Flow characteristics analysis for flow past the porous spheres: wake structures and drag force coefficients

Flow past a permeable sphere is different from that of a solid sphere due to the penetration of the fluid within porous structures, which can arise a change of flow fields. In this work, flow past porous spheres with Darcy numbers (Da) ranging from [0,10−3 ] were measured using planar Particle Image Velocimetry (PIV). The whole flow fields, including both leading edge and trailing edge, were captured at six different Reynolds numbers (Re) varying from 400 to 1400. Time-average flow fields were calculated based on instantaneous flow fields within fully-developed stages. Local minimum method was used to search for stagnation point positions. The results show positions of stagnation points are nearly proportional to the logarithm of Re. For most porous spheres, positions of stagnation points are extended to farther downstream positions than that of a solid sphere. However, at some certain Darcy numbers, ranging from 5 ∗ 10−6 to 2 ∗ 10−5, positions of stagnation points are closer to the sphere centers than that of an impermeable one.