# A Numerical Analysis of Dynamic Slosh Dampening Utilising Perforated Partitions in Partially-Filled Rectangular Tanks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Numerical Methodology

#### 2.1. Physical Setups

#### 2.2. Computational Setup

^{2}and 0.0035 m

^{2}, respectively.

^{3}/cell; the final mesh is illustrated in Figure 5. The verified average cell volume was imposed on the supplementary tank domains. The meshes were imposed with a prism layer at no-slip surfaces with an appropriate cell height to achieve a y-plus (${y}^{+}$) value of 30 ≤ ${y}^{+}$ ≤ 300. The CFD computations were performed by running six Intel Core i7-7800X 3.50 GHz cores and 32 GB of RAM; a sloshing simulation was completed within an average of 55 wall-clock hours and 330 core-hours. Mesh independent parameters were established utilising ITTC recommended meshing procedures and guidelines [30]:

## 3. Numerical Model Characterisation

#### 3.1. Physical Modelling

#### 3.2. CFD Modelling

## 4. Numerical Modelling Validation of a Turbulent Dam-Break Wave

## 5. Numerical Sloshing Performance of an Open-Bore, Partitioned, and Perforated-Partitioned Tank

#### 5.1. 20% Fill

#### 5.2. 40% Fill

#### 5.3. 60% Fill

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

## References

- Olsen, H. What is Sloshing? In Seminar on Liquid Sloshing; Den Nørske Veritas (DNV): Hovik, Norway, 1976. [Google Scholar]
- Det Nørske Veritas (DNV). DNVGL-CG-0158 Sloshing Analysis of LNG Membrane Tanks; Technical Report; Den Nørske Veritas (DNV): Hovik, Norway, 2016. [Google Scholar]
- Türk Loydu. S.P 01/20 Guidelines for the Assessment of Sloshing Impact Loads. Technical Report. 2020. Available online: https://turkloydu.org/pdf-files/teknik-sirkulerler/tekne/S-P-01-20.pdf (accessed on 18 January 2022).
- Budiansky, B. Sloshing of Liquids in Circular Canals and Spherical Tanks. J. Aero/Space Sci.
**1960**, 27, 161–173. [Google Scholar] [CrossRef] - Abramson, H. The Dynamic Behavior of Liquids in Moving Containers, with Applications to Space Vehicle Technology; Technical Report; National Aeronautics and Space Administration (NASA): Washington, DC, USA, 1966. [Google Scholar]
- Slibar, A.; Troger, H. The Steady State Behaviour of Tank Trailer System carrying Rigid or Liquid Cargo. Veh. Syst. Dyn.
**1977**, 6, 167–169. [Google Scholar] [CrossRef] - Ranganathan, R. Rollover Threshold of Partially Filled Tank Vehicles with Arbitrary Tank Geometry. J. Automot. Eng.
**1993**, 207, 241–244. [Google Scholar] [CrossRef] - Salem, M.I.; Mucino, V.H.; Saunders, E.; Gautam, M.; Lozano-Guzman, A. Lateral sloshing in partially filled elliptical tanker trucks using a trammel pendulum. Int. J. Heavy Veh. Syst.
**2009**, 16, 207–224. [Google Scholar] [CrossRef] - Gabl, R.; Davey, T.; Ingram, D.M. Roll Motion of a Water Filled Floating Cylinder—Additional Experimental Verification. Water
**2020**, 12, 2219. [Google Scholar] [CrossRef] - Celebi, M.S.; Akyildiz, H. Nonlinear modeling of liquid sloshing in a moving rectangular tank. Ocean Eng.
**2002**, 29, 1527–1553. [Google Scholar] [CrossRef] - Akyildiz, H. A numerical study of the effects of the vertical baffle on liquid sloshing in two-dimensional rectangular tank. J. Sound Vib.
**2012**, 331, 41–52. [Google Scholar] [CrossRef] - He, T.; Feng, D.; Liu, L.; Wang, X.; Jiang, H. CFD Simulation and Experimental Study on Coupled Motion Response of Ship with Tank in Beam Waves. J. Mar. Sci. Eng.
**2022**, 10, 113. [Google Scholar] [CrossRef] - Bulian, G.; Botia-Vera, E.; Mas-Soler, J.; Souto-Iglesias, A.; Castellana, F. Repeatability and Practical Ergodicity of 2D Sloshing Experiments. In Proceedings of the Twenty-Second International Offshore and Polar Engineering Conference, Rhodes, Greece, 17–22 June 2012. [Google Scholar]
- Thiagarajan, K.P.; Rakshit, D.; Repalle, N. The air–water sloshing problem: Fundamental analysis and parametric studies on excitation and fill levels. Ocean Eng.
**2011**, 38, 498–508. [Google Scholar] [CrossRef] - Tao, K.; Zhou, X.; Ren, H. A Novel Improved Coupled Dynamic Solid Boundary Treatment for 2D Fluid Sloshing Simulation. J. Mar. Sci. Eng.
**2021**, 9, 1395. [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] - Liu, D.; Lin, P. Three-dimensional liquid sloshing in a tank with baffles. Ocean Eng.
**2009**, 36, 202–212. [Google Scholar] [CrossRef] - Jung, J.H.; Yoon, H.S.; Lee, C.Y.; Shin, S.C. Effect of the vertical baffle height on the liquid sloshing in a three-dimensional rectangular tank. Ocean Eng.
**2009**, 44, 79–89. [Google Scholar] [CrossRef] - Yu, Y.-M.; Ma, N.; Fan, S.-M.; Gu, X.-C. Experimental and numerical studies on sloshing in a membrane-type LNG tank with two floating plates. Ocean Eng.
**2017**, 129, 217–227. [Google Scholar] [CrossRef] - Lin, L.; Jiang, S.; Zhao, M.; Tang, G. Two-dimensional viscous numerical simulation of liquid sloshing in rectangular tank with/without baffles and comparison with potential flow solutions. Ocean Eng.
**2015**, 108, 662–677. [Google Scholar] - Molin, B. Hydrodynamics Modeling of Perforated Structures. Appl. Ocean Res.
**2011**, 33, 1–11. [Google Scholar] [CrossRef] - Faltisen, O.M.; Firoozkoohi, R.; Timokha, A.N. Steady-State Liquid Sloshing in a Rectangular Tank with a Slat-Type Screen in the Middle: Quasilinear Modal Analysis and Experiments. Phys. Fluids
**2011**, 23, 042101. [Google Scholar] [CrossRef] [Green Version] - Molin, B.; Remy, F. Experimental and Numerical Study of the Sloshing Motion in a Rectangular Tank with a Perforated Screen. J. Fluids Struct.
**2013**, 43, 463–480. [Google Scholar] [CrossRef] - Jin, H.; Liu, Y.; Li, H.-J. Experimental Study on Sloshing in a Tank with an Inner Horizontal Perforated Plate. Ocean Eng.
**2014**, 82, 75–84. [Google Scholar] [CrossRef] - Chanson, H. Application of the method of characteristics to the dam break wave problem. J. Hydraul. Res.
**2009**, 47, 41–49. [Google Scholar] [CrossRef] [Green Version] - Ship Structure Committee (SSC). SSC-336 Liquid Sloshing in Cargo Tanks; Technical Report; Ship Structure Committee: Washington, DC, USA, 1990. [Google Scholar]
- ANSYS Inc. FLUENT User’s Guide, 5th ed.; ANSYS Inc.: Lebanon, NH, USA, 1998. [Google Scholar]
- Seakeeping Committee of the 28th ITTC. Recommended Procedures and Guidelines: Sloshing Model Tests. Technical Report. 2017. Available online: https://www.ittc.info/media/8111/75-02-07-027.pdf (accessed on 18 January 2022).
- Resistance Committee of the 28th ITTC. Recommended Procedures and Guidelines: Uncertainty Analysis in CFD Verification and Validation Methodology and Procedures. Technical Report. 2017. Available online: https://www.ittc.info/media/8153/75-03-01-01.pdf (accessed on 18 January 2022).

**Figure 1.**First-angle projection of the dam-break channel geometrical model; shaded volume represents the secondary-phase sub-domain.

**Figure 5.**Meshed representation of the open-bore tank with highlighted surface zones for area-averaged static pressure data acquisition.

**Figure 6.**Dam-break wave-tip displacement (${x}_{s}$) comparison between the CFD model and theoretical values derived by Chanson [26].

**Figure 7.**Dam-break free-surface wave profile (${h}_{w}$) comparison between the CFD model and theoretical values derived by Chanson [26]. (

**a**) $t=$ 3 s. (

**b**) $t=6$ s. (

**c**) $t=$ 9 s. (

**d**) $t=$ 12 s.

**Figure 8.**Cycle-averaged torque coefficient (C

_{Q}) with angular displacement (${\theta}_{t}$) at 20% fill. (

**a**) Open-bore. (

**b**) Partitioned. (

**c**) Perforated-partitioned.

**Figure 9.**Cycle-averaged torque coefficient (C

_{Q}) with angular displacement (${\theta}_{t}$) at 40% fill. (

**a**) Open-bore. (

**b**) Partitioned. (

**c**) Perforated-partitioned.

**Figure 10.**Cycle-averaged pressure coefficient (C

_{P}) with angular displacement (${\theta}_{t}$) of the open-bore tank at 40% fill.

**Figure 11.**Cross-sectional contoured illustrations of the sloshing dynamics within the open-bore tank at 40% fill. (

**a**) ${\theta}_{t}=-15\xb0$ (initial position). (

**b**) ${\theta}_{t}=0\xb0$ (quarter-stroke). (

**c**) ${\theta}_{t}=15\xb0$ (mid-stroke). (

**d**) ${\theta}_{t}=0\xb0$ (three-quarter-stroke).

**Figure 12.**Cross-sectional contoured illustrations of the sloshing dynamics within the partitioned tank at 40% fill. (

**a**) ${\theta}_{t}=-15\xb0$ (initial position). (

**b**) ${\theta}_{t}=0\xb0$ (quarter-stroke). (

**c**) ${\theta}_{t}=15\xb0$ (mid-stroke). (

**d**) ${\theta}_{t}=0\xb0$ (three-quarter-stroke).

**Figure 13.**Cross-sectional contoured illustrations of the sloshing dynamics within the perforated-partitioned tank at 40% fill. (

**a**) ${\theta}_{t}=-15\xb0$ (initial position). (

**b**) ${\theta}_{t}=0\xb0$ (quarter-stroke). (

**c**) ${\theta}_{t}=15\xb0$ (mid-stroke). (

**d**) ${\theta}_{t}=0\xb0$ (three-quarter-stroke).

**Figure 14.**Cycle-averaged torque coefficient (C

_{Q}) with angular displacement (${\theta}_{t}$) at 60% fill. (

**a**) Open-bore. (

**b**) Partitioned. (

**c**) Perforated-partitioned.

**Figure 15.**Cycle-averaged pressure coefficient (C

_{P}) with angular displacement (${\theta}_{t}$) at 60% fill. (

**a**) Open-bore. (

**b**) Perforated-partitioned.

Cell Number | ${\mathit{r}}_{\mathit{i}}$ | ${\mathit{S}}_{\mathit{i}}$ | %_{difference} | ${\mathit{\epsilon}}_{\mathit{i}}$ | ${\mathit{R}}_{\mathit{i}}$ |
---|---|---|---|---|---|

669,600 | 1.247 | 14.83 | 1.85 | 0.270 | 0.626 |

536,970 | 1.277 | 14.56 | 3.04 | 0.431 | |

420,500 | 14.13 |

Cell Number | ${\mathit{r}}_{\mathit{i}}$ | ${\mathit{S}}_{\mathit{i}}$ | %_{difference} | ${\mathit{\epsilon}}_{\mathit{i}}$ | ${\mathit{R}}_{\mathit{i}}$ |
---|---|---|---|---|---|

1,008,640 | 1.215 | 3.93 | 2.80 | 0.111 | 0.781 |

830,160 | 1.197 | 3.82 | 4.97 | 0.141 | |

693,530 | 3.63 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Borg, M.G.; DeMarco Muscat-Fenech, C.; Tezdogan, T.; Sant, T.; Mizzi, S.; Demirel, Y.K.
A Numerical Analysis of Dynamic Slosh Dampening Utilising Perforated Partitions in Partially-Filled Rectangular Tanks. *J. Mar. Sci. Eng.* **2022**, *10*, 254.
https://doi.org/10.3390/jmse10020254

**AMA Style**

Borg MG, DeMarco Muscat-Fenech C, Tezdogan T, Sant T, Mizzi S, Demirel YK.
A Numerical Analysis of Dynamic Slosh Dampening Utilising Perforated Partitions in Partially-Filled Rectangular Tanks. *Journal of Marine Science and Engineering*. 2022; 10(2):254.
https://doi.org/10.3390/jmse10020254

**Chicago/Turabian Style**

Borg, Mitchell G., Claire DeMarco Muscat-Fenech, Tahsin Tezdogan, Tonio Sant, Simon Mizzi, and Yigit Kemal Demirel.
2022. "A Numerical Analysis of Dynamic Slosh Dampening Utilising Perforated Partitions in Partially-Filled Rectangular Tanks" *Journal of Marine Science and Engineering* 10, no. 2: 254.
https://doi.org/10.3390/jmse10020254