Simulations of dilute sedimenting suspensions at finite-particle Reynolds numbers

An alternative numerical method for suspension flows with application to sedimenting suspensions at finite-particle Reynolds numbers Re-p 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 Re-p, there exists a range of domain sizes in which particle velocity fluctuation amplitudes have a strong domain size dependence, and above which the fluctuation amplitudes become weakly dependent. The size range strongly relates with Re-p and the particle volume fraction phi(p). Furthermore, a transition in the fluctuation amplitudes is found at Re-p around 0.08. The magnitude and length scale dependence of the fluctuation amplitudes at finite Re-p are well represented by introducing new fluctuation amplitude scaling functions C-1,C- (parallel to,C-perpendicular to)(Re-p, phi(p)) and characteristic length scaling function C-2(Re-p, phi(p)) in the correlation derived by Segre et al. from their experiments at low Re-p ["Long-range correlations in sedimentation," Phys. Rev. Lett. 79, 2574-2577 (1997)] in the form = <V-parallel to > C-1,C- (parallel to,C-perpendicular to)(Re-p, phi(p))phi(p1/3) {1 - exp[-L/(C-2(Re-p, phi(p))r(p)phi(-1/3)(p))]}. (C) 2012 American Institute of Physics. [http:// dx. doi. org/ 10.1063/ 1.4770310]