Numerical simulation of droplet motion and two-phase flow field in an oscillating container Tadashi Watanabe Center for Computational Science and e-Systems.

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Numerical simulation of droplet motion and two-phase flow field in an oscillating container Tadashi Watanabe Center for Computational Science and e-Systems Japan Atomic Energy Agency Multiphysics 2009, Dec. 12, 2009 o Background and Objectives o Numerical Method o Flow Field o Comparison o 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 Continuity Navier-Stokes Surface Tension Force Curvature Interpolation Pseudo Compressibility

Numerical Method (3) Governing Equations for Level Set Function interface Transport Reinitialization Mass Conservation

Numerical Method (4) FDM: 2 nd order Adams-Bashforth method 2 nd order upwind difference SMAC method for pressure and velocity Bi-CGSTAB method for Poisson equation Parallelization Gas Simulation region : 10 mm x 17 mm (100x170) Droplet radius : 2 mm Time step : 1.0e -6 s Oscillation frequency : 20 kHz Sound pressure : 0.25~0.5 kPa Droplet : density = kg/m 3 viscosity = 0.998e -3 Ns/m2 surface tension = N/m Gas : density =1.166 kg/m 3 viscosity = 1.819e -5 Ns/m2 sound speed = 340 m/s Liquid droplet Oscillation

x=-5.0sin  t :  =6.0578s x100 Liu and Lin, J. Comp. Phys. 227(2008)p3921 Numerical Method (5) Validation : Sloshing Experiment probe2probe1 probe3

Flow Field (1) pressure node : 0.0pressure node : Vertical Position Example of Pressure Distribution/Variation

Pressure node Flow Field (2) Velocity Field and Droplet Motion

t=0.00 s0.1 s0.2 s0.05 s0.15 s0.25 s Pressure node : middle Flow Field (3) Velocity Field and Droplet Motion

t=0.00 s0.1 s0.2 s0.05 s0.15 s0.25 s Pressure node : bottom Flow Field (4) Velocity Field and Droplet Motion

t=0.00 s0.1 s0.2 s0.05 s0.15 s0.25 s Pressure node : top Flow Field (5) Velocity Field and Droplet Motion

Pressure node Bottom Middle Vertical Position Top Flow Field (6) Droplet Position

Comparison (1) Incompressible Case t=0.00 s0.1 s0.2 s0.05 s0.15 s0.25 s Pressure node : bottom Pressure node : top

Comparison (2) Stationary Droplet (oscillating container) Oscillating Droplet (stationary container) t=0.00 s0.1 s0.2 s0.05 s0.15 s0.25 s scale x4 Stationary/Oscillating Droplet

Tatsuno, Bull. Kyushu Univ. Appl. Mech., １２８ (2005)p23 Comparison (3) Oscillating Circular Cylinder with 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.