On maximum forces exerted by floating ice on a structure due to constrained thermal expansion of ice

The problem of interaction between a floating ice cover and an engineering structure is considered, in which the ice–structure contact forces are caused by an increase in ice temperature due to solar radiation in situations, when the lateral thermal expansion of ice is constrained. The focus is on the determination of the maximum thermally-induced horizontal force exerted on a structure wall, assuming that the magnitude of this force is bound by the smallest force capable of fracturing the ice cover due to its buckling. The ice cover is modelled as a rectangular plate of uniform thickness, with its four edges being constrained by vertical rigid walls, and it is assumed that ice deforms, and eventually fails, by the mechanism of viscous creep buckling. The plate is subjected to in-plane axial compressive stresses developing in ice to prevent its thermal expansion due to solar heating, and is transversely (vertically) bent by the forces caused by the reaction of underlying water. The floating ice is treated as a material whose elastic and viscous properties depend on temperature and the ice porosity, and therefore they vary with time and the depth of ice. The results of numerical simulations, conducted for a variety of the ice plate horizontal dimensions, thicknesses and daytime temperature-change scenarios, illustrate the evolution of the plate deflection surface prior to its failure, and show the time variation of the maximum forces exerted by ice on a structure wall as functions of the ice thickness and maximum daytime temperature rise at the top surface of ice.     

A comparative analysis of the fluid-structure interaction method and the constant added mass method for ice-structure collisions

The constant added mass (CAM) method and the fluid-structure interaction (FSI) method are widely used to simulate ship-ship and ship-ice collisions. In the CAM method, the hydrodynamic effect of the surrounding water is treated as a constant added mass, whereas in the FSI method the surrounding fluid flow is explicitly modelled. The objective of the paper is to compare the two methods and to explain the causes of the differences in the results. We considered collision between a freshwater ice mass and a floating steel structure. For both methods, the numerical simulations were performed with the LS-DYNA software. The behaviour of the ice mass was modelled using an elliptic yield criterion and a strain-based pressure-dependent failure criterion. To ensure realistic ice behaviour, the ice model was calibrated using general trends found in laboratory and in-situ indentation tests with focus on the laboratory-grown ice and the fluid model in the LS-DYNA was verified by comparing the added mass coefficients for a spherical body and a rectangular block with the corresponding WADAM results. To validate and benchmark the numerical simulations, experimental data on ice-structure interactions in water were used, including the acceleration of the floater wall measured with the dynamic motion unit (DMU), the relative velocity between the ice mass and the floater before the impact and some images extracted from video recording of the test. The comparisons indicated that the FSI method yields better results for the motion of the floater, i.e., the acceleration of the floater wall caused by the ice mass’s impact and the relative velocity were in reasonably good agreement with experimental measurements. It was also found that the CAM method was faster but predicted a higher peak contact force and more dissipated energy in the ice mass than in the FSI method.     

Repeatability of ice-tank tests with broken ice

This study investigates the repeatability of ice-tank tests with broken ice. Ice-tank test campaigns normally do not perform multiple repetitions of tests with the same initial conditions. Therefore, the repeatability of ice-tank tests with broken ice is not well understood. Data from two test campaigns are analysed. The first test campaign studied the interaction between a 4-legged structure with a vertical waterline and several broken and intact level ice conditions. In the second test campaign, a ship hull geometry was tested. We analyse selected test cases from each test campaign. The ice-tank tests are reproduced using a 3-D discrete element method (DEM) model. Each analysed test case is simulated 20 times. The only difference between each simulation is the initial position of the ice floes. The numerical simulation results show that changes in the initial floe positions can cause large changes in the statistical properties of the ice load. Often, a single random interaction event can be identified that is responsible for the change in the results. Such interaction events can cause additional floe accumulation ahead of the structure, thereby influencing the load statistics for a large portion of the interaction length. The observed events occur both in the numerical simulations and in the physical ice-tank tests. This result indicates that ice-tank tests with broken ice have a poor repeatability; a change in an uncontrolled condition, such as the exact initial floe positions, can lead to a large variation in the experimental results.     

Ship resistance when operating in floating ice floes: A combined CFD&DEM approach

Whilst climate change is transforming the Arctic into a navigable ocean where small ice floes are floating on the sea surface, the effect of such ice conditions on ship performance has yet to be understood. The present work combines a set of numerical methods to simulate the ship-wave-ice interaction in such ice conditions. Particularly, Computational Fluid Dynamics is applied to provide fluid solutions for the floes and it is incorporated with the Discrete Element Method to govern ice motions and account for ship-ice/ice-ice collisions, by which, the proposed approach innovatively includes ship-generated waves in the interaction. In addition, this work provides two algorithms that can implement computational models with natural ice-floe fields, which takes floe size distribution and randomness into consideration thus achieving high-fidelity modelling of the problem. Following validation against experiments, the model is shown accurate in predicting the ice-floe resistance of a ship, and then a series of simulations are performed to investigate how the resistance is influenced by ship speed, ice concentration, ice thickness and floe diameter. This paper presents a useful approach that can provide power estimates for Arctic shipping and has the potential to facilitate other polar engineering purposes.     

A tri-axial ice model for simulating ice-stiffened panel impact: Experiments and numerical modeling

The interaction of ice with a polar ship is complex, which may involve several ice failure mechanisms such as local crushing, tensile, cracking, bending, shearing, sliding and the ship structures could attain permanent deformations. A reasonable modeling of ice behavior is, therefore, critical to the analysis of ship-ice interactions. This paper reports an experimental and numerical study on the behavior of stiffened panels subject to the impact of a wedge-shaped ice block/indenter. The tested stiffened panel was mounted to a Falling Weight Impact Tester, and measurements were taken to help understand the dynamic responses of the structure and the ice, and also the permanent deformations. Finite element analyses using ABAQUS/EXPLICIT were also performed for the lab tests. The proposed ice model features a multi-surface yield function, empirical failure criteria for a few ice failure modes, and a representation of the remaining load carrying capacity of crushed ice. This ice model is implemented in a user-defined subroutine VUMAT and uses the cohesive element in a numerical solution. The predicted and measured impact force and structural deformation compared very well with the tests, indicating that the proposed ice model coded in VUMAT is reasonable. A series of parametric studies was then carried out to identify the key parameters of this new ice model that would have major effects on the prediction of ice impacts. The paper intends to provide test data that may be useful in understanding the complex ice-ship interaction and to introduce a numerical solution with a new ice model that improves the simulation of high-energy ice-ship impacts.     

Dynamic ice loads for offshore wind support structure design

For offshore wind farms which are planned in sub-arctic regions like the Baltic Sea and Bohai Bay, support structure design has to account for load effects from dynamic ice-structure interaction. There is relatively high uncertainty related to dynamic ice loads as little to no load- and response data of offshore wind turbines exposed to drifting ice exists. In the present study the potential for the development of ice-induced vibrations for an offshore wind turbine on monopile foundation is experimentally investigated. The experiments aimed to reproduce at scale the interaction of an idling and operational 14 MW turbine with ice representative of 50-year return period Southern Baltic Sea conditions. A real-time hybrid test setup was used to allow the incorporation of the specific modal properties of an offshore wind turbine at the ice action point, as well as virtual wind loading. The experiments showed that all known regimes of ice-induced vibrations develop depending on the magnitude of the ice drift speed. At low speed this is intermittent crushing and at intermediate speeds is ‘frequency lock-in’ in the second global bending mode of the turbine. For high ice speeds continuous brittle crushing was found. A new finding is the development of an interaction regime with a strongly amplified non-harmonic first-mode response of the structure, combined with higher modes after moments of global ice failure. The regime develops between speeds where intermittent crushing and frequency lock-in in the second global bending mode develop. The development of this regime can be related to the specific modal properties of the wind turbine, for which the second and third global bending mode can be easily excited at the ice action point. Preliminary numerical simulations with a phenomenological ice model coupled to a full wind turbine model show that intermittent crushing and the new regime result in the largest bending moments for a large part of the support structure. Frequency lock-in and continuous brittle crushing result in significantly smaller bending moments throughout the structure.     

基于接触问题的桩土相互作用机理

采用子结构凝聚自由度法推导出桩土接触问题的非线性有限元平衡方程,引入接触问题的约束条件,并通过增广拉格朗日乘子法对约束条件进行处理,得到数值计算的迭代格式,进而对桩土相互作用进行非线性数值计算,结果表 明：数值计算结果与实测结果吻合较好,接触问题的引入可以合理地解释桩土相互作用的机理问题。     

复合材料表面加强时冰层的应力应变状态研究（英文）

Ice crossings have been used for several reasons. First, due to the active development of the Arctic shelf, supplies and minerals are provided and transferred on special transports on the surface of ice covers. Second, ice crossings across rivers are used to reduce the length of transport routes. Traditional methods of increasing the load bearing capacity of ice are ice freezing from above, ice freezing from below, and ice strengthening through a wooden copepod flooring. Practical experience shows that the physical and mechanical properties of ice covers are unreliable and changeable in time and strongly depend on various external factors.Therefore, ice covers should be strengthened through alternative methods. Thus, predicting the bearing capacity of ice crossings and exploring methods for their strengthening are important. In this study, we consider the results of experimental and numerical studies on the bearing and deformation capacity of ice beams upon destruction from pure bending. Under pure bending, ice breaks down in the ice crossing when transports move along it. Tests were carried out with a specified reinforcement scheme. The results of the model experiments were compared with numerical calculations in the ANSYS software package. Experiments on ice beams reinforced with various composite materials were also performed. Destruction of samples in all cases occurred as a result of the formation of extensive cracks in the ice caused by the bending moment in the middle of the beam span. Based on the experimental and numerical research results, the use of a surface reinforcement in ice with various materials can increase the bearing capacity from 65% to 99% for this reinforcement scheme.     

船舶抗冰碰撞舷侧结构加强方案及优化设计

本文介绍了船-冰碰撞数值仿真中涉及的关键技术,以船舶肩部舷侧区域与棱角冰发生碰撞作为计算工况,对所选船舶舷侧与冰体碰撞进行数值仿真,根据舷侧响应特征指出其进行结构加强的必要性.由此提出几种舷侧常规加强方案,通过分析各自与冰体接触区域船体外板上受到的平均应力以及碰撞过程中船体结构发生塑性破坏的程度,指出结构仍然存在的问题以及后续加强的方向.最后,设计了2种新型舷侧结构并对其进行优化,验证了其具有较优的抗冰碰撞性能,得到了抗冰碰撞舷侧结构设计的相关结论.     

Dilated-polyhedron-based DEM analysis of the ice resistance on ship hulls in escort operations in level ice

The ice resistance on ships in escort operations in level ice are investigated using the discrete element method (DEM). A dilated polyhedron—generated by the Minkowski sum of a sphere and a polyhedron—is employed in the DEM; this dilated polyhedron-based DEM (DPDEM) is adopted to simulate the ship–ice interaction, wherein the contact force and bond-failure criterion are considered for the collision and fracture of sea ice, respectively. A three-point bending test was simulated with DPDEM, and a field test was conducted in the Bohai Sea to validate the DEM results. Further, a parametric analysis of flexural strength was conducted to identify the parameters involved in the bond-failure criterion. The ice resistance on icebreakers and cargo ships in level ice are simulated using DPDEM. The simulated ice resistances are compared with the Lindqvist and Riska formulas and the model test, which proves the validity of the DEM simulation. The interaction between ships and level ice is simulated parametrically to investigate the ice resistance on cargo ships with and without the icebreaker escort. Influencing factors such as ship speed, ice thickness, and ship breadth were examined to investigate the ice resistance on the escorted cargo ship. Analysis and change rules of the ice resistance on cargos affected by those factors were given.     

Research on short-term dynamic ice cases for dynamic analysis of ice-resistant jacket platform in the Bohai Gulf

Jacket platforms in the Bohai Gulf are often victims of random ice-induced vibrations. Their design originally did not account for dynamic ice loading on the jacket structures and significant ice-induced vibrations have been observed during winters. So it is urgent to find out as to how to consider the dynamic ice loading in the design stage of an ice-resistant jacket platform in the Bohai Gulf. In this paper, based on the state-of-art developments of dynamic ice load and ice–structure interaction, the authors proposed two different approaches to determine the short-term dynamic ice cases for dynamic analysis of ice-resistant jacket platform in the Bohai Gulf, named as the failure probability-based approach and the expected loss-based approach. Considering the variation of the ice environments and the variability of ice-resistant structure's properties, the random ice spectrum and the pseudo-excitation method (PEM) are employed to improve the efficiency of the procedure. Through finite element method (FEM) modeling of the real ice-resistant jacket platforms in the Bohai Gulf, such as MSW, MUQ and NW, the characteristics of the two proposed approaches have been investigated and compared. This paper provides an open and universal framework to assist designers and owners for determining the short-term dynamic ice cases in the Bohai Gulf, in which more information can be considered in the procedure to update and modify the results if available.     

基于完全耦合算法的绕水翼流固耦合特性研究

基于完全耦合算法对绕二维NACA0009水翼流固耦合特性进行了数值模拟研究。采用Theodorsen模型和Munch模型对刚性和弹性水翼的水弹性响应进行了数值计算,分析了流体与结构的相互作用关系,研究了影响结构水弹性响应和流固耦合特性的因素。研究结果表明:考虑了流体黏性的Munch模型与基于势流理论的Theodorsen模型对气动弹性响应的数值计算结果基本一致,而Theodorsen模型由于没有考虑流体黏性在一定程度上低估了结构的水弹性响应。结构的惯性、阻尼和刚度力矩与流体的相应附加载荷均处于同一数量级,故流体与结构的相互作用不可忽略,尤其对于弹性水翼,流体的惯性、附加阻尼作用增大,流固耦合算法的数值稳定性对流固耦合特性的计算结果影响将更大。外部激励频率为非共振频率时,结构的刚度作用是影响水弹性响应的主要因素,外部激励频率为共振频率时,流体的附加阻尼和附加刚度作用减弱,除结构的刚度作用外,流体与结构的惯性作用对水弹性响应和流固耦合特性的影响也较大。     

基于流固耦合的螺旋桨水动力性能数值仿真

根据螺旋桨理论,将基于粘流理论的计算流体动力学方法与结构有限元分析方法相结合,构建螺旋桨的流固耦合数值仿真方法。运用该方法对螺旋桨进行计算分析,并与试验结果进行对比,两者吻合较好。证明了利用构建的FSI方法与传统的CFD方法计算同一金属材料螺旋桨时,在低进速下计算所得结果较传统CFD方法更为准确。从多角度阐明所建立的流固耦合数值方法在复合材料螺旋桨研究方面的独特优势,为复合材料螺旋桨性能分析提供了必要的工具。     

基于B样条的三维船体水动力数值计算

本文采用基于B样条的一种新的数值方法计算三维船体水动力，用B样条函数表达三维船体表面的几何形状以及流场中未知物理量的分布，为了验证该数值方法的可行性和精确度首先对处于无限流体域中的圆球体绕流问题进行了计算；其次计算了由ITTC所推荐的Wigley船型的兴波阻力以及以一攻角斜航时的操纵水动力；最后在一些假设下对两船作平行航行时的干扰水动力作了相应计算工作。数值计算结果与其它试验或理论结果在定量或定性上吻合良好。     

Numerical simulation of level ice impact on landing craft bow considering the transverse isotropy of Baltic Sea ice based on XFEM

Ice bending is a major failure mechanism of level ice when ships and marine structures interact with level ice. This paper aims to investigate the ice bending and ice load when level ice collides on ships and marine structures using numerical simulation method, and compare the numerical results with field test. The fracture of ice is simulated with extended finite element method (XFEM), and cohesive zone concept is used to describe the crack propagation. In order to consider the characteristics of S2 columnar ice, a transversely isotropic elastic material model is used for the ice bulk elements, and a transversely isotropic Tsai-Wu failure criterion is adopted to predict the initiation of cracks. A well-controlled field test of a landing craft bow colliding with level ice in Baltic Sea is simulated to verify the numerical scheme. The ice plate's continuous deformation, crack initiation and crack propagation at different impact velocities and angles are simulated and the results are discussed. In the simulation, the bending crack emerges at the midline of the top surface of ice plate, then propagates towards free boundary, and finally a circumferential crack forms. It is found that with the impact velocity increases, the bending load increases and the fracture size (perpendicular distance from the crack to the contact edge) decreases. And as the angle between the landing craft bow and vertical direction increases, the bending load and the fracture size decrease. The simulated results corresponds well with the field test. The competition between the circumferential crack and radial crack is also found in the simulation and will be discussed in this paper. The results show that this method well simulates the bending of level ice and predict the ice load, and provides a good approach for investigating the mechanism of different forms of level ice fracture.     

冰区航行船舶冰阻力研究方法综述

船舶在冰区航行时的冰阻力性能一直是国内外关注和研究的重点。冰阻力的研究主要集中在经验方法、数值模拟和实验研究三个方面。同时,由于冰区船舶在航行过程中频繁地与冰层或浮冰产生碰撞,海冰的材料结构和力学性质对冰阻力的研究有重要影响。文章从冰的物理力学特性出发,简要回顾几种重要的冰本构关系模型及其适用性;并从经验方法及试验与数值模拟相结合两个角度,回顾和讨论浮冰区和平整冰区中船舶的冰阻力性能研究进展;最后,基于研究现状提出尚需进一步解决的问题。文章旨在介绍冰区船舶冰阻力性能的研究进展,望能为后续冰阻力研究提供参考。     

Distributed mass/discrete floe model for pack ice rheology computation

A new model, called the distributed mass/discrete floe model, is proposed for performing practical computations of mesoscale pack ice rheology. This model possesses the advantages of both the continuum and the discrete element models: it can express the discrete nature of pack ice, for which it is difficult to use a continuum model, and requires a much shorter computation time than a discrete element model. The pack ice is divided into ice bunches in which the floes, assumed to be distributed uniformly, are modeled as inelastic disks or rectangles floating on the water. The ice interaction forces are formulated from the relationship between the impulse on the bunch and the variation of momentum in the bunch. The ocean flow is calculated simultaneously with the floe movement using a multilayer model. In a circulating water channel, drift tests of physical model floes were performed in order to investigate the characteristics of their motion and interaction with ocean structure models. Near the structure, the floe motion depends on the floe shape. Disk floes show a lateral motion in front of the structure. They flow out around both sides of the structure and the number of floes in front of the structure decreases with the lapse of time. On the other hand, rectangular floes scarcely flow laterally. The number of floes in front of the structure remains constant over time. These experiments indicate that when the motion of pack ice around a structure is simulated, it is important to consider the floe shape. The disk floe motion and the rectangular floe motion can be regarded as extreme cases of pack ice motion. Actual pack ice motion may be between these two extremes. Computations were carried out using the distributed mass/discrete floe (DMDF) model. Simulation results were compared with the circulating water channel experiment results and sea ice motion in the southern part of the Sea of Okhotsk. The DMDF model predicted the circulating water channel drift test results quite closely. The DMDF model results also compared quite well with the sea ice motion.     

Finite element based meta-modeling of ship-ice interaction at shoulder and midship areas for ship performance simulation

The climate change has made the transit through Arctic area more feasible, which demands reliable methods to evaluate ship performance. Ship performance in ice is a cross-scale problem, where the desired output such as ship speed lies in larger scale while the actual ship-ice interaction happens in smaller scale. Due to insufficient knowledge in ice mechanics and the demand for computational efficiency, existing approaches for modelling ship-ice interaction from ship performance perspective are mostly either (semi-) empirical, or simplified analytical, with reduced dimensions and extensively simplified mechanics. This paper presents a novel approach to model ship-ice interaction, which maintains the accuracy of the modelling with Finite Element Method (FEM) in ship-ice interaction scale, while being computationally very cheap, therefore is capable to be applied in ship scale simulations. The ice failure is firstly qualitatively investigated through full-scale and model-scale observations, as well as a numerical simulation with Extended Finite Element Method (XFEM). The model is then simplified and executed by Abaqus to automatically run a large database. A neural network is used to fit the results to get a simulation-free tool for ship-ice interaction calculation. Finally, the uncertainty in the results due to an important assumption is quantified. The results show that the obtained neural network fits the database with excellent performance. Therefore, it can be applied in ship scale simulations with improved accuracy compared to empirical or analytical approaches.     

Experimental study on a model azimuthing podded propulsor in ice

The objective of this study was to investigate the performance of a model azimuthing podded propulsor in ice-covered water. Model tests were carried out with two different depths of cut into the ice (15 and 35 mm), two different ice conditions (presawn and pack ice conditions), and four different azimuthing angles. The depth of cut is the maximum penetration depth of the propeller blade into the ice block. The 0.3-m-diameter model propeller was operated in a continuous ice milling condition. Ice loads were measured by several sensors which were installed in various positions on the model. Six one-axis pancake-style load cells on the top of the model measured the global loads and two six-component dynamometers were installed on the shaft to measure the shaft loads. One six-component dynamometer was attached to the one of the propeller blades inside the hub to measure the blade loads. The pod unit and propeller performance in ice are presented. Ice-related loads, which were obtained when the blade was inside the ice block, are introduced and discussed. During the propeller–ice interaction, a blade can experience the path generated by the previous blade, which is called the shadowing effect. The effects of shadowing, depth of cut, azimuthing angle, and advance coefficient on propulsor performance are presented and discussed.     

考虑流场影响下破冰船艏部结构响应研究

通常考虑船-冰碰撞附连水的水动力效应有附加质量法和流固耦合法。本文建立了破冰船破冰场景,基于流固耦合法进行了数值仿真计算,分析了水域流场对船体的冲击压力变化、流场的速度分布变化以及流场的动能变化。同时与附加质量法的计算结果进行了比较,对比分析了船艏的碰撞力大小、损伤变形以及局部冰载荷等差异,揭示了流场对船-冰碰撞的影响规律,对于破冰船结构设计具有重要的参考价值。