# Application of Discrete Element Method Coupled with Computational Fluid Dynamics to Predict the Erosive Wear Behavior of Arctic Vessel Hulls Subjected to Ice Impacts

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

**Table 1.**The summary of reference studies which evaluate floe behavior on the fluid flow of the route.

Author | Numerical Scheme | Floe Shape | Purpose |
---|---|---|---|

Kim et al. [18] | ALE-based FEA | Rectangular box | - Evaluating the ice resistance of the icebreaker - The ice resistance of the icebreaker was measured and compared with that of ALE-based FEA |

Robb et al. [19] | SPH-DEM | Sphere | - Simulating the behavior of an ice floe on a free surface |

Huang et al. [20] | CFD-DEM Coupling (DEM embedded in CFD) | Pancake | - Evaluating the ship resistance in response to ice collision |

Liu et al. [21] | CFD-DEM Coupling (DEM embedded in CFD) | Spherical | - Evaluate hull resistance by accounting for the motion of ice floes - Comparing one-way and two-way coupling schemes in CFD-DEM coupling |

Zhang et al. [23] | CFD-DEM Coupling (DEM embedded in CFD) | Glued sphere | - Simulate the behavior of ice floes surrounding a moving ship - Compare results from experiments and analysis - Analyze how variable settings affect analysis results in numerical simulations |

Shunying et al. [33] | CFD-DEM Coupling | Pancake | - Evaluating the ice impact loads under different operating conditions |

## 3. Numerical Scheme

#### 3.1. Analysis Process

#### 3.2. Theoretical Background of DEM

#### 3.3. Theoretical Background of CFD [42]

#### 3.4. Theoretical Background of DEM-CFD Coupling [43]

#### 3.5. Archard Wear Law

## 4. Evaluation of Hull Wear Due to Collision with Ice Floes

^{3}/J was defined as 100 m

^{3}/J, then $N$ is 100. According to Equation (26), shear work accumulated for 1 s of simulation time can be evaluated as shear work accumulated for 100 s of real time by $N$. Therefore, the volume of wear loss that occurred for 100 s can be evaluated through the 1 s analysis result. N can be determined according to the acceptable analysis time and how much micro material loss can be tolerated. The purpose of this study is to develop a numerical model for assessing wear in ships traveling Arctic routes. The shape of ship, operating conditions, and wear-inducing material properties were not of primary interest in this study. Therefore, the wear magnitude evaluated in this study is not representative of actual operational ships.

#### 4.1. Evaluation Conditions

^{3}and the viscosity as 0.001003 kg/m

^{−s}.

#### 4.2. Coating Material Wear Assessment

^{−7}m

^{3}/J, which is the same as the value applied in the following section. The wear depth according to ship speed and ice concentration for each hull position was evaluated as shown in Table 5. Considering the distance traveled by the ship, the predicted wear is very large. By adjusting the parameters of the Archard law, smaller wear values that align more closely with expectations can be achieved. However, the primary focus of the present study was to propose a numerical model capable of predicting the wear resulting from ice collisions. Therefore, the development of the numerical model was our priority rather than the achievement of accurate wear predictions.

#### 4.3. Hull Material Wear Assessment

^{3}/J, and the shape deformed by wear was automatically updated every 0.005 s. That is, the shape change due to abrasive wear was added in the analysis conditions described in Section 4.1.

#### 4.4. Comparison of the Results According to the Evaluation Method

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Overlap–normal force relationship in the HLS model [41].

**Figure 4.**HLS normal force model (ESSS Rocky [40]).

**Figure 5.**LSCL tangential force model (ESSS Rocky [40]).

**Figure 7.**Mechanism of shape change caused by wear (ESSS Rocky [40]).

**Figure 8.**Ice concentration (Transport Canada [47]).

**Figure 35.**Accumulated wear process of the shape change reflection model (

**left**) and non-reflected models (

**right**) (4 knots, 60%).

**Figure 36.**Accumulated wear process of the shape change reflection model (

**left**) and non-reflected models (

**right**) (10 knots, 80%).

Ice | Ship | |
---|---|---|

Density (kg/m^{3}) | 900 | 7850 |

Bulk Young’s modulus (MPa) | 61 | 2.0 × 10^{5} |

Poisson’s ratio | 0.003 | 0.3 |

Ice-Ice | Ice-Ship | |
---|---|---|

Friction coefficient | 0.1 | 0.131 |

Tangential stiffness ratio | 1 | 1 |

Restitution coefficient | 0.1 | 0.2 |

Speed [Knots] | (1) Affected Area [m ^{2}] | (2) Total Shear Work/(1) [N·m/m ^{2}] | (3) Ratio to Bow in (2) (%) | ||||
---|---|---|---|---|---|---|---|

Ice Concentration | |||||||

60% | 80% | 60% | 80% | 60% | 80% | ||

Bow (Forward) | 4 | 15.69 | 19.63 | 4.60 × 10^{3} | 6.90 × 10^{3} | - | - |

6 | 15.90 | 19.36 | 8.92 × 10^{3} | 1.21 × 10^{4} | - | - | |

10 | 17.71 | 21.38 | 2.06 × 10^{4} | 2.54 × 10^{4} | - | - | |

Midship | 4 | 30.12 | 30.69 | 209.72 | 270.49 | 4.56 | 3.92 |

6 | 18.85 | 24.05 | 215.60 | 244.86 | 2.42 | 2.02 | |

10 | 8.46 | 17.90 | 343.09 | 583.56 | 1.67 | 2.30 | |

Stern (After) | 4 | 5.28 | 5.44 | 229.31 | 296.24 | 4.99 | 4.29 |

6 | 3.06 | 3.28 | 254.47 | 346.18 | 2.85 | 2.86 | |

10 | 0.95 | 1.52 | 247.15 | 264.33 | 1.20 | 1.04 |

Speed [Knots] | Ice Concentration = 60% | Ice Concentration = 80% | |||
---|---|---|---|---|---|

Average [mm] | Max [mm] | Average [mm] | Max [mm] | ||

Bow (Forward) | 4 | 2.38 | 90.83 | 3.51 | 109.81 |

6 | 4.59 | 284.00 | 6.20 | 412.03 | |

10 | 10.76 | 863.34 | 13.06 | 953.36 | |

Mid Ship | 4 | 0.11 | 5.78 | 0.14 | 4.14 |

6 | 0.11 | 5.00 | 0.13 | 3.38 | |

10 | 0.19 | 4.83 | 0.30 | 10.38 | |

Stern (AFTER) | 4 | 0.12 | 1.90 | 0.16 | 2.22 |

6 | 0.14 | 2.39 | 0.25 | 9.95 | |

10 | 0.12 | 2.63 | 0.13 | 2.52 |

Ice Concentration | Numerical Model | Average Wear Depth [mm] | Maximum Wear Depth [mm] | Area [m ^{2}] | ||||||
---|---|---|---|---|---|---|---|---|---|---|

4 Knots | 6 Knots | 10 Knots | 4 Knots | 6 Knots | 10 Knots | 4 Knots | 6 Knots | 10 Knots | ||

60% | With deformed geometry | 2.97 | 5.18 | 8.28 | 37.73 | 66.89 | 110.3 | 26.38 | 26.56 | 31.25 |

Without deformed geometry | 2.38 | 4.59 | 10.76 | 90.83 | 284.0 | 863.3 | 15.69 | 15.90 | 19.36 | |

80% | With deformed geometry | 4.13 | 6.39 | 10.38 | 46.10 | 84.53 | 138.8 | 29.00 | 30.88 | 35.65 |

Without deformed geometry | 3.51 | 6.20 | 13.06 | 109.8 | 512.0 | 953.4 | 19.63 | 19.36 | 21.38 |

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**MDPI and ACS Style**

Lee, S.-J.; Lee, J.H.
Application of Discrete Element Method Coupled with Computational Fluid Dynamics to Predict the Erosive Wear Behavior of Arctic Vessel Hulls Subjected to Ice Impacts. *J. Mar. Sci. Eng.* **2023**, *11*, 1774.
https://doi.org/10.3390/jmse11091774

**AMA Style**

Lee S-J, Lee JH.
Application of Discrete Element Method Coupled with Computational Fluid Dynamics to Predict the Erosive Wear Behavior of Arctic Vessel Hulls Subjected to Ice Impacts. *Journal of Marine Science and Engineering*. 2023; 11(9):1774.
https://doi.org/10.3390/jmse11091774

**Chicago/Turabian Style**

Lee, Sung-Je, and Jang Hyun Lee.
2023. "Application of Discrete Element Method Coupled with Computational Fluid Dynamics to Predict the Erosive Wear Behavior of Arctic Vessel Hulls Subjected to Ice Impacts" *Journal of Marine Science and Engineering* 11, no. 9: 1774.
https://doi.org/10.3390/jmse11091774