NMR measurements of flow profiles in a coarse bed of packed spheres

The velocity profiles of water flowing in a circular pipe filled with coarse, uniform, spherical beads, as well as the evolution of velocity profiles from clear flow into the bed of beads and visa versa, were measured by nuclear magnetic resonance (NMR) imaging using the phase-encoding method. Corrections for partial-volume effects were necessary in order to obtain accurate flow parameters. Phase errors due, for example, to electrical eddy currents induced by switching gradients, were minimized by the use of a static reference sample. For a tube diameter that is eight times the particle diameter, the flow reaches a steady state condition within one bead diameter into the packed bed after having a parabolic velocity profile only 1.5 tube diameters before encountering the bed. Within the packed bed, there are velocity spikes up to 16 times the average velocity in the unobstructed part of the pipe. The velocity distribution in the packed bed has a maximum that approaches the average velocity in the bed for increasing slice thickness along the flow. This distribution decreases exponentially with increasing velocity on the high-velocity side of the maximum. Even at modest flows, where velocity is steady upstream of the packed bed as well as in the bed, unsteady flow is detected downstream of the beads.