Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres

Extensive lattice-Boltzmann simulations were performed to obtain the drag force for random arrays of monodisperse and bidisperse spheres. For the monodisperse systems, 35 different combinations of the Reynolds number Re (up to Re = 1,000) and packing fraction were studied, whereas for the bidisperse systems we also varied the diameter ratio (from 1:1.5 to 1:4) and composition, which brings the total number of different systems that we considered to 150. For monodisperse systems, the data was found to be markedly different from the Ergun equation and consistent with a correlation, based on similar type of simulations up to Re = 120. For bidisperse systems, it was found that the correction of the monodisperse drag force for bidispersity, which was derived for the limit Re = 0, also applies for higher-Reynolds numbers. On the basis of the data, a new drag law is suggested for general polydisperse systems, which is on average within 10% of the simulation data for Reynolds numbers up to 1,000, and diameter ratios up to 1:4