Discrete elementmodeling of ice loads on ship hulls in broken ice fields

Ice loads on a ship hull affect the safety of the hull structure and the ship maneuvering performance in ice-covered regions. A discrete element method （DEM） is used to simulate the interaction between drifting ice floes and a moving ship. The pancake ice floes are modelled with three-dimensional （3-D） dilated disk elements considering the buoyancy, drag force and additional mass induced by the current. The ship hull is modelled with 3D disks with overlaps. Ice loads on the ship hull are determined through the contact detection between ice floe element and ship hull element and the contact force calculation. The influences of different ice conditions （current velocities and directions, ice thicknesses, concentrations and ice floe sizes） and ship speeds are also examined on the dynamic ice force. The simulated results are compared qualitatively well with the existing field data and other numerical results. This work can be helpful in the shil3 structure design and the navigation securitv in ice-covered fields.     

极地吊舱推进船舶回转性能的离散元分析

吊舱推进装置在极地船舶中被广泛应用,其转舵模块可以带动螺旋桨摆动从而产生任意方向的推进力,使船舶操纵更为灵活。提出了一种吊舱推进船舶冰区操纵的离散元方法,对具有吊舱推进装置的冰区船舶破冰过程进行了数值模拟。以“雪龙2”号破冰船为研究对象,计算分析了船舶定速直航时的冰阻力,并通过与Lindqvist经验公式的对比验证了冰阻力计算的合理性。在此基础上进一步对船舶在不同冰厚、不同吊舱转向角下的回转破冰运动进行了离散元模拟,分析了回转半径与船长比值随冰厚的变化规律。计算结果表明：船舶的回转性能随冰厚的增大而降低,并随吊舱转向角的增大而显著提高。     

锥体导管架海洋平台冰激振动的DEM-FEM耦合分析及高性能算法

在寒区海域,冰荷载是影响海洋平台安全运行的主要环境荷载之一,由其引起的冰激振动给平台结构及其上部设备带来了严重危害。为分析不同冰况下平台的振动响应,本文建立了导管架海洋平台冰激振动的离散元（DEM）-有限元（FEM）耦合模型。采用具有黏接-破碎性能的等粒径球体离散单元对海冰的破碎特性进行模拟,通过由梁单元构建的海洋平台有限元模型获得结构的振动响应。在离散元与有限元的接触区域中实现了两个模型间计算参数的传递。为提高该耦合模型的计算效率和规模,发展了基于动力子结构方法的DEM-FEM耦合模型。为验证该耦合模型的有效性和可行性,将不同冰况下得到的冰荷载与ISO19906和JTS 144-1-2010标准进行了对比。结果表明,计算得到的冰荷载与标准相近,且冰厚与冰荷载呈二次非线性关系。同时,从冰速和冰厚两方面对比了渤海四桩腿JZ20-2 MUQ锥体导管架平台冰激振动加速度的数值结果和现场实测数据,发现冰速与振动加速度呈线性关系,冰厚与振动加速度呈二次非线性关系,并且振动加速度与冰速和冰厚平方的乘积呈线性关系。     

Influence of Ice Size Parameter Variation on Hydrodynamic Performance of Podded Propulsor

During ice-breaking navigation, a massive amount of crushed ice blocks with different sizes is accumulated under the hull of an ice-going ship. This ice slides into the flow field in the forward side of the podded propulsor, affecting the surrounding flow field and aggravating the non-uniformity of the propeller wake. A pulsating load is formed on the propeller, which affects the hydrodynamic performance of the podded propulsor. To study the changes in the propeller hydrodynamic performance during the ice podded propulsor interaction, the overlapping grid technique is used to simulate the unsteady hydrodynamic performance of the podded propulsor at different propeller rotation angles and different ice block sizes. Hence, the hydrodynamic blade behavior during propeller rotation under the interaction between the ice and podded propulsor is discussed. The unsteady propeller loads and surrounding flow fields obtained for ice blocks with different sizes interacting with the podded propulsor are analyzed in detail. The variation in the hydrodynamic performance during the circular motion of a propeller and the influence of ice size variation on the propeller thrust and torque are determined. The calculation results have certain reference significance for experiment-based research, theoretical calculations and numerical simulation concerning ice podded propulsor interaction.     

海冰动力过程的改进离散元模型及在渤海的应用

海冰的断裂、重叠和堆积等离散分布特性广泛地存在于极区和副极区的不同海域,并对海冰的生消、运移过程有着重要影响。针对海冰在不同尺度下的离散分布特点,发展海冰动力过程的离散元方法有助于完善海冰数值模式,提高海冰数值模拟的计算精度。为此,本文针对海冰生消运移过程中的非连续分布和形变特性,发展了适用于海冰动力过程的改进离散元模型(MDEM)。不同于传统离散元方法,该模型将海冰离散为具有一定厚度、尺寸和密集度的圆盘单元。海冰单元设为诸多浮冰块的集合体,其在运移和相互接触碰撞过程中,依照质量守恒发生单元尺寸、密集度和厚度的相应变化。基于海冰离散性和流变性的特点,该模型采用黏弹性接触本构模型计算单元间的作用力,并依据Mohr-Coulomb准则计算海冰法向作用下的塑性变形及切向摩擦力。为验证该模型的可靠性,本文对海冰在规则水域内的运移和堆积过程进行了分析,离散元计算结果与解析值相一致;此外,对旋转风场下海冰漂移规律的模拟进一步验证了本文方法的精确性。在此基础上,对渤海辽东湾的海冰动力过程进行了48h数值分析,计算结果与卫星遥感资料和油气作业区的海冰现场监测数据吻合良好。在下一步工作中将考虑海冰离散元模拟中的热力因素影响,发展具有冻结、断裂效应的海冰离散元模型,更精确地模拟海冰动力-热力耦合作用下的生消和运移过程。     

多桩锥体海洋平台结构冰荷载遮蔽效应离散元分析

在海冰与多桩锥体海洋平台结构的相互作用中,平台结构总冰力在海冰流向和桩腿方位的影响下呈现出显著的遮蔽效应。采用具有粘结-破碎效应的离散元方法,基于GPU并行的高性能计算,对不同冰向下锥体海洋平台结构的冰荷载进行了数值分析,确定了不同冰向下平台结构各桩腿的冰力衰减系数并分析了总冰力的遮蔽效应。最后,对自由边界影响下多桩平台结构冰荷载遮蔽效应的产生机理进行了讨论。本文工作可为多桩腿平台结构的冰荷载特性、冰激结构振动以及冰区结构设计提供参考。     

Ice resistance measurements in ridges with IB APU in the Baltic sea

Ice ridges form a difficult obstacle for ice navigation. Despite this fact, the resistance of ships in ridges has been investigated very little.A trial was performed with the Finnish icebreaker APU (propulsion machinery power of 8·8 MW) in April 1974 in the Baltic, in order to measure its resistance in ridges.Most of the 11 ridges were so massive that the ship could not penetrate through them by a continuous mode, the ramming mode had to be used.When the ship was penetrating a ridge, its speed and the propeller revolutions were registered for determining the resistance. A doppler radar was used for measuring ship spped.In case the ship was stopped in the ridge it was extracted, reversed and accelerated for the next ram. The time history was registered for determining the ship's speed of advance.Before starting a test, the ridge profile above the water level was measured. This was simply done by using a levelling instrument.The main object of the test was to determine the ship's speed of advance. The results, i.e. ice resistance, ship speed and ridge characteristics were analysed on three levels: momentary values average values for rams and average values for a series of rams in one ridge.The test series presented in the article was the first one in full scale in which the speed of the advance of a ship moving by ramming was determined and the ridge profiles were mapped. The measuring system developed worked well. As results the tests gave data of the ship's resistance and of the ship's speed of advance in ridges.     

锥角对锥体结构抗冰性能影响的离散元分析

在寒区海洋工程中,锥体海洋结构的尺寸参数对其破冰性能具有重要影响。采用具有黏结-破碎功能的离散元方法模拟海冰与锥体结构的相互作用过程中海冰的破坏模式及冰载荷分析。该离散元方法的计算参数通过与渤海油气平台的实测数据对比进行了可靠性验证。在此基础上,当设计海域的潮差固定时,对不同锥角下风电单桩锥体结构的冰载荷和海冰破坏模式进行了离散元分析。计算结果表明:锥体冰载荷随锥角的增大而增大,海冰的平均断裂长度则随锥角的增大而减小;当锥角小于70°时海冰的破碎模式主要为弯曲破坏,而当锥角大于70°时海冰破坏模式则主要为挤压破碎。以上研究结果可为冰区海上风电单桩结构的抗冰锥设计提供参考。     

Ice Height and Backscattering Coefficient Variability over Greenland Ice Sheets Using SARAL Radar Altimeter

Ice sheets investigation is important with regard to climate change and contribution to the sea level rise or fall. Radar altimetry in complement with laser altimetry can serve as a suitable candidate for precise monitoring of ice sheet evaluations. SARAL due to higher observation into the polar region (up to 82.5°N) can cover nearly 100% of the Greenland ice sheet. Continuous ice tracking mode retracker can provide useful information about ice surfaces, that is, determining the snow coverage, ice sheet transaction margin, and the evolution of snow depth during winter more accurately. This study present the results obtained with SARAL satellite Altika radar altimeter over the Greenland ice sheet region. The altimeter high rate waveforms products are used for utilizing the full capability of the instrument. High resolution DEM (1 km) generated using ICESAT/GLAS altimeter has been used for selecting the good quality data over the study region. Four different retrackers—Ocean, ICE-1, ICE-2, and Sea-Ice—were tested on the SARAL altimeter data set and compared with the DEM extracted ice sheet elevations. Three different data analysis—region of interest (ROI), track analysis, and cross-over analysis—were performed for in-depth analysis of the ice height changes and back scattering coefficient variability. ROI's (1° × 0.5°) were selected based on accumulation dry snow zone, percolation zone, wet snow zone, and ablation zone. Finally to observe the effect of Ka band, SARAL results has been compared with the Envisat altimeter in terms of back scatter and error in the height retrieval due to penetration problem within the ice sheet layer. The new SARAL data set confirms the potential of ice altimetry and provides a new opportunity to monitor the ice sheet surface topography evolution.     

Numerical Simulation on the Resistance Performance of Ice-Going Container Ship Under Brash Ice Conditions

Ice resistance prediction is a critical issue in the preliminary design of ships navigating brash ice conditions, which is closely related to the safety of a ship to navigate encounter brash ice, and has significant effects on the kinds of propellers and motor power needed. In research on this topic, model tests and full-scale tests on ships have thus far been the primary approaches. In recent years, the application of the finite element method (FEM) has also attracted interest. Some researchers have conducted numerical simulations on ship–ice interactions using the fluid–structure interaction (FSI) method. This study used this method to predict and analyze the resistance of an ice-going ship, and compared the results with those of model ship tests conducted in a towing tank with synthetic ice to discuss the feasibility of the FEM. A numerical simulation and experimental methods were used to predict the brash ice resistance of an ice-going container ship model in a condition with three concentrations of brash ice (60%, 80%, and 90%). A comparison of the results yielded satisfactory agreement between the numerical simulation and the experiments in terms of both observed phenomena and resistance values, indicating that the proposed numerical simulation has significant potential for use in related studies in the future.     

A Simple Empirical Formula for Predicting the Ultimate Strength of Ship Plates with Elastically Restrained Edges in Axial Compression

An investigation is conducted on the static ultimate limit state assessment of ship hull plates with elastically restrained edges subjected to axial compression. Both material and geometric non-linearities were considered in finite element(FE) analysis. The initial geometric imperfection of the plate was considered, while the residual stress introduced by welding was not considered. The ultimate strength of simply supported ship hull plates compared well with the existing empirical formula to validate the correctness of the applied boundary conditions, initial imperfection and mesh size. The extensive FE calculations on the ultimate strength of ship hull plates with elastically restrained edges are presented. Then a new simple empirical formula for plate ultimate strength is developed, which includes the effect of the rotational restraint stiffness, rotational restraint stiffness, and aspect ratios. By applying the new formula and FE method to ship hull plates in real ships, a good coincidence of the results between these two methods is obtained, which indicates that the new formula can accurately predict the ultimate strength of ship hull plates with elastically restrained edges.     

Modeling calving process of glacier with dilated polyhedral discrete element method

Mass loss caused by glacier calving is one of the direct contributors to global sea level rise. Reliable calving laws are required for accurate modelling of ice sheet mass balance. Both continuous and discontinuous methods have been used for glacial calving simulations. In this study, the discrete element method(DEM) based on dilated polyhedral elements is introduced to simulate the calving process of a tidewater glacier. Dilated polyhedrons can be obtained from the Minkowski sum of a sphere and a core polyhedron. These elements can be utilized to generate a continuum ice material, where the interaction force between adjacent elements is modeled by constructing bonds at the joints of the common faces. A hybrid fracture model considering fracture energy is introduced. The viscous creep behavior of glaciers on long-term scales is not considered. By applying buoyancy and gravity to the modelled glacier, DEM results show that the calving process is caused by cracks which are initialized at the top of the glacier and spread to the bottom. The results demonstrate the feasibility of using the dilated polyhedral DEM method in glacier simulations, additionally allowing the fragment size of the breaking fragments to be counted. The relationship between crack propagation and internal stress in the glacier is analyzed during calving process. Through the analysis of the Mises stress and the normal stress between the elements, it is found that geometric changes caused by the glacier calving lead to the redistribution of the stress. The tensile stress between the elements is the main influencing factor of glacier ice failure. In addition, the element shape,glacier base friction and buoyancy are studied, the results show that the glacier model based on the dilated polyhedral DEM is sensitive to the above conditions.     

压力公式的修正及其在波浪荷载计算中的应用

计入前进速度流动与非定常流动之间的干扰,修正了切片法中计算压力的公式,从而建立了计算波浪荷载的方法,开发了相应的计算机程序。计算实例同国内外有关资料的比较表明结果吻合良好,为船舶与海洋结构物结构有限元分析程序提供了有效的前处理模块     

螺旋桨对海冰切削作用的DEM-FEM耦合分析

当船舶在冰区航行时,螺旋桨会与海冰相互碰撞并导致桨叶的变形和损坏,进而影响船舶的航行安全。为研究海冰与螺旋桨的相互作用过程,采用离散元(DEM)—有限元(FEM)耦合方法构建海冰—螺旋桨切削模型。海冰和螺旋桨模型分别采用具有黏结—破碎特性的球体离散单元和8节点六面体有限单元构造。基于该DEM-FEM耦合模型讨论了不同切削深度下,螺旋桨所承受冰载荷的特点和规律;最后,研究了螺旋桨切削海冰过程中进速系数、推力系数、扭矩系数之间的对应关系,并讨论了海冰—螺旋桨相互作用过程中冰压力、Mises应力和变形的分布特点。以上研究可为寒区船舶安全航行和螺旋桨设计提供有益的参考。     

Heat Transfer Coefficient between Ice Cover and Water in the Bohai Sea

The calculative method of heat transfer coefficient between ice cover and water is analyzed considering the heat balance at ice cover bottom firstly. The heat transfer coefficient is calculated with the meteorological, oceanographic data and sea ice conditions measured on the JZ20-2 Oil/Gas Platform in the Bohai Sea during the winter of 1997/1998. From the results, it is shown that the heat transfer coefficient is smaller in the freezing and melting periods, which is about 0.16× 10-3 and 0.04× 10-3 respectively. In the middle of ice season, the heat transfer coefficient has a larger value, which is about 0.5 × 10-3. Lastly, the influences of ice thickness and ice type on the heat transfer coefficient are discussed. With the heat transfer coefficient determined above, the oceanic heat flux in the winter of 1997～1998 is calculated, and its trend in the winter is analyzed. This study can be referenced in the sea ice numerical simulation and prediction in the Bohai Sea.     

Parallel trajectory planning for shipborne Autonomous collision avoidance system

Collision at sea is always a significant issue affecting the safety of ship navigation. The shipborne autonomous collision avoidance system (SACAS) has the great advantage to minimize collision accidents in ship navigation. A parallel trajectory planning architecture is proposed in this paper for SACAS system. The fully-coupled deliberative planner based on the modified RRT algorithm is developed to search for optimal global trajectory in a low re-planning frequency. The fully-coupled reactive planner based on the modified DW algorithm is developed to generate the optimal local trajectory in a high re-planning frequency to counteract the unexpected behavior of dynamic obstacles in the vicinity of the vessel. The obstacle constraints, ship maneuvering constraints, COLREGs rules, trajectory optimality, and real-time requirements are satisfied simultaneously in both global and local planning to ensure the collision-free optimal navigation in compliance with COLREGs rules. The on-water tests of a trimaran model equipped with a model-scale SACAS system are presented to demonstrate the effectiveness and efficiency of the proposed algorithm. The good balance between the computational efficiency and trajectory optimality is achieved in parallel trajectory planning.     

An efficient and robust approach to predict ship self-propulsion coefficients

Achieving a reliable and accurate numerical prediction of the self-propulsion performance of a ship is still an open problem that poses some relevant issues. Several CFD methods, ranging from boundary element methods (BEM) to higher-fidelity viscous Reynolds averaged Navier–Stokes (RANS) based solvers, can be used to accurately analyze the separate problems, i.e. the open water propeller and the hull calm water resistance. However, when the fully-coupled self-propulsion problem is considered, i.e. the hull advancing at uniform speed propelled by its own propulsion system, several complexities rise up. Typical flow simplifications adopted to speed-up the simulations of the single analysis (hull and propeller separately) lose their validity requiring a more complex solver to tackle the fully-coupled problem. The complexity rises up further when considering a maneuver condition. This aspect increases the computational burden and, consequently, the required time which becomes prohibitive in a preliminary ship design stage.The majority of the simplified methods proposed in literature to include propeller effects, without directly solve the propeller flow, in a high-fidelity viscous solver are not able to provide all the commonly required self-propulsion coefficients. In this work, a new method to enrich the results from a body force based approach is proposed and investigated, with the aim to reduce as much as possible the computational burden without losing any useful result. This procedure is tested for validation on the KCS hull form in self-propulsion and maneuver conditions.     

船体曲面几何表达及水动力性能计算的NURBS方法

采用非均匀有理B样条(NURBS)对船体曲面形状进行几何表达,所生成的网格直接用于后续的有关船体水动力性能计算工作中。对Wigley船型的线性兴波阻力和斜航操纵运动的船体,结合近似的Kutta条件作了相应的数值计算,从与试验结果的比较来看,该方法具有较好的工程精度,对船舶及海洋工程领域中的计算机辅助设计(CAD)与计算流体动力学(CFD)之间的相互集成,具有推动与促进作用。     

冰脊形成过程的离散元模拟及影响因素分析

冰脊对极地船舶及海洋工程结构的冰载荷设计及冰区安全运行具有重要的影响,其几何形态是重要的考虑因素。为研究冰脊的几何形态,本文基于Voronoi切割算法构造扩展多面体海冰单元,并使其相互冻结形成平整冰;采用离散单元法模拟海冰在相对运动时挤压形成冰脊的动力过程,统计分析脊帆高度、龙骨宽度、龙骨深度、龙骨水平倾角等主要几何参数,并确定这些几何参数间的对应关系。将离散元模拟结果同冰脊现场观测资料对比分析以验证扩展多面体离散元方法模拟冰脊形成过程的可行性。在此基础上讨论冰厚、冰速、海冰强度等因素对冰脊形态的影响。本文采用离散元方法对冰脊形成过程及几何特性的数值分析可为深入开展冰脊的形成机理及其对船舶、海洋工程结构物的冰载荷分析提供参考依据。     

A stochastic method for the prediction of icebreaker bow extreme stresses

It is well established that the ship-ice interaction process is quite complex and associated ice loads on the icebreaker hull is a stochastic process. Obviously, novel accurate statistical methods and models should be developed and applied to estimate extreme bow stresses.This paper studies icebreaker bow stresses based on measured distribution of ice thickness in the Arctic Ocean on the way to and from the North Pole. Since the vessel route was carefully selected searching for easier ice conditions, the Arctic Ocean crossing was not a straight linear but a meandering path. Thus, the specific ship route data was biased with respect to general ice statistics in the region, but true with respect to the route specific ice data encountered by a ship navigating in that region. Therefore the route specific ice thickness data is directly needed for ship design and navigation analysis. It is assumed that captains are competent and knowledgeable, and therefore will select a route that provides the most favourable ice conditions.This paper contributes to study of the newest Chinese self-designed polar icebreaker, serving the purpose of enhancing icebreaker operational reliability. Finite Element Method software package ANSYS/LS-DYNA has been employed to simulate bow stress pattern for a particular icebreaker operating in the Arctic Ocean. Extreme bow stresses were estimated using Naess-Gaidai method. The latter is a first application of Naess-Gaidai method to a distribution with lower bound. Thus this paper aims at introducing an efficient method of estimating route-specific icebreaker extreme bow stresses.