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.
It is widely acknowledged that the development of sprays in the near-field is of primary importance for the spray formation downstream, as it affects both the spray angle, as well as the intact core length. In this frame, the present work aims to study the effects of turbulence inlet boundary condition on the spray formation by means of Direct Numerical Simulations on a real condition at low Reynolds number. To this extent, the code Paris-Simulator has been used, while a digital filter-based algorithm was used in order to generate synthetic turbulence at the inlet boundary condition. The influence of turbulence intensity and lengthscale on the atomization process has been studied and analyzed through 3 simulation for which these parameters have been varied. The results clearly highlight how the atomization is heavily affected by the inlet turbulence configuration. An analysis of the different atomizing conditions has been conducted, aiming to understand how the variation introduced by the inlet boundary condition on the velocity field is affecting the local atomization dynamics.
Paris (PArallel, Robust, Interface Simulator) is a finite volume code for simulations of immiscible multi fluid or multiphase flows. It is based on the "one-fluid" formulation of the Navier-Stokes equations where different fluids are treated as one material with variable properties, and surface tension is added as a singular interface force. The fluid equations are solved on a regular structured staggered grid using a second-order explicit projection method. The interface separating the different fluids is tracked either using a Front-Tracking (FT) method where the interface is represented by connected marker points, or by a volume of fluid (VOF) method where the marker function is advected directly on the fixed grid. Paris is written in Fortran95/2002 and parallelized using MPI and domain decomposition. It is based on several earlier FT or VOF codes such as FTC3D, Surfer or Gerris. These codes and similar ones, as well as PARIS, have been used to simulate a wide range of multifluid and multiphase flows.
The dynamics of droplet fragmentation in turbulence is described by the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at Rλ ≈ 140, the highest attained up to now. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality.
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