(243h) High-Resolution Simulations of Turbulently Flowing Liquid-Liquid Dispersion

The present study demonstrates feasibility of multi-scale direct numerical simulations of turbulently agitated liquid-liquid dispersion using a free energy lattice Boltzmann equation model revealing a spectrum of scales in the range from the dispersed phase size to integral eddy scale. The utilized method refers to the class of diffuse interface methods which require an explicit specification of the interface thickness. Two dimensionless parameters determine this additional degree of freedom: the interface Peclet number Pe that describes the diffusivity of the interface, and the Cahn number Ch that is the ratio of the interface thickness and the drop size. Based on simulations of a single drop deformation and breakup in simple shear flow, an influence of Pe, Ch and mesh resolution on accuracy and stability was investigated. A wide range of physical conditions (Reynolds number Re=0.0625-50) was examined. It was demonstrated that the accuracy of the results is primarily determined by the mesh resolution. The guidelines for a selection of Pe and Ch leading to stable simulations were outlined.

Based on the results obtained in the sheared drop simulations, the numerical parameters related to the interface were determined for turbulently flowing two-phase systems. Three-dimensional simulations were carried out in a fully-periodic cubic domain of 500³. The liquids were of equal density and varying viscosities to provide the viscosity ratio from 0.33 to 3.0. Three levels of resolution at Kolmogorov length scale η_k=1, 5 and 10 [lu] were considered. High-resolution simulations with η_k=5 and 10 [lu] allowed to capture the drop/eddy interactions on scales smaller than Kolmogorov one where energy dissipation takes place. Thus, the numerical tool can be used to determine the drop size distributions of dispersed systems in the viscous sub-range of the turbulent energy spectrum. A velocity magnitude field over a drop cross-section (black curve is the interface) is shown in Fig.1.

Fig.1. A velocity magnitude field in a section crossing the droplet at η_k=5 [lu].