# Numerical Modeling of Sloshing Frequencies in Tanks with Structure Using New Presented DQM-BEM Technique

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## Abstract

**:**

## 1. Introduction

## 2. Governing Equations

#### 2.1. Flow-Field Governing Equations

#### 2.2. Developing the Boundary Element Model

#### 2.3. Fluid–Solid Interaction Modeling

## 3. Numerical Results

#### 3.1. Test Case 1

#### 3.2. Test Case 2

#### 3.3. Test Case 3

#### 3.4. Test Case 4

## 4. Conclusions

- 1-
- According to the model outputs, the existence of fluid in the investigated system leads to the reduction in the frequencies.
- 2-
- Comparing the results of the model to the data of previous studies shows a maximum relative error of 1.5% between the DQM-BEM model and literature, indicating the reliability of the results obtained by the developed model.
- 3-
- The effect of the immersed structures on the dynamic response of the sloshing is more tangible than the submerged structure.
- 4-
- The sloshing effect on the structural frequencies is revealed itself in a high-flexibility parameter for both submerged and immersed structures.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 5.**Comparison of non-dimensional frequencies vs. flexibility parameter of the represented model with literature [37].

UINT (rad/s) | h/d | |||||
---|---|---|---|---|---|---|

Present | Ghalandari et al. | Choun and Yun | S. Mitra, K.P. Sinhamahapatra | ANSYS | ||

0.2 | ||||||

MODE1 | 0.9091 | 0.9127 | 0.897 | 0.898 | 0.9094 | |

MODE2 | 1.4312 | 1.428 | 1.415 | 1.415 | 1.4612 | |

MODE3 | 1.7645 | 1.7647 | 1.744 | 1.746 | 1.7644 | |

0.4 | ||||||

MODE1 | 0.8391 | 0.8396 | 0.849 | 0.842 | 0.8392 | |

MODE2 | 1.4042 | 1.3964 | 1.404 | 1.406 | 1.4306 | |

MODE3 | 1.7577 | 1.7564 | 1.742 | 1.74 | 1.7588 | |

0.6 | ||||||

MODE1 | 0.725 | 0.7251 | 0.731 | 0.731 | 0.7252 | |

MODE2 | 1.3222 | 1.3109 | 1.343 | 1.347 | 1.3437 | |

MODE3 | 1.7225 | 1.7215 | 1.733 | 1.734 | 1.73 | |

0.8 | ||||||

MODE1 | 0.5355 | 0.5333 | 0.55 | 0.552 | 0.5383 | |

MODE2 | 1.1011 | 1.0691 | 1.19 | 1.192 | 1.1044 | |

MODE3 | 1.5661 | 1.5522 | 1.73 | 1.732 | 1.5809 |

Tank Walls | Rigid |
---|---|

Submerged Walls | Elastic |

Modes | Ghalandari et al. [32] | Represented Model |
---|---|---|

1 | 1.8358 | 1.82844 |

2 | 4.9269 | 4.7921 |

3 | 11.8579 | 11.853 |

**Table 4.**ANSYS FEM results vs. presented differential quadrature method-boundary element method (DQM-BEM) model.

Sloshing Mode | ANSYS (rad/s) | Present Method (rad/s) | Error Difference (%) |
---|---|---|---|

1 | 1.911 | 1.9299 | 0.9375 |

2 | 3.2518 | 3.2021 | 1.5786 |

3 | 3.3296 | 3.3100 | 0.6387 |

Tank Walls | Rigid |
---|---|

Immersed Walls | Elastic |

Structure modes | 1 | 4.8287 |

2 | 14.0805 | |

3 | 32.5552 |

Slosh dominant modes | 1 | 1.42815 |

2 | 1.8763 | |

3 | 1.9789 |

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/sym12040655

**AMA Style**

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(4):655.
https://doi.org/10.3390/sym12040655

**Chicago/Turabian Style**

Wei, Zhenda, Junwen Feng, Mohammad Ghalandari, Akbar Maleki, and Zahra Abdelmalek.
2020. "Numerical Modeling of Sloshing Frequencies in Tanks with Structure Using New Presented DQM-BEM Technique" *Symmetry* 12, no. 4: 655.
https://doi.org/10.3390/sym12040655