implementation of breakup and coalescence models in cfd chemical reaction engineering laboratory...
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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
CHEMICAL REACTION ENGINEERING LABORATORY
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.
CHEMICAL REACTION ENGINEERING LABORATORY
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).
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY
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.
CHEMICAL REACTION ENGINEERING LABORATORY
,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
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY
Overall: 17.5%; Experiment, 19%.
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY
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
CHEMICAL REACTION ENGINEERING LABORATORY