# Breakdown of wing tip vortex in water induced by air injection

Pedro Solís García, Thomas Leweke, Eduardo Durán Venegas

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Pedro Solís García, Thomas Leweke, Eduardo Durán Venegas. Breakdown of wing tip vortex in water induced by air injection. 3rd Spanish Fluid Mechanics Conference, Jun 2025, Malaga, Spain. hal-05235054

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Submitted on 2 Sep 2025

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# Breakdown of a wing tip vortex in water induced by air injection

Pedro Solís García¹,², Thomas Leweke², and Eduardo Durán Venegas¹

Email for contact: pedrosg97@gmail.com

¹Department of Mechanical Engineering, University of Malaga, 29071 Málaga, Spain
²IRPHE, CNRS, Aix-Marseille Université, Centrale Méditerranée, 13384 Marseille, France

## Abstract

We report a previously unobserved phenomenon where, under specific Reynolds numbers and angles of attack, air injected into the core of a water wing tip vortex forms a stable bubble that can persist for several minutes before dissipating.

## 1 Introduction

Concentrated vortices in a liquid fluid, such as water, can develop a hollow gaseous core by trapping ambient air bubbles in the low-pressure region near the rotation axis [1], or by cavitation [2], when the core pressure is sufficiently low. Such two-phase vortices are typically found in the wake of lifting surfaces (hydrofoils) moving at high speed under water [3]. In this contribution, we present an unreported two-phase vortex phenomenon, different to the ones previously mentioned. For certain Reynolds numbers and angles of attack, if air is injected in the core of a water wing tip vortex, a bubble forms. This bubble moves through the vortex core to a particular position, where it can remain stable for several minutes before disappearing. The shape of the bubble and the behaviour of the flow, which must create a stagnation point at the tip of the bubble, bear similarities to the vortex breakdown phenomenon [4].

## 2 Methodology

Experiments were conducted in a recirculating free-surface water channel with a test section of dimensions 150 cm × 38 cm × 50 cm (length × width × height). Wing tip vortices were generated with a rectangular wing with a NACA 0012 cross-section, an aspect ratio *AR* = 2.5, a chord length *c* = 9.8 cm and a rounded tip, placed vertically in the test section. To create the bubbles, air was injected into the vortex core through an L-shaped cannula. Figure 1 shows a

schematic of the setup. It is important to note that, if the air is not injected against the flow direction, the bubble does not form. We performed experiments under different conditions, varying the angle of attack $α$ and the Reynolds number $Re = Uc/ν$, where $U$ is the free-stream velocity and $ν$ the kinematic viscosity. The lifetime of the bubbles was measured with a chronometer, and other properties like size, shape and position were obtained via visualizations.

<figure><img src="image_3.png" /><figcaption>FIGURE 1: Schematic of the experimental setup.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>FIGURE 2: Image of an air bubble trapped inside a vertically mounted water wing tip vortex.</figcaption></figure>
# 3 Results

Figure 2 shows a typical example of an air bubble inside the tip vortex, located about half a chord length behind the wing. This phenomenon, where the bubble remains stable for several minutes despite the free-stream flow and buoyancy effects, can be observed for sufficiently high angles of attack and Reynolds numbers. If either parameter is too low, the bubble does not form. Conversely, if they are too high, the bubble moves upstream until it reaches the wing, where it breaks. Figure 3 presents a flow regime map summarizing the observations for the parameter space considered in this study ($Re = 6–10 \times 10^3$, $\alpha = 10–17°$).

In the stable regime, the bubble size decreases slowly in time, since the turbulence surrounding the vortex detaches small pockets of air at the rear. The bubble volume was estimated from visualization images, by identifying the perimeter and fitting an ellipse to its shape, as shown in figure 4. Assuming axisymmetry, the bubble volume is given by $V = \frac{4}{3}\pi a^2 b$, where *a* and *b* are the minor and major semi-axes. Figure 5 shows the average bubble volume for each experiment, as function of the Reynolds number, revealing that the maximum bubble size increases with it. This growth is primarily due to an elongation of the bubble's longitudinal axis, while the radial axis remains relatively constant.

The bubble lifetime in the stable regime is given in figure 6, indicating the existence of optimal conditions at $Re = 8 \times 10^4$ and $\alpha = 12°$.

# 4 Conclusions

This study reveals a previously unreported phenomenon, reminiscent of vortex breakdown, in which

<figure><img src="image_5.png" /><figcaption>FIGURE 3: Flow regime map of bubble stability.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>FIGURE 4: Example of a bubble image, with the detected perimeter (orange), and the fitted ellipse.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>FIGURE 5: Bubble size distribution.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>FIGURE 6: Average bubble lifetime.</figcaption></figure>

air injected into the core of a wing tip vortex in water forms a stable bubble under specific conditions. Visualizations show that the maximum bubble size increases with Reynolds number, primarily due to an increase in the bubble length rather than its width. Lifespan measurements reveal the existence of optimal conditions for bubble stability. Further details concerning the bubble characteristics and dynamics, and their relation to the vortex properties (circulation, core size, axial flow) will be presented at the conference.

# References

[1] Jha, N.K., Govardhan, R.N. (2015). "Interaction of a vortex ring with a single bubble: bubble and vorticity dynamics". *Journal of Fluid Mechanics*, 733, 460-497.

[2] Arndt, R.E.A. (2002). "Cavitation in vortical flows". *Annual Review of Fluid Mechanics*, 34, 143-175.

[3] Molland, A.F., Turnock, S.R. (2022). *Machine Rudders, Hydrofoils and Control Surfaces*. Butterworth-Heinemann.

[4] Lucca-Negro, O., O'Doherty, T. (2001). "Vortex breakdown: a review". *Progress in Energy and Combustion Science*, 27(4), 431-481.