覆冰导线舞动非线性数值模拟方法及风洞模型试验
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摘要
输电线舞动是导线在风激励下产生的一种低频、大幅度自激振动。导线发生舞动时可能会造成相间闪络、断线和倒塔等事故,对整个供电系统的安全运行造成严重的危害。对覆冰导线舞动的研究具有极其重要的理论意义和工程实用价值。
论文首先利用风洞试验获得了不同厚度新月形覆冰四分裂导线各子导线在不同风速下的阻力系数、升力系数和扭矩系数随攻角的变化曲线。结果表明,覆冰厚度对覆冰导线空气动力系数的影响明显;在测试的风速范围内风速对空气动力系数的变化规律影响较小;迎风侧子导线尾流对背风侧子导线空气动力系数的影响明显。在研究覆冰导线的舞动时有必要考虑不同子导线空气动力载荷的差异。
覆冰导线的舞动是一非线性问题。论文研究了模拟覆冰导线舞动的非线性数值方法。基于覆冰导线所受空气动力载荷的非线性和导线大幅运动的几何非线性,利用虚功原理建立非线性运动方程,采用具有三个平动自由度和一个扭转自由度的三结点等参单元模拟覆冰导线,得到基于更新Lagrange格式的覆冰导线的非线性动力学有限元方程。采用Newmark时间积分和Newton-Raphson非线性迭代法求解有限元方程。编制了相应的计算程序,利用算例验证了方法和程序的正确性。进而对典型覆冰线路的舞动进行数值模拟,揭示了当覆冰导线的竖向和横向固有频率之间存在整数倍关系的情况下,可能出现的一种新的舞动模式。该舞动模式可理解为非线性动力系统的饱和现象,有待试验观测结果的验证。
在获得覆冰单导线舞动数值模拟方法的基础上,考虑分裂导线舞动过程中间隔棒的几何非线性,采用欧拉梁单元模拟间隔棒,建立覆冰分裂导线的非线性有限元方程。编制了相应的计算程序,通过算例验证了方法和程序的正确性。利用由风洞实验获得的覆冰四分裂导线的空气动力系数,模拟研究了不同档距覆冰四分裂导线的舞动,并对其舞动特性进行了分析,结果表明,小档距情况下导线以低阶模态舞动模式为主,大档距导线则会出现高阶模态舞动模式,在研究舞动防治技术时应予以考虑。此外,通过数值模拟分析比较了考虑子导线尾流影响和不考虑子导线尾流影响情况下导线的舞动,结果表明,考虑尾流对气动载荷的影响得到的竖向振动幅值更大,并更容易激发舞动的产生,这一结果可对舞动防治技术的研究提供参考。
基于空间风场的随机性,首次采用数值方法模拟研究覆冰四分裂导线在随机风场中的舞动。利用考虑风速沿高度变化的Kaimal风速谱和Davenport互相干函数,用谐波分解法数值模拟考虑沿线路方向和高度方向相关性的多点互相关风速时程样本,进而确定作用于覆冰导线上的空气动力载荷。数值模拟研究了不同档距覆冰导线在随机风场中的舞动,通过对导线的运动特性的分析表明,随机风作用下导线的振动包括稳定风成份引起的舞动和脉动风引起的强迫振动两部分,其舞动特性和稳定风作用下的特性差别不大。此外,小档距线路在随机风作用下导线的竖向振动幅值大于稳定风作用下的结果;而大档距线路在随机风作用下的竖向舞动幅值小于稳定风作用下的结果。
为了验证舞动数值模拟方法的正确性,进行了新月形覆冰单导线和四分裂导线舞动风洞模型试验,获得了相应模型的舞动轨迹。建立了两个模型试验的有限元模型,利用本论文提出的舞动非线性有限元模拟方法,模拟了试验模型的舞动过程。比较模型试验和数值方法得到的舞动轨迹,两者吻合,从而验证了本论文提出的数值模拟方法和程序的正确性。
本论文研究成果为覆冰分裂导线舞动研究提供了必要的试验数据和有效的数值方法,为研究覆冰导线的舞动防治技术奠定了重要的理论基础。
Galloping of an electrical transmission line is characterized by large amplitude, low frequency, self-excited oscillation under aerodynamic forces. It may deduce flashover between different phase conductors and cause damage to the conductors and even collapsing of transmission tower, which may in turn severely imperils the safe operation of the high voltage transmission line. Therefore, the study on galloping of iced transmission lines behaves great significance in power supply engineering.
The curves of aerodynamic coefficients, including drag, lift and moment coefficients, of quad-bundled conductors accreted ices with typical cross-section shapes versus wind attck angle under different wind speeds were determined by wind tunnel test. It is shown that the ice thick has obvious effect on the aerodynamic characteristics of the ice conductors but the wind speed has a slightly effect. The wake of the upwind iced sub-conductor greatly affects the aerodynamic characteristics of the leeward iced sub-conductor. The difference of the aerodynamic loads on all the sub-conductors should be considered in the analysis of galloping of iced bundle conductors.
Galloping of iced conductor is a typical nonlinear problem.In this thesis, the study on the nonlinear numerical simulation method for galloping of iced conductor is performed. Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In the procedure of numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is, are employed to discretize the transmission line; and the nonlinear dynamic system equation is solved by the Newmark time integration method and the Newton-Raphson nonlinear iteration strategy. Numerical examples are employed to demonstrate the efficiency of the presented method and the developed finite element program. Furthermore, a new possible galloping mode, which may reflect the saturation phenomenon of nonlinear dynamic system, is discovered on the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.
Based on the obtained nonliear finite element formulation for galloping of iced single conductor, a numerical method, in which the spacers are simulated with Euler beam, for galloping of iced bundle conductors is obtained, and the corresponding computer program is also developed. A numerical example is used to demonstrate the efficiency of the presented method and the developed finite element program. Furthermore, the galloping of the quad-bundled conductors with different span lengths is numerically investigated. It is observed that the transmission lines with shorter length of span gallope mainly with lower vibraion modes, and higher modes may occure for the lines with larger span when galloping takes place, which provides some references for the development of anti-galloping technology. In addition, the galloping of iced quad-bundled conductors in the case of considering and without considering the inference of wake around the iced sub-conductors is compared. The results indicate that the galloping amplitude as the wake inference being considered is lager than that as the wake inference not being considered.
Galloping of iced qua-bundled conductor in stochastic wind field is firstly investigated by the numerical method developed in this paper. The stochastic wind fields are simulated by the Kaimal spectrum, with which the variation of wind velocity fluctuation with height above ground is taken into account, and the Davenport mutual spectrum. The correlation simples of stochastic wind at the points along the line direction are numerically simulated by means of the WAWS, based on which the aerodynamic loads of iced conductor are calculated. The galloping of iced quad-bundled conductor in stochastic wind filed with different span length is then numerically investigated, and some meaningful conclusions are obtained.The results show that galloping characteristics of the iced transmission lines in stochastic wind field are similar to those of the line in steady wind field. Moreover, the vibration amplitudes of the lines with smaller span length in stochastic wind are bigger than those of the line in steady wind field, but the vibration amplitudes of the lines with larger span in stochastical wind are less than those of the lines in steady wind.
To verify the numerical simulation method of nonlinear galoping of iced onductor, two wind tunnel tests of typical galloping models, one for siced single conductor and the other for quad-bundled conductor, were performed, in which the galloping tracks of iced single conductor and iced quad-bundled conductor were obtained. The finite element models of the two tests are set up by the nonlinear finite element simulation methods presented in this paper, and they are used to simulate galloping of the test conductor models. The concidence between the numerical simulation results and wind tunnel tests demonstrate the correctness and efficiency of the presented numerical methods.
Research results in this paper provides necessary test data and effective numerical method for the study on galloping of iced bundle conductor, so as to found the theory bases for anti-galloping method of iced bundle conductor.
论文首先利用风洞试验获得了不同厚度新月形覆冰四分裂导线各子导线在不同风速下的阻力系数、升力系数和扭矩系数随攻角的变化曲线。结果表明,覆冰厚度对覆冰导线空气动力系数的影响明显;在测试的风速范围内风速对空气动力系数的变化规律影响较小;迎风侧子导线尾流对背风侧子导线空气动力系数的影响明显。在研究覆冰导线的舞动时有必要考虑不同子导线空气动力载荷的差异。
覆冰导线的舞动是一非线性问题。论文研究了模拟覆冰导线舞动的非线性数值方法。基于覆冰导线所受空气动力载荷的非线性和导线大幅运动的几何非线性,利用虚功原理建立非线性运动方程,采用具有三个平动自由度和一个扭转自由度的三结点等参单元模拟覆冰导线,得到基于更新Lagrange格式的覆冰导线的非线性动力学有限元方程。采用Newmark时间积分和Newton-Raphson非线性迭代法求解有限元方程。编制了相应的计算程序,利用算例验证了方法和程序的正确性。进而对典型覆冰线路的舞动进行数值模拟,揭示了当覆冰导线的竖向和横向固有频率之间存在整数倍关系的情况下,可能出现的一种新的舞动模式。该舞动模式可理解为非线性动力系统的饱和现象,有待试验观测结果的验证。
在获得覆冰单导线舞动数值模拟方法的基础上,考虑分裂导线舞动过程中间隔棒的几何非线性,采用欧拉梁单元模拟间隔棒,建立覆冰分裂导线的非线性有限元方程。编制了相应的计算程序,通过算例验证了方法和程序的正确性。利用由风洞实验获得的覆冰四分裂导线的空气动力系数,模拟研究了不同档距覆冰四分裂导线的舞动,并对其舞动特性进行了分析,结果表明,小档距情况下导线以低阶模态舞动模式为主,大档距导线则会出现高阶模态舞动模式,在研究舞动防治技术时应予以考虑。此外,通过数值模拟分析比较了考虑子导线尾流影响和不考虑子导线尾流影响情况下导线的舞动,结果表明,考虑尾流对气动载荷的影响得到的竖向振动幅值更大,并更容易激发舞动的产生,这一结果可对舞动防治技术的研究提供参考。
基于空间风场的随机性,首次采用数值方法模拟研究覆冰四分裂导线在随机风场中的舞动。利用考虑风速沿高度变化的Kaimal风速谱和Davenport互相干函数,用谐波分解法数值模拟考虑沿线路方向和高度方向相关性的多点互相关风速时程样本,进而确定作用于覆冰导线上的空气动力载荷。数值模拟研究了不同档距覆冰导线在随机风场中的舞动,通过对导线的运动特性的分析表明,随机风作用下导线的振动包括稳定风成份引起的舞动和脉动风引起的强迫振动两部分,其舞动特性和稳定风作用下的特性差别不大。此外,小档距线路在随机风作用下导线的竖向振动幅值大于稳定风作用下的结果;而大档距线路在随机风作用下的竖向舞动幅值小于稳定风作用下的结果。
为了验证舞动数值模拟方法的正确性,进行了新月形覆冰单导线和四分裂导线舞动风洞模型试验,获得了相应模型的舞动轨迹。建立了两个模型试验的有限元模型,利用本论文提出的舞动非线性有限元模拟方法,模拟了试验模型的舞动过程。比较模型试验和数值方法得到的舞动轨迹,两者吻合,从而验证了本论文提出的数值模拟方法和程序的正确性。
本论文研究成果为覆冰分裂导线舞动研究提供了必要的试验数据和有效的数值方法,为研究覆冰导线的舞动防治技术奠定了重要的理论基础。
Galloping of an electrical transmission line is characterized by large amplitude, low frequency, self-excited oscillation under aerodynamic forces. It may deduce flashover between different phase conductors and cause damage to the conductors and even collapsing of transmission tower, which may in turn severely imperils the safe operation of the high voltage transmission line. Therefore, the study on galloping of iced transmission lines behaves great significance in power supply engineering.
The curves of aerodynamic coefficients, including drag, lift and moment coefficients, of quad-bundled conductors accreted ices with typical cross-section shapes versus wind attck angle under different wind speeds were determined by wind tunnel test. It is shown that the ice thick has obvious effect on the aerodynamic characteristics of the ice conductors but the wind speed has a slightly effect. The wake of the upwind iced sub-conductor greatly affects the aerodynamic characteristics of the leeward iced sub-conductor. The difference of the aerodynamic loads on all the sub-conductors should be considered in the analysis of galloping of iced bundle conductors.
Galloping of iced conductor is a typical nonlinear problem.In this thesis, the study on the nonlinear numerical simulation method for galloping of iced conductor is performed. Based on the principle of virtual work, an updated Lagrangian finite element formulation for the geometrical large deformation analysis of galloping of the iced conductor in an overhead transmission line is developed. In the procedure of numerical simulation, a three-node isoparametric cable element with three translational and one torsional degrees-of-freedom at each node is, are employed to discretize the transmission line; and the nonlinear dynamic system equation is solved by the Newmark time integration method and the Newton-Raphson nonlinear iteration strategy. Numerical examples are employed to demonstrate the efficiency of the presented method and the developed finite element program. Furthermore, a new possible galloping mode, which may reflect the saturation phenomenon of nonlinear dynamic system, is discovered on the condition that the lowest order of vertical natural frequency of the transmission line is approximately two times of the horizontal one.
Based on the obtained nonliear finite element formulation for galloping of iced single conductor, a numerical method, in which the spacers are simulated with Euler beam, for galloping of iced bundle conductors is obtained, and the corresponding computer program is also developed. A numerical example is used to demonstrate the efficiency of the presented method and the developed finite element program. Furthermore, the galloping of the quad-bundled conductors with different span lengths is numerically investigated. It is observed that the transmission lines with shorter length of span gallope mainly with lower vibraion modes, and higher modes may occure for the lines with larger span when galloping takes place, which provides some references for the development of anti-galloping technology. In addition, the galloping of iced quad-bundled conductors in the case of considering and without considering the inference of wake around the iced sub-conductors is compared. The results indicate that the galloping amplitude as the wake inference being considered is lager than that as the wake inference not being considered.
Galloping of iced qua-bundled conductor in stochastic wind field is firstly investigated by the numerical method developed in this paper. The stochastic wind fields are simulated by the Kaimal spectrum, with which the variation of wind velocity fluctuation with height above ground is taken into account, and the Davenport mutual spectrum. The correlation simples of stochastic wind at the points along the line direction are numerically simulated by means of the WAWS, based on which the aerodynamic loads of iced conductor are calculated. The galloping of iced quad-bundled conductor in stochastic wind filed with different span length is then numerically investigated, and some meaningful conclusions are obtained.The results show that galloping characteristics of the iced transmission lines in stochastic wind field are similar to those of the line in steady wind field. Moreover, the vibration amplitudes of the lines with smaller span length in stochastic wind are bigger than those of the line in steady wind field, but the vibration amplitudes of the lines with larger span in stochastical wind are less than those of the lines in steady wind.
To verify the numerical simulation method of nonlinear galoping of iced onductor, two wind tunnel tests of typical galloping models, one for siced single conductor and the other for quad-bundled conductor, were performed, in which the galloping tracks of iced single conductor and iced quad-bundled conductor were obtained. The finite element models of the two tests are set up by the nonlinear finite element simulation methods presented in this paper, and they are used to simulate galloping of the test conductor models. The concidence between the numerical simulation results and wind tunnel tests demonstrate the correctness and efficiency of the presented numerical methods.
Research results in this paper provides necessary test data and effective numerical method for the study on galloping of iced bundle conductor, so as to found the theory bases for anti-galloping method of iced bundle conductor.
引文
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