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Technische Universität MünchenLehrstuhl für Aerodynamik
Stefan AdamiGarching, 18. Nov. 2008
Simulations of multiphase phenomena using Smoothed Particle Hydrodynamics (SPH)
S. Adami, X.Y. Hu, N.A. AdamsInstitute of AerodynamicsTU München
Excellence Cluster Universe:“Workshop on Turbulence andHydrodynamical Instabilties”Garching, 17.19. Nov. 2008
Technische Universität MünchenLehrstuhl für Aerodynamik
2Stefan AdamiGarching, 18. Nov. 2008
OUTLINE
• Motivation
• Numerical Modeling
• Validation
• Applications
• Summary and Outlook
OUTLINE
Technische Universität MünchenLehrstuhl für Aerodynamik
3Stefan AdamiGarching, 18. Nov. 2008
MOTIVATION
• DFG – Project: Protective Artificial Respiratory
MOTIVATION
“Experimental and numerical investigation on the flowinduced stresses on the alveolar – epithelial – air interface”
Technische Universität MünchenLehrstuhl für Aerodynamik
4Stefan AdamiGarching, 18. Nov. 2008
MOTIVATION
• DFG – Project: Protective Artificial Respiratory
MOTIVATION
Numerical modeling of the dynamic behavior of lung surfactant
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
Discretization of Gefen geometry (Gefen et al., J. Biomechanics,
1999)
The Alveoli and Associated Capillaries of Lungs of Humans
Cavity of alveolus is coated with a lining liquid containing surfactant (“surface active agent”) which reduces the surface tension
“Experimental and numerical investigation on the flowinduced stresses on the alveolar – epithelial – air interface”
Technische Universität MünchenLehrstuhl für Aerodynamik
5Stefan AdamiGarching, 18. Nov. 2008
MOTIVATION
• Numerical model:
– Surface tension effects
– Surfactant dynamics (“active scalar”)
– Complex geometry, dynamic interface
• Smoothed Particle Hydrodynamics (SPH)
– Introduced by Lucy (1977) and Gingold and Monaghan (1977)
– Fully Lagrangian, grid free method with particle approximation
– Mass and momentum conservation even when evolving interfaces
– Adaptive interface representation
MOTIVATION
Technische Universität MünchenLehrstuhl für Aerodynamik
6Stefan AdamiGarching, 18. Nov. 2008
THEORETICAL BACKGROUND
• Particle approximation:
THEORETICAL BACKGROUND
r i = i =1V i
∫i r r dr
limh 0
W r−r ' , h = r−r '
i r =W r−r i , h
r =
W ir
r
Particle number densityr
Kernel function W(r) with smoothing length h
Technische Universität MünchenLehrstuhl für Aerodynamik
7Stefan AdamiGarching, 18. Nov. 2008
THEORETICAL BACKGROUND
• Particle approximation:
• Navier – Stokes – Equation:
THEORETICAL BACKGROUND
r i = i =1V i
∫i r r dr
limh 0
W r−r ' , h = r−r '
i r =W r−r i , h
r =
W ir
r
d v i
dt= ...
1mi
∑j
∂W∂ r ij
e ij is V i
2 j
s V j2
d vdt
= g1
v−∇ p∇⋅s
i
j
r
s
Particle number density
Surface stress tensor
Kernel function W(r) with smoothing length h
Technische Universität MünchenLehrstuhl für Aerodynamik
8Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Couette flow (Re = 0.0125)
VALIDATION
Comparison of SPH and series solution
vmax
y
Technische Universität MünchenLehrstuhl für Aerodynamik
9Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Couette flow (Re = 0.0125)
VALIDATION
Comparison of SPH and series solution
vmax
y
• Poiseuille flow (Re = 0.0125)
Comparison of SPH and series solution
F
y
Technische Universität MünchenLehrstuhl für Aerodynamik
10Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Constant surface tension:
– Young – Laplace – Law:
VALIDATION
cos = 1w−2w /12
Phase 1 Phase 2
Wall
1w
2w
12
Technische Universität MünchenLehrstuhl für Aerodynamik
11Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Constant surface tension:
– Young – Laplace – Law:
VALIDATION
αcontact
= 120° αcontact
= 90° αcontact
= 60°
cos = 1w−2w /12
Phase 1 Phase 2
Wall
1w
2w
12
Technische Universität MünchenLehrstuhl für Aerodynamik
12Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Drop deformation in shear flow
VALIDATION
Ca=2 U 1 R
l y 12 =viscous forcesurface tension = viscosity ratio
D =a−bab
a
b
Technische Universität MünchenLehrstuhl für Aerodynamik
13Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Drop deformation in shear flow
– Small – deformation theory:(Taylor, 1934)
VALIDATION
D ≈19161616
Ca
Ca=2 U 1 R
l y 12 =viscous forcesurface tension = viscosity ratio
D =a−bab
a
b
Technische Universität MünchenLehrstuhl für Aerodynamik
14Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
VALIDATION
d m s
dt=
d A dt
=A Ds ∇ s2
d M s
dt=
d C V dt
=V D∞ ∇ 2C−d ms
dt
• Surfactant transportation on the interface
– Surface diffusion
– Coupling with bulk solution
Technische Universität MünchenLehrstuhl für Aerodynamik
15Stefan AdamiGarching, 18. Nov. 2008
VALIDATION
• Surfactant transportation on the interface
– Surface diffusion
– Coupling with bulk solution
VALIDATION
d m s
dt=
d A dt
=A Ds ∇ s2
d M s
dt=
d C V dt
=V D∞ ∇ 2C−d ms
dt
Convergence studyEvolution of surfactant profiles on the interface
Technische Universität MünchenLehrstuhl für Aerodynamik
16Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Marangoniforce driven bubble
– Surface tension coefficient depends on surfactant concentration Г
– Gradients of surface tension coefficient σ force bubble to deform
APPLICATIONS
12 x , t = [1− x ,t
max ]F s =12
n∇ s 12
Capillary force Marangoni force
F(s)F(s)
Arbitrary interface with surfactant molecules
∇ s12
∇ s
Technische Universität MünchenLehrstuhl für Aerodynamik
17Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Marangoniforce driven bubble
APPLICATIONS
Technische Universität MünchenLehrstuhl für Aerodynamik
18Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Marangoniforce driven bubble
APPLICATIONS
Technische Universität MünchenLehrstuhl für Aerodynamik
19Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
Surface tension loopCircumference of bubble over time
Technische Universität MünchenLehrstuhl für Aerodynamik
20Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
k 1k 2
C∞A C 1− − A , 0 *
0, * max
1k2T
max
d Ad t
, max
1k2T
d Ad t
=
Nomenclature:
A Surface AreaC Bulk concentrationГ Interfacial concentrationk
1Adsorption coefficient
k2
Desorption coefficient
σ Surface tension coefficientD Diffusion coefficientT Time scaler Radius of bubble
Technische Universität MünchenLehrstuhl für Aerodynamik
21Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)
– Adsorption / Desorption
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
k1/k
2 C = 10.0
k2T = 0.1
Technische Universität MünchenLehrstuhl für Aerodynamik
22Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)
– Adsorption / Desorption
– Insoluble regime
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
k1/k
2 C = 10.0
k2T = 0.1
Technische Universität MünchenLehrstuhl für Aerodynamik
23Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)
– Adsorption / Desorption
– Insoluble regime
– “Squeeze – out” regime
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
k1/k
2 C = 10.0
k2T = 0.1
Technische Universität MünchenLehrstuhl für Aerodynamik
24Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)
– Adsorption / Desorption
– Insoluble regime
– “Squeeze – out” regime
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
k1/k
2 C = 10.0
k2T = 0.1
k2T = 1.0
Technische Universität MünchenLehrstuhl für Aerodynamik
25Stefan AdamiGarching, 18. Nov. 2008
APPLICATIONS
• Dynamic surface tension
– Oscillation of bubble
– Surface tension coefficientthrough Young – Laplace – Equation
• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)
– Adsorption / Desorption
– Insoluble regime
– “Squeeze – out” regime
– Pseudo film collapse
APPLICATIONS
Pulsating bubble surfactometer
Electron micrographs of alveolar ducts
(Bachofen and Schürch, 2001)
k1/k
2 C = 10.0
k2T = 0.1
k2T = 1.0
k2T = 10.0
Technische Universität MünchenLehrstuhl für Aerodynamik
26Stefan AdamiGarching, 18. Nov. 2008
SUMMARY
• A twodimensional method to simulate phase interfaces with surfactants has been developed
• Mass of surfactant is conserved exactly
• Good agreement with analytic solutions and experimental observations
SUMMARY
• Development of a highly efficient parallel code using the PPM – library (Sbalzarini et al., JCP 2006)
• Extension to 3D
• Fluid – Structure – Interaction (FSI) with soft tissue model (SPH)
OUTLOOK