Effect of droplet size on the fluctuation velocity of single droplets suspended in forced homogeneous isotropic turbulent flow

Direct Numerical Simulations (DNS) of single droplet motion in forced homogeneous isotropic turbulent flow are performed by a Volume of Fluid (VoF) method at a Taylor-scale Reynolds number of 57. The density and viscosity ratios between the carrier and droplet phases are equal to one. Droplet breakup is prevented by maintaining a small Weber number. Spurious currents are shown to be considerably reduced by a geometric VoF method, compared to an algebraic one. The turbulent kinetic energy spectrum aligns well with reference DNS data from the literature. By the evaluation of kinetic energy conservation, numerical dissipation is shown to be negligibly small. Enhanced viscous dissipation near the phase interface causes the level of kinetic energy in the droplet phase to be significantly smaller than in the surrounding carrier phase. A correlation between droplet diameter and droplet fluctuation velocity is evaluated. A variation of droplet diameter between 10 and 60 Kolmogorov lengths has only a minor effect on the droplet fluctuation velocity, challenging the state-of-the-art sub-grid scale closures of droplet interaction kernels employed in population balance models.