As an important lightning protection device in substations, lightning rods are susceptible to vibration and potential structural damage under wind loads. In order to understand their vibration mechanism, it is necessary to conduct flow analysis. In this study, numerical simulations of the flow field around a 330 kV cylindrical lightning rod with different diameters were performed using the SST k-ω model. The flow patterns in different segments of the lightning rod at the same reference wind speed (wind speed at a height of 10 m) and the flow patterns in the same segment at different reference wind speeds were investigated. The variations of lift coefficient, drag coefficient, and vorticity distribution were obtained. The results showed that vortex shedding phenomena occurred in all segments of the lightning rod, and the strength of vortex shedding increased with decreasing diameter. The vorticity magnitude and the root mean square magnitudes of the lift coefficient and drag coefficient also increased accordingly. The time history curves of the lift coefficient and drag coefficient on the surface of the lightning rod exhibited sinusoidal patterns with a single dominant frequency. For the same segment, as the wind speed increased in a certain range, the root mean square values of the lift coefficient and drag coefficient decreased, while their dominant frequencies increased. Moreover, there was a proportional relationship between the dominant frequencies of the lift coefficient and drag coefficient. The findings of this study can provide valuable insights for the refined design of lightning rods with similar structures.

Lightning rods, as crucial devices for dissipating lightning energy within substations, are the fundamental and critical component of lightning protection systems. They directly affect the safe operation of substations and the stability of power supply systems. Common lightning rod structures are composed of interconnected circular steel rods with varying diameters, forming slender and elongated structures with high flexibility. Wind loads can easily induce frequent and intense vibrations in such flexible structures, leading to component brittleness, cracks, and potential fractures at the joints of lightning rod segments [

Regarding the flow around a stationary cylinder under uniform inflow, several scholars have conducted theoretical and experimental research. Von Karman theoretically proved that after fluid flows past a cylinder, a wake consisting of alternating shedding vortices, resembling a street, is formed. This phenomenon is known as the Karman vortex street [

In this study, ANSYS Fluent was used as the simulation platform, and the SST k-ω turbulence model was employed to analyze the flow around segments of a 330 kV circular steel lightning rod with different diameters at the same wind speed. Additionally, the flow around a single segment was analyzed at different wind speeds. The study obtained the variations of lift and drag coefficients for each segment, transient flow field vorticity distributions, and flow field velocity vectors. These findings provide a basis for the refined design of such lightning rods.

A 330 kV circular lightning rod in the northwest China consists of five steel tube segments with different diameters. These segments are numbered from bottom to top as DXZ-1, BLZ-1, BLZ-2, BLZ-3, and BLZ-4, as shown in

In order to simulate the three-dimensional flow around the lightning rod in a wind field, the computational grid for the entire structure can reach a scale of billions of grid cells when the grid resolution meets the accuracy requirements of the viscous sublayer calculation. This requires significant computational resources and time. Therefore, in this study, the three-dimensional flow around the lightning rod structure is approximated by simulating the flow around five cylinders with different diameters.

The computational domains corresponding to each segment of the lightning rod are shown in

Based on the terrain roughness of the area where the 330 kV lightning rod is located, it can be determined that it belongs to the Class B terrain according to the “Load code for the design of building structures” (GB 50009-2012) in China. According to the expression

To simulate and analyze the flow field for different segments at the same reference wind speed and for the same segment at different reference wind speeds, the following parameters were set, as shown in

Segment | D (mm) | Midpoint height (m) | Midpoint wind speed at 5 m/s (m/s) | Midpoint wind speed at 10 m/s (m/s) | Midpoint wind speed at 15 m/s (m/s) |
---|---|---|---|---|---|

DXZ-1 | 470 | 2.5 | 4.06 | – | – |

BLZ-1 | 351 | 8.75 | 4.90 | 9.80 | 14.70 |

BLZ-2 | 245 | 16.25 | 5.38 | 10.76 | 16.14 |

BLZ-3 | 121 | 23.75 | 5.69 | 11.38 | 17.07 |

BLZ-4 | 38 | 28.75 | 5.86 | 11.72 | 17.58 |

The surrounding region of the circular tube and the wake region are the key areas of concern for the flow simulation around the lightning rod. The grid division in the near-wall region of the circular tube significantly affects the accuracy of the calculation results. Therefore, appropriate grid division is required for these areas. In this study, the Y^{+} value is used to control the boundary layer grid division.

The Y^{+} value is a dimensionless number that measures the height of the first layer. For the SST k-ω model, it is recommended that the Y^{+} value should not exceed 1.0. Therefore, in this study, the Y^{+} value is set to 1.0 for subsequent calculations to ensure accuracy.

The process of calculating the height of the first layer based on the Y^{+} value is as follows [

Calculate the Reynolds number:

Calculate the wall friction coefficient:

Calculate the wall shear stress:

Calculate the friction velocity:

Calculate the height of the first grid layer:

Where ^{3}), ^{−5} Pa).

Considering the distribution characteristics of the flow field and the required computational accuracy [^{+} value.

Roughly speaking, turbulence is generated due to the instability of the system during fluid flow. Generally, in two-equation models, the k-epsilon (k-ε) model is suitable for simulating fully-developed turbulence away from the wall, while the k-omega (k-ω) model provides good accuracy and stability for simulation in the near-wall region. The SST k-ω turbulence model used in this study combines the advantages of these two models. By using a blending function, the k-ω model is employed near the wall, while the k-ε model is used in free shear layer and the region away from the wall. The SST k-ω model exhibits good computational performance and has been widely applied in engineering [

According to the “Load code for the design of building structures” (GB 50009-2012), an empirical formula is provided for the along-wind turbulence intensity [

For different types of terrains (A, B, C, D), the values of _{10} are 0.12, 0.14, 0.23, and 0.29, respectively. By using

Number | Segments | Midpoint height/m | Turbulence intensity | |
---|---|---|---|---|

1 | DXZ-1 | 2.5 | 0.14 | 0.1724 |

2 | BLZ-1 | 8.75 | 0.14 | 0.1428 |

3 | BLZ-2 | 16.25 | 0.14 | 0.1302 |

4 | BLZ-3 | 23.75 | 0.14 | 0.1230 |

5 | BLZ-4 | 28.75 | 0.14 | 0.1195 |

In this paper, the SIMPLE algorithm is initially used for steady-state calculations. The initial iteration steps are set to 300, which may vary depending on the convergence. Once the flow has sufficiently developed, the PISO algorithm is used for transient calculations to obtain the temporal variations of the physical quantities. The convergence criteria are set as follows: continuity residual of 10^{−4}, velocity residual of 10^{−6}, turbulent kinetic energy residual of 10^{−5}, and turbulent dissipation rate residual of 10^{−5}.

The verification of mesh independence of BLZ-3 is taken as an example here. As shown in _{d}

Case | Grids | _{d} |
St |
---|---|---|---|

G1 | 589968 | 0.9580 | 0.2167 |

G2 | 1624989 | 1.0523 | 0.2133 |

G3 | 3346135 | 1.0602 | 0.2135 |

Others’ results [ |
- | 1.051∼1.223 | 0.189∼0.223 |

It can be concluded from figures above that:

In

The vortices in the wake region exhibit a gradual increase in size and a decrease in vorticity magnitude. This suggests that energy dissipation occurs as the vortices move downstream.

Comparing these five figures, it can be observed that as the diameter of the cylinder decreases, the magnitude of vorticity increases, indicating a stronger vortex shedding phenomenon.

Additionally,

The following observations can be made from

After the airflow reaches the surface of the cylinder, the airflow velocity at the top of the windward surface becomes zero. This point is called the stagnation point. Subsequently, the airflow splits into two streams along the upper and lower surfaces of the cylinder.

As the airflow passes along the windward half of the cylinder’s surface, the velocity increases continuously and exceeds the incoming wind speed. On the leeward half of the cylinder’s surface, the velocity decreases continuously, and a reverse flow region can be observed.

On the leeward side of the lightning rod, vortices are formed due to the airflow, and with the progression of time, the shedding of vortices occurs.

The lift coefficient _{l}_{d}

Under the condition of a reference wind speed of 5 m/s, the flow analysis is conducted for each segment of the lightning rod. This allows us to obtain the time history curves of the drag coefficient and the lift coefficient (

From

By analyzing the time history curves of the drag coefficient and lift coefficient for each segment of the lightning rod after reaching a stable state, we can obtain their mean values and RMS magnitudes. Furthermore, by performing a fast Fourier transform on the time history curves of the drag coefficient and lift coefficient, we can obtain the frequencies of the lift and drag coefficients for each segment, as shown in

Number | Segments | Drag coefficient | Lift coefficient | |||
---|---|---|---|---|---|---|

Mean | RMS magnitude | Frequency | RMS magnitude | Frequency | ||

1 | DXZ-1 | 0.7349 | 0.02064 | 5.06 | 0.29585 | 2.53 |

2 | BLZ-1 | 0.7835 | 0.02868 | 7.59 | 0.33858 | 3.39 |

3 | BLZ-2 | 0.8230 | 0.02953 | 10.12 | 0.46928 | 5.06 |

4 | BLZ-3 | 1.0523 | 0.03225 | 20.05 | 0.58159 | 10.03 |

5 | BLZ-4 | 1.2227 | 0.03561 | 64.07 | 0.61183 | 31.02 |

From

Based on the numerical analysis of the lift and drag coefficients for different segments of the lightning rod at the same reference wind speed, further analysis is conducted on the variation characteristics of the lift and drag coefficients for the same lightning rod segment at different reference wind speeds.

Reference wind speed (m/s) | Reynolds number | Drag coefficient RMS | Lift coefficient RMS | Vortex shedding frequency |
---|---|---|---|---|

5 | 41417 | 1.0583 | 0.5816 | 20.05 |

10 | 82835 | 0.9206 | 0.4713 | 40.20 |

15 | 124253 | 0.8617 | 0.4609 | 67.67 |

20 | 165670 | 0.8596 | 0.4456 | 80.00 |

From the time-domain curves in

Further analysis of the frequency characteristics of the lift and drag coefficients under different wind speeds reveals that the lift and drag coefficient curves approximate sinusoidal waves with complete periodicity. They exhibit a single dominant peak frequency, and the peak frequency of the drag coefficient is approximately twice that of the lift coefficient. According to

The same parameters of flow around other segments at different reference wind speeds were also investigated and listed below in

Segment | Reference wind speed (m/s) | Reynolds number | Drag coefficient RMS | Lift coefficient RMS | Vortex shedding frequency |
---|---|---|---|---|---|

BLZ-1 | 10 | 235446 | 0.7646 | 0.4173 | 15.31 |

15 | 353169 | 0.5203 | 0.3026 | 22.12 | |

20 | 470892 | 0.4830 | 0.2919 | 30.51 | |

BLZ-2 | 10 | 180333 | 0.7959 | 0.4442 | 19.23 |

15 | 270500 | 0.7294 | 0.3819 | 30.62 | |

20 | 360667 | 0.6817 | 0.3004 | 41.21 | |

BLZ-4 | 10 | 30469 | 1.1163 | 0.5838 | 118.42 |

15 | 45703 | 1.0667 | 0.5685 | 208.33 | |

20 | 60938 | 1.0267 | 0.4986 | 286.29 |

In this section, the time-history curves of lift and drag coefficients for the BLZ-3 segment at a reference wind speed of 5 m/s are presented in

At t = 0.912 s, vortex shedding occurs on the lower side of the cylinder, resulting in both lift and drag coefficients reaching their peak values. Subsequently, both coefficients start to decrease. At t = 0.932 s, no vortex shedding is observed on the cylinder’s lateral surface, and the drag coefficient reaching its minimum value while the lift coefficient continues to decrease. At t = 0.952 s, vortex shedding occurs on the upper side of the cylinder, causing the drag coefficient to reach its peak value again, and the lift coefficient to reach its minimum value. Finally, at t = 1.012 s, vortex shedding occurs again on the lower side of the cylinder, and both lift and drag coefficients once again reach their peak values.

It can be observed that when vortex shedding occurs on the cylinder’s lateral surface, the drag coefficient reaches its peak value, while the corresponding lift coefficient alternates between peak and trough values. The time difference between two vortex shedding events on one side of the cylinder corresponds to one cycle of the lift coefficient.

In this paper, numerical simulations were conducted using the computational fluid dynamics method with ANSYS Fluent. The flow field around a 330 kV cylindrical lightning rod was simulated to investigate and compare the lift and drag coefficients of different sections of the lightning rod at the same reference wind speed of 5 m/s, and the variations of lift and drag coefficients for the same lightning rod section at different reference wind speeds were analyzed. The following main conclusions were drawn:

1. The presence of the cylindrical steel tube obstructs incoming flow, causing velocity redistribution in the flow field. This leads to higher velocities on the tube’s lateral sides and lower velocities on the windward and leeward surfaces, creating vortex shedding in the wake region.

2. All sections of the lightning rod demonstrate vortex shedding phenomena. The shedding of vortices results in the oscillation of lift and drag coefficients on the lightning rod surface. The time-domain curves of lift and drag coefficients exhibit sinusoidal patterns with a single peak frequency.

3. Segments with smaller diameters exhibit more pronounced vortex shedding, higher vortex intensities, and larger root mean square magnitudes of lift and drag coefficients at the same reference wind speed.

4. In a certain range, increasing wind speed leads to reduced root mean square values of lift and drag coefficients.

Mean wind speed at a height of z (m)

_{10}

Mean wind speed at a height of 10 m (reference wind speed)

Roughness exponent

Turbulence intensity at a height of z (m)

_{10}

Turbulence intensity at a height of 10 m

_{l}

Lift coefficient

_{d}

Drag coefficient

_{l}

Lift force acting on the cylinder surface

_{d}

Drag force acting on the cylinder surface

Density of the medium

Incoming velocity

Diameter of the cylinder

Length of the cylinder

None.

This study was supported by State Grid Ningxia Electric Power Co., Ltd. under Grant 5229CG220006 and Natural Science Foundation of Ningxia Province under Grant 2022AAC03629.

The authors confirm contribution to the paper as follows: study conception and design: Wei G, Bo H; simulations: Jiazheng M, Mengqin H; analysis and interpretation of results: Yanliang L, Xuqiang W, Jiazheng M, Mengqin H; draft manuscript preparation: Jiazheng M, Mengqin H. All authors reviewed the results and approved the final version of the manuscript.

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

The authors declare that they have no conflicts of interest to report regarding the present study.