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Institute of Safety Research26.04.2007
Mitglied der Leibniz-Gemeinschaft
CFD Simulation of the Two-Phase Flow
around an Obstacle applying an
Inhomogeneous Multiple Bubble Size Class
Approach
E. Krepper, D. Lucas, H.-M. Prasser , M. Beyer, Th. Frank
Multiphase Flows: Simulation, Experiment and Application
Hotel Park Plaza, Dresden
25 – 27 April 2007
Institute of Safety Research26.04.2007
2Mitglied der Leibniz-Gemeinschaft
Outline
1. The concept of the inhomogeneous MUSIG model
• role of the lift force for the flow regime
2. Application to the simulation of a complex flow situation
Institute of Safety Research26.04.2007
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Nondrag bubble forces:
Forces perpendicular to the flow direction
• Turbulence Dispersion:
– transfer of the turbulent fluctuations of the liquid on the bubbles
� smoothing of radial volume fraction profiles
• Wall Force:
– pushes bubbles away from the wall
• Lift Force:
– gaseous bubbles in a shear flow: pressure differences from the liquid surrounding on the bubble surface
– proportional to the gradient of the liquid flow field
� direction dependent on the bubble size
Lift
WandkraftDispersion
Institute of Safety Research26.04.2007
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Tomiyama (1998): Experimental Investigation of single bubbles in a laminar shear flow (Glycol)
• application of this correlation to air/water:
• CLIFT changes the sign at dB = 5.8 mm0 2 4 6 8 10
dB [mm]
-0.4
-0.2
0
0.2
0.4
CL
IFT
474.00204.00159.000105.0)(
1027.0
104)(
4)](Re),121.0tanh(288.0min[
23+−−=
>−
<<
<
=
dddd
d
dd
dd
Lift
EoEoEoEofwith
Eo
EoforEof
EoEof
C
σ
ρρ 2)( hgl
d
dgEo
−=
Institute of Safety Research26.04.2007
5Mitglied der Leibniz-Gemeinschaft
Conditions for steam/water
• evaluation of the Tomiyamacorrelation:
� with higher pressure the critical bubble size dB(CLIFT=0) is decreased
0 50 100 150 200P [105 Pa]
0.0
2.0
4.0
6.0
dB [
mm
]
Institute of Safety Research26.04.2007
6Mitglied der Leibniz-Gemeinschaft
Measurements in FZD: Decomposition of the gas volume fraction distribution according bubble size
Institute of Safety Research26.04.2007
7Mitglied der Leibniz-Gemeinschaft
TOPFLOW experimentsJL = 1 m/s and JG = 0.22 m/s (FZR-118), L/D = 40, Injection valves: Dinj = 4 mm
• Horst-Michael Prasser et. al (2005): evolution of the structure of a gas-
liquid two-phase flow in a large vertical pipe, NURETH-11, paper 399
Institute of Safety Research26.04.2007
8Mitglied der Leibniz-Gemeinschaft
Influence of bubble forces on the flow regime in a vertical upward bubbly flow
• Lift Force:
– small bubbles are pushed towards the wall
– large bubbles are moved towards the centre
• bubble break-up
– turbulent dissipation
– only near the wall
• bubble coalescence :
– at bubble accumulation
�radial phenomena have important influence on the flow regime
�a model approach has to be able to describe radial separation of small and large bubbles
Institute of Safety Research26.04.2007
9Mitglied der Leibniz-Gemeinschaft
Population balance approach
• Definition of different bubble size classes
– interact via models for bubble coalescence and bubble break-up
• In the Euler/Euler approach in principle the definition of several bubble classes is possible
• For the adequate description decades of bubble classes would be necessary (shown by separate investigations)
• Numerical problems: CPU time, convergence, stability
Institute of Safety Research26.04.2007
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Multiple bubble size group model (MUSIG)
• S. Lo (1996 CFX-4):
• for the gaseous phase only one velocity field
• only one momentum equation for the gaseous phase
• consideration of bubble break-up and coalescence only in the continuity equation
VG
d1 dM
bubblecoalescence
bubblebreak-up
Gas velocity
Size fractionsK=1..M dk
Institute of Safety Research26.04.2007
11Mitglied der Leibniz-Gemeinschaft
Concept for the improvement of the MUSIG Model
• The gaseous momentum equation is solved for at least two gaseous phases
� the description of the separation of small and large bubbles becomes possible
• simulation of bubble coalescence and break-up over all gaseous subsizefractions (continuity equation)
V1 V2 VN
d1 dM1 dM1+1 dM1+M2
bubblecoalescence
bubble break-up
Velocity groupsJ=1..N
Size fractions
K=1..ΣMJ
...
dΣMJ
Institute of Safety Research26.04.2007
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TOPFLOW FZR-118: JL=1.0 m/s, JG=0.2194 m/s
2 dispersed Phases, 34 sub-size fractions
0 6 12 18 24 30 36 42 48 54 60DBub [mm]
0.00
0.40
0.80
1.20
1.60
2.00dV
F/d
DB [%
mm
-1]
R: 7.802 mexp
CFX
0.000 0.020 0.040 0.060 0.080 0.100Radius [m]
0.00
0.10
0.20
0.30
Ga
s v
olu
me
fra
ctio
n [-]
R: 7.802 mExperiment
CFX-10 (total)
dB< 6 mm
dB> 6 mm
0 6 12 18 24 30 36 42 48 54 60DBub [mm]
0.00
0.20
0.40
0.60
dV
F/d
DB [%
mm
-1]
C: 0.335 mexp
CFX
0.000 0.020 0.040 0.060 0.080 0.100Radius [m]
0.00
0.10
0.20
0.30
Ga
s v
olu
me
fra
ctio
n [-]
C: 0.335 mExperiment
CFX-10 (total)
dB< 6 mm
dB> 6 mm
Institute of Safety Research26.04.2007
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Investigation of a complex flow situation: Flow around an obstacle
Institute of Safety Research26.04.2007
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Comparison of calculated and measured timely averaged gas volume fraction and liquid velocity distributions
Run 096: JL = 1.017 m/s; JG = 0.0898 m/s
water velocity air volume fraction
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Calculated Turbulence Dissipation
Institute of Safety Research26.04.2007
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Comparison of measured and calculated cross
sectional averaged bubble size distributions
0 5 10 15 20 25DB [mm]
0.0
1.0
2.0
3.0
4.0
dV
F/d
DB [%
mm
-1]
run 096-0.52 m
0.08 m
0.52 m
Run 096 JL = 1.017 m/s; JG = 0.0898 m/s
0 5 10 15 20 25DB [mm]
0.0
1.0
2.0
3.0
4.0
dV
F/d
DB [%
mm
-1]
run 096Z = -0.52 m
Z = 0.08 m
Z = 0.52 m
measurement calculation
Institute of Safety Research26.04.2007
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streamlines for large and small bubbles
Run 096:
JL = 1.017 m/s;
JG = 0.0898 m/s
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Lift forces
Run 096:
JL = 1.017 m/s;
JG = 0.0898 m/s
Institute of Safety Research26.04.2007
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mean sauter bubble diameter
Run 096:
JL = 1.017 m/s;
JG = 0.0898 m/s
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Gas distributions for different bubble size classes
run 096 (JL = 1.017 m/s; JG =0.0898 m/s)
measurement calculation
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Run 097:
JL = 1. 611 m/s;
JG = 0.0898 m/s
Water Velocity
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Run 097:
JL = 1. 611 m/s;
JG = 0.0898 m/s
Total Air Volume Fraction
Institute of Safety Research26.04.2007
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Gas distributions for different bubble size classes
Run 097:
JL = 1.611 m/s;
JG = 0.0898 m/s
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Obstacle: Summary of observations
1. Phenomena in the wake of the obstacle
• Small bubbles are transported behind the obstacle (lift force)
• Bubble accumulation behind the obstacle causes coalescence
• in the measurements behind the obstacle mainly large bubbles are
found
2. Phenomena in the jet beside the obstacle in the non-obstructed cross sectional area
• Generated large bubbles are rejected into the jet beside by the
obstacle
• Near the jet margin large shear rates are found
• fragmentation of large bubbles (not considered in the calculations)
• small bubbles are rejected out of the jet (lift force)
Institute of Safety Research26.04.2007
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Summary
• correct function of the inhomogeneous MUSIG model approach confirmed
• thoroughly understanding of the complex flow situation
• closure models for bubble forces in agreement with experiment
• most weak point: Models for simulation of bubble coalescence and bubble break-up
– With the actual implemented models tuning coefficients are
necessary:
• air/water in vertical tube: FB = 0.25; FC = 0.05
• steam/water in vertical tube: FB = 0.02; FC = 0.05
• complex flow: tuning factors depend on flow situation
• Further work is considered for future investigations