Coupling of VOF with LPT to improve cavitation modeling · Introduction Multi-scale modelBubbles...
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Introduction Multi-scale model Bubbles identification Results Conclusions Coupling of VOF with LPT to improve cavitation modeling Aur´ elia Vallier 1 Johan Revstedt 1 H˚ akan Nilsson 2 1 Fluid Mechanics/Energy Sciences, LTH Lund University, Sweden 2 Applied Mechanics/Fluid Dynamics, Chalmers University of Technology, Sweden 2011-06-15 Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 1 / 17
Transcript of Coupling of VOF with LPT to improve cavitation modeling · Introduction Multi-scale modelBubbles...
Introduction Multi-scale model Bubbles identification Results Conclusions
Coupling of VOF with LPTto improve cavitation modeling
Aurelia Vallier 1
Johan Revstedt 1
Hakan Nilsson 2
1 Fluid Mechanics/Energy Sciences, LTH Lund University, Sweden2 Applied Mechanics/Fluid Dynamics, Chalmers University of Technology, Sweden
2011-06-15
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 1 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Experiments
Numerical simulations
ImprovementModel the small bubbles which are present after thebreakup of the attached cavity.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 2 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Experiments
Numerical simulations
ImprovementModel the small bubbles which are present after thebreakup of the attached cavity.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 2 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Experiments
Numerical simulations
ImprovementModel the small bubbles which are present after thebreakup of the attached cavity.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 2 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Mass transfer cavitation modelbased on VOF (Volume Of Fluid)
Bubbles larger than the grid size
High vapor volume fraction
Irregular structures: need todescribe the interface
Bubble cavitation model based onLPT (Lagrangian Particle Tracking)
Bubbles smaller than the grid size
Low vapor volume fraction
Shape can be considered spherical
1 Coupling of Eulerian and Lagrangian models : multi-scale model
2 Identify the small bubbles suitable for LPT
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 3 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Mass transfer cavitation modelbased on VOF (Volume Of Fluid)
Bubbles larger than the grid size
High vapor volume fraction
Irregular structures: need todescribe the interface
Bubble cavitation model based onLPT (Lagrangian Particle Tracking)
Bubbles smaller than the grid size
Low vapor volume fraction
Shape can be considered spherical
1 Coupling of Eulerian and Lagrangian models : multi-scale model
2 Identify the small bubbles suitable for LPT
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 3 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Mass transfer cavitation modelbased on VOF (Volume Of Fluid)
Bubbles larger than the grid size
High vapor volume fraction
Irregular structures: need todescribe the interface
Bubble cavitation model based onLPT (Lagrangian Particle Tracking)
Bubbles smaller than the grid size
Low vapor volume fraction
Shape can be considered spherical
1 Coupling of Eulerian and Lagrangian models : multi-scale model
2 Identify the small bubbles suitable for LPT
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 3 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Mass transfer cavitation modelbased on VOF (Volume Of Fluid)
Bubbles larger than the grid size
High vapor volume fraction
Irregular structures: need todescribe the interface
Bubble cavitation model based onLPT (Lagrangian Particle Tracking)
Bubbles smaller than the grid size
Low vapor volume fraction
Shape can be considered spherical
1 Coupling of Eulerian and Lagrangian models : multi-scale model
2 Identify the small bubbles suitable for LPT
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 3 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
VOF for mass transfer cavitation model
Liquid volume fraction α ∈ [0, 1].
ρ = αρg + (1− α)ρl,
µ = αµg + (1− α)µl,
Transport equation for the vapor volume fraction
∂α
∂t+∇ · (αU) +∇ · (α(1− α)Ur) = Sα
Sα = − mρv
Mass and momentum equations for the mixture
∇ ·U = 0,∂ρU∂t
+∇ · (ρU⊗U) = −∇p+ µ∇2U + ρg − Sst + SP.
Sst = σstκδn.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 4 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
VOF for mass transfer cavitation model
Liquid volume fraction α ∈ [0, 1].
ρ = αρg + (1− α)ρl,
µ = αµg + (1− α)µl,
Transport equation for the vapor volume fraction
∂α
∂t+∇ · (αU) +∇ · (α(1− α)Ur) = Sα
Sα = − mρv
Mass and momentum equations for the mixture
∇ ·U = 0,∂ρU∂t
+∇ · (ρU⊗U) = −∇p+ µ∇2U + ρg − Sst + SP.
Sst = σstκδn.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 4 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
VOF for mass transfer cavitation model
Liquid volume fraction α ∈ [0, 1].
ρ = αρg + (1− α)ρl,
µ = αµg + (1− α)µl,
Transport equation for the vapor volume fraction
∂α
∂t+∇ · (αU) +∇ · (α(1− α)Ur) = Sα
Sα = − mρv
Mass and momentum equations for the mixture
∇ ·U = 0,∂ρU∂t
+∇ · (ρU⊗U) = −∇p+ µ∇2U + ρg − Sst + SP.
Sst = σstκδn.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 4 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
VOF for mass transfer cavitation model
Liquid volume fraction α ∈ [0, 1].
ρ = αρg + (1− α)ρl,
µ = αµg + (1− α)µl,
Transport equation for the vapor volume fraction
∂α
∂t+∇ · (αU) +∇ · (α(1− α)Ur) = Sα
Sα = − mρv
Mass and momentum equations for the mixture
∇ ·U = 0,∂ρU∂t
+∇ · (ρU⊗U) = −∇p+ µ∇2U + ρg − Sst + SP.
Sst = σstκδn.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 4 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
VOF for mass transfer cavitation model
Liquid volume fraction α ∈ [0, 1].
ρ = αρg + (1− α)ρl,
µ = αµg + (1− α)µl,
Transport equation for the vapor volume fraction
∂α
∂t+∇ · (αU) +∇ · (α(1− α)Ur) = Sα
Sα = − mρv
Mass and momentum equations for the mixture
∇ ·U = 0,∂ρU∂t
+∇ · (ρU⊗U) = −∇p+ µ∇2U + ρg − Sst + SP.
Sst = σstκδn.Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 4 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
LPT for bubble cavitation model
Particle P : position xP, diameter DP , velocity UP and density ρP .
dxP
dt= UP,
mPdUP
dt=∑
F.
Two-way coupling:
SP =1
Vcell∆t
∑P
mP ((Up)tout − (Up)tin)
Rayleigh-Plesset equation:
pB − p∞ρ
= Rd2R
dt2+
32
(dR
dt
)2
+4µR
dR
dt+
2σstρR
.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 5 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
LPT for bubble cavitation model
Particle P : position xP, diameter DP , velocity UP and density ρP .
dxP
dt= UP,
mPdUP
dt=∑
F.
Two-way coupling:
SP =1
Vcell∆t
∑P
mP ((Up)tout − (Up)tin)
Rayleigh-Plesset equation:
pB − p∞ρ
= Rd2R
dt2+
32
(dR
dt
)2
+4µR
dR
dt+
2σstρR
.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 5 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
LPT for bubble cavitation model
Particle P : position xP, diameter DP , velocity UP and density ρP .
dxP
dt= UP,
mPdUP
dt=∑
F.
Two-way coupling:
SP =1
Vcell∆t
∑P
mP ((Up)tout − (Up)tin)
Rayleigh-Plesset equation:
pB − p∞ρ
= Rd2R
dt2+
32
(dR
dt
)2
+4µR
dR
dt+
2σstρR
.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 5 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
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27 28 29 30 31 32 33 34 35
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Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
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27 28 29 30 31 32 33 34 35
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Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
12 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
12 0
15 1
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
12 0
15 1
16 1
19 0
20 0
21 0
22 0
24 1
25 1
29 0
30 0
31 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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VP =
ZΩ
(1− α) dΩ =X
cell@ID
(1− α)Vcell@ID
Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
12 0
15 1
16 1
19 0
20 0
21 0
22 0
24 1
25 1
29 0
30 0
31 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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VP =
ZΩ
(1− α) dΩ =X
cell@ID
(1− α)Vcell@ID
xP =1
VP
Xcell@ID
(1− α) xcell@ID
Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
12 0
15 1
16 1
19 0
20 0
21 0
22 0
24 1
25 1
29 0
30 0
31 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
0 1 2 3 4 5 6 7 8
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VP =
ZΩ
(1− α) dΩ =X
cell@ID
(1− α)Vcell@ID
xP =1
VP
Xcell@ID
(1− α) xcell@ID
VP < 10%VLAG?
Mark the cells with α < 0.95(i.e. at least 5% of gas.)
Cell Number Bubble ID
10 0
11 0
12 0
15 1
16 1
19 0
20 0
21 0
22 0
24 1
25 1
29 0
30 0
31 0
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 6 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
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Equivalent spherical bubble determined from the irregular vaporstructure
DP = (6πVP )1/3
Create the point particle P (DP ,xP,UP) for the LPT simulation
Remove the bubble from the VOF simulation : α set to 1
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 7 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 1
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 8 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 1
Figure: VOF simulation
Figure: Andersson R. and Andersson B., Modeling the breakup of particles inturbulent flows, AIChE Journal 2006.
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 9 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 1
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 10 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 2
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 11 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 2
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 12 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 13 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 14 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
0
100
200
300
400
500
600
0 50 100 150 200 250 300 350 400
Particle diameter [µm]
Particle size distribution
αlim=0.9αlim=0.95αlim=0.99
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 15 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
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9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
Mark the cells with α < 0.95 0.99
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 16 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
More small bubbles are captured (The”isolated” cells with α ∈ [0.95, 0.99[ arenot neglected anymore)
Mark the cells with α < 0.95 0.99
Cell Number Bubble ID
0 0
4 1
8 2
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 16 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
More small bubbles are captured (The”isolated” cells with α ∈ [0.95, 0.99[ arenot neglected anymore)
Mark the cells with α < 0.95 0.99
Cell Number Bubble ID
0 0
4 1
8 2
10 3
11 3
12 3
14 4
15 4
16 4
19 3
20 3
21 3
22 3
23
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 16 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
More small bubbles are captured (The”isolated” cells with α ∈ [0.95, 0.99[ arenot neglected anymore)
Mark the cells with α < 0.95 0.99
Cell Number Bubble ID
0 0
4 1
8 2
10 3
11 3
12 3
14 /4 3
15 /4 3
16 /4 3
19 3
20 3
21 3
22 3
23 3
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 16 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Test case 3
0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
18 19 20 21 22 23 24 25 26
27 28 29 30 31 32 33 34 35
36 37 38 39 40 41 42 43 44
More small bubbles are captured (The”isolated” cells with α ∈ [0.95, 0.99[ arenot neglected anymore)
Less medium and large bubbles arecaptured (The ”connecting” cells withα ∈ [0.95, 0.99[ merge bubbles and thecondition VP < 10%VLAG isn’t satisfiedanymore)
Mark the cells with α < 0.95 0.99
Cell Number Bubble ID
0 0
4 1
8 2
10 3
11 3
12 3
14 /4 3
15 /4 3
16 /4 3
19 3
20 3
21 3
22 3
23 3
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 16 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Implementation of a multi-scale model.
VOF model complemented with a two-way coupling LPT model.Identification of the small bubbles suitable for LPT approach.
Model applied to simple cases of air bubbles breaking up under theimpact of a water jet.
Ability to capture and track the small bubbles which a pure VOF modelfails to describe.Particles size and distribution depend on the parameters introduced.
Future work : test on a cavitating case.
Include mass transfer with the VOF approach
Include the description of the small bubbles dynamics with the LPTapproach
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 17 / 17
Introduction Multi-scale model Bubbles identification Results Conclusions
Implementation of a multi-scale model.
VOF model complemented with a two-way coupling LPT model.Identification of the small bubbles suitable for LPT approach.
Model applied to simple cases of air bubbles breaking up under theimpact of a water jet.
Ability to capture and track the small bubbles which a pure VOF modelfails to describe.Particles size and distribution depend on the parameters introduced.
Future work : test on a cavitating case.
Include mass transfer with the VOF approach
Include the description of the small bubbles dynamics with the LPTapproach
Aurelia Vallier Coupling of VOF with LPT to improve cavitation modeling 2011-06-15 17 / 17
