The motion of a single heavy sphere in ambient fluid: a benchmark for interface-resolved particulate flow simulations with significant relative velocities

Abstract: Detailed data describing the motion of a rigid sphere settling in unperturbed fluid is generated by means of highly-accurate spectral/spectral-element simulations with the purpose of serving as a future benchmark case. A single solid-to-fluid density ratio of 1.5 is chosen, while the value of the Galileo number is varied from 144 to 250 such as to cover the four basic regimes of particle motion (steady vertical, steady oblique, oscillating oblique, chaotic). This corresponds to a range of the particle Reynolds number from 185 to 365. In addition to the particle velocity data, extracts of the fluid velocity field are provided, as well as the pressure distribution on the sphere's surface. Furthermore, the same solid-fluid system is simulated with a particular non-boundary-conforming approach, i.e. the immersed boundary method proposed by Uhlmann (JCP 2005), using various spatial resolutions. It is shown that the current benchmark case allows to adjust the resolution requirements for a given error tolerance in each flow regime.