Drag anisotropy of cylindrical solids in fluid-saturated granular beds

TL;DR

This study investigates how the drag force on cylindrical objects in water-saturated granular beds varies with orientation, speed, and aspect ratio, revealing rate-dependent anisotropy influenced by material friction and flow conditions.

Contribution

It provides new insights into the rate-dependent drag anisotropy of cylinders in granular media, highlighting the effects of aspect ratio, surface friction, and flow regime.

Findings

Drag anisotropy increases with driving rate and aspect ratio.

Froude number influences the magnitude of anisotropy.

Skin friction dominates the sediment flow around the cylinder.

Abstract

We study the direction-dependent drag acting on a cylindrical solid intruder with length $L$ and diameter $D$ as it moves in water-saturated granular beds at constant depth. Polysterene and hydrogel grains with diameter $d$ are used to investigate materials which have high contact friction and those which are nearly frictionless, respectively. The drag on the intruder is measured while oriented perpendicular $F_\perp$ and parallel $F_\parallel$ to its axis as a function of speed $U$ from the quasi-static to the rate-dependent regime. We find that the drag anisotropy $\xi = F_\perp/F_\parallel$ is not constant, and increases significantly with driving rate and $L/D$ in both mediums. In particular for $L/D = 40$, $\xi$ increases from 2.6 to 4.5, and from 7.0 to 8.2 in the high and low friction beds, respectively, as the nondimensional Froude number $Fr =U/\sqrt{g(D+d)}$ is varied between $10^{-4}$ and $2 \times 10^{-2}$. On average, $\xi$ is observed to increase logarithmically with $L/D$ for $L/D \gg 1$. Exploiting the index-matched nature of hydrogel grains in water, we further show that the sediment flow around the cylinder in the two orientations is consistent with skin friction dominated drag. The relative contributions of the cylindrical side and the circular flat-ends on $\xi$ are estimated with thin disks to understand the observed variation of drag with aspect ratio and surface friction.