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

international journal of multiphase flow

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