Estimating the filtering of turbulence properties by finite-sized particles using analytical energy spectra

Abstract

Finite-sized neutrally buoyant particles suspended in a turbulent flow do not typically follow the fluid motion, whereas sufficiently small neutrally buoyant particles, known as tracers, do. Turbulence properties probed by the two types of particles, thus, differ primarily due to spatial filtering, whereby scales of motion in the energy spectrum smaller than the particle diameter D are suppressed, whereas those larger are retained. In this study, this filtering effect is quantified for flows with Reynolds numbers in the range [Formula: see text] using a model of isotropic and homogeneous turbulence based on analytical wavenumber and Lagrangian frequency energy spectra. The coefficients scaling these spectra are estimated by comparing the dissipation rate, amplitude of the frequency spectrum, and acceleration variance for the fluid motion, as well as the acceleration and velocity variances of the particle motion, with laboratory experiments and numerical simulations. The model reproduces scalings for the acceleration variances of both the fluid and the particles at high Reynolds number. The model is then used to predict the ratios of the velocity variance, acceleration variance, and the dissipation rate obtained from the particles to those of the flow. These ratios depart from 1 as D increases (as expected), but the fluid velocity variance is much less severely underestimated by the particle motion than the acceleration variance and dissipation rate, for a given D and [Formula: see text]. These results allow delimiting more systematically the conditions under which finite-sized neutrally buoyant particles could be as useful to probe turbulent flows as tracer particles in laboratory experiments.