Iceberg towing in open water: Mathematical modeling and analysis of model tests

Two scenarios of towing an iceberg with a boat using floating and submerged tow lines are considered in this work. Equations governing the towing process and the tension in the mooring lines are formulated. The stability of steady solutions describing the towing process at a constant speed is studied. Numerical simulations are performed to compare the modeling results with the experimental results of towing a model iceberg and to investigate towing a full-scale iceberg.     

Experiments on level ice loading on an icebreaking tanker with different ice drift angles

A series of tests was performed with a laboratory-scale model ship to simulate the effects of ice load parameters on an icebreaking tanker. A model of the icebreaking tanker Uikku was mounted on a rigid carriage and towed through an unbroken ice sheet in the ice tank of the Marine Technology Group at Aalto University. Two ice sheets and 11 different experimental configurations were used. The carriage speed, heading angle of the model ship, and ice thickness were varied, and the forces, accelerations, ice cusp sizes, carriage positions, and ice pile dimensions under the intact ice sheets were measured.This paper includes results for the measurements of ice rubble loads against the model hull in the horizontal plane. Phenomena such as ice failure modes and ice rubble accumulation on the upstream side of the hull beneath the ice sheet were observed in some tests. The icebreaking lengths and dimensions of ice rubble were analyzed for some tests. The effects of towing speed, heading angle under the intact ice sheet in front of the hull, and the accompanying ice loads on the formation and build-up of ice rubble were analyzed. In addition, the evolution of ice rubble geometry, in cross sections and the horizontal plane, was investigated. There was good agreement over several orders of magnitude between the measured and calculated values of the lateral ice forces. These results are relevant to the modeling of ice loading on hulls and the design of moored or dynamic positioned structures for operation in ice-covered waters. Some parameters obtained from these tests can be used as input for future numerical simulations.     

A non-deterministic model of populations of iceberg scour depths

In this paper a non-deterministic model of iceberg scour depth distributions is developed. The model employs data on an initial distribution of scour depths, annual iceberg scour rates and annual sedimentation rates to generate populations of ‘observable’ iceberg scour depths, such as can be obtained from present-day deep-tow seismic data. Relationships between initial and observed populations are established. These theoretical relationships provide a basis from which a variety of inferences regarding present day iceberg scour rates, depth exceedence probabilities, etc. can be inferred from an existing data base of iceberg scour depths. In particular, we show how these inferences can in turn be used to generate design criteria for pipelines and glory-holes in seabeds subject to scour from icebergs or sea ice. As a test of the predictive capabilities of the model, iceberg scour data from three sites on the Grand Banks are analysed and an annual scour rate determined. This rate is compared to an annual scour rate derived from iceberg arrival rates and size exceedence data for the region. Very good agreement is found.     

Multi-surface failure criterion for saline ice in the brittle regime

In this paper, the development of a 3-D failure criterion for saline ice is presented. The need for such general 3-D failure formulation stems from the fact that, during ice–ship interactions, ice undergoes a complex state of deformation and stress before it fails and breaks away, and the use of the uniaxial strength of ice to compute impact ice loads may lead to inaccurate load calculations and non-conclusive results.In recent years, with the availability of High Power Computers (HPC), numerical methods are being used more than ever before in marine and ice engineering problems. Numerical models based on computational techniques such as finite elements, boundary elements and discrete elements require 3-D constitutive models and failure criteria to represent the behavior of the materials involved (such as the behavior of the ship structure, ice and water “fluid”).At high-speed impacts (strain rates >10⁻³ s⁻¹), ice behaves as a linear elastic material with a brittle mode of failure. Previously, Derradji-Aouat [Derradji-Aouat, A., 2000. A unified failure envelope for isotropic freshwater ice and iceberg ice. ASME/OMAE-2000, Int. Conference on Offshore Mechanics and Arctic Engineering, Polar and Arctic section, New Orleans, US, PDF file # OMAE-2000-P/A # 1002] developed a unified 3-D failure envelope for both fresh water isotropic ice and iceberg ice. In this paper, that formulation is extended to include failure of saline ice (in addition to fresh water ice and iceberg ice). The results of a significant number of true triaxial tests using Laboratory Grown Ice (LGSI) were obtained from the open literature. The results of these tests formed a database that enables the existing failure model [Derradji-Aouat, A., 2000. A unified failure envelope for isotropic freshwater ice and iceberg ice. ASME/OMAE-2000, Int. Conference on Offshore Mechanics and Arctic Engineering, Polar and Arctic section, New Orleans, US, PDF file # OMAE-2000-P/A # 1002] to be extended from the isotropic fresh water ice and iceberg ice to columnar saline ice.Mroz's [J. Mech. Phys. Solids 15 (1967) 163] concept for the multi-surface failure theory is used in both studies (the present study, for saline ice, as well as in the previous study, for the fresh water isotropic ice and iceberg ice). It appears that the same set of the equations is applicable to the failure of all three types of ice. The possibility of the existence of a universal and general failure criterion for all types of ice is discussed.The validation of the present multi-surface failure criterion was discussed on the basis of comparisons between predicted failure curves and actual true triaxial test results. An overall discrepancy of predicted versus measured strength values of less than 20% was calculated.     

A brief study of the force balance between a small iceberg,the ocean,sea ice,and atmosphere in the Weddell Sea

Icebergs are an important source of freshwater to the Weddell Sea. A unique set of oceanographic and other observations made during the Maud Rise Nonlinear Equation of State Study around one of the small icebergs, ubiquitous in the winter Weddell Sea, give us the opportunity to examine the dynamics of the interaction between an iceberg and the ocean. The iceberg was mapped using radar ranges and bearings from our ship, the research icebreaker Nathaniel Palmer, and found to be about 200 m wide above the water with a draft estimated to be 219 m. For this size, form drag dominates skin friction in both the atmosphere and ocean. Sea ice was ridged against the upwind side of the iceberg and thin sea ice and open water were on the downwind side. The iceberg was drifting 0.14 m s^− 1, or about 3% of the wind speed and 23° to the left. An automated CTD operating through the ship's moon-pool was used to measure temperature and salinity profiles upstream, downstream, and to the side of the iceberg. These profiles show a mixed upper layer 150 m deep upstream and 60 m deep downstream of the iceberg. The difference in density across the pycnocline was 0.05 kg m^− 3, which for the average pycnocline depth of 105 m and size of the iceberg corresponds to an interfacial internal wave speed equal to 0.166 m s^− 1. This and the upstream–downstream difference in pycnocline depth are consistent with a ± 45 m internal wave wake being generated by the motion of the iceberg. We estimate the contributions to total water drag from form drag and generation of the internal wake to be about equal. Consistent with theory, a qualitative argument using the observed pycnocline displacements suggests that internal wake drag should be a maximum when iceberg drafts are near the pycnocline depth. The drift rate of the iceberg (and sea ice) relative to wind speed was near the relative drift rate for the Weddell Sea ice we encountered during MaudNESS, but three times greater than what would result from a pure balance of atmospheric form drag against ocean form drag on the iceberg. Therefore, the force of sea ice on the iceberg, evidenced by ridging on the upwind side was dominant in moving the iceberg with the sea ice drift speed. The force transmitted through the sea ice required to drive the ice at the observed rate would be equivalent to the wind stress acting on an area of sea ice of 7.5 km². Maximum ridging forces in the 0.5 m thick sea ice should be adequate to drive the iceberg with this 219-m draft at 0.56 m s^− 1, much more than the observed drift rate but similar to the sea ice velocities during Weddell Sea storms.     

Resistance to ship-hull motion through brash ice

A three-metre long model hull of a tanker ship with simplified bow shapes was towed through a simulated brash ice channel in the model-ice towing tank of the Iowa Institute of Hydraulic Research (IHR). The study was to investigate resistance forces encountered by commercial ships, with hulls characterized by a long parallel middlebody, transisting brash ice channels.The model hull was structurally divided into a bow portion and an aft portion, which were coupled and instrumented so that resistance forces exerted on the bow as well as the total towing force could be measured. Two bow forms were used; a wedge bow and a simplified icebreaker bow.From the results of the experiments, it is shown that resistance to hull motion through brash ice may consist of the following components: bow resistance due to internal friction and accumulation of brash ice; bow resistance due to submergence of brash ice beneath hull; bow resistance due to momentum exchange between hull and brash ice; parallel-part resistance due to friction between hull and brash ice; stern thrust due to ascension of brash ice at the hull's stern; and open-water resistance. The ratio of each component to the total resistance depends on bow shape, hull speed, brash-ice characteristics and channel dimensions. The effects of brash-ice layer thickness and channel width on resistance are discussed. Additionally, some insight into the effect of brash-ice refreezing on resistance is also offered.     

EG/AD/S: A new type of model ice for refrigerated towing tanks

A new type of model ice has been developed for use in refrigerated towing basins. The ice is grown from an aqueous solution containing three different chemical dopants - ethylene glycol (EG), aliphatic detergent (AD) and sugar (S). In this paper, the concepts and development of this model ice are discussed. Analysis of the structure of the ice indicates that it is single layered, fine-grained and strictly columnar. A number of the mechanical properties of EG/AD/S model ice have been measured including the flexural strength, uni-axial and confined compressive strength, strain modulus and critical stress intensity factor. The results of these tests are compared to appropriately scaled sea ice values and the corresponding properties for carbamide (urea) model ice. This comparison shows that this new ice is far superior to urea model ice in all respects.     

Ice crushing tests with variable structural flexibility

To learn more on ice crushing phenomena against a compliant stiffened plate structure, near full-scale ice crushing tests were conducted in Aker Arctic test basin with a 1:3 scaled model. The dimensions of the to be crushed ice sheet and the stiffened plate were chosen to present a full size ship or offshore structure steel plating which are designed to withstand the crushing loads of 60 cm thick level ice. A major difference to the crushing tests published earlier in literature was that the compliance of one stiffener could be adjusted. The instrumentation in the plate included both strain gauges for load paths from the plate to the stiffeners and a large tactile sensor for detailed direct crushing pressure distribution measurement. In order to have repeatable and homogeneous model ice properties the ice blocks were manufactured by snow ice technique with low salinity water impregnation under vacuum in the mould. Altogether 22 ice blocks were crushed with different ice velocities and plate compliancy. The well-known line like contact prevailed in continuous crushing. The test data indicates that the crushing load distribution is independent from the underlying plate stiffness distribution and no higher crushing pressure at the location of stiffeners was found.     

A study of the tensile behaviour of flax tows and their potential for composite processing

To study the potential of flax tows in composite processing as an alternative to flax spun yarns, a flat flax tow consisting of aligned fibre bundles held together by a natural binder was used and characterised in tension under various conditions. The effect of the gauge length was studied on the dry reinforcement. The experimental results showed that the mechanical properties and failure mechanism varied significantly depending on the gauge length and are discussed in relation to the distribution of elementary fibres within the tow. A characteristic length as from which the mechanical properties are stable has been identified. At this length, the effect of the strain rate on the tensile properties was measured and their sensitivity to the strain rate suggests a viscous effect in the behaviour of the flax tow. To approach process conditions such as wet filament winding, a batch of specimens was impregnated with epoxy prior to tensile testing. The tensile properties under wet conditions were found to be close to the properties under dry conditions and shows that the tow can withstand typical processing tensions. Finally, tensile tests on cured-impregnated tows showed interesting mechanical properties for composite application.     

Characterisation of material properties for draping of dry woven composite material

Three test methods, uniaxial bias extension, biaxial and picture frame tests are used to characterise the shear behaviour of dry woven fabric during draping. The deformation of the bias extension and biaxial specimens is measured from images of a central gauge section. The forces applied to the material are resolved into forces along and parallel to the tow directions. The deformation of the material in the bias extension and biaxial tests is found to behave in a manner which is reasonably well described by a pin-jointed net analysis. There is negligible change in the shear resistance of the material during biaxial loading, while a slight increase in shear resistance is observed in the picture frame tests. Microscopic examination of the tow architecture [Compos Sci Technol 63 (2003) 99], which shows a significantly smaller crimp amplitude for picture frame tests than for the bias extension and biaxial tests, supports the suggestion raised by Harrison et al. [Proceedings of the 10th European Conference on Composite Materials, 2002], that the increase in resistance in the picture frame tests is associated with an increase in tow cross-over force generated by large loads along the tows.     

Evaluation of bergy bit populations on the Grand Banks

Shuttle tankers and hydrocarbon production platforms operating on the Grand Banks of Newfoundland must be designed for some level of ice loading. In some cases, high ice loads can result from relatively small icebergs, bergy bits, or growlers. This is particularly true when wave-induced ice motions are significant (in high sea states) or when vessel speeds are high (e.g., a transiting tanker).Safe and economic operations can be achieved by designing structures that are strong enough to withstand ice loads, planning for and managing ice to reduce the risk of collisions, or a combination of the two. In all cases, accurate information on the number of small ice masses is important. Unfortunately, reliable information on small ice mass populations is not available. The extensive, detailed aerial surveys that would be required to build up meaningful statistics on bergy bit populations would be prohibitively expensive, and other methods of estimating bergy bit populations are required for the development of a reliable database.The approach used in this study was a reanalysis of International Ice Patrol (IIP) operational iceberg observations. Although the IIP does not detect and report all bergy bits and growlers, their database contains critical information on the location of small ice masses in relation to the aircraft track, and the prevailing visibility and sea-state conditions. By resampling only those ice masses observed when detection conditions were favourable, and within a prescribed distance from the aircraft, more accurate bergy bit statistics have been determined.A convenient measure of the number of bergy bits and growlers is the ‘small ice mass to parent iceberg’ (SIMPI) ratio. This relates the number of small glacial ice masses to the number of parent icebergs from which most small ice masses are calved. The average SIMPI ratio for the study region was 0.59. Some interesting phenomena revealed in the study include the apparent geographical variation in the small ice mass to parent iceberg ratio, with increasing values to the north and west. The ratio also varied seasonally. Of the months in which sufficiently large numbers of icebergs were observed to produce meaningful statistics, the SIMPI ratio was lowest in March (0.25) and highest in May (0.81).     

Modeling the impact of capillary pressure and air entrapment on fiber tow saturation during resin infusion in LCM

Traditionally, capillary effects have been neglected when modeling the filling stage of Liquid Composite Molding processes. This simplification is justified because the inlet resin pressures are much higher than the capillary pressure. This simplification is also acceptable when impregnating fabrics in which their fiber tows saturate at the same rate as the bulk preform. However, this assumption is questionable for fabrics that exhibit dual scale in which the fiber tows saturate at a much slower rate than the bulk preform. In such cases, the capillary pressure can influence the time to saturate a fiber tow significantly and impact the overall impregnation dynamics. Since the flow front velocity inside the fiber tows is significantly smaller than the flow around them, it is important to include the capillary pressure that may aid the saturation of the tow. In this paper, we modify our existing simulation that can predict the filling of the bulk preform and the saturation of the fiber tows to include the capillary forces at the fiber tow level. Important parameters are identified and grouped in non-dimensional form. A parametric study is conducted to examine the role of these dimensionless parameters on the overall tow saturation levels. The modeling is extended to include the effect of entrapped air inside the tows on the overall saturation of the preform. An experimental technique using the optical properties of vinyl ester and glass fiber was used to qualitatively validate the proposed model.     

Tensile properties and failure mechanisms of 3D woven GRP composites

Tensile tests were performed on glass reinforced polymer (GRP) composites with three-dimensional (3D) orthogonal, normal layered interlock, and offset layered interlock woven fibre architectures. The mechanical properties and failure mechanisms under tensile loading were similar for the three composites. Cracks formed at low strains within the resin-rich channels between the fibre tows and around the through-thickness binder yarns in the composites, although this damage did not alter the tensile properties. At higher applied tensile stresses the elastic modulus was reduced by 20–30% due to inelastic tow straightening and cracking around the most heavily crimped in-plane tows. Further softening occurred at higher strains by inelastic straightening of all the tows. Composite failure occurred within a localised region and the discrete tow rupture events that have caused tow lock-up and pullout mechanisms in other 3D woven composites were not observed.     

渤海北部冰厚重现值的极大似然法区间估计

不同重现期的年极值冰厚是有冰海区建筑物设计的关键指标。目前在确定设计冰厚时,往往只给出点估计。而求解设计冰厚的置信区间,在某一置信水平下获取设计值的范围,可以确定设计重现值的不确定性,给海工结构物的设计与建造提供指导。采用极大似然方法区间估计,给出了Gumbel分布、三参数Weibull分布、三参数对数正态分布和P-III型分布置信区间的求解过程。利用渤海北部营口和葫芦岛海区历年总冰厚极大值的实测数据,基于以上4种分布型式,采用极大似然法求得不同重现期下冰厚重现值的置信区间,并对各分布型式进行了优选比较。结果表明,选取P-III型分布求解这两地海冰厚度重现值的置信区间较优。     

Laboratory calibration of upward looking sonars for measuring suspended frazil ice concentration

This paper describes a series of laboratory experiments conducted at the University of Alberta Cold Room Facility, investigating the use of upward looking sonars to measure frazil ice concentration. Two upward looking sonars, one high (546 kHz) frequency and one low (235 kHz) frequency were deployed on the bottom of a custom built frazil ice tank located in the cold room. A step by step procedure is provided for processing the raw sonar signal to compute the volume backscatter strength. A sieving technique was used to make direct measurements of frazil ice concentrations in the tank and sieved frazil ice particles were examined under a microscope to determine their average shape and size. Measured mass concentrations ranged from 0.012% to 0.135% and the majority of observed frazil particles were disk shaped, varying in diameter from 0.25 to 4.25 mm. The sonar measurements showed that the high frequency model is more sensitive to the presence of suspended frazil particles than the low frequency model, especially at lower concentrations. The depth averaged volume backscatter strength, computed from both the high and low frequency data, was found to be correlated with the frazil ice concentration and the resulting regression equations are provided. These correlations need to be tested in the field prior to being used for quantitative measurements of frazil ice concentration in rivers. The applicability of simplified theoretical backscatter models to estimate frazil ice properties is also discussed.     

Modelling the effect of material properties and process parameters on tow impregnation in out-of-autoclave prepregs

Out-of-autoclave prepregs based on woven fabrics initially consist of dry tows and resin-rich areas. The tows allow air evacuation in the initial stages of processing and are subsequently infiltrated by surrounding matrix. The following study analyzes the relationship between material properties, process parameters and tow impregnation for three OOA prepregs. First, a representative model for tow impregnation is developed. Then, the model parameters are determined and the model predictions are correlated to impregnation data measured by X-ray microtomography. Finally, the model is used in a parametric study to investigate the effect of fibre architecture, cure cycle temperature and resin initial degree of cure on tow impregnation rate and to predict the possible occurrence of flow-induced micro-voids.     

Contrast enhancement in visualisation of woven composite architecture using a MicroCT Scanner. Part 2: Tow and preform coatings

MicroCT scanning is a non-destructive method which was used to visualise tow architecture in woven composites, with the ultimate goal of three-dimensional model generation. It is difficult to discriminate between elements of carbon-fibre composites using MicroCT, particularly the region between co-aligned neighbouring tows. Methods used to facilitate visualisation by enhancing contrast during scanning were discussed in part one [Djukic LP, Herszberg I, Walsh WR, Schoeppner GA, Prusty BG, Kelly DW. Contrast enhancement in visualisation of woven composite tow architecture using a MicroCT Scanner. Part 1: fabric coating and resin additives. Compos Part A 2009;40:553–65.]. In order to improve upon these methods, tows were coated in a material of higher density and subsequently woven into a fabric. The most successful coatings were found to be gold and iodine. Adequate visualisations of glass tows were possible without contrast enhancement. These methods can be combined to allow multiple levels of contrast within a sample, as demonstrated with a three-dimensional woven preform. Three-dimensional reconstructions of interior tow architectures were made from the scans of contrast enhanced specimens.     

Boundary Layer Flow on a Model Propeller

Flash photographs have been made of a model screw propeller under test in a towing tank, to show the areas of laminar and turbulent flow in the boundary layers over the blades. These areas may be defined from the surface patterns made by ejecting a liquid dye from fine holes in the rotating blade, and the change in extent of each region with change of Reynolds number is coupled with the scale effect evident in model tests.     

Treating matrix nonlinearity in the binary model formulation for 3D ceramic composite structures

A computationally-efficient numerical approach to treating matrix nonlinearity in ceramic matrix composite components has been developed and validated. The model employs a dual mesh comprising strings of line elements that represent the fiber tows and 3D effective medium elements that define the external geometry and embody the matrix-dominated properties. Validation addressed test data for unnotched and open-hole tension specimens. For these tests, the onset of nonlinearity and subsequent plasticity due to matrix microcracking and interfacial debonding and sliding are satisfactorily represented by a linear Drucker–Prager model for failure initiation in the effective medium along with a fully-associated flow rule with isotropic, perfectly-plastic flow. Composite failure is assumed to be correlated with the maximum local stress averaged over a gauge volume dictated by the fiber tow width. Using one set of specimens for calibration, very good predictions of the nonlinear stress–strain response and ultimate strength of other specimens are obtained.