Crossover between Rayleigh-Taylor Instability and turbulent cascading atomization mechanism in the bag-breakup regime

TL;DR

This paper provides experimental evidence that both Rayleigh-Taylor instability and turbulent cascade mechanisms are essential to explain the droplet size distribution in liquid atomization, especially in the bag-breakup regime.

Contribution

It demonstrates the coexistence of instability dynamics and turbulent cascades in atomization, linking droplet size distribution to a log-Lévy stable law and recent vortex stretching models.

Findings

Large droplets governed by Rayleigh-Taylor instability.

Small droplets follow a log-Lévy stable distribution with stability parameter ~1.68.

The stability parameter relates to vortex stretching intermittency models.

Abstract

The question whether liquid atomization (or pulverization) resorts to instability dynamics (through refinements of Rayleigh-Plateau, Rayleigh-Taylor or Kelvin-Helmholtz mechanism) or to turbulent cascades similar to Richardson and Kolmogorov first ideas seems to be still open. In this paper, we report experimental evidences that both mechanisms are needed to explain the spray drop PDF obtained from an industrial nozzle. Instability of Rayleigh-Taylor kind governs the size of the largest droplets while the smallest ones obey a PDF given by a turbulent cascading mechanism resulting in a log-L\'evy stable law of stability parameter close to 1.68. This value, very close to the inverse of the Flory exponent, can be related to a recent model for intermittency modeling stemming from self-avoiding random vortex stretching.