Pseudo-turbulence induced by settling spheroids in a quiescent fluid

In this study, we investigate the sedimentation of spheroidal particles in an initially quiescent fluid by means of particle-resolved direct numerical simulations. Settling particles with three different shapes – oblate spheroid, sphere and prolate spheroid – but fixed Galileo number $Ga=80$ and density ratio $\gamma =2$ at volume fraction $\phi =1\%$ are considered. Oblate and prolate particles are found to form column-like clusters as a consequence of the wake-induced hydrodynamic interactions in the suspension. This effect, together with the change of particle orientation, enhances the mean settling velocity of the dispersed phase. In contrast, spherical particles do not exhibit clustering, and settle with hindered velocity in the suspension. Furthermore, we focus on the pseudo-turbulence induced by the settling particles. We report a non-Gaussian distribution of the fluid velocity and a robust $-3$ power law of the energy spectra. By scrutinizing the scale-by-scale budget, we find that the anisotropy of the particle-induced pseudo-turbulence is manifested not only by the uneven allocation of turbulence kinetic energy among the different velocity components, but also by the anisotropic distribution of energy in spectral space. The fluid–particle interactions inject energy into the vertical velocity component, thus sustaining the turbulence, while pressure redistributes the kinetic energy among the different velocity components. The clustering of oblate/prolate particles significantly increases the energy input at large scales, forcing elongated flow structures. Moreover, the redistribution and nonlinear transfer of the energy are also intensified in the presence of particle clustering, which reduces the anisotropy of the particle-induced pseudo-turbulence.