Numerical simulation of droplet motion and two-phase flow field in an oscillating

container Tadashi WatanabeCenter for Computational Science and e-Systems Japan Atomic Energy Agency

Multiphysics 2009, Multiphysics 2009, Dec. 12, 2009Dec. 12, 2009

o Background and Objectiveso Numerical Methodo Flow Fieldo Comparisono Summary

Background and Objectives

Levitated Droplet 　：　 Free from effects of container wall

Oscillation

Rotation

Measurement of material properties of high-temperature molten metal,,,

Surface tension --- Oscillation frequency, Rotating shape,,, Viscosity --- Damping, Shape deformation,,,

Numerical simulations are performed to study the dynamic motion of the droplet in the oscillating flow fields.

Levitation : electromagnetic, ultrasonic,,, Rotation : acoustic,,,

Numerical Method (1)

Oscillating Boundary

Slip Boundary

Gas

Liquid Droplet

Oscillating Boundary

Incompressible + pseudo compressible

Arbitrary Lagrangian-Eulerian mesh with oscillation speed of boundary

Numerical Method (2)Governing Equations for Fluid Motion

0 u

sFpuUutu )2(])(/[ D

sF|)|/(

Hlgl )( Hlgl )(

H

1

)]sin(1

1[2

1

0

),(

)(

)(

Continuity

Navier-Stokes

Surface Tension Force

Curvature

Interpolation

2/ cp Pseudo Compressibility

Numerical Method (3)

Governing Equations for Level Set Function

0)(/ Uut

2/122 )/(|)|1(/

||)1)((/ AAo0

0

0

interface

Transport

Reinitialization

Mass Conservation

Numerical Method (4)FDM: 2nd order Adams-Bashforth method 2nd order upwind difference SMAC method for pressure and velocity Bi-CGSTAB method for Poisson equationParallelization

Gas

Simulation region : 10 mm x 17 mm (100x170)Droplet radius : 2 mmTime step : 1.0e-6 s

Oscillation frequency : 20 kHzSound pressure : 0.25~0.5 kPa

Droplet : density = 998.2 kg/m3

viscosity = 0.998e-3 Ns/m2 surface tension = 0.0145 N/m Gas : density =1.166 kg/m3 viscosity = 1.819e-5 Ns/m2 sound speed = 340 m/s

Liquiddroplet

Oscillation

x=-5.0sint : =6.0578s-1

190x100

Liu and Lin, J. Comp. Phys. 227(2008)p3921

Numerical Method (5) Validation : Sloshing Experiment

probe2 probe1 probe3

Flow Field (1)

-0.0085

0.0085

0.0

pressure node : 0.0 pressure node : -0.0085

Vertical Position

Example of Pressure Distribution/Variation

Pressure node

Flow Field (2)Velocity Field and Droplet Motion

t=0.00 s 0.1 s 0.2 s0.05 s 0.15 s 0.25 s

Pressure node : middle

Flow Field (3)Velocity Field and Droplet Motion

t=0.00 s 0.1 s 0.2 s0.05 s 0.15 s 0.25 s

Pressure node : bottom

Flow Field (4)Velocity Field and Droplet Motion

t=0.00 s 0.1 s 0.2 s0.05 s 0.15 s 0.25 s

Pressure node : top

Flow Field (5)Velocity Field and Droplet Motion

Pressure node

Bottom

Middle

-0.0085

0.0085

0.0

Vertical Position

Top

Flow Field (6)Droplet Position

Comparison (1) Incompressible Case

t=0.00 s 0.1 s 0.2 s0.05 s 0.15 s 0.25 s

Pressure node : bottom

Pressure node : top

Comparison (2)Stationary Droplet (oscillating container)

Oscillating Droplet (stationary container)

t=0.00 s 0.1 s 0.2 s0.05 s 0.15 s 0.25 s

scale x4

Stationary/Oscillating Droplet

Tatsuno, Bull. Kyushu Univ. Appl. Mech., １２８ (2005)p23

Comparison (3)Oscillating Circular Cylinderwith Experiment

Summary

Motions of the droplet and the flow field in an oscillating container have been simulated numerically using the coupled level set and ALE method.

・ Upward and downward flows from the droplet surface to the container wall appeared in the oscillating direction.

・ The droplet moved toward the pressure node, but this is not the case for incompressible case.

・ Induced flow field was similar to the flow field around an oscillating droplet/cylinder.