Publication
The suspension of a heavy sphere by an upward jet is a classical fluid mechanics experiment to demonstrate the fluid forces acting on an object. In the range of the parameter space where the sphere can be suspended, the dynamics can either be regular, i.e., with oscillations around an equilibrium position, or chaotic, with extreme events leading to large deviations from that equilibrium region. The existence and characteristics of suspension regimes of several heavy spheres in such flow configurations remain open questions. Spheres compete for the equilibrium position and come very close to each other, resulting in large local particle concentrations that prevent direct imaging. Relatively high speed X-ray radiography along with the radioSphere analysis technique is leveraged here to study the time-resolved 3D trajectory of each individual sphere in a vertical jet. radioSphere is an X-ray analysis method that retrieves the 3D information out of a single 2D radiography using a priori knowledge of the imaging geometry (E. Ando et al., 2021), which due to the imaging modality imposes no limitations on the optical properties of the water. The 3D + time kinematics yield the evolution of the statistics of the position and velocity of the spheres as a function of the number of spheres and for two jet Reynolds numbers. Drastic changes in behavior occur when many spheres are present, leaving a clear signature on the temporal dynamics and on the exploration of the flow volume, where spheres can remain on the bottom of the vessel for long periods of time, resulting in only partial suspension. In addition to the suspension capacity, the interactions between spheres are explored with statistics of pair separation distances, which, together, allow for quantitative arguments to introduce suspension regimes of a collection of spheres in an upward vertical jet.