# Evolution of an eroding cylinder in single and lattice arrangements

## TL;DR

This study investigates the erosion process of cylinders in fluid flow, revealing how their shape evolves and how arrangements affect their terminal forms, using advanced simulations and mesh algorithms.

## Contribution

Introduces a novel node shuffle algorithm for mesh quality preservation and explores the evolution of eroding cylinders in various arrangements with detailed flow analysis.

## Key findings

- Cylinders evolve into a rounded triangular shape with uniform wall shear stress.
- Flow features like vortex shedding occur on smaller time scales than erosion.
- Large spacings lead to similar terminal forms, with intermediate shapes in closely packed arrangements.

## Abstract

The coupled evolution of an eroding cylinder immersed in a fluid within the subcritical Reynolds range is explored with scale resolving simulations. Erosion of the cylinder is driven by fluid shear stress. K\'arm\'an vortex shedding features in the wake and these oscillations occur on a significantly smaller time scale compared to the slowly eroding cylinder boundary. Temporal and spatial averaging across the cylinder span allows mean wall statistics such as wall shear to be evaluated; with geometry evolving in 2-D and the flow field simulated in 3-D. The cylinder develops into a rounded triangular body with uniform wall shear stress which is in agreement with existing theory and experiments. We introduce a node shuffle algorithm to reposition nodes around the cylinder boundary with a uniform distribution such that the mesh quality is preserved under high boundary deformation. A cylinder is then modelled within an infinite array of other cylinders by simulating a repeating unit cell and their profile evolution is studied. A similar terminal form is discovered for large cylinder spacings with consistent flow conditions and an intermediate profile was found with a closely packed lattice before reaching the common terminal form.