﻿ 海床倾斜水域潜艇水下标量电位分布特征分析
 舰船科学技术  2018, Vol. 40 Issue (3): 49-54 PDF

Characteristics analysis on the underwater electric scalar potential produced by a submarine in inclined seabed waters
FENG Ya-min, CHEN Cong, TAN Hao, CHEN Fu-yu
College of Sciences, Navy University of Engineering, Wuhan 430033, China
Abstract: In order to explore the distribution of underwater electric scalar potential produced by a submarine in complex waters, inclined seabed waters was taken as a breakthrough point, after the expressions for UEP in there was derived by using mirror image method, the numerical simulation method had been used to analyze the characteristics, and compare to the parallel seabed waters. The results show that: the UEP is suitable for submarine detection and position fixing because of its measureable magnitude and obvious distribution characteristic; in a small angel range, the inclined angle of seabed and the electrical conductivity of seawater will produce an effect on the value of UEP but not the regional characteristics, the value increases linearly with the increase of the inclined angle, degenerates quadratically with the increase of electrical conductivity; there is no zero potential point and symmetry along the direction of the dipole moment when the seabed is tilted. The results lay a foundation for further researching on the distribution of corrosion related electric field produced by a submarine in more complex waters.
Key words: corrosion related static electric field     underwater electric scalar potential     horizontal direct-current dipole     inclined seabed waters     characteristics analysis
0 引　言

1 海床倾斜水域水平直流电偶极子水下标量电位分布表达式的推导

 图 1 空气—海水—倾斜海床三层媒质模型 Fig. 1 Three-layered conductive media model of air, seawater and inclined seabed

$\eta = \displaystyle\frac{{{\sigma _1} - {\sigma _2}}}{{{\sigma _1} + {\sigma _2}}}$ ，令 ${\theta _k} = \left[ {k + \frac{1}{2} + {{\left( {{{ - }}1} \right)}^{k + 1}} \cdot \frac{1}{2}} \right]\theta$ ${m_k} \!=\! \displaystyle\frac{k}{2} -$ $\displaystyle\frac{1}{4} + {\left( {{{ - }}1} \right)^k} \cdot \frac{1}{4}$ ${\eta _k} = {\eta ^{\frac{1}{4} + {{\left( {{{ - }}1} \right)}^{k + 1}} \cdot \frac{1}{4} + \frac{k}{2}}}$ $\left( {{x_{k{{a}}}},{y_{ka}},{z_{ka}}} \right)$ 表示位于空气—海水界面以下电偶极子及所有镜像电偶极子的位置坐标， ${P_{ka}}$ 表示对应其偶极矩， $k = 0,1,2 \cdots$ $\left( {{x_{kb}},{y_{kb}},{z_{kb}}} \right)$ 表示位于空气—海水界面以上所有镜像电偶极子的位置坐标， ${P_{kb}}$ 表示对应其偶极矩， $k = 1,2,3 \cdots$ 。在满足分界面两边标量电位及电流密度的法向分量连续的边界条件下，经求解（具体求解过程在此不再一一列出）可求得场源和各镜像源的位置坐标及相应的电偶极矩为：

 \small \begin{align}& \left( {{x_{k{{a}}}},{y_{ka}},{z_{ka}}} \right) = {\left(\!\!\! \begin{array}{l}{x_0}\cos {\theta _k} + {\left( { - 1} \right)^{k + 1}}{z_0}\sin {\theta _k} + 2D\sum\limits_{l = 0}^{{m_k}} {\sin 2l\theta } \\{y_0}\\{x_0}\sin {\theta _k} + {\left( { - 1} \right)^k}{z_0}\cos {\theta _k} - 2D\left( {\sum\limits_{l = 0}^{{m_k}} {\cos 2l\theta } - 1} \right)\end{array} \!\!\! \right)^{ T}},\\& {{P}_{ka}} = {\eta _k}Idl\cos {\theta _k}{i} + {\eta _k}Idl\sin {\theta _k}{k},k = 0,1,2,3 \cdots {\text{；}}\end{align}
 $\scriptsize\begin{array}{l}\left( {{x_{kb}},{y_{kb}},{z_{kb}}} \right) = {\left(\!\! \begin{array}{l}{x_0}\cos {\theta _{k - 1}} + {\left( { - 1} \right)^k}{z_0}\sin {\theta _{k - 1}} + 2D\sum\limits_{l = 0}^{{m_{k{{ - }}1}}} {\sin 2l\theta } \\{y_0}\\2D - \left\{ {{x_0}\sin {\theta _{k - 1}} + {{\left( { - 1} \right)}^{k - 1}}{z_0}\cos {\theta _{k - 1}} - 2D\left( {\sum\limits_{l = 0}^{{m_{k{{ - }}1}}} {\cos 2l\theta } - 1} \!\!\right)} \right\}\end{array} \right)^{ T}}\! ,\\{{ P}_{kb}} = {\eta _{k - 1}}Idl\cos {\theta _{k - 1}}i - {\eta _{k - 1}}Idl\sin {\theta _{k - 1}}{ k}, k = 1,2,3 \cdots {\text{。}}\end{array}$

 $\begin{array}{l} {\mathit{\Phi }_1} = \sum\limits_{k = 0}^n {\frac{{{\eta _k}Idl\cos {\theta _k}(x - {x_{ka}}) - {\eta _k}Idl\sin {\theta _k}(z + {z_{ka}} - 2D)}}{{4\pi {\sigma _1}{r_{(k + 1)b}}^3}}} + \\ \sum\limits_{k = 0}^n {\frac{{{\eta _k}Idl\cos {\theta _k}(x - {x_{ka}}) + {\eta _k}Idl\sin {\theta _k}(z - {z_{ka}})}}{{4\pi {\sigma _1}{r_{ka}}^3}}} , \end{array}$ (1)

 ${{{\varPhi }}_0} = \sum\limits_{k = 0}^n {\frac{{\frac{{2{\varepsilon _0}}}{{{\sigma _1}}}{\eta _k}Idl\cos {\theta _k}(x - {x_{ka}}) + \frac{{2{\varepsilon _0}}}{{{\sigma _1}}}{\eta _k}Idl\sin {\theta _k}(z - {z_{ka}})}}{{4\pi {\varepsilon _0}{r_{ka}}^3}}},$ (2)
 \small\begin{align}& {\varPhi _2} = \frac{{\frac{{2{\sigma _2}}}{{{\sigma _1} + {\sigma _2}}}Idl(x - {x_0})}}{{4\pi {\sigma _2}{r_1}^3}} + \\&\sum\limits_{k = 1}^n {\frac{{\frac{{2{\sigma _2}}}{{{\sigma _1} \!+\! {\sigma _2}}}{\eta _{k - 1}}Idl\cos {\theta _{k - 1}}(x \!-\! {x_{kb}}) \!+\! \frac{{2{\sigma _2}}}{{{\sigma _1} \!+\! {\sigma _2}}}{\eta _{k - 1}}Idl\sin {\theta _{k \!-\! 1}}(z \!-\! {z_{kb}})}}{{4\pi {\sigma _2}{r_{kb}}^3}}} {\text{。}}\end{align} (3)

2 海床倾斜水域潜艇水下标量电位的特征分析

2.1 海床倾斜水域标量电位的分布特征

 图 2 x=10，y=10及z=50平面上水下标量电位分布 Fig. 2 Underwater electric scalar potential distribution at x=10, y=10 and z=50

 图 3 标量电位随x、y、z的变化 Fig. 3 Variation of electric scalar potential with x、y、z

2.2 海水电导率对电位分布的影响

 图 4 不同海水电导率时标量电位随x的变化 Fig. 4 Variation of electric scalar potential with x at different electrical conductivity of seawater

 图 5 标量电位随海水电导率的变化 Fig. 5 Variation of electric scalar potential with the electrical conductivity of seawater

2.3 标量电位随海床倾斜角度的变化特征

 图 6 不同海床倾斜角度时标量电位随x的变化 Fig. 6 Variation of electric scalar potential with x at different inclined angle of seabed

 图 7 标量电位随海床倾斜角度的变化 Fig. 7 Variation of electric scalar potential with the inclined angle of seabed

3 倾斜海床水域与传统平行海床水域电位分布的对比

 图 8 倾斜海床水域与平行海床水域电位分布的比较 Fig. 8 Electric scalar potential distribution comparisons between the inclined seabed waters and parallel seabed waters

1）电位分布特征的区域性相同；

2）平行海床时存在电位为0的场点，而海床倾斜时无；

3）平行海床时电位分布关于源的投影点，沿偶极矩方向反对称，而倾斜海床时该对称性丧失。

4 结　语

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