Four-dimensional flow field near a sphere settling in Newtonian fluid

Abstract

This paper presents time-resolved, three-dimensional measurements coupling particle trajectories with flow fields around settling spheres in Newtonian fluids. The experiments cover a range of particle Reynolds numbers (Re), spanning from 1.6 to 6. Our calculated drag coefficients, derived from sphere trajectories, closely align with values reported in the literature. Notably, our high spatial resolution reveals oscillations, potentially corresponding to the “streamwise oscillations” phenomenon discussed by Horowitz and Williamson [“The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres,” J. Fluid Mech. 651, 251 (2010)]. For a single sphere, we extract the three-dimensional flow field using particle tracking velocimetry. Discrete particle tracks are meticulously interpolated onto a regular grid using a fine-scale reconstruction based on the vortex-in-cell method. Leveraging the known sphere position, we introduce a sphere-centered coordinate system, enabling time-averaging of flow properties. Additionally, we interpolate and analyze the pressure field on the sphere's surface, employing proper orthogonal decomposition to unveil distinct pressure fluctuation modes.