中南大学学士学位论文 外文翻译 译文
图 9不同风速下的舞动椭圆，?0??30,fvf??0.98
在这种情况下，旋转对垂直振幅的影响减小，对垂直振幅的影响主要为不断变化的舞动椭圆的斜率。但在其他情况下可能会有相反的结果。事实上，更加重要的是迎风角的变化。迎风角的变化和垂直运动之间相位的转变也会影响竖向振幅。
?图10显示了积冰初始角为-165的结果（对应反向风）。这个角下的舞动行为与前述角度下的不同。当风速小于20m/s时，振幅保持在限制值之下，且三个方向运动的振幅都是稳定的。在不同的风速下，舞动椭圆的形状保持不变。在12m/s的风速下，峰值扭转幅度差为13?，舞动频率为0.86Hz。
??在这个频率比下(ff?0.98)，该系统除了在-20—-0之间是稳定的,其它
v?
???-180-20情况下显得十分不稳定。在—之间，系统显得十分不稳定以至在风洞
允许的最小风速下舞动就发生了。所以临界风速不能通过测量得到。有时系统自
然条件下是不稳定的，无论是小幅的转动还是垂直方向小的位移，有时必须会有扰动。对一些积冰角，观察到了特别不稳定现象。它是一个在水平面上绕覆冰中心的旋转，像一个飞机的偏航运动。
Den-Hartog舞动的特点是垂直运动和缺乏显著的扭转运动。但是对频率比约为1的情况下，有可能存在这样一个积冰角，它既遵循Den-Hartog 准则,又很容易发生颤振。在覆冰形状气动力曲线中运用的Den-Hartog准则表明有两个不稳定区
????（-180—0），其中一个在-180附近（实际覆冰的典型形状），另一个在-35附近。因此，该系统第二次形成了垂直和扭转频率的最大可用失谐。竖向的弹簧放置在离中心0.36米处。这样的布局，在无风的条件下测得垂直、扭转和水平方向的频率分别为0.85、1.54和0.96Hz（fvf??0.55）。这也同样适用于证实失谐对
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中南大学学士学位论文 外文翻译 译文
颤振的影响。试验中观察了与Den-Hartog不稳定相应的两个积冰角区域。图11显
?示了积冰角为-180的舞动。这不是极限环（振幅太大，导线碰到了开孔的平板），但很显然舞动的椭圆是垂直方向的，而且非常薄。结束时记录的旋转幅度峰值差
?小于3。各个运动方向的频率是不同的，垂直方向的频率为0.85HZ，水平频率为1.27Hz，扭转频率为1.71Hz。
图10竖向位移和舞动椭圆，U0?12m/s,?0??165,fv?
f??0.98,U0/fd?429
图11竖向位移和舞动椭圆，U0?8.5m/s,?0??180,fvf??0.55,U0/fd?308
?
5. 结论
这个试验表明，用悬挂的弹簧的模型来模拟舞动的装置是合理的。试验中观察到的（风的影响，失谐率，舞动椭圆，扰动的影响）跟数值模拟真实架空导线十分吻合。无论是对稳定性还是三维极限环来说，这是用来验证数值模拟的一个很好的工具。
在不久的将来，将进行用来评估分裂导线在尾流效应下的气动力系数的试验。这将带来一个与单导线相当的更加适合的分裂导线模型。还将进行其它的试验，以更好的确定阻尼对舞动稳定性和振幅的影响（在三个自由度上）。还将进行不同失谐率下的单导线和分裂导线的测试。不幸的是，我们的风洞不能方便评价湍流的影响，这也是一个极大的关注点。
致谢
作者非常感谢”la Communauté Francaise de Belgique”在这个项目中提供的经济支持。感谢“cêblerise de Dour”为我们提供导线试样。特别感谢来自全国高压电线路网的Mike Tunstall为我们提供接近自然覆冰的人工覆冰试样。
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中南大学学士学位论文 外文翻译 原文
Journal of Wind Engineering
and Industrial Aerodynamics 74—76 (1998) 967—976
Galloping of electrical lines in wind tunnel facilities
O. Chabart, J.L. Lilien*
Abstract
Galloping is a large amplitude, low frequency, wind-induced oscillation of overhead electrical lines. In the vast majority of cases, an ice accretion is present on the conductor: this has the effect of modifying the conductor?s cross-sectional shape such that it becomes aerodynamically and/or aeroelastically unstable. This paper deals with galloping generated during wind tunnel testing. A typical eccentric ice shape has been reproduced on a classical stranded overhead line conductor. In the first part, the quasi-static aerodynamic coefficients have been measured for different wind speeds in the range of galloping observations. In the second part the same sample has been suspended in the wind tunnel by springs in order to obtain a system as close as possible to an overhead line (vertical, horizontal and rotational movements are allowed). For appropriate angles of attack, galloping has been obtained. For an electrical engineer, there are two kinds of galloping: Den-Hartog galloping and flutter galloping. The first one is an aerodynamic instability because the main factor at the origin of this problem is the aerodynamic properties of the ice deposit. The flutter galloping is an aeroelastic problem. For this type of instability, the structural properties of the line are also important and there is a coupling between at least two degrees of freedom. Both of them were recorded. These tests make available a full set of data and recordings of limit cycles during galloping events. Such measurements can be used for numerical model validation and for efficiency evaluation of some anti-galloping means (detuning, increase of damping in vertical, torsion, modification of rotational inertia, etc.).
Keywords: Overhead lines; Vibrations; Galloping; Wind tunnel
1. Introduction
Overhead lines galloping may bring flashover between phases and cause damage to the conductors, the fittings or the towers. It affects the reliability of energy transmission; moreover, construction costs must be increased to reduce the flashover probability. Numerous practical observations have been summarized in the literature [9—11], mainly on single conductors.
Despite some nice papers on the wind tunnel approach [2,3,6,13], there are no published papers, known to the authors, on the full experimental set of data of galloping, except for one case on a single conductor with partial results [14]. On the field there are many videos, but no access to the data on the conductor lines and/or the wind speed and/or the ice shape, and of course (but obviously) no aerodynamic properties of the ice coating during an observed event! Some recent tests on a full-scale site will give access in the near future to some extraordinary attractive results [17].
In fact in the past some field tests were performed with an artificial D shape
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中南大学学士学位论文 外文翻译 原文
which easily causes Den-Hartog galloping [1]. From our point of view such tests do not reproduce actual galloping on an overhead line, or only exceptionally. None of the wet snow, rime or glaze ice on overhead line conductors could reproduce a D shape [15]. Only a very thin eccentric layer could induce Den-Hartog galloping for the natural position of the ice eccentricity facing the wind [2,5,13,16]. But most of the deposits would not be like that.
A simple and cheap way to get a full data set is a laboratory test. As it is impossible to put overhead lines in a wind tunnel and as a reduced scale model will not simulate the true phenomenon, we decided to experiment a string suspended model of a small section of the line. The conductor, the artificial ice and the wind remain as in the field but the span and interaction between spans in a line is replaced by giving to the model the appropriate frequencies of oscillations. As we were convinced like others [4,6—8] of the fundamental influence of the three frequencies (horizontal, vertical and torsion), appropriate test arrangements were installed. We have not obtained the feedback related to tension changes in the cable, but this phenomena is very easily reproduced by simulation, and is not a fundamental parameter to evaluate galloping instabilities and influences of some parameters (like detuning, damping, etc.).
Our wind tunnel tests will give access to a full complete set of data for the validation of a numerical model. Moreover, a nice experimental set is available to test many parameters, like different frequencies for each degree of freedom (including the effect of detuning), the wake effect on galloping for a bundle conductor (2 conductors will be put in the tunnel), damping effects (appropriate dampers will be inserted in the test arrangement), etc.
After validation of a numerical model [12,17,18], the same model can then be used for full-scale simulations, including tension variation, full inter-spans effects, spacers effects, inter-phase spacers effects, etc.
2. Test sample
This paper will be restricted to one kind of ice shape, very eccentric (Fig. 1). Other slightly eccentric shape has also been studied during our tests.
The overhead line conductor is the one used in Belgium for 400 kV networks: AMS(all aluminum alloy conductor) 620;10\\ m (diameter 32.5;10\\ m). The outside layer of a conductor was placed on an aluminum tube of appropriate diameter in order to maintain a straight line of the sample for approximately one meter. Artificial ice has been chosen close to Mike Tunstall shape C1 [13] and adapted to our outside diameter. The ?ice? in silicone (density 1.13) has been modeled on the cable with a wooden mold on which the roughness pattern has been printed (Fig. 2). This pattern has been copied from the original sample (itself obtained from a sample of real ice accretion). The length of the artificial ice is 0.8 m and its eccentricity, the ratio between the ice thickness and the radius of the conductor, is 1.32. The distance between the center of gravity of the ice and the center of the cable is 2.17?10?2m.
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中南大学学士学位论文 外文翻译 原文
Fig.1.Ice shape and sign convention.
Fig. 2. View of the ice sample.
3. Wind tunnel facilities
The wind tunnel of our university is small and originally designed and used by the aeronautical department. The 46 kW electrical engine allows a wind speed of 60 m/s, but the minimum wind speed is about 8 m/s. It is a close loop with an open section for the testing area. The diameter of the useful circular cross-section is 0.8 m. The turbulence intensity is about 1%.
The sample is suspended by a rigid rod to a frame and 3 dynamometers (10 kg maximal load, 0.1% of deviation on full-scale measurement) are used to measure the aerodynamic coefficients. Two vertical dynamometers (set at 1 and 2 in Fig. 5) measure the vertical force (?) and the moment (M). The last one (set at 3) measures the drag (D). The average of the forces over 1 min is taken three times for each angle of attack and this for five different wind speeds (between 8 and 20 m/s). The 360° range of angle of attack has been covered with an increment of 5°. Fig. 3 shows the experimental measurements for a specific wind speed.
In order to obtain usable curves, we apply different data processing (average, spine or Fourier interpolation). Fig. 4 is an illustration of the final result.
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