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

We study the settling of suspensions of relatively large particles with diameters of the order of ten Kolmogorov scales and densities slightly greater than that of 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 of buoyancy and viscous forces. We analyze the problem using high-resolution 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 (PRS, Fornari et al., 2016; Fornari et al., 2016), against which we compare. The results of the point-wise simulations are in good agreement with those of the PRS, showing a reduced settling speed for the range of parameters studied, relevant for suspensions settling in aqueous media, at volume fractions up to a few percent for density ratios of the order of one. The results are obtained neglecting the inter-particles and particle–fluid interactions, while the various forces (e.g. Stokes drag, added mass, lift force) are deliberately included/excluded in the equations of motion of the particles to highlight their respective contributions. At a high Galileo number, the mean settling velocity is only slightly affected by turbulent fluctuations, and it is the same as that obtained for the settling velocity of a single particle in a quiescent fluid. As the Galileo number is reduced, the settling velocity is increasingly affected by turbulent fluctuations that cause a significant decrease in the particle sedimentation speed. The transition occurs in a parameter range where the settling velocity of the isolated particle in a quiescent fluid is the order of the root mean square value of the turbulent fluctuations.

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 (Fornari et al., 2016a; Fornari et al., 2016b).