CN115169267A - A numerical simulation method for the growth of ice-covered ice on the surface of transmission line insulators without overflow - Google Patents

A numerical simulation method for the growth of ice-covered ice on the surface of transmission line insulators without overflow Download PDF

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CN115169267A
CN115169267A CN202211098383.1A CN202211098383A CN115169267A CN 115169267 A CN115169267 A CN 115169267A CN 202211098383 A CN202211098383 A CN 202211098383A CN 115169267 A CN115169267 A CN 115169267A
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insulator
ice
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胡玉耀
刘宗源
赵冲
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Shandong University of Technology
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Abstract

A numerical simulation method for the increase of ice coating on the surface of an insulator of a power transmission line without overflow belongs to the technical field of prediction of ice coating on the insulator of the power transmission line. S1, establishing an equal-proportion insulator three-dimensional geometric model and constructing an external flow field area; s2, determining the motion tracks of the insulator icing continuous phase air flow field and the dispersed phase water drop; s3, obtaining a local collision coefficient of the surface of the insulator by a triangular area projection method; s4, judging the icing growth type according to the freezing coefficient value; s5, reconstructing an icing boundary by a point-line-surface-body modeling method to obtain a three-dimensional model of the insulator icing growth form; and S6, taking the three-dimensional model as an initial condition of an air flow field in the next time step, and repeating the steps to perform the circulation iteration of ice coating growth until the ice coating form in the required time is obtained. The method can predict the icing growth form, the icing growth thickness at any position on the surface of the insulator and the icing quality, and can be used for constructing an icing early-warning mechanism of the power transmission line in an extreme environment.

Description

一种输电线路绝缘子表面无溢流覆冰增长数值模拟方法A numerical simulation method for the growth of icing on the surface of transmission line insulators without overflow

技术领域technical field

一种输电线路绝缘子表面无溢流覆冰增长数值模拟方法，属于输电线路绝缘子覆冰预测技术领域。The invention discloses a numerical simulation method for the growth of ice coating without overflow on the surface of a transmission line insulator, belonging to the technical field of ice coating prediction of transmission line insulators.

背景技术Background technique

随着国民经济的快速发展，为满足日益增长的电力需求，实现我国大范围的电力资源优化配置，国家电网公司建设了多条特高压交、直流输电线路。特高压输电线路在输送容量、电能损耗、经济性等方面有明显优势。但由于输送距离远，不可避免地穿越气候环境复杂的地区，绝缘子作为电力系统中重要的器件，其电气特性对电力系统的安全稳定运行起着决定性的作用。在正常环境下，绝缘子的性能能够满足线路运行的要求。但在低温天气，绝缘子表面的覆冰积雪将严重降低绝缘子的电气及机械强度，导致绝缘子闪络、倒杆倒塔等严重影响电网安全稳定运行的事故发生，故需要针对上述问题提高输电线路绝缘子的设计标准和防灾水平。With the rapid development of the national economy, the State Grid Corporation of China has constructed a number of UHV AC and DC transmission lines in order to meet the growing demand for electricity and realize the optimal allocation of power resources in a wide range of my country. UHV transmission lines have obvious advantages in transmission capacity, power loss and economy. However, due to the long transmission distance, it is inevitable to pass through areas with complex climate and environment. As an important device in the power system, the electrical characteristics of the insulator play a decisive role in the safe and stable operation of the power system. Under normal circumstances, the performance of insulators can meet the requirements of line operation. However, in low temperature weather, the ice and snow on the surface of the insulator will seriously reduce the electrical and mechanical strength of the insulator, resulting in the occurrence of accidents such as insulator flashover, falling poles and towers that seriously affect the safe and stable operation of the power grid. Design standards and disaster prevention levels of insulators.

目前对于输电线路覆冰预测模型的研究大多集中在输电导线方面，由于绝缘子结构复杂，目前尚无较成熟的绝缘子覆冰预测模型。At present, most of the research on the prediction model of icing on transmission lines focuses on the transmission wire. Due to the complex structure of insulators, there is no mature prediction model for icing on insulators.

发明内容SUMMARY OF THE INVENTION

本发明要解决的技术问题是：克服现有技术的不足，提供一种输电线路绝缘子表面无溢流覆冰增长数值模拟方法，用以建立极端环境下输电线路防冰减冰预警机制。The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art, and provide a numerical simulation method for the growth of ice-covering without overflow on the surface of transmission line insulators, so as to establish an anti-icing and de-icing early warning mechanism for transmission lines in extreme environments.

本发明解决其技术问题所采用的技术方案是：输电线路绝缘子表面无溢流覆冰增长数值模拟方法，其特征在于：包括以下步骤：The technical solution adopted by the present invention to solve the technical problem is: a numerical simulation method for the growth of ice coating without overflow on the surface of a transmission line insulator, which is characterized by comprising the following steps:

S1建立等比例绝缘子三维几何模型并构建外流场区域；S1 establishes a three-dimensional geometric model of an isometric insulator and constructs an external flow field area;

S2根据实际气象数据设置流场的边界条件，得到绝缘子覆冰连续相空气流场及分散相水滴的运动轨迹；S2 sets the boundary conditions of the flow field according to the actual meteorological data, and obtains the air flow field of the insulator icing continuous phase and the movement trajectory of the dispersed phase water droplets;

S3提取水滴从释放到被绝缘子捕获整个过程的三维坐标、速度大小与方向，通过三角面积投影法获得绝缘子表面局部碰撞系数；S3 extracts the three-dimensional coordinates, velocity and direction of the entire process from release to capture by the insulator, and obtains the local collision coefficient on the surface of the insulator by the triangular area projection method;

S4根据能量守恒原理构建热平衡方程确定绝缘子表面各位置冻结系数，并根据冻结系数值的大小判断覆冰增长类型；S4 constructs a heat balance equation according to the principle of energy conservation to determine the freezing coefficient of each position on the surface of the insulator, and judges the growth type of icing according to the value of the freezing coefficient;

S5确定一个时间步长内的覆冰增长，由“点-线-面-体”建模法对覆冰边界进行重构，得到绝缘子覆冰增长形态的三维模型；S5 determines the icing growth within a time step, reconstructs the icing boundary by the "point-line-surface-body" modeling method, and obtains a three-dimensional model of the insulator icing growth pattern;

S6将三维模型作为下一个时间步长内空气流场的初始条件，重复上述步骤进行覆冰增长的循环迭代，直至获得所需时间内的覆冰形态。S6 takes the three-dimensional model as the initial condition of the air flow field in the next time step, and repeats the above steps to perform the cyclic iteration of icing growth until the icing shape within the required time is obtained.

优选的，S2中的所述边界条件为：Preferably, the boundary conditions in S2 are:

Figure 261537DEST_PATH_IMAGE001
Figure 261537DEST_PATH_IMAGE001

Figure 352990DEST_PATH_IMAGE002
Figure 352990DEST_PATH_IMAGE002

Figure 593478DEST_PATH_IMAGE003
；
Figure 593478DEST_PATH_IMAGE003
;

Figure 137592DEST_PATH_IMAGE004
；
Figure 137592DEST_PATH_IMAGE004
;

其中，

Figure 837343DEST_PATH_IMAGE005
为湍流场入口速度，
Figure 658668DEST_PATH_IMAGE006
为环境风速，
Figure 194692DEST_PATH_IMAGE007
为湍流场出口压力，
Figure 101468DEST_PATH_IMAGE008
为湍流强度，
Figure 381140DEST_PATH_IMAGE009
为湍流尺度，
Figure 56971DEST_PATH_IMAGE010
为计算域的水力直径，
Figure 763896DEST_PATH_IMAGE011
为雷诺数。 in,
Figure 837343DEST_PATH_IMAGE005
is the inlet velocity of the turbulent field,
Figure 658668DEST_PATH_IMAGE006
is the ambient wind speed,
Figure 194692DEST_PATH_IMAGE007
is the outlet pressure of the turbulent flow field,
Figure 101468DEST_PATH_IMAGE008
is the turbulence intensity,
Figure 381140DEST_PATH_IMAGE009
is the turbulence scale,
Figure 56971DEST_PATH_IMAGE010
is the hydraulic diameter of the computational domain,
Figure 763896DEST_PATH_IMAGE011
is the Reynolds number.

优选的，所述方法还包括，覆冰绝缘子空气外流场视为常温、低速、不可压缩湍流流动，建立湍流模型：Preferably, the method further includes: establishing a turbulent flow model by treating the air outer flow field of the ice-covered insulator as a normal temperature, low speed, incompressible turbulent flow:

Figure 157969DEST_PATH_IMAGE012
；
Figure 157969DEST_PATH_IMAGE012
;

其中，

Figure 975752DEST_PATH_IMAGE013
是流场中的速度矢量；
Figure 771670DEST_PATH_IMAGE014
是空气的动力粘度；
Figure 383916DEST_PATH_IMAGE015
是由于空气湍流额外产 生的动力粘度；
Figure 530864DEST_PATH_IMAGE016
是空气密度；
Figure 152338DEST_PATH_IMAGE017
为湍流动能；
Figure 802762DEST_PATH_IMAGE018
是湍流耗散率；
Figure 851490DEST_PATH_IMAGE019
是主应力张量；
Figure 954575DEST_PATH_IMAGE020
为体积 力；
Figure 117091DEST_PATH_IMAGE021
、
Figure 887601DEST_PATH_IMAGE022
分别为
Figure 107229DEST_PATH_IMAGE017
和
Figure 697611DEST_PATH_IMAGE018
的有效普朗特常数的倒数；
Figure 660887DEST_PATH_IMAGE023
、
Figure 285904DEST_PATH_IMAGE024
、
Figure 676434DEST_PATH_IMAGE025
为湍流模型参数；
Figure 754111DEST_PATH_IMAGE026
为 湍流动能源项。 in,
Figure 975752DEST_PATH_IMAGE013
is the velocity vector in the flow field;
Figure 771670DEST_PATH_IMAGE014
is the dynamic viscosity of air;
Figure 383916DEST_PATH_IMAGE015
is the additional dynamic viscosity due to air turbulence;
Figure 530864DEST_PATH_IMAGE016
is the air density;
Figure 152338DEST_PATH_IMAGE017
is the turbulent kinetic energy;
Figure 802762DEST_PATH_IMAGE018
is the turbulent dissipation rate;
Figure 851490DEST_PATH_IMAGE019
is the principal stress tensor;
Figure 954575DEST_PATH_IMAGE020
is body force;
Figure 117091DEST_PATH_IMAGE021
,
Figure 887601DEST_PATH_IMAGE022
respectively
Figure 107229DEST_PATH_IMAGE017
and
Figure 697611DEST_PATH_IMAGE018
the reciprocal of the effective Prandtl's constant;
Figure 660887DEST_PATH_IMAGE023
,
Figure 285904DEST_PATH_IMAGE024
,
Figure 676434DEST_PATH_IMAGE025
are turbulence model parameters;
Figure 754111DEST_PATH_IMAGE026
is the turbulent flow energy term.

优选的，所述方法还包括，忽略较小的Saffman 升力、附加质量力、压差力等，可认为过冷却水滴只受到气流曳力及重力的作用，单个水滴拉格朗日运动控制方程为：Preferably, the method further includes, ignoring the small Saffman lift force, additional mass force, pressure differential force, etc., it can be considered that the supercooled water droplet is only affected by the drag force of the airflow and the gravity, and the Lagrangian motion control equation of a single water droplet is: :

Figure 255500DEST_PATH_IMAGE027
Figure 255500DEST_PATH_IMAGE027

其中，等式右侧第一项为水滴的剩余重力，即水滴重力减去空气浮力的剩余部分；

Figure 735023DEST_PATH_IMAGE028
和
Figure 296454DEST_PATH_IMAGE029
分别是水滴的重量和重力加速度；
Figure 861428DEST_PATH_IMAGE030
是水滴密度；等式右侧第二项为水滴受到的 气体曳力；
Figure 166507DEST_PATH_IMAGE031
和
Figure 500536DEST_PATH_IMAGE032
分别为空气流体相和水滴相瞬时速度；
Figure 232869DEST_PATH_IMAGE033
为液滴直径；
Figure 285139DEST_PATH_IMAGE034
为空气流体 的动力粘度。 Among them, the first term on the right side of the equation is the residual gravity of the water droplet, that is, the remainder of the water droplet gravity minus the air buoyancy;
Figure 735023DEST_PATH_IMAGE028
and
Figure 296454DEST_PATH_IMAGE029
are the weight of the droplet and the acceleration of gravity, respectively;
Figure 861428DEST_PATH_IMAGE030
is the droplet density; the second term on the right side of the equation is the gas drag force on the droplet;
Figure 166507DEST_PATH_IMAGE031
and
Figure 500536DEST_PATH_IMAGE032
are the instantaneous velocities of the air fluid phase and the water droplet phase, respectively;
Figure 232869DEST_PATH_IMAGE033
is the droplet diameter;
Figure 285139DEST_PATH_IMAGE034
is the dynamic viscosity of the air fluid.

优选的，S3中通过三角面积投影法获得绝缘子表面局部碰撞系数的方法如下：Preferably, the method for obtaining the local collision coefficient on the surface of the insulator by the triangular area projection method in S3 is as follows:

Figure 594242DEST_PATH_IMAGE035
；
Figure 594242DEST_PATH_IMAGE035
;

其中，

Figure 907411DEST_PATH_IMAGE036
为局部碰撞系数；
Figure 686011DEST_PATH_IMAGE037
、
Figure 22315DEST_PATH_IMAGE038
、
Figure 872459DEST_PATH_IMAGE039
分别为三个过冷却水滴撞击绝缘子表面时 的速度；
Figure 305715DEST_PATH_IMAGE040
为三个水滴释放时初速度，三个水滴初速度一致；
Figure 255216DEST_PATH_IMAGE041
为三个水滴初始释放位置 组成的三角形的面积；
Figure 406712DEST_PATH_IMAGE042
为三个水滴撞击在绝缘子表面后所组成三角形的面积。 in,
Figure 907411DEST_PATH_IMAGE036
is the local collision coefficient;
Figure 686011DEST_PATH_IMAGE037
,
Figure 22315DEST_PATH_IMAGE038
,
Figure 872459DEST_PATH_IMAGE039
are the velocities of the three supercooled water droplets hitting the surface of the insulator;
Figure 305715DEST_PATH_IMAGE040
is the initial velocity of the three water droplets when they are released, and the initial velocity of the three water droplets is the same;
Figure 255216DEST_PATH_IMAGE041
is the area of the triangle formed by the initial release positions of the three water droplets;
Figure 406712DEST_PATH_IMAGE042
is the area of the triangle formed by three water droplets hitting the surface of the insulator.

优选的，所述方法还包括，冻结系数基于热平衡方程推导出，绝缘子覆冰过程中的热平衡方程为：Preferably, the method further includes: deriving the freezing coefficient based on a heat balance equation, and the heat balance equation during the insulator icing process is:

Figure 467072DEST_PATH_IMAGE043
；
Figure 467072DEST_PATH_IMAGE043
;

Figure 754833DEST_PATH_IMAGE044
；
Figure 754833DEST_PATH_IMAGE044
;

Figure 140815DEST_PATH_IMAGE045
；
Figure 140815DEST_PATH_IMAGE045
;

Figure 779607DEST_PATH_IMAGE046
；
Figure 779607DEST_PATH_IMAGE046
;

Figure 643658DEST_PATH_IMAGE047
；
Figure 643658DEST_PATH_IMAGE047
;

Figure 51506DEST_PATH_IMAGE048
；
Figure 51506DEST_PATH_IMAGE048
;

Figure 342810DEST_PATH_IMAGE049
；
Figure 342810DEST_PATH_IMAGE049
;

Figure 206248DEST_PATH_IMAGE050
；
Figure 206248DEST_PATH_IMAGE050
;

Figure 608410DEST_PATH_IMAGE051
；
Figure 608410DEST_PATH_IMAGE051
;

Figure 870764DEST_PATH_IMAGE052
；
Figure 870764DEST_PATH_IMAGE052
;

Figure 332970DEST_PATH_IMAGE053
；
Figure 332970DEST_PATH_IMAGE053
;

Figure 680775DEST_PATH_IMAGE054
。
Figure 680775DEST_PATH_IMAGE054
.

其中，

Figure 886628DEST_PATH_IMAGE055
为绝缘子表面某控制单元碰撞并捕获水滴的部分由0℃水冻结为0℃冰 过程中释放的潜热；
Figure 3488DEST_PATH_IMAGE056
为所取控制单元面积；
Figure 902174DEST_PATH_IMAGE057
、
Figure 737275DEST_PATH_IMAGE058
、
Figure 746819DEST_PATH_IMAGE059
分别为碰撞系数、捕获系数和冻 结系数，捕获系数恒为1；
Figure 718187DEST_PATH_IMAGE060
为液态水含量；
Figure 787774DEST_PATH_IMAGE061
为环境风速；
Figure 110171DEST_PATH_IMAGE062
，为冰的融化 潜热；
Figure 657827DEST_PATH_IMAGE063
为气流的摩擦加热；
Figure 749279DEST_PATH_IMAGE064
为水滴碰撞动能；
Figure 989768DEST_PATH_IMAGE065
为0℃的冰冻结至覆冰绝缘子表面稳 态温度
Figure 530952DEST_PATH_IMAGE066
时释放的热量；
Figure 882299DEST_PATH_IMAGE067
为冰的比热；
Figure 31521DEST_PATH_IMAGE068
为短波辐射所获能量；
Figure 567544DEST_PATH_IMAGE069
为对流热损失；
Figure 474320DEST_PATH_IMAGE070
是 覆冰表面对流换热系数；
Figure 488413DEST_PATH_IMAGE071
为环境温度；
Figure 695403DEST_PATH_IMAGE072
为覆冰动态平衡时覆冰表面温度；
Figure 136749DEST_PATH_IMAGE073
为液态水 蒸发或冰的升华所带走的热量；
Figure 796400DEST_PATH_IMAGE074
为蒸发或升华系数；
Figure 614183DEST_PATH_IMAGE075
为温度为
Figure 144522DEST_PATH_IMAGE076
时的覆冰表面的水 面或冰面的饱和水汽压；
Figure 22348DEST_PATH_IMAGE077
为温度在
Figure 903716DEST_PATH_IMAGE076
时的蒸发或升华潜热；
Figure 525191DEST_PATH_IMAGE078
为空气 比热；
Figure 175615DEST_PATH_IMAGE079
为气压；
Figure 164955DEST_PATH_IMAGE080
为大气中的过冷却水滴冻结在绝缘子表面时，由过冷却状态的
Figure 658253DEST_PATH_IMAGE071
迅速 上升至0℃过程中过冷却水滴吸收的热量；
Figure 693205DEST_PATH_IMAGE081
为液态水的比热；
Figure 588349DEST_PATH_IMAGE082
为长波辐射损失的热量；
Figure 417765DEST_PATH_IMAGE083
为冰面发射率，
Figure 398359DEST_PATH_IMAGE084
为 Stefan-Boltzman 常量；
Figure 237002DEST_PATH_IMAGE085
为传导热损失；
Figure 721073DEST_PATH_IMAGE086
为热传导法线 方向的温度梯度；
Figure 986969DEST_PATH_IMAGE087
为未冻结部分过冷却水滴离开冰面带走的热量。 in,
Figure 886628DEST_PATH_IMAGE055
It is the latent heat released in the process of freezing water at 0°C into ice at 0°C when a control unit on the surface of the insulator collides and captures water droplets;
Figure 3488DEST_PATH_IMAGE056
is the area of the control unit taken;
Figure 902174DEST_PATH_IMAGE057
,
Figure 737275DEST_PATH_IMAGE058
,
Figure 746819DEST_PATH_IMAGE059
are the collision coefficient, capture coefficient and freezing coefficient, respectively, and the capture coefficient is always 1;
Figure 718187DEST_PATH_IMAGE060
is the liquid water content;
Figure 787774DEST_PATH_IMAGE061
is the ambient wind speed;
Figure 110171DEST_PATH_IMAGE062
, the latent heat of melting ice;
Figure 657827DEST_PATH_IMAGE063
Frictional heating of the airflow;
Figure 749279DEST_PATH_IMAGE064
is the kinetic energy of the water droplet collision;
Figure 989768DEST_PATH_IMAGE065
Freeze from 0°C to the steady-state temperature of the ice-coated insulator surface
Figure 530952DEST_PATH_IMAGE066
heat released during
Figure 882299DEST_PATH_IMAGE067
is the specific heat of ice;
Figure 31521DEST_PATH_IMAGE068
Energy obtained from shortwave radiation;
Figure 567544DEST_PATH_IMAGE069
is convective heat loss;
Figure 474320DEST_PATH_IMAGE070
is the convective heat transfer coefficient of the ice-covered surface;
Figure 488413DEST_PATH_IMAGE071
is the ambient temperature;
Figure 695403DEST_PATH_IMAGE072
is the icing surface temperature when icing is in dynamic equilibrium;
Figure 136749DEST_PATH_IMAGE073
The heat removed by the evaporation of liquid water or the sublimation of ice;
Figure 796400DEST_PATH_IMAGE074
is the evaporation or sublimation coefficient;
Figure 614183DEST_PATH_IMAGE075
for the temperature
Figure 144522DEST_PATH_IMAGE076
The water surface or the saturated water vapor pressure of the ice surface at the time of the ice-covered surface;
Figure 22348DEST_PATH_IMAGE077
for the temperature at
Figure 903716DEST_PATH_IMAGE076
the latent heat of evaporation or sublimation;
Figure 525191DEST_PATH_IMAGE078
is the specific heat of air;
Figure 175615DEST_PATH_IMAGE079
is air pressure;
Figure 164955DEST_PATH_IMAGE080
When the supercooled water droplets in the atmosphere freeze on the surface of the insulator, the supercooled state
Figure 658253DEST_PATH_IMAGE071
The heat absorbed by the supercooled water droplets during the rapid rise to 0°C;
Figure 693205DEST_PATH_IMAGE081
is the specific heat of liquid water;
Figure 588349DEST_PATH_IMAGE082
is the heat lost by long-wave radiation;
Figure 417765DEST_PATH_IMAGE083
is the ice surface emissivity,
Figure 398359DEST_PATH_IMAGE084
is the Stefan-Boltzman constant;
Figure 237002DEST_PATH_IMAGE085
is the conduction heat loss;
Figure 721073DEST_PATH_IMAGE086
is the temperature gradient in the normal direction of heat conduction;
Figure 986969DEST_PATH_IMAGE087
The heat carried away by the supercooled water droplets leaving the ice for the unfrozen part.

优选的，所述方法还包括，冻结系数

Figure 189281DEST_PATH_IMAGE088
为：Preferably, the method further comprises: freezing coefficient
Figure 189281DEST_PATH_IMAGE088
for:

Figure 831614DEST_PATH_IMAGE089
。
Figure 831614DEST_PATH_IMAGE089
.

优选的，所述方法还包括，湿增长覆冰时，覆冰沿着绝缘子表面法向增长；干增长覆冰时，覆冰沿着液滴碰撞方向增长。Preferably, the method further comprises: when the ice is grown wet, the ice is grown along the normal direction of the surface of the insulator; when the ice is grown dry, the ice is grown along the collision direction of the droplets.

优选的，所述方法还包括，覆冰增长速率为：Preferably, the method further includes that the ice-covering growth rate is:

Figure 435771DEST_PATH_IMAGE090
；
Figure 435771DEST_PATH_IMAGE090
;

其中，

Figure 872569DEST_PATH_IMAGE060
为液态水含量；
Figure 562176DEST_PATH_IMAGE061
为环境风速；
Figure 742622DEST_PATH_IMAGE091
为覆冰密度，计算方式为： in,
Figure 872569DEST_PATH_IMAGE060
is the liquid water content;
Figure 562176DEST_PATH_IMAGE061
is the ambient wind speed;
Figure 742622DEST_PATH_IMAGE091
is the ice-covered density, calculated as:

Figure 198355DEST_PATH_IMAGE092
；
Figure 198355DEST_PATH_IMAGE092
;

其中，

Figure 806054DEST_PATH_IMAGE093
，
Figure 982957DEST_PATH_IMAGE094
为水滴半径，
Figure 701515DEST_PATH_IMAGE095
为覆冰表面温度，
Figure 280264DEST_PATH_IMAGE096
为风速。 in,
Figure 806054DEST_PATH_IMAGE093
,
Figure 982957DEST_PATH_IMAGE094
is the droplet radius,
Figure 701515DEST_PATH_IMAGE095
is the icing surface temperature,
Figure 280264DEST_PATH_IMAGE096
is wind speed.

优选的，所述方法还包括，覆冰形态的重构通过“点-线-面-体”从低维到高维的建模方法实现。Preferably, the method further includes that the reconstruction of the ice-covered shape is realized by a "point-line-surface-body" modeling method from low-dimensional to high-dimensional.

优选的，所述方法还包括，冰形重构完成后以该形态作为下一时间段空气流场计算初始条件，反复迭代计算直至获得所求时间的覆冰形状和覆冰量。Preferably, the method further includes: after the ice shape reconstruction is completed, the shape is used as the initial condition for calculating the air flow field in the next time period, and the calculation is repeated iteratively until the ice-covered shape and amount of ice-covered at the required time are obtained.

与现有技术相比，本发明所具有的有益效果是：Compared with the prior art, the present invention has the following beneficial effects:

本输电线路绝缘子表面无溢流覆冰增长数值模拟方法不仅可以预测覆冰增长形态，还可以预测绝缘子表面任何位置覆冰增长厚度及覆冰质量，通过迭代空气流场的计算方法实现了较于现有方法更强的精确性，可用于构建极端环境下输电线路覆冰预警机制，具有良好的应用前景。The numerical simulation method for the growth of ice coating on the surface of insulators of transmission lines without overflow can not only predict the growth pattern of ice coating, but also predict the growth thickness and quality of ice coating at any position on the insulator surface. The higher accuracy of the existing method can be used to construct an early warning mechanism for transmission line icing in extreme environments, which has a good application prospect.

附图说明Description of drawings

图1为输电线路绝缘子表面无溢流覆冰增长数值模拟方法的流程图；Fig. 1 is a flow chart of a numerical simulation method for the growth of icing without overflow on the surface of transmission line insulators;

图2是三角面积投影法示意图；Fig. 2 is a schematic diagram of a triangular area projection method;

图3是绝缘子杆径覆冰重构建模法示例图；Figure 3 is an example diagram of an ice-covered reconstruction modeling method for the diameter of an insulator rod;

图4是覆冰一小时内的覆冰形态预测与试验对比示意图；Figure 4 is a schematic diagram showing the comparison between the prediction of the ice coating shape and the test within one hour of ice coating;

图5是绝缘子覆冰长度试验实例与仿真对比；Figure 5 is a comparison between an example of an insulator icing length test and a simulation;

图6是绝缘子覆冰质量试验实例与仿真对比。Figure 6 is a comparison between an example of an insulator icing quality test and a simulation.

具体实施方式Detailed ways

下面结合具体实施例对本发明做进一步说明，然而熟悉本领域的人们应当了解，在这里结合附图给出的详细说明是为了更好的解释，本发明的结构必然超出了有限的这些实施例，而对于一些等同替换方案或常见手段，本文不再做详细叙述，但仍属于本申请的保护范围。The present invention will be further described below in conjunction with specific embodiments, but those familiar with the art should understand that the detailed description given here in conjunction with the accompanying drawings is for better explanation, and the structure of the present invention must exceed these limited embodiments, However, some equivalent alternatives or common means will not be described in detail herein, but still belong to the protection scope of the present application.

图1~6是本发明的最佳实施例，下面结合附图1~6对本发明做进一步说明。1 to 6 are the preferred embodiments of the present invention, and the present invention will be further described below in conjunction with the accompanying drawings 1 to 6 .

如图1所示：一种输电线路绝缘子表面无溢流覆冰增长数值模拟方法，包括以下步骤：As shown in Figure 1: A numerical simulation method for the growth of ice-covered ice without overflow on the surface of a transmission line insulator, including the following steps:

S1建立等比例绝缘子三维几何模型并构建外流场区域。S1 establishes a three-dimensional geometric model of an isometric insulator and constructs an external flow field area.

S2根据实际气象数据设置流场的边界条件，得到绝缘子覆冰连续相空气流场及分散相水滴的运动轨迹。S2 sets the boundary conditions of the flow field according to the actual meteorological data, and obtains the air flow field of the insulator icing continuous phase and the movement trajectory of the dispersed phase water droplets.

具体的，根据实际气象数据设置流场的边界条件，计算得到绝缘子覆冰连续相空 气流场及分散相水滴的运动轨迹。所需气象数据包括环境温度、大气压强、风速、风向、液态 水含量、过冷却水滴中值直径。气流入口边界设置为速度入口，大小为风速

Figure 58864DEST_PATH_IMAGE097
，且方向垂直 于入口截面；选择湍流强度
Figure 988643DEST_PATH_IMAGE008
、湍流尺度
Figure 245311DEST_PATH_IMAGE009
来表征湍流场的湍流参数，可分别由经验公式
Figure 678567DEST_PATH_IMAGE003
和
Figure 628068DEST_PATH_IMAGE004
确定，其中
Figure 779564DEST_PATH_IMAGE010
为计算域的水力直径；出口为压力出口，设置静压 力为0；对于离散相过冷却水滴，以面入射的形式均匀从计算域入口处入射，水滴初始速度 与自由来流速度相等。覆冰绝缘子空气外流场可视为常温、低速、不可压缩湍流流动。湍流 模型采用
Figure 105503DEST_PATH_IMAGE098
模型构建，计算公式为： Specifically, the boundary conditions of the flow field are set according to the actual meteorological data, and the air flow field of the continuous phase of the ice-covered insulator and the movement trajectory of the water droplets of the dispersed phase are calculated. The required meteorological data include ambient temperature, atmospheric pressure, wind speed, wind direction, liquid water content, and median diameter of supercooled water droplets. The airflow inlet boundary is set as the velocity inlet and the size is the wind speed
Figure 58864DEST_PATH_IMAGE097
, and the direction is perpendicular to the inlet section; choose the turbulence intensity
Figure 988643DEST_PATH_IMAGE008
, turbulence scale
Figure 245311DEST_PATH_IMAGE009
to characterize the turbulence parameters of the turbulent field, which can be determined by the empirical formulas
Figure 678567DEST_PATH_IMAGE003
and
Figure 628068DEST_PATH_IMAGE004
sure, where
Figure 779564DEST_PATH_IMAGE010
is the hydraulic diameter of the computational domain; the outlet is the pressure outlet, and the static pressure is set to 0; for the discrete-phase supercooled water droplets, they are uniformly incident from the inlet of the computational domain in the form of surface incidence, and the initial velocity of the water droplets is equal to the free flow velocity. The air flow field outside the ice-coated insulator can be regarded as a normal temperature, low speed, incompressible turbulent flow. The turbulence model uses
Figure 105503DEST_PATH_IMAGE098
Model construction, the calculation formula is:

Figure 393265DEST_PATH_IMAGE012
； （1）
Figure 393265DEST_PATH_IMAGE012
; (1)

其中，

Figure 513668DEST_PATH_IMAGE013
是流场中的速度矢量；
Figure 152459DEST_PATH_IMAGE014
是空气的动力粘度；
Figure 750931DEST_PATH_IMAGE015
是由于空气湍流额外产 生的动力粘度；
Figure 161708DEST_PATH_IMAGE016
是空气密度；
Figure 46488DEST_PATH_IMAGE017
为湍流动能；
Figure 782363DEST_PATH_IMAGE018
是湍流耗散率；
Figure 574738DEST_PATH_IMAGE019
是主应力张量；
Figure 446879DEST_PATH_IMAGE020
为体积 力；
Figure 564877DEST_PATH_IMAGE021
、
Figure 788048DEST_PATH_IMAGE022
分别为
Figure 118535DEST_PATH_IMAGE017
和
Figure 110762DEST_PATH_IMAGE018
的有效普朗特常数的倒数；
Figure 134081DEST_PATH_IMAGE023
、
Figure 578969DEST_PATH_IMAGE024
、
Figure 713147DEST_PATH_IMAGE025
为湍流模型参数；
Figure 825460DEST_PATH_IMAGE026
为 湍流动能源项。 in,
Figure 513668DEST_PATH_IMAGE013
is the velocity vector in the flow field;
Figure 152459DEST_PATH_IMAGE014
is the dynamic viscosity of air;
Figure 750931DEST_PATH_IMAGE015
is the additional dynamic viscosity due to air turbulence;
Figure 161708DEST_PATH_IMAGE016
is the air density;
Figure 46488DEST_PATH_IMAGE017
is the turbulent kinetic energy;
Figure 782363DEST_PATH_IMAGE018
is the turbulent dissipation rate;
Figure 574738DEST_PATH_IMAGE019
is the principal stress tensor;
Figure 446879DEST_PATH_IMAGE020
is body force;
Figure 564877DEST_PATH_IMAGE021
,
Figure 788048DEST_PATH_IMAGE022
respectively
Figure 118535DEST_PATH_IMAGE017
and
Figure 110762DEST_PATH_IMAGE018
the reciprocal of the effective Prandtl's constant;
Figure 134081DEST_PATH_IMAGE023
,
Figure 578969DEST_PATH_IMAGE024
,
Figure 713147DEST_PATH_IMAGE025
are turbulence model parameters;
Figure 825460DEST_PATH_IMAGE026
is the turbulent flow energy term.

过冷却水滴在绝缘子周围运动时，忽略较小的Saffman 升力、附加质量力、压差力等，可认为过冷却水滴只受到气流曳力及重力的作用，单个水滴拉格朗日运动控制方程为：When the supercooled water droplet moves around the insulator, ignoring the small Saffman lift force, additional mass force, pressure difference force, etc., it can be considered that the supercooled water droplet is only affected by the drag force and gravity of the air flow, and the Lagrangian motion control equation of a single water droplet is: :

Figure 754101DEST_PATH_IMAGE027
； （2）
Figure 754101DEST_PATH_IMAGE027
; (2)

其中，等式右侧第一项为水滴的剩余重力，即水滴重力减去空气浮力的剩余部分。

Figure 300268DEST_PATH_IMAGE028
和
Figure 847924DEST_PATH_IMAGE029
分别是水滴的重量和重力加速度；
Figure 939377DEST_PATH_IMAGE030
是水滴密度；等式右侧第二项为水滴受到的 气体曳力。
Figure 914286DEST_PATH_IMAGE031
和
Figure 723980DEST_PATH_IMAGE032
分别为空气流体相和水滴相瞬时速度；
Figure 75326DEST_PATH_IMAGE099
为液滴直径；
Figure 286865DEST_PATH_IMAGE100
为空气流体的 动力粘度。Among them, the first term on the right side of the equation is the residual gravity of the water droplet, that is, the remainder of the water droplet gravity minus the air buoyancy.
Figure 300268DEST_PATH_IMAGE028
and
Figure 847924DEST_PATH_IMAGE029
are the weight of the droplet and the acceleration of gravity, respectively;
Figure 939377DEST_PATH_IMAGE030
is the droplet density; the second term on the right side of the equation is the gas drag on the droplet.
Figure 914286DEST_PATH_IMAGE031
and
Figure 723980DEST_PATH_IMAGE032
are the instantaneous velocities of the air fluid phase and the water droplet phase, respectively;
Figure 75326DEST_PATH_IMAGE099
is the droplet diameter;
Figure 286865DEST_PATH_IMAGE100
is the dynamic viscosity of the air fluid.

对式（2）的微分方程进行积分，即可获得水滴运动轨迹各点的速度分布，然后再在每个时间步长内对水滴速度进行积分获得水滴运动轨迹，从而获得水滴任意位置的物理参数。Integrate the differential equation of formula (2) to obtain the velocity distribution of each point of the water droplet trajectory, and then integrate the water droplet velocity in each time step to obtain the water droplet trajectory, so as to obtain the physical parameters of any position of the water droplet .

S3提取水滴从释放到被绝缘子捕获整个过程的三维坐标、速度大小与方向，通过 三角面积投影法获得绝缘子表面局部碰撞系数

Figure 698255DEST_PATH_IMAGE101
。 S3 extracts the three-dimensional coordinates, velocity and direction of the entire process from release to capture by the insulator, and obtains the local collision coefficient on the surface of the insulator by the triangular area projection method
Figure 698255DEST_PATH_IMAGE101
.

具体的，三角面积投影法如图2所示，计算公式为：Specifically, the triangular area projection method is shown in Figure 2, and the calculation formula is:

Figure 729665DEST_PATH_IMAGE035
； （3）
Figure 729665DEST_PATH_IMAGE035
; (3)

其中，

Figure 619123DEST_PATH_IMAGE036
为局部碰撞系数；
Figure 685168DEST_PATH_IMAGE037
、
Figure 1880DEST_PATH_IMAGE038
、
Figure 520586DEST_PATH_IMAGE039
分别为三个过冷却水滴撞击绝缘子表面时 的速度；
Figure 213736DEST_PATH_IMAGE040
为三个水滴释放时初速度，三个水滴初速度一致；
Figure 134287DEST_PATH_IMAGE041
为三个水滴初始释放位置 组成的三角形的面积；
Figure 887479DEST_PATH_IMAGE042
为三个水滴撞击在绝缘子表面后所组成三角形的面积。 in,
Figure 619123DEST_PATH_IMAGE036
is the local collision coefficient;
Figure 685168DEST_PATH_IMAGE037
,
Figure 1880DEST_PATH_IMAGE038
,
Figure 520586DEST_PATH_IMAGE039
are the velocities of the three supercooled water droplets hitting the surface of the insulator;
Figure 213736DEST_PATH_IMAGE040
is the initial velocity of the three water droplets when they are released, and the initial velocity of the three water droplets is the same;
Figure 134287DEST_PATH_IMAGE041
is the area of the triangle formed by the initial release positions of the three water droplets;
Figure 887479DEST_PATH_IMAGE042
is the area of the triangle formed by three water droplets hitting the surface of the insulator.

S4根据能量守恒原理构建热平衡方程确定绝缘子表面各位置冻结系数

Figure 896411DEST_PATH_IMAGE059
，并根 据冻结系数值的大小判断覆冰增长类型。 S4 According to the principle of energy conservation, the heat balance equation is constructed to determine the freezing coefficient of each position on the surface of the insulator
Figure 896411DEST_PATH_IMAGE059
, and judge the growth type of icing according to the value of freezing coefficient.

具体的，绝缘子覆冰过程中的热平衡方程为：Specifically, the heat balance equation in the process of insulator icing is:

Figure 127672DEST_PATH_IMAGE043
； （4）
Figure 127672DEST_PATH_IMAGE043
; (4)

其中，

Figure 105993DEST_PATH_IMAGE055
为绝缘子表面某控制单元碰撞并捕获水滴的部分由0℃水冻结为0℃冰 过程中释放的潜热： in,
Figure 105993DEST_PATH_IMAGE055
It is the latent heat released in the process of freezing water at 0°C into ice at 0°C for the part of a control unit on the surface of the insulator that collides and captures water droplets:

Figure 154720DEST_PATH_IMAGE044
； （5）
Figure 154720DEST_PATH_IMAGE044
; (5)

其中，

Figure 523385DEST_PATH_IMAGE056
为所取控制单元面积；
Figure 682971DEST_PATH_IMAGE057
、
Figure 187901DEST_PATH_IMAGE058
、
Figure 407530DEST_PATH_IMAGE059
分别为碰撞系数、捕获系数和冻结系 数，捕获系数恒为1；
Figure 263490DEST_PATH_IMAGE060
为液态水含量；
Figure 961188DEST_PATH_IMAGE061
为环境风速；
Figure 586204DEST_PATH_IMAGE062
，为冰的融化潜 热。 in,
Figure 523385DEST_PATH_IMAGE056
is the area of the control unit taken;
Figure 682971DEST_PATH_IMAGE057
,
Figure 187901DEST_PATH_IMAGE058
,
Figure 407530DEST_PATH_IMAGE059
are the collision coefficient, capture coefficient and freezing coefficient, respectively, and the capture coefficient is always 1;
Figure 263490DEST_PATH_IMAGE060
is the liquid water content;
Figure 961188DEST_PATH_IMAGE061
is the ambient wind speed;
Figure 586204DEST_PATH_IMAGE062
, the latent heat of melting ice.

Figure 976735DEST_PATH_IMAGE063
为气流的摩擦加热，空气对于覆冰绝缘子的加热是通过气流对冰表面的摩擦 产生的，由于空气的流速不大，此项可以忽略，即：
Figure 976735DEST_PATH_IMAGE063
For the frictional heating of the airflow, the heating of the ice-covered insulator by the air is generated by the friction of the airflow on the ice surface. Since the air velocity is not large, this item can be ignored, namely:

Figure 54412DEST_PATH_IMAGE045
。 （6）
Figure 54412DEST_PATH_IMAGE045
. (6)

Figure 821380DEST_PATH_IMAGE064
为水滴碰撞动能：
Figure 821380DEST_PATH_IMAGE064
is the kinetic energy of the droplet collision:

Figure 300903DEST_PATH_IMAGE046
。 （7）
Figure 300903DEST_PATH_IMAGE046
. (7)

Figure 859404DEST_PATH_IMAGE065
为0℃的冰冻结至覆冰绝缘子表面稳态温度
Figure 424378DEST_PATH_IMAGE066
时释放的热量：
Figure 859404DEST_PATH_IMAGE065
Freeze from 0°C to the steady-state temperature of the ice-coated insulator surface
Figure 424378DEST_PATH_IMAGE066
Heat released when:

Figure 463878DEST_PATH_IMAGE047
； （8）
Figure 463878DEST_PATH_IMAGE047
; (8)

其中，

Figure 63487DEST_PATH_IMAGE067
为冰的比热，
Figure 795819DEST_PATH_IMAGE102
。 in,
Figure 63487DEST_PATH_IMAGE067
is the specific heat of ice,
Figure 795819DEST_PATH_IMAGE102
.

Figure 848089DEST_PATH_IMAGE068
为短波辐射所获能量，因为覆冰一般发生在雾天、雨天或阴天，无阳光直射，故 通常忽略该项，即：
Figure 848089DEST_PATH_IMAGE068
The energy obtained by shortwave radiation, because icing generally occurs in foggy, rainy or cloudy days without direct sunlight, so this item is usually ignored, namely:

Figure 956859DEST_PATH_IMAGE048
。 （9）
Figure 956859DEST_PATH_IMAGE048
. (9)

Figure 410974DEST_PATH_IMAGE069
为对流热损失：
Figure 410974DEST_PATH_IMAGE069
For convective heat loss:

Figure 48629DEST_PATH_IMAGE049
； （10）
Figure 48629DEST_PATH_IMAGE049
; (10)

其中，

Figure 853774DEST_PATH_IMAGE070
是覆冰表面对流换热系数；
Figure 500656DEST_PATH_IMAGE071
为环境温度；
Figure 809277DEST_PATH_IMAGE072
为覆冰动态平衡时覆冰表 面温度。 in,
Figure 853774DEST_PATH_IMAGE070
is the convective heat transfer coefficient of the ice-covered surface;
Figure 500656DEST_PATH_IMAGE071
is the ambient temperature;
Figure 809277DEST_PATH_IMAGE072
It is the temperature of the icing surface when the icing is in dynamic equilibrium.

Figure 883413DEST_PATH_IMAGE073
为液态水蒸发或冰的升华所带走的热量：
Figure 883413DEST_PATH_IMAGE073
Heat removed by evaporation of liquid water or sublimation of ice:

Figure 644695DEST_PATH_IMAGE050
； （11）
Figure 644695DEST_PATH_IMAGE050
; (11)

其中，

Figure 95268DEST_PATH_IMAGE074
为蒸发或升华系数；
Figure 258396DEST_PATH_IMAGE075
为温度为
Figure 506363DEST_PATH_IMAGE076
时的覆冰表面的水面或冰面的饱和 水汽压；
Figure 20521DEST_PATH_IMAGE103
为温度在
Figure 9205DEST_PATH_IMAGE076
时的蒸发或升华潜热；
Figure 26840DEST_PATH_IMAGE078
为空气比热；
Figure 708357DEST_PATH_IMAGE079
为气压。 in,
Figure 95268DEST_PATH_IMAGE074
is the evaporation or sublimation coefficient;
Figure 258396DEST_PATH_IMAGE075
for the temperature
Figure 506363DEST_PATH_IMAGE076
The water surface or the saturated water vapor pressure of the ice surface at the time of the ice-covered surface;
Figure 20521DEST_PATH_IMAGE103
for the temperature at
Figure 9205DEST_PATH_IMAGE076
the latent heat of evaporation or sublimation;
Figure 26840DEST_PATH_IMAGE078
is the specific heat of air;
Figure 708357DEST_PATH_IMAGE079
for air pressure.

Figure 444232DEST_PATH_IMAGE080
为大气中的过冷却水滴冻结在绝缘子表面时，由过冷却状态的
Figure 971028DEST_PATH_IMAGE071
迅速上升至0 ℃过程中过冷却水滴吸收的热量：
Figure 444232DEST_PATH_IMAGE080
When the supercooled water droplets in the atmosphere freeze on the surface of the insulator, the supercooled state
Figure 971028DEST_PATH_IMAGE071
Heat absorbed by supercooled water droplets during rapid rise to 0 °C:

Figure 108748DEST_PATH_IMAGE051
； （12）
Figure 108748DEST_PATH_IMAGE051
; (12)

其中，

Figure 961167DEST_PATH_IMAGE081
为液态水的比热。 in,
Figure 961167DEST_PATH_IMAGE081
is the specific heat of liquid water.

Figure 246654DEST_PATH_IMAGE082
为长波辐射损失的热量：
Figure 246654DEST_PATH_IMAGE082
Heat lost for longwave radiation:

Figure 718087DEST_PATH_IMAGE052
； （13）
Figure 718087DEST_PATH_IMAGE052
; (13)

其中，

Figure 834948DEST_PATH_IMAGE083
为冰面发射率，
Figure 264792DEST_PATH_IMAGE104
，
Figure 303155DEST_PATH_IMAGE084
为Stefan-Boltzman常量，
Figure 312699DEST_PATH_IMAGE105
。 in,
Figure 834948DEST_PATH_IMAGE083
is the ice surface emissivity,
Figure 264792DEST_PATH_IMAGE104
,
Figure 303155DEST_PATH_IMAGE084
is the Stefan-Boltzman constant,
Figure 312699DEST_PATH_IMAGE105
.

Figure 956170DEST_PATH_IMAGE085
为传导热损失：
Figure 956170DEST_PATH_IMAGE085
For conduction heat loss:

Figure 350724DEST_PATH_IMAGE053
； （14）
Figure 350724DEST_PATH_IMAGE053
; (14)

其中，

Figure 407542DEST_PATH_IMAGE017
为介质的导热系数，
Figure 220777DEST_PATH_IMAGE086
为热传导法线方向的温度梯度。 in,
Figure 407542DEST_PATH_IMAGE017
is the thermal conductivity of the medium,
Figure 220777DEST_PATH_IMAGE086
is the temperature gradient in the normal direction of heat conduction.

Figure 312230DEST_PATH_IMAGE087
为未冻结部分过冷却水滴离开冰面带走的热量：
Figure 312230DEST_PATH_IMAGE087
The heat taken away by the unfrozen part of the supercooled water droplets leaving the ice surface:

Figure 287139DEST_PATH_IMAGE054
。 （15）
Figure 287139DEST_PATH_IMAGE054
. (15)

冻结系数

Figure 96832DEST_PATH_IMAGE088
为： Freeze factor
Figure 96832DEST_PATH_IMAGE088
for:

Figure 448179DEST_PATH_IMAGE089
。 （16）
Figure 448179DEST_PATH_IMAGE089
. (16)

绝缘子表面无溢流情况下的覆冰类型可通过冻结区域水膜的有无来进行判断，当 冻结系数

Figure 394138DEST_PATH_IMAGE106
时为湿增长覆冰，而当
Figure 539949DEST_PATH_IMAGE107
时为干增长覆冰。湿增长覆冰时，覆冰沿着绝缘 子表面法向增长，干增长覆冰时，覆冰沿着液滴碰撞方向增长。 The type of ice coating in the case of no overflow on the surface of the insulator can be judged by the presence or absence of water film in the freezing area.
Figure 394138DEST_PATH_IMAGE106
When wet grows ice, and when
Figure 539949DEST_PATH_IMAGE107
ice for dry growth. During wet growth, the ice grows along the normal direction of the insulator surface, and during dry growth, the ice grows along the direction of droplet collision.

S5确定一个时间步长内的覆冰增长，由“点-线-面-体”建模法对覆冰边界进行重构，得到绝缘子覆冰增长形态的三维模型。S5 determines the growth of icing within a time step, reconstructs the boundary of icing by the "point-line-surface-body" modeling method, and obtains a three-dimensional model of the growth pattern of icing on the insulator.

具体的，根据覆冰增长速率计算公式，计算一个时间步长内的覆冰增长厚度，覆冰增长速率公式为：Specifically, according to the calculation formula of the growth rate of ice coating, the thickness of the growth of ice coating in a time step is calculated, and the formula of the growth rate of ice coating is:

Figure 571359DEST_PATH_IMAGE090
； （17）
Figure 571359DEST_PATH_IMAGE090
; (17)

其中，

Figure 991976DEST_PATH_IMAGE060
为液态水含量；
Figure 792441DEST_PATH_IMAGE061
为环境风速；
Figure 374732DEST_PATH_IMAGE091
为覆冰密度，计算方式为： in,
Figure 991976DEST_PATH_IMAGE060
is the liquid water content;
Figure 792441DEST_PATH_IMAGE061
is the ambient wind speed;
Figure 374732DEST_PATH_IMAGE091
is the ice-covered density, calculated as:

Figure 893438DEST_PATH_IMAGE092
； （18）
Figure 893438DEST_PATH_IMAGE092
; (18)

其中，

Figure 586588DEST_PATH_IMAGE093
，
Figure 510069DEST_PATH_IMAGE094
为水滴半径，
Figure 591158DEST_PATH_IMAGE095
为覆冰表面温度，
Figure 206947DEST_PATH_IMAGE096
为风速。 in,
Figure 586588DEST_PATH_IMAGE093
,
Figure 510069DEST_PATH_IMAGE094
is the droplet radius,
Figure 591158DEST_PATH_IMAGE095
is the icing surface temperature,
Figure 206947DEST_PATH_IMAGE096
is wind speed.

如图3所示，通过连接碰撞点的相邻点和增长后新形成的点，形成两条曲线，将两条曲线的端点连接在一起，形成二维曲面。通过连接每组曲面的边界来构建三维实体，从而构建出新的覆冰边界。As shown in Figure 3, by connecting the adjacent points of the collision point and the newly formed points after growth, two curves are formed, and the endpoints of the two curves are connected together to form a two-dimensional surface. A new icing boundary is constructed by connecting the boundaries of each set of surfaces to build a 3D solid.

S6将新的覆冰形态作为下一个时间步长内空气流场的初始条件，重复上述步骤进行覆冰增长的循环迭代，直至获得所需时间内的覆冰形态。S6 takes the new icing form as the initial condition of the air flow field in the next time step, and repeats the above steps to perform cyclic iterations of icing growth until the icing form within the required time is obtained.

具体的，当环境温度为-10℃，风速10m/s，液滴中值直径为50

Figure 828421DEST_PATH_IMAGE108
，空气中液态水含 量为
Figure 478845DEST_PATH_IMAGE109
时，
Figure 527573DEST_PATH_IMAGE110
绝缘子一小时内覆冰形态的预测与试验对比如图4所示。 图5为复合绝缘子伞裙边缘及杆径处覆冰增长长度与试验对比，图6为复合绝缘子覆冰质量 与试验对比。 Specifically, when the ambient temperature is -10°C, the wind speed is 10m/s, the median diameter of the droplets is 50
Figure 828421DEST_PATH_IMAGE108
, the liquid water content in the air is
Figure 478845DEST_PATH_IMAGE109
hour,
Figure 527573DEST_PATH_IMAGE110
Figure 4 shows the comparison between the prediction and the test of the ice-covered shape of the insulator within one hour. Figure 5 shows the comparison of the growth length of the ice coating at the edge of the composite insulator shed and the diameter of the rod with the test, and Figure 6 shows the comparison of the ice coating quality of the composite insulator with the test.

上述输电线路绝缘子表面无溢流覆冰增长数值模拟方法具有预测精度高、方法简单有效、误差小的优点。本发明的技术方案不仅可以应用到本专利所述型号的绝缘子，还可以扩展到任何型号的绝缘子。The above numerical simulation method for the growth of icing without overflow on the surface of the transmission line insulator has the advantages of high prediction accuracy, simple and effective method, and small error. The technical solution of the present invention can not only be applied to insulators of the type described in this patent, but also can be extended to insulators of any type.

以上所述，仅是本发明的较佳实施例而已，并非是对本发明作其它形式的限制，任何熟悉本专业的技术人员可能利用上述揭示的技术内容加以变更或改型为等同变化的等效实施例。但是凡是未脱离本发明技术方案内容，依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化与改型，仍属于本发明技术方案的保护范围。The above are only preferred embodiments of the present invention, and are not intended to limit the present invention in other forms. Any person skilled in the art may use the technical content disclosed above to make changes or modifications to equivalent changes. Example. However, any simple modifications, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solutions of the present invention still belong to the protection scope of the technical solutions of the present invention.

Claims (10)

1. A numerical simulation method for the increase of ice coating without overflow on the surface of an insulator of a power transmission line is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing an equal-proportion insulator three-dimensional geometric model and constructing an outer flow field area;
s2, setting boundary conditions of a flow field according to actual meteorological data to obtain a continuous phase air flow field of the ice-coated insulator and a motion trail of dispersed phase water drops;
s3, extracting three-dimensional coordinates, speed and direction of the water drops in the whole process from releasing to being captured by the insulator, and obtaining a local collision coefficient of the surface of the insulator through a triangular area projection method;
s4, constructing a thermal balance equation according to an energy conservation principle to determine the freezing coefficient of each position on the surface of the insulator, and judging the icing growth type according to the freezing coefficient value;
s5, determining the icing growth within a time step, and reconstructing an icing boundary by a point-line-surface-body modeling method to obtain a three-dimensional model of the icing growth form of the insulator;
and S6, taking the three-dimensional model as an initial condition of the air flow field in the next time step, and repeating the steps to perform the cycle iteration of ice coating growth until the ice coating form in the required time is obtained.
2. The method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the boundary conditions in S2 are:
Figure DEST_PATH_IMAGE001
Figure 236065DEST_PATH_IMAGE002
Figure DEST_PATH_IMAGE003
；
Figure 683358DEST_PATH_IMAGE004
；
wherein,
Figure 187151DEST_PATH_IMAGE005
is the inlet velocity of the turbulent flow field,
Figure 466252DEST_PATH_IMAGE006
is the ambient wind speed and is,
Figure DEST_PATH_IMAGE007
in order to obtain the outlet pressure of the turbulent flow field,
Figure 623564DEST_PATH_IMAGE008
in order to be the intensity of the turbulent flow,
Figure DEST_PATH_IMAGE009
in order to be of a turbulent flow scale,
Figure 89311DEST_PATH_IMAGE010
in order to calculate the hydraulic diameter of the domain,
Figure 131217DEST_PATH_IMAGE011
is the reynolds number.
3. The method for simulating the numerical value of the ice accretion on the surface of the insulator of the electric transmission line according to claim 1, wherein: the method also comprises the following steps that the ice-coated insulator air external flow field is regarded as normal-temperature, low-speed and incompressible turbulent flow, and a turbulent flow model is established:
Figure 975807DEST_PATH_IMAGE012
；
wherein,
Figure 444966DEST_PATH_IMAGE013
is the velocity vector in the flow field;
Figure 584960DEST_PATH_IMAGE014
is the kinetic viscosity of air;
Figure 758452DEST_PATH_IMAGE015
due to the dynamic viscosity additionally generated by air turbulence;
Figure 582183DEST_PATH_IMAGE016
is the air density;
Figure 487822DEST_PATH_IMAGE017
is turbulent kinetic energy;
Figure 443009DEST_PATH_IMAGE018
is the turbulent dissipation ratio;
Figure 311870DEST_PATH_IMAGE019
is the principal stress tensor;
Figure 177058DEST_PATH_IMAGE020
is a volume force;
Figure 237286DEST_PATH_IMAGE021
、
Figure 181234DEST_PATH_IMAGE022
are respectively as
Figure 368633DEST_PATH_IMAGE017
And
Figure 540857DEST_PATH_IMAGE018
the inverse of the effective prandtl constant of (a);
Figure 319457DEST_PATH_IMAGE023
、
Figure 813018DEST_PATH_IMAGE024
、
Figure 725479DEST_PATH_IMAGE025
is a turbulence model parameter;
Figure 502942DEST_PATH_IMAGE026
are turbulent flow energy terms.
4. The method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method further comprises the following step that the Lagrangian motion control equation of the single water drop is as follows:
Figure 203176DEST_PATH_IMAGE027
wherein,
Figure 636562DEST_PATH_IMAGE028
and
Figure 477348DEST_PATH_IMAGE029
the weight and the gravitational acceleration of the water drop, respectively;
Figure 843739DEST_PATH_IMAGE030
is the water drop density;
Figure DEST_PATH_IMAGE031
and
Figure 777191DEST_PATH_IMAGE032
the instantaneous velocities of the air fluid phase and the water droplet phase respectively;
Figure DEST_PATH_IMAGE033
is the droplet diameter;
Figure 979764DEST_PATH_IMAGE034
is the dynamic viscosity of the air fluid.
5. The method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method for obtaining the local collision coefficient of the surface of the insulator through the triangular area projection method in the S3 comprises the following steps:
Figure DEST_PATH_IMAGE035
；
wherein,
Figure 171711DEST_PATH_IMAGE036
is the local collision coefficient;
Figure DEST_PATH_IMAGE037
、
Figure 346603DEST_PATH_IMAGE038
、
Figure DEST_PATH_IMAGE039
the velocities of the three supercooled water droplets when impacting the surface of the insulator are respectively;
Figure 293699DEST_PATH_IMAGE040
the initial speeds of the three water drops during release are consistent;
Figure DEST_PATH_IMAGE041
is the area of a triangle formed by the initial release positions of the three water drops;
Figure 717990DEST_PATH_IMAGE042
the area of a triangle formed by three water drops after impacting the surface of the insulator.
6. The method for simulating the numerical value of the ice accretion on the surface of the insulator of the electric transmission line according to claim 1, wherein: the method further comprises the step of deducing the freezing coefficient based on a heat balance equation, wherein the heat balance equation in the insulator icing process is as follows:
Figure DEST_PATH_IMAGE043
；
Figure 775944DEST_PATH_IMAGE044
；
Figure DEST_PATH_IMAGE045
；
Figure 726714DEST_PATH_IMAGE046
；
Figure 720078DEST_PATH_IMAGE047
；
Figure 897243DEST_PATH_IMAGE048
；
Figure 837517DEST_PATH_IMAGE049
；
Figure 282274DEST_PATH_IMAGE050
；
Figure 384222DEST_PATH_IMAGE051
；
Figure 986367DEST_PATH_IMAGE052
；
Figure 714021DEST_PATH_IMAGE053
；
Figure 560754DEST_PATH_IMAGE054
；
wherein,
Figure 584336DEST_PATH_IMAGE055
the method is characterized in that a part of a control unit on the surface of an insulator, which collides with and captures water drops, is released from latent heat in the process of freezing water at 0 ℃ into ice at 0 ℃;
Figure 985361DEST_PATH_IMAGE056
the area of the control unit is taken;
Figure 923230DEST_PATH_IMAGE057
、
Figure 86186DEST_PATH_IMAGE058
、
Figure 326674DEST_PATH_IMAGE059
respectively is a collision coefficient, a capture coefficient and a freezing coefficient, and the capture coefficient is constant at 1;
Figure 729843DEST_PATH_IMAGE060
is liquid water content;
Figure 284452DEST_PATH_IMAGE061
is the ambient wind speed;
Figure 325351DEST_PATH_IMAGE062
the latent heat of fusion of ice;
Figure 940004DEST_PATH_IMAGE063
friction heating for air flow;
Figure 971413DEST_PATH_IMAGE064
is the collision kinetic energy of water drops;
Figure 346025DEST_PATH_IMAGE065
freezing at 0 deg.C to the stable temperature of the surface of the ice-coated insulator
Figure 490699DEST_PATH_IMAGE066
Heat released at the time;
Figure 791099DEST_PATH_IMAGE067
is the specific heat of ice;
Figure 450750DEST_PATH_IMAGE068
energy obtained for short wave radiation;
Figure 363474DEST_PATH_IMAGE069
heat loss by convection;
Figure 628233DEST_PATH_IMAGE070
the convection heat transfer coefficient of the ice-coated surface;
Figure 99535DEST_PATH_IMAGE071
is ambient temperature;
Figure 184165DEST_PATH_IMAGE072
the surface temperature of the ice coating during the dynamic equilibrium of the ice coating;
Figure 635000DEST_PATH_IMAGE073
heat removed for liquid water evaporation or ice sublimation;
Figure 754266DEST_PATH_IMAGE074
is the evaporation or sublimation coefficient;
Figure 396469DEST_PATH_IMAGE075
is at a temperature of
Figure 391232DEST_PATH_IMAGE076
The water surface or the saturated vapor pressure of the ice surface of the ice coating;
Figure 691763DEST_PATH_IMAGE077
is at a temperature of
Figure 914803DEST_PATH_IMAGE076
Latent heat of vaporization or sublimation in time;
Figure 213060DEST_PATH_IMAGE078
is the specific heat of air;
Figure 23016DEST_PATH_IMAGE079
is the air pressure;
Figure 251872DEST_PATH_IMAGE080
the supercooled state being a state in which supercooled water droplets in the atmosphere are frozen on the surface of the insulator
Figure 80151DEST_PATH_IMAGE071
The heat absorbed by the supercooled water drops is rapidly increased to 0 ℃;
Figure 831200DEST_PATH_IMAGE081
specific heat of liquid water;
Figure 112140DEST_PATH_IMAGE082
heat lost to long wave radiation;
Figure 207004DEST_PATH_IMAGE083
in order to obtain the emissivity of the ice surface,
Figure 952106DEST_PATH_IMAGE084
Stefan-Boltzman constant;
Figure 342898DEST_PATH_IMAGE085
to conduct heat loss;
Figure 298085DEST_PATH_IMAGE086
a temperature gradient in the normal direction of heat conduction;
Figure 947372DEST_PATH_IMAGE087
the heat removed for the unfrozen portion of the supercooled water droplets to leave the ice surface.
7. The method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 6, wherein the method comprises the following steps: the method further comprises freezing the coefficients
Figure 766554DEST_PATH_IMAGE088
Comprises the following steps:
Figure DEST_PATH_IMAGE089
。
8. the method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method further comprises, during wet growth icing, the icing grows normally along the surface of the insulator; dry growth ice coating grows along the direction of droplet impingement.
9. The method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method further comprises the following steps of:
Figure 764466DEST_PATH_IMAGE090
；
wherein,
Figure 816736DEST_PATH_IMAGE060
is liquid water content;
Figure 20446DEST_PATH_IMAGE061
is the ambient wind speed;
Figure 677824DEST_PATH_IMAGE091
the ice density is calculated as follows:
Figure 174533DEST_PATH_IMAGE092
；
wherein,
Figure 340197DEST_PATH_IMAGE093
，
Figure 331287DEST_PATH_IMAGE094
is the radius of the water drop,
Figure 358018DEST_PATH_IMAGE095
in order to obtain the surface temperature of the ice coating,
Figure 776361DEST_PATH_IMAGE096
is the wind speed.
10. The method for simulating the overflow-free icing growth numerical value on the surface of the insulator of the power transmission line according to claim 1, wherein the method comprises the following steps: the method also comprises that the reconstruction of the ice coating form is realized by a modeling method from low dimension to high dimension through point-line-plane-body.
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