Numerical study of icebreaking process with two different bow shapes based on developed particle method in parallel scheme

Hightlight

• A fast contact detection algorithm (FCDA) for ice-ship interaction (ISI) is proposed

• The MPI parallelization for 2-D Peridynamic (PD) theory is first introduced

• The newly developed ice-ship interaction (ISI) model is effective in predicting ice damage and crack propagation in the icebreaking process

• The developed ice-ship interaction (ISI) model is applied to investigate icebreaking effectiveness for two different bow shapes

Abstract

The bow shape is the most critical factor to determine the icebreaking performance of an icebreaker. Mechanism study on the icebreaking process for different bow types is necessary for the initial design of the icebreaker hull form. This paper proposed an ice-ship interaction model based on the meshfree method, Peridynamics, in which the geometric mathematics concept is embedded to detect the contact between material points and ship hull. Furthermore, a fast contact detection algorithm based on Massage Passing Interface (MPI) solver is built to improve the computational efficiency of the developed numerical method. Two typical icebreaker bows, the conventional bow and the unconventional bow, breaking the level ice with constant speed is numerically studied by the above model. The results of the conventional icebreaker bow are compared with the experimental results, which verifies the simulation accuracy of the model developed in the present work. Afterwards, the icebreaking modes and icebreaking loads of two different shapes of icebreaker bows are compared and analysed. The results show that the developed ice-ship interaction model effectively predicts differences of icebreaking processes between different icebreakers, such as ice damage pattern, ice loads, and channel, despite their common point in domain bending failure mode. Moreover, this research significantly improves computational efficiency and provides theoretical guidance for designing the icebreaker bow.

Introduction

With increased shipping activities, scientific investigation, resource exploitation, and military application value in arctic regions, the demand for high-performance ice-going ships rises accordingly (Gao and Erokhin, 2020; Larsen et al., 2016; Skripnuk et al., 2020). The icebreaker is a special-purpose ship designed to move and navigate through ice-covered waters and provides safe waterways for other ice-going ships. The bow is the main component to break the ice layer and push ice pieces, so the bow shape largely determines the icebreaking efficiency, icebreaking mode, and ice movement trajectory. Icebreaker bow also directly affects the clearing efficiencies by submerging broken ice in different ways (Guard, 1972; Riska, 2011). Consequently, understanding the influence of bow profile characteristics on the icebreaking process contributes to the design consideration and performance evaluation of icebreakers and helps guide the ice navigation in addressing the ice condition for different icebreakers. This makes it necessary numerically investigate and analyze the icebreaking mode of different bow shapes.

Five characteristic parameters describe the shape of icebreakers bow: flare angle, waterline angle, buttock angle, stem angle, and bow length (Aamot, 2015; Dick and Laframboise, 1989; Hu and Zhou, 2015; Sodhi, 1995). The ship's ability to break the ice layer and submerge floating broken ice floes is mainly determined by the flare angle, while the removal of brash ice accumulated on both sides and in front of the bow largely depends on the waterline angle. The buttock angle and stem angle are the secondary parameters that influence the icebreaking process and sinking of the broken ice. Therefore, the bow design revolves around the characteristics mentioned above according to ice conditions and icebreakers' mission planning. According to the outline, the typical icebreaker bow can be divided into conventional bows and unconventional bows. The conventional bows, including straight bow with parallel buttocks, concave bow (White bow), high flare angle bow (Melville bow), have smooth hulls and good resistance performance in open water. The unconventional bow shapes are further classified as spoon-shaped bow with reamers, half spoon-shaped bow with chines, flat bow, and Thyssen-Waas bow (Jones, 2008, 2004; Sodhi, 1995). In this paper, a conventional straight bow with parallel buttocks and an unconventional Thyssen-Waas bow are modeled to investigate the differences in the icebreaking process.

The research on the icebreaking process of different bow shapes started as early as the 18th century; at the very beginning of the icebreaker appearance, there were few special regulations or recommendations on the icebreaker bow design except a larger machinery power in icebreakers. Not until the 19th century, icebreaker design developed much with several technological innovations; a very small stem angle $\beta$ characterised the bow shape in this time, and the rounded stem that emerged as a sharp bow in the 1980s had always been considered to be desirable for icebreaking (Riska, 2019). White (1969) predicted the performance of the icebreaking bow using a purely analytical method and summarised its’ characteristics, which would be beneficial for improving icebreaking capability. Proc. 6th STAR Symposium compared and analysed resistance performance of icebreaker with different bow shapes according to the model tests carried out by different organisations. The results showed that the rounded bows with low stem angle performed best in breaking ice (Michailidis and Murdey, 1981; Noble and Bulat, 1981; Schwarz et al., 1981). In the 1990s, the INSROP, International Northern Sea Route Programme, carried out a series of model tests for icebreakers' design and summarised the effect of ship bow shape on icebreaking resistance in low and high ship speed range. It is concluded that the smaller the stem angle, the lower the icebreaking resistance (Ishikawa and Kawasaki, 1995; Izumiyama and Uto, 1995; Kishi and Narita, 1995; Suzuki et al., 1997; Yamaguchi et al., 1997). Ierusalimsky and Tsoy (1994) and Glen et al. (1998) carried out a series of comparison model tests on different bow forms and concluded that the non-traditional bows showed better icebreaking performance in level ice but poorer performance in open water. Warntjen et al. (2018) studied the relationship between the structural response and the bow shape by MATLAB and revealed that the smaller buttock angle and the average waterline angle are conducive to reduce ice resistance in the channel. Tao et al. (2019) developed a prototype parametric icebreaker model using CAESES software and established the qualitative relationship between the main factor of bow shape and the ice resistance. The icebreaking force, mainly dependent on the bow shape, contributes a lot to the icebreakers' resistance to level ice (Puntigliano, 2003; Riska, 2011; Valanto, 2001).

Moreover, some theoretical methods, including empirical or semi-empirical formulas, have been proposed and applied to predict icebreaking force (Lindqvist, 1989; Lindstrom, 1990; Sawamura, 2012; Su et al., 2010); for example, the influence of icebreaking patterns and geometric bow parameters on icebreaking resistance was researched and evaluated by model tests (Myland and Ehlers, 2016). It is found that the research on the differences in the icebreaking process among different bow shapes mainly relies on the conclusions from early experiments and analysis. There is still a lack of efficient or accurate numerical methods for the comparative study of the detailed phenomenon and mechanism of the icebreaking process.

As for the numerical study on the ice-ship interaction, much work has been done to capture the further physical process of ice-ship interaction, which was reviewed in a very recent article (Xue et al., 2020). Of all the methods reviewed in Xue et al. (2020), the meshfree particle methods, such as Smoothed Particle Hydrodynamics (SPH) and Peridynamics (PD), demonstrated their superior and robust potential to solve ice damage problems. The PD method especially predicts the evolution of crack propagation in ice failure realistically and accurately with its own fracture criterion. This was well demonstrated by previous work: ice-propeller interaction (Wang et al., 2018; Ye et al., 2017), submarine surfacing through ice (Ye et al., 2020), and ice-structure interaction (Vazic et al., 2019). Therefore, the meshfree particle method, PD, is utilised as the basic methodology for the ice model in the present paper.

The present work aims to analyze the differences in icebreaking modes and icebreaking loads between a traditional and a non-traditional bow using numerical simulation. For this purpose, a meshfree method-based ice-ship interaction (ISI) model, which embedded a proposed fast contact detection algorithm into PD theory, is developed to achieve the numerical model. This is introduced in Section 2 and Section 3. Furthermore, in Section 4, the MPI parallel scheme is developed to the framework of the above numerical model to improve computational efficiency. The numerical prediction program is compiled in the FORTRAN language environment, and the specific programming strategy is presented in Section 5. Finally, the icebreaking process of two typical bow shapes is predicted in Section 6. The comparison between numerical results with conventional bow and experiment data shows reasonable and efficient prediction, verifying the present model. Then, the differences in icebreaking mode and icebreaking loads of two kinds of icebreaker bow are concluded and analysed.

The unique contributions of the present paper are summarised here:

• A fast contact detection algorithm (FCDA) for ISI is proposed to solve the impact between the material particle calculation domain and the solid body. The FCDA can be applied to various numerical engineering applications that relate to the collision of irregular-shaped objects. The numerical strategy for FCDA is demonstrated here, in Section 5.1.

• The MPI parallelisation for the PD theory, one of the frameworks of the meshfree particle method, is first introduced to the developed ISI model, and the numerical analysis for ISI in MPI scheme is conducted in Section 5.3.

• The above-developed method is applied to engineering cases, icebreaker breaking level ice, and compared with experimental results. The icebreaking pattern of two different-shaped bows is realistically and accurately simulated in Section 6, which demonstrates the superiority of the proposed method in modeling the phenomenon of crack propagation over other numerical methods.