Xiaoyi Li. Advisor: Dr. Kausik Sarkar

Transcription

1 iaoyi Li United Technologies Research Center Advisor: Dr. Kausik Sarkar Mechanical Engineering, University of Delaware Andreas Acrivos Dissertation Award Presentation 62 nd APS DFD meeting, Minneapolis, MN, Nov 24 th 2009

2 Overview of dissertation Navier-Stokes Deforming interface Front-tracking Dynamics of drop Oscillating extensional flow (OE) Phys. Fluids Vortex flow J. Fluid Mech. Rheology of emulsion OE flow J. Non-Newtonian Fluid Mech. Phys. Rev. Letters Shear flow J. Rheology Mechanics of cell In unbounded shear J. Comp. Phys. In shear near a wall Cell adhesion... R 2

3 Emulsions: applications and challenges Material Energy Biology Food processing Polymer manufacturing Oil recovery & refinement Blood diagnosis Interfacial restoring force Effective stress Complex microstructure Dynamic & inertial environment 3 Iza & Bousmina (2000) J. Rhoelogy Rheology

4 Oscillating extensional (OE) flow Computer-controlled four-roll mill Taylor (1932), Bentley & Leal (1986) Inertia & time-dependency: less investigated Turbulent flow oscillatory forcing Drop in oscillating extensional flow Stokes flow analysis Asymptotic: small deformation Taylor (1932), Cox (1969) BEM: arbitrary deformation Rallison & Acrivos (1978) Amplitude Frequency Oscillating four-roll mill 4

5 D Drop deformation and phase in OE flow Drop in OE: complex 3D flow with moving interface B L L B D L B Taylor (1932) Deformation D Initial zero strain rate, flow-center Initial maximum strain rate, flow-center Initial maximum strain rate, non flow-center t' D max Time forcing 5 Time Deformation Phase Rheology

6 Deformation Computational result Reduced-order analysis Resonance 6 D max Re=0.1 Re=1.0 D max Re=0.1 k= Re=1.0 k=200 St St -1 Re=0.1 k=45 Re=1.0 k= Natural frequency St St -1 Frequency R^e=0 1 St ˆ ˆRe k^=200 ˆ ( kr^e=0.1 St ˆ Re ˆ ) k^=45 St ˆ R^e=1.0 k^= R^e=0 k^=200 R^e=0.1 k^=45 R^e=1.0 k^= Re increase S^t S^t

7 Resonance breakup Deformation Drop breakup Inertia increases Efficient energy transfer at appropriate frequency Frequency selective breakup in turbulence!!! Gas bubble breakup in turbulence Risso & Fabre (1998) Frequency 7

8 Rheology computation Assume dilute emulsion: Excess stress: n A V σ Interface tensor q excess d σ 1 nn I da V 3 Drop-shape Stress A d excess q d Stress Strain Strain rate Elastic stress ~ flow strain Viscous stress ~ flow strain rate 8

9 ^ non-dimensional moduli Rhoelogy in OE flow (Re=0.1) Modulus (stress/strain) 10 3 Phase (behind strain rate) π/2 1.5 Viscous Elastic E Re=0.1 Re= E E d ' int E d '' int E d int ' Oldroyd and Bousmina E d int '' Oldroyd and Bousmina St Re=0.1 Flow frequency Re=0.1 k=45 Re=1.0 k= St Flow frequency 9

10 non-dimensional moduli Negative elasticity (Re=1) Modulus (stress/strain) E d int ' E d int '' E d ' Oldroyd and Bousmina int E d '' Oldroyd and Bousmina int Resonance E Re=1 E Effective property Due to inertia induced microstructure change Elastic response in the same direction as forcing Negative Elasticity! St Flow frequency

11 Rheology in shear 2 1 In Stoke s flow of emulsions N 3 int >0 N int <0 Choi and Schowalter (1975) 11

12 Interfacial normal stress difference ( o ) Sign change of normal stress difference N int Re=0.1 Re= int N Re= Ca=0.02 Ca=0.05 Ca= Orientation Angle Re= Ca Ca 0.2 R Ca Ca

13 Cell modeling: membrane and bond Lipid-bilayer + network of proteins Elastic membrane Leukocyte (WBC) adhesion Molecular bond Elastic spring Stochastic formation and rupture 13

14 Cell adhesion: effects of cell deformation Equilibrium rupture rate k r0 k = k exp(γf/k T) r r0 b Bell (1987) k r ADS Simulation by Hammer's group CFD Simulation EG =33.3 h =100 CFD Simulation EG =133 h =400 CFD Simulation EG =333 h = Deformable Detachment No Adhesion Deformable particle in shear flow near a wall Adhesion 5E E-05 Sensitivity of rupture rate to forces γ Hydrodynamic LIFT Pushing particle from wall Leal (1980) 14

15 Summary Drop deformation Rheology Oscillating extensional flow (OE) dynamic & inertial : turbulent flow Drop in OE at finite inertia resonance breakup in turbulence negative phase negative elasticity in emulsion Drop in shear at finite inertia orientation angle > 45 o sign change of normal stress difference in emulsion Effects of cell deformation Lift force Adhesion 15

16 amplitude Current activities: High Re two-phase flow Propulsion /power generation Fire suppression Models at various levels of fidelity Lubrication High fidelity direct Simulation filmer Mesoscale CFD Simulation Dynamic Reduced Order Modeling f [Hz]

17 Acknowledgement Dr. Kausik Sarkar, University of Delaware Dr. Gretar Tryggvason, Worcester Polytechnic Institute Dr. Antony Beris, Dr. Lian-Ping Wang, Dr. Ajay K Prasad, University of Delaware Dr. Marios Soteriou, Dr. Marco Arienti 17