# Wind Field Characteristics of Butte and the Influence on the Wind-Induced Responses of Transmission Towers

Authors: Yan Zhang; Wenfeng Huang; Lisha Wang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

The computational fluid dynamics (CFD) simulation on the butte was carried out to obtain the wind field characteristics for a specific mountain in the hilly area of eastern China. Then, the speed-up ratios of butte at each location distributed by height were calculated. The simulation results were compared with the specified value of mountain wind field acceleration ratio in various codes. The finite element model of the transmission tower line system is established by ANSYS, and the wind-induced vibration response of the structural system under the single mountain wind field is calculated, which is compared with the results of flat ground. The results show that the mountain will hinder the fluid passing through it. There is a deceleration zone in front of the mountain and a flow separation phenomenon behind the mountain. The speed-up ratios at the butte top where accelerating effect are the biggest among all positions of the butte. As the height increases, they approach 1. The speed-up ratios calculated by the Chinese code and the Australian code are linearly changing along the ridge of the butte and are symmetric at the windward side and leeward side. The biggest speed-up ratios are calculated by the Chinese code, and the smallest ratios are calculated by CFD. The wind-induced vibration response of the transmission tower line system is influenced by the wind speed-up ratios and reaches the maximum at the top of the butte. The simulation results at the windward side are close to the values calculated by the Australia code and the Euro code, but at the top and leeward side, they are far smaller than others.


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## Body

## 1. Introduction

The topography of China is high in the west and low in the east with rolling country and plains in the east, which has obvious characteristics of the mountain wind field. As the carrier of cross-regional power transmission, the transmission tower line system will inevitably be built on the mountain, which is correspondingly related to the influence of complex geological/natural environments [1–3]. Transmission tower belongs to the category of high-rise structure which has flexible stiffness and is very sensitive to wind load effect [4, 5]. For high-rise structures with complex shape and high height, it is necessary to consider not only the downwind wind load but also the vortex caused by the flow effect under the crosswind load or even temperature effect [6–8]. The alternating vortex shedding generates the pulsating loads, and when it is close to the natural frequency of the structure, it will lead to crosswind vortex-induced resonance (VIR), which would do tremendous harm to the transmission tower [9]. At the same time, the mountain wind field is much more complicated considering its unique and changeable geometry and the interaction between rocks mass and ground. The wind field characteristics of the atmospheric boundary layer will accelerate the incoming wind speed in some areas above the mountain surface after being disturbed by the terrain, resulting in the acceleration effect [4]. Such changes may have an adverse impact on the stability of transmission lines. Therefore, it is of great value to study the wind action and wind-induced response of transmission tower line system in mountainous terrain.So far, the research on the impact of mountain wind on structures is still in its infancy. Most of the researches are mainly focused on the mountain wind field characteristics [6–8] and established microclimate analysis system over complex terrain by using numerical simulation methods such as turbulence model and finite volume method in order to predict local weather conditions [10]. Kikuchi et al. modified the terrain factor, which is related to the wind direction variation, and proposed the terrain change coefficient to represent the difference of terrain factors [11]. Bitsuamlak et al. reviewed numerical evaluation of wind flow over different types of topographies with various boundary conditions, grid type and density, and suggested that the numerical results agreed with field data better on the upstream as opposed to the downstream areas of complex terrain [12]. However, there are fewer studies reported on the impact of wind load on structures under mountain wind field. Li et al. [13] presented the discrete variables-based topology combination optimization (TCO) method and layer combination optimization (LCO) method to optimize the long-span transmission tower structure. Okamura et al. confirmed the factors which have a great impact on the response of transmission tower through actual measurements [14]. Ronaldo C et al. used the 3D finite element (3D-FEM) model to analyze the dynamic coupled behavior of transmission towers under wind load [15]. Huang et al. [16] used a hybrid numerical simulation method to predict the typhoon wind field over complex terrain; they found that, after taking the effect of topography into account, the hybrid numerical simulation method can give a better prediction of the hourly mean wind speed and direction. To make full use of mountain environmental resources, in recent years, the efficient combination of geotechnical engineering design [17–20] and related mountain construction projects has further enhanced the complexity of the mountain environment where the transmission tower is located [21–25]. Based on the actual environmental conditions of undulating terrain, it is necessary to fully study the impact of external actual soil and mountains on the wind site of the transmission tower.


### 1.1. Three-Dimensional (3D) Modelling and Boundary Setting of Butte

#### 1.1.1. Numerical Modelling

Since a two-dimensional (2D) mountain wind field cannot accurately describe the wind movement process in the whole space, this paper chooses to simulate a three-dimensional (3D) axisymmetric butte for the wind field calculation. The selected mountain model is a 3D cosine typical butte with a diameter of 400 m at the bottom and a height of 100 m. The mountain contour can match the following equation:(1)zx,y=Hcos2πx2+y20.5D,where z is the coordinate of mountain height direction; x and y refer to the horizontal coordinate; H is the height of the mountain; D is the diameter of the bottom of the mountain.The combination of Gambit and ICEM was utilized to establish the 3D mountain terrain calculation domain model with a size of 4 km × 3 km × 1 km (x × y × z). This model is centered on the mountain top; the calculation domain size is 1.6 km upstream and is 2.4 km downstream with a blocking rate of less than 3%. The illustration of the 3D model is shown in Figure 1. The ICEM CFD hexahedral structured grid is used to grid division of the computational area in the whole flow field.Figure 1
Schematic diagram of mountain calculation domain.After grid independence verification, the grid division is determined as follows: the grid resolution of the calculation area, which is centered on the top of the mountain within 600 meters along and perpendicular to the flow direction, is 4 m and is increased at a growth rate of 1.05 times in outward direction, the grid at the inlet and side of the flow field is increased to 30 m, and the grid at the outlet of the flow field is increased to 40 m. In the vertical direction, the height of the first layer grid is selected as 2 m, the growth rate is 1.05, and the resolution of the top grid is 30 m. The overall number of grids is about 6.045 million. The grid of the 3D single mountain computing domain is shown in Figure2 from which we can find that the grid has a good mesh fit.Figure 2
Mountain meshing: (a) mountain overall computing domain grid; (b) mountain local grid.
(a)(b)


### 1.2. Boundary Conditions and Numerical Algorithms

It is assumed that the negative direction of thex-axis is the incoming wind direction. Due to the large turbulence in the atmospheric boundary layer, a standard k-ε calculation turbulence model then is utilized to correctly simulate the mountain wind field, in which the average wind speed profile, the turbulence intensity, and the turbulent kinetic energy could be expressed as(2)u=u∗κ×lnz+z0z0,k=u∗2CuC1lnz+z0/z0+C2,ε=u∗3κz+z0C1lnz+z0/z0+C2,where u∗ is the ground friction speed; κ is the von Karman constant, usually taken as 0.4; z0 is the ground rough length; z refers to the height; Cu is the turbulence model constant, usually taken as 0.09; C1 and C2 are constants, which can be obtained by the fitting results of the measured turbulence data. The other parameters are the same as those mentioned before.Setting the computational boundary needs to be considered before the numerical simulation of mountain terrain [26–28]. The side and top surfaces of the calculation area are set as symmetrical boundary conditions according to engineering experience [29, 30]. It is considered that the gas flow to the outlet plane has been fully developed and set as the free outflow boundary condition. The ground is considered to be no-slip, so the no-slip wall boundary condition is adopted for the lower interface, and the wall roughness height κs is taken as 0.2. The gas is an incompressible fluid, and the velocity inlet is selected as the inlet interface. The self-preservation of the inlet wind velocity profile before reaching the peak is the premise to ensure the accuracy and reliability of the complex terrain numerical simulation. Therefore, it is necessary to understand the self-preservation of the inlet profile before numerical calculation.The distance from the inlet to the butte edge along the flow direction is 1.4 km. Therefore, the average wind velocity and turbulent kinetic energy profiles at the inlet and 1.4 km away from the inlet are selected to observe the self-preservation of the inlet wind velocity profile and turbulent kinetic energy profile (the average wind velocity at 10 m height is 18 m/s). The obtained results are shown in Figures3 and 4.Figure 3
Comparison of wind speed profiles.Figure 4
Kinetic energy profile comparison.It can be found from the above data that the inlet wind velocity profile error is the largest at 5 m height with a value of 11.67% and an error at about 2.67%. The maximum inlet turbulent kinetic energy profile error is obtained at the ground, which is 29.83%, with an average error at about 5.14%. The error is affected by the bottom boundary conditions of the calculation domain. The closer to the bottom, the greater the influence of the bottom boundary conditions and the greater the error. From the above results, it can be considered that the inlet profile at other heights is in good self-preservation condition except below 10 m, which lays a foundation for subsequent numerical calculation.


### 1.3. Numerical Simulation of the Butte Wind Field Characteristics

The mountain wind field is obtained by CFD numerical calculation [31–33], including many laboratories’ experimental verification under complex stratum conditions [34, 35]. The wind velocity clouds are intercepted at different heights from the mountain surface and the longitudinal section velocity clouds at the mountain peak in the downstream field direction of the calculation area. Figure 5 shows the wind speed clouds at sections 10 m and 100 m away from the mountain surface, and Figure 6 shows the wind speed clouds at the longitudinal section of the mountain.Figure 5
Velocity nephogram at different heights of mountain surface.
(a)(b)Figure 6
Peak profile velocity cloud map.It can be seen from Figures5 and 6 that the flow direction of the whole field is from left to right. The inlet wind velocity profile has been fully developed before reaching the butte. After passing through the mountain, the flow field has been fully developed due to the long distance from the terrain to the outlet. As the wake flow at different heights is basically dissipated, it has no adverse impact on the flow field near the terrain. Besides, since the side and top surfaces are far enough from the terrain, their boundary conditions have no obvious effect on the flow field at the terrain boundary. At the same time, due to the mountain blocking effect, there exists a large deceleration zone in front of the butte when the wind flows through. In addition, the wind velocity increased significantly at the mountain peak, forming an acceleration zone, and there is an obvious flow separation phenomenon on the leeward slope, resulting in an eddy current.Figure7 shows the wind velocity acceleration ratio along the ridgeline of the windward and leeward mountain foot, the windward and leeward half mountain top, and the mountain top (i.e., the ratio of the wind velocity at z height from the mountain surface to the wind velocity at the same height on the flat ground) obtained from the CFD calculation. The following can be found: (1) The wind acceleration ratio at the top of the mountain is the largest, greater than 1, and decreases with the increase of the height. (2) The wind acceleration ratio at the windward half mountain is greater than that at the leeward half mountain below 100 m and is slightly greater than 1, while the wind acceleration ratio at the leeward half mountain is less than 1 below 50 m height, is greater than 1 above 50 m, and tends to approach 1. (3) The wind acceleration ratio at the mountain foot is the smallest, which is generally less than 1, and tends to approach 1 with the increased height.Figure 7
CFD calculation of acceleration ratio at each ridgeline.


### 1.4. Provisions and Comparison of Mountain Wind Field Characteristics in the Code

(1)
The variation law of mountain wind field in China’s load specification for building structures is considered by the topographic correction coefficient of wind pressure height variation coefficient. For the butte peak, the correction coefficient can be calculated according to the following formula [36]:(3)ηB=1+κtanα1−z2.5H2,where tanα is the slop of windward hillside or windward butte peak. When tanα >0.3, it is taken as 0.3; κ is the coefficient, usually taken as 2.2 for mountain peaks and 1.4 for hillsides; H is the mountain height; z is the height from the calculated position of the building to the ground. When z > 2.5 H, z is taken as 2.5 H. The correction coefficient of the starting point before and after the mountain is 1, and the correction coefficient of other positions on the mountain is determined according to linear interpolation.(2)
In the European specification EN2004-1-4, the mountain wind field is considered by the correction factor C0, which is based on wind velocity, and its values are as follows [37]:(4)C0=1,φ<0.05,1+2sφ,0.05≤φ<0.3,1+0.6s,φ≥0.3,whereφ = H/Lu is the peak windward slope; Lu is the horizontal distance of windward slope; H is the height of the mountain; s is the topographic coefficient.(3)
In Australian specification as AS/NZS1170.2 : 2011, the correction factorMh based on wind velocity is adopted to consider the mountain wind field, and the value of Mh is as follows [38]:When H/2L < 0.05,(5)Mh=1.0.When 0.05≤H/2L < 0.45,(6)Mh=1+H3.5z+L11−xL2.WhenH/2L > 0.45 and is in the flow separation area,(7)Mh=1+0.71−xL2,whereH is the mountain height; L is the horizontal distance from the mountain top to half mountain windward side. L1 is the larger one between 0.36 L and 0.4H; L2 is taken as 4L1 for windward side, 10L1 for leeward hillside, and 4L1 for peak.Actually,Mh would be calculated according to formulae (5)–(7) when being outside the flow separation area. Based on the mountain characteristics selected in this work, the specified acceleration ratio is obtained through calculation. The wind acceleration ratios at 10 m and 100 m heights along the mountain ridgeline are given in the following, as shown in Figure 8. The following can be found: (1) Among the wind acceleration ratios calculated by the above three codes, the wind acceleration ratio at the mountain top is the largest, and the calculated value in the Chinese code is the largest. (2) The wind acceleration ratio at 10 m from the mountain surface on the ridgeline is greater than that at 100 m height. The wind acceleration ratio of the Australian code and the Euro code is basically the same at the height of 10 m from the top of the mountain, but the wind acceleration ratio of the Australian code is much smaller than that of the Euro code at 100 m height from the mountain top. (3) The data of wind acceleration ratio calculated by the Chinese and Australian codes are symmetrical on the windward and leeward sides, while the data obtained by the Euro code are asymmetric, and the data on the leeward side are slightly larger than those on the windward side. (4) In the whole process, Chinese norms and Australian norms presented an obvious linear change law.Figure 8
Specified values of wind acceleration ratio at different heights of various codes on the ridgeline: (a) 10 m height on the mountain surface; (b) 100 m height of mountain surface.
(a)(b)Figure9 shows the wind acceleration ratios calculated by various codes at the foot of the mountain on the windward and leeward sides, the middle of the mountain on the windward and leeward sides, and the top of the mountain, respectively. The following can be seen: (1) At the foot of the mountain, the calculated value of the Chinese code is 1, and the calculated value of the Australian code is less than 1, while that of the Euro code one is greater than 1, and the calculated values of the Euro code and the Australian code tend to be 1 with the increase of height. (2) On the leeward side, the data from the Euro code are greater than that of the windward side, the acceleration ratio from the Chinese code is the largest in the area below 120 m height in the middle of the mountain, and the data from the Euro code are greater than those from the Australian code. (3) On the windward side, the acceleration ratio from the Chinese code is the largest in the area below 180 m height in the middle of the mountain, and the data from the Euro code are greater than those from the Australian code, but the Australian code is greater than that from the Euro code below 30 m height. Meanwhile, the calculation data of various codes at the top of the mountain and the acceleration ratio obtained by CFD numerical simulation in this work are also given in Figure 9(c). It can be found that the data given by the three codes are greater than the CFD numerical calculation results at a height higher than 30 m, but the simulation value is larger at the lower height.Figure 9
Specified values of wind acceleration ratio at different positions of the mountain in various specifications: (a) windward mountain foot; (b) windward half mountain; (c) mountain top; (d) leeward half mountain; (e) leeward mountain foot.
(a)(b)(c)(d)(e)


## 1.1. Three-Dimensional (3D) Modelling and Boundary Setting of Butte

### 1.1.1. Numerical Modelling

Since a two-dimensional (2D) mountain wind field cannot accurately describe the wind movement process in the whole space, this paper chooses to simulate a three-dimensional (3D) axisymmetric butte for the wind field calculation. The selected mountain model is a 3D cosine typical butte with a diameter of 400 m at the bottom and a height of 100 m. The mountain contour can match the following equation:(1)zx,y=Hcos2πx2+y20.5D,where z is the coordinate of mountain height direction; x and y refer to the horizontal coordinate; H is the height of the mountain; D is the diameter of the bottom of the mountain.The combination of Gambit and ICEM was utilized to establish the 3D mountain terrain calculation domain model with a size of 4 km × 3 km × 1 km (x × y × z). This model is centered on the mountain top; the calculation domain size is 1.6 km upstream and is 2.4 km downstream with a blocking rate of less than 3%. The illustration of the 3D model is shown in Figure 1. The ICEM CFD hexahedral structured grid is used to grid division of the computational area in the whole flow field.Figure 1
Schematic diagram of mountain calculation domain.After grid independence verification, the grid division is determined as follows: the grid resolution of the calculation area, which is centered on the top of the mountain within 600 meters along and perpendicular to the flow direction, is 4 m and is increased at a growth rate of 1.05 times in outward direction, the grid at the inlet and side of the flow field is increased to 30 m, and the grid at the outlet of the flow field is increased to 40 m. In the vertical direction, the height of the first layer grid is selected as 2 m, the growth rate is 1.05, and the resolution of the top grid is 30 m. The overall number of grids is about 6.045 million. The grid of the 3D single mountain computing domain is shown in Figure2 from which we can find that the grid has a good mesh fit.Figure 2
Mountain meshing: (a) mountain overall computing domain grid; (b) mountain local grid.
(a)(b)


## 1.1.1. Numerical Modelling

Since a two-dimensional (2D) mountain wind field cannot accurately describe the wind movement process in the whole space, this paper chooses to simulate a three-dimensional (3D) axisymmetric butte for the wind field calculation. The selected mountain model is a 3D cosine typical butte with a diameter of 400 m at the bottom and a height of 100 m. The mountain contour can match the following equation:(1)zx,y=Hcos2πx2+y20.5D,where z is the coordinate of mountain height direction; x and y refer to the horizontal coordinate; H is the height of the mountain; D is the diameter of the bottom of the mountain.The combination of Gambit and ICEM was utilized to establish the 3D mountain terrain calculation domain model with a size of 4 km × 3 km × 1 km (x × y × z). This model is centered on the mountain top; the calculation domain size is 1.6 km upstream and is 2.4 km downstream with a blocking rate of less than 3%. The illustration of the 3D model is shown in Figure 1. The ICEM CFD hexahedral structured grid is used to grid division of the computational area in the whole flow field.Figure 1
Schematic diagram of mountain calculation domain.After grid independence verification, the grid division is determined as follows: the grid resolution of the calculation area, which is centered on the top of the mountain within 600 meters along and perpendicular to the flow direction, is 4 m and is increased at a growth rate of 1.05 times in outward direction, the grid at the inlet and side of the flow field is increased to 30 m, and the grid at the outlet of the flow field is increased to 40 m. In the vertical direction, the height of the first layer grid is selected as 2 m, the growth rate is 1.05, and the resolution of the top grid is 30 m. The overall number of grids is about 6.045 million. The grid of the 3D single mountain computing domain is shown in Figure2 from which we can find that the grid has a good mesh fit.Figure 2
Mountain meshing: (a) mountain overall computing domain grid; (b) mountain local grid.
(a)(b)


## 1.2. Boundary Conditions and Numerical Algorithms

It is assumed that the negative direction of thex-axis is the incoming wind direction. Due to the large turbulence in the atmospheric boundary layer, a standard k-ε calculation turbulence model then is utilized to correctly simulate the mountain wind field, in which the average wind speed profile, the turbulence intensity, and the turbulent kinetic energy could be expressed as(2)u=u∗κ×lnz+z0z0,k=u∗2CuC1lnz+z0/z0+C2,ε=u∗3κz+z0C1lnz+z0/z0+C2,where u∗ is the ground friction speed; κ is the von Karman constant, usually taken as 0.4; z0 is the ground rough length; z refers to the height; Cu is the turbulence model constant, usually taken as 0.09; C1 and C2 are constants, which can be obtained by the fitting results of the measured turbulence data. The other parameters are the same as those mentioned before.Setting the computational boundary needs to be considered before the numerical simulation of mountain terrain [26–28]. The side and top surfaces of the calculation area are set as symmetrical boundary conditions according to engineering experience [29, 30]. It is considered that the gas flow to the outlet plane has been fully developed and set as the free outflow boundary condition. The ground is considered to be no-slip, so the no-slip wall boundary condition is adopted for the lower interface, and the wall roughness height κs is taken as 0.2. The gas is an incompressible fluid, and the velocity inlet is selected as the inlet interface. The self-preservation of the inlet wind velocity profile before reaching the peak is the premise to ensure the accuracy and reliability of the complex terrain numerical simulation. Therefore, it is necessary to understand the self-preservation of the inlet profile before numerical calculation.The distance from the inlet to the butte edge along the flow direction is 1.4 km. Therefore, the average wind velocity and turbulent kinetic energy profiles at the inlet and 1.4 km away from the inlet are selected to observe the self-preservation of the inlet wind velocity profile and turbulent kinetic energy profile (the average wind velocity at 10 m height is 18 m/s). The obtained results are shown in Figures3 and 4.Figure 3
Comparison of wind speed profiles.Figure 4
Kinetic energy profile comparison.It can be found from the above data that the inlet wind velocity profile error is the largest at 5 m height with a value of 11.67% and an error at about 2.67%. The maximum inlet turbulent kinetic energy profile error is obtained at the ground, which is 29.83%, with an average error at about 5.14%. The error is affected by the bottom boundary conditions of the calculation domain. The closer to the bottom, the greater the influence of the bottom boundary conditions and the greater the error. From the above results, it can be considered that the inlet profile at other heights is in good self-preservation condition except below 10 m, which lays a foundation for subsequent numerical calculation.


## 1.3. Numerical Simulation of the Butte Wind Field Characteristics

The mountain wind field is obtained by CFD numerical calculation [31–33], including many laboratories’ experimental verification under complex stratum conditions [34, 35]. The wind velocity clouds are intercepted at different heights from the mountain surface and the longitudinal section velocity clouds at the mountain peak in the downstream field direction of the calculation area. Figure 5 shows the wind speed clouds at sections 10 m and 100 m away from the mountain surface, and Figure 6 shows the wind speed clouds at the longitudinal section of the mountain.Figure 5
Velocity nephogram at different heights of mountain surface.
(a)(b)Figure 6
Peak profile velocity cloud map.It can be seen from Figures5 and 6 that the flow direction of the whole field is from left to right. The inlet wind velocity profile has been fully developed before reaching the butte. After passing through the mountain, the flow field has been fully developed due to the long distance from the terrain to the outlet. As the wake flow at different heights is basically dissipated, it has no adverse impact on the flow field near the terrain. Besides, since the side and top surfaces are far enough from the terrain, their boundary conditions have no obvious effect on the flow field at the terrain boundary. At the same time, due to the mountain blocking effect, there exists a large deceleration zone in front of the butte when the wind flows through. In addition, the wind velocity increased significantly at the mountain peak, forming an acceleration zone, and there is an obvious flow separation phenomenon on the leeward slope, resulting in an eddy current.Figure7 shows the wind velocity acceleration ratio along the ridgeline of the windward and leeward mountain foot, the windward and leeward half mountain top, and the mountain top (i.e., the ratio of the wind velocity at z height from the mountain surface to the wind velocity at the same height on the flat ground) obtained from the CFD calculation. The following can be found: (1) The wind acceleration ratio at the top of the mountain is the largest, greater than 1, and decreases with the increase of the height. (2) The wind acceleration ratio at the windward half mountain is greater than that at the leeward half mountain below 100 m and is slightly greater than 1, while the wind acceleration ratio at the leeward half mountain is less than 1 below 50 m height, is greater than 1 above 50 m, and tends to approach 1. (3) The wind acceleration ratio at the mountain foot is the smallest, which is generally less than 1, and tends to approach 1 with the increased height.Figure 7
CFD calculation of acceleration ratio at each ridgeline.


## 1.4. Provisions and Comparison of Mountain Wind Field Characteristics in the Code

(1)
The variation law of mountain wind field in China’s load specification for building structures is considered by the topographic correction coefficient of wind pressure height variation coefficient. For the butte peak, the correction coefficient can be calculated according to the following formula [36]:(3)ηB=1+κtanα1−z2.5H2,where tanα is the slop of windward hillside or windward butte peak. When tanα >0.3, it is taken as 0.3; κ is the coefficient, usually taken as 2.2 for mountain peaks and 1.4 for hillsides; H is the mountain height; z is the height from the calculated position of the building to the ground. When z > 2.5 H, z is taken as 2.5 H. The correction coefficient of the starting point before and after the mountain is 1, and the correction coefficient of other positions on the mountain is determined according to linear interpolation.(2)
In the European specification EN2004-1-4, the mountain wind field is considered by the correction factor C0, which is based on wind velocity, and its values are as follows [37]:(4)C0=1,φ<0.05,1+2sφ,0.05≤φ<0.3,1+0.6s,φ≥0.3,whereφ = H/Lu is the peak windward slope; Lu is the horizontal distance of windward slope; H is the height of the mountain; s is the topographic coefficient.(3)
In Australian specification as AS/NZS1170.2 : 2011, the correction factorMh based on wind velocity is adopted to consider the mountain wind field, and the value of Mh is as follows [38]:When H/2L < 0.05,(5)Mh=1.0.When 0.05≤H/2L < 0.45,(6)Mh=1+H3.5z+L11−xL2.WhenH/2L > 0.45 and is in the flow separation area,(7)Mh=1+0.71−xL2,whereH is the mountain height; L is the horizontal distance from the mountain top to half mountain windward side. L1 is the larger one between 0.36 L and 0.4H; L2 is taken as 4L1 for windward side, 10L1 for leeward hillside, and 4L1 for peak.Actually,Mh would be calculated according to formulae (5)–(7) when being outside the flow separation area. Based on the mountain characteristics selected in this work, the specified acceleration ratio is obtained through calculation. The wind acceleration ratios at 10 m and 100 m heights along the mountain ridgeline are given in the following, as shown in Figure 8. The following can be found: (1) Among the wind acceleration ratios calculated by the above three codes, the wind acceleration ratio at the mountain top is the largest, and the calculated value in the Chinese code is the largest. (2) The wind acceleration ratio at 10 m from the mountain surface on the ridgeline is greater than that at 100 m height. The wind acceleration ratio of the Australian code and the Euro code is basically the same at the height of 10 m from the top of the mountain, but the wind acceleration ratio of the Australian code is much smaller than that of the Euro code at 100 m height from the mountain top. (3) The data of wind acceleration ratio calculated by the Chinese and Australian codes are symmetrical on the windward and leeward sides, while the data obtained by the Euro code are asymmetric, and the data on the leeward side are slightly larger than those on the windward side. (4) In the whole process, Chinese norms and Australian norms presented an obvious linear change law.Figure 8
Specified values of wind acceleration ratio at different heights of various codes on the ridgeline: (a) 10 m height on the mountain surface; (b) 100 m height of mountain surface.
(a)(b)Figure9 shows the wind acceleration ratios calculated by various codes at the foot of the mountain on the windward and leeward sides, the middle of the mountain on the windward and leeward sides, and the top of the mountain, respectively. The following can be seen: (1) At the foot of the mountain, the calculated value of the Chinese code is 1, and the calculated value of the Australian code is less than 1, while that of the Euro code one is greater than 1, and the calculated values of the Euro code and the Australian code tend to be 1 with the increase of height. (2) On the leeward side, the data from the Euro code are greater than that of the windward side, the acceleration ratio from the Chinese code is the largest in the area below 120 m height in the middle of the mountain, and the data from the Euro code are greater than those from the Australian code. (3) On the windward side, the acceleration ratio from the Chinese code is the largest in the area below 180 m height in the middle of the mountain, and the data from the Euro code are greater than those from the Australian code, but the Australian code is greater than that from the Euro code below 30 m height. Meanwhile, the calculation data of various codes at the top of the mountain and the acceleration ratio obtained by CFD numerical simulation in this work are also given in Figure 9(c). It can be found that the data given by the three codes are greater than the CFD numerical calculation results at a height higher than 30 m, but the simulation value is larger at the lower height.Figure 9
Specified values of wind acceleration ratio at different positions of the mountain in various specifications: (a) windward mountain foot; (b) windward half mountain; (c) mountain top; (d) leeward half mountain; (e) leeward mountain foot.
(a)(b)(c)(d)(e)


## 2. Influence of Butte Wind Field on Wind-Induced Response of Transmission Tower Line System

### 2.1. Transmission Tower Line System Model

The selected research object in this work is a 110 kV “T” shaped mixed voltage narrow base tower on a transmission line of the East China Power Grid. The transmission line model is based on the tower, with a length upstream and downstream of 200 m, respectively. The conductor is LGJ-300/40 steel cord aluminum strand, and the ground wire is JLBv20A-80 aluminum clad steel strand. The tower height is 68.4 m, the tower nominal height is 48 m, and the tower foundation size is 3.5m × 3.5 m. Q345 angle steel is used as the main material and cross arm of the transmission tower. Q235 angle steel is used as the inclined material and other auxiliary materials. The section sizes of angle steel vary at different heights. The four-tower columns are the main components under stress, the components are bolted at both ends, and the transmission tower and the base are connected by fixed ends. The transmission line is the general name of transmission conductor and ground wire, which has the characteristics of high flexibility and large deformation. Under the action of gravity, the conductor (ground) fixed at two different points will be in a catenary shape, and the model shall be treated according to the provisions on sag in the design code. In ANSYS, the beam element is used to simulate the main stressed components of the transmission tower, and the rod element is used to simulate other rods and transmission lines to establish the finite element model of the transmission tower line system, as shown in Figure 10. It is placed at different positions of the mountain to analyze the response under wind load excitation.Figure 10
Finite element model of transmission tower line system.


### 2.2. Response Analysis of Transmission Tower Line System

The natural wind with an average wind velocity of 18 m/s at 10 m height is taken as the reference load; the Davenport wind velocity spectrum and the harmonic synthesis method are applied to simulate the fluctuating wind velocity, which is the time history of the fluctuating wind speed at the tower top simulated at the flat ground, as shown in Figure11. The wind acceleration ratio under the mountain wind field calculated by the above code and CFD can be corrected to the simulated wind velocity and then generate the corrected wind load [39–44].Figure 11
Fluctuating wind speed time history.Input the load into the transmission tower line system finite element model to accomplish the dynamic time history analysis using ANSYS and generate the response of the transmission tower line system under a mountain wind field. The obtained data are shown in Table1 and Figure 12.Table 1
Displacement response of transmission tower top.
Chinese codeAustralia codeEuro codeCFDFoot of windward mountain0.3090.3080.3570.307Windward half mountain0.5300.4400.4210.391Mountain top0.7520.5780.7210.509Leeward half mountain0.5300.4400.4720.364Foot of leeward mountain0.3090.3080.3590.267Figure 12
The displacement magnification factor of transmission tower top.The following can be seen from the above results: (1) The response variation law of transmission tower line system under mountain wind environment is basically the same, which is the largest at the top of the mountain and the smallest at the foot of the mountain. (2) The displacement magnification factor obtained from the Chinese code and the Australian code is symmetrical between the windward side and the leeward side. The displacement magnification factor from the Euro code on the windward side is smaller than that on the leeward side. The CFD calculation is opposite to that from the Euro code, and the windward side is larger. (3) The Chinese code is generally conservative and has the highest safety redundancy among various codes. CFD calculation data are close to the Australian and Euro codes on the windward side and smaller than other specifications on the leeward side.


## 2.1. Transmission Tower Line System Model

The selected research object in this work is a 110 kV “T” shaped mixed voltage narrow base tower on a transmission line of the East China Power Grid. The transmission line model is based on the tower, with a length upstream and downstream of 200 m, respectively. The conductor is LGJ-300/40 steel cord aluminum strand, and the ground wire is JLBv20A-80 aluminum clad steel strand. The tower height is 68.4 m, the tower nominal height is 48 m, and the tower foundation size is 3.5m × 3.5 m. Q345 angle steel is used as the main material and cross arm of the transmission tower. Q235 angle steel is used as the inclined material and other auxiliary materials. The section sizes of angle steel vary at different heights. The four-tower columns are the main components under stress, the components are bolted at both ends, and the transmission tower and the base are connected by fixed ends. The transmission line is the general name of transmission conductor and ground wire, which has the characteristics of high flexibility and large deformation. Under the action of gravity, the conductor (ground) fixed at two different points will be in a catenary shape, and the model shall be treated according to the provisions on sag in the design code. In ANSYS, the beam element is used to simulate the main stressed components of the transmission tower, and the rod element is used to simulate other rods and transmission lines to establish the finite element model of the transmission tower line system, as shown in Figure 10. It is placed at different positions of the mountain to analyze the response under wind load excitation.Figure 10
Finite element model of transmission tower line system.


## 2.2. Response Analysis of Transmission Tower Line System

The natural wind with an average wind velocity of 18 m/s at 10 m height is taken as the reference load; the Davenport wind velocity spectrum and the harmonic synthesis method are applied to simulate the fluctuating wind velocity, which is the time history of the fluctuating wind speed at the tower top simulated at the flat ground, as shown in Figure11. The wind acceleration ratio under the mountain wind field calculated by the above code and CFD can be corrected to the simulated wind velocity and then generate the corrected wind load [39–44].Figure 11
Fluctuating wind speed time history.Input the load into the transmission tower line system finite element model to accomplish the dynamic time history analysis using ANSYS and generate the response of the transmission tower line system under a mountain wind field. The obtained data are shown in Table1 and Figure 12.Table 1
Displacement response of transmission tower top.
Chinese codeAustralia codeEuro codeCFDFoot of windward mountain0.3090.3080.3570.307Windward half mountain0.5300.4400.4210.391Mountain top0.7520.5780.7210.509Leeward half mountain0.5300.4400.4720.364Foot of leeward mountain0.3090.3080.3590.267Figure 12
The displacement magnification factor of transmission tower top.The following can be seen from the above results: (1) The response variation law of transmission tower line system under mountain wind environment is basically the same, which is the largest at the top of the mountain and the smallest at the foot of the mountain. (2) The displacement magnification factor obtained from the Chinese code and the Australian code is symmetrical between the windward side and the leeward side. The displacement magnification factor from the Euro code on the windward side is smaller than that on the leeward side. The CFD calculation is opposite to that from the Euro code, and the windward side is larger. (3) The Chinese code is generally conservative and has the highest safety redundancy among various codes. CFD calculation data are close to the Australian and Euro codes on the windward side and smaller than other specifications on the leeward side.


## 3. Conclusions

The mountain blocks the movement of the fluid flowing through the mountain. There will be a large deceleration area in front of the mountain, and an acceleration area will be formed at the top of the mountain, which will increase the wind velocity. Besides, there appears an obvious flow separation phenomenon on the leeward slope, resulting in an eddy current. The wind acceleration ratio at the top of the mountain is the largest, greater than 1, and decreases with the increased height. The wind acceleration ratio at the windward half mountain below 100 m is greater than that at the leeward half mountain, and both are slightly greater than 1. The wind acceleration ratio at the leeward half mountain is smaller than 1 at 50 m high, greater than 1 at 50 m, and tends to approach 1. The wind acceleration ratio at the foot of the mountain is the smallest, which is smaller than 1, and tends to approach 1 with the increased height.Compared with the specification data, the acceleration ratio specified in the Chinese and the Australian codes varies linearly with height and is symmetrical on the windward and leeward sides. The acceleration ratio on the windward side of the Euro code is lower than that on the leeward side. The acceleration ratio specified in the Chinese code is the largest.Considering the response of the transmission tower line system, the results of CFD numerical calculation are smaller than those of various codes. On the windward side, they are close to the Australian and the Euro codes and far less than the code in other positions. The code has a large safety margin but increases the project cost to a certain extent which needs further optimization.



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*Source: 1026329-2022-02-27.xml*