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Numerical Simulation of Effects of Building Tip on Atmospheric Electric Field Distortion
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摘要: 建筑物尖端周围大气电场畸变特征研究是大气电学的重要分支之一。假定建筑物为理想导体并与地面充分连接，通过有限差分法计算二维泊松方程，得出建筑物周围的电位空间分布。讨论建筑物尖端的高度、宽度以及相对位置对大气电场畸变的影响，结果表明：最大电场畸变系数λi随高度呈线性增加，且线性方程斜率随宽度增加而减小；λi随尖端位置沿建筑屋顶的中心线向两边呈对称递增趋势，此趋势随建筑物高度增加更为显著; λi随尖端宽度呈指数递减关系，且宽度对畸变系数的影响随高度增加变得尤为显著。Abstract: The effects of building tip on atmospheric electric field distortion are an important part of atmospheric electricity, especially in the research of corona layer above the inhomogeneous underlying surface, upward lightning leader and even upward lightning initiated from tall building, and also an influencing factor in lightning protection. For the account that the existing measurements are ineffectual in measuring the electric intensity above the tip, numerical simulation becomes very helpful.Assuming the building to be an ideal conductor and fully connected with earth and the potential is 0, which satisfies the Dirichlet boundary condition; three other air boundaries all satisfying Numann boundary condition and the electric potential gradient on these boundaries are constants. A two-dimensional finite difference method of calculation is used to obtain the potential distribution around the building and electric intensity near the tip in further. What's more, the two-dimensional finite difference equation is solved by successive over-relaxation method.The effects on the atmospheric electric field distortion by the height, width and location of building's tip are discussed, respectively. The result shows that λi (maximum distort coefficient of electric field) is linearly increasing with height and the slope of linear equation is decreasing with width. λi shows symmetrical increasing trend when the tip is located from the center to the each edge on the roof of a structure. It grows evidently with the increasing height of structure. Furthermore, λi is declined exponentially with the tip width, particularly when less than five meters, λi has a sensitive response to width, and the effect on λi by width is more obviously presented with the increasing height. Taking no account of the extinction effect of corona layer, electric field intensification shows much greater on the top when the structure is taller and thinner. In actual problems, the effects on electric field distortion mainly depend on the structure height when the top is flat. But when there is an obvious tip such as lightning conductor and so on, the height, width and location of tip should be taken into consideration.
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图 2 不同尖端高度周围大气电场的电位等值线分布 (单位：kV)
(a) 尖端高度为530 m, (b) 尖端高度为230 m
Fig. 2 Plot of equipotentials around building and tip in different heights under the atmospheric electric field (unit:kV)(a) the height of tip is 530 m, (b) the height of tip is 230 m
图 3 不同建筑物宽度条件下最大电场畸变系数 (E/E0) 随尖端高度 (HT) 变化的关系曲线
Fig. 3 Variation of E/E0 with HT when the structure width are fixed at 100 m, 50 m and 30 m, respectively
图 4 不同尖端宽度周围大气电场的电位等值线分布 (单位：kV)
(a) 尖端宽度为1 m, (b) 尖端宽度为30 m
Fig. 4 Plot of equipotentials around building and tip in different widths under the atmospheric electric field (unit:kV)(a) the width of tip is 1 m, (b) the width of tip is 30 m
图 5 地面上 (HT=30 m) 最大电场畸变系数E/E0随尖端宽度w变化的关系曲线
Fig. 5 Variation of E/E0 with w when tip on the ground (HT=30 m)
图 6 不同高度建筑物条件下最大电场畸变系数E/E0随尖端宽度w变化的关系曲线
Fig. 6 Variation of E/E0 with w by buildings with different heights
图 7 不同尖端位置周围大气电场的电位等值线分布 (单位：kV)
(a) 尖端设置于顶面的左边界上，(b) 尖端设置与顶面的中间部分
Fig. 7 Plot of equipotentials around building and tip in different tip locations under the atmospheric electric field (unit:kV)
(a) the tip locates at the left edge of the roof, (b) the tip locates at the center of the roof
图 8 不同高度建筑物条件下最大电场畸变系数E/E0随尖端位置s变化的关系曲线
Fig. 8 Variation of E/E0 with tip location by buildings with different heights of the structure
表 1 不同宽度建筑物λi与HT的拟合方程中常量的取值
Table 1 The constant values of fitting equation of λi and HT by buildings with different widths
W/m a b 30 2.3574 0.097 50 2.4849 0.092 100 2.5462 0.090 
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表 2 不同高度建筑物λi与w的拟合方程中常量的取值
Table 2 The constant values of fitting equation of λi and w by buildings with different heights
H/m a t b R2 0 3.10802 4.62834 4.75243 0.988 100 10.63255 4.54626 12.74505 0.989 300 25.55048 4.46437 28.78252 0.990 500 40.37338 3.89759 46.42381 0.995
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表 3 不同高度建筑物下λi与s拟合方程中常量取值
Table 3 The constant values of fitting equation of λi and s by buildings with different heights
H/m a b c R2 500 0.00228 -0.22207 78.69342 0.983 300 0.00137 -0.13339 50.20669 0.982
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