# Optimal Design of Circular Baffles on Sloshing in a Rectangular Tank Horizontally Coupled by Structure

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## Abstract

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## 1. Introduction

## 2. Mathematical Model

#### Setup

## 3. Results and Discussion

#### 3.1. Validation and Grid Independence

#### 3.2. Effect of Gap with the Bottom Wall

#### 3.3. Effect of Filling Level

#### 3.4. Distance from the Side Wall

## 4. Conclusions

- The near wall zone plays an important role in dampening the fluid momentum in the tank.
- The baffle located close to the free surface is effective in control of surface fluctuations, as well as concomitant force and pressure.
- The filling ratio affects the wet wall fraction and sloshing frequency.
- The existence of distances from the wall influences the wet wall area (surface tension effect), and liquid can climb up to the baffle if the baffle is near the surface.
- As the sloshing in the tank is steady, baffles can do little with wave breaking and have no influence on the behavior of liquid.
- The liquid thickness has more importance in slosh damping than wet area.
- The parameter studied here based on importance are the distances, filling ratio, and gaps of the baffle
- Based on a detailed study of transient structure motion coupled with sloshing dynamics, and by optimizing the parameters of baffle, optimal baffle location was achieved.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

$\mathbf{u}$ | Velocity | m/s |

$\rho $ | Density | kg· m${}^{-3}$ |

p | Dynamic pressure | Pa |

L | Length of fluid tank | m |

$\nu $ | Kinematic viscosity | m${}^{2}$/s |

$\alpha $ | Thermal expansion coefficient | 1/K |

H | Vertical height of fluid tank | m |

$\mu $ | Viscosity | Pa·s |

${\rho}_{0}$ | Reference density | kg· m${}^{-3}$ |

$\mathrm{B}$ | Buoyancy ratio | $\frac{\Delta \rho}{{\rho}_{0}\alpha \Delta T}$ |

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**Figure 4.**Pressure distribution of fill level = 37% and $0.6\times {h}_{f}$ distance from the bottom at $t=0.1\times \left(s\right)$.

**Figure 5.**Pressure and velocity in liquid for filling level = 37% and $0.6\times {h}_{f}$ distance from bottom at $t=1\times \left(s\right)$.

**Figure 12.**Time histories and average solid displacement of different side gaps between baffles and wall.

Parameters | Group of Setups |
---|---|

Fill level | 6 cm, 11 cm, 20 cm |

Distance from left | 10 cm, 25 cm |

Gap | 1 cm, 2 cm, 3 cm, 5 cm, 10 cm |

Flow Regimes | |
---|---|

fully laminar | $Re$ < 180–200 |

transition in the wake | $Re$ < 350–400 |

transition in the free shear-layer | $Re<1.0\times {10}^{5}\u20132.0\times {10}^{5}$ |

transition in the boundary-layer | $Re<2\times {10}^{5}\u20135.0\times {10}^{6}$ |

fully turbulent boundary-layer | $Re>5\times {10}^{6}$ |

Parameter | Value |
---|---|

Mass | 18.9 kg |

Natural frequency | 1.09 1/s |

Damping ratio | 0.0019 |

© 2018 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**

Jamalabadi, M.Y.A.; Ho-Huu, V.; Nguyen, T.K.
Optimal Design of Circular Baffles on Sloshing in a Rectangular Tank Horizontally Coupled by Structure. *Water* **2018**, *10*, 1504.
https://doi.org/10.3390/w10111504

**AMA Style**

Jamalabadi MYA, Ho-Huu V, Nguyen TK.
Optimal Design of Circular Baffles on Sloshing in a Rectangular Tank Horizontally Coupled by Structure. *Water*. 2018; 10(11):1504.
https://doi.org/10.3390/w10111504

**Chicago/Turabian Style**

Jamalabadi, Mohammad Yaghoub Abdollahzadeh, Vinh Ho-Huu, and Truong Khang Nguyen.
2018. "Optimal Design of Circular Baffles on Sloshing in a Rectangular Tank Horizontally Coupled by Structure" *Water* 10, no. 11: 1504.
https://doi.org/10.3390/w10111504