Flow and dispersion through a close-packed fixed bed of spheres

Fluid flow through a close-packed fixed bed of spheres in a face-centered cubic arrangement is investigated in numerical simulations using a lattice-Boltzmann formulation. The dispersion of a tracer gas is studied both experimentally and numerically. At low Reynolds numbers, $\mathrm{Re}l~14,$ the flow is steady with a distribution of normalized local kinetic energies that follows a power law over roughly three orders of magnitude. Consequently the ``stagnant'' zones play a significant role in determining transport through the packed bed in contrast with the dangling ends for the analogous electrical transport problem, where the distribution of local currents is log binomial. At higher Reynolds numbers transitions to time-oscillatory and chaotically (turbulently) varying flows are predicted to occur with a crossover to a log-normal distribution of local kinetic energies. At the onset of transverse velocity fluctuations the simulated trajectories of tracer particles can cross planes of symmetry, resulting in an abrupt enhancement of dispersion. The dispersion of tracer particles in the time-oscillatory and chaotic varying flows is predicted to be Fickian in the far field. Model predictions for dispersion in a chaotic flow with $\mathrm{Re}\ensuremath{\sim}100$ are shown to be in good agreement with experiment.