# Simulations of the Concentration Fields of Rosette-Type Multiport Buoyant Discharges Using Combined CFD and Multigene Genetic Programming Techniques

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The 3D CFD Model

#### 2.2. The MGGP Technique

#### 2.3. The Combined CFD–MGGP Method

## 3. Results

#### 3.1. CFD Results

^{2}/s

^{2}and 0.002061 m

^{2}/s

^{2}, respectively. The initial velocity and initial fraction of the fluid for discharges were both set at zero. The computational mesh was generated using the open-source software Salome. An unstructured computation mesh with hexahedral cells with local refinements near the port was employed for domain discretization. Using the method reported by Yan and Mohammadian [2,13], mesh sensitivity analyses were performed. A relatively coarse grid resolution was firstly utilized, and then finer grids were tried until convergence criterion was met. In the final mesh, the smallest grid size was 0.001 m, and the largest one was 0.005 m.

#### 3.2. Results Obtained by the Combined Method

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of a rosette-type diffuser (

**a**), the sub-domains (

**b**), and the coordinate setup (

**c**).

**Figure 2.**Comparison of the experimental and simulated results. The dots = the experimental data [1]; the line = the numerical predictions.

**Figure 3.**The normalized concentration field at the central plane for different cases obtained by the CFD model.

**Figure 4.**The fitness of the MGGP models in each evolutionary step: (

**a**) the best fitness, and (

**b**) the mean fitness and standard deviations.

**Figure 5.**The normalized concentration field at the central plane for different cases obtained by the MGGP model.

**Figure 6.**Comparison of the actual and predicted normalized concentration: (

**a**) training dataset, and (

**b**) testing dataset.

σ_{k} | σ_{ε} | c_{1ε} | c_{2ε} | c_{μ} | η_{0} | β |
---|---|---|---|---|---|---|

0.71942 | 0.71942 | 1.42 | 1.68 | 0.0845 | 4.38 | 0.012 |

Cases | ρj (kg/m ^{3}) | ρa (kg/m ^{3}) | ∆ρ (kg/m ^{3}) | g’ (m/s2) | D (m) | U (m/s) | Fr (—) |
---|---|---|---|---|---|---|---|

Case 01 | 997 | 998.3 | 1.3 | 0.013 | 0.0044 | 0.185 | 24.676 |

Case 02 | 997 | 999.5 | 2.5 | 0.025 | 0.0044 | 0.185 | 17.805 |

Case 03 | 997 | 1000.2 | 3.2 | 0.031 | 0.0044 | 0.185 | 15.743 |

Case 04 | 997 | 1001.1 | 4.1 | 0.040 | 0.0044 | 0.185 | 13.914 |

Case 05 | 997 | 1001.3 | 4.3 | 0.042 | 0.0044 | 0.185 | 13.588 |

Case 06 | 997 | 1001.4 | 4.4 | 0.043 | 0.0044 | 0.185 | 13.433 |

Case 07 | 997 | 1002.5 | 5.5 | 0.054 | 0.0044 | 0.185 | 12.022 |

Case 08 | 997 | 1004.8 | 7.8 | 0.076 | 0.0044 | 0.185 | 10.107 |

Case 09 | 997 | 1005.9 | 8.9 | 0.087 | 0.0044 | 0.185 | 9.467 |

Case 10 | 997 | 1009.0 | 12.0 | 0.117 | 0.0044 | 0.185 | 8.165 |

Case 11 | 997 | 1009.9 | 12.9 | 0.125 | 0.0044 | 0.185 | 7.879 |

Case 12 | 997 | 1013.5 | 16.5 | 0.160 | 0.0044 | 0.185 | 6.979 |

Case 13 | 997 | 1014.4 | 17.4 | 0.168 | 0.0044 | 0.185 | 6.799 |

Case 14 | 997 | 1020.2 | 23.2 | 0.223 | 0.0044 | 0.185 | 5.905 |

Case 15 | 997 | 1021.0 | 24.0 | 0.231 | 0.0044 | 0.185 | 5.808 |

Case 16 | 997 | 1021.5 | 24.5 | 0.235 | 0.0044 | 0.185 | 5.750 |

Case 17 | 997 | 1023.1 | 26.1 | 0.250 | 0.0044 | 0.185 | 5.575 |

Case 18 | 997 | 1023.9 | 26.9 | 0.258 | 0.0044 | 0.185 | 5.494 |

Case 19 | 997 | 1024.3 | 27.3 | 0.261 | 0.0044 | 0.185 | 5.454 |

Case 20 | 997 | 1025.9 | 28.9 | 0.276 | 0.0044 | 0.185 | 5.305 |

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**MDPI and ACS Style**

Yan, X.; Wang, Y.; Mohammadian, A.; Liu, J. Simulations of the Concentration Fields of Rosette-Type Multiport Buoyant Discharges Using Combined CFD and Multigene Genetic Programming Techniques. *J. Mar. Sci. Eng.* **2021**, *9*, 1311.
https://doi.org/10.3390/jmse9111311

**AMA Style**

Yan X, Wang Y, Mohammadian A, Liu J. Simulations of the Concentration Fields of Rosette-Type Multiport Buoyant Discharges Using Combined CFD and Multigene Genetic Programming Techniques. *Journal of Marine Science and Engineering*. 2021; 9(11):1311.
https://doi.org/10.3390/jmse9111311

**Chicago/Turabian Style**

Yan, Xiaohui, Yan Wang, Abdolmajid Mohammadian, and Jianwei Liu. 2021. "Simulations of the Concentration Fields of Rosette-Type Multiport Buoyant Discharges Using Combined CFD and Multigene Genetic Programming Techniques" *Journal of Marine Science and Engineering* 9, no. 11: 1311.
https://doi.org/10.3390/jmse9111311