覆冰输电导线气动力特性风洞试验及数值模拟研究
|
摘要
在特殊的气象条件下,输电导线可能在其迎风面结冰,具有翼形的某些特征,从而使导线发生大幅、低频的自激振动,即舞动。近年来我国电网规模发展迅速,恶劣气候频繁出现,输电线路的覆冰和积雪以及由此衍生的导线舞动已经严重威胁着电力及通信网络的安全运行。覆冰导线的气动力参数是舞动试验研究及计算分析的关键因素,虽然已有一些试验结果,但由于覆冰的随机性和多样性,数据仍十分缺乏,积累更多覆冰导线的气动力参数具有重要的意义。
本文详细回顾了国内外有关覆冰导线的气动力试验研究,提出了存在的缺点与不足。在此基础上通过风洞试验及CFD数值模拟方法研究了不同厚度新月形覆冰和D形覆冰截面单导线及分裂导线的气动力特性。
风洞试验方面：制作了刚性节段模型,通过高频测力天平试验研究了D形和4种新月形覆冰厚度输电导线的气动力特性。设计了考虑流场二维特性和风洞的边界层效应的试验装置,获得了各覆冰截面单导线和分裂导线子导线在均匀流、5%均匀湍流和13%均匀湍流3种流场中各风攻角下的气动力特性,研究了气动力系数对攻角的变化规律,以及湍流度对气动力特性的影响。比较了单导线与二、四、六分裂导线之间气动力特性的区别与联系。根据Den Hartog和Nigol舞动理论分别计算了各种工况下覆冰导线可能发生舞动的风攻角范围。
CFD数值模拟方面：通过CFD数值模拟方法,对雷诺数为3900的经典圆柱绕流问题进行了非定常计算,详细研究了近壁面网格及展向长度对结果的影响。在此基础上,通过k-ωSST湍流模型计算了新月形薄覆冰单导线及四分裂导线的气动三分力系数,研究了展向长度、网格尺寸等参数对计算结果的影响,通过不同工况下数值模拟结果与试验结果的对比,验证了薄覆冰导线可行的数值模型。由于条件所限,风洞试验往往只得到分裂导线的整体气动力,通过数值模拟方法则明确了分裂导线各子导线的气动力系数对整体扭转系数的贡献。
本文的成果丰富了现有覆冰导线的气动力参数,为深入进行覆冰导线舞动试验及仿真提供了宝贵的参数并为进一步精确计算其他覆冰形状的气动力系数提供了参考。
In special weather conditions, transmission lines may be iced in windward side, with some features of the wing. It may cause a large amplitude and low-frequency self-excited vibration, which is so called galloping. In recent years, with the rapid development of the power systems and frequent occurrence of the extreme weather, the galloping due to the icing and snowing of the transmission lines has been a serious threat to the security of the electricity and communication network operations. The aerodynamic parameter of the iced conductor is a key factor that affects the calculation and analysis for dancing. Although there have been some test results of the aerodynamic parameter, due to the randomness and variability of the accreted shape, the data for anti-galloping design has not been obtained enough and there is a great value to accumulate more aerodynamic parameters of iced conductors.
In this study, the domestic and foreign wind tunnel test researches on aerodynamic characteristics of iced conductors were reviewed in detail, and the shortcomings and inadequacies were proposed. Then the aerodynamic characteristics of single and multi-bundled conductors with difference thickness crescent-shaped and D-shaped were studied by wind tunnel test and numerical simulation (CFD). The main contents of the wind tunnel test and numerical study were as follows:
Wind tunnel test:Rigid segment models of D-shaped and 4 kinds of crescent-shaped were made, and the aerodynamic characteristics were then measured by high-frequency force balance. A wind tunnel test device taking the two-dimensional flow characteristics and the effect of boundary layer into account was designed. Under the homogeneous turbulence of 0%,5% and 13%, the aerodynamic force coefficients of single and bundled conductors with different ice section were obtained, and the effects of turbulence on the aerodynamics were discussed. Subsequently, the relationships between the aerodynamic characteristics of single conductors and those of bundled conductors were described. Furthermore, based on the Den Hartog and Nigol's mechanisms of galloping, the wind angle ranges sensitive to galloping were analyzed.
Numerical study. Wind flow around a cylinder with Reynolds number of 3900 was simulated adopting LES. The effects of near-wall grids and span-wise length on the numerical result were studied in detail. The aerodynamic coefficients of single and 4-bundled conductors with thin crescent-shaped ice were then calculated by k-ωSST turbulence model. The parameters such as span-wise length, grid size and turbulence model, which affect the calculation result were discussed. By comparisons of numerical results with those of corresponding experiments, the appropriate numerical model was verified. While the wind tunnel test is only able to obtain the overall moment coefficients of 4-bundled conductors, numerical study is capable of quantifying three parts of torsion on the bundle conductors respectively.
The results of this paper enrich the current data of aerodynamic characteristics for iced conductors. It can provide valuable parameters for studying on galloping test and simulation. Moreover, it can provide a reference for accurately calculating aerodynamic coefficients of other ice-shaped conductors.
本文详细回顾了国内外有关覆冰导线的气动力试验研究,提出了存在的缺点与不足。在此基础上通过风洞试验及CFD数值模拟方法研究了不同厚度新月形覆冰和D形覆冰截面单导线及分裂导线的气动力特性。
风洞试验方面：制作了刚性节段模型,通过高频测力天平试验研究了D形和4种新月形覆冰厚度输电导线的气动力特性。设计了考虑流场二维特性和风洞的边界层效应的试验装置,获得了各覆冰截面单导线和分裂导线子导线在均匀流、5%均匀湍流和13%均匀湍流3种流场中各风攻角下的气动力特性,研究了气动力系数对攻角的变化规律,以及湍流度对气动力特性的影响。比较了单导线与二、四、六分裂导线之间气动力特性的区别与联系。根据Den Hartog和Nigol舞动理论分别计算了各种工况下覆冰导线可能发生舞动的风攻角范围。
CFD数值模拟方面：通过CFD数值模拟方法,对雷诺数为3900的经典圆柱绕流问题进行了非定常计算,详细研究了近壁面网格及展向长度对结果的影响。在此基础上,通过k-ωSST湍流模型计算了新月形薄覆冰单导线及四分裂导线的气动三分力系数,研究了展向长度、网格尺寸等参数对计算结果的影响,通过不同工况下数值模拟结果与试验结果的对比,验证了薄覆冰导线可行的数值模型。由于条件所限,风洞试验往往只得到分裂导线的整体气动力,通过数值模拟方法则明确了分裂导线各子导线的气动力系数对整体扭转系数的贡献。
本文的成果丰富了现有覆冰导线的气动力参数,为深入进行覆冰导线舞动试验及仿真提供了宝贵的参数并为进一步精确计算其他覆冰形状的气动力系数提供了参考。
In special weather conditions, transmission lines may be iced in windward side, with some features of the wing. It may cause a large amplitude and low-frequency self-excited vibration, which is so called galloping. In recent years, with the rapid development of the power systems and frequent occurrence of the extreme weather, the galloping due to the icing and snowing of the transmission lines has been a serious threat to the security of the electricity and communication network operations. The aerodynamic parameter of the iced conductor is a key factor that affects the calculation and analysis for dancing. Although there have been some test results of the aerodynamic parameter, due to the randomness and variability of the accreted shape, the data for anti-galloping design has not been obtained enough and there is a great value to accumulate more aerodynamic parameters of iced conductors.
In this study, the domestic and foreign wind tunnel test researches on aerodynamic characteristics of iced conductors were reviewed in detail, and the shortcomings and inadequacies were proposed. Then the aerodynamic characteristics of single and multi-bundled conductors with difference thickness crescent-shaped and D-shaped were studied by wind tunnel test and numerical simulation (CFD). The main contents of the wind tunnel test and numerical study were as follows:
Wind tunnel test:Rigid segment models of D-shaped and 4 kinds of crescent-shaped were made, and the aerodynamic characteristics were then measured by high-frequency force balance. A wind tunnel test device taking the two-dimensional flow characteristics and the effect of boundary layer into account was designed. Under the homogeneous turbulence of 0%,5% and 13%, the aerodynamic force coefficients of single and bundled conductors with different ice section were obtained, and the effects of turbulence on the aerodynamics were discussed. Subsequently, the relationships between the aerodynamic characteristics of single conductors and those of bundled conductors were described. Furthermore, based on the Den Hartog and Nigol's mechanisms of galloping, the wind angle ranges sensitive to galloping were analyzed.
Numerical study. Wind flow around a cylinder with Reynolds number of 3900 was simulated adopting LES. The effects of near-wall grids and span-wise length on the numerical result were studied in detail. The aerodynamic coefficients of single and 4-bundled conductors with thin crescent-shaped ice were then calculated by k-ωSST turbulence model. The parameters such as span-wise length, grid size and turbulence model, which affect the calculation result were discussed. By comparisons of numerical results with those of corresponding experiments, the appropriate numerical model was verified. While the wind tunnel test is only able to obtain the overall moment coefficients of 4-bundled conductors, numerical study is capable of quantifying three parts of torsion on the bundle conductors respectively.
The results of this paper enrich the current data of aerodynamic characteristics for iced conductors. It can provide valuable parameters for studying on galloping test and simulation. Moreover, it can provide a reference for accurately calculating aerodynamic coefficients of other ice-shaped conductors.
引文
[1]郭应龙,李国兴,尤传永.输电线路舞动[M].北京：中国电力出版社,2003.
[2]蒋兴良,马俊,王少华等.输电线路冰害事故及原因分析[J].中国电力,2005(11)：27-30.
[3]马俊,蒋兴良,张志劲等.交流电场对绝缘了覆冰形成的影响机理[J].电网技术,2008(5)：7-11.
[4]杨靖波,李正,杨风利等.2008年电网冰灾覆冰及倒塔特征分析[J].电网与水力发电进展,2008,24(4)：4-8.
[5]Lenhard RW. An indirect method for estimating the weight of glaze on wires[J].Bull Amer Meteor Soc,1955,36(3):1-5
[6]Mccomber P, Govoni JW. An analysis of selected ice accretion measurements on a wire at Mount Washington[C]. Proceedings of the Forty-second Annual Eastern Snow Conference. Montreal,1985
[7]Mckay GA, Thompson HA. Estimating the hazard of ice accretion in Canada from climatological data[J]. J AppI Meteor,1969(8):927-935
[8]Poots G., Skelton EL.I. Thermodynamic models of wet-snow accretion:axial growth and liquid water content on a fixed conductor[J]. International Journal of Heat and Fluid Flow,1995,16(1):43-49.
[9]Porcu F., Smargiassi E. and Prodi.F.2-D and 3-D modelling of low density ice accretion on rotating wires with variable surface irregularities [J]. Atmospheric Research,1995.36(3-4):233-242.
[10]Makkonen L. Modeling power line icing in freezing precipitation[C].7th International Workshop on Atmospheric Icing of Structures. Montreal,1996
[11]Masoud F, Konstantin S. Statistical Analysis of Field Data for PrecipitationIcing Accretion on Overhead Power Lines[J]. IEEE Transactions On Power Delivery,2005,20(2):1080-1087
[12]CIGRE, State of the art of conductor galloping, CIGRE Technical Brochure, No,322, TF B2.11.O6. 2007
[13]胡红春.三峡至万县Ⅰ回500kV输电线路鄂西段设计冰厚取值[J].电力建设.2000,1(10)：22-24
[14]廖玉芳,段丽洁.湖南电线覆冰厚度估算模型研究[J].大气科学学报.2010,33(4)：395-400
[15]黄浩辉,宋丽莉,秦鹏等.粤北地区导线覆冰气象特征与标准厚度推算[J].热带气象学报.2010,26(1)：7-12
[16]谢运华.三峡地区导线覆冰与气象要素的关系[J].中国电力,2005,38(3)：35-39.
[17]Desai YM., Yu P. Shah A.H., Popplewell N.. Perturbation-based finite element analyses of transmission line galloping[J].Journal of Sound and Vibration.1996,191 (4):469-489.
[18]Van Dykea P, Laneville A. Galloping of a single conductor covered with a D-section on a high-voltage overhead test line[J]. Journal of Wind Engineering and Industrial Aerodynamics.2008,(96):1141-1151
[19]Chabart O., Lilien JL. Galloping of electrical lines in wind tunnel facilities[J]. Journal of Wind Engineering and Industrial Aerodynamics,1998,74(6):967-976.
[20]McComber P, Paradis A. A cable galloping model for thin ice accretions[J].Atmospheric Research,1998,46(12):13-25.
[21]李万平,杨新祥,张立志.覆冰导线群的静气动力特性[J].空气动力学学报,1995.13(4)：427-435.
[22]李万平.覆冰导线群的动态气动力特性[J].空气动力学学报,2000.18(4)：413-420.
[23]Zhang Q., Poppleweil N. A.H.Shah. Galloping of bundle conductor[J].Journal of Sound and Vibration,2000.34(1):115-134.
[24]白海峰,李宏男.分裂式覆冰导线横风弛振响应研究[J].振动工程学报,2008.21(3)：298-303
[25]李万平,黄河,何锃.特大覆冰导线气动力特性测试[J].华中科技大学学报,2001.29(8)：84-86
[26]Den Hartog J P. Transmission line vibration due to sleet[J]. AIEE Transactions,1932,51(4): 1074-1086
[27]Nigol O, Buchan P.G. Conductor Galloping Part1-Den Hartog Mechanism[J]. IEEE Transactions on Power Apparatus and System,1981,100(2):699-707
[28]Nigol O, Buchan P G. Conductor galloping, part Ⅰ:Den Hartog mechanism; part Ⅱ:torsional mechanism[J]. IEEE Transactions on Power Apparatus and Systems,1981,100(2):699-720.
[29]Yu P, Popplewell N, Shah A. H. Instability trends of inertially coupled galloping[J]. Journal of Sound and Vibration,1995,183(4):663-678.
[30]蔡廷湘.输电线舞动新机理研究[J].中国电力,1998,31(10)：62-66.
[31]唐校友.线路舞动的低阻尼共振激发机理[J].东北电力大学学报,2006,26(1)：65-70.
[32]Kimura K., M. lnoue Y. Fujino T. et al. Unsteady forces on an ice-accreted four-conductor bundle transmission line[C]. Proc. of the 10th Int. Conference on Wind Engineering, Copenhagen (Denmark), Wind Engineering into the 21st Century, Eds. A. Larsen, G.L. Larose and F.M. Livesey, A.A. Balkema,1999:467-472.
[33]Shimizu M., Ishihara T. and P.V. Phuc. A wind tunnel study on steady and unsteady aerodynamic characteristics of ice-accreted transmission lines[C]. Proc. of the 18th Symposium on Wind Engineering, Tokyo (Japan),2004:245-250.
[34]Breuer M. Large eddy simulation of the subcritical flow past a circular cylinder:numerical and modeling aspects[J]. Int. J. Numer. Meth. Fluids.1998,28:1281-1302
[35]Arthur G. Kravchenkoa and Parviz Moin. Numerical studies of flow over a circular cylinder at ReD=3900[J]. Phys. Fluids,2000,12(2):403-417
[36]Tutar M. Computational modelling of flow around a circular cylinder in sub-critical flow regime with various turbulence models[J]. Int. J. Numer. Meth. Fluids,2001,35:763-784
[37]黄河.覆冰导线气动力特性的数值模拟[D].华中科技大学硕士学位论文.2001：43-52
[38]姚育成.高雷诺数下覆冰导线气动力特性的数值模拟[D].华中科技大学硕士学位论文.2003：40-51
[39]滕二甫.新月形覆冰导线横风向驰振气动力参数的数值模拟[D].哈尔滨工业大学硕士学位论文.2007
[40]吕翼.覆冰导线气动力特性数值模拟研究[D].浙江大学硕士学位论文.2008
[41]吕翼,楼文娟,孙珍茂,等.覆冰三分裂导线气动力特性的数值模拟[J].浙江大学学报(工学版),2010,44(1)：174-179
[42]Shinichi O, Ishihara T. Numerical study on steady aerodynamic characteristics of ice accreted transmission lines[C]. The 5th International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA,2010:23-27.
[43]Nigol O. and Clarke GJ. Conductor galloping and control based on torsional mechanism[C].IEEE Power Engineering Society Winter Meeting,1974:74016-2
[44]Chadha J. and Jaster W. Influence of turbulence on the galloping instability of iced conductors[J]. IEEE Transactions on Power Apparatus and System,1975,94(5):1489-1499
[45]Stumpf P. and H.C.M.NG. Investigation of aerodynamic stability for selected inclined cables and conductor cables[D]. University of Manitoba, Winnipeg, Canada.1990
[46]Ishihara T. A wind tunnel study on aerodynamic characteristics of ice accreted transmission lines[C]. 5th International colloquium on bluff body aerodynamics and applications, Ottawa,2004:369-372.
[47]Kimura K. Unsteady forces on an ice-accreted four-conductor bundle transmission line[M].Wind Engineering into the 21st Century, Rotterdam,1999,467-472.
[48]Phuc P.V, Ishihara T. Shimizu M. A wind tunnel study on unsteady forces of ice accreted transmission lines,5th International colloquium on bluff body aerodynamics and applications, Ottawa, 2005:374-476.
[49]李万平,杨新祥,王海期等,大跨越覆冰导线空气动力学特性的测试[J].超高压输变电运行技术.1990,(8)：95-107.
[50]周松,蔡萌琦,唐杰等,新月形覆冰导线的空气动力特性[C].重庆力学学会2009年学术年会论文集.2009,34-37.
[51]顾明,马文勇,全涌等,两种典型覆冰导线气动力特性及稳定性分析[J].同济大学学报(自然科学版),2009,37(10)：1328-1332
[52]马文勇,顾明,全涌等.准椭圆形覆冰导线气动特性试验研究[J].同济大学学报(自然科学版),2010,38(10)：1409-1413
[53]张雁宏,严波,周松等.覆冰四分裂导线静态气动力特性试验[J].空气动力学学报.2011,29(2)：150-154
[54]肖正直,晏致涛,李正良等.八分裂输电导线结冰风洞及气动力特性试验[J].电网技术,2009,33(5)：90-94
[55]王昕,楼文娟,许福友等.覆冰导线气动力特性风洞试验研究[J].空气动力学学报,2011,29(5)：573-579
[56]程厚梅.洞实验干扰与修正[M].北京：国防工业出版社,2003
[57]解万川.NF-3风洞二元侧壁附面层控制技术研究[D].西北工业大学,2007
[58]恽起麟.风洞实验[M].北京：国防工业出版社,2000
[59]黄本才.结构抗风分析原理及应用(第二版)[M].上海：同济大学出版社,2008
[60]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京：清华大学出版社,2006
[61]王福军,计算流体动力学分析——CFD软件原理与应用[M].北京：清华大学出版社.2006
[62]Franke R.& Rodi W. Calculation of vortex shedding past a square cylinder with various turbulence models[M], in F. Durst et al. (eds.), Turbulent Shear Flows 8, Springer, New York,1993: 189-204.
[63]Felten F., Fautrelle Y. Du Y. Terrail, et al. Numerical modeling of electrognetically-riven turbulent flows using LES methods[J]. Applied Mathematical Modeling,2004,28(1):15-27
[64]Bouris D., Bergeles G. 2D LES of vortex shedding from a square cylinder[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999,80:31-36
[65]Germano,M., Piomelli, U. Moin, P., et al. A dynamic subgrid-scal eddy viscosity model[J]. Physics of Fluid,1991,3(7):1760-1765
[66]Lily D.K. A proposed modification of the Germano subgrid-scal closure model[J]. Physics of Fluid, 1992,4:633-635
[67]Fluent 6.3 documentation. Fluent Inc,2005
[68]陶文铨.数值传热学[M].第2版.西安：西安交通大学出版社,2001：347-349.
[69]顾罡,二维单圆柱、双圆柱绕流问题和三维垂荡板运动的数值模拟[D].上海：上海交通大学.2007
[70]Kravchenko, A.G., Moin, P. Numerical studies of flow over a circular cylinder at ReD=3900[J].Physics of Fluids.2000,12(2):403-417
[71]Oka S.& Ishihara T. Numerical study of aerodynamic characteristics of a square prism in a uniform flow[J].Journal of Wind Engineering and Industrial Aerodynamics,2009,97,548-599
[72]Lourenco L.M. & Shih C. Characteristics of the plane turbulent near wake of a circular cylinder, a particle image velocimetry study, Private Communication,1993.
[73]Ong L. & Wallace J. The velocity field of the turbulent very near wake of a circular cylinder[J], Exp. Fluids, Springer Verlag, Berlin,1996,20:441-453,.
[74]Son J. & Hanratty T.J. Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from 5×103 to 105[J]. Fluid Mech.,1969,35:353-368.
[75]Breuer M. Large eddy simulation of the subcritical flow past a circular cylinder:numerical and modeling aspects[J]. Int. J. Numer. Meth. Fluids 1998,28:1281-1302
[76]严波,胡景,周松等.覆冰四分裂导线舞动数值模拟及参数分析[J].振动工程学报,2010,23(3)：310-316
[2]蒋兴良,马俊,王少华等.输电线路冰害事故及原因分析[J].中国电力,2005(11)：27-30.
[3]马俊,蒋兴良,张志劲等.交流电场对绝缘了覆冰形成的影响机理[J].电网技术,2008(5)：7-11.
[4]杨靖波,李正,杨风利等.2008年电网冰灾覆冰及倒塔特征分析[J].电网与水力发电进展,2008,24(4)：4-8.
[5]Lenhard RW. An indirect method for estimating the weight of glaze on wires[J].Bull Amer Meteor Soc,1955,36(3):1-5
[6]Mccomber P, Govoni JW. An analysis of selected ice accretion measurements on a wire at Mount Washington[C]. Proceedings of the Forty-second Annual Eastern Snow Conference. Montreal,1985
[7]Mckay GA, Thompson HA. Estimating the hazard of ice accretion in Canada from climatological data[J]. J AppI Meteor,1969(8):927-935
[8]Poots G., Skelton EL.I. Thermodynamic models of wet-snow accretion:axial growth and liquid water content on a fixed conductor[J]. International Journal of Heat and Fluid Flow,1995,16(1):43-49.
[9]Porcu F., Smargiassi E. and Prodi.F.2-D and 3-D modelling of low density ice accretion on rotating wires with variable surface irregularities [J]. Atmospheric Research,1995.36(3-4):233-242.
[10]Makkonen L. Modeling power line icing in freezing precipitation[C].7th International Workshop on Atmospheric Icing of Structures. Montreal,1996
[11]Masoud F, Konstantin S. Statistical Analysis of Field Data for PrecipitationIcing Accretion on Overhead Power Lines[J]. IEEE Transactions On Power Delivery,2005,20(2):1080-1087
[12]CIGRE, State of the art of conductor galloping, CIGRE Technical Brochure, No,322, TF B2.11.O6. 2007
[13]胡红春.三峡至万县Ⅰ回500kV输电线路鄂西段设计冰厚取值[J].电力建设.2000,1(10)：22-24
[14]廖玉芳,段丽洁.湖南电线覆冰厚度估算模型研究[J].大气科学学报.2010,33(4)：395-400
[15]黄浩辉,宋丽莉,秦鹏等.粤北地区导线覆冰气象特征与标准厚度推算[J].热带气象学报.2010,26(1)：7-12
[16]谢运华.三峡地区导线覆冰与气象要素的关系[J].中国电力,2005,38(3)：35-39.
[17]Desai YM., Yu P. Shah A.H., Popplewell N.. Perturbation-based finite element analyses of transmission line galloping[J].Journal of Sound and Vibration.1996,191 (4):469-489.
[18]Van Dykea P, Laneville A. Galloping of a single conductor covered with a D-section on a high-voltage overhead test line[J]. Journal of Wind Engineering and Industrial Aerodynamics.2008,(96):1141-1151
[19]Chabart O., Lilien JL. Galloping of electrical lines in wind tunnel facilities[J]. Journal of Wind Engineering and Industrial Aerodynamics,1998,74(6):967-976.
[20]McComber P, Paradis A. A cable galloping model for thin ice accretions[J].Atmospheric Research,1998,46(12):13-25.
[21]李万平,杨新祥,张立志.覆冰导线群的静气动力特性[J].空气动力学学报,1995.13(4)：427-435.
[22]李万平.覆冰导线群的动态气动力特性[J].空气动力学学报,2000.18(4)：413-420.
[23]Zhang Q., Poppleweil N. A.H.Shah. Galloping of bundle conductor[J].Journal of Sound and Vibration,2000.34(1):115-134.
[24]白海峰,李宏男.分裂式覆冰导线横风弛振响应研究[J].振动工程学报,2008.21(3)：298-303
[25]李万平,黄河,何锃.特大覆冰导线气动力特性测试[J].华中科技大学学报,2001.29(8)：84-86
[26]Den Hartog J P. Transmission line vibration due to sleet[J]. AIEE Transactions,1932,51(4): 1074-1086
[27]Nigol O, Buchan P.G. Conductor Galloping Part1-Den Hartog Mechanism[J]. IEEE Transactions on Power Apparatus and System,1981,100(2):699-707
[28]Nigol O, Buchan P G. Conductor galloping, part Ⅰ:Den Hartog mechanism; part Ⅱ:torsional mechanism[J]. IEEE Transactions on Power Apparatus and Systems,1981,100(2):699-720.
[29]Yu P, Popplewell N, Shah A. H. Instability trends of inertially coupled galloping[J]. Journal of Sound and Vibration,1995,183(4):663-678.
[30]蔡廷湘.输电线舞动新机理研究[J].中国电力,1998,31(10)：62-66.
[31]唐校友.线路舞动的低阻尼共振激发机理[J].东北电力大学学报,2006,26(1)：65-70.
[32]Kimura K., M. lnoue Y. Fujino T. et al. Unsteady forces on an ice-accreted four-conductor bundle transmission line[C]. Proc. of the 10th Int. Conference on Wind Engineering, Copenhagen (Denmark), Wind Engineering into the 21st Century, Eds. A. Larsen, G.L. Larose and F.M. Livesey, A.A. Balkema,1999:467-472.
[33]Shimizu M., Ishihara T. and P.V. Phuc. A wind tunnel study on steady and unsteady aerodynamic characteristics of ice-accreted transmission lines[C]. Proc. of the 18th Symposium on Wind Engineering, Tokyo (Japan),2004:245-250.
[34]Breuer M. Large eddy simulation of the subcritical flow past a circular cylinder:numerical and modeling aspects[J]. Int. J. Numer. Meth. Fluids.1998,28:1281-1302
[35]Arthur G. Kravchenkoa and Parviz Moin. Numerical studies of flow over a circular cylinder at ReD=3900[J]. Phys. Fluids,2000,12(2):403-417
[36]Tutar M. Computational modelling of flow around a circular cylinder in sub-critical flow regime with various turbulence models[J]. Int. J. Numer. Meth. Fluids,2001,35:763-784
[37]黄河.覆冰导线气动力特性的数值模拟[D].华中科技大学硕士学位论文.2001：43-52
[38]姚育成.高雷诺数下覆冰导线气动力特性的数值模拟[D].华中科技大学硕士学位论文.2003：40-51
[39]滕二甫.新月形覆冰导线横风向驰振气动力参数的数值模拟[D].哈尔滨工业大学硕士学位论文.2007
[40]吕翼.覆冰导线气动力特性数值模拟研究[D].浙江大学硕士学位论文.2008
[41]吕翼,楼文娟,孙珍茂,等.覆冰三分裂导线气动力特性的数值模拟[J].浙江大学学报(工学版),2010,44(1)：174-179
[42]Shinichi O, Ishihara T. Numerical study on steady aerodynamic characteristics of ice accreted transmission lines[C]. The 5th International Symposium on Computational Wind Engineering (CWE2010) Chapel Hill, North Carolina, USA,2010:23-27.
[43]Nigol O. and Clarke GJ. Conductor galloping and control based on torsional mechanism[C].IEEE Power Engineering Society Winter Meeting,1974:74016-2
[44]Chadha J. and Jaster W. Influence of turbulence on the galloping instability of iced conductors[J]. IEEE Transactions on Power Apparatus and System,1975,94(5):1489-1499
[45]Stumpf P. and H.C.M.NG. Investigation of aerodynamic stability for selected inclined cables and conductor cables[D]. University of Manitoba, Winnipeg, Canada.1990
[46]Ishihara T. A wind tunnel study on aerodynamic characteristics of ice accreted transmission lines[C]. 5th International colloquium on bluff body aerodynamics and applications, Ottawa,2004:369-372.
[47]Kimura K. Unsteady forces on an ice-accreted four-conductor bundle transmission line[M].Wind Engineering into the 21st Century, Rotterdam,1999,467-472.
[48]Phuc P.V, Ishihara T. Shimizu M. A wind tunnel study on unsteady forces of ice accreted transmission lines,5th International colloquium on bluff body aerodynamics and applications, Ottawa, 2005:374-476.
[49]李万平,杨新祥,王海期等,大跨越覆冰导线空气动力学特性的测试[J].超高压输变电运行技术.1990,(8)：95-107.
[50]周松,蔡萌琦,唐杰等,新月形覆冰导线的空气动力特性[C].重庆力学学会2009年学术年会论文集.2009,34-37.
[51]顾明,马文勇,全涌等,两种典型覆冰导线气动力特性及稳定性分析[J].同济大学学报(自然科学版),2009,37(10)：1328-1332
[52]马文勇,顾明,全涌等.准椭圆形覆冰导线气动特性试验研究[J].同济大学学报(自然科学版),2010,38(10)：1409-1413
[53]张雁宏,严波,周松等.覆冰四分裂导线静态气动力特性试验[J].空气动力学学报.2011,29(2)：150-154
[54]肖正直,晏致涛,李正良等.八分裂输电导线结冰风洞及气动力特性试验[J].电网技术,2009,33(5)：90-94
[55]王昕,楼文娟,许福友等.覆冰导线气动力特性风洞试验研究[J].空气动力学学报,2011,29(5)：573-579
[56]程厚梅.洞实验干扰与修正[M].北京：国防工业出版社,2003
[57]解万川.NF-3风洞二元侧壁附面层控制技术研究[D].西北工业大学,2007
[58]恽起麟.风洞实验[M].北京：国防工业出版社,2000
[59]黄本才.结构抗风分析原理及应用(第二版)[M].上海：同济大学出版社,2008
[60]张兆顺,崔桂香,许春晓.湍流理论与模拟[M].北京：清华大学出版社,2006
[61]王福军,计算流体动力学分析——CFD软件原理与应用[M].北京：清华大学出版社.2006
[62]Franke R.& Rodi W. Calculation of vortex shedding past a square cylinder with various turbulence models[M], in F. Durst et al. (eds.), Turbulent Shear Flows 8, Springer, New York,1993: 189-204.
[63]Felten F., Fautrelle Y. Du Y. Terrail, et al. Numerical modeling of electrognetically-riven turbulent flows using LES methods[J]. Applied Mathematical Modeling,2004,28(1):15-27
[64]Bouris D., Bergeles G. 2D LES of vortex shedding from a square cylinder[J]. Journal of Wind Engineering and Industrial Aerodynamics,1999,80:31-36
[65]Germano,M., Piomelli, U. Moin, P., et al. A dynamic subgrid-scal eddy viscosity model[J]. Physics of Fluid,1991,3(7):1760-1765
[66]Lily D.K. A proposed modification of the Germano subgrid-scal closure model[J]. Physics of Fluid, 1992,4:633-635
[67]Fluent 6.3 documentation. Fluent Inc,2005
[68]陶文铨.数值传热学[M].第2版.西安：西安交通大学出版社,2001：347-349.
[69]顾罡,二维单圆柱、双圆柱绕流问题和三维垂荡板运动的数值模拟[D].上海：上海交通大学.2007
[70]Kravchenko, A.G., Moin, P. Numerical studies of flow over a circular cylinder at ReD=3900[J].Physics of Fluids.2000,12(2):403-417
[71]Oka S.& Ishihara T. Numerical study of aerodynamic characteristics of a square prism in a uniform flow[J].Journal of Wind Engineering and Industrial Aerodynamics,2009,97,548-599
[72]Lourenco L.M. & Shih C. Characteristics of the plane turbulent near wake of a circular cylinder, a particle image velocimetry study, Private Communication,1993.
[73]Ong L. & Wallace J. The velocity field of the turbulent very near wake of a circular cylinder[J], Exp. Fluids, Springer Verlag, Berlin,1996,20:441-453,.
[74]Son J. & Hanratty T.J. Velocity gradients at the wall for flow around a cylinder at Reynolds numbers from 5×103 to 105[J]. Fluid Mech.,1969,35:353-368.
[75]Breuer M. Large eddy simulation of the subcritical flow past a circular cylinder:numerical and modeling aspects[J]. Int. J. Numer. Meth. Fluids 1998,28:1281-1302
[76]严波,胡景,周松等.覆冰四分裂导线舞动数值模拟及参数分析[J].振动工程学报,2010,23(3)：310-316