# Flow and air-entrainment around partially submerged vertical cylinders

## TL;DR

This study investigates the flow and air-entrainment phenomena around partially submerged vertical cylinders moving through water, revealing two modes of air-entrainment, a scaling law for critical velocity, and a linear drag-Froude number relationship.

## Contribution

It provides new experimental insights into air-entrainment mechanisms and drag behavior around submerged cylinders in turbulent flow regimes.

## Key findings

- Two modes of air-entrainment identified: cavity along the wall and wake.
- Scaling law for critical velocity of air-entrainment matches a simple model.
- Drag force varies linearly with Froude number for Fr > 1.2.

## Abstract

In this study, a partially submerged vertical cylinder is moved at constant velocity through water, which is initially at rest. During the motion, the wake behind the cylinder induces free-surface deformation. Eleven cylinders, with diameters from $D=1.4$ to 16 cm, were tested at two different conditions: (i) constant immersed height $h$ and (ii) constant $h/D$. The range of translation velocities and diameters are in the regime of turbulent wake with experiments carried out for $4500<Re<240 \,000$ and $0.2<Fr<2.4$, where $Re$ and $Fr$ are the Reynolds and Froude numbers based on $D$. The focus here is on drag force measurements and relatively strong free-surface deformation up to air-entrainment. Specifically, two modes of air-entraiment have been uncovered: (i) in the cavity along the cylinder wall and (ii) in the wake of the cylinder. A scaling for the critical velocity for air-entrainment in the cavity has been observed in agreement with a simple model. Furthermore, for $Fr>1.2$, the drag force varies linearly with $Fr$.