# A Simplified Method of Iceberg Hydrodynamic Parameter Prediction

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## Abstract

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## 1. Introduction

- irregular shape of the above-water and underwater parts of icebergs, determination of which is complicated in real environment conditions;
- significant displacement of the iceberg compared to the vessel towing it;
- influence of various environmental factors (wind, currents, sea waves, etc.).

## 2. Simplified Approach to Iceberg Hydrodynamic Parameter Prediction

- designation of a vessel with sufficient shaft thrust and suitable towing equipment for the specific world ocean sailing area;
- planning and carrying out a change in the drift trajectory of an iceberg with known surface shape;
- estimation of the iceberg’s stability during towing;
- minimizing the duration of the transitional processes during towing [17];
- determination of the stress state parameters of the towing system under various environmental conditions, including the evaluation of oscillatory processes [18].

#### 2.1. Equivalent Icebergs

#### 2.2. Reynolds-Averaged Navier–Stokes Approach and Closure Problem

#### 2.3. Results of CFD Simulations of the Flow over an Elliptical Cylinder and Half-Ellipsoid

#### 2.4. Hydrodynamic Forces of Equivalent Icebergs

## 3. Comparison of the Hydrodynamic Parameters of Icebergs Computed with the Help of the Simplified Method and CFD Results

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**An example for iceberg no. 15 numerical simulation settings; (

**a**) the boundary conditions; (

**b**) the computational mesh for iceberg no. 15.

**Figure 3.**Streamlines around the elliptical cylinders when towed along the minor axis (

**a**) $L/B=1.5$; (

**b**) $L/B=2.0$; (

**c**) $L/B=2.5$; and (

**d**) $L/B=3.0$.

**Figure 4.**The velocity vectors and relative excess pressure field around the elliptical cylinders when towed along the minor axis at a drift angle $\beta ={45}^{\circ}$ (

**a**) $L/B=1.5$; (

**b**) $L/B=2.0$; (

**c**) $L/B=2.5$; and (

**d**) $L/B=3.0$.

**Figure 5.**Hydrodynamic coefficients of cylindrical icebergs with various aspect ratios: (the blue line with circles is $L/B=1.5$, the red line with squares is $L/B=2.0$, the green line with triangles is $L/B=2.5$, and the black line with diamonds is $L/B=3.0$).

**Figure 6.**Hydrodynamic coefficients of half-ellipsoid icebergs with various aspect ratios: (the blue line with circles is $L/B=1.5$, the red line with squares is $L/B=2.0$, the green line with triangles is $L/B=2.5$, the black line with diamonds is $L/B=3.0$).

**Figure 7.**Drag coefficient of iceberg no. 15 depending on ${y}^{+}$; (

**a**) the area of minimal ${y}^{+}$ values; (

**b**) area of maximal ${y}^{+}$ values of the drag coefficient ${C}_{d}$ according to (2), friction part of drag coefficient ${C}_{f}$, and viscous pressures part of the drag coefficient ${C}_{p}$.

**Figure 8.**An example of the CFD simulation of the flow over iceberg no. 15, $\beta ={270}^{\circ}$; (

**a**) streamlines over the underwater part; (

**b**) velocity field in the waterplane area.

**Figure 9.**Considered icebergs and their equivalent ellipsoids; (

**a**) iceberg no. 15, (

**b**) iceberg no. 124, (

**c**) iceberg no. 1960, and (

**d**) iceberg no. 1961.

**Figure 10.**Comparison of the hydrodynamic coefficients of iceberg no. 15. (blue lines with circles are measurements, and red lines with squares are approximations).

**Figure 11.**Comparison of the hydrodynamic coefficients of iceberg no. 124. (blue lines with circles are measurements, and red lines with squares are approximations).

**Figure 12.**Comparison of the hydrodynamic coefficients of iceberg no. 1960. (blue lines with circles are measurements, and red lines with squares are approximations).

**Figure 13.**Comparison of the hydrodynamic coefficients of iceberg no. 1961. (blue lines with circles are measurements, and red lines with squares are approximations).

**Figure 14.**Full drag force coefficient ${C}_{d}$ (as a function of the drift angle $\beta $) of: (

**a**) iceberg no. 15, (

**b**) iceberg no. 124, (

**c**) iceberg no. 1960, and (

**d**) iceberg no. 1961. Blue lines with circles are measurements, and red lines with squares are approximations.

Parameter | Elliptical Cylinders | |||
---|---|---|---|---|

Length-to-beam ratio | 1.5 | 2.0 | 2.5 | 3.0 |

Length, m | 75 | 100 | 125 | 150 |

Beam, m | 50 | 50 | 50 | 50 |

Draught, m | 124.3 | 93.2 | 74.6 | 62.2 |

Volume displacement, m^{3} | 366,159 | |||

Characteristic area, m^{2} | 5118.15 | |||

Characteristic linear size, m | 71.54 |

Parameter | Ellipsoids | |||
---|---|---|---|---|

Length-to-beam ratio | 1.5 | 2.0 | 2.5 | 3.0 |

Length, m | 75 | 100 | 125 | 150 |

Beam, m | 50 | 50 | 50 | 50 |

Draught, m | 186.8 | 140.1 | 113 | 93.4 |

Volume displacement, m^{3} | 1,467,080.5 | |||

Characteristic area, m^{2} | 12,972.5 | |||

Characteristic linear size, m | 113.1 |

Value | ${\mathit{a}}^{4}$ | ${\mathit{a}}^{3}$ | ${\mathit{a}}^{2}$ | ${\mathit{a}}^{1}$ | ${\mathit{a}}^{0}$ |
---|---|---|---|---|---|

Cylindrical iceberg | |||||

${C}_{x}$ | 0.110 | 0.085 | 0.145 | −0.84 | 1.3 |

${C}_{y}$ | 0 | −0.075 | −0.055 | 0.365 | 0.475 |

${C}_{m}$ | 0 | −0.131 | 0.955 | −2.485 | 1.655 |

Elliptical iceberg | |||||

${C}_{x}$ | 0 | 0 | 0.0855 | −0.4603 | 0.6269 |

${C}_{y}$ | 0 | 0 | −0.25 | 1.335 | −0.2055 |

${C}_{m}$ | 0 | 0 | −0.21 | 1.1476 | −0.8795 |

Parameter | Iceberg No. 15 | Iceberg No. 124 | Iceberg No. 1960 | Iceberg No. 1961 |
---|---|---|---|---|

Length, m | 148 | 39.0 | 72.6 | 158 |

Beam, m | 148 | 31.1 | 76.4 | 301 |

Hight, m | 25.93 | 5.25 | 12.433 | 13.808 |

Draught, m | 114 | 46.5 | 51.0 | 59.9 |

Volume, m^{3} | 854,565 | 26,713 | 157,483 | 1,575,309 |

Volume displacement, m^{3} | 764,435 | 23,895 | 140,874 | 1,409,162 |

Overwater volume, m^{3} | 90,130 | 2818 | 16,609 | 166,147 |

Characteristic linear size, m | 95 | 30 | 54 | 116 |

Characteristic area, m^{2} | 9005 | 894 | 2916 | 13,539 |

Waterline area, m^{2} | 12,840.666 | 833.84 | 2913.696 | 21,065.82 |

Center of gravity, m | −34.0 | −16.6 | −20.2 | −24.5 |

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**MDPI and ACS Style**

Nikushchenko, D.; Stepin, A.; Nikitina, E.; Tryaskin, N.; Makovsky, A.; Kornishin, K.; Efimov, Y.
A Simplified Method of Iceberg Hydrodynamic Parameter Prediction. *Water* **2023**, *15*, 1843.
https://doi.org/10.3390/w15101843

**AMA Style**

Nikushchenko D, Stepin A, Nikitina E, Tryaskin N, Makovsky A, Kornishin K, Efimov Y.
A Simplified Method of Iceberg Hydrodynamic Parameter Prediction. *Water*. 2023; 15(10):1843.
https://doi.org/10.3390/w15101843

**Chicago/Turabian Style**

Nikushchenko, Dmitry, Anton Stepin, Ekaterina Nikitina, Nikita Tryaskin, Alexander Makovsky, Konstantin Kornishin, and Yaroslav Efimov.
2023. "A Simplified Method of Iceberg Hydrodynamic Parameter Prediction" *Water* 15, no. 10: 1843.
https://doi.org/10.3390/w15101843