Scale-to-scale turbulence modification by small settling particles

Abstract

Despite decades of investigations, there is still no consensus on whether inertial particles augment or dampen turbulence. Here, we perform the first experimental study in which the particle concentration is varied systematically across a broad range of volume fractions $\varPhi _{v}$ , from nominally one-way coupled to heavily two-way coupled regimes, keeping all other parameters constant. We utilize a zero-mean flow chamber where steady, homogeneous and approximately isotropic air turbulence is realized, with a Taylor-microscale Reynolds number $Re_{\lambda } = 150\unicode{x2013}300$ . We consider spherical solid particles of two sizes, both much smaller than the Kolmogorov length, and yielding Stokes numbers $St_{\eta } = 0.3$ and 2.6 based on the Kolmogorov time scale. By adjusting the turbulent intensity, the settling velocity parameter is kept constant for both cases, $Sv_{\eta } = V_{t}/u_{\eta }\approx 3$ (where $V_{t}$ is the still-air terminal velocity, and $u_{\eta }$ is the Kolmogorov velocity scale). Unlike previous studies focused on massively inertial particles, we find that the turbulent kinetic energy increases with particle loading, being more than doubled at $\varPhi _{v} =5\times 10^{-5}$ . This is attributed to the energy input associated with gravitational settling: the particles release their potential energy into the fluid and increase its dissipation rate, while the time scale associated with the inter-scale energy transfer is not strongly changed. Two-point statistics indicate that the energy-containing eddies become vertically elongated in the presence of falling particles, and that the latter redistribute the energy more homogeneously across the scales compared to unladen turbulence. This is rooted in an enhanced cascade, as shown by the nonlinear inter-scale energy transfer rate.