# Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Method

#### 2.1. Overview

#### 2.2. Floating Infra-Red Reflective Markers

#### 2.3. Copper Tape Resistive Wave Gauges

## 3. Results

#### 3.1. Influence of Variable Inner Water Depth h

#### 3.2. Influence of Variable Inclination Angle of the Tank

#### 3.3. Transient Behaviour

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

LNG | liquefied natural gas |

Q | Qualisys |

VLFS | very large floating structures |

WG | wave gauge |

## References

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**Figure 1.**Experimental set-up—acrylic cylindrical tank mounted on an inclinable framework including table tennis balls (TTB) and wave gauges made of copper tape (CT)—rotation axis R—(

**a**) overview of the inclined structure and (

**b**) detail of the inner water surface.

**Figure 2.**Basic geometry (

**a**) plan view of the upright cylinder including the numbering of the wave gauges and (

**b**) side view of the inclined geometry with an example pitch angle $\beta $—R is the rotation axis and $TP4$ the reference point introduced in Section 3.2—all dimensions in [m].

**Figure 3.**Comparison of the methods with a variable water depth h inside the cylinder—(

**a**) comparison between water depth captured with the marker balls via Qualisys (Q) and wave gauges (WG); (

**b**) absolute differences between the methods; (

**c**,

**d**) standard deviation (std) for each method.

**Figure 4.**Influence of variable pitch angle $\beta $ on the wave gauges (WG)—(

**a**,

**b**) analysis of the measured changes in the free surface; (

**c**,

**d**) comparison between the measured angle ${\beta}_{Q}$ and the calculated ${\beta}_{WG}$ based on the wave gauges pairs.

**Figure 5.**Influence of variable pitch angle $\beta $ on the floating markers—(

**a**) comparison of the theoretical with the measured z-coordinate of the reference point $TP4$ and the free surface; (

**b**) standard deviation of the measured balls; (

**c**–

**e**) absolute difference of the z-coordinate in relation to all three rotation axes.

**Figure 7.**Results of the transient experiment—wave gauges (WG) in pairs as defined in Figure 2—normalised surface elevation $\eta /h$.

**Figure 8.**Results of the transient experiment—3D location of the measured marker balls; four different time periods (columns) and three different view directions (rows).

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## Share and Cite

**MDPI and ACS Style**

Gabl, R.; Steynor, J.; Forehand, D.I.M.; Davey, T.; Bruce, T.; Ingram, D.M.
Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure. *Water* **2019**, *11*, 50.
https://doi.org/10.3390/w11010050

**AMA Style**

Gabl R, Steynor J, Forehand DIM, Davey T, Bruce T, Ingram DM.
Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure. *Water*. 2019; 11(1):50.
https://doi.org/10.3390/w11010050

**Chicago/Turabian Style**

Gabl, Roman, Jeffrey Steynor, David I. M. Forehand, Thomas Davey, Tom Bruce, and David M. Ingram.
2019. "Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure" *Water* 11, no. 1: 50.
https://doi.org/10.3390/w11010050