Droplet oscillations in a turbulent flow

Abstract

The oscillations of an initially unperturbed spherical droplet immersed in a homogeneous and isotropic turbulent background flow are investigated through spherical harmonic decomposition. As suggested in the literature, the shape oscillations under turbulent conditions are related to the frequency of droplets oscillating in a fluid without background flow. A series of direct numerical simulations (DNS) of droplets with single deformation modes in a fluid at rest are first performed. The frequency and damping rate are compared with weakly viscous linear theory. Then, a database of 220 droplets deformed under turbulent conditions for a single Weber and Reynolds number is generated with an identical numerical set-up. Each spherical harmonic coefficient shows an oscillatory motion with comparable frequency to the single deformation mode simulations. The power spectrum of the coefficients provides the amount of surface of each mode. After a transient regime, the surface area reaches a stationary saturation level. The saturation level of each mode is linked to the turbulence and the energy stored at the interface. Droplets after a high deformation are studied with and without background flow. As expected, the physics of relaxation is driven by capillary forces.