Effects of periodicity on flow and dispersion through closely packed fixed beds of spheres

A lattice-Boltzmann formulation is used to investigate the effects of "periodicity" (geometry) on fluid flow and tracer-particle dispersion through fixed beds of spheres comprising of closely packed layers. In the "period-1" arrangement, spheres in the adjacent layers contact at their poles while the "period-2" and "period-3" arrangements correspond to hexagonal and faced-centered cubic close packing. For all three packing arrangements, there is a transition with increasing Reynolds number from a power law to a log-normal distribution of kinetic energies and, velocity and vorticity become more closely aligned giving rise to helical tracer-particle trajectories. It is suggested that these flow characteristics, unlike the stability of flow and the distribution of helicity, are largely insensitive to geometry, even when the geometry creates direct channels through the pack bed orientated along the gradient in applied pressure. For steady flows and strongly turbulent flows, such channels are predicted to provide direct routes for dispersion through a packed bed, while for weakly turbulent flows they influence dispersion primarily by destabilizing the flow and thereby promoting dispersion throughout a bed. The dispersion of tracer-particles released from a source located on or close to a "stagnation streamline" is predicted to be faster than ballistic in the near field and the transition to long-time Fickian diffusion is predicted to be distinguished by a regime of subdiffusion.