# Roll Motion of a Water Filled Floating Cylinder—Additional Experimental Verification

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Experimental Set-up

#### 2.2. Instrumentation

#### 2.3. Experimental Conditions

## 3. Results

#### 3.1. Overview

#### 3.2. Position in the Tank

#### 3.3. Length of the Test

#### 3.4. Wave Amplitudes

#### 3.5. Direction Including Comparison with the Solid Case

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Notation

${a}_{R}$ | amplitude waves (mm) measured |

${a}_{W}$ | amplitude waves (mm) requested from the wave makers |

d | cylinder draft (m) |

D | cylinder diameter (m) |

${f}_{R}$ | response frequency (Hz) measured |

${f}_{W}$ | frequency wave (Hz) requested from the wave makers |

h | water depth inside the cylinder (m) |

H | height of the cylinder (m) |

x | distance (m) in the main wave direction defined as 90° |

X | motion in x-direction (mm) |

y | distance orthogonal to the main wave direction (m) |

Y | motion in y-direction (mm) |

z | distance vertical direction (m) |

Z | motion in z-direction (mm) |

DoF | degree of freedom |

MoCAP | motion capturing system |

RAO | response amplitude operator |

RQ | research question |

WG | wave gauge |

## References

- Gabl, R.; Davey, T.; Nixon, E.; Steynor, J.; Ingram, D.M. Comparison of a Floating Cylinder with Solid and Water Ballast. Water
**2019**, 11, 2487. [Google Scholar] [CrossRef][Green Version] - Gabl, R.; Davey, T.; Nixon, E.; Steynor, J.; Ingram, D.M. Experimental Data of a Floating Cylinder in a Wave Tank: Comparison Solid and Water Ballast. Data
**2019**, 4, 146. [Google Scholar] [CrossRef][Green Version] - Fossen, T.; Nijmeijer, H. Parametric Resonance in Dynamical Systems; Springer: New York, NY, USA, 2012. [Google Scholar]
- France, W.; Levadou, M.; Treakle, T.; Paulling, J.; Michel, R.; Moore, C. An Investigation of Head-Sea Parametric Rolling and Its Influence on Container Lashing Systems; The Society of Naval Architects and Marine Engineers: Alexandria, VA, USA, 2001; pp. 1–24. [Google Scholar]
- Cheng, P.; Liang, N.; Li, R.; Lan, H.; Cheng, Q. Analysis of Influence of Ship Roll on Ship Power System with Renewable Energy. Energies
**2020**, 13, 1. [Google Scholar] [CrossRef][Green Version] - Li, C.T.; Wang, D.Y.; Cai, Z.H. Experimental and numerical investigation on the scaled model of lashing bridge coupled with hull structure and container stack. Ships Offshore Struct.
**2020**. [Google Scholar] [CrossRef] - Neves, M.A.S.; Rodríguez, C.A. On unstable ship motions resulting from strong non-linear coupling. Ocean Eng.
**2016**, 33, 1853–1883. [Google Scholar] [CrossRef] - Wang, L.; Tang, Y.; Li, Y.; Zhang, J.C.; Lui, L.Q. Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method. China Ocean Eng.
**2020**, 34, 289–298. [Google Scholar] [CrossRef] - Guze, S.; Wawrzynski, W.; Wilczynski, P. Determination of Parameters Describing the Risk Areas of Ships Chaotic Rolling on the Example of LNG Carrier and OSV Vessel. J. Mar. Sci. Eng.
**2020**, 8, 91. [Google Scholar] [CrossRef][Green Version] - Kianejad, S.S.; Enshaei, H.; Duffy, J.; Ansarifard, N. Prediction of a ship roll added mass moment of inertia using numerical simulation. Ocean Eng.
**2019**, 173, 77–89. [Google Scholar] [CrossRef] - Olivieri, A.; Francescutto, A.; Campana, E.F.; Stern, F. Parametric Roll: Highly Controlled Experiments for an Innovative Ship Design. In Proceedings of the ASME 2008 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal, 15–20 June 2008; Volume 4, pp. 291–299. [Google Scholar]
- Huang, S.; Duan, W.; Han, X.; Nicoll, R.; You, Y.G.; Sheng, S.W. Nonlinear analysis of sloshing and floating body coupled motion in the time-domain. Ocean Eng.
**2018**, 164, 350–366. [Google Scholar] [CrossRef] - Zhou, Y.; Ma, N.; Lu, J.; Gu, M. A study of hybrid prediction method for ship parametric rolling. J. Hydrodyn.
**2016**, 28, 617–628. [Google Scholar] [CrossRef] - Zhou, Y. Further validation study of hybrid prediction method of parametric roll. Ocean Eng.
**2019**, 186, 106103. [Google Scholar] [CrossRef] - Zhao, W.; Taylor, P.; Wolgamot, H.; Taylor, R.E. Identifying linear and nonlinear coupling between fluid sloshing in tanks, roll of a barge and external free-surface waves. J. Fluid Mech.
**2018**, 844, 403–434. [Google Scholar] [CrossRef] - Zhao, W.H.; McPhail, F. Roll response of an LNG carrier considering the liquid cargo flow. Ocean Eng.
**2017**, 129, 83–91. [Google Scholar] [CrossRef] - Zhu, X.; Yoo, W. Numerical modeling of a spar platform tethered by a mooring cable. Chin. J. Mech. Eng.
**2015**, 28, 785–792. [Google Scholar] [CrossRef] - Orszaghova, J.; Wolgamot, H.; Draper, S.; Taylor, P.H.; Rafiee, A. Onset and limiting amplitude of yaw instability of a submerged three-tethered buoy. Proc. R. Soc. A
**2020**, 476, 20190762. [Google Scholar] [CrossRef] - Tarrant, K.; Meskel, C. Investigation on parametrically excited motions of point absorbers in regular waves. Ocean Eng.
**2016**, 111, 67–81. [Google Scholar] [CrossRef] - Radhakrishnan, S.; Datla, R.; Hires, R.I. Theoretical and experimental analysis of tethered buoy instability in gravity waves. Ocean Eng.
**2007**, 34, 261–274. [Google Scholar] [CrossRef] - Jiang, H.; You, Y.; Hu, Z.; Zheng, X.; Ma, Q. Comparative Study on Violent Sloshing with Water Jet Flows by Using the ISPH Method. Water
**2019**, 11, 2590. [Google Scholar] [CrossRef][Green Version] - Trimulyono, A.; Hashimoto, H.; Matsuda, A. Experimental Validation of Single- and Two-Phase Smoothed Particle Hydrodynamics on Sloshing in a Prismatic Tank. J. Mar. Sci. Eng.
**2019**, 7, 247. [Google Scholar] [CrossRef][Green Version] - Kim, D.H.; Kim, E.S.; Shin, S.-C.; Kwon, S.H. Sources of the Measurement Error of the Impact Pressure in Sloshing Experiments. J. Mar. Sci. Eng.
**2019**, 7, 207. [Google Scholar] [CrossRef][Green Version] - Delorme, L.; Colagrossi, A.; Souto-Iglesias, A.; Zamora-Rodríguez, R.; Botía-Vera, E. A set of canonical problems in sloshing, Part I: Pressure field in forced roll-comparison between experimental results and SPH. Ocean Eng.
**2009**, 36, 168–178. [Google Scholar] [CrossRef] - Amicarelli, A.; Manenti, S.; Albano, R.; Agate, G.; Paggi, M.; Longoni, L.; Mirauda, D.; Ziane, L.; Viccione, G.; Todeschini, S.; et al. 2020 SPHERA v.9.0.0: A Computational Fluid Dynamics research code, based on the Smoothed Particle Hydrodynamics mesh-less method. Comput. Phys. Commun.
**2009**, 250, 107157. [Google Scholar] [CrossRef] - Gunn, D.F.; Rudman, M.; Cohen, R.C.Z. Wave interaction with a tethered buoy: SPH simulation and experimental validation. Ocean Eng.
**2018**, 156, 306–317. [Google Scholar] [CrossRef] - Guo, K.; Sun, P.-N.; Cao, X.-Y.; Huang, X. A 3D SPH model for simulating water flooding of a damaged floating structure. J. Hydrodyn.
**2017**, 29, 831–844. [Google Scholar] [CrossRef] - Ming, F.R.; Zhang, A.M.; Cheng, H.; Sun, P.N. Numerical simulation of a damaged ship cabin flooding in transversal waves T with Smoothed Particle Hydrodynamics method. Ocean Eng.
**2018**, 165, 336–352. [Google Scholar] [CrossRef] - Cheng, H.; Zhang, A.M.; Ming, F.R. Study on coupled dynamics of ship and flooding water based on experimental and SPH methods. Phys. Fluids
**2017**, 29, 107101. [Google Scholar] [CrossRef] - Royon-Lebeaud, A.; Hopfinger, E.J.; Cartellier, A. Liquid Sloshing and Wave Breaking in Circular and Square-Base Cylindrical Containers. J. Fluid Mech.
**2007**, 577, 467–494. [Google Scholar] [CrossRef] - Frosina, E.; Senatore, A.; Andreozzi, A.; Fortunato, F.; Giliberti, P. Experimental and Numerical Analyses of the Sloshing in a Fuel Tank. Energies
**2018**, 11, 682. [Google Scholar] [CrossRef][Green Version] - Chong, W.; Hongde, Q.; Ge, L.; Ting, G. Study on Sloshing of Liquid Tank in Large LNG-FSRU Based on CLSVOF Method. Int. J. Heat Technol.
**2016**, 34, 616–622. [Google Scholar] - Liu, J.; Zang, Q.S.; Ye, W.B.; Lin, G. High performence of sloshing problem in cylindrical tank with various barrels by isogeometric boundary element method. Eng. Anal. Bound. Elem.
**2020**, 114, 148–165. [Google Scholar] [CrossRef] - Wei, Z.; Feng, J.; Ghalandari, M.; Maleki, A.; Abdelmalek, Z. Numerical Modeling of Sloshing Frequencies in Tanks with Structure Using New Presented DQM-BEM Technique. Symmetry
**2020**, 12, 655. [Google Scholar] [CrossRef][Green Version] - Sanapala, V.S.; Sajish, S.D.; Velusamy, K.; Ravisankar, A.; Patnaik, B.S.V. An experimental investigation on the dynamics of liquid sloshing in a rectangular tank and its interaction with an internal vertical pole. J. Sound Vib.
**2019**, 449, 43–63. [Google Scholar] [CrossRef] - Ye, W.B.; Liu, J.; Lin, G.; Zhou, Y.; Yu, L. High performance analysis of lateral sloshing response in vertical cylinders with dual circular or arc-shaped porous structures. Appl. Ocean Res.
**2018**, 81, 47–71. [Google Scholar] [CrossRef] - Demirel, E.; Aral, M.M. Liquid Sloshing Damping in an Accelerated Tank Using a Novel Slot-Baffle Design. Water
**2018**, 10, 1565. [Google Scholar] [CrossRef][Green Version] - Dinçer, A.E. Investigation of the sloshing behavior due to seismic excitations considering two-way coupling of the fluid and the structure. Water
**2019**, 11, 2664. [Google Scholar] [CrossRef][Green Version] - Gabl, R.; Davey, T.; Ingram, D.M. Additional Experimental Data of a Floating Cylinder in a Wave Tank—Verification Experiments; DataShare Edinburgh [Dataset]; University of Edinburgh: Edinburgh, UK, 2020. [Google Scholar] [CrossRef]
- 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. [Google Scholar] [CrossRef][Green Version] - Ingram, D.; Wallace, R.; Robinson, A.; Bryden, I. The Design and Commissioning of the First, Circular, Combined Current and Wave Test Basin. In Proceedings of the Oceans 2014 MTS/IEEE, Taipei, Taiwan, 7–10 April 2014. [Google Scholar]
- Draycott, S.; Sellar, B.; Davey, T.; Noble, D.R.; Venugopal, V.; Ingram, D. Capture and Simulation of the Ocean Environment for Offshore Renewable Energy. Renew. Sustain. Energy Rev.
**2019**, 104, 15–29. [Google Scholar] [CrossRef] - Noble, D.R.; Draycott, S.; Nambiar, A.; Sellar, B.G.; Steynor, J.; Kiprakis, A. Experimental Assessment of Flow, Performance, and Loads for Tidal Turbines in a Closely-Spaced Array. Energies
**2020**, 13, 1977. [Google Scholar] [CrossRef] - Jourdain de Thieulloy, M.; Dorward, M.; Old, C.; Gabl, R.; Davey, T.; Ingram, D.M.; Sellar, B.G. On the Use of a Single Beam Acoustic Current Profiler for Multi-Point Velocity Measurement in a Wave and Current Basin. Sensors
**2020**, 20, 3881. [Google Scholar] [CrossRef] - Jourdain de Thieulloy, M.; Dorward, M.; Old, C.; Gabl, R.; Davey, T.; Ingram, D.M.; Sellar, B.G. Single-Beam Acoustic Doppler Profiler and Co-Located Acoustic Doppler Velocimeter Flow Velocity Data. Data
**2020**, 5, 61. [Google Scholar] [CrossRef] - Gabl, R.; Davey, T.; Cao, Y.; Li, Q.; Li, B.; Walker, K.L.; Giorgio-Serchi, F.; Aracri, S.; Kiprakis, A.; Stokes, A.; et al. Experimental Force Data of a hung up ROV under Wave and Current. Data
**2020**, 5, 57. [Google Scholar] [CrossRef] - MARINET (2012) Work Package 2: Standards and Best Practice—D2.1 Wave Instrumentation Database. Revision: 05. Available online: http://www.marinet2.eu/wp-content/uploads/2017/04/D2.01-Wave-Instrumentation-Database.pdf (accessed on 30 May 2020).

**Figure 1.**Experimental set-up in the tank on the raised tank floor (

**a**) including the global coordinate system and the labelled mooring lines—(

**b**) solid ballast case under waves coming from 180°—(

**c**) side view of the experiments including the wave gauge (WG) array in the back—(

**d**) overview of the full experimental setting in the tank.

**Figure 2.**Rendered view of the cylinder from top (

**a**) and from the side (

**b**)—coordinate system moved due to better visibility.

**Figure 3.**Analysis of the five individual wave gauge (WG) data, as well as the mean value conducted for the wave amplitude (

**upper row**) and frequency (

**lower row**)—difference $\Delta a$ = ${a}_{R}-{a}_{W}$ (measured amplitude minus the requested amplitude); similar for the frequency.

**Figure 4.**Average value of the repeat time for all DoF—the reference measurement uses data from Gabl et al. [1] and is compared to the repetition of those experiments as well as changes of the pretension and different initial position in the tank.

**Figure 6.**Frequency response ${f}_{R}$ normalised by and presented in relation to the requested wave frequency ${f}_{W}$ for the amplitude results in Figure 5.

**Figure 7.**Detailed view of roll (

**upper row**) and pitch (

**lower row**) presented in Figure 5—the used boundaries for wave frequency ${f}_{W}$ are limited to focus on a specific frequency band for each DoF.

**Figure 8.**Sample time series of roll and pitch for six test runs with different requested wave frequency ${f}_{W}$ and expanded capture time—(

**a**) ${f}_{W}$ = 0.90 Hz, 180 s, (

**b**,

**c**) 0.90 Hz, 512 s, (

**d**) 0.925 Hz, 180 s, (

**e**) 0.925 Hz, 512 s, (

**f**) 0.9375 Hz, 512 s—vertical red line indicates the 52 s rump-up time. The horizontal red lines mark the response amplitude $\pm {a}_{R}$ and the connected response frequency ${f}_{R}$ is provided in the title of the individual graph.

**Figure 9.**Direct comparison of pitch and roll as well as the comparison of pitch and roll angle with the corresponding velocity for the time series presented in Figure 8—(

**a**) ${f}_{W}$ = 0.90 Hz, 180 s, (

**b**,

**c**) 0.90 Hz, 512 s, (

**d**) 0.925 Hz, 180 s, (

**e**) 0.925 Hz, 512 s, (

**f**) 0.9375 Hz, 512 s—the first 52 s are presented in red.

**Figure 10.**Amplitude response in the six DoF in relation to the measured wave amplitude ${a}_{R}$—individual graphs with a fixed requested wave frequency ${f}_{W}$ and wave direction.

**Figure 11.**Frequency response ${f}_{R}$ normalised by the requested wave frequency ${f}_{W}$ and presented in relation to the measured wave amplitude ${a}_{R}$ in addition to Figure 10.

**Figure 12.**Roll, pitch and heave response for the wave directions 180° and ±135° compared for the references data (90°; [1])—water ❍ and solid ● ballast option.

**Figure 13.**Frequency response ${f}_{R}$ normalised by the wave frequency ${f}_{W}$ in addition to Figure 12—water ❍ and solid ● ballast option, which is multiplied by 0.95 to allow a better visibility of the results.

**Figure 14.**Sample time series of roll and pitch for six test runs with different requested wave frequency ${f}_{W}$ and comparison of the wave direction of 90° and 180°— (

**a**) ${f}_{W}$ = 0.85 Hz, 90°, (

**b**) 0.85 Hz, 180°, (

**c**) 0.90 Hz, 90°, (

**d**) 0.90 Hz, 180°, (

**e**) 0.95 Hz, 90°, (

**f**) 0.95 Hz, −180°—vertical red line indicates the 52 s ramp-up time. The horizontal red lines mark the response amplitude $\pm {a}_{R}$ and the connected response frequency ${f}_{R}$ is provided in the title of the individual graph.

**Figure 15.**Direct comparison of pitch and roll for the time series presented in Figure 14—(

**a**) ${f}_{W}$ = 0.85 Hz, 90°, (

**b**) 0.85 Hz, 180°, (

**c**) 0.90 Hz, 90°, (

**d**) 0.90 Hz, 180°, (

**e**) 0.95 Hz, 90°, (

**f**) 0.95 Hz, −180°—the first 52 s are presented in red.

**Figure 16.**Roll, pitch and heave response for different wave directions with a fixed wave frequency of 0.95 Hz—water ❍ and solid ● ballast option.

**Figure 17.**Frequency response ${f}_{R}$ normalised by the wave frequency ${f}_{W}$ in addition to Figure 16—the reference values (either 0.5 or 1[-]) are multiplied by a factor to make them better visible—water ❍ and solid ● ballast option.

**Table 1.**Location of the wave gauges (WG) in relation to the global coordinate system. The origin is in the centre of the tank and the spacing is defined by a Golomb ruler—outside diameter of the cylinder D equal 0.5 m.

WGNr | WG1 | WG2 | WG3 | WG4 | WG5 |
---|---|---|---|---|---|

x (m) | −0.82 | −0.73 | −0.45 | 0.00 | 0.18 |

y (m) | −1.50 = 3$\xb7D$ |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gabl, R.; Davey, T.; Ingram, D.M. Roll Motion of a Water Filled Floating Cylinder—Additional Experimental Verification. *Water* **2020**, *12*, 2219.
https://doi.org/10.3390/w12082219

**AMA Style**

Gabl R, Davey T, Ingram DM. Roll Motion of a Water Filled Floating Cylinder—Additional Experimental Verification. *Water*. 2020; 12(8):2219.
https://doi.org/10.3390/w12082219

**Chicago/Turabian Style**

Gabl, Roman, Thomas Davey, and David M. Ingram. 2020. "Roll Motion of a Water Filled Floating Cylinder—Additional Experimental Verification" *Water* 12, no. 8: 2219.
https://doi.org/10.3390/w12082219