Modulation of isotropic turbulence by particles of Taylor length-scale size

This study investigates the two-way coupling effects of finite-size solid spherical particles on decaying isotropic turbulence using direct numerical simulation with an immersed boundary method. We fully resolve all the relevant scales of turbulence around freely moving particles of the Taylor length-scale size, 1.2≤ d /λ≤2.6. The particle diameter and Stokes number in terms of Kolmogorov length- and time scales are 16≤ d /η≤35 and 38≤τ p /τ k ≤178, respectively, at the time the particles are released in the flow. The particles mass fraction range is 0.026≤φ m ≤1.0, corresponding to a volume fraction of 0.01≤φ v ≤0.1 and density ratio of 2.56≤ρ p /ρ f ≤10. The maximum number of dispersed particles is 6400 for φ v =0.1. The typical particle Reynolds number is of O (10). The effects of the particles on the temporal development of turbulence kinetic energy E ( t ), its dissipation rate ( t ), its two-way coupling rate of change Ψ p ( t ) and frequency spectra E (ω) are discussed. In contrast to particles with d η, is that E ( t ) is always smaller than that of the single-phase flow. In addition, Ψ p ( t ) is always positive for particles with d > η, whereas it can be positive or negative for particles with d < η.