Simulations of dilute sedimenting suspensions at finite-particle Reynolds numbers

Abstract

An alternative numerical method for suspension flows with application to sedimenting suspensions at finite-particle Reynolds numbers Rep is presented. The method consists of an extended lattice-Boltzmann scheme for discretizing the locally averaged conservation equations and a Lagrangian particle tracking model for tracking the trajectories of individual particles. The method is able to capture the main features of the sedimenting suspensions with reasonable computational expenses. Experimental observations from the literature have been correctly reproduced. It is numerically demonstrated that, at finite Rep, there exists a range of domain sizes in which particle velocity fluctuation amplitudes ⟨ΔV∥, ⊥⟩ have a strong domain size dependence, and above which the fluctuation amplitudes become weakly dependent. The size range strongly relates with Rep and the particle volume fraction ϕp. Furthermore, a transition in the fluctuation amplitudes is found at Rep around 0.08. The magnitude and length scale dependence of the fluctuation amplitudes at finite Rep are well represented by introducing new fluctuation amplitude scaling functions C1, (∥, ⊥)(Rep, ϕp) and characteristic length scaling function C2(Rep, ϕp) in the correlation derived by Segre et al. from their experiments at low Rep [“Long-range correlations in sedimentation,” Phys. Rev. Lett. 79, 2574–2577 (1997)10.1103/PhysRevLett.79.2574] in the form \documentclass[12pt]{minimal}\begin{document}$\langle \Delta V_{\parallel , \perp } \rangle = \langle V_{\parallel } \rangle C_{1, ( \parallel , \perp )} ( Re_{p},\phi _{p} ) \phi _{p}^{1/3} \lbrace 1 - \text{exp} [ -L / ( C_{2} ( Re_{p}, \phi _{p} ) r_{p} \phi _{p}^{-1/3} )] \rbrace$\end{document}⟨ΔV∥,⊥⟩=⟨V∥⟩C1,(∥,⊥)(Rep,ϕp)ϕp1/3{1−exp[−L/(C2(Rep,ϕp)rpϕp−1/3)]}.