indicated more uniform flow in thedowner. The value of D significantly deceased towards the walldue to enhanced clustering behavior in the annulus, and therewas a minimum D at r/R of ca. 0.85, corresponding to the peakof es in the dower, which was likely to be due to the more regu-lar flow of relatively large clusters. The value of D increased inthe region very close to the wall (r/R> 0.9) in both the riserand the downer. The increase of D at the wall of the riser waslikely to be due to the enhanced intermittent clustering behav-ior (see Fig. 9), while the increase of D at the wall of the down-er was likely due to the complex flow of small clusters and dis-persed particles, and the reduced cycling behavior of largeclusters.Values of H were generally around 0.45 in the core region,

indicating very “random” and anti-persistent flow behavior,while values of H were over 0.5 in the wall region, especially inthe riser, which showed persistent behavior due to flow of clus-

ters. High H values at the wall of the riser were also likely to bedue to the flow of the large clusters, while high H values at thewall of the downer were due to the slow and cyclic flow behav-ior of solids (see Fig. 9). In agreement with the high K valuesat an h value of 0.512 m in the wall region of the downer, Dwas high and H was low due to very intermittent clusteringbehavior. Radial flow development could generally be consis-tently examined from different chaos parameters, but differentchaos parameters reflected flow characters with different physi-cal meanings. Therefore, the chaos parameters followed differ-ent trends compared with those of time-averaged solids con-centration. The combination of the three parameters generateda comprehensive picture of the flow dynamics inside the riserand downer. Finer flow dynamics were gained using chaosanalysis compared to statistical analysis.

4.3 Relationships between Chaos Parameters andTime-Averaged Solids Concentration

The value of chaos parameters significantly varied with the op-erating conditions (see Figs. 6–8). The time-averaged solidsconcentration, es, were also significantly affected by the operat-ing conditions (see Fig. 5). Knowledge of the relationshipsbetween chaos parameters and es would be helpful to directlyunderstand the dynamic behavior from the operating condi-tions. Hence, relationships between the chaos parameters andes were examined in different regions in the riser and downer.Fig. 10 shows the relationships between the chaos parame-

ters and es in the upper section of the riser and lower devel-


Downer

0.0 0.1 0.2 0.3 0.4

0.00

0.05

0.10

0.15

0.20

h=4.4 m, r/R=0.866

Time, (s)

0.00

0.05

0.10

0.15

0.20

h=2.11 m, r/R=0.866

0.00

0.05

0.10

0.15

0.20

So

lids c

on

cen

tra

tio

n,

(-)

h=1.20 m, r/R=0.866

0.0 0.1 0.2 0.3 0.4

0.0

0.1

0.2

0.3

0.4

h=4.51 m, r/R=0.866

Time, (s)

0.0

0.1

0.2

0.3

0.4

h=2.59 m, r/R=0.866

0.0

0.1

0.2

0.3

0.4

h=0.95 m, r/R=0.866

Riser

So

lids c

on

ce

ntr

atio

n,

(-)

Figure 4. Time series of solids concentration at Gs of 100 kg/m2/s and Ug of ca. 3.6 m/s in the development regions of the riser and thedowner.



0.0 0.2 0.4 0.6 0.8 1.00.00

0.06

0.12

0.18h=0.950 m

Riser

Gs(kg/m

2/s) U

g(m/s)

50 5.5

100 3.5

108 5.5

101 8.2

201 5.5

Tim

e-a

ve

rag

ed

solid

sho

ldu

p,

ε s (

-)

r/R, (-)

0.00

0.05

0.10

0.15

h=14.080 m

Tim

e-a

ve

rag

ed

solid

sh

old

up,

ε s (

-)

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

h=0.512 m

Downer

Gs(kg/m

2/s) U

g(m/s)

49 3.7

101 3.7

101 5.7

101 8.1

194 3.7

Tim

e-a

ve

rage

d s

olid

s h

old

up

,ε s

(-)

r/R, (-)

0.00

0.02

0.04

0.06

h=2.112 m

Tim

e-a

ve

rag

ed

so

lids

hold

up,

ε s (

-)

0.000

0.008

0.016

0.024

h=6.227 m

Tim

e-a

ve

rag

ed

so

lids

ho

ldup

,ε s

(-)

0.000

0.008

0.016

0.024 h=9.155 m

Tim

e-a

vera

ge

d s

olid

s h

old

up

,ε s

(-)

DownerRiser

0.00

0.06

0.12

0.18

h=2.590 m

Tim

e-a

ve

rag

ed

so

lids h

old

up

,ε s

(-)

0.00

0.05

0.10

0.15

h=8.160 m

Tim

e-a

ve

rag

ed

solid

s h

old

up

,ε s

(-)

Figure 5. Radial profiles of es in the riser and the downer (data from Zhang et al. [3]).



0.0 0.2 0.4 0.6 0.8 1.00

150

300

450h=0.950 m

Riser

Gs(kg/m

2/s) U

g(m/s)

50 5.5

100 3.5

108 5.5

101 8.2

201 5.5

K (

bit/s

)

r/R, (-)

0

150

300

450

h=14.080 m

K (

bit/s

)

0.0 0.2 0.4 0.6 0.8 1.0

150

300

450

600

h=0.512 mDowner

Gs(kg/m

2/s) U

g(m/s)

49 3.7

101 3.7

101 5.7

101 8.1

194 3.7

K (

bit/s

)

r/R, (-)

0

150

300

450

h=2.112 m

K (

bit/s

)

0

150

300

450

h=6.227 m

K (

bit/s

)

0

150

300

450

h=9.155 m

K (

bit/s

)

DownerRiser

0

150

300

450

h=2.590 m

K (

bit/s

)

0

150

300

450

h=8.160 m

K (

bit/s

)

Figure 6. Radial profiles of K, estimated from solids concentration measured in the riser and the downer.



0.0 0.2 0.4 0.6 0.8 1.00

3

6

9

h=0.950 m

Riser

Gs(kg/m

2/s) U

g(m/s)

50 5.5

100 3.5

108 5.5

101 8.2

201 5.5

Corr

ela

tion D

imensio

n, D

(-)

r/R, (-)

0.0 0.2 0.4 0.6 0.8 1.0

6

9

12

h=0.512 m

Downer

Gs(kg/m

2/s) U

g(m/s)

49 3.7

101 3.7

101 5.7

101 8.1

194 3.7

Corr

ela

tion D

imensio

n, D

(-)

r/R, (-)

3

6

9

12 h=14.080 m

Corr

ela

tion D

imen

sio

n, D

(-)

3

6

9

12

h=2.112 m

Corr

ela

tion

Dim

en

sio

n, D

(-)

3

6

9

12

h=6.227 m

Corr

ela

tio

n D

imen

sio

n, D

(-)

3

6

9

12

h=9.155 m

Co

rrela

tio

n D

ime

nsio

n, D

(-)

DownerRiser

3

6

9

12h=2.590 m

Corr

ela

tion

Dim

ensio

n, D

(-)

3

6

9

12

h=8.160 m

Co

rre

latio

n D

ime

nsio

n,

D (

-)

Figure 7. Radial profiles of D, estimated from solids concentration measured in the riser and the downer.



0.0 0.2 0.4 0.6 0.8 1.0

0.45

0.60

0.75h=0.512 m

Downer

Gs(kg/m

2/s) U

g(m/s)

49 3.7

101 3.7

101 5.7

101 8.1

194 3.7

Hu

rst e

xp

on

en

t, H

(-)

r/R, (-)

0.30

0.45

0.60h=14.080 m

Hu

rst e

xp

on

en

t, H

(-)

0.30

0.45

0.60 h=2.112 m

Hu

rst

exp

on

en

t, H

(-)

0.30

0.45

0.60 h=6.227 m

Hu

rst

exp

on

en

t, H

(-)

0.30

0.45

0.60h=9.155 m

Hu

rst e

xp

on

en

t,H

(-)

0.0 0.2 0.4 0.6 0.8 1.00.30

0.45

0.60

h=0.950 mRiser

Gs(kg/m

2/s) U

g(m/s)

50 5.5

100 3.5

108 5.5

101 8.2

201 5.5

Hu

rst e

xpo

ne

nt,

H (

-)

r/R, (-)

DownerRiser

0.30

0.45

0.60

h=2.590 m

Hu

rst e

xp

on

ent,

H (

-)

0.30

0.45

0.60h=8.160 m

Hu

rst

exp

on

ent,

H (

-)

Figure 8. Radial profiles of H, estimated from solids concentration measured in the riser and the downer.


oped section of the downer. In the core region, es was generallylow. K and D were high, and H was low in both the riser andthe downer due to the complex flow of dispersed particles andsmall clusters, indicating similar flow behavior in the two reac-tors. In the wall region, there were many low values of K and Dand high values of H at an es value of ca. 0.01, compared tothose in the core region. This was due to enhanced clusteringbehavior. At es > 0.02, in the wall region of the riser, K and Ddecreased and H increased with increasing es, and became rela-tively constant at es > 0.04.The flow behavior of larger clusters at higher solids concen-

tration was more regular than dispersed particles. The compet-ing flow behavior of clusters and particles under denser flowresulted in relatively constant chaos parameters at very highsolids concentration, es > 0.04. In the wall region of the down-er, the formation and breakage of clusters was enhanced underdenser flow, es > 0.02, since very large clusters could not beformed due to relatively high slip velocities between large clus-ters and the gas phase. Intermittent flow of clusters with differ-ent sizes and dispersed particles caused more complex localflow behavior in the downer, with high K and low H. However,the value of D only slightly increased under denser flow in thedower, since the regular cycling flow behavior of relatively largeclusters kept D from increasing too quickly.In order to more clearly examine the different relationships

between chaos parameters and time-averaged solids concentra-tion under relatively dense flow, all data in the wall region areplotted in Fig. 11. Quite different absolute values of the chaosparameters in the riser and downer were clearly seen. Differentflow directions of solids and gas in the riser and the downershould be the cause of these different relationships. In the riser,large clusters were easily formed in the wall region in order toconsume less energy for transport. However, in the wall regionof the downer, very large clusters could not be formed, sincethe increased drag force between gas and cluster would breakthe clusters. Frequent formation and breakage of clusters inthe wall region caused more chaotic and anti-persistent local

flow behavior, with relatively high K, high D, and low H. Thesedistinguished flow properties in the wall region of downercould be an advantage for reactions requiring high gas-solidscontact efficiency.


0.0 0.1 0.2 0.3 0.4 0.5

0.0

0.1

0.2

0.3

(b) Riser, h=10 m, r/R=0.975

Gs=108 kg/m

2/s and U

g=5.5 m/s

So

lids h

old

up

, (-

)

Time, (s)

0.0 0.1 0.2 0.3 0.4 0.5

0.00

0.01

0.02

0.03 (a) Downer, h=6.23 m, r/R=0.975

Gs=101 kg/m

2/s and U

g=5.7 m/s

So

lids h

old

up

, (-

)

Time, (s)

Figure 9. Time series of solids concentration at the wall in the ri-ser and the downer.

0.00 0.02 0.04 0.06 0.08 0.10

0

100

200

300

400

500 (a)

Ko

lmo

go

rov e

ntr

op

y,

K (

bit/s

)

Time-averaged solids holdup, εs (-)

riser, core region at h>6.34 m

riser, wall region at h>6.34 m

downer, core region at h>4.4 m

downer, wall region at h>4.4 m

0.00 0.02 0.04 0.06 0.08 0.10

2

4

6

8

10

12(b)

Co

rre

latio

n D

ime

nsio

n, D

(-)






0.00 0.02 0.04 0.06 0.08 0.10

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

(c)

Hu

rstexp

on

en

t, H

(-)






Figure 10. Relationships between chaos parameters and es inthe upper section of the riser and in the lower section of thedowner.


5 Conclusions

Chaos parameters varied more significantly along the axis inthe entrance region of the downer compared to the riser. Thevalue of K decreased along the axis in the wall region of the en-trance section in the downer due to the intermittent flow ofclusters with different size and dispersed particles. Flow wasrelatively regular in the wall region of the dense bottom sectionof the riser due to more frequent and larger clusters, and K in-creased along the axis of the riser in the entrance section. Ingeneral, axial flow development can be consistently examinedfrom axial profiles of chaos parameters, and a high K generallycorresponds to a low H.Flow in the downer was more uniform with a flatter core in

all of the radial profiles of the chaos parameters. A low H valueof ca. 0.45 in the core region, and a higher H value of over 0.5in the wall region in both the riser and the downer, indicatingsimilar anti-persistent flow in the core region and persistentflow behavior near the wall.The radial profiles of K in the downer varied significantly

with increasing axial levels due to different clustering behavioralong the axis in the wall region of the downer. Very intermit-tent flow of clusters and dispersed particles increased the com-plexity of the local flow behavior in the wall region of the de-velopment section of the downer. The value of D significantlydeceased near to the wall in the riser due to the regular flowbehavior of large clusters. At the wall, the flow of small clustersand dispersed particles and reduced clustering behavior at thewall of the downer caused D to increase, while very intermit-tent aggregating behavior at the wall of the riser also caused Dto increase.In the core region of the riser and the downer, the values of

the chaos parameters were close under comparable dilute flowdue to the complex flow of dispersed particles. In the wall re-gion of both the riser and downer, moderate and regular clus-tering behavior corresponded to low K, low D, and high H. Inthe wall region of the riser, the chaos parameters became al-most constant at es > 0.04 due to the competing flow behaviorof clusters and particles. In the wall region of the downer, ates > 0.02, K and D increased and H decreased with increasing esdue to the enhanced intermittent flow of clusters with differentsize and dispersed particles.

Acknowledgements

The authors are grateful to the Natural Sciences and Engineer-ing Research Council of Canada for the financial support andto Dr. H. Zhang and Dr. W. Huang who performed the mea-surements of solids concentration in the downer and the riser,respectively.

Symbols used

dp [lm] particle diameterf [Hz] frequencyGs [kg/m2/s] solid flux


0.00 0.05 0.10 0.15 0.20

0

100

200

300

400

500

(a)K

olm

og

oro

v e

ntr

op

y, K

(b

it/s

)


Riser, wall region (r/R>0.74)

Downer, wall region (r/R>0.74)

0.00 0.05 0.10 0.15 0.20

2

4

6

8

10

12 (b)

Co

rre

latio

n D

ime

nsio

n, D

(-)




0.00 0.05 0.10 0.15 0.20

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70 (c)

Hurs

t e

xp

on

en

t, H

(-)




Figure 11. Relationships between chaos parameters and es inthe wall region of the riser and the downer.


H [–] Hurst exponentI.D. [m] inner diameterK [bits/s] Kolmogorov entropyLOA [m] length of solids accelerationO.D. [m] outer diameterr/R [–] reduced radial positionUg [m/s] superficial gas velocities

Greek symbols

es [–] time-averaged local solidsvolume concentration

qp [kg/m3] particle density

Abbreviations

CFB circulating fluidized bedD correlation dimensionFCC fluid catalytic cracking

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a comparison of flow dynamics and flow structure in a riser and a downer

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