Ice Accretion on Cables of Various Cross-sections

Poots & Rodgers (1976) gave analytical and numerical resultson the icing of a cable having circular cross-section. The windcarrying freezing fog or supercooled cloud droplets impingeson the cable and a spike of rime ice grows outward into thewind. A linear Stokes law of resistance was assumed in calculatingthe drag force on individual droplets. Consequently the theoreticalpredictions on ice accretion are shown to be restricted to smallcable radii and high wind speeds (i.e. for large Stokes number). The purpose of this paper is to give detailed numerical solutionsfor ice accretion on cables of various cross-sections. Empiricaldrag formulae for droplets in motion, with local Reynolds numbersup to 10², are now employed in the numerical solution of droplettrajectories and impaction velocities on the ice accretion surface.Cables having circular, elliptical, square, and equilateraltriangular cross-section are investigated; also included areresults for a cylinder of elliptic cross-section the major axisof which is aligned at an angle to the upstream wind direction.For fixed wind speed and cable size and cross-section the massof ice accreted is given as a function of the time. These resultsare relevant to the evolution of ice accretion on structures.     

Approximate Predictions of Ice Accretion on an Overhead Transmission Line which Rotates with Constant Angular Velocity

An airflow carrying either freezing-fog droplets or wet snowimpinging on an overhead transmission line causes ice to accreteon the windward side of the conductor. In the vicinity of theconductor anchors (at the towers), axial growth, in the formof a spike of ice growing outward into the wind, is observed.Near the centre of the span this eccentric ice loading causesthe conductor to twist so that cylindrical-sleeve growth isobserved. For small-diameter conductors of low torsional stiffnessthe conductor rotation can amount to many complete revolutions.It is useful to obtain some understanding of this mode of iceaccretion prior to undertaking any investigation of the aeroelasticsystem under icing conditions and it has direct relevance toice loading on small-diameter conductors. To this end, a simple‘icing-clock’ model for sleeve growth in which theconductor rotates with constant angular velocity is proposed,enablinganalytical results on the mechanics of the ice evolution processto be obtained.     

黑龙江漠河地区冰雪情自动监测系统的设计与应用

基于空气、冰、雪与水物理特性的差异,设计了适应高寒地区内陆河道冰雪情定点自动检测的传感器和数据采集系统设备.该系统被安装在黑龙江省漠河县北极村水位站黑龙江河道断面,进行了3个半月的冰雪情定点连续监测,获取了系统的黑龙江河道内部冰水情以与积雪深度现场数据.采集数据完整地反映了黑龙江河道冬季冰层和雪层生消变化过程,为分析高寒地区冬季冰雪情变化规律以及春季凌汛预警提供了科学的预测数据,并探索出了一种适合野外恶劣环境下工程应用的冰雪情检测方法和系统设备.     

Simulation of ice under mechanical and thermal load

The contact physics of the wheel-rail contact of a railway vehicle under presence of water and ice at low temperatures is still not completely understood. For the investigation of the particular process in the contact zone a simulation is required, which is able to calculate the normal and tangential contact, the temperature field and the fluid-structural interaction between wheel and rail at low temperatures under presence of snow and ice. For that purpose the behaviour of ice under wheel-rail contact conditions is an important part. In this paper the thermal dynamic model of TSHIJOV [1], [3] for an adiabatic ice probe is updated by the new IAPWS equations of state for water [5] and ice phase Ih [4]. In a first approximation an ice specimen is loaded by specific wheel-rail contact pressure distributions calculated by the half-space formulation to clarify if phase transitions of ice can exist. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The sector design and assignment problem for snow disposal operations

Winter road maintenance operations involve a host of decision-making problems at the strategic, tactical, operational, and real-time levels. Those operations include spreading of chemicals and abrasives, snow plowing, loading snow into trucks, and hauling snow to disposal sites. In this paper, we present a model and two heuristic solution approaches based on mathematical optimization for the problem of partitioning a road network into sectors and allocating sectors to snow disposal sites for snow disposal operations. Given a road network and a set of planned disposal sites, the problem is to determine a set of non-overlapping subnetworks, called sectors, according to several criteria related to the operational effectiveness and the geographical layout, and to assign each sector to a single snow disposal site so as to respect the capacities of the disposal sites, while minimizing relevant variable and fixed costs. Our approach uses single street segments as the units of analysis and we consider sector contiguity, sector balance and sector shape constraints, hourly and annual disposal site capacities, as well as single assignment requirements. The resulting model is based on a multi-commodity network flow structure to impose the contiguity constraints in a linear form. The two solution approaches were tested on data from the city of Montreal in Canada.     

辽河口附近海冰单轴压缩强度的试验与统计特征

为研究影响海冰单轴压缩强度的因素,在渤海辽河口附近海域采集冰坯,加工成方柱状冰样.在试验温度分别为-3℃,-5℃,-7℃,-10℃和-15℃下,对225个冰样沿平行和垂直自然冰表面方向进行加载.研究试样温度,加载方向,应变速率和孔隙率对海冰单轴压缩强度的影响.试验结果表明:海冰单轴强度随试样温度的降低而增加;垂直方向冰样的峰值强度高于水平方向,海冰表现为各向异性.利用试验结果建立了韧性区内海冰单轴压缩强度与应变速率和孔隙率的统计关系.     

Nonlinear mechanics of accretion

We formulate a geometric nonlinear theory of the mechanics of accretion. In this theory, the material manifold of an accreting body is represented by a time-dependent Riemannian manifold with a time-independent metric that at each point depends on the state of deformation at that point at its time of attachment to the body, and on the way the new material is added to the body. We study the incompatibilities induced by accretion through the analysis of the material metric and its curvature in relation to the foliated structure of the accreted body. Balance laws are discussed and the initial boundary value problem of accretion is formulated. The particular cases where the growth surface is either fixed or traction-free are studied and some analytical results are provided. We numerically solve several accretion problems and calculate the residual stresses in nonlinear elastic bodies induced from accretion.

     

Hopf bifurcation in a conceptual climate model with ice–albedo and precipitation–temperature feedbacks

In this paper we analyse a dynamical system based on the so-called KCG (Källén, Crafoord, Ghil) conceptual climate model. This model describes an evolution of the globally averaged temperature and the average extent of the ice sheets. In the nondimensional form the equations can be simplified facilitating the subsequent analysis. We consider the limiting case of a stationary snow line for which the phase plane can be completely analysed and the type of each critical point can be determined. One of them can exhibit the Hopf bifurcation and we find sufficient conditions for its existence. Those, in turn, have a straightforward physical meaning and indicate that the model predicts internal oscillations of the climate. Using the typical real-world values of appearing parameters we conclude that the obtained results are in the same ballpark as the conditions on our planet during the quaternary ice ages. Our analysis is a rigorous justification of a generalization of some previous results by KCG and other authors.     

On the Optimal Insulation of Conductors

We coat a conductor with an insulator and equate the effectiveness of this procedure with the rate at which the body dissipates heat when immersed in an ice bath. In the limit, as the thickness and conductivity of the insulator approach zero, the dissipation rate approaches the first eigenvalue of a Robin problem with a coefficient determined by the shape of the insulator. Fixing the mean of the shape function, we search for the shape with the least associated Robin eigenvalue. We offer exact solutions for balls; for general domains, we establish existence and necessary conditions and report on the results of a numerical method.     

基于DS18B20的冰层温度梯度-厚度传感器的设计

根据高寒地区河流结冰时,河道冰情监测点垂直柱面内空气、冰与水三种介质所表现出的不同温度特性,设计了基于DS18820温度传感器的高显示分辨率冰层温度梯度一厚度自动化检测传感器,传感器内部采用单总线结构,通过MSP430单片机的控制实现了温度梯度各监测点的数字化数据采集,使传感器具有结构简单、功耗低、抗干扰能力强等优点.将新型传感器安装在内蒙古三湖口黄河河道并进行了连续两个月的现场冰情数据采集试验,传感器获得了黄河河道监测点系统的温度梯度数据.通过对采集获得的冰层温度梯度数据的进一步分析,可以全面掌握河道冰层变化的状况,实验结果表明这一新的冰层温度梯度一厚度传感器是一种更加适应于工程应用的冰情检测设备.     

基于PS021的电容式冰层厚度检测系统的设计

根据空气、冰和水的电容特性差异,本文设计了一种新型的电容式冰层厚度检测系统.该检测系统应用了德国acam公司的电容数字转换器PS021,可以把电容式传感器采集到的电容信号转换成数字信号输出.黄河的现场实验数据分析结果表明,系统结构简单,可靠性高,可以应用于冬季河道冰层厚度及冰下水位的定点、连续自动测量.     

The snowblower problem

We introduce the snowblower problem (SBP), a new optimization problem that is closely related to milling problems and to some material-handling problems. The objective in the SBP is to compute a short tour for the snowblower to follow to remove all the snow from a domain (driveway, sidewalk, etc.). When a snowblower passes over each region along the tour, it displaces snow into a nearby region. The constraint is that if the snow is piled too high, then the snowblower cannot clear the pile.We give an algorithmic study of the SBP. We show that in general, the problem is NP-complete, and we present polynomial-time approximation algorithms for removing snow under various assumptions about the operation of the snowblower. Most commercially available snowblowers allow the user to control the direction in which the snow is thrown. We differentiate between the cases in which the snow can be thrown in any direction, in any direction except backwards, and only to the right. For all cases, we give constant-factor approximation algorithms; the constants increase as the throw direction becomes more restricted. Our results are also applicable to robotic vacuuming (or lawnmowing) with bounded-capacity dust bin.     

An Interactive Algorithm for Vehicle Routeing for Winter — Gritting

In winter, when roads may become dangerously slippery due to frost, ice or snow, a de-icing agent (usually salt) is spread on them by a local authority for safety reasons. A gritter only needs to travel once down all those roads requiring treatment, as it can spread the salt onto both sides of the carriageway. The problem studied is how to design routes for gritters which will minimise costs. This problem is a type of Capacitated Arc Routeing Problem including consideration of multiple depot locations, limited vehicle capacities, time constraints on when roads must be gritted, roads with different priorities for gritting, the existence of one-way roads and salt-refilling locations. The objective function to be optimised depends on both the total distance travelled and the number and capacity of the gritters. A heuristic algorithm is devised with a computer program which allows user-interaction, and provides a practical tool for planning gritter routes. The model is linked to a GIS containing information on the road network for the County of Lancashire. Test results from the interactive algorithm are found to outperform another existing approach which solves the same problem.     

Phase-Field Modeling and Numerical Simulation for Ice Melting

In this paper, we propose a mathematical model and present numerical simulations for ice melting phenomena. The model is based on the phase-field modeling for the crystal growth. To model ice melting, we ignore anisotropy in the crystal growth model and introduce a new melting term. The numerical solution algorithm is a hybrid method which uses both the analytic and numerical solutions. We perform various computational experiments. The computational results confirm the accuracy and efficiency of the proposed method for ice melting.     

Solution procedures for three-dimensional eddy current problems

The problem under consideration is that of the scattering of time periodic electromagnetic fields by metallic obstacles. A common approximation here is that in which the metal is assumed to have infinite conductivity. The resulting problem, called the perfect conductor problem, involves solving Maxwell's equations in the region exterior to the obstacle with the tangential component of the electric field zero on the obstacle surface. In the interface problem different sets of Maxwell equations must be solved in the obstacle and outside while the tangential components of both electric and magnetic fields are continuous across the obstacle surface. Solution procedures for this problem are given. There is an exact integral equation procedure for the interface problem and an asymptotic procedure for large conductivity. Both are based on a new integral equation procedure for the perfect conductor problem. The asymptotic procedure gives an approximate solution by solving a sequence of problems analogous to the one for perfect conductors.     

Über die Führer von Gaußschen Summen als Größencharaktere

Let K be an absolute abelian number field. The conductor of the Hecke characters of K formed by Gaussian sums is investigated. In some cases we obtain formulas for this conductor while in others a bound is given. These enable us to obtain a general upper bound for the conductor in terms of the class field theoretic conductor of K. Our bound is an improvement on existing bounds in the literature.     

Upper bounds for Euclidean minima of algebraic number fields

The aim of this paper is to give new upper bounds for Euclidean minima of algebraic number fields. In particular, to show that Minkowski's conjecture holds for the maximal totally real subfields of cyclotomic fields of prime power conductor.