避雷针接闪特性的影响因素分析外文翻译资料

The potential of the stepped leader channel and the striking distance

The potential of the leader channel cannot be measured directly but has to be inferred from other experimental data or theory.

Armstrong and Whitehead [6]

Armstrong and Whitehead [6] appealed to the return stroke model of Wagner [34] to obtain the potential of the leader channel as a function of the prospective return stroke current. According to the model of Wagner, the potential of the leader channel is given by the equation

V frac14; 3:7 x 106I 2=3

p

eth;20:6THORN;

In the above equation, the voltage, V, is in volts and the peak return stroke current,

Ip, in kA.

Leader potential extracted from the charge neutralized by the return stroke

How the potential of the stepped leader channel can be extracted from the charge dissipated by the first 100 ms of the return stroke channel as measured by Cooray et al. [31] is illustrated below. The description given is identical to the procedure used by Cooray and Rakov [35] to extract the stepped leader potential from the same data.

Cooray et al. [31] analysed the negative first return stroke currents measured by Berger and Vogelsanger [36, 37] at Monte San Salvatore to find out whether there is any relationship between the peak current and the charge brought to ground during the first 100 ms. They reasoned that the time interval of 100 ms is

representative of the time for the return stroke front to reach the charge centre in the cloud and therefore the charge brought to ground during this time is a result of the neutralization of the section of the leader channel located below the charge centre. They found that there is a strong correlation between the two parameters. Figure 20.3 shows the results obtained by Cooray et al. [31]. The relationship between the two parameters can be represented by the equation

Q frac14; 0:061 Ip eth;20:7THORN;

where Ip is the first return stroke peak current in kA and Q is the charge, in Coulombs, transported to ground by the return stroke during the first 100 ms. Cooray et al. [31] extended their analysis further to obtain the distribution of the linear charge density along the leader channel as a function of return stroke peak current. The procedure adopted by Cooray et al. [31] to extract the leader charge distribution corresponding to a given prospective return stroke peak current is the following. First, they assumed that the stepped leader channel can be represented by a vertical, finitely conducting channel with a given potential gradient. The length of the channel was selected by Cooray et al. [31] to be 4 km, a representative value for the height of the charge centre from the measuring station used by Berger and Vogelsanger [36, 37]. Second, they assumed that, since the negative charge region extends more in a horizontal direction than vertical, as far as the distribution of the charge along the leader channel is concerned, the effects of the charges in the cloud can be represented by a conducting plane charged to a given potential.

100

80

60

Peak current (kA)

40

20

0

0 1 2 3 4 5

Charge Q

Figure 20.3 The charge dissipated by first return strokes in the first 100 ms into the stroke (circular points). The first return stroke current waveforms used in the study are from Berger and Vogelsanger [36] and Berger [37]. The solid line shows the linear fit to the data and the dashed line the power fit [from Reference 31]

This assumption led to a uniform electric field below the cloud. Third, they assumed that the charge brought to ground during the return stroke is the sum of positive charge necessary to neutralize the negative charge on the leader channel and the additional positive charge induced on the leader channel due to the pre- sence of the background electric field caused by the remaining negative charge in the cloud. Once these assumptions are made, the analysis is carried out as follows. First, from the observed relationship between the return stroke peak current and the charge, as depicted in Figure 20.3, the charge corresponding to a given peak return stroke current is obtained. Second, the background electric field was adjusted so that the estimated total charge deposited in the leader channel by the return stroke is equal to this charge. The resulting distribution of the charge along the leader channel is the one corresponding to the prospective return stroke current selected. Since the background electric field corresponding to a given charge is known (or estimated), the leader tip potential as a function of this charge can be estimated. This potential can be expressed as a function of return stroke peak current with the aid of (20.7). The resulting relationship between the potential of the tip of the stepped leader and the peak return stroke current is given by

V frac14; 3 x 106 I 0:813

p

eth;20:8THORN;

where Ip is the first return stroke peak current in kA and V is the potential of the tip of the fully extended stepped leader channel in volts. Note that the potential gra- dient of the thermalized leader channel is about 1–2 kV/m, and the potential of the leader channel increases (by about 1–2 kV/m) as one moves along the channel towards the cloud.

It is important to point out here that the stepped leader tip potential obtained by Cooray and Rakov [35] using an identical analysis is different from the one given by (20.8). The reason for this difference is that Cooray and Rakov [35] fitted a power curve instead of a line (as done by Cooray et al. [31]) to the data in Figure 20.3. The best-fit curve used by Coora

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20.5 梯级先导通道电场和闪击距离

先导通道的电势不能被直接测量，需要借助实验数据或相关理论进行推断。

20.5.1 Armstrong and Whitehead [6]

Armstrong and Whitehead [6]认为Wagner [34]的回击模型中估计回击电流的函数应当包含先导通道的电势。根据Wagner的模型，先导通道的电势由下式给出：

（20.6）

式中电压V以伏特V为单位，回击峰值电流I_p以千安kA为单位。

20.5.2 从回击过程中中和的电荷推算先导电势

以下说明Cooray等[31]如何从回击前100 ms中和的电荷中推算出梯级先导通的电势。分析中采用的数据与Cooray和 Rakov [35]在推算中所使用的数据一致。

Cooray等[31]分析了Berger和Vogelsanger [36, 37] 在Monte San Salvatore测量的负地闪首次回击电流，以找出在回击前100 ms内峰值电流和入地电荷之间是否存在任何关系。他们认为100 ms的时间间隔是回击通道从地表到达云内电荷中心的时间，因此在此期间泄放入地的电荷是先导通道内电荷中和的结果。Cooray等发现这两个参数之间存在很强的相关性。图20.3显示了Cooray等[31]获得的结果。峰值电流和入地电荷之间的关系可以通过下式表示：

（20.7）

式中I_p为首次回击峰值电流以千安kA为单位，Q是回击前100 ms内通过回击通道入地的电荷量以库伦C为单位。Cooray等[31]进行进一步的分析以获得先导通道的线电荷密度分布，包含在回击峰值电流的函数中。Cooray等[31]由给定的回击峰值电流推算先导通道电荷分布的方法如下。对回击过程先做出三个假设：(1) 假设梯级先导通道可以由具有给定电位梯度的垂直导电通道表示，通道长度取为4 km（Berger和Vogelsanger [36, 37]通过测站测量的云内电荷中心高度的典型值）；(2)由于负电荷区水平尺度远大于其垂直尺度，就电荷沿先导通道的分布而言， 云内电荷可以看做是一个具有给定电位导电平板，这个假设意味着云下的电场分布看作是均匀的；(3)假设回击过程中入地的电荷量包含两个部分，中和先导通道内负电荷所需的正电荷量以及环境电场感应出的正电荷量。有了以上这些假设，便可以作出分析。首先，根据图20.3所示关系，给定回击峰值电流就可以得到回击电荷量。接着，调整环境电场以使预期在回击中进入通道的电荷量与第一步中求出的电荷量相等，电荷沿通道的分布与所选的预期回击峰值电流相对应。环境电场是已知（或预估）的，由此可以推算出先导尖端的电势，这个电势也可以借助式（20.7）表示成回击峰值电流的函数。最终得到的梯级先导尖端的电势与回击峰值电流的关系如下：

（20.8）

式中，I_p为首次回击峰值电流以千安kA为单位，V是充分发展的梯级先导尖端的电势以伏特V为单位。应当注意，炽热的先导通道的电势梯度为1-2 kV/m，取从先导尖端向云内的方向为电势增的方向。

图 20.3 原点处表示回击前100 ms内被中和的电荷进入回击通道。研究中使用的首次回击电流波数据来自Berger和Vogelsanger [36] 以及Berger [37]。实线是对数据进行线性拟合后得到，虚线是对功率的线性拟合[见参考文献 31]。

值得注意的是，Cooray和Rakov[35]采用相同分析方法获得的梯级先导尖端电势与式（20.8）不同。产生差异的原因是Cooray和Rakov [35]使用功率的拟合曲线而不是Cooray等[31]使用的如图20.3所示的实线。作为对比，Cooray和Rakov [35]使用的最佳拟合曲线也在图20.3中给出（虚线）。由于Cooray等[31]是基于实线得到的梯级先导线电荷分布，因而采用式(20.8) 和Cooray等[31]推算出的先导电势是合适的。

20.5.3 基于先导尖端电势推算闪击距离

在计算闪击距离时，知道梯级先导尖端的电势是十分必要的，因为最后一跃的产生取决于连接先导与梯级先导之间间隙的平均电势梯度，在没有连接先导的情况下，则取决于建筑与梯级先导之间间隙的平均电势梯度。

在连接先导很短或缺失的情况下，闪击距离S由S=V/E_S给出， 我们将其定义为在给定电势下的EGM闪击距离，用S_egm表示。在这个表达式中，E_S是在达到产生最终一跃条件时梯级先导头部与建筑尖端间的平均电场。因此，根据Armstrong 和Whitehead [6]的研究，EGM闪击距离可以表示为（结合式(20.1) 和式(20.6)）：

（20.9）

另一方面，如果使用式(20.8)的先导尖端电势，并且假定产生最后一跃的平均电场位500 kV/m，那么可以EGM闪击距离可以表示为回击峰值电流的函数 ：

（20.10）

应当注意，式(20.9)和式 (20.10)的相似仅仅是个巧合。在上面的分析中，产生最终一跃的电场为5 x 10⁵ V/m。另外，假定地面完全平坦，最终一跃的条件在梯级先导前部的负极性流光接地后达到，这在先导尖端与地物尖端间平均电场等于 (1–2) x10⁶ V/m（亦即负极性流光区的电场）时发生。平均电场如果采用1.5 x10⁶ V/m ，那么负极性梯级先导到完全平坦地面的闪击距离为：

（20.11）

上式与Cooray等[31]得到的闪击距离表达式大致相同，些许的不同之处在于，这里的计算采用确切的通道电荷分布，而Cooray等[31]采用了电荷分布的近似解析式来估计先导尖端与地表的平均电场。还要注意的是，Cooray等[31]在计算闪击距离时误将流光区电场取为5 x 10⁵ V/m。

20.6 EGM模型与SLIM模型的比较

Cooray [1]以及Cooray和Becerra [2]比较了Becerra和Cooray [19, 20, 24]提出的SLIM模型 (self- consistent leader inception and propagation model， SLIM)与EMG模型的预测结果。Cooray和Becerra [2]使用Cooray和Rakov [35]的公式计算先导尖端电势，但在这里，我们采用Cooray等[31] 的测量数据的线性拟合，即等式（20.8）来计算，这样做的原因会在下面说明。SLIM模型使用Cooray等[31]得到的先导电荷解析式计算先导产生的电场，这个解析式通过对Cooray等[31]中的实验数据进行线性拟合得到，因此在SLIM模型中使用式（20.8）计算最终一跃的条件是合适的。还有一点需要注意，在Cooray 和Becerra [2]的研究中计算的是水平和垂直导体的吸引半径，而在这里我们计算的是闪击距离。

闪击距离的定义详见第20.2节。在此，我们讨论圆柱形的垂直导体。其顶端是一个半径等于圆柱半径的半球，半径在计算中取为0.1m，垂直导体的高度从5m到100m不等。计算导体在5–90 kA回击峰值电流下的闪击距离，计算中假设先导直接击中导体顶端。在此强调要计算的闪击距离还受分析中使用的最终一跃条件的影响，这里假设当连接先导与梯级先导间的平均电场等于500 kV/m 时达到最终一跃条件。

在继续分析之前，先让我们考虑一下EGM模型。如前文所述，在EGM模型中梯级先导是否击中地物上的某点取决于该点与梯级先导尖端间的电场是否达到临界值，这里我们假设临界值为500 kV/m。回想一下，在SLIM模型中当连接先导尖端和梯级先导尖端间电场达到500 kV/m引发最终一跃。由于在EGM模型中忽略了连接先导的存在， 在一定的梯级先导电场下，EGM模型会给出较小的闪击距离。而在SLIM模型中闪击距离会随着连接先导长度的增加而增加，因而其给出的闪击距离会大于EGM模型。这当然是正确的，只要在最终一跃条件上使用相同的临界标准（即相同的间隙电场）。例如，Cooray和Becerra [38]在吸引半径的计算中，假设间隙每点的电场都应当超过500 kV/m才能达到最终一跃条件，这相比间隙平均电场超过500 kV/m的要求更严格。图20.4说明了闪击距离如何随地物高度的增加而变化。作为对比， EGM模型的闪击距离(即式(20.10)) 也在图中标出。表20.1列出了不同高度下，闪击距离随电流峰值变化而变化的解析式。

注意，在图20.4给出的数据中，随着建筑高度的增加，SLIM模型与EGM模型的闪击距离计算值的差异越来越大。在一定的建筑高度下，小峰值电流引起的差异要小于大峰值电流的。但对高度低于30m的建筑而言，即使是高达90kA的回击峰值电流，两个模型闪击距离的差异也是可以忽略的。对回击峰值电流小于16 kA，高度低于50m的建筑，二者的差值约小于30%。

Figure 20.4 不同高度圆柱形垂直导体的闪击距离。实线是Becerra 和Cooray [19, 20, 24] 的模型的计算结果。虚线是在忽略连接先导情况下的闪击距离计算结果（即EGM模型）。导体的高度分别取为 (a) 10 m, (b) 20 m, (c) 30 m, (d) 50 m, (e) 70 m, (f) 100 m。

Table 20.1 不同建筑高度下，利用回击峰值电流Ip计算闪击距离的解析式