Assessment of the point-wise approach for the Turbulent Settling of finite-size particles

Abstract

We study the settling of suspensions of relatively large particles with a diameter of the order of ten Kolmogorov scales and density slightly larger than the carrier fluid in statistically steady homogeneous isotropic turbulence. The particle-to-fluid density ratio is varied to obtain a wide range of Galileo numbers, which are the ratios between buoyancy and viscous forces. We analyse the problem through high-resolved one-way coupled direct numerical simulations where the particles are modeled as material points. The physical parameters are chosen in the same range used in recent particle-resolved simulations, against which we compare (PRS, [1, 2]). The results of the point-wise simulations are in good agreement with the PRS ones, showing a reduced settling speed for the range of parameters under investigation, relevant to suspensions settling in aqueous media, at volume fractions up to a few percent for density ratios order of one. Results are obtained neglecting the inter-particles and particle-fluid interactions while purposely including/not including the different forces (e.g. Stokes drag, added mass, lift force) in the particles' equations of motion to highlight their contributions respectively. At a high Galileo number, the mean settling velocity is only slightly affected by turbulent fluctuations, and it is the same obtained for the settling velocity of a single particle in a quiescent fluid. When the Galileo number is reduced, the settling velocity is progressively affected by turbulent fluctuations that cause a substantial decrease in the particle sedimentation speed. The present results are particularly relevant for applications. Point-wise models endowed with an accurate description of the hydrodynamic force are effective in capturing the particle settling speed and other higher-order statistics as demonstrated by direct comparison against particle-resolved simulations [1, 2].