Passive control of a falling sphere by elliptic-shaped appendages

TL;DR

This study investigates how elliptic-shaped appendages on a sphere influence its fall dynamics, revealing an instability that causes drift and identifying appendage parameters that maximize this effect.

Contribution

It introduces the concept of an inverted-pendulum-like instability in spheres with elliptic appendages and analyzes how appendage shape affects drift during free fall.

Findings

Appendages can induce a stable or unstable equilibrium, causing drift.

The aspect ratio and length of appendages significantly affect the magnitude of side forces.

The physical mechanism involves the balance of flow exposure on the appendage surfaces.

Abstract

The majority of investigations characterizing the motion of single or multiple particles in fluid flows consider canonical body shapes, such as spheres, cylinders, discs, etc. However, protrusions on bodies -- being either as surface imperfections or appendages that serve a function -- are ubiquitous in both nature and applications. In this work, we characterize how the dynamics of a sphere with an axis-symmetric wake is modified in the presence of thin three-dimensional elliptic-shaped protrusions. By investigating a wide range of three-dimensional appendages with different aspect ratios and lengths, we clearly show that the sphere with an appendage may robustly undergo an inverted-pendulum-like (IPL) instability. This means that the position of the appendage placed behind the sphere and aligned with the free-stream direction is unstable, in a similar way that an inverted pendulum is unstable under gravity. Due to this instability, non-trivial forces are generated on the body, leading to turn and drift, if the body is free to fall under gravity. Moreover, we identify the aspect ratio and length of the appendage that induces the largest side force on the sphere, and therefore also the largest drift for a freely falling body. Finally, we explain the physical mechanisms behind these observations in the context of the IPL instability, i.e., the balance between surface area of the appendage exposed to reversed flow in the wake and the surface area of the appendage exposed to fast free-stream flow.