Implementation of Breakup and Coalescence Models in CFD CHEMICAL REACTION ENGINEERING LABORATORY Peng Chen, Chemical Reaction Engineering Laboratory Washington

Implementation of Breakup and Coalescence Models in CFD

CHEMICAL REACTION ENGINEERING LABORATORY

Peng Chen,

Chemical Reaction Engineering Laboratory

Washington University

St. Louis, MO 63130

CREL Group Meeting

December 14, 2000

Overview

• Introduction

• Bubble number density approach

• Result

• Future work


Introduction• The drag force term in one of the key issue of two-fluid model and the

predictive capabilities of this model depend crucially on the closure.

• Most numerical simulation resorts to single particle drag correlation with a “mean” bubble size. This is mostly because modeling different sizes of bubbles as individual phase lead to unrealistic computational cost and has numerical convergence problem.

• However, in reality, bubble-bubble interaction results in local variation in bubble sizes that are substantially different from the “mean” bubble size assumption.

• In order to get reasonably good simulation result, the “mean” bubble size need to be adjusted so that it could be far away reality.


Motivation

• Bubble size distribution should be resolved locally by implement bubble coalescence and breakup into CFD framework.

• There is rare implementation of such bubble breakup/coalescence model in CFD simulation of bubble column reactors.

• Bubble breakup (Martínez-Bazán, 1999) and coalescence (Luo, 1993) model was implemented using bubble number density approach into FLUENT 5.48 in the context of Algebraic Slip Mixture Model (ASMM).


Bubble Number Density Approach

The population balance equation for the ith bubble class

The source term may be written as

tvxStvxftvxutvxft p ,,,,,,,,

rpphv

v

SSStvxfvbdvtvxfvvPvbvm

dvtvxfvvatvxfdvtvxftvvxfvvvatvxS

,,)(',',',''

',',',,,',',,',','2

1,,

00


N

iii

N

iii

sm

af

vfD 1

6

i

icigi d

ddKdg

12,

32

*

max

*min

*35923*3532*

35923*3532*

10

1

1,

D

DDdDD

DDDDf

Closures - Breakup


Martínez-Bazán et al. (1999)

250

1

23

0min*min

12

DDDD

313*

min*max 1 DD

01* DDD

10

52530 12 DDDC

Closure - Coalescence


21

321

2132

1

1175.0exp, ij

ijcd

ijijjiC WecddP

2132312 1 jiijijiij dddnnddk

jiCijij ddPQ ,

, ij = di/dj, 21322122 1 ijijiij uuuu

2ijic ud

We

Luo (1993)

Geometric Grid was used, xi+1 = 2vi. x0 = 1mm.


,11rr

ii

iri

ii vxvxv

M

iii xvNtvxf

0

,,

',',',''',',,',','2

1,,

0dvtvxfvvPvbvmdvtvxftvvxfvvvatvxS

v

v

dvvtvxSdvvtvxS ii

x

x

ii

x

x

i

i

i

i

1

1

,,,, 1 Source term for particles of size xi is

dvxvPvdvxvPv

NxbxbxmNNxxaN

NNxxaxx

NNxxaxxtxS

j

x

x

iij

x

x

iiji

iijij

M

ijjjj

M

jjii

kjjkkji

i

kj

xxxxjk

kjjkkji

i

kj

xxxxjki

i

i

i

i

ikji

ikji

,,

,

,2

11

,2

11,

1

1

1

1

1,

,0

1


Result

Comparison of Axial Velocity Profile

-30

-20

-10

0

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

r/R

Ax

ial

Ve

loci

ty (

cm/s

ec)

Simulation

CARPT


Comparison of Gas Holdup

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.2 0.4 0.6 0.8 1r/R

Gas

Ho

ldu

p

Simulation

CT


Overall: 17.5%; Experiment, 19%.


00.0020.0040.0060.0080.01

0.0120.0140.0160.0180.02

0 0.2 0.4 0.6 0.8 1

r/R

volu

mn

fra

ctio

nClass 4

Class 6

Class 4: d = 2.5 mm; Class 6: d = 4.0 mm


0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 0.2 0.4 0.6 0.8 1

r/R

Vo

lum

n F

ract

ion

Class 12

Class 14

Class 12: d = 16.0 mm; Class 14: d = 25.4 mm

Future Work

• Tune up the parameters, try to got a universal one or some sort of correlation.

• Test the sensitivity of boundary condition

• Test other breakup/coalescence closure

• Implement area transport equation approach

• Run 3D simulation

• Expand to Euler-Euler two fluid model

• With optical probe data, verify the closures and propose own closures


Documents

Implementation of Breakup and Coalescence Models in CFD CHEMICAL REACTION ENGINEERING LABORATORY Peng Chen, Chemical Reaction Engineering Laboratory Washington