水下生产系统脐带缆温度场与载流量分析的有限元方法
水下脐带缆水动力性能分析
水下脐带缆水动力性能分析作者：李泯孙新蕾黄刚来源：《中国水运》2017年第11期摘要：脐带缆的水动力性能对水下作业装备的设计具有重要意义，本文在建立水下脐带缆动力学模型的基础上，通过对边值问题微分方程的求解分析，对分段绑扎脐带和ROV携带自由端脐带两种工况进行了定量数值计算，为解决类似工程问题提供了有效途径。
关键词：脐带缆；水动力；水下作业中图分类号：U661.33+1 文献标识码：A 文章编号：1006—7973（2017）11-0044-03随着海洋开发活动的不断深入，多样化的水下作业装备如遥控潜器、自主潜器、载人潜器、饱和潜水等装备不断涌现。
由于海洋环境的复杂性，自主作业潜器（如智能水下机器人）的智能化程度尚不足以独立完成一些较为复杂的水下作业，当前可应用于水下作业的装备主要为遥控潜器（ROV）、载人潜器、饱和潜水等，其共同特点是需要脐带缆，一方面为作业装备持续提供电力。
另一方面可以为作业装备和水面支持母船之间提供信息交互，如视频、控制信号、通讯等。
脐带缆在水下作业装备中的应用主要分为两种形式，一是作业装备携带脐带缆自由运动，脐带缆的两端分别为水面母船和水下装备，连琏等曾对该种形式脐带缆的水动力性能进行了分析。
另一种是脐带缆绑扎在固定引导缆上，随着水下作业装备的布放进行分段绑扎，饱和潜水作业通常采用该种形式。
本文根据某水下作业装备的应用开展了两种形式的水动力计算，一是分段绑扎脐带缆的水动力学数值分析，二是ROV携带自由脐带缆的水动力学数值分析。
如上图所示，假设ROV从导缆的正下方向前运动，若设定末端坐标为（0， 18），则ROV的坐标位置则从（0， 0）向（-5， 0），计算结果如下表所示：3 结论本文在对脐带缆微元进行动力学建模的基础上，对脐带缆在水下的力学特性进行了分析，对分段绑扎脐带、自由端移动脐带在水下的受力进行了定量化的数值计算。
计算结果表明，脐带缆在海流作用下的水动力不容忽视，必须在工程设计中加以考虑。
水下生产系统脐带缆抗疲劳设计的开题报告
水下生产系统脐带缆抗疲劳设计的开题报告一、研究背景水下生产系统是指在海底进行石油和天然气的开采，生产和输送的一套设施，其关键组成部分之一就是脐带缆。
脐带缆是连接海底设备和船舶的重要部件，承受着复杂的水流，海浪和潮汐的力量。
因此，对脐带缆的抗疲劳设计十分重要。
目前，国内外对于水下生产系统脐带缆的研究还比较局限，这使得脐带缆的可靠性和安全性难以保证。
因此，有必要开展水下生产系统脐带缆抗疲劳设计相关的研究工作。
二、研究目的本研究的目的是设计一种脐带缆抗疲劳的方案。
通过分析脐带缆在水下环境中所受的力和外界环境对其影响，为脐带缆的设计提供依据和优化方案。
同时，研究还将提出一些实用性较强的设计建议和一些实验检测方法。
三、研究内容1.脐带缆的工作原理，结构设计原则。
2.分析水流、水压和海底环境等因素对脐带缆的影响，建立数学模型。
3.分析脐带缆受力情况，研究脐带缆的应力减缓和控制方法。
4.设计并优化脐带缆的材料、几何结构和连接方式，提出可行的设计方案。
5.开展模拟实验和现场试验，验证所提出的方案的有效性和实用性。
四、研究意义1.对于水下生产系统脐带缆抗疲劳设计的研究，可以提高脐带缆在复杂水下环境中的可靠性和安全性。
2.对于优化脐带缆的设计方案和材料选用，可以降低工程成本，提高工程效率。
3.对于开展模拟实验和现场试验，可以验证所提出方案的可行性和实用性，为下一步设计提供可靠数据。
五、研究方法本研究将采用理论分析和模拟实验相结合的方法。
通过对脐带缆的结构设计、数学模型建立和力学分析等环节进行理论研究。
并通过模拟实验和现场试验对所提出的方案进行验证。
六、预期结果预期的研究结果包括：1.确定脐带缆的工作原理、结构设计原则和数学模型。
2.分析水流、水压和海底环境等因素对脐带缆的影响，建立较为完善的理论模型。
3.通过理论分析，研究脐带缆应力减缓和控制的方法，并提出优化的设计方案。
4.开展模拟实验和现场试验，验证所提出的方案的可行性和实用性。
脐带缆电单元参数计算的有限元方法
A Finite-Element Approach for Calculating Electrical Parameters of Umbilical CablesBjørn Gustavsen ,Senior Member,IEEE ,Are Bruaset,Jarle J.Bremnes,and Arild HasselAbstract—This paper presents a systematic approach for cal-culating electrical per-unit-length parameters of signal cables by the finite-element method.The associated software (UFIELD)has been specifically adapted to umbilical cables used in offshore con-trol applications.Efficient and robust case specification is achieved through a library of predefined,parametrized models for the um-bilical elements (signal cables,pipes,armors).Additional features include automated specification of boundary conditions and exci-tations,adaptive mesh generation,and the handling of twisted el-ements and layers.The approach is validated against analytical solutions.Application to the Snøhvit control umbilical shows ex-cellent agreement with measured signal parameters,for the triad element alone,and for the triad element inside the umbilical.Sim-ilar results are obtained for the Ormen Lange quad element.Index Terms—Capacitance,electrical parameters,finite-element method (FEM),impedance,umbilical cable.N OMENCLATUREBold,capital letter()Matrix of elements.Bold,small letter ()Vector of elements.I.I NTRODUCTIONTHE electrical modeling of cables for the simulation of electromagnetic (EM)transients,harmonics,and signal transfer requires calculating the per-unit-length parameters of the series impedance and shunt capacitance.For the modeling of high-voltage power cables,the impedance calculations are usually performed by using analytical expressions that assume a cylindrically,symmetric current distribution (skin effect)over conductor surfaces [1]–[3].Although this approach is computationally highly efficient,it can lead to noticeable errors since the proximity effects cause an uneven current distribution over conductor surfaces.The errors can be quite substantial in the case of signal cables since the insulation is often very thin compared to the conductor diameter,and because there is no metallic screening associated with each conductor.Also,theManuscript received November 05,2008;revised February 12,2009.This work was supported by Nexans Norway.Current version published September 23,2009.Paper no.TPWRD-00796-2008.B.Gustavsen and A.Bruaset are with SINTEF Energy Research,Trondheim N-7465,Norway (e-mail:bjorn.gustavsen@sintef.no).J.J.Bremnes and A.Hassel are with Nexans Norway,Halden N-1752,Norway (e-mail:jarle.bremnes@).Color versions of one or more of the figures in this paper are available online at .Digital Object Identifier 10.1109/TPWRD.2009.2028481capacitance is difficult to calculate because the electric-field pattern is noncoaxial.The limitations of the traditional modeling approach have be-come a major issue in the modeling of umbilical cables for off-shore applications.These cables are used for the control and monitoring of subsea equipment,which is needed for operating oil and gas fields.Umbilical cables normally contain a package of hydraulic flow lines and electrical wires for the transfer of signal and power.Some of the recent developments involve um-bilical cables in excess of 100km,being the dominating cost of the control system.For these long cables,the signal attenuation in the kilohertz range is often a dimensioning criterion for the cable design and,thus,its cost.The ability to accurately calcu-late the electrical parameters of these cables is made difficult even further by magnetic induction effects in the hydraulic flow lines and the external armor as well as the rotation of elements within the cable.One way of accurately taking the skin and proximity effects into account is with the use of the partial subconductor equiva-lent circuit method [4]but the approach can be very demanding in computer resources [5].The capacitance associated with non-coaxial fields can be calculated by using the harmonic expansion method [6]but that method can be difficult to apply for the non-homogenous insulations encountered in signal cables.On the other hand,the finite-element method (FEM)[7]al-lows to take into account the actual (uneven)current distribution over conductor surfaces and to handle noncoaxial electric fields.A particularly suitable formulation for impedance calculations is the one introduced by Weiss and Csendes [8],which gives the impedances as part of the solution vector.That approach has later been adopted in many works [9]–[11].Other formulations can also be used (e.g.,[12]).This paper describes a computational tool (UFIELD)that has been created specifically for the modeling of umbilical cables.The approach is based on 2-D FEM for calculating the series impedance and the shunt capacitance.Within UFIELD,a dedi-cated signal module has been developed which is used for the design and analysis of umbilical cables for control applications.The module achieves a highly effective work environment through a library of predefined,high-level elements,such as signal cables,pipes,and armoring.Appropriate excitations and boundary conditions are automatically generated while considering the effect of twisting.The FEM implementation is validated against an analytical solution for a coaxial con-ductor arrangement.Finally,the implementation is compared with measurements on the Snøhvit control umbilical and an electrical element of the Ormen Lange control umbilical.0885-8977/$26.00©2009IEEEFig.1.1System matrix.II.I MPEDANCE AND C APACITANCE C ALCULATIONS A.ImpedanceThe objective is to obtain the per-unit-length voltage drop along a set of parallel conductors due to a specific current ap-plication.At any longitudinalposition ,the series impedancematrix relates the phase currents to the voltagedrops(1)The relevant 2-D field problemis(2)where the magnetic vectorpotential and the current sourceterm are inthe direction.The voltage drops in (1)due to a current application can be directly calculated by an FEM formulation for (2)that was in-troduced by Weiss and Csendes [8].That approach leads to theaugmented (3),shown for the single conductorcase.is the conductor surface area and is the total conductor current.The left partition of (3)has one column for each mesh node.For de-tails regarding matrix assembly,we refer to[8](3)Equation (3)naturally extends to the multiconductor case by introducing one additional row and column for each conductor.For a given current application ,the voltagedropsare now directly available in the solution vector.The building of the system is illustrated in Fig.1for a two-conductor system,assuming a triangular mesh and first-orderelements.denotes the triangle area.B.CapacitanceThe relevant field problem in nonconductive regions is given by the ellipticequation(4)where is the scalar electric potential.With the voltage on conductor surfaces and the cable surface taken as boundary conditions,the fieldsolution in the solution region is calculated by using the FEM via theenergyFig.2.Two-layer control umbilical.Twisting of electrical elements and layers.(5).The approach is standard and can be found in many works[12](5)III.T WISTING E FFECTSControl umbilicals contain a number of elements,such as signal cables and steel pipes,for hydraulic flow (see Fig.2).The objective is to calculate the electrical parameters with re-spect to a selected signal element,the active element.In prac-tice,every electrical element (pair,triad,quad)is twisted around its own axis to minimize crosstalk.In addition,the elements are often organized in layers that are twisted in opposite directions to achieve torsion stability.The following twisting effects occur for the electrical parameters of the active element.1)Element twisting:The twisting of the active element causes the lateral distance between a conductor within the element to conductors and pipes outside the element to vary peri-odically along the umbilical.As a consequence,currents in the active element without external return will not induce any net current in conductors/pipes external to the element.In addition,a small increase of the loop inductance results due to a magnetic-field component in the longitudinal di-rection [13].2)Layer twisting:For a fixed rotational position of the ac-tive element,the lateral distance to elements in other layers varies periodically along the umbilical.In addition,the el-ements within the layer experience a small length increase which increases the electrical parameters of signal cables within the layer.The twisting effects are in this paper accounted for by aver-aging the impedance parameters for several rotational positions and by usage of appropriate boundary conditions,more about this in Section V.IV .E XCITATIONSA.Operational ModesA dedicated signal module has been created for the analysis of control umbilicals.The user selects an electrical element (pair,GUSTA VSEN et al.:FINITE-ELEMENT APPROACH FOR CALCULATING ELECTRICAL PARAMETERS 2377TABLE IO PERATIONAL M ODE ,A CTIVE E LEMENT ,P ARAMETER TYPETABLE IIP ARAMETER T YPE AND A SSOCIATED EXCITATIONtriad,quad)within the umbilical,for which electrical parameters are to be calculated (active element),and specifies a mode of operation.Valid combinations of operational modes and active elements are listed in Table I,as well as the type of parameters that are generated.For instance,for a triad element,the user can in the three-phase mode request to calculate positive-and zero-sequence parameters,and in the signal mode,request to calculate loop parameters associated with two of the phases.Table II lists the excitations that are associated with the various parameter types.(The phantom mode is used for power supply over quad elements).In Table II,the quad phase numbering is such that the loop excitation constitutes a diagonal pair.B.Impedance CalculationThe impedance associated with a parameter type is calculated via a single current excitation,applied to the active element.For instance,the positive-sequence impedance of a triad is calcu-lated by applying the currentvector(6)From the obtained column vector ofimpedances ,the posi-tive-sequence impedance is calculatedas(7)In calculations without ground return (i.e.,positive sequence,phantom,and loop),the rotation of the active element will pre-vent the induction of any net current in other conductors and pipes;only eddy currents will be induced.This condition is en-forced by specifying zero (net)current on neighbor conductors and pipes.In zero-sequence calculations,the rotation of the active el-ement will not prevent net currents from flowing in grounded pipes and armors.This situation is handled as follows.Consider a triad element.The triad phases are given conductor numbers 1,2,3,and all grounded conductors (pipes,armors)are given a common conductor number 4.Conductors of other electricalelements are given separate phase numbers().Equa-tion (3)is solved two times,the first time when applying a cur-rentand the second time with acurrent .The calculated voltage drops on the triad con-ductors are averaged and the induced voltage on ungrounded conductors is ignored.This defines the22system (8),where subscripts 1and 2,respectively,denote the triad equivalent con-ductor and the grounded pipes/armors equivalentconductor(8)In order to take into account the effect of zero-sequence cur-rents in the sea external to the FEM solution boundary,we adda common impedanceterm to allelementsof (8),similar to [9].This term is taken as the inner surface impedance of a conductor with infinite thickness and innerradius and is equalto the radius of the (circular)FEM solution boundary().The surface impedance [14]can be writtenas(9)Finally,the equivalent pipe/armor conductor is eliminated byspecifying in (8).This modeling permits net cur-rents to flow to earth through grounded conductors as well as currents to circulate among them.The effect of the twisting on lateral distances is accounted for by calculating the series impedance for several rotational posi-tions,from which an average value is calculated.This accounts for element twisting and layer twisting.The FEM solution boundary is taken as circular with radius at least ten times the conductor separation of the active cableelement.The Dirichletconditionis specified on the boundary.C.Capacitance CalculationThe capacitance associated with an excitation type (Table II)is calculated via a single voltage excitation.For instance,the positive-sequence capacitance is calculated by applying a voltagevector(10)The capacitance obtained from the energy by (5)is directly equal to the positive-sequence capacitance.Umbilical cables are always flooded when in service.This means that the sea water penetrates the cable and,therefore,produces a zero electric potential on the surface of all elements.This greatly simplifies the capacitance calculation since only the (active)electrical element needs to be considered in the analysis.V .I MPLEMENTATION I SSUESputational PlatformMatlab with the PDE Toolbox [15]was selected as a computa-tional platform.The PDE Toolbox is a collection of open-source m-files that can create and solve the relevant field problems,and it has support routines for mesh generation and plotting of re-sults.The toolbox is used for generating the partition2378IEEE TRANSACTIONS ON POWER DELIVERY,VOL.24,NO.4,OCTOBER2009Fig.3.Signal pair element and userinput.of the system matrix for the impedance problem(3),whilethe remaining rows and columns are created separately as shownin Fig.1.The toolbox is also used for creating and solving thecapacitance problem,directly giving the requiredenergy in(5).Another advantage of this platform is the ability to seam-lessly create and integrate user interfaces and auxiliary pro-grams within the Matlab environment.B.Parametrized ElementsA complete umbilical cable is assembled by picking prede-fined elements from a menu.For instance,the specification ofa pair element without armor is performed as shown in Fig.3.(Extra menus are available for changing material properties).With each element,a routine is associated that creates a defini-tion of geometry and material properties for the element.Thisapproach has several advantages as follows.1)Automated computation of the exact geometry data asso-ciated with a given element.2)Automated specification of boundary conditions associ-ated with a given excitation,see Sections V-B and C.3)Robust mesh generation.For instance,small overlaps be-tween the insulators in Fig.3are deliberately introduced toavoid the problem of extremely sharp elements at boundaryintersections in the capacitance problem.Fig.4shows the row-wise decomposition of the pair ele-ment in Fig.3into subelements.(The current implementation ofUFIELD defines elements from circular subelements).Thefirstcolumn defines the phase numbering.Negative integers “”and“”denote semiconductors and insulators,respectively.Grounded conductors would be denoted by a zero.Further pa-rameters are the subelementposition and the elementouterradius.The last column(ph#)is used for associatingaFig.4.Generated datafile for the pair element(loop excitation).semiconductor with a conductor,for use in the capacitance cal-culations.Only thefirst few digits are shown in Fig.4due tospace limitations.By concatenating the datafiles of all elements in the givencase,a complete description is obtained which is further pro-cessed for use in the impedance and capacitance calculations.C.Mode of OperationThe user chooses a mode of operation(signal,power,or threephase)and selects the element(pair,triad,quad)for which theelectrical parameters are to be calculated.This information isneeded for assigning the phase numbering and for the postpro-cessing of the result from the FEM computations as describedin Section V.For the impedance calculation,the user must alsospecify the frequency and temperature.D.Adaptive Mesh GenerationThe mesh is generated by using the routine adaptmesh.m inthe PDE toolbox.Here,an initial mesh isfirst generated andnew triangles are added where the change to the electric(ormagnetic)field is largest.The process of solving and addingnew triangles is repeated until a specified number of triangles isreached.E.Semiconductive ScreensSemiconductive screens are normally in contact with metallicconductors and can therefore be removed from the impedanceproblem due to their poor conductivity compared to a metal.In the capacitance problem,the screens are handled by ex-tending the metallic surface to cover the semiconductor.Thiscan be done since the screens effectively short-circuits the elec-tricalfield.F.Temperature EffectsThe impact of the actual temperature on electrical resistivityis accounted for by the standardformula(11)VI.V ALIDATION A GAINST THE A NALYTICAL S OLUTIONThe FEM approach is validated by comparison with the an-alytical solution of the cylindrically,symmetric geometry inFig.5.GUSTA VSEN et al.:FINITE-ELEMENT APPROACH FOR CALCULATING ELECTRICAL PARAMETERS2379Fig.5.Coaxial transmissionline.Fig.6.Loop resistance.The loop impedance associated with the core-sheath loop is given as[1](12)(13)(14)(15)(16)whereand denote the modified Bessel function of the first and second kind,respectively.Figs.6and 7compare the resistance and inductance of the loop inductance with the result from UFIELD,for two different mesh densities.It is seen that the FEM solution approaches the theoretically correct solution as the number of triangular ele-ments ing a 1.3-GHz Pentium processor,the com-putation time for solving the FEM problem was 0.35s and 4.7s for the two mesh densities (excluding the time needed for mesh generation).With the outer shell in Fig.5on ground potential,the loop capacitance is givenby(17)Fig.7.Loop inductance.TABLE III L OOP CAPACITANCETable III compares the theoretical loop capacitance with the solution by FEM.It is seen that increasing the number of trian-gles gives a result that tends to the theoretical solution.VII.E XAMPLE :S NØHVIT C ONTROL U MBILICALA.ProjectThe Snøhvit control umbilical connects the Snøhvit gas field [16]in the Barents Sea with the Melkøya gas treatment plant in Hammerfest,North Norway.The cable length is 144km.The cable contains two triad elements that are used for a three-phase power supply at 3kV ,and two fiber-optics cables for signal transmission,see Fig.8.Backup of the signal transmis-sion is achieved by superimposing a signal voltage on two of the conductors.B.Modeling of Triad Single Element Each conductor of the 25mm triad elements (Fig.8)consists of seven round strands that have been compacted and squeezed through a nozzle.A semiconductive layer has been sprayed on top of the conductors.Each triad is fitted with polyethylene (PE)filler elements and a PE jacket,with petroleum jelly filling the voids.Fig.9shows a UFIELD representation of the triad element by seven round (uncompressed)strands.The outer surface of the semiconductive layer is seen to be parallel to that of the strands,similar to that as in Fig.8.The conductor resistance is chosen to be equal to the measured resistance at dc.Geometrical data and material properties are given in Table IV.The capacitance associated with the signal transfer on twophases is calculated by applyingvoltagesto the three ing adaptive meshing,an initial mesh of 2287elements was increased to 5133elements (total computa-tion time:4.4s).This gave a capacitance of 69.1nF/km.The re-sulting field pattern is shown in Fig.10.Note that the conductors2380IEEE TRANSACTIONS ON POWER DELIVERY ,VOL.24,NO.4,OCTOBER2009Fig.8.Snøhvit umbilicalcable.Fig.9.UFIELD representation of Snøhvit 3-kV triad element.TABLE IVT RIAD E LEMENT DATAhave been automatically extended to cover the semiconductors,as explained in Section VI-E.The series impedance is calculated by specifying a currentapplication.Fig.11shows the resulting current density (magnitude)on the conductors at 10.1kHz,calculated by (18)as a postprocessing step.It is seen that the current on the twoactiveFig.10.Electricpotential.Fig.11.Current density (f =10.1kHz).conductors is affected by the skin effect and proximity effects,and that eddy currents are induced on the third conductor.The adaptive meshing increased an initial mesh of 8184triangles to 24712triangles in six iterations.Total computation time:30.6s(18)C.Modeling of Triad in UmbilicalFig.12shows the UFIELD geometry model of the complete umbilical cable.The umbilical has two triads,four hydraulicflow lines of super-duplex steel(,),two armored fiber-optics cable,and one 0.4-mm external steeltape armor(200,S/m).The extruded filler elements used for mechanical support (Fig.8)are excluded from the calculations since they do not affect the electrical properties since the sea water will penetrate the umbilical cable.The signal-loop capacitance is the same as for a triad alone,since the triad surface is on ground potential for a flooded um-bilical.In the impedance calculations,the loop impedance de-pends on the rotational angle for the electrically active triad.Here,UFIELD is requested to calculate the impedance as anGUSTA VSEN et al.:FINITE-ELEMENT APPROACH FOR CALCULATING ELECTRICAL PARAMETERS2381Fig.12.Snøhvit umbilical:geometry inUFIELD.Fig.13.Magnetic vector potential (10.1kHz).average of eight rotational angles.Fig.13shows the magnetic vector potential for one of the positions.The associated mesh is shown in Fig.14.A comparison with Fig.13shows that the mesh density is high where the change in the field is high,which is due to the adaptive mesh parison With MeasurementsThe signal (loop)parameters were measured on a 273-m straight segment of the triple element,when submerged in sea water.The parameters are shown in the left part of Table V,as function of frequency,and they are compared with calculated parameters by UFIELD.It can be seen that excellent agreement has been achieved.The right part of Table V shows the corresponding result when the triad has been placed inside the umbilical.In the measurements,the cable is straight and about 300m in length.Again,very good agreement is achieved between measure-ments and computations.A comparison with the left part (triad alone)shows that the presence of neighbor pipes and armor appreciably affects the resistance and inductance.ThecauseFig.14.Triangular mesh.TABLE VM EASURED VERSUS C ALCULATED L OOP PARAMETERSfor the deviations can be related to errors in the assumed values for the resistivity and permeability of the steel tape.In addition,some error will exist for the measurements.It is further observed that the discrepancies between calcula-tions and measured results tend to increase with increasing fre-quency.This result is most likely a consequence of more pro-nounced eddy current effects.At 10.1kHz,the penetration depth in copper is 0.65mm,which is a fraction of the strand diameter of the phase conductors (2.0mm).At such high frequencies,the actual surface shape of the phase conductors will significantly affect the current distribution on the conductors and,hence,the impedance.Indeed,Fig.8shows that the outer surface of the strands have been flattened in the production process,thus de-viating from the assumed circular shape in Fig.9.In order to further improve the accuracy of the computations,one would have to represent the actual shape of the conductors.It is also possible that the measurement errors increase with increasing frequency.2382IEEE TRANSACTIONS ON POWER DELIVERY ,VOL.24,NO.4,OCTOBER 2009TABLE VIC OMPUTATION T IME (IN SECONDS)TABLE VIIC ALCULATED L OOP P ARAMETERS VERSUS S TEEL T APE PERMEABILITYE.Timing ResultsIn order to save computation time,the mesh was created at the highest frequency point (10.1kHz).The obtained mesh was then assumed to be adequate for all of the five frequencies.Table VI summarizes the computation time for analyzing the triad alone and triad in umbilical cases (1.3-GHz Pentium processor).The computation time for the triad in umbilical is for a single rota-tional position,requiring a minimum of 45000triangles.(The computation time with the eight rotational positions in Table V is about eight times higher.)F .Sensitivity AnalysisThe steel tape armor has,in reality,a nonlinear relative per-meability whereas a constant valueof 200was used in this study,similar to [17].The relative permeability is usually taken as 300for three-phase cables with steel-tape armoring,ac-cording to IEC 60287[18].For the considered umbilical cable,one can,however,expect lower magnetic-field strengths than in power cables,due to the much lower current levels.It is there-fore possible that the permeability is substantially lower than 300.Table VII shows the calculated resistance and inductance at 50Hz and 6kHz,for alternative valuesof .It is seen that increasing the permeability from 200to 400changes the elec-trical parameters by less than 1%.Reducing the permeability to a value of 10reduces the inductance by 3.2%at 50Hz and by 2.6%at 6kHz,while the reduction in resistance is by 1.3%at 6kHz.VIII.E XAMPLE :O RMEN L ANGE Q UAD E LEMENTThe Ormen Lange gas field [19]in the Norwegian Sea is con-trolled from Nyhamna in Møre,mid-Norway,via two umbilical cables.Cable length:125km.In the following text,we show results for one of the 13.3mm quad elements that is used in the umbilicals,see data in Table VIII.The quad element is used for the power supply (phantom)and signal transmission (loop)on diagonal pairs.Each conductor has seven copper strands and is fitted with a semiconductive layer,see Fig.15.It is observed that the strands are almost completely round and that theouterFig.15.Ormen Lange 3-kV quadelement.Fig.16.UFIELD representation of the Ormen Lange quad element.TABLE VIII Q UAD E LEMENT DATAsurface of the semiconductors follows that of the strands.The representation in UFIELD is shown in Fig.16.Table IX compares measured and calculated values for loop and phantom parameters.The impedance measurements were made on a 272-m straight cable on land while the capacitance measurements were made on a 280-m cable on drum,sub-merged in water.It can be seen that very good agreement has been obtained for the resistance and inductance,both for the loop mode and the phantom mode.The deviation is,however,substantial for the loop resistance at 15.5kHz and 50kHz.Also,the calculated capacitance is too low by about 2%for the loop and phantom modes,respectively.Note that the loopGUSTA VSEN et al.:FINITE-ELEMENT APPROACH FOR CALCULATING ELECTRICAL PARAMETERS 2383TABLE IXM EASURED VERSUS .C ALCULATED P ARAMETERS .(16C )(Q UAD A LONE)inductance values as calculated by UFIELD have been scaled by a factor of 1.02to account for the twisting of the element (300-mm lay length).The factor was obtained based on the procedure described in [13]which considers the magnetic-field component in the longitudinal direction.IX.D ISCUSSIONApplication of UFIELD to the Snøhvit control umbilical has demonstrated its ability to predict electrical parameters in the kilohertz range with high accuracy.Close agreement with mea-surements was achieved for the loop values of resistance,in-ductance,and capacitance,although the resistance was under-estimated at high frequencies.It was also shown that the re-sistance and inductance values increase substantially when the signal cable is placed within a complete umbilical.In practice,this means that the impedance must be recalculated for each um-bilical cable design.Good agreement with measurements was also achieved for loop and phantom parameters of the Ormen Lange quad element.The cable parameters are quite sensitive to the inaccuracies in the geometry description.In particular,the representation of the conductors is difficult since the conductor surface depends on the manufacturing process.Table X shows the effect of treating the conductors of the Snøhvit triad cable as massive (single strand)rather than seven round strands.(The massive conductor has the same outside diameter and dc resistance).It is seen that ignoring the stranding leads to a substantial reduction of the loop inductance,at all frequencies.In addition,representation by a single strand increases the loop capacitance,as shown in Table XI.Other errors result from variations in the thickness of the insulation layers and from the deviation of their assumed circular shape.The latter is easily observed by comparing the outer surface of the Ormen Lange quad element (Fig.15)with that of the model (Fig.16).TABLE XT RIAD L OOP I NDUCTANCE VERSUS C ONDUCTOR M ODELING (T RIAD A LONE)TABLE XIT RIAD L OOP C APACITANCE VERSUS C ONDUCTOR M ODELING (T RIAD A LONE)TABLE XIIT RIAD L OOP I NDUCTANCE VERSUS B OUNDARYC ONDITIONS (T RIAD IN U MBILICAL)The material properties may also be difficult to acquire.In this paper,the correct dc resistance was obtained from mea-surements.The relative permittivity of the jelly was obtained by measurements while all remaining material parameters are assumed values.Correct specification of boundary conditions is also im-portant.Table XII shows the effect of incorrectly treating the steel pipes and armoring as grounded,during the impedance calculations.As was explained in Section V-B,grounding these conductors (and the copper conductors)will result in net cur-rent flows in these conductors in addition to the eddy currents.The net current component leads to a magnetic shielding effect which,in turn,reduces the loop inductance at high frequencies.X.C ONCLUSIONThis paper has introduced a systematic approach for the cal-culation of electrical parameters of umbilical cables by 2-D fi-nite-element computations.1)The impedance matrix is calculated by the approach by Weiss and Csendes and the capacitance matrix is calculated via the energy of the electrical field.2)Usage of predefined definitions for the various cable ele-ments (signal cables,pipes,armors)allows assembling a complete umbilical in a short time.3)The twisting of elements and layers is accounted for by averaging the impedances for several rotational positions,and by appropriate usage of boundary conditions.4)The accuracy of the procedure has been verified against theoretical solutions.。
海底脐带缆系统软件的设计与分析
海底脐带缆系统软件的设计与分析作者：王劭文隋国荣来源：《软件工程》2020年第10期摘 ;要：海底脐带缆为海底设备提供必要的能源动力、传输状态控制信号以及注入相关化学药剂。
在深海作用下，构件之间的非线性效应使脐带缆的设计和分析非常重要。
在脐带缆的结构和力学分析等理论基础上，根据不同用途的脐带缆特性，通过基于软件编程，实现海底脐带缆分析和设计软件，可以实时显示截面图，并输出相关结构尺寸和电气参数特性，具有截面力学分析等功能。
与国外同类软件设计结果相比，平均相差在5%以内，可以很好地满足国内生产实践和实际铺设的需求。
关键词：海底脐带缆;非线性效应;结构设计;力学分析;WPF编程中图分类号：TP319 ; ; 文献标识码：ADesign and Analysis of Submarine Umbilical Cable System SoftwareWANG Shaowen， SUI Guorong（School of Optical-Electrical and Computer Engineering， University of Shanghai for Science and Technology， Shanghai 200093， China）wangsw28@; suigr@Abstract： Submarine umbilical cable provides necessary energy and power， transmits the status control signals and injects the relevant chemicals for submarine equipment. Under the deep sea， the nonlinear effect between components makes the design and analysis of umbilical cable very important. Based on the theory of structural and mechanical analysis of umbilical cable， and the characteristics of umbilical cable for different purposes， the software for analysis and design is realized through software programming. The software can display the cross-section in real time， and output the relevant structural size and electrical parameter features. It has the function of cross-section mechanical analysis， etc. Compared with the same kinds of foreign software， the average difference is less than 5%， which can meet the needs of domestic production and the actual laying.Keywords： submarine umbilical cable; nonlinear effect; structural design; mechanical analysis; WPF （WindowsPresentation Foundation） programming1 ; 引言（Introduction）目前，深海油气资源开发采用水下生产系统技术，将海洋油气生产设备及辅助设施部分或者全部置于海底，完成自動采油、集油、输油生产等工作。
水下生产系统用脐带缆试制关键工艺介绍
水下生产系统用脐带缆试制关键工艺介绍陈凯;夏峰;叶信红;郭宏;张永明;钟科星【摘要】水下生产系统用脐带缆一般由电、光纤、液压管道、化学药剂管道等多种不同单元组成.用于连接上部平台与水下生产系统,并作为电液控制、电力和化学药剂的通道[1].脐带缆制造对生产设备、工艺等有特殊的要求.介绍了脐带缆多单元多层次截面设计及成缆和钢管单元形变控制等关键制造工艺.【期刊名称】《电线电缆》【年(卷),期】2012(000)002【总页数】3页(P11-13)【关键词】脐带缆;多单元多层次成缆;钢管单元;形变控制【作者】陈凯;夏峰;叶信红;郭宏;张永明;钟科星【作者单位】宁波东方电缆股份有限公司,浙江宁波315040;宁波东方电缆股份有限公司,浙江宁波315040;宁波东方电缆股份有限公司,浙江宁波315040;中海油研究总院,北京100027;宁波东方电缆股份有限公司,浙江宁波315040;宁波东方电缆股份有限公司,浙江宁波315040【正文语种】中文【中图分类】TM2490 引言脐带缆是水下生产系统的关键组成部分之一，主要作用是为水下生产系统提供电气液压动力、化学注入通道，同时为上部模块控制信号以及水下生产系统提供数据传输通道。
长期以来，我国使用的脐带缆全部依赖进口，对这一产品的关键技术研究尚属空白，且不具备脐带缆系统设计、分析、制造等的能力，这些都在一定程度上制约了我国深海油气田的开发。
宁波东方电缆股份有限公司通过承担由中海油研究总院牵头的863脐带缆项目的子课题——脐带缆的生产制造，成功试制出一条针对我国南海深海油气田用脐带缆初样缆。
近期交于上海电缆研究所、大连理工大学等相关合作单位完成力学和电气性能等测试。
1 多单元多层次截面设计及成缆不同于普通海缆的单芯或三芯结构，脐带缆除电单元和光纤单元外，往往还包含数量不等的液压、化学药剂管道单元。
本次试制的脐带缆包含:3根4芯6 mm2电缆单元;6根内径12.7 mm的不锈钢管单元;1根光单元。
钢管脐带缆弯曲刚度有限元分析
Ｆｉ ． Ｓ ｃ ｉ ｎ ｏ ｔｅ ｕ ｅ ｇ２ ｅ ｔ ｆ ｅｌ ｂ ｏ ｓ ｔ ｕ ｍｂ ｌ ａ ａ ｌ ｉｃ ｌ ｂｅ ｉ ｃ
种滑动假设 ， 认为随着弯曲变形 ， 螺旋应沿最短的路 径进 行 滑动 ， 即除沿 轴 向有 滑 动之 外 还应 考 虑侧 向
滑动， 由此得到螺旋曲率 的变化 ， 进而得到螺旋的应 力分布和滑动位移情况 ； Ｕ Ｏ Ｔ等 采用相同的假设 进行分析， 认为该假设得 到的滑动值是实 际值 的上 界 ；Ｒ ＩＣ ＮＣ等 认 为 由于 摩擦 和 接 触 压 力 的 Ｋ ＡＮ Ａ Ｉ 存在 ， 弯曲刚度应随曲率变化．
快速预测刚度值 ， 但结果的精度往往不高． 由于钢管 脐带缆结构复杂且涉及大变形 、 间接触和摩擦等 层 非线性 问题 ， 在计算力学和计算机科学飞速发展的 今天 ， 越来越多的钢管脐带缆结构分析采用以有 限 元法为代表 的数值模拟方法． 钢管脐带缆数值分析
可 很好 地克 服理 论 分 析 的缺 点 ， 仅 可 以 考 虑构 件 不
件以一定角度缠绕 中心钢 管组成 ， 最外层 由聚合物 护套进行 保护 ， 钢管脐带
缆截 面 见 图 ２ 钢 管 脐 带 ． 缆 的功 能构 件如 下 ： （ ） 单 元 ． 括 中 １管 包 心 管单 元 和 外 部 管 单 元 ， 其 内部 为 钢 管 、 部 为 聚 外
图 ２ 钢管脐带缆截面
填充和聚合物 护套组成 ， 见
图 １ ．
很多学者对预测弯曲载 图１ 典型钢管脐带缆
荷 作用 下螺 旋结 构 的响应进 Ｆｇ１ ｙｉｌｔ ｌｕｅ ｉ Ｔｐ ａｓｅｔ ・ ｃ ｅ ｂ 行 研 究 ． Ｏ Ｔ Ｌ Ｏ 等 以 Ｃ ＳＥ Ｌ ｕ ｉｃｌａｌ ｍｂｉ ｂ ｌａｃ ｅ
一种海底电缆载流量和温度场的确定方法[发明专利]
![一种海底电缆载流量和温度场的确定方法[发明专利]](https://img.taocdn.com/s3/m/9bf69213aef8941ea66e05df.png)
专利名称：一种海底电缆载流量和温度场的确定方法专利类型：发明专利
发明人：宣耀伟,张健,徐政,刘畅
申请号：CN201310615883.2
申请日：20131127
公开号：CN103616588A
公开日：
20140305
专利内容由知识产权出版社提供
摘要：本发明公开了一种海底电缆载流量和温度场的确定方法，包括如下步骤：（1）确定电缆截面所在二维平面中的土壤感温区域；（2）对土壤感温区域进行有限元网格剖分得到有限元三角形网络，进而对有限元三角形网络中各结点进行编号；（3）根据电缆电流计算有限元三角形网络中每个三角单元的刚度系数和内热系数；（4）根据刚度系数和内热系数，通过有限元总体合成建立温度场模型如下：KT＝P；求解得到温度场T；（5）根据电缆线芯导体的最高工作温度确定温度场T并代入温度场模型中作为目标向量，求解得到电缆的载流量。
本发明能够灵活地模拟复杂的边界条件和环境参数，相比现有技术更接近电缆实际运行状况，能够得到更准确的结果。
申请人：国网浙江省电力公司舟山供电公司,浙江大学
地址：316000 浙江省舟山市定海区定沈路669号
国籍：CN
代理机构：杭州天勤知识产权代理有限公司
代理人：胡红娟
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一种高压交流海底电缆载流量和温度仿真方法[发明专利]
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专利名称：一种高压交流海底电缆载流量和温度仿真方法专利类型：发明专利
发明人：张镱议,刘捷丰,陈潇铭
申请号：CN202010072838.7
申请日：20200121
公开号：CN111382531A
公开日：
20200707
专利内容由知识产权出版社提供
摘要：本发明涉及一种高压交流海底电缆载流量和温度仿真方法，通过建立基于电磁场、传热场和流体场的海底电缆多物理耦合仿真模型，提出一种计算海底电缆温度和载流量的计算方法，该方法基于电‑热‑流多物理场耦合方程，结合海底电缆实际敷设条件，对海底电缆的温度场和载流量进行监测，可以更方便对海底电缆的运行情况进行监测分析，基于COMSOL仿真的APP可以最大限度用户的需要，运行人员可以根据海底电缆的不同情况设置不同的参数得到海底电缆的温度场和载流量，本技术方法和系统克服海底电缆实体实验成本高、实施困难、数据难以测量等缺点，高效实现海底电缆温度和载流量的仿真计算，对保证电网完全可靠运行和海底电缆的稳定运行有重要意义。
申请人：广西大学
地址：530004 广西壮族自治区南宁市大学东路100号
国籍：CN
代理机构：南宁东之智专利代理有限公司
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有缆无人潜水器用多层脐带缆温度场仿真研究
有缆无人潜水器用多层脐带缆温度场仿真研究
关宇洋;刘志杰;全亚明;张慧甍;陈慧雄
【期刊名称】《电线电缆》
【年(卷),期】2024(67)2
【摘要】脐带缆作为有缆无人潜水器(ROV)电力和信号传输的关键组件,工作时须缠绕在绞车上。
在运行过程中,脐带缆的温升易受内部损耗的影响,并且长期处在高温环境下,会加速绝缘老化,甚至诱发击穿。
为保证脐带缆在作业下安全运行,需要对其电磁和温度特性进行分析。
基于有限元仿真软件COMSOL建立电磁和温度等多物理场耦合模型,结合筒体结构、电缆缠绕层数,以及工作过程中的热传导、热对流等因素,研究了线芯损耗特征与多物理场耦合后的温度分布、散热特性,并分析了脐带缆在不同负载、绕组下对温度场分布的影响,以期为脐带缆的设计和多层脐带缆的配置提供理论支持。
【总页数】4页(P33-36)
【作者】关宇洋;刘志杰;全亚明;张慧甍;陈慧雄
【作者单位】中航宝胜海洋工程电缆有限公司
【正文语种】中文
【中图分类】TM247.9
【相关文献】
1.基于AMESim的脐带缆液压传输特性及等效方法仿真研究
2.全海深ROV脐带缆动力传输验证及温度场研究
3.深海遥控无人潜水器脐带缆动态特性及张力抑制方法
4.6000m无人无缆潜水器无动力潜浮计算机仿真和实测
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基于有限元分析的深海机器人用脐带缆传热特性研究
基于有限元分析的深海机器人用脐带缆传热特性研究
方可可;张维佳;张定华;王勇;涂绍平
【期刊名称】《电线电缆》
【年(卷),期】2024(67)2
【摘要】为研究水上堆叠的脐带缆在海上运行过程中的温升情况,对不同堆叠层数以及缠绕圈数的脐带缆,采用有限元法,分析了脐带缆的最高温度,同时研究了电流、环境温度和太阳辐射对堆叠6层脐带缆最高温度的影响,并利用最小二乘法得到了回归方程。
结果表明,堆叠一层与堆叠两层时,脐带缆的最高温度几乎不变。
而后每增加1层,最高温度上升2℃左右。
随着缠绕圈数的增加,脐带缆温度先增加后减少,为保证良好的脐带缆散热条件,脐带缆缠绕圈数要大于等于6圈。
以电流、环境温度和太阳辐射与脐带缆最高温度之间的变化规律所提出的回归方程,最大误差为1.73%,可为水上堆叠脐带缆最高温度的计算提供一种更简便快速的方法。
【总页数】6页(P27-32)
【作者】方可可;张维佳;张定华;王勇;涂绍平
【作者单位】上海中车艾森迪海洋装备有限公司;中国南方电网有限责任公司、超高压输电公司广州局
【正文语种】中文
【中图分类】TM247;TK11
【相关文献】
1.深海脐带缆总体响应特性研究
2.深海海底钻机用铠装脐带缆有限元分析
3.深海采矿车布放回收中脐带缆轴向张力响应特性研究
4.深海采矿装备布放回收过程中脐带缆动力学响应特性研究
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水下生产系统用动态脐带缆疲劳问题的研究进展与展望
水下生产系统用动态脐带缆疲劳问题的研究进展与展望
尹原超;吴尚华;卢青针;卢海龙;阎军
【期刊名称】《电线电缆》
【年(卷),期】2024(67)2
【摘要】围绕水下生产系统用动态脐带缆(以下简称动态脐带缆)多构件、多层螺旋缠绕的结构特点,全面总结了动态脐带缆疲劳失效形式、疲劳寿命分析方法和疲劳试验测试技术等方向的研究进展。
通过对动态脐带缆疲劳问题研究方法与热点的详细阐述,揭示了该领域的主要研究成果和关键技术难点,展望了动态脐带缆未来发展的主要技术需求和研究方向,为动态脐带缆在海洋油气资源开发中的长寿命工程应用提供了基础理论和技术参考(引用文献104篇)。
【总页数】10页(P1-10)
【作者】尹原超;吴尚华;卢青针;卢海龙;阎军
【作者单位】大连理工大学化工海洋与生命学院;大连理工大学宁波研究院;大连理工大学力学与航天学院
【正文语种】中文
【中图分类】TE53;TM247
【相关文献】
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2.水下生产系统液压控制系统脐带缆液容效应研究
3.半潜式生产平台水下安全关断阀脐带缆系统陆地安装方法
4.水下生产系统脐带缆故障实例应用分析
5.水下生产系统用钢管脐带缆力学性能研究
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圆导线， 电缆材料的传热参数为常数； （ 2 ） 电缆负荷电流和环境温度不变， 温度分布 不考虑电缆分布电容对温度分布的 不随时间变化， 影响；
· 6·
2013 年第 3 期 No． 3 2013
电线电缆 Electric Wire ＆ Cable
图5 不同缆芯结构温度分布
6
结束语
5
优化确定载流量
脐带缆是由电缆、 光纤、 不锈钢管等多种结构单 涉及多种工程材料， 必须采用 元组成的复杂组合体， 有限元数值分析求出脐带缆复杂截面各部分温度实 际分布情况， 计算其最热点温度， 从而找到最热点， 验证整体结构在运行中的长期散热合理性 ， 同时按 照有限元温度场分析， 可以得到实际的载流量。 本文采用基于有限元法的 ANSYS 软件对不同 结构脐带缆温度场进行分析， 通过对脐带缆结构温 度场的分析发现， 脐带缆端面各单元、 各部件之间的 结构散热效果好， 载流量也越大。 空气隙比例越少， 对温度场分布而言， 其分布受缆芯结构的影响较大， 当电缆单元集中在中心位置时， 散热情况较差， 此时 载流量仅为中心管单元结构的 53% ， 应当避免在设 计脐带缆时要避免将电缆单元置于中心位置 。
0
引
言
不适于计算结构复杂的脐带缆 其计算存在局限性， 因此本文采用有限元法确定脐带缆 中温度场分布， 载流量与各部分温度。
经济的快速发展必然导致人类对能源需求的加 大， 尤其是不可再生资源石油， 作为国家经济的血 石油的储存量越来越少， 为缓解这种现状， 加快 液， 海洋油气资源开发已成为国家战略需求 。水下生产 系统脐带缆 （ 以下简称脐带缆 ） 作为水下生产作业 设备的生命线， 在我国长期以来依赖进口， 对这一方 因而在一定程度上制 面的关键技术研究尚属空白， ［1 ］ 约了我国深海油气田的开发 。 从国内外发展现状来看， 发达国家对水下生产 ［2 ］ 系统脐带缆的研究已较为成熟 ， 国外很多学者采 用解析和数值方法对脐带缆整体和截面进行了分 析， 但这些分析大多是关于力学性能方面的研 究
图4 脐带缆计算单元剖分
图 5b 为中心钢管单元的脐带缆端面结构 ， 在脐 带缆管单元内液体最大工作温度同样为 70 ℃ ， 工作 电流 58A 时， 脐带缆最热点温度为 88. 974 ℃ ， 接近 交联聚乙烯的允许温度 90 ℃ 。可见， 中心电缆单元 的散热情况极差， 其理论载流量仅为中心管单元的 53% ， 实际设计脐带缆端面结构时应尽量避免采用 电缆单元位于脐带缆中心部分的绝缘结构 。 可见， 采用有限元分析的方法分析复杂结构的 温度情况， 得出最热点温度值， 可以最终得到电缆导 体的理论载流量值。这种分析方法比传统的热阻热 路计算法更适宜复杂截面或特殊环境下的电缆载流 量计算。
［3 ］
1
水下生产系统脐带缆简介
水下生产系统脐带缆的主要作用是连接上部模 块与水 下 生 产 设 施， 主要由电缆（ 动力缆或信号 缆） 、 光缆（ 单模或多模 ） 、 液压或化学药剂管 （ 钢管 聚合物护套、 铠装钢丝以及填充物等组 或软管 ） 、 紧凑和圆整， 本 成。脐带缆各单元排布上讲求对称、 文将对两种典型脐带缆缆芯结构进行载流量分析 （ 见图 1 ） 。
ห้องสมุดไป่ตู้
2 传统热路法计算电缆载流量
根据电缆绝缘材料的种类、 运行和使用经验， 各 种型式电缆的长期和短时允许最高工作温度都有规 定。一般说来， 如果电缆长期和短时工作温度不超 过规定值， 电缆应能在至少 15 年内安全运行； 反之， 如果电缆工作温度过高， 绝缘材料老化就会加速， 电 缆寿命就会缩短， 甚至立刻遭到破坏。因此， 在设计 或选用电缆时， 除了充分考虑电气、 机械性能外， 还
· 7·
2013 年第 3 期 No． 3 2013
电线电缆 Electric Wire ＆ Cable
2013 年 6 月 Jun．， 2013
图6
载流量优化曲线
2 导线截面积 （ mm ） ； ρ20 为铜导体 20 ℃ 电阻率， 取
0. 0175 Ω·mm2 / m； α 为 铜 导 体 电 阻 温 度 系 数， 取 0. 0039 / ℃ 。 根据式（ 6 ） ， 当电缆绝缘达到交联聚乙烯的允 90℃ ， 许温度 时 中心钢管单元脐带缆的载流量理论 计算结果为 I n = 59. 4 A。
图3
ANSYS 温度场分析流程
虑到导体集肤效应和邻近效应的影响， 导体交流电 阻 R C 为： R C = R0 （ 1 + Y s + Y p ） （ 4） R0 为导体在 20 ℃ 时的直流电阻； Y s 为导体集 式中， 肤效应系数； Y p 为导体邻近效应系数。 除导体损耗外， 结构的发热还与绝缘材料有关， 根据电介质物理理论， 介质损耗与外施电压及材料 特性有关， 每相单位长度的介质损耗 P D 为： P D = ωCU2 tan δ （ 5） 式中， ω = 2 πf ； C 为单位长度电缆电容 （ F / m ） ； U 为相电压（ V） ； tan δ 为材料介质损耗因数。 由于计算的脐带缆电压等级并不高， 而且电缆 单元绝缘一般采用聚乙烯等非极性材料，tan 值极 小， 因而这部分损耗也较小， 一般可忽略不计。 在大多数情况下， 电缆金属护套 （ 包括铠装 ） 要 求牢固接地， 因为这样的联接方法简单， 可以免除护 套中感应电势造成对电缆安全运行的危害 ， 同时系 统往往需要金属护套作为接地电流通路， 因此会产 生损耗。电缆金属护套损耗的计算中， 多芯电缆的 ， 线芯中电流之和为零 且线芯的几何中心重合时， 多 芯电缆护套中感应电动势和损耗才等于零 ， 而事实 上， 线芯的几何中心并不重合， 他们之间的距离和线 芯直径是同一数量级的数值。 因此， 多芯电缆护套
， 关于电场、 温度场的分析较少。 研究脐带缆的载流量、 各部分温度分布是确保
［4 ］
脐带缆安全可靠运行的基础
0301 收稿日期： 2013-
。 传统热路法由于
基金项目： 国家 863 计划资助项目（ 2009AA09Z301 － 1 ） 作者简介： 郭 宏（ 1968 － ） ， 女， 高级工程师． 100027］ ． 作者地址： 北京市东城区东直门外小街 6 号［
T 为温度场内各点温度； λ 、 c、 Q 分别为微元的 式中， 比热、 导热量。 导热系数、 对于脐带缆情况符合第三类边界条件， 即已知 对流换热系数与流体温度， 其平衡方程组为：
{
2 2 T T 2 + 2 = 0 x y T －λ | = h（ T － T f ） | n Γ
（ 2）
应仔细分析其热性能， 使电缆在保证传输容量的条 件下， 各部分损耗发热不致超过电缆允许最高温度 。 通常， 根据热路法计算使线芯导体达到最大允 许温度时的连续电流， 原理如图 2 所示。
图2
载流量热路计算原理
一般有限元分析步骤如下： 首先利用软件自带 建模平台或借助第三方 CAD 软件建立分析所对应 的二维或三维模型； 而后对模型中涉及到的各部分 材料相关特性参数进行分别定义； 选择适当的三角 或其它单元类型与网格精度划分计算网格 ； 在对应 边界加载各种正确的载荷条件； 最后运行求解器， 进 行有限元计算， 得到各单元温度分布情况。 本文分 析脐带缆温度场的流程如图 3 所示。 3. 3 热负荷计算与加载 根据上面分析的热平衡控制方程和边界条件可 以看出， 若要计算温度场的分布， 除了边界条件为已 知值外， 还需获得场域内热源的单位发热率。 对于 电缆单元， 其热源主要有导体交流损耗、 绝缘层介质 损耗和金属层涡流损耗。 单位长度的电缆内导体的发热功率 P C 为： P C = I2 C ·R C （ 3） I C 为导体负荷电流； R C 为导体交流电阻。 考 式中，
对于特定结构电缆， 参照各类标准， 可以根据电 缆结构及敷设条件给出等值热路， 求出线芯电阻及 电缆和周围媒质的热阻， 最后列出电缆热平衡方程， 即可得电缆恒定负载连续额定载流量 。但由于海底 脐带缆内部结构复杂， 且敷设环境比较特殊， 所以传 统的计算方法无法满足要求。
3
3. 1
稳态载流量计算的有限元法
Γ
W/（ m · K） ］ ； h 为对流换热系 式中， λ 为导热系数［ W/（ m · K） ］ 。 数［
图1 典型的脐带缆结构示意图
温度场分析即对脐带缆整个区域进行总体合 ， 成 得到相应的矩阵， 求解后可以得到各点温度值。 实际脐带缆绝缘结构温度场分析中上述矩阵的求解 ［56 ］ 。 ANSYS 作为 是借助大型有限元软件来实现的 它在分析温度场方面有 大型通用有限元分析软件， ANSYS 程序有着 着许多别的软件不可比拟的优势， Workbench 界面操作起来， 良好的图形界面， 其快速 的网格划分功能以及强大的结果后处理功能 ， 都让 分析得心应手。 3. 2 计算流程
2013 年 6 月 Jun．， 2013
中的损耗并不等于零， 只是比单芯电缆护套中损耗 小得多， 为便于分析， 暂不考虑影响。
4
结果与分析
实际计算采用四层铠装脐带缆结构， 实际分析 2 计算的导体线芯面积 6. 0 mm ， 对比中心电缆和中 心钢管两种结构， 详细的温度场模型单元剖分如图 4 所示。对两种截面的脐带缆进行热分析， 结果如 图 5 所示。图 5a 为中心电缆单元的端面结构， 在脐 带缆管单元内液体最大工作温度为 70 ℃ ， 工作电流 31A 时， 脐带缆最热点温度为 89. 885 ℃ ， 接近交联 聚乙烯的允许温度 90 ℃ 。
The Finite Element Method of Temperature Field and Ampacity Analysis of Umbilical Cable GUO Hong1 ，GAO Huan2
（ 1． CNOOC Research Institute，Beijing 100027 ，China； 2． Shanghai Electrical Cable Research Institute，Shanghai 200093 ，China） Abstract ： The finite element method was used in this paper solving the limitation of traditional thermal circuit analytical method． The software of ANSYS was used to analyze the submarine umbilical cables models with complex structure，and results of the whole temperature field distribution were shown by comparing the difference of temperature field distribution in different cables． Moreover， the optimum calculating method of ampacity is given for design of umbilical cables． Key words： umbilical cable； ampacity； finite element method