Long-term temporal dependence of droplets transiting through a fixed spatial point in gas-liquid twophase turbulent jets

TL;DR

This study introduces a novel rescaled range analysis method to examine long-term dependencies in gas-liquid turbulent jets, revealing universal scaling properties of droplet transit signals.

Contribution

The paper presents a new rescaled range analysis technique for unevenly sampled signals and demonstrates invariant scaling exponents across different jet configurations.

Findings

Hurst exponent of velocity is approximately 0.59

Fractal dimension is approximately 1.41

Scaling exponents are configuration-independent

Abstract

We perform rescaled range analysis upon the signals measured by Dual Particle Dynamical Analyzer in gas-liquid two-phase turbulent jets. A novel rescaled range analysis is proposed to investigate these unevenly sampled signals. The Hurst exponents of velocity and other passive scalars in the bulk of spray are obtained to be 0.59$\pm $0.02 and the fractal dimension is hence 1.41$\pm $ 0.02, which are in remarkable agreement with and much more precise than previous results. These scaling exponents are found to be independent of the configuration and dimensions of the nozzle and the fluid flows. Therefore, such type of systems form a universality class with invariant scaling properties.