Slip-velocity of large neutrally-buoyant particles in turbulent flows

TL;DR

This paper introduces simple, robust definitions of stochastic slip velocity for large particles in turbulent flows, enabling better characterization of particle-fluid interactions across experiments and simulations.

Contribution

It proposes new, easy-to-calculate definitions of stochastic slip velocity that do not require complex filtering or conditional averaging, applicable in various experimental and numerical contexts.

Findings

Slip velocity definitions are practical for laboratory, field, and numerical data.

Reynolds number based on stochastic slip exceeds 1, indicating complex particle-fluid dynamics.

Particle velocities show nonlinear dependence on fluid velocities.

Abstract

We discuss possible definitions for a stochastic slip velocity that describes the relative motion between large particles and a turbulent flow. This definition is necessary because the slip velocity used in the standard drag model fails when particle size falls within the inertial subrange of ambient turbulence. We propose two definitions, selected in part due to their simplicity: they do not require filtration of the fluid phase velocity field, nor do they require the construction of conditional averages on particle locations. A key benefit of this simplicity is that the stochastic slip velocity proposed here can be calculated equally well for laboratory, field, and numerical experiments. The stochastic slip velocity allows the definition of a Reynolds number that should indicate whether large particles in turbulent flow behave (a) as passive tracers; (b) as a linear filter of the velocity field; or (c) as a nonlinear filter to the velocity field. We calculate the value of stochastic slip for ellipsoidal and spherical particles (the size of the Taylor microscale) measured in laboratory homogeneous isotropic turbulence. The resulting Reynolds number is significantly higher than 1 for both particle shapes, and velocity statistics show that particle motion is a complex non-linear function of the fluid velocity. We further investigate the nonlinear relationship by comparing the probability distribution of fluctuating velocities for particle and fluid phases.