Conference Agenda

This study presents a new interpretation of the turbulence-interface interactions during the interfacial fragmentation process based on the concept of enstrophy transport. We carried out fully-resolved volume of fluid simulations of the decaying homogeneous isotropic turbulence in the presence of interfacial structures and analyzed the spectral fluxes of enstrophy production/destruction due to different vorticity transport mechanisms. We highlight the scale-dependent nature of the surface tension mechanism in competition with the vortex stretching mechanism that eventually features two characteristic length scales: (i) the length scale where the spectral rate of surface tension changes sign from negative to positive and distinguishes between enstrophy-reducing fragmentation process and enstrophy-releasing coalescence events across the scales. (ii) The length scale where the rate of enstrophy production by the surface tension balances the disruptive mechanism of vortex stretching. This corresponds to a similar length scale where the energy cascade of two-phase turbulence starts to pile up energy at small scales compared to its single-phase similitude. We further connect the latter to the interfacial statistics and reveal that at this length scale, the size distribution of droplets distinctly changes to a sharper slope. The analysis further discloses that decreasing the surface tension coefficient or viscosity as well as increasing the density of the dispersed phase enhances the vortex stretching effect and dilates the spectral range at which the surface tension contribution is negative toward the smaller scales, and thus facilitates the fragmentation. Whereas the higher surface tension coefficient, higher viscosity, or lower density ratio expands the spectral range associated with a positive contribution of surface tension toward the larger scales and suppresses the fragmentation events. This analysis offers a new interpretation of the Hinze scale in turbulence that is essential for the DNS and LES of two-phase flows.

The flow generated by the breaking of free-surface waves in a periodic domain is simulated numerically by means of a gas-liquid multiphase Navier-Stokes solver. The solver relies on the Volume-of-Fluid (VOF) approach, and interface tracking is carried out by using a novel algebraic scheme based on a tailored TVD limiter (Pirozzoli et al., 2019). The solver is proved to be characterized by low numerical dissipation, thanks to the use of the MAC scheme, which guarantees discrete preservation of total kinetic energy in the case of a single

phase. The low artificial dissipation and the potentiality of the algebraic VOF used is analyzed and highlighted through the simulation of the benchmark proposed by Estivalezes et al., 2022, where the ability of algebraic VOF to work for both miscible and immiscible fluids is demonstrated, allowing lower dissipated energy. After, both two- and three-dimensional simulations of wave breaking have been carried out, and the analysis is presented in terms of energy dissipation, air entrainment, bubble fragmentation, statistics and distribution. Particular attention is paid to the analysis of the mechanisms of viscous dissipation. For this purpose, coherent vortical structures (Horiuti and Takagi, 2005), are identified and the different behaviour of vortex sheets and vortex tubes are highlighted, at different Re. The correlation between vortical structures and energy dissipation demonstrates clearly their close link both in the mixing zone and in the pure water domain, where the coherent structures propagate as a consequence of the downward transport. Notably, it is found that the dissipation is primarily connected with vortex sheets, whereas vortex tubes are mainly related to flow intermittency.

The tendency of initially distant droplets in gas flows to convene and form clusters - known as droplet grouping - is an important phenomenon which affects evaporation rates and combustion dynamics, for example. Despite its relevance to technical applications, this grouping behavior and its governing factors are not yet fully understood, in particular in turbulent, compressible flows. Therefore, related work often focuses on a laminar, monodisperse droplet stream, which consitutes the most fundamental configuration subject to grouping and has been studied analytically, numerically as well as experimentaly.

While those investigations consider incompressible gas flows, this talk examines the grouping behavior in the compressible regime through direct numerical simulation (DNS), using a high-order level-set ghost fluid framework. We address arising challenges such as the mass loss inherent to the level-set method and propose a simple approach to track the individual droplets through the computational domain. In order to gain insights into the grouping mechanics, the impact of the initial droplet alignment, the Reynolds number and other parameters is studied in detail. The results are also compared with reference data from experiments and incompressible DNS to unveil compressibility effects in droplet grouping.

Most industrial processes involve multiphase turbulent flows. Therefore, understanding the underlying physics is of primary importance for reducing pollutant emissions and also for improving the safety protocols in industry processes. In this regard, numerical simulations provide a valuable tool due to their lower cost compared to experiments. Furthermore, simulations allow us to overcome current instrumentation limits. In this context, the phase-field method is coming to the fore for its ease of implementation and good scalability. However, its most well-known implementations, based on the conservative Cahn-Hilliard equation, have limitations on the density and viscosity ratios preventing us from studying realistic cases. Recently, novel approaches proposed a conservative Allen-Cahn equation which guarantees the solution boundedness. We show the results of a 2D rising bubble in a quiescent fluid at Reτ = 10 where the motion is only due to the density ratio between the carrier and dispersed phase. In particular, two different density ratios are analysed: ρr = 0.1−0.01. We characterize the shrinkage phenomenon by comparing the instantaneous profiles of the phase field with the theoretical profiles, then we quantify the mass loss in each case.

We investigate the heat transfer process in a multiphase turbulent system composed by a swarm of large and deformable drops and a continuous carrier phase. For a fixed shear Reynolds number, 𝑅𝑒𝜏 = 300, a constant drops volume fraction, Φ ≃ 5.4%, and a fixed Weber number, 𝑊𝑒 = 3.0, we perform a campaign of direct numerical simulations (DNS) of turbulence coupled with a phase-field method and the energy equation; the Navier-Stokes equations are used to describe the flow field, while the phase-field method and the energy equation are used to describe the dispersed phase topology and the temperature field, respectively. Considering several Prandtl numbers, 𝑃𝑟 = 1, 2, 4 and 8, we study the heat transfer process from warm drops to a colder turbulent flow. Using detailed statistics, we first characterize the time evolution of the temperature field in both the dispersed and carrier phase. Then, we develop an analytic model able to accurately reproduce the behaviour of the dispersed and continuous phase temperature. We find that an increase of the Prandtl number, obtained via a decrease of the thermal diffusivity, leads to a slower heat transfer between the dispersed and carrier phase. Finally, we correlate the drop diameters and their average temperatures.