# Size Distribution of Contamination Particulate on Porcelain Insulators

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Size Distribution Characteristics of Adhered Particle

#### 2.1. Measurement Method

#### 2.2. Typical Particle Size Distribution Characteristics

#### 2.3. Particle Size Distribution Characteristics

#### 2.4. Particle Size Measurment Results of References

## 3. Motion Characteristics of Particle

#### 3.1. Aerodynamic Characteristics of Particle

#### 3.1.1. Mathematical Model of Airflow Phase

^{3}; p is the average pressure, Pa; μ is dynamic viscosity coefficient of air.

_{k}and σ

_{ε}are Prandtl numbers corresponding to turbulent kinetic energy k and dissipation rate ε, respectively, σ

_{k}= σ

_{ε}= 1.393; μ

_{eff}is effective dynamic viscosity coefficient of air, μ

_{eff}= μ + μ

_{t}; μ

_{t}is turbulent viscosity coefficient of air, μ

_{t}= ρC

_{μ}k

^{2}/ε; C

_{μ}= 0.0845; S is the modulus of the mean rate of strain tensor; C

_{1ε}= 1.42, C

_{2ε}= 1.68; φ = Sk/ε, φ

_{0}= 4.38, β = 0.012.

#### 3.1.2. Mathematical Model of Particle Phase

_{D}is fluid drag force, N; G is gravity, N; F

_{q}is electric field force, N.

_{D}). In the mathematical model, the particles are assumed to be spherical, and their radius is R. The fluid drag force is calculated using the Stokes Equation [32].

_{p}is the density of particle, kg/m

^{3}; R is particle radius, m.

_{q}). If the charge of particles is q, the electric field force is

#### 3.2. Collision Process between Particles and Surface

#### 3.2.1. Injection Stage

_{1}, in which V

_{1x}is the tangential component of V

_{1}, and V

_{1y}is the normal component of V

_{1}. When the particles move toward the surface, it will be affected by the water molecular layer attached to the surface [33], and then its velocity will change to V

_{2}. However, the measurement results by Asay et al. [34] showed that the thickness of the water molecule layer varies only in the range of 0.5–2.5 nm, under different relative humidity. Compared with the particle size (1–100 μm), there is a great difference in magnitude. At the same time, the action distance of this process is too short, and the effect on the particles is so small that it can be neglected. Therefore, it can be considered that the particles hit the surface directly at the injection stage.

#### 3.2.2. Collision Deformation Stage

_{3}after deformation recovery, and the direction of its velocity is outward along the surface normal. The theoretical model of Johnson collision recovery coefficient was used to analyze the velocity of particles in this paper, as outlined in [17]. The recovery coefficient e is:

_{s}is yield limit, σ

_{s}= 200 N/mm

^{2}; E* is the effective elasticity modulus, GPa; E

_{1}is elastic modulus of particle, GPa; E

_{2}is the elastic modulus of surface, GPa; λ

_{1}and λ

_{2}are the Poisson’s ratios of particles and surface, respectively.

#### 3.2.3. Ejection Stage

_{ad}produced by surface and liquid bridge, and the direction of adhesion force is downward along the surface normal. If the adhesion force is too weak, the particles cannot be adhered, and its velocity will change to V

_{5}. If the adhesion force is strong, the particles will be adhered to the surface. After this stage, the collision process between particle and surface is concluded.

_{vdw}) and capillary force (F

_{cap}) play an important role in the adhesion force (F

_{ad}). The contact model diagram between particle and surface is shown in Figure 4. The adhesion force can be expressed as the following series of equations, as described in [35,36].

_{1}and H

_{2}are the Hamaker constant, and the magnitudes of these values are related to the medium: in the air medium H

_{1}= 10.38 × 10

^{−20}J, in the water medium H

_{2}= 1.90 × 10

^{−20}J [35]. D is the distance between particle and surface, m; h is the height of the liquid bridge, m; r

_{k}is the Kelvin radius, m; θ

_{1}and θ

_{2}are the contact angles of the bottom liquid bridge and upper liquid bridge, respectively; β is liquid bridge angle of the particle; c is contact angle coefficient; γ

_{w}is the surface tension of water, γ

_{w}= 0.073 N/m; V

_{0}is the molar volume of water, V

_{0}= 18 × 10

^{−6}m

^{3}/mol; R

_{g}is the gas constant, R

_{g}= 8.31 J/(mol K); T is the absolute temperature, T = 290 K; p is vapor pressure, Pa; p

_{0}is saturated vapor pressure, Pa; c

_{RH}is relative humidity.

#### 3.3. Adhesion Criterion of Particles

_{3}.

_{1}) by adhesion force is

_{max}is the maximum effect distance of Van der Waals force, a

_{max}= 0.4 nm; a

_{min}is the minimum effect distance of Van der Waals force, a

_{min}= 0.165 nm [17].

_{1}, and then through three stages of injection, collision deformation, and ejection, the final velocity V

_{5}becomes

_{1})

^{2}− 2W

_{1}/m > 0, it can be considered that the particles cannot be adhered to the surface. However, if (eV

_{1})

^{2}− 2W

_{1}/m < 0, it can be considered that the particles will be adhered to the surface.

## 4. Simulation Model

^{®}(5.2a). In the simulation model, four types of insulators were considered, including bell type insulator XP-160, aerodynamic type insulator XMP-160, double umbrella type insulator XWP-160, and the three-umbrella type insulator XSP-160. The structure and parameter of these four kinds of insulators are shown in Table 2. In Table 2, H, D and L, respectively, represent height, umbrella skirt size and leakage distance.

^{12}. In each simulation test, 9000 particles were released from the left side of the insulator. Among them, 3000 particles carried positive charges, its charge-mass ratio was 1.58 × 10

^{−4}C/kg; 3000 particles carried negative charges, and its charge-mass ratio was −3.04 × 10

^{−4}C/kg [37]; 3000 particles had no charge. Previous studies have shown that CaSO

_{4}is the major component of contamination [38], so the particle density was set to 2960 kg/m

^{3}.

## 5. Influence of Different Factors on Particle Adhesion

#### 5.1. Influence of Relative Humidity

_{RH}= 30% and 40%), particles with sizes in the range of 10–30 μm were easily adhered, and the D

_{50}of adhered particles were 19.84 μm and 21.52 μm, respectively. With high relative humidity (c

_{RH}= 70% and 80%), the particles with sizes in the range of 25–70 μm were easily adhered, and the D

_{50}of the adhered particles were 48.76 μm and 37.42 μm, respectively. With normal relative humidity (c

_{RH}= 50% and 60%), the particles with sizes in the range of 15–40 μm were easily adhered, and the D

_{50}of the adhered particles were 29.47 μm and 30.14 μm, respectively. The measurement results were consistent with the statistical characteristics obtained above. In addition, it could also be found that the size distribution of adhered particles on the upper surface was similar to that of on all surface, and there was a small amount of adhered particles on the bottom surface. Moreover, the influence of relative humidity on the adhesion number of particles was relatively limited when the particle size was less than 15 μm and greater than 90 μm. However, when the particle size was in the range of 20–80 μm, the influence of relative humidity on the adhesion number of particles was quite significant.

_{cap}will increase accordingly, and then the adhesion loss will also increase. Finally, the particles will be easier to adhere to the insulator surface with the same initial kinetic energy. For small particle (size ≤ 20 μm), the effect of fluid drag force is more obvious, and the trajectory of the particle is more likely to follow the change of wind direction. Therefore, it is easy to follow the movement of airflow, and bypass the insulator surface. So, collision and adhesion are difficult to happen. Although the small particles are easily adhered after collision, the number of adhered particles is rare due to the lower collision probability. For larger particles (size ≥ 80 μm), the effect of fluid drag force is remarkably weak, and the trajectory of particles cannot quickly follow the change of wind direction. Thus, the particles find it easy to pass through the boundary layer and achieve the collision. However, the energy loss during the collision process is so limited that the particles are not easily adhered, so there is a small number of adhered particles. However, for particles with sizes in the range of 20–80 μm, the order of magnitude of their initial kinetic energy and energy loss in collision are similar, so the adhesion is greatly affected by other external parameters. As relative humidity increases, the adhesion loss will increase correspondingly, which will cause the particles to be easily adhered to the surface. Therefore, the relative humidity has a significant influence on the adhesion number of particles, especially for particles with sizes in the range of 20–80 μm.

#### 5.2. Influence of Wind Speed

_{RH}= 60% and U = 30 kV.

_{50}is 49.22 μm. At high wind speed (v = 10 m/s), the particles with smaller size were easily adhered, and the size of adhered particles was mainly distributed in the range of 10–30 μm, and the D

_{50}is 20.14 μm. When wind speed was in the range of 2–6 m/s, there were obvious changes of the size distribution of adhered particles. However, when wind speed was in the range of 6–10 m/s, the size distribution of the adhered particles showed little change, and it showed saturation. Therefore, for the area in which annual average wind speed is about 4 m/s, the particles with sizes in the range of 20–40 μm are more likely to be adhered. These simulation results support the statistical characteristics of the particle size distribution obtained from the above measurement results. In addition, the size distribution of adhered particles on the upper surface was similar to that of on the all surface, and there were a small number of adhered particles on the bottom surface.

#### 5.3. Influence of Electric Field Type

_{RH}= 60%, v = 4 m/s.

#### 5.4. Influence of Electric Field Strength

_{RH}= 60%, v = 4 m/s.

#### 5.5. Influence of Aerodynamic Shape

_{RH}= 60%, v = 4 m/s, positive DC electric field, and U = 30 kV.

## 6. Conclusions

- The size distribution of adhered particles on the porcelain insulator surface is basically in logarithmic normal distribution, and the D
_{50}is about 20 μm, and the distribution of particles (R ≤ 5 μm and R ≥ 50 μm) is rare. - For small particles, their trajectory is easily affected by the fluid drag force, and it is difficult to experience collision and adhesion. For large particles, it is difficult to adhere to the surface due to great initial kinetic energy. Thus, there are significant size distribution characteristics of contaminated particles on the porcelain insulator surface.
- In the process of adhesion, the influences of relative humidity and wind speed on the adhesion were remarkable, whilst the influences of electric field type, electric field strength, and aerodynamic shape were relatively weak.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scanning electron microscopy diagram of typical contaminated particle samples: (

**a**) +800 kV (DC); (

**b**) −800 kV (DC); and (

**c**) 1000 kV (AC).

**Figure 5.**Adhesion number of particles with different size under different relative humidity: (

**a**) all surface; (

**b**) upper surface; and (

**c**) bottom surface.

**Figure 6.**Adhesion number of particle with different size under different wind speed: (

**a**) all surface; (

**b**) upper surface; and (

**c**) bottom surface.

**Figure 7.**Adhesion number of particles with different size under different electric field types: (

**a**) all surface; (

**b**) upper surface; and (

**c**) bottom surface.

**Figure 8.**Adhesion number of particles with different size under different electric field strength: (

**a**) all surface; (

**b**) upper surface; and (

**c**) bottom surface.

**Figure 9.**Adhesion number of particles with different size under different electric field strength: (

**a**) all surface; (

**b**) upper surface; and (

**c**) bottom surface.

**Figure 10.**Airflow field diagram of different aerodynamic shapes under 4 m/s wind speed: (

**a**) bell type insulator; (

**b**) aerodynamic type insulator; (

**c**) double umbrella type insulator; and (

**d**) three umbrella type insulator.

Province/Line | Voltage Level (kV) | Insulator Type | SPS Level * | Average Relative Humidity (%) | Average Wind Speed (m/s) | D_{10} (μm) | D_{50} (μm) | D_{90} (μm) | Contamination Accumulation Year |
---|---|---|---|---|---|---|---|---|---|

Heilongjiang/Xin-fu Line | 110 | XP-7 | B | 64 | 2.9 | 5.87 | 15.74 | 38.48 | 1 |

Hunan/Jin-ming Line | 500 | XWP-160 | E | 77 | 1.2 | 7.54 | 17.04 | 51.48 | 2 |

Shanghai/Si-du Line | 500 | XP-160 | E | 75 | 2.3 | 9.94 | 25.94 | 49.49 | 1 |

Fujian/Xing-zeng Line | 220 | XWP-70 | D | 72 | 2.4 | 4.15 | 16.57 | 35.71 | 4 |

Anhui/Hua-xia Line | 110 | XP-70 | B | 70 | 2.4 | 14.39 | 27.46 | 48.38 | 2 |

Ningxia/Wa-long Line | 110 | XP-70 | D | 55 | 2.2 | 15.67 | 36.09 | 59.45 | 1 |

Jilin/Yu-long Line | 220 | XP-70 | E | 62 | 3.5 | 3.87 | 11.11 | 34.87 | 1 |

Beijing/Li-da Line | 110 | XWP-7 | C | 54 | 2.3 | 3.62 | 10.04 | 37.14 | 1 |

Chongqin/Bai-tian Line | 110 | XP-7 | C | 80 | 1.4 | 2.27 | 9.88 | 21.61 | 2 |

Tianjin/Hou-hua Line | 110 | XWP-70 | D | 61 | 2.4 | 10.36 | 23.14 | 43.45 | 7 |

Jiangxi/Shang-ding Line | 110 | XP-7 | B | 75 | 2.3 | 8.46 | 20.35 | 40.19 | 10 |

Shanxi/Xi-shi Line | 500 | XP-160 | E | 61 | 3.1 | 13.21 | 33.37 | 58.74 | 3 |

Gansu/Zhang-tan Line | 110 | XP-70 | C | 48 | 2.1 | 4.48 | 13.72 | 27.39 | 8 |

Hubei/Guang-xian Line | 500 | XP-160 | D | 75 | 1.5 | 5.74 | 22.56 | 37.67 | 2 |

Zhejiang/Fang-tang Line | 110 | XP-70 | D | 73 | 1.8 | 2.81 | 13.83 | 29.74 | 11 |

Hebei/Shi-liu Line | 220 | XP-70 | E | 60 | 2.0 | 6.14 | 26.83 | 34.59 | 2 |

Henan/Jia-xiang Line | 500 | XP-160 | C | 62 | 2.0 | 4.92 | 16.83 | 37.71 | 4 |

Sichuan/Na-da Line | 110 | XWP-70 | B | 66 | 1.5 | 7.48 | 20.77 | 44.74 | 10 |

Liaoning/An-hong Line | 220 | XWP-100 | C | 65 | 2.6 | 5.93 | 17.18 | 38.38 | 2 |

Henan/Chang-nan Line | 1000 | XP-160 | C | 62 | 2.0 | 7.39 | 23.55 | 45.78 | 1 |

Henan/Chang-nan Line | 1000 | XP-160 | C | 62 | 2.0 | 6.87 | 17.18 | 41.90 | 1 |

Hunan/Jiang-cheng Line | ±500 | XP-160 | E | 78 | 1.9 | 9.73 | 23.14 | 52.47 | 2 |

Hunan/Jiang-cheng Line | ±500 | XP-160 | E | 78 | 1.9 | 11.35 | 20.64 | 41.90 | 2 |

Anhui/Yi-hua Line | ±500 | XP-70 | D | 76 | 2.8 | 6.10 | 16.63 | 38.76 | 1 |

Anhui/Long-zheng Line | ±500 | XP-70 | C | 75 | 1.9 | 6.34 | 18.80 | 38.86 | 2 |

Shanxi/Yin-dong Line | ±660 | XP-210 | E | 51 | 2.8 | 5.65 | 19.02 | 35.74 | 2 |

Shanxi/Yin-dong Line | ±660 | XP-210 | D | 51 | 2.8 | 9.59 | 22.84 | 48.86 | 2 |

Hebei/Yin-dong Line | ±660 | XP-210 | C | 60 | 2.0 | 8.71 | 16.12 | 47.29 | 1 |

Hebei/Yin-dong Line | ±660 | XP-210 | D | 60 | 2.0 | 6.46 | 23.57 | 52.43 | 1 |

Hubei/Jin-su Line | ±800 | XZP-210 | D | 77 | 1.4 | 5.74 | 17.08 | 36.72 | 1 |

Hubei/Fu-feng Line | ±800 | XZP-210 | D | 74 | 2.8 | 8.59 | 19.56 | 38.17 | 2 |

Henan/Tian-zhong Line | ±800 | XP-160 | C | 62 | 2.0 | 3.46 | 11.06 | 21.19 | 1 |

Henan/Tian-zhong Line | ±800 | XP-160 | B | 62 | 2.0 | 8.47 | 23.20 | 33.48 | 1 |

Henan/Tian-zhong Line | ±800 | XP-160 | B | 62 | 2.0 | 4.92 | 15.15 | 24.91 | 1 |

Type | Parameter | Shape | ||
---|---|---|---|---|

H (mm) | D (mm) | L (mm) | ||

XP-160 | 170 | 280 | 405 | |

XMP-160 | 155 | 425 | 385 | |

XWP-160 | 170 | 340 | 525 | |

XSP-160 | 170 | 330 | 545 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, M.; Wang, R.; Li, L.; Jiang, Y.
Size Distribution of Contamination Particulate on Porcelain Insulators. *Coatings* **2018**, *8*, 339.
https://doi.org/10.3390/coatings8100339

**AMA Style**

Zhang M, Wang R, Li L, Jiang Y.
Size Distribution of Contamination Particulate on Porcelain Insulators. *Coatings*. 2018; 8(10):339.
https://doi.org/10.3390/coatings8100339

**Chicago/Turabian Style**

Zhang, Ming, Rumeng Wang, Lee Li, and Yunpeng Jiang.
2018. "Size Distribution of Contamination Particulate on Porcelain Insulators" *Coatings* 8, no. 10: 339.
https://doi.org/10.3390/coatings8100339