A computational (DEM) study of fluidized beds with particle size distribution, APT2003 Tagami & Horio

19th/12/2003 N.Tagami and M.Horio 1

A Computational Study of Fluidized

beds with Particle Size Distribution

N. Tagami and M. Horio

Tokyo University of Agriculture and Technology

Department of Chemical Engineering

Tokyo, Japan

Presented at:

The Second Asian Particle Technology Symposium (APT 2003)

17th-19th December 2003, Penang, Malaysia


Contents

1. Introduction

2. Modifications of fluid drag calculation

3. Calculation results

4. Conclusions


Introduction

With our code SAFIRE, we have

demonstrated that the discrete element

method (DEM) can be a powerful tool for

industrial chemical reactor design issues.

However, so far, most of the work in the literature

has limited within uniformly sized particles.

There is insufficient consideration about the

effect of particle size distribution (PSD)

present in a fluidized bed


What happens with the introduction of

PSD ?

(1) Fluid drag acting on each

particle should be assigned

depending on relative velocity

and particle size.

(2) Three dimensional calculation

becomes inevitable

(3) Drag force is assigned to each

particle depending on the

particle alignment

In this work SAFIRE was

modified in terms of (1) and (2).

(2) 2D → 3D

(1) non-even

fluid drag

(3) fluid drag

dependency

on alignment

thickness

2D → 3D


Pressure drop in a dense phase is given by

Ergun(1952)

Determination of CD from fixed bed data

vuvu1.75ρ

d

με1150

d

ε-1

LgρΔPΔP

fp

f

p

f

*

densityFluid:ρ

fractionVoid:ε

diameterParticle:d

areaProjected:A

f

p

p

Drag coefficient defined with mean diameter:

2

f

2p

pf

D

vuρd

F8C

Equation of fluid motion for 1D steady flow:

0gερFnΔL

ΔPε fpf /6dπ/ε1n

3p

2.33

vuερd

με1200C

fp

fErgunD,


Approximate expression for CD

corresponding to Ergun correlation

2.33

vuερd

με1200C

fp

fErgunD,

2.33

vuερd

με1200C

fp

fErgunD,

extension for individual particle

extension to a system with a wide PSD

2.33

ε

ε1

vuρd

200μC

fp

fErgunD,

effect of could be different in the mixed particle

system, but let’s use the same expression


Dense phase

2.33vuερd

με1200C

fp

fErgunD,

Drag coefficients

Wen-Yu(1966) correlation

sD,

3.7

WYD, CεC

where

700Re0.44

700Re0.15Re1Re

24C 0.687

sD,

0.40.6

0.8

1.0

1

10

100

1000

10000

0.0 0.4 0.8 1.2 1.6

Single particle

From Ergun Eq.

From Wen-Yu Eq.

Ap

pa

ren

t d

rag

co

effic

ien

t [-

]

Interstitial fluid velocity [m/s]

Void

age [-]

Dilute phase


Governing equations Translational motion of particle

Rotational motion of particle

Equation of continuity for fluid

Equation of motion for fluid

gFFFFv

mdt

dm fpcohesionpwcollision,ppcollision,

wallfpcohesionpwcollision,ppcollision,dt

dI MMMMMω

0

t

ε

t

ε

u

gFσuu

fpff ερnx

εx

ut

ερ

velocityAngular

tensorStress

fractionVoid

particleaofVelocityv

fluidofVelocityu

particleaofMassm

MomentM

inertiaofMomentI

ForceF

:

:

:

:

:

:

:

:

:


Objectives of the present

computation

To

•confirm the present fluid-particle interaction

treatment satisfy Ergun correlation

macroscopically for systems with PSD.

•analyze the effect of PSD on macroscopic

fluidized bed behavior for cases with the same

mean particle size (dpsv) and total bed volume.


dp1/dp2 [mm/mm] Number of particles

1.00 30000

1.10 / 0.917 (1.20) 11270 / 19474

1.20 / 0.857 (1.40) 8681 / 23819

1.50 / 0.750 (2.00) 4444 / 35556

][00.12

3

mmdN

dN

p

p

The average surface to

volume diameter is identical

for each calculation as

The total volume and surface

area of the particles are also

held constant

][1043.9

][1057.1

22

35

mS

mV

total

total

Computational Conditions

(continued)

dpsv=

19th/12/2003 N.Tagami and M.Horio 11 Air

(continued)

App. 54mm

50mm

10mm

200mm

0

0.5

1.122

1.0 Time[s] S

up

erf

icia

l ve

locity [m

/s]

Linear Spring Spring constant : 800N/m

Linear dashpot Restitution coefficient : 0.9

Particle density : 2650 kg/m3

Friction coefficient : 0.3


Calculation results

1.00mm 30000 1.10mm 11270

0.917mm 19474

1.20mm 8681

0.857mm 23819 1.50mm 4444

0.750mm 35556

dp1/dp2= 1.2 1.4 2.0


Comparison of fluid drag force

acting on each fluid cell Blue zone: fluid drag force numerically determined

agrees with Ergun correlation + 20% in each fluid cell

(Fdrag coefficitent) / (FErgun,fluid cell)

dp1/dp2= 1.2 1.4 2.0

-


Total translational kinetic energy increases

as the difference in particle size increases

Total translational kinetic energy

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0

0.2

0.4

0.6

0.8

Uniform system

Binary system

dp1/dp2=1.2

dp1/dp2=1.4

dp1/dp2=2.0

To

tal tr

ansla

tional kin

etic e

nerg

y [

mJ]

Time [s]


0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

Cumulative number of collisions

Uniform system

dp=1.00mm

Binary system

dp=1.10mm Binary system

dp=0.917mm

Cum

ula

tive n

um

ber

of colli

sio

ns [

#]

Time [s] (continued)

Ten particles are

traced in each

component

dp1/dp2

= 1.2


0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

dp1/dp2

= 1.4

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

Binary system

dp=1.50mm

Binary system

dp=1.20mm

Binary system

dp=0.857mm

Binary system

dp=0.750mm

Cum

ula

tive n

um

ber

of colli

sio

n [

#]

(continued)

Time [s]

dp1/dp2

= 2.0

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000

Uniform system

dp=1.00mm In the binary system

momentum transportation

between particles is

emphasized


Conclusions

To achieve the DEM simulation with PSD,

modification of fluid drag force calculation is needed.

In the present study, the drag force is

computed using the drag coefficient combined

with Ergun correlation.

The calculation results show that reasonable fluid

drag force is calculated for each fluid cell.

The bed motion activity increases due to

the existence of particle size distribution

A computational (DEM) study of fluidized beds with particle size distribution, APT2003 Tagami & Horio

Technology

d p f u v n

d p f u v d p f u vextension

particle u u

void fraction d p d

n d p stotal

d p f u v effect

constant n d

f u v u v