# Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Fluid Flow

#### 2.2. Rigid Body Dynamics in Space

#### 2.3. Coupling Algorithm

## 3. Validation

#### 3.1. Water Entry of a Non-Buoyant Wedge

#### 3.2. Water Entry of a Buoyant Wedge

#### 3.3. Water Entry and Exit of a Buoyant Cylinder

#### 3.3.1. Experimental Setup

^{®}, with an internal volume of $1.5\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\times 1.85\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\times 0.7\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$. The tank is filled with water up to a level of $0.4\phantom{\rule{0.166667em}{0ex}}\mathrm{m}$. Two transparent sides grant optical access to the tank. The specimen, a hollow PVC cylinder filled with polystyrene with a diameter $d=0.16$ m and a breadth $l=0.295$ m, is rigidly connected to a wood sledge that is allowed to move along two vertical aluminum rails. We consider four drop heights of $0.25$ m, $0.50$ m, $0.75$ m and $1.00$ m and two specimen masses, $m={m}_{0}$ and $m={m}_{0}+1$ kg, being ${m}_{0}=2.214$ kg.

^{®}Miro 110 monochromatic high speed camera operating at a frame-rate of 2500 Hz for $m={m}_{0}$ and of 2700 Hz for $m={m}_{0}+1$ kg.

- (i)
- Numerical differentiation of the displacement measurement through central difference approximation;
- (ii)
- Numerical integration of the measured acceleration through the trapezoid rule;
- (iii)
- Least square fitting of the specimen displacement to a second order function and algebraic differentiation.

#### 3.3.2. Numerical Setup

#### 3.3.3. Results and Dicussion

#### 3.4. Roll Motion of a Rectangular Structure

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Comparison between numerical and experimental results for the specimen velocity during the water impact of a rigid wedge. Experimental data are retrieved from Reference [78].

**Figure 4.**Impact velocity of the specimen as a function of the drop height. Experimental data retrieved from Reference [79].

**Figure 5.**Displacement of the specimen center of mass. Comparison between CFD and experiments [79] for different h: (

**a**) $h=0.25$ m; (

**b**) $h=0.50$ m; (

**c**) $h=0.75$ m; (

**d**) $h=1.00$ m.

**Figure 6.**Evolution of the free surface during water impact for $h=0.5$ m. CFD results for: (

**a**) $t=0$ ms; (

**b**) $t=6$ ms; (

**c**) $t=12$ ms; (

**d**) $t=18$ ms; (

**e**) $t=24$ ms.

**Figure 7.**Impact velocity of the specimen as a function of the drop height and of the mass of the impacting cylinder.

**Figure 8.**Displacement of the specimen center of mass. Comparison between CFD and experiments for different h and m: (

**a**) $h=0.25$ m and $m={m}_{0}$; (

**b**) $h=0.5$ m and $m={m}_{0}$; (

**c**) $h=0.75$ m and $m={m}_{0}$; (

**d**) $h=1.00$ m and $m={m}_{0}$; (

**e**) $h=0.25$ m and $m={m}_{0}+1$ kg; (

**f**) $h=0.5$ m and $m={m}_{0}+1$ kg; (

**g**) $h=0.75$ m and $m={m}_{0}+1$ kg; (

**h**) $h=1.00$ m and $m={m}_{0}+1$ kg.

**Figure 9.**Evolution of the free surface for $m={m}_{0}$ and $h=0.5$ m. Comparison between CFD and experiments for different times after water impact: (

**a**) $t=0$ S; (

**b**) $t=0.08$ s; (

**c**) $t=0.16$ s; (

**d**) $t=0.24$ s; (

**e**) $t=0.32$ (s).

**Figure 10.**Convergence history for $h=0.5$ m and $m={m}_{0}$. Note that only 25 time-steps are represented for clarity. Each mark represents a FSI subcycle.

**Figure 11.**Rotation of the specimen about its center of mass. Comparison between CFD and experiments from Reference [40].

**Figure 12.**Representation of the flow field in the vicinity of the oscillating box for different times. For clarity, vectors are represented only in water. (

**a**) $t=0.08$ s, (

**b**) $t=0.8$ s, (

**c**) $t=0.16$ s, (

**d**) $t=0.24$ s and (

**e**) $t=0.32$ s.

**Table 1.**Relative average error evaluated comparing ${\delta}_{\mathrm{CFD}}$ and ${\delta}_{\mathrm{EXP}}$.

h [m] | $0.25$ | $0.50$ | $0.75$ | $1.00$ |

${\epsilon}_{\delta}$ [%] | $2.81$ | $2.24$ | $2.68$ | $3.47$ |

**Table 2.**Percent error on the displacement of the center of mass of the buoyant cylinder as a function of h and m.

$\mathit{m}={\mathit{m}}_{0}$ | $\mathit{m}={\mathit{m}}_{0}$ + 1 kg | |
---|---|---|

$h=0.25$ m | $9.93\%$ | $7.33\%$ |

$h=0.50$ m | $9.82\%$ | $6.32\%$ |

$h=0.75$ m | $10.0\%$ | $9.03\%$ |

$h=1.00$ m | $8.93\%$ | $10.8\%$ |

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**MDPI and ACS Style**

Facci, A.L.; Falcucci, G.; Agresta, A.; Biscarini, C.; Jannelli, E.; Ubertini, S.
Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation. *Water* **2019**, *11*, 1048.
https://doi.org/10.3390/w11051048

**AMA Style**

Facci AL, Falcucci G, Agresta A, Biscarini C, Jannelli E, Ubertini S.
Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation. *Water*. 2019; 11(5):1048.
https://doi.org/10.3390/w11051048

**Chicago/Turabian Style**

Facci, Andrea Luigi, Giacomo Falcucci, Antonio Agresta, Chiara Biscarini, Elio Jannelli, and Stefano Ubertini.
2019. "Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation" *Water* 11, no. 5: 1048.
https://doi.org/10.3390/w11051048