Can Drag on a Bluff Body Increase with Porosity?

Previous observations generally support a decrease in drag when homogeneous perforations are added to a bluff body. Experiments on flat plates normal to the flow, square bars, and cylinders all demonstrate a decrease in drag with increasing porosity. We show that, perhaps counterintuitively, the opposite is true for a sphere.

Porous spheres exposed to a uniform flow are studied experimentally using force and flow-field measurements. The parameter space includes moderate to high Reynolds numbers (5 x 10⁴ ≤ Re ≤ 4 x 10⁵) and porosities from 0% to 80%. Force measurements reveal that, at super-critical Reynolds numbers, the drag on a sphere increases with porosity for all studied porosities. This trend is robust to different mounting configurations and is further supported by free-fall experiments where porous spheres are dropped from a tall building.

We show that changes in the separation point can explain the drag increases only at low porosity (less than 9%). To explain the drag increases at higher porosities, we consider an energy budget, where the power to drive a porous bluff body through a quiescent fluid is balanced by kinetic energy dissipation from two sources: (1) shear on the scale of the body and (2) expansion losses of flow through the holes. The former generally decreases with porosity due to wake bleeding, while the latter can increase. In a sphere, relatively weak vortex structures in the wake reduce the impact of wake bleeding, allowing increasing hole losses to yield an overall increase in drag.