Modelling of acoustic cavitation on a large scale with ...€¦ · 100cm³ reactor and...
Transcript of Modelling of acoustic cavitation on a large scale with ...€¦ · 100cm³ reactor and...
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 1
Modelling of acoustic cavitation on a
large scale with OpenFOAM
Sergey Lesnik, Gunther Brenner
Institute of Applied Mechanics / TU Clausthalin cooperation with University Göttingen
German OpenFoam User meetiNg, Online, 22.04.2020
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 2
Acoustic cavitation
Source: Industrial Sonomechanics, LLC
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 3
Acoustic cavitation: multiscale problem
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 4
Motivation
State of the art
fundamental physics of microscopic phenomena well
understood
macroscopic computations: only linear bubble oscillations
with homogeneous distribution
Current ansatz
non-linear cavitation bubble oscillations
spatially inhomogeneous bubble distribution
relatively large geometries (~1-10dm³)
prediction of
ultrasound field
location of cavitation bubble clustering
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 5
Outline
2. Radial Bubble
Dynamics
3. Bubble Motion
1. Ultrasound:
Helmholtz Eqn.
Model Coupling
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 6
Outline
2. Radial Bubble
Dynamics
3. Bubble Motion
1. Ultrasound:
Helmholtz Eqn.
Model Coupling
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 7
Helmholtz equation (HE)
Wave equation in frequency
domain
𝑃ac - complex sound pressure
amplitude
𝑘m - complex wave number of the
gas-liquid mixture
Computation with OpenFOAM
no complex numbers
decompose HE in two equations
solving in segregated manner
leads to divergence in most cases
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 8
HE discretization and solution
Discretized with block-coupled matrix to couple
equations implicitly (foam-extend)
The matrix of discretized HE is highly indefinite
iterative solvers diverge
=> Interface implemented to a direct solver (MUMPS)
MUltifrontal Massively Parallel sparse direct Solver
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 9
Outline
2. Radial Bubble
Dynamics
3. Bubble Motion
1. Ultrasound:
Helmholtz Eqn.
Model Coupling
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 10
Radial bubble dynamics (RBD)
Toegel model: 3 ODEs Keller-Miksis eqn. (𝑅 – bubble radius)
energy transfer (𝜃 – temperature)
mass (vapor) transfer (𝑛 – amount of substance)
Source: University of Göttingen, Drittes Physikalisches Institut
R
Time period
𝑇 = 50µs(𝑓 = 20kHz)
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 11
Coupling non-linear RBD and sound field
Coupling via 𝑘m (Louisnard model)
𝛽 – void fraction / bubble density
ΠVi,Th – integrals over one oscillation period; physically:
energy dissipated per bubble;
ΠVi,Th indirectly dependent on 𝑃ac
100cm³ reactor and 𝛽 = 10−5 => 2.3e+6 bubbles
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 12
Coupling non-linear RBD and sound field
Approach as pre-processing step:
1. choose parameter range for 𝑃ac2. solve RBD (implemented in python)
3. compute integral values and save as interpolation tables
RBD
• 1D Model
• Python
Tabulated
integrals
Helmholtz eqn.
• Finite Volumes
• OpenFOAM
Integrate
over 𝑇
Look up 𝑘m2 𝑃ac
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 13
Coupling non-linear RBD and sound field
Iterative process
highly non-linear, under-relaxation not sufficient
damped Newton-Raphson method implemented
jacobian with numeric differentiation
RBD
• 1D Model
• Python
Tabulated
integrals
Helmholtz eqn.
• Finite Volumes
• OpenFOAM
Integrate
over 𝑇
Look up 𝑘m2 𝑃ac
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 14
Boundary conditions
Sonotrode immersed in a
cylindrical geometry
typical setup also for large scale
reactors
axisymmetric
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 15
Free surface Sound soft 𝑃ac = 0
Sonotrode surface In-phase
displacement 𝑈0
𝛻𝑃ac~𝑈0
Sonotrode wall Anti-phase
displacement 𝑈0
𝛻𝑃ac~ 𝑈0, 𝜙0
Symmetry axis Symmetry axis Empty
Walls Sound hard 𝛻𝑃ac = 0
Free surface Sound soft 𝑃ac = 0
Boundary conditions
Sonotrode immersed in a
cylindrical geometry
typical setup also for large scale
reactors
axisymmetricsound soft
sound hard
symmetry
axis
Geometry Acoustics Numerics
Symmetry axis Symmetry axis Empty
anti-phase
displacement
in-phase
displacement
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 16
Linear vs. non-linear bubble oscillations
Linear Non-linear
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 17
Linear vs. non-linear bubble oscillations
Linear Non-linear
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 18
Outline
2. Radial Bubble
Dynamics
3. Bubble Motion
1. Ultrasound:
Helmholtz Eqn.
Model Coupling
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 19
Bubble motion
Euler-Lagrange (foam-extend)
Force balance
𝑚b, 𝑈b- bubble mass and velocity
Forces:
𝐹G - gravitation
𝐹Am - added mass
𝐹D - drag
𝐹Bj - Bjerknes, due to interaction of non-linear oscillation
and acoustic pressure gradient
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 20
OpenFOAM
Coupling bubble motion
Bjerknes force contains bubble volume term averaged
over 𝑇
RBD
• 1D Model
• Python
Tabulated
integrals
Helmholtz eqn.
• Euler-Euler
Integrate
over 𝑇
Look up 𝑘m2 𝑃ac
Bubble Motion
• Euler-Lagrange
Look up < 𝑉b >𝑇 𝑃ac
Interpolate 𝛻𝑃ac
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 21
1D case
Bjerknes force
Stagnation locations
sound softdisplacement = 5µmx
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 22
1D case inhomogeneous void fraction
Void fraction kept constant at transducer (on the right)
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 23
Coupling Liquid motion
OpenFOAM
RBD
• 1D Model
• Python
Tabulated
integrals
Helmholtz eqn.
• Euler-Euler
Momentum
transfer
Bubble Motion
• Euler-Lagrange
Interpolate 𝛻𝑃ac
Liquid Motion
• Euler-Euler
• URANS
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 24
Liquid and bubble motion
2D axisymmetric wedge case
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 25
Summary
Computation of cavitation flows in large scale reactors
apply different models to different scales
coupling needs caution
Validation of sub-models with the data from
experiments
Nucleation process needs more consideration
where do bubbles nucleate and dissolve?
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Sergey Lesnik, Gunther Brenner Modelling of acoustic cavitation on a large scale with OpenFOAM 26
Source code for Helmholtz solver (MUMPS interface):
https://github.com/technoC0re
Questions?