one-dimensional modeling of hydrodynamics in a swirling

International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:12 No:06 13

127506-4848-IJMME-IJENS © December 2012 IJENS I J E N S

One-Dimensional Modeling of Hydrodynamics

in a Swirling Fluidized Bed Tan Chee Sheng, Shaharin Anwar Sulaiman, Vinod Kumar

Abstract— The present work studies the hydrodynamics of a

swirling fluidized bed (SFB) for packed and swirling regimes

using an analytical model that draws inspiration from the order-

of-magnitude analysis approach. In minimizing the complexity in

solving the hydrodynamics model in SFB, the multiple-dimensional modeling in a cylindrical coordinate (r,θ,z), which

requires a complex partial differential equation solution, is

reduced to one-dimensional formulation in only the axial

direction (z). The model is based on the principles of force and

moment equilibrium when the fluid passing through the bed particles. It is used for predicting the axial variation of

hydrodynamic properties such as angular velocity of bed

particles, linear velocity of bed particles and gas velocity across

the bed. Hydrodynamics of SFB are related as a function of angle

of injection, mass of bed, superficial velocity of fluid and the density of particle and fluid gas. Pressure drop across the bed

height is further estimated using hydrodynamics of SFB.

Experiment is carried out in a swirling fluidized bed with two

different sizes of spherical PVC particles. The model shows good

agreement between the theoretical and experimentally obtained bed pressure drop.

Index Term-- Swirling fluidized bed ; one-dimensional model ;

hydrodynamics

I. INTRODUCTION

Fluidization is a process that involves passing a fluid with a

certain velocity upwards through a packed bed of solid

particles to produce fluid drag on the particles to overcome

each of the particle‟s weight. The particles will therefore no

longer rest on each other and thus be able to behave and flow

like a fluid. As stated by Kunii and Levenspiel [1], fluidization

has been widely used for industrial applications as it could

obtain vigorous agitation of the solids movement in contact

resulting in high transfer coefficients of heat and mass while

maintaining the bed‟s temperature and concentration

uniformity. Fluid Catalytic Cracking (FCC) systems in the oil

and gas industry, for example, have been using fluidization

technology to produce gasoline [2],[3]. In another instance,

Fluidized Bed Gasifiers and Fluidized Bed Combustors for

carbonaceous fuels have been utilized for chemical synthesis,

process heat supply, steam generation and power generation

[2],[4]. The design of a distributor plate in fluidized bed has

high impact on the quality of fluidization and the amount of

fluid bypassing the bed. Ouyang and Levenspiel [5] stated that

one of the major concerns of using fluidization technology is

the relatively high power consumption of the blower, which is

contributed by pressure drop through the bed Ouyang and

Levenspiel suggested a type of the spiral distributor that

would result in a better quality of fluidization with low

pressure fluctuations as compared to the sintered plate

distributor. Fig. 1 shows the basic configuration of a swirling

fluidized bed. Air is fed tangentially through a horizontal pipe

into a circular air plenum causing it to swirl prior to entering

the spiral distributor. As air passes through the distributor

blades, it leaves the distributor in a swirling motion within the

column. Shown in Fig. 2 (a) is the spiral distributor, which

comprises a number of overlapping plates, shaped as sectors

of a circle with an opening area between plates. The spiral

distributor allows the fluidizing medium enters the bed at an

inclination angle through it with two velocity components.

Fig.2 (b) illustrates a jet of fluid entering the bed‟s distributor

at an angle θ, with horizontal and vertical components of the

velocity, V cos θ and, V sin θ, respectively. Fig.3 shows the

velocity forces acting on a particle in the bed. The horizontal

component, V cos θ, is responsible for the swirl motion of the

bed and the vertical component, V sin θ, causes fluidization.

Such configuration is referred as Swirling Fluidized Bed

(SFB).

Fig. 1. Schematic of basic configuration for a swirling fluidized bed.

Fig. 2. (a) Spiral distributor plate by Ouyang and Levenspiel [3].

Fig. 2.(b) Fluid velocity‟s components at distributor.

Vg

Vg Fluid flow after passing distributor

Blade inclination angle, θ

Fluid flow before entering distributor Tangential

Axial

y

x

Distributor blade

Direction of air flow

V

Axial (z)

Radial (r)

Peripheral (θ)

Plexiglas Column

Metal Cone

Distributor

Blades

Centre body

support

Air inlet (Tangential)

Fluidizing Air

Swirling Motion

(counter clockwise)

Inlet air to bed



Fig. 3. Velocity forces acting on a particle in the bed.

In SFB, hydrodynamics of the bed is an essential component

responsible to the bed pressure drop. Fig. 1 shows the basic

configuration of a swirling fluidized bed. It is characterized in

cylindrical coordinates which involves radial, peripheral and

axial (r,θ,z) directions across the bed. The analytical model for

the SFB hydrodynamics, which involves partial differential

equation, is complex and requires huge effort to solve.

An early study of hydrodynamics of SFB was done by Shu,

Lakshmanan, and Dodson. [6] on a toroidal fluidized bed

reactor based on force balances on particles movement in the

bed. In a later work Sreenivasan and Raghavan [7] assumed

swirling at an average uniform angular velocity with no

variation across the bed in any direction. Their model showed

that the angular velocity of gas at free surface of the bed was

approximately equal to the mean angular velocity of the bed,

with good agreement with experiment results. They also

observed co-existence of two different fluidization regimes;

swirling at the lower layer but aggregative at the upper layer.

The earlier authors [5],[7] agreed on the favorable aspect of

swirling fluidization that large open area fractions and low

pressure drops at the distributor could be employed without

any ill-effects. Vikram, Raghavan, and Martin [8] further

studied the analytical model of SFB using a two-dimensional

formulation, in which the bed was composed of a stack of

discs in the axial and the discs were further discretized to a

number of rings at different radii. The study found that the

radial variation in bed properties was less by 20% as

compared to that of the axial variation. It was observed that

the superficial velocity and blade angle were the main factors

that affect the swirl characteristics. The pressure drop was

suggested to have a quadratic variation with superficial

velocity. In a more recent work, Kamil, Fahmi, and Raghavan

[9] considered a parametric analysis of SFB relating to the

particle density, gas density, and blade angle. They concluded

that the gas density and the particle density as the most

influential parameters followed by the blade angle.

The preliminary studies [7],[8] proposed that the peripheral

variation in SFB would be trivial and thus suggested that axial

variation would be more dominant as compared to radial

variation. Therefore, the objective of the present work is to

reduce the effort or complexity in solving the analytical model

by concerning only the variation in axial direction. Mohideen,

Sreenivasan, Sulaiman, and Raghavan [10] investigated the

heat transfer characteristics for SFB with Geldart type D

particles by located the thermocouples at different height in

the bed to determine the desired parameters. The approach of

discretizing the bed height from [10] is used in this present

work to determine the hydrodynamic characteristics of SFB.

This analytical model simplifies the bed into a stack of discs

in the axial direction. During the steady swirling regime,

forces acting on the horizontal and vertical direction of the

disc are used to evaluate the hydrodynamic properties of

particle. Pressure drop across the bed height is then estimated

using the ratio of force balance acting on the disc in the

vertical direction to the area of force applied. The single

dimensional model was validated by comparison with the

experiment results. To investigate the relative important

parameters of the swirling characteristics, experimental

studies are also performed on the inclination angle of fluid

leaving the bed, fluid velocity leaving the bed and the average

velocity of particles.

II. DESCRIPTION OF THE ANALYTICAL MODEL In the present study, the assumptions made in the analysis of

hydrodynamics characteristics of a swirling bed were that:

a. all particles were spheres of uniform size,

b. the packing arrangement of particles in packed bed was

body centered cubic structure with the coordination

number, Np , of 8,

c. all particles at a same elevation had the same velocity,

d. the bed was in steady swirling regime once fluidized, and

e. the gas velocity output was uniform throughout the

distributor.

This model was categorized into packed bed and steady state

swirling regime. Simulation was done by inserting the force

and moment equilibrium and equation of continuity that

applied for every disc in the bed in an M-file. Then, it was

compiled and simulated using a program developed in

MATLAB. The boundary conditions of this model were:

a. hydrodynamics of the bed particles in radial (r) and

peripheral (θ) directions were negligible,

b. bed area across the height was constrained by the radius

of plexiglas wall column, bottom radius and height of the

metal cone placed in the middle, and

c. angle of fluid gas leaving discs was not more than ninety

degrees relative to the horizontal plane.

A. Scope of study and limitations

This hydrodynamics study only focuses on the axial

direction for SFB. Hydrodynamic properties across the bed

height that were of the interest in this study were the velocity

of particle, angular velocity of the bed and pressure drop. The

approach to solve the velocity and angular velocity properties

was based on the principles of angular momentum

conservation and moment equilibrium across the bed height.

The force equilibrium acting on plate was used to find the

pressure drop across the plates. The overall pressure drop

across the bed would be the summation of pressure drop for

each plate. The design model was able to predict the

hydrodynamics of the bed for packed bed and steady swirling

bed. Limitation of this study was that the analytical modeling

was not applicable in the transition regime between packed

and steady swirling bed.

Vertical velocity force, Vg sin𝜃, acting on particle

Particle Horizontal velocity force, Vg cos 𝜃, acting on particle

Tangential

Axial

y

x

Particle‟s motion direction with the velocity,

Vp =



The program was started by determining the sphericity,

voidage of particles in packed bed and height of bed. The

sphericity of particle, φ, was predicted using the equations

recommended by Wadell [11]:

)1(

2

D

D

s

v

in which, volume diameter was given as:

)2(6 3

1

V pvD

and surface diameter, was defined as:

)3(2

1

SD

ps

where Vp was the volume of particle (m3) and Sp was the

surface area of particle (m2).

The voidage of bed particles ,ε, in the simulation was

calculated using the equation recommended by Haughey and

Beveridge [12]:

)4(6

13

dN pp

where Np was the coordination number and dp was the

diameter of particle (m).

Fig. 4 shows the bed geometry in one dimensional. It was

represented whereby ri is the cone‟s radius at the base, hcone is

the cone‟s height, ro is the distributor‟s outer radius, hbed is the

bed height at a particular bed weight, r is the cone‟s radius at a

particular bed weight, θ is the cone‟s half angle at the top from

the vertical plane and ε is the voidage of bed particle. The

height of bed for a desired value of bed weight was predicted

based on the assumption that the total volume of particles,

Vtotal of particles, was the difference between volume of cylinder,

Vbed, and volume of cone, Vcone.

Fig. 4. Bed geometry in one dimensional view.

The total volume of particles is calculated by:

)5(3

1 2220 rrrrhhrV iiconebedparticlesoftotal

in which,

)6()( hhr bedcone

)7(h

r

cone

i

and total volume of particles was given that:

)8()1(

V

m

mV

sp

sp

bparticlesoftotal

Rearranging the terms for (5) to (8), gave:

)9(0])1(

[]3

1

3

1

3

1[

23

1

3

1

22220

232

V

m

mhrrhhr

hrhh

sp

sp

bbediiconecone

bediconebed

where mb is the mass of bed (kg), msp is the mass of a single

particle (kg), Vsp is the volume of a single particle (m3) and ε

is the voidage of bed particle.

Solving the third degree polynomials, hbed or the bed height in

the column for the desired bed weight was then found. Then,

the bed was further divided into a number of discs with the

ratio of total bed height to particle‟s diameter.

In the next sequence of the program the minimum fluidization

velocity for the particles was determined Using the equations

recommended by Wen and Yu [13] for coarse particles in a

conventional bed where, C1=28.7, C2=0.0494, the minimum

fluidization velocity, Umf , was predicted by:

(10)

Re

dU

pg

gmf

mf

in which the minimum fluidization Reynolds number was

given by:

)11(CCCRe 122

21 Ar

mf

And the Archimedes number was calculated by:

)12()(

Ar2

3

g

gpgp gd

where ρp was the density of particle (kg/m3), μg was the

dynamic fluid viscosity (Pa.s), ρg was the fluid density

(kg/m3), g was the gravitational constant (m/s

2) and dp was the

effective particle diameter (m).

B. Packed Bed Region

At minimum fluidization velocity, the bed now could be

categorized into two regions: packed bed region and steady

swirling region. The former happened at flow velocity lower

than the minimum fluidization velocity, and vice versa for the

latter. In the packed bed region, the particles did not have any

ℎ𝑏𝑒𝑑 𝑟𝑖

𝑟𝑜

ℎ𝑐𝑜𝑛𝑒

𝑟 𝜃

Wall Column

Metal Cone

Distributor

Space occupied by particles

ℎ𝑏𝑒𝑑 𝑟𝑖

𝑟𝑜

ℎ𝑐𝑜𝑛𝑒

𝑟 𝜃

Wall Column

Metal Cone

Distributor

Space occupied by particles



movement, and thus there was no hydrodynamic property to

be considered. The pressure drop across bed, ∆P, in the unit of

Pascal (Pa) for packed bed was predicted using the Ergun‟s

Equation [14]:

)13()1(

75.1)1(

150 2

3223

2

Ud

UdL

gP

pp

f

pp

gc

where L was the height of bed (m), μg was the dynamic fluid

viscosity (Pa.s) , ρf was the fluid density (kg/m3), U was its

superficial fluid velocity (m/s) , ε was the voidage, gc was the

gravitational constant (m/s2), dp was the effective particle

diameter (m) and φp was the particle‟s sphericity.

C. Steady Swirling Region

For steady swirling region, the velocity of particles in bed was

evaluated by solving the quadratic equation to find the angular

velocity of particles, ω, and was given as:

)14(0coscos2]1))((

2[ 2222

VrVr

rhrrC

mgg

disciogd

discw

To find the value of velocity of fluid gas leaving the disc,

, and angle of fluid gas leaving the disc, , at

the exit of each disc, the continuity and momentum equations

were expressed as:

)15(

2

r

VmF

pdiscwallf

)16()cos()(cos)( FV gmV gV gm f

Assuming that for small pressure drop and incompressibility

of fluid, the equation of continuity was expressed as:

)17(sin)(sin)( VVV ggg

Eliminating the term of ( ) and rearranging the term in

(15) and (17) gave:

)18(tansincos

tan)(tan

FVmVm

tF

fgg

f

where m was the mass flow rate of fluid entering the plate in

(kg/s), θ was the angle of fluid gas entering the disc, μwall was

the dynamic viscosity of wall (N.s/m2), mdisc was the mass of

disc (kg), Vp was the particle‟s velocity in the plate (m/s2), r

was the particular radius at disc (m), Vg was the velocity of

fluid entering the plate (m/s2), Cd was the drag coefficient

perpendicular to a rectangular plate, ρg was the fluid density

(kg/m3), ri was the inner radius disc (m), ro was the outer

radius of disc (m), hdisc was the height of disc (m), and ω was

the angular velocity of particles (rad/s).

As the fluid infiltrates into the bed, its horizontal velocity

momentum would be attenuated and the angle of fluid leaving

the bed would be larger than that entering into the bed . Fig. 5

shows the velocity of fluid leaving the bed and its inclination

angle relative to the horizontal plane, which implies the

significance of lost in momentum of the fluid as it penetrates

the bed from the bottom.

Fig. 5. Illustration of velocity gas vector before and after crossing the bed.

An increase in the inclination angle of fluid, θ, would result in

a decrease in the horizontal component of fluid velocity since

cos θ would be smaller as θ gets larger. In contrast,

fluidization would be much easier to occur since sin θ would

become larger. Reducing the horizontal component of fluid

velocity would lead to lesser angular momentum transferred to

particles, and hence would reduce the average velocity of

particles in the bed and would consequently reduce the

swirling motion. The average velocity of particles in bed is an

indicator of the ease for momentum transfer from fluid to

particles. The faster of particle motion in the tangential

direction, the lesser would be the resistance for fluid to

transfer its momentum to particles for swirling motion. The

horizontal momentum would be fully diminished, keeping

only the vertical momentum once the angle of leaving fluid

reached ninety-degrees. In this case, the particles will

experience only vertical fluidization with no swirling motion.

The program would then continue with determination of

pressure drop across the bed in steady swirling by using force

balance (vertical component) of the disc, which included the

weight of the disc and the downward frictional force due to

the centrifugal weight. The downward forces were supported

by the pressure drop across the disc and the buoyancy of fluid

on disc. The pressure drop across disc, ∆P, was expressed by

the ratio of net force acting on disc to the area of force

applied, Aforce, as:

)19(

2

A

r

Vgm

Pforce

p

wdisc

disc

V cos 𝜃𝑛

V sin𝜃𝑛

V cos 𝜃1

V sin𝜃1

Blade angle 𝜃1

Fluid gas leaving angle, 𝜃𝑛

1st

layer of disc

2nd

layer of disc

nth

layer of disc

After passing nth

layer of disc

Fluid flow after passing distributor

with velocity, V

Before passing the bed

y

Horizontal

Vertical

x



Total pressure drop across the bed was the summation of each

pressure drop across the disc:

)20(

1

discofnumbern

i

itotal PP

Hydrodynamics characteristic of the bed was first evaluated at

the first layer of disc for superficial velocity range of 0 to 8

m/s at an increment of 0.1 m/s. The output from the first layer

would be the input for the following layer until the last disc

layer, and hence this would solve the hydrodynamics

simulation for the whole bed. The simulation program was

then continued with new superficial velocity and then totally

stopped when the maximum indicated superficial velocity was

reached.

III. EXPERIMENTAL STUDY

Fig. 6 shows experimental set up of the SFB of the present

study, which was similar to the design used by Sreenivasan

and Raghavan [7]. A Plexiglas acrylic column formed the bed

wall. To eliminate the possible creation of „dead zone‟ at the

center of the beds a hollow metal cone was located at the base

center. The cone could also reduce particle elutriation for

deeper beds at high velocity operation [7]. The inner holders

were placed at the center to support the annular spiral

distributor that consisted of sixty overlapping blades arranged

at a deflection angle of 10° relative to the horizontal plane. An

orifice flow meter was placed upstream in the pipeline to

determine the air flow rate through the bed. There were three

pressure tapings, P1, P2 and P3, two on the bed wall and one

below the distributor plane. Pressure drops across distributor

was defined as, P2-P1. The bed pressure drop was then

obtained by subtracting the distributor drop from the total

pressure drop, P3-P1. All pressure drops were measured in mm

of water using a Yokogawa EJX 110 digital pressure gauge.

The bed was loaded with 0.5 kg, 1.0 kg and 1.5 kg of sphere

particles with the diameters of 3.9 mm and 2.7 mm. The air

flow rate was increased progressively with the total pressure

drops were recorded.

Fig. 6. Set up of SFB

Fig.7 shows the area of cross sections for finding the

superficial velocity from the experiment in SFB. Using the

equation of continuity, the superficial velocity at the bed

entrance was expressed as the ratio of fluid flow rate before

the distributor to the bed area,

(21)supA

AUU

bed

sserficial

where Us was the fluid gas velocity before entering distributor

(m/s), As was the area of cross section available for fluid flow

before entering distributor (m2) and Abed was the area of cross

section for the bed (m2). The operating parameters of the

experiments were summarized in Table.I.

T ABLE I

Operating parameters of experiment

Parameters Range

Particle density 800 kg/m3

Number of blades 60

Angle of inclination of blade 10°

Radius of Plexiglas Column 0.15 m

Radius of cone at the bottom 0.10 m

Height of cone 0.26 m

Fig. 7. Area of cross section in SFB.

IV. RESULTS AND DISCUSSIONS

A. Analytical model

The centrifugal forces due to rotation and drag acting on the

disc caused the bed pressure drop to increase with gas velocity

as reported by [8]. The results of simulation using the

analytical model are plotted together, for comparison, with the

experimental results for different bed weights and particle

sizes. Shown in Figs. 8 and 9 are the variations of average bed

pressure drop with superficial gas velocity for the 2.7 mm and

3.9 mm diameter particles, respectively, and bed weights of

0.5 kg, 1.0 kg, and 1.5 kg. The one-dimensional analytical

model of SFB (continuous line) shows good agreement with

the experimental results (triangle, cross and circle markers) in

both Figs. 8 and 9, and hence this supports the statement that

pressure drop is directly proportional to the centrifugal friction

force and drag force of fluid. It led to a two degree of

Area of cross section for fluid

flow before entering distributor

Area of cross section for the bed

Superficial velocity

Fluid tangential

velocity

Plexiglas

Column

Metal Cone

Blades

distributor

Centre body

support

P1

P2

P3

General direction

of air flow

Air inlet

Dimensions in (mm)



polynomials variation trend of plot for the pressure drop with

the increasing of superficial velocity. It is shown in Figs. 8 and 9 that the predicted minimum

fluidizing velocities were larger than those obtained through

the experiments. This was probably due to the actual particles

used, which were not perfectly spherical in shape as they had a

tiny cylindrical hollow in the middle. The deviation between

the simulation and experiment results are shown to be greater

for the smaller particles (2.7 mm). In the experiment, the

smaller particles were observed to swirl more aggressively and

there were clear regimes of swirling and bubbling with

increasing superficial velocity. Consequently, the pressure

drops in smaller sizes of particle were slightly higher than

those of larger particles for the same shape and material.

B. Parametric Analysis

Parametric analyses were carried out on how blade inclination

angle, number of blades, fluid density, superficial velocity and

bed weight affect the inclination angle and velocity of fluid

leaving the bed and the average velocity of particles in bed.

These three effects were regarded as important for the study of

hydrodynamics characteristics of the bed as the fluid passed

and traveled through the bed in the axial direction. The range

of parameters in the study is shown in Table II.

T ABLE II

Range of parameters for parametric study

Parameters Range

Blade inclination angle at the distributor 10°– 45°

Number of blades 40 – 80

Fluidization fluid density 1.0 – 50.0 kg/m3

Superficial velocity 0 – 8 m/s

Bed weight 0 – 6.6 kg

Influence of Blade Inclination Angle at Distributor

Figs. 10 to 12 show the variation of blade inclination angle ,θb,

on the fluid velocity, average velocity of particles and

inclination angle of fluid gas relative to horizontal plane

obtained through simulation. It is shown that high blade

inclination angle at the distributor will lead to high inclination

angle of fluid leaving the bed and also high fluid velocity, Vf.

The fluid velocity in higher blade inclination angle was having

higher velocity or momentum but it is shown to be not helpful

as the horizontal component of fluid velocity decayed as it

traveled through the bed. Consequently, it was difficult for the

fluid to transfer its tangential momentum in the bed operation,

and this led to a lower average velocity of particles , Vp. It is

shown in Fig. 12 that at a high blade inclination angle ,θ, the

average velocity of particles would not change much across

the bed height.

Fig. 8. Variation of theoretical and actual bed pressure drop with superficial velocity for 2.7 mm diameter particle, at different bed

weight.

Fig. 9. Variation of theoretical and actual bed pressure drop with superficial velocity for 3.9 mm diameter particle, at different bed

weight .

Fig. 10. Influence of θb on Vf in axial direction.

Fig. 11. Influence of θb on Vp in axial direction.



Influence of Number of Blades at Distributor

Figs. 13 to 15 show the variation of number of blades ,nb, at

distributor on the fluid velocity, average velocity of particles

and inclination angle of fluid gas relative to horizontal plane

obtained through simulation. Figs. 13 to 15 show that the

greater the number of blades at the distributor will result in a

higher average velocity of particles ,Vp, and also a smaller

inclination angle of fluid leaving the bed, θ, as well as a higher

fluid velocity, Vf. It is also found that with higher number of

blades would result in a more uniform fluid flow into the bed

and hence better momentum can be transferred to the particles.

Influence of Fluid Density

Figs. 16 to 18 show the variation of fluid density ,ρf, on the

fluid velocity, average velocity of particles and inclination

angle of fluid gas relative to horizontal plane obtained through

simulation. Figs. 16 to 18 show that high density of fluid used

for fluidization would result higher average velocity of

particles, Vp, but not effective on fluid velocity leaving the

bed, Vf . It is shown in Fig. 18 that the inclination angle of

fluid in the bed ,θ, would decrease with fluid density. By

increasing the fluid density, would also increase the mass flow

rates of fluid, and therefore a higher momentum can be

delivered by the fluid to the particles.

Fig. 12. Influence of θb on θ in axial direction.

Fig. 13. Influence of nb on Vf in axial direction.

Fig. 14. Influence of nb on Vp in axial direction.

Fig. 15. Influence of nb on θ in axial direction.

Fig. 16. Influence of ρf on Vf in axial direction.

Fig. 17. Influence of ρf on Vp in axial direction.



Influence of Superficial Velocity

Figs. 19 to 21 show the effect of superficial velocity on the

fluid velocity ,Us, average velocity of particles and inclination

angle of fluid gas relative to horizontal plane obtained through

simulation. It is shown that of average velocity of particles , Vp,

is linearly proportional to superficial velocity. Although

higher superficial velocity carries higher energy or momentum

of fluid, which is favorable for swirling bed operation but this

would increase the power consumption of blower. The fluid

velocity leaving the bed, Vf, also increased linearly with the

superficial velocity. This can be explained that higher

superficial velocity still has its momentum after it has used for

the bed operation compared to lower superficial velocity.

Superficial velocity does not have significant influence on the

inclination angle of fluid in the bed, θ.

Influence of Bed Weight

Figs. 22 to 24 show the effects of bed weight ,Wb, on the fluid

velocity, average velocity of particles and inclination angle of

fluid gas relative to horizontal plane obtained through

simulation. From the figures, it is shown that the inclination

angle of fluid ,θ, fluid velocity leaving the bed ,Vf,, and

average velocity of particles , Vp,, are affected by the bed

weight. As the bed weight (of the same particle density) is

increased the volume of bed and height also increases. The

fluid gas needs to travel a long distance in the axial direction

before leaving the bed, and hence less momentum from fluid

is transferred to the particles. This led to the increased of fluid

velocity, average velocity of particles and inclination angle of

fluid gas relative to horizontal plane as the bed weight

increased.

Fig. 18. Influence of ρf on θ in axial direction.

Fig. 19. Influence of Us on Vf in axial direction.

Fig. 20. Influence of Us on Vp in axial direction.

Fig. 21. Influence of Us on θ in axial direction.

Fig. 22. Influence of Wb on Vf in axial direction.

Fig. 23. Influence of Wb on Vp in axial direction.



Overall Findings from Parametric Analysis

Through parametric analysis, it was revealed that the

inclination angle of fluid gas relative to the horizontal plane

would be a function of blade inclination angle and the number

of distributor blades and the bed weight. The analysis also

showed that the fluid velocity leaving the bed would be

mainly affected by blade inclination angle, superficial velocity

of fluid and bed weight. As for the average velocity of

particles, the parametric analysis results showed that it would

be mainly affected by all the five parameters: blade inclination

angle and the number of distributor blades, density of fluid for

fluidization, superficial velocity of fluid and bed weight. The

parametric analysis was summarized in Table III.

T ABLE III

Summary of parametric analysis

Parameters

Impact on hydrodynamics effect of

Fluid

velocity leaving the

bed (m/s)

Average

velocity of particles

(m/s)

Inclination

angle of fluid with horizontal

(degrees)

Blade inclination

angle at distributor Medium High High

Number of blades Low High Medium

Fluid density Low High Medium

Superficial velocity

Medium High Low

Bed weight High High High

Among all the variables, blade inclination angle and number

of blades, fluid density and bed weight were found to be the

major factors that affect the swirl characteristics for SFB

following by the superficial velocity. In the future, it is

recommended that experimental and analytical study be made

for packed bed region using SFB. Ergun‟s equation [14] that

was used in the present prediction model was not found to be

highly effective as the Ergun‟s equation was originally

developed from conventional fluidized bed.

V. CONCLUSION

The presented model has been able to show that reduction

from a three dimensional model consisting peripheral, radial

and axial variations to only axial variation for the study of

hydrodynamics and pressure drop of SFB is justified. It was

observed that the pressure drop of bed displayed a quadratic

variation with superficial velocity, which agreed with the

results in previous studies [5]-[8], [14]. It was also found in

the study that the analytical study is able to predict the

pressure drop across the bed with deviations of less than 15%

from the experimental results.

As for the future improvement, it was recommended that:

a. Analytical study of packed bed region in SFB should

be revised as the Ergun‟s equation that was used in

the present prediction model was not found to be

highly effective because it was originally developed

from conventional fluidized bed,

b. Simulation model can be revised by considering the

voidage change and the frictional force between

particles as the superficial velocity increases to

further reduce the percentage errors,

c. Perfect solid sphere particles can be used for bed‟s

operation in the experiments as the actual particles

that used had tiny cylindrical hollow in the middle,

which deviated from the ideal assumption that made

in the model,

d. Particle movement tracking to be conducted to

further investigate the angular and tangential velocity

of particles in SFB in order to compare the predicted

values from the analytical model, and

e. Different particle sizes, different number of

distributor blades and different distributor blade

angle inclination are to be examined in the

experiment to further strengthen and validate the one-

dimensional analytical model.

ACKNOWLEDGMENT

The authors wish to thank the Universiti Teknologi

PETRONAS for providing financial support to carry out this

research. They would also like to record their deep gratitude

to Prof. Dr. Vijay R. Raghavan for all his guidance

particularly at the early stage of the work.

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Fig. 24. Influence of Wb on θ in axial direction.



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one-dimensional modeling of hydrodynamics in a swirling

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