For a fundamental assessment of state-of-the-art sub-grid scale closures of droplet interaction kernels used in population balance models, Direct Numerical Simulations (DNS) of single droplet motion in forced homogeneous isotropic turbulent flow are conducted using a geometric Volume of Fluid method. A Taylor-scale Reynolds number at a value of 59 is investigated. The droplet diameter is varied between 10 and 52 Kolmogorov lengths, encompassing the entire range of turbulent length scales at this Reynolds number. Equal values of the density within the droplet and the carrier phase are applied, whereas the viscosity ratio is varied between values of 1 and 100. The Weber number is varied between values of 0.5 and 1.5, bordering on droplet breakup conditions. An extensive validation of the flow solver verifies that the simulation results are not distorted by spurious currents or numerical energy dissipation. The kinetic energy of the smallest droplet is approximately equal to the turbulent kinetic energy within the carrier phase. For a larger droplet, enhanced viscous dissipation at the phase interface significantly reduces the kinetic energy of the droplet relative to the surrounding carrier phase. Variations of the viscosity ratio and Weber number have no discernible effect on the kinetic energy of the droplet, although the individual terms of the kinetic energy balance in the droplet phase are significantly affected. A novel low-pass filter model is proposed to approximate the droplet fluctuation velocity in droplet interaction kernels, aligning much closer with our DNS results compared with a state-of-the-art longitudinal structure function model.
Hermes et al. (Wed,) studied this question.