S. Adami, X.Y. Hu, N.A. Adams Institute of Aerodynamics TU M

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


2Stefan AdamiGarching, 18. Nov. 2008

OUTLINE

• Motivation

• Numerical Modeling

• Validation

• Applications

• Summary and Outlook

OUTLINE



MOTIVATION

• DFG – Project: Protective Artificial Respiratory

MOTIVATION

“Experimental and numerical investigation on the flowinduced stresses on the alveolar – epithelial – air interface”



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”



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



THEORETICAL BACKGROUND

• Particle approximation:


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




• Particle approximation:

• Navier – Stokes – Equation:


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



VALIDATION

• Couette flow (Re = 0.0125)

VALIDATION

Comparison of SPH and series solution

vmax

y



VALIDATION

• Couette flow (Re = 0.0125)

VALIDATION


vmax

y

• Poiseuille flow (Re = 0.0125)


F

y



VALIDATION

• Constant surface tension:

– Young – Laplace – Law:

VALIDATION

cos = 1w−2w /12

Phase 1 Phase 2

Wall

1w

2w

12



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



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



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



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



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



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



APPLICATIONS


APPLICATIONS



APPLICATIONS

• Dynamic surface tension

– Oscillation of bubble

– Surface tension coefficientthrough Young – Laplace – Equation

APPLICATIONS

Pulsating bubble surfactometer



Surface tension loopCircumference of bubble over time



APPLICATIONS




• Surfactant kinetics(Otis et al., J. Appl. Physiol. 1994)

APPLICATIONS




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



APPLICATIONS





– Adsorption / Desorption

APPLICATIONS




k1/k

2 C = 10.0

k2T = 0.1



APPLICATIONS






– Insoluble regime

APPLICATIONS




k1/k

2 C = 10.0

k2T = 0.1



APPLICATIONS







– “Squeeze – out” regime

APPLICATIONS




k1/k

2 C = 10.0

k2T = 0.1



APPLICATIONS








APPLICATIONS




k1/k

2 C = 10.0

k2T = 0.1

k2T = 1.0



APPLICATIONS








– Pseudo film collapse

APPLICATIONS




k1/k

2 C = 10.0

k2T = 0.1

k2T = 1.0

k2T = 10.0



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

S. Adami, X.Y. Hu, N.A. Adams Institute of Aerodynamics TU M

Documents

Transcript of S. Adami, X.Y. Hu, N.A. Adams Institute of Aerodynamics TU M