Drag on a hollow sphere can increase with porosity

Previous literature has shown that the introduction of homogeneous perforation on plates and cylinders decreases aerodynamic drag. Here, it is shown that the opposite is true for a sphere; drag can increase with porosity. Hollow porous spheres exposed to a uniform free stream are studied experimentally using force and flow field measurements. The parameter space encompasses moderate to high Reynolds numbers (5 × 10⁴ ≤ Re ≤ 4 × 10⁵) and porosities ranging from 0 % to 80 %. The main conclusion is that drag increases with porosity, at super-critical Reynolds numbers, for all studied porosities. At low porosities (less than 9 %), the effect of porosity on drag can be explained by shifts in the separation point. At higher porosities the drag increase cannot be explained by separation shifts, and instead is explained by two competing forms of kinetic energy dissipation: (i) shear on the macro-scale of the body, and (ii) hole losses from flow through the pores. The former generally decreases with porosity, as bleeding flow passing through the body decreases the characteristic velocity difference in the body-scale wake. In a sphere, hole losses increase with porosity sufficiently fast to overcome decreasing body-scale shear losses, in contrast to plates and cylinders where this is not the case. Relatively weak wake vortex structures, and associated low drag coefficient at zero porosity, for a sphere reduce the impact of wake bleeding. Moreover, fluid entering the fore of a sphere can exit perpendicular to the free stream, further reducing wake bleeding while still contributing to hole losses.