Plans and Parameters

1. Plans and Parameters

2. Dimensionless parameters

6. Research Plan: short term • 2D axisymmetric simulation of full contactor. Evaluate role of z-direction Laplacian missing from analytical models. Compare to analytical models. Extend models and simulation to 3 phase axisymmetric. Compute z-intervals for Couette, Taylor-Couette, Turbulent flows. • Evaluate need for slip model or for grid resolution needed to achieve good resolution at air-liquid interface. Use 2D axisymmetric simulations

7. Research plans: short term • Solve 3D full contactor with LES code, three phase, and if needed slip boundary conditions at air-liquid interface. Investigate rippled interface, wave numbers and amplitudes. Compare to a dispersion relation. Recompute z-intervals for Couette, Taylor-Couette, Turbulent flows. Also We, critical droplet size.

8. Research plans -- short term • Based on 3D LES simulations of full contactor, predict turbulence intensity and length scales. The wedge for final computations should overlap the transition from the Kolmogorov scalilng region and the dissapation region. Thus the fluctuating velocity v’ should be small, especially at a grid level. But v_z and v_r, being mean values, do not need to be small. What to do about this when we restrict to a thin wedge?

9. Research Plans-short term • To answer question on previous slide, we consider 3D simulation in a long (z-direction) wedge. Big enough to support r-z vortices, Taylor vortices, etc. Assess needed boundary conditions for flow in thin wedge • 3D simulation in thin wedge. Use above to guide initialization

10. Parameters and Flow Regimes • Contactor is well beyond the transition to Taylor vortices, the transition to unsteady vortices, and the transition to turbulent flow • Grid resolution needed to resolve 10-100 micron bubbles. (I.e. 3 to 30 micron grid resolution) • Kolmogorov length scale >> grid scale, hence simulation is DNS

11. Literature Survey • Many authors have studied the pre-chaotic and transition to turbulence regimes • Dispersion relations, transition to Taylor vortices • Hopf bifurcations, transition to wavy vortices • The turbulent regime • Single phase flow • M. Bilson and K. Bremhorst, Direct numerical simulation of turbulent Taylor-Couette flow, J. Fluid Mech. (2007) 579, -- 227-370 • Two phase flow?

12. Verification Tests • Kelvin-Helmholtz growth rates compared to theory (based on dispersion relations) • Planar geometry, surface tension, two distinct viscosities • Mesh convergence tests; Orders of accuracy tests

13. Kelvin-Helmholtz growth rates compared to theory (based on dispersion relations)

14. Validation Tests • Compare statistics of simulation flow to experimental measurements • Droplet size mean diameter • Total surface area • Turbulent statistics • Other measurements recorded? • Or published elsewhere? • Air-liquid interface; air entrainment in liquid; dependence on air-liquid surface tension; height of mixing region. Use effective liquid to describe aqueous-organic mixture, for viscosity; majority phase for surface tension to air. • Minority phase radial distribution liquid minority phase drops (tests droplet insertion algorithm); Are minority phase liquid drops in shape of disks, while organic minority phase droplets are spheres

15. Needed Code Upgrades • Conservative tracking • Second order geometry • Partially in place • Second order space and time propagation • Discontinuous viscosity in distinct fluids, with associated pressure discontinuity

16. Initialization • By droplet insertion into single phase flow to reach specified volume fraction. Insert into fully developed turbulent flow. • For air-liquid, initialize with couette flow • Assess initialization uncertainty in the volume flow ratios. • Periodic flow in z-direction (but might be no flow instead) • Move inner boundary out to air-fluid interface, modify rotation rate to rotation rate of inner fluid surface (if air entrainment is not considered, if drag effects of perturbed air-fluid interface is not considered)

17. Statistical Data Analysis • Lognormal distribution of droplets? • Mean diameter, Slater mean diameter • Interfacial surface area (as a function of Weber number, Re, volume ratio of two fluids, …) • Characterize the flow environment near a bubble or droplet • What is the effective local shear rate, and the effective diffusion rate? • Rate limiting parameters for chemical reactions • Interfacial area, effective local diffusion rate near interface • Turbulent flow statistics • Explanation of difference of shapes of organic vs. aqueous drops (spheres vs. disks): viscosity ratio? Density ratios? • Compute, analyze means and fluctuations of quantities that will be averaged to define (later on) averaged equations. Including velocities, velocity gradients, …

18. Engineering Applications • Main purpose of questions posed is to • Validate code • Support the derivation of averaged equations • Discover scientific explanations for various observed phenomena • Contribute to the understanding of experimental data

19. Quarterly Progress Report Status • Plans for next quarter

20. Simulation Progress onRelated Problem • Primary breakup of high speed jet

21. 3D Simulation of Primary Jet Breakup

22. Droplet distribution • Total droplets: 217 • SMD: 25 micrometers

23. 3D simulation • Simulation