Heavy Kolmogorov-size spheres suppress the inertial cascade in homogeneous and isotropic turbulence

Abstract

The effect of Kolmogorov-size spherical particles on homogeneous and isotropic turbulence is investigated using particle-resolved direct numerical simulations at a Taylor-scale Reynolds number of $150$. Four monodisperse suspensions of particles with identical diameter and volume fraction $10^{-3}$ are considered, while the particle-to-fluid density ratio varies between $100$ and $1500$ and the mass fraction between $0.1$ and $0.6$. As particle inertia increases, the energy spectrum departs from the canonical Kolmogorov $\kappa^{-5/3}$ scaling and approaches a peculiar regime with $\kappa^{-1}$. In this limit, the nonlinear energy transfer is strongly suppressed and the kinetic energy balance is dominated by the fluid-solid interaction and the viscous dissipation. Consistently, the second-order structure function shows logarithmic scaling at separations larger than the particle diameter, indicating velocity decorrelation. Increasing particle inertia promotes axial strain and vortex compression in the vicinity of the particles and enhances the particle-fluid relative velocity. Particle clustering weakens as the density ratio and the Stokes number increase, with the volume and the population of the clusters decreasing when inertia is enhanced. Nevertheless, when clustering occurs, particles preferentially sample regions of high strain and low vorticity, for all the values of the density ratio and the mass fraction considered here.