# On Air-Cavity Formation during Water Entry of Flexible Wedges

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## Abstract

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## 1. Introduction

## 2. Cavitation Onset in Rigid Bodies’ Water Entry as Predicted by Analytical Formulations

## 3. Preliminary Experimental Evidences

## 4. Experimental Setup

#### Specimens

## 5. Experimental Results

#### 5.1. Wedge Deformation during Water Entry

#### 5.2. Evidence of Cavity Formation from High-Speed Images

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Sketch of the problem of the water entry of a rigid wedge. The wedge enters the water surface at $t=0$ (

**left**) and penetrates the water by an entry depth $\xi $ as time advances (

**right**).

**Figure 2.**Wagner’s predicted normalized pressure as a function of normalized wet length $x/r$ at several instants. The solution was calculated for a wedge weighing 5 kg/m, with a 20${}^{\xb0}$ deadrise angle, entering the water at $2\text{}\mathrm{m}/\mathrm{s}$ with pure vertical velocity.

**Figure 3.**(

**Left**) Normalized pressure versus entry depth for varying deadrise angles. (

**Right**) Normalized minimum pressure versus deadrise angle.

**Figure 4.**Schematics of a water-entry apparatus. The two possible locations (side and front) of the camera are showed. The sketch highlights the end-run cable used to stop the motion.

**Figure 5.**Details of the vertex of the keel at several time instants, presenting the evolution of the cavity formation. Images are taken from the side.

**Figure 6.**Deformation over time of a fiberglass/vinylester wedge with a deadrise angle of 30${}^{\xb0}$ entering the water at 4.2 $\mathrm{m}/\mathrm{s}$. Time advances left to right, top to bottom.

**Figure 7.**Signal recorded by two strain gauges during the water entry of a fiberglass/polyester wedge 4 mm thick with a deadrise angle of ${35}^{\xb0}$ entering the water from an impact height of 1.5 m (approximately 5 $\mathrm{m}/\mathrm{s}$). The graph on the right shows the strain measured at the center of the panel, while the graph on the left shows the strain close to the wedge tip. The full and the dashed lines represent two repetitions of the same experiment.

**Figure 8.**Deformation over time of wedge (V) 2 mm thick ($\beta $ = 20${}^{\xb0}$) entering the water at 6.7 $\mathrm{m}/\mathrm{s}$. Time advances left to right, top to bottom.

**Figure 9.**Signal acquired by two strain gauges during the water entry. The graph on the right shows the strain measured at the center of the panel, while the graph on the left shows the strain close to the wedge tip. Full and dashed lines are two repetitions of the same experiment.

**Figure 10.**Evolution of the water entry of a wedge (W) ($\beta ={30}^{\xb0}$) entering the water at ≈4.2 m/s at 25, 40, and 55 ms from the impact.

**Figure 11.**Evolution of the water entry of a wedge (W) ($\beta ={15}^{\xb0}$) entering the water at ≈6.7 m/s at 16.6, 20, and 23.3 ms from the impact. The arrow highlights the cylindrical front of the cavitating area.

**Figure 12.**Evolution of the water entry of a wedge (V) ($\beta ={20}^{\xb0}$) entering the water at ≈4.3 m/s at 40, 53.3, and 66.6 ms from the impact. The arrow highlights the cylindrical front of the cavitating area.

**Figure 13.**Evolution of the water entry of a wedge (V) ($\beta ={20}^{\xb0}$) entering the water at ≈6 m/s at 40, 53.3, and 66.6 ms from the impact. The arrow highlights the cylindrical front of the cavitating area.

**Figure 14.**Maximum dimension of the wavefront during the water entry of a wedge (V) ($\beta ={20}^{\xb0}$) entering the water at 4.3, 6, and 6.7 m/s.

**Figure 15.**Graph of the recorded acceleration of a wedge (V) 2 mm thick ($\beta ={20}^{\xb0}$) entering the water at 5.6 m/s, and high-speed camera images captured at 0, 5, 15, 20, 22.5, and 25 ms.

Material | Abbr. | Elastic Moduli | Poisson Ratio | Density |
---|---|---|---|---|

${\mathit{E}}_{1}={\mathit{E}}_{2}$ | ${\mathit{\nu}}_{12}$ | $\mathit{\rho}$ (kg/m${}^{3}$) | ||

6068 T6 | A | 68.0 GPa | 0.32 | 2700 |

E-Glass/Vinylester | V | 20.4 GPa | 0.28 | 2050 |

E-Glass/Epoxy | W | 30.3 GPa | 0.28 | 2015 |

Abbr. | Material | Thickness | ${\mathit{\omega}}_{1}$ (Hz) | ${\mathit{\omega}}_{2}$ (Hz) | ${\mathit{\omega}}_{3}$ (Hz) |
---|---|---|---|---|---|

A2 | Aluminum | 2.0 mm | 18.0 | 112.8 | 316.1 |

A4 | Aluminum | 4.0 mm | 36.0 | 225.7 | 632.2 |

V2 | Fiberglass | 2.0 mm | 9.7 | 61.2 | 171.4 |

V4 | Fiberglass | 4.0 mm | 19.7 | 123.6 | 346.2 |

W2 | Fiberglass | 2.2 mm | 19.6 | 123.4 | 345.5 |

W4 | Fiberglass | 4.4 mm | 37.8 | 236.9 | 663.4 |

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**MDPI and ACS Style**

Panciroli, R.; Pagliaroli, T.; Minak, G. On Air-Cavity Formation during Water Entry of Flexible Wedges. *J. Mar. Sci. Eng.* **2018**, *6*, 155.
https://doi.org/10.3390/jmse6040155

**AMA Style**

Panciroli R, Pagliaroli T, Minak G. On Air-Cavity Formation during Water Entry of Flexible Wedges. *Journal of Marine Science and Engineering*. 2018; 6(4):155.
https://doi.org/10.3390/jmse6040155

**Chicago/Turabian Style**

Panciroli, Riccardo, Tiziano Pagliaroli, and Giangiacomo Minak. 2018. "On Air-Cavity Formation during Water Entry of Flexible Wedges" *Journal of Marine Science and Engineering* 6, no. 4: 155.
https://doi.org/10.3390/jmse6040155