Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

TL;DR

This study examines how large inertial particles respond to turbulent fluctuations in a closed flow, analyzing velocity and acceleration correlations to understand their dynamics and improve stochastic modeling.

Contribution

It provides new insights into the effects of particle size and density on Lagrangian time scales in inhomogeneous turbulence, using an unbiased trajectory analysis method.

Findings

Size and density influence velocity and acceleration time scales.

Unbiased Lagrangian integral times can be obtained despite mean flow bias.

Comparison with fluid particles reveals scale separation effects.

Abstract

We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization using two-time models (for instance Saw-ford's). As particles are tracked over long times in the quasi totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration.