Sharp Interface Tracking in Rotating Microflows of Solvent Extraction Hyunkyung Lim, Valmor de Almeida, and James Glimm OAK RIDGE NATIONAL LABORATORY & DEPT. OF APPLIED MATHEMATICS AND STATISTICS, STONY BROOK UNIVERSITY 23 September 2011

Fluid properties for the test problem We are running a case with realistic physical properties. Aqueous phase (this is essentially an aqueous nitric acid solution) mass density: 1.03 g/cm3 viscosity: kg/(m s) Organic phase (this is a diluted tri-butyl-phosphate in dodecane) mass density: g/cm3 viscosity: kg/(m s) Interfacial tension can be varied from 10 to 20 mN/m

The code problems and updates  Higher order normal and curvature calculation: Very large curvature happened in some cases. The problem should be cured with a limiter.  Wrong phase problem  wrong default phase  fill the correct phase using previous time step phase  (more robust)   Automatic global reconstruction  Only a few global interface reconstruction is used.  Output format changed  Solution quantities of interest  Compile and run the code on INL machine  All code changes are kept under git version control in github: Frontier-µMix

Wrong phase problem has been fixed

Previous simulation with small domain in theta Looking at this interface from the old simulation, we decided to increase the length of the domain in the theta direction to about 3 times the gap-length while keeping the axial direction as 2 gap lengths.

Comparison with different initial velocity field 12.5 ms11 ms56.5 ms laminar flow initial field constant velocity with average of the inner and outer wall speed zero initial velocity We decided to use the initial velocity in the fluid as zero and reduce the inner cylinder angular speed to 2500 rpm. There will be additional reduction, say, 2000 or 1500 rpm.

New simulation of 1M case (two phases)

Results and observations

(Results and observations cont.)  Initially good results but later times, when mixing is increased, present challenges...

(Results and observations cont.)

Movies of interface evolution Inside view Outside view

Current status We are trying to take the system to a fully developed mixing regime. This regime will be achieved when the interfacial area reaches an statistical average. We are running two simulations for 8M (1024 processors) and 16M (2048 processors) cells on INL machines.  8M case : the length of the domain in the theta direction is  about 3 times the gap length  16M case : the length of the domain in the theta direction is  about 6 times the gap length

Work Plan 1) Work toward reaching fully developed mixing regime Prioritize what is most valuable to reach the goal  Consider initial and boundary conditions (lower rotating speed)  Consider domain size (longer axial direction and angular direction)  Mesh refinement to avoid catastrophic loss of convergence  Revisit global reconstruction to conserve mass  Revisit local reconstruction to conserve mass 1) Work to compute solution derived quantities to help guide work in 1) Prioritize what is most valuable to reach the goal  Volume calculation improvement  Interfacial mesh resolution PDF  Other pending visualization items: domain boundary surfaces; phases  Connectivity of phases and drop distribution  Volumetric flow rates in/out of domain