Modulation of homogeneous and isotropic turbulence in emulsions

Abstract

We present a numerical study of emulsions in homogeneous and isotropic turbulence (HIT) at $Re_\lambda =137$ . The problem is addressed via direct numerical simulations, where the volume of fluid is used to represent the complex features of the liquid–liquid interface. We consider a mixture of two iso-density fluids, where fluid properties are varied with the goal of understanding their role in turbulence modulation, in particular the volume fraction ( $0.03<\alpha <0.5$ ), viscosity ratio ( $0.01<\mu _d/\mu _c<100$ ) and large-scale Weber number ( $10.6< We_\mathcal {L}<106.5$ ). The analysis, performed by studying integral quantities and spectral scale-by-scale analysis, reveals that energy is transported consistently from large to small scales by the interface, and no inverse cascade is observed. Furthermore, the total surface is found to be directly proportional to the amount of energy transported, while viscosity and surface tension alter the dynamic that regulates energy transport. We also observe the $-10/3$ and $-3/2$ scaling on droplet size distributions, suggesting that the dimensional arguments that led to their derivation are verified in HIT conditions.

FluTAS: A GPU-accelerated finite difference code for multiphase flows

“…This method combines the exact mass conservation properties of certain geometric VoF methods with the reduced number of local operations for the interface reconstruction of the algebraic VoFs, making it a good candidate for properly exploiting hybrid and accelerated architectures. The version available in our group has been validated in [34] and extensively employed in a different variety of multiphase configurations, both for laminar [35,36,37] and turbulent [38,39,40,41] flows. Note that it has been extended to phase changing flows [42] and also to handle weakly compressible multiphase flows (low-Mach approximation) [43,44].…”

Effect of turbulence intensity and surface tension on the emulsification process and its stationary state—A numerical study

“…By fitting experimental data, Deane and Stokes [ 19 ] proposed a d −3/2 power law in this region. Recent numerical studies [ 16,17,25 ] adopted these power laws for emulsions and observed a good agreement for dense emulsions, especially for d < d H . Although a lot of studies have already investigated droplet size distributions, certain aspects are still not yet clarified.…”

“…Recently a finite‐volume approach has been employed to study emulsions. Using the volume of fluid method (VOF), Crialesi‐Esposito et al [ 17 ] studied the effect of variations in the viscosity ratio, the volume fraction, and the surface tension on size distributions and the energy transport between different scales. The emulsification process, that is, the breakup of a liquid structure in HIT, was also the focus of various numerical investigations, such as, for example, Komrakova et al [ 33 ] , Komrakova, [ 34 ] Zhong and Komrakova [ 35 ] using a free‐energy LBM.…”

“…Therewith, we extend previous numerical studies by considering emulsions of fluids with matching densities. [ 14,16,17 ] We vary the turbulence intensity, which affects the dissipation rate ε , and the surface tension coefficient σ , and thus focus on the parameters altering the Hinze scale (see Equation ). We consider a void fraction of the dispersed phase of 12.5% and the kinematic viscosity of both phases is set to ν = ν c = ν d = 0.001 m 2 /s.…”

“…[ 39 ] Hence, here we also investigate the applicability of the linear forcing approach to multiphase flows, with a particular focus on the emulsification process, where breakup dominates and draws TKE. For comparison with theories derived for homogeneous isotropy, we follow previous studies [ 14,16,17 ] and consider the general configuration of a HIT in a periodic box of length L = 2 π .…”