(458e) High-Resolution Simulations of One- and Two-Phase Homogeneous Isotropic Turbulent Flows

A way to produce a liquid-liquid dispersion or emulsion is to agitate two immiscible liquids in a stirred tank at sufficiently large Reynolds number. Since the dispersion is primarily formed as a result of drops interacting with turbulent eddies leading to drop breakup, it is necessary to know the energy input into the system that can provide the required intensity of the flow. To obtain this information, experiments are usually performed. With the rapid development of computational facilities, numerical simulations become a valuable addition to experimental studies.

In the present study, direct numerical simulations of a turbulently agitated liquid-liquid dispersion have been performed using a free energy lattice Boltzmann method. Large parallel computations were carried out in a three-dimensional, fully-periodic, cubic domain with an edge size of L=500 lattice units [lu] resulting in 125 million cells. Throughout this domain, statistically stationary homogeneous isotropic turbulence was generated by means of linear forcing. It sustains a constant turbulence source during the entire simulation. Also it produces realistic energy input at integral length scales (~L) that eventually dissipates at small scales (Kolmogorov length scale η_k). Kolmogorov scales of 1, 5 and 10 lattice units were considered. The possibility to generate turbulence with these η_k in a domain of 500³ was examined. The viscous sub-range of the turbulent energy spectrum was always reproduced. The reproduction of the inertial sub-range depended on the L/η_k ratio. High-resolution simulations with η_k=10 [lu] revealed the smallest (~η_k) turbulent structures, while the large domain size allowed to capture integral eddies. The velocity magnitude fields in a cross-section corresponding to different Kolmogorov length scales are shown in Fig.1. The influence of numerical parameters on turbulence generation was also investigated.

With the adopted turbulence generation method the energy input into the system ε is known a priory. Thus, when liquid-liquid systems are considered, it is possible to determine if the specified ε is sufficient to obtain a dispersion effect desired. During the two-phase flow simulations the second phase was instantaneously injected into the fully-developed turbulent flow. The entire dispersion formation process was visualized capturing the drop/eddy interactions. A dispersed phase field is shown in Fig.2 for the case of η_k=1 [lu], the dispersed phase volume fraction of 0.008 at a time instant of 332τ_k (a Kolmogorov time scale). The final drop size distributions (DSDs) for different energy input values were determined. Since the final emulsion properties, such as apparent viscosity, rheology, interfacial area, depend on the DSD, the developed numerical tool allows estimating these properties.

Fig 1. The velocity magnitude fields in the cross-sections (500x500 [lu]); (a) η_k=1 [lu]; (b) η_k=5 [lu]; (c) η_k=10 [lu].

Fig.2. A dispersed phase field at time instant 332τ_k, η_k=1 [lu], the dispersed phase volume fraction is 0.008.