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Onset Corona Field Based on Isolated Metal Tip
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摘要: 为了得到金属尖端在发生电晕放电时尖端处的电场强度，该文首先采用实验室实验得到不同高度、不同形状、不同材质的金属尖端发生电晕放电时的环境电场阈值；再采用有限元法计算二维泊松方程，得到尖端处电晕触发阈值，由此得出以下结论：环境电场阈值随金属尖端高度的增大基本呈线性减小趋势，随着尖端越来越尖，环境电场阈值呈先减小后增大的变化趋势；高度、形状对金属物尖端处电晕触发阈值无影响，尖端处电晕阈值为定值；给出尖端处电晕触发阈值为158.75 kV·m-1与空间分辨率的拟合公式，可为今后电晕放电数值模拟中判断电晕放电的起始时刻提供参考。Abstract: Corona discharges characterized by much lower current densities are often generated in a strong atmospheric electric field. What's more, corona discharges are very important because the corona charge layers can change the distribution of the electric field near the ground and affect conditions of the initiation and development of an upward leader near different tall objects. Therefore, corona discharges have attracted the attention of scholars at home and abroad, especially in the onset corona field. However, how to effectively show corona emission threshold is still a difficult problem in the study of atmospheric electricity.In order to obtain the electric field strength at the tip of metal in the case of corona discharge, the onset corona voltages must be obtained by laboratory test for different heights, shapes and materials of metal tips which are arranged on the middle of lower plate of two parallel metal plates. Dimensions of two horizontal plates are 1.2 m by 1.2 m and the distance between them is 1 m. Then environmental threshold electric fields are calculated for different heights, shapes and materials of metal tips. The two-dimensional Poisson equation is solved using finite element method and the corona emission thresholds at the tip of different types of metal tips are obtained.Effects on threshold electric fields by the height, material and shape are discussed, respectively. The following conclusions can be drawn from the experimental study. First, the environmental threshold fields are basically a linear decrease with heights of metal. The environmental threshold fields decrease first and then increase when metal tips are becoming sharp increasingly. Second, the height and shape of mental tips have no effects on corona emission threshold at the tip of metal tips. The corona threshold at the tip of mental tip is a constant. Finally, the corona triggering threshold is determined which is Ec=158.75 kV·m-1 and the fitting function between corona emission threshold and spatial resolution is given. It will provide a reference for the judgment of starting moment of corona discharge for the future numerical simulation of corona discharge.
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图 1 实验采用的不同高度的金属尖端 (a) 及不同形状的金属尖端 (b)
Fig. 1 Experiment with different heights of the lightning rod (a) and different shapes of lightning rod (b)
图 2 铁制尖端触发电晕放电时环境电场强度随高度变化 (a) 以及Hb/D变化 (b)
Fig. 2 The change of environmental field strength when iron lightning rod trigger corona discharge with heights (a) and with Hb/D(b)
图 3 不同空间分辨率的尖端处电晕触发阈值
Fig. 3 The corona trigger threshold at the tip of metal cusps with different spatial resolutions
表 1 不同高度、不同形状的铁质尖端发生电晕放电时上板电晕电压值 (单位：kV)
Table 1 Corona voltage value of iron material rods with different heights and different shapes (unit:kV)
铁棒类型 第1次 第2次 第3次 第4次 第5次 平均值 Ha=25 cm -25.6 -26.0 -26.3 -25.7 -26.1 -25.94 Ha=30 cm -23.6 -23.2 -23.4 -22.9 -23.0 -23.22 Ha=39 cm -20.6 -20.1 -20.3 -20.6 -20.0 -20.32 Ha=50 cm -17.6 -17.1 -17.5 -17.8 -17.6 -17.52 Ha=30 cm，Hb=2.3 cm -22.4 -21.9 -22.6 -22.3 -22.4 -22.32 Ha=30 cm，Hb=3.0 cm -23.3 -23.5 -23.3 -23.7 -23.1 -23.38 Ha=30 cm，Hb=4.5 cm -24.1 -24.4 -24.1 -23.9 -24.2 -24.14 Ha=30 cm，Hb=6.0 cm -25.6 -25.1 -25.4 -24.9 -25.1 -25.22 
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表 2 同一形状、同一高度、不同材质的尖端上板电晕电压值 (单位：kV)
Table 2 Corona voltage value of lightning rod with the same shape, the same height and different materials (unit:kV)
材质 第1次 第2次 第3次 第4次 第5次 平均值 铁棒 -23.6 -23.2 -23.4 -22.9 -23.0 -23.22 铝棒 -22.6 -22.9 -23.2 -22.5 -22.7 -22.78 铜棒 -22.9 -22.3 -22.6 -22.3 -22.6 -22.54
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表 3 不同高度、不同形状的铁质尖端发生电晕放电时尖端处触发阈值 (单位：kV·m-1)
Table 3 Corona field threshold of iron material rods with different heights and different shapes (unit:kV·m-1)
类型 第1次 第2次 第3次 第4次 第5次 平均值 Ha=25 cm 132.510 134.581 136.133 133.028 135.098 134.270 Ha=30 cm 135.715 133.415 134.565 131.690 132.265 133.529 Ha=39 cm 136.773 133.453 134.781 136.773 132.789 134.914 Ha=50 cm 138.779 134.836 137.990 140.356 138.779 138.148 Ha=30 cm, Hb=2.3 cm 134.861 136.065 131.850 134.258 134.861 134.379 Ha=30 cm, Hb=3.0 cm 135.335 136.496 135.335 137.658 134.173 135.799 Ha=30 cm, Hb=4.5 cm 133.992 135.660 133.992 132.880 134.548 134.215 Ha=30 cm, Hb=6.0 cm 138.772 136.062 137.688 134.977 136.062 136.712
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表 4 不同形状、不同高度铁制金属物体尖端电晕电场阈值的相对误差 (单位：%)
Table 4 The relative error of corona field threshold of iron metal objects with different shapes and different heights (unit:%)
类型 第1次 第2次 第3次 第4次 第5次 Ha=25 cm 1.976 0.444 0.704 1.593 0.061 Ha=30 cm 0.395 1.307 0.456 2.583 2.158 Ha=39 cm 1.178 1.279 0.296 1.178 1.770 Ha=50 cm 2.662 0.255 2.078 3.829 2.662 Hb=2.3 cm 0.237 0.654 2.465 0.683 0.237 Hb=3.0 cm 0.114 0.973 0.114 1.832 0.746 Hb=4.5 cm 0.880 0.354 0.880 1.702 0.469 Hb=6.0 cm 2.658 0.652 1.855 0.151 0.652
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表 5 同一形状、同一高度、不同材质的尖端发生电晕放电时尖端处触发值 (单位：kV·m-1)
Table 5 Corona field threshold of lightning rod with the same shape and the same height and different materials (unit:kV·m-1)
类型 第1次 第2次 第3次 第4次 第5次 平均值 铁棒 135.715 133.414 134.565 131.690 132.265 133.529 铝棒 129.965 131.690 133.415 129.380 130.540 130.980 铜棒 131.690 128.245 129.965 128.240 129.965 129.621
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表 6 不同材质的尖端电晕电场阈值的相对误差 (单位：%)
Table 6 The relative error of corona field threshold of metal objects with different materials (unit:%)
类型 第1次 第2次 第3次 第4次 第5次 铁棒 0.395 1.307 0.456 2.583 2.158 铝棒 3.859 2.582 1.307 4.291 3.433 铜棒 2.582 5.121 3.859 5.435 3.859
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