Direct numerical simulation of free falling sphere in creeping flow

In the present study, direct numerical simulations (DNS) are performed on single and a swarm of particles settling under the action of gravity. The simulations have been carried out in the creeping flow range of Reynolds number from 0.01 to 1 for understanding the hindrance effect, of the other particles, on the settling velocity and drag coefficient. The DNS code is a non-Lagrange multiplier-based fictitious-domain method, which has been developed and validated by Jin et al. (2008 Jin, S. A parallel algorithm for the direct numerical simulation of 3D inertial particle sedimentation. Conference proceedings of the 16th annual conference of the CFD Society of Canada. Edited by: Bergstrom, D. J. and Spiteri, R. 9–11, June. Saskatoon, Saskatchewan, , Canada [Google Scholar]; A parallel algorithm for the direct numerical simulation of 3D inertial particle sedimentation. In: Conference proceedings of the 16th annual conference of the CFD Society of Canada). It has been observed that the time averaged settling velocity of the particle in the presence of other particles, decreases with an increase in the number of particles surrounding it (from 9 particles to 245 particles). The effect of the particle volume fraction on the drag coefficient has also been studied and it has been observed that the computed values of drag coefficients are in good agreement with the correlations proposed by Richardson and Zaki (1954 Richardson, J. F. and Zaki, W. N. 1954. Sedimentation and fluidization: part I. Transactions of the Institution of Chemical Engineers, 32: 35–53.  [Google Scholar]; Sedimentation and fluidization: part I. Transactions of the Institution of Chemical Engineers, 32, 35–53) and Pandit and Joshi (1998 Pandit, A. B. and Joshi, J. B. 1998. Pressure drop in packed, expanded and fluidized beds, packed columns and static mixers – a unified approach. Reviews in Chemical Engineering, 14: 321–371. [Crossref], [Web of Science ®] , [Google Scholar]; Pressure drop in packed, expanded and fluidised beds, packed columns and static mixers – a unified approach. Reviews in Chemical Engineering, 14, 321–371). The suspension viscosity-based model of Frankel and Acrivos (1967 Frankel, N. A. and Acrivos, A. 1967. On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 22: 847–853. [Crossref], [Web of Science ®] , [Google Scholar]; On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 22, 847–853) shows good agreement with the DNS results.