Method for predicting three-dimensional aerodynamic forces of a cross-armed asymmetric tower

Abstract

A generalized wind load power spectrum prediction method of aerodynamic three-component forces of T-shaped tower, characterized in that, comprising the steps: 1: constructing a T-shaped tower model; 2: segmenting the T-shaped tower model; 3: calculating the mutual power spectral density of the aerodynamic three-component forces of the T-shaped tower model; 4a: calculating the aerodynamic three-component force power spectrum of the T-shaped tower model; 4b: calculating the aerodynamic force coefficient of the T-shaped tower model according to the relative height z / H, the relative width y / B and the eccentricity e; 4c: calculating the correlation coefficient; 5: calculating the generalized wind load power spectrum; 6: calculating the power spectrum of the generalized displacement; 7. Calculating the standard deviation of the generalized displacement; 8. Calculating the peak displacement; 9. Comparing the peak displacement with the specification displacement; 8: obtaining the construction scheme of the entity T-shaped tower and implementing. Effect: Through the prediction of the generalized wind load power spectrum, the finally constructed T-shaped tower has better wind resistance performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field, in particular to a generalized wind load power spectrum prediction method for aerodynamic three-component forces of T-shaped tower. BACKGROUND

[0002] In recent years, due to the demand of structural design and the irregular shape of available land, a large number of irregular high-rise structures have emerged. The irregular shape of the structure may cause the existence of aerodynamic eccentricity, which means that the aerodynamic shape is not axisymmetric. The aerodynamic eccentricity of the structure may be more sensitive to wind load, especially in the crosswind direction and torsional moment, and the change in the wake area may cause nonlinear coupling effects of torsional moment and crosswind load. Existing researches mostly consider the wind load effects of high-rise structures with symmetric aerodynamic shape in each direction separately. In fact, there is no simplified formula to consider the three-direction wind load to evaluate the influence of wind on aerodynamic eccentric high-rise structures, so it is necessary to conduct extensive research on this topic.

[0003] The existing technology has the following disadvantages: the existing technology has carried out research on the aerodynamic characteristics of the aerodynamic shape symmetric structure, but rarely involves the analysis of aerodynamic eccentric structure and aerodynamic three-component force correlation, and lacks a unified prediction method considering the downwind, crosswind and torsional three-direction wind load. SUMMARY

[0004] The present application provides a generalized wind load power spectrum prediction method for aerodynamic three-component forces of T-shaped tower, which can uniformly predict the generalized force spectrum of aerodynamic three-component forces of T-shaped tower.

[0005] To achieve the above purpose, the present application provides a generalized wind load power spectrum prediction method for aerodynamic three-component forces of T-shaped tower, which comprises the following steps:

[0006] Step 1: constructing a T-shaped tower model, setting the parameter values of the vertical column height H, vertical column radius r, horizontal column length L, horizontal column radius r and horizontal column long side L' of the T-shaped tower model, and defining the eccentricity e as the ratio of the horizontal column long side L' to the horizontal column length L; s h h h h h

[0007] Step 2: segmenting the T-shaped tower model to determine the windward area of each measurement layer and the wind speed at each height;

[0008] ​​​​​​Step 3: determining the frequency f of the T-shaped tower according to the stiffness, elastic modulus and density of the T-shaped tower building material; and obtaining the mutual power spectral density of the aerodynamic three-component force of the T-shaped tower model according to the dimensionless integral tower aerodynamic three-component force spectrum, correlation coefficient and aerodynamic force at each position;

[0009] Step 4a: obtaining the aerodynamic three-component force power spectral density of the T-shaped tower model according to the frequency f, eccentricity e and numerical simulation result;

[0010] Step 4b: calculating the aerodynamic three-component force coefficient of the T-shaped tower model according to the relative height z / H of the vertical column, relative width y / B of the horizontal column and eccentricity e;

[0011] Step 4c: calculating the correlation coefficient of the T-shaped tower model according to the eccentricity e;

[0012] Step 5: obtaining the generalized wind load power spectrum according to the aerodynamic force coefficient, front area model thickness of the measuring layer at each position and the k-th order vibration mode at each position;

[0013] Step 6: obtaining the power spectrum of the generalized displacement according to the generalized wind load power spectrum and frequency response function;

[0014] Step 7: obtaining the standard deviation of the generalized displacement according to the power spectrum of the generalized displacement;

[0015] Step 8: obtaining the peak displacement x according to the standard deviation of the generalized displacement, combined with the peak factor and vibration mode;

[0016] Step 9: comparing the peak displacement x with the specification displacement, when the peak displacement x is less than the specification displacement, entering step 11; otherwise, entering step 10;

[0017] Step 10: adjusting the parameter value of the horizontal column long side L' h , and then adjusting the value of the eccentricity e, and entering step 4a;

[0018] Step 11: determining the building scheme of the entity T-shaped tower according to the parameter values of the vertical column height H, vertical column radius r s , horizontal column length L h , horizontal column radius r h and horizontal column long side L' h , and building the entity T-shaped tower.

[0019] Through the above design, the vertical column height H, vertical column radius r s , horizontal column length L h , horizontal column radius r h and horizontal column long side L' h, the T-shaped tower is modeled, and the generalized wind load power spectrum is calculated by adjusting the eccentricity. Then, the generalized displacement standard deviation is obtained. Finally, the peak displacement is obtained by combining the peak factor and the vibration mode. The peak displacement x is compared with the standard displacement to determine the final construction plan of the physical T-shaped tower. By predicting the generalized wind load power spectrum and calculating the peak displacement x, the final constructed T-shaped tower has better wind resistance. At the same time, according to the climatic conditions and wind speed conditions of different regions, T-shaped towers suitable for local environmental conditions can be built to ensure the stability and reliability of the T-shaped tower, thereby extending the service life of the tower and reducing the cost of using the tower.

[0020] At the same time, this method is also applicable to the predictive erection of tower cranes with T-shaped tower structural characteristics, which can effectively improve the reliability and stability of tower cranes and ensure the safety of tower cranes during use.

[0021] Preferably, in step 1, the tower body in the T-shaped tower model is a T-shaped tower structure composed of two cylinders, wherein the horizontal column is installed on the top of the vertical column.

[0022] Preferably, in step 3, the calculation formula for the mutual power spectrum density of the aerodynamic three-force is as follows:

[0023] S Fi (x1, x2; f) = F i (x1)F i (x2)S Fi ′(f)Cor Fi (x1, x2) (1)

[0024]

[0025] Among them, x1 and x2 represent the coordinates of two points in the tower column or horizontal column space, x1 is the relative height of the column, and x2 is the relative width of the column; f represents the frequency, F i (x1) represents the aerodynamic force at x1, F i (x2) represents the aerodynamic force at x2, Cor Fi (x1, x2) represents the correlation coefficient, S Fi ′(f) represents the dimensionless aerodynamic three-dimensional force spectrum of the whole tower, S Fi (f) represents the power spectrum density function of the aerodynamic three-force under wind load, represents the root mean square aerodynamic three-component force.

[0026] Preferably, in step 4a, the pneumatic three-force power spectrum density formula is as follows:

[0027]

[0028]

[0029] wherein ε it represents a function of the eccentricity e, χ t , δ t , represents a calculation parameter, e represents the eccentricity; i = 1, 2, 3, i = 1 represents the model resistance, i = 2 represents the model lift, i = 3 represents the model torque; t = 1, 2, 3, 4, 5.

[0030] As preferred: in the step 4b, the aerodynamic three-component force coefficient calculation formula is as follows:

[0031] C Fij = θ ij1 + θ ij2 (x j )+ θ ij3 (x j ) 2 (5)

[0032]

[0033] θ iig = a i +b i e+c i e 2 , g = 1, 2, 3 (7)

[0034] wherein C Fij represents the aerodynamic three-component force coefficient in the j direction; j = 1, 2, j = 1 represents the vertical direction, i.e. the vertical column extension direction, j = 2 represents the horizontal direction, i.e. the horizontal column extension direction; z / H represents the relative height of the vertical column, y / B represents the relative width of the horizontal column; a i , b i , c i , θ ijg represent calculation parameters, y represents the horizontal coordinate of the geometric center of the n-th section in the vertical direction of the tower, and z represents the vertical coordinate of the geometric center of the n-th section in the horizontal direction of the tower.

[0035] As preferred: in the step 4c, the correlation coefficient calculation formula is as follows:

[0036] Cor Fij = C r1 x exp(-C r2 x), x = |x1-x2| / H (8)

[0037] wherein Cor Fij represents the correlation coefficient, C r1 , C r2where exp denotes the exponential function with base e, and

[0038] C ru =A u +B u e+C u e 2 +D u e 3 , u = 1, 2 (9)

[0039] where A u , B u , C u , D u represent the calculation parameters.

[0040] As preferred: in the step 5, the calculation formula of the kth order generalized force spectrum is as follows:

[0041]

[0042] where, represents the kth order generalized force spectrum, represents the kth order mode shape at the x1 position, represents the kth order mode shape at the x2 position; the integral tower aerodynamic three-component forces are respectively the drag force, the lift force, and the torque;

[0043] The original aerodynamic three-component force coefficient expression is as follows:

[0044]

[0045] where C Fnij represents the average or root mean square aerodynamic three-component force coefficient of the n-th segment in the direction, F nij represents the average or root mean square aerodynamic three-component force of the n-th segment in the direction; i = 1, 2, 3, i = 1 represents the model drag force, i = 2 represents the model lift force, and i = 3 represents the model torque; j = 1, 2, j = 1 represents the vertical direction, i.e., the vertical column extension direction, and j = 2 represents the horizontal direction, i.e., the horizontal column extension direction; U Hn is the average wind speed at the n-th segment height, A sn is the windward area of the n-th segment of the model, and p represents the density of air.

[0046] When formula (1) is substituted into formula (11) and combined with formula (12), the calculation formula of the generalized wind load power spectrum is as follows:

[0047]

[0048] where, represents the aerodynamic force coefficient at x1 in the j direction, C(x2) represents the aerodynamic force coefficient at x2 in the j direction, A(x1) represents the measured layer front area at x1, A(x2) represents the measured layer front area at x2, and D represents the model thickness in the direction parallel to the wind. φ k (x1) represents the kth mode shape at x1 position, φ k (x2) represents the kth mode shape at x2 position. r represents the correlation coefficient.

[0049] As a preferred: in step 6, the calculation formula of the power spectrum of the generalized displacement is as follows:

[0050]

[0051] wherein, σ k (x) represents the power spectrum of the generalized displacement, H k φ k (f) represents the kth order frequency response function of the tower, f k ω k represents the kth order frequency of the tower, ζ k ξ k represents the damping ratio of the kth mode shape.

[0052] As a preferred: in step 7, the calculation formula of the generalized displacement standard deviation is as follows:

[0053]

[0054] wherein, σ represents the generalized displacement standard deviation.

[0055] As a preferred: in step 8, the calculation formula of the peak displacement is as follows:

[0056]

[0057] wherein, g s = 2.5, φ k (x) represents the kth mode shape at x, M k * M k represents the generalized mass of the kth mode shape.

[0058]

[0059] wherein, m(x) represents the mass at x.

[0060] The beneficial effects of the present application: through the prediction of the generalized wind load power spectrum and the calculation of the peak displacement x, the finally built T-shaped tower has better wind resistance performance; at the same time, according to the climate conditions and wind speed conditions of different regions, the T-shaped tower suitable for local environmental conditions can be built, so as to ensure the stability and reliability of the T-shaped tower, thereby prolonging the service life of the tower and reducing the use cost of the tower. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1A schematic diagram of the calculation process of the present application;

[0062] Figure 2 A calculation domain boundary condition and model segmentation in the embodiment;

[0063] Figure 3 A wind tunnel test diagram in the embodiment;

[0064] Figure 4 A correlation diagram of the aerodynamic three-force of the tower with the eccentricity in the embodiment;

[0065] Figure 5 A windward surface pressure distribution diagram of the tower under different eccentricities in the embodiment;

[0066] Figure 6 A leeward surface pressure distribution of the tower under different eccentricities in the embodiment;

[0067] Figure 7 An average velocity contour map on the central vertical plane with time-averaged flow lines in the embodiment;

[0068] Figure 8 An average velocity contour and time-averaged flow line diagram on different height horizontal planes in the embodiment;

[0069] Figure 9 A centerline view of a medium calculation grid in the embodiment.

[0070] Figure 10 A time evolution diagram of vertical instantaneous vortex structure in the embodiment;

[0071] Figure 11 A time evolution diagram of transverse instantaneous vortex structure in the embodiment;

[0072] Figure 12 An aerodynamic three-force spectrum diagram of a T-shaped tower model with different eccentricities in the embodiment;

[0073] Figure 13 A comparison diagram of correlation coefficient simulation results in the embodiment. DETAILED DESCRIPTION

[0074] The present application will be further described in detail below in conjunction with the drawings and specific examples. The following examples or drawings are used to illustrate the present application, but not to limit the scope of the present application.

[0075] As shown in Figure 1 : a generalized wind load power spectrum prediction method of T-shaped tower aerodynamic three-force, the key of which includes the following steps:

[0076] Step 1: build a T-shaped tower model through a finite element analysis software, set the vertical column height H and the vertical column radius r of the T-shaped tower model s, the horizontal column length L h , the horizontal column radius r h , and the horizontal column long side L' h , the eccentricity e is defined as the ratio of the horizontal column long side L' h to the horizontal column length L h ;

[0077] Step 2: segmenting the T-shaped tower model, determining the windward area of each measurement layer and the wind speed at each height;

[0078] Step 3: determining the frequency f of the T-shaped tower according to the stiffness, elastic modulus and density of the T-shaped tower building material, and obtaining the mutual power spectral density of the aerodynamic three-component force of the T-shaped tower model according to the dimensionless whole-tower aerodynamic three-component force spectrum, the correlation coefficient and the aerodynamic force at each position;

[0079] Step 4a: obtaining the aerodynamic three-component force power spectral density of the T-shaped tower model according to the frequency f, the eccentricity e and the numerical simulation result;

[0080] Step 4b: calculating the aerodynamic three-component force coefficient of the T-shaped tower model according to the relative height z / H of the vertical column, the relative width y / B of the horizontal column and the eccentricity e;

[0081] Step 4c: calculating the correlation coefficient of the T-shaped tower model according to the eccentricity e;

[0082] Step 5: obtaining the generalized wind load power spectrum according to the aerodynamic force coefficient, the front area model thickness of the measurement layer at each position and the k-th order mode shape at each position;

[0083] Step 6: obtaining the power spectrum of the generalized displacement according to the generalized wind load power spectrum and the frequency response function;

[0084] Step 7: obtaining the standard deviation of the generalized displacement according to the power spectrum of the generalized displacement;

[0085] Step 8: obtaining the peak displacement x according to the standard deviation of the generalized displacement, in combination with the peak factor and the mode shape;

[0086] Step 9: comparing the peak displacement x with the specification displacement, when the peak displacement x is less than the specification displacement, entering Step 11; otherwise, entering Step 10;

[0087] Step 10: adjusting the parameter value of the horizontal column long side L' h , and further adjusting the value of the eccentricity e, entering Step 4a;

[0088] Step 11: obtaining the specification displacement according to the vertical column height H, the vertical column radius r s , the horizontal column length L h , the horizontal column radius rh and the horizontal column long side L' h determine the construction scheme of the physical T-shaped tower and construct the physical T-shaped tower.

[0089] In the step 1, the tower body in the T-shaped tower model is a T-shaped tower structure composed of two cylinders, wherein the horizontal column is installed on the top of the vertical column.

[0090] The aerodynamic three-component forces are respectively drag force, lift force and torque.

[0091] Before the construction of the T-shaped tower model, the construction site of the physical T-shaped tower needs to be selected according to the actual demand, and the vertical column height H, the vertical column radius r s , the horizontal column length L h and the horizontal column radius r h and other parameters of the T-shaped tower are determined according to the actual situation of the terrain and climate, and the appropriate construction material is selected to ensure that the physical T-shaped tower can adapt to the changes of the local climate conditions, improve the safety, stability and service life of the T-shaped tower.

[0092] The determination of the construction scheme of the physical T-shaped tower includes the determination of the T-shaped tower structure, the number of construction materials, the number of workers, the construction process and the matters needing attention.

[0093] In this embodiment, the ANSYS FLUENT numerical software is used to model and divide the grid of the eccentric T-shaped circular tube tower, and the numerical simulation results are verified by using the high-frequency balance force wind tunnel test, then the flow field changes under different eccentricity rates are analyzed from three aspects of wind pressure distribution, drainage pattern and turbulent kinetic energy, to explore the influence of aerodynamic eccentricity on the aerodynamic three-component forces of the T-shaped circular tube tower. Combined with the numerical simulation and test data, the aerodynamic three-component force coefficients, power spectral density and correlation function are given and discussed, and finally the generalized force spectrum expression of the aerodynamic three-component force is given based on the random vibration theory.

[0094] The fluid mechanics calculation accuracy mainly depends on the selection of the calculation domain size and the grid pattern, the tower body is a cylindrical structure, and the flow is mainly side flow. The tower flow fluid calculation domain grid is determined by controlling the drainage resistance rate, the model position and the wall surface grid thickness. If the blockage rate is too high, it will have an adverse effect on the turbulent degree of the flow field of the side surface of the cylinder and the wind pressure on the surface of the cylinder, thereby leading to inaccurate calculation results. In addition, the construction of the calculation domain also involves the position of the model studied in the domain, such as the position of the outflow being too close to the building model studied, and the flow may not have reached a fully developed state, or even may still be in the wake backflow area formed by the obstruction of the building. Referring to the previous research and the relevant provisions of AIJ, the calculation domain arrangement and the boundary condition setting are as follows Figure 2(a) shown, the upper symmetry plane is 5H away from the top of the model, the left and right surfaces and the top surface are symmetry boundary conditions, in order to eliminate unnecessary dissipation of the required wind profile, 5H is set as the distance between the inlet surface and the center of the model. Likewise, the downstream outlet is 10H away from the center of the model to ensure the full development of the wake, the side surface is set with a gap of 3H, and the upper symmetry plane is 5H away from the top of the model, where the column height H is 0.45m.

[0095] The eccentricity size design is shown in Table 1:

[0096] Table 1 Model size

[0097]

[0098]

[0099] In Table 1, M1-M6 represent the sizes of six different eccentricity models, respectively, the column radius r s is 15mm, and the cross column radius r h is 3mm. The important analysis parameter eccentricity e is defined as the ratio of the cross column long side L' h to the full length of the cross column L h . Under this arrangement, the blockage rate is 0.31%. The eccentric T-shaped circular tubular tower model is segmented to facilitate the determination of the correlation of the local truss of the tower, and the segmentation and numbering are shown in Figure 2 (b) shown, where the column and the cross column are each divided into 6 equal segments.

[0100] This embodiment uses large eddy simulation LES to simulate turbulence, and the simulation results of LES are greatly affected by the inflow boundary conditions of the calculation domain. At present, there is still a lack of effective verification of the accuracy and reliability of the simulation. In the calculation domain, due to the dissipation effect, the initial inflow condition will inevitably change along the flow direction. It is usually difficult to generate a target wind spectrum at the model position. This embodiment mainly focuses on the influence of aerodynamic eccentricity on the change of the flow field, so a way of setting the turbulence intensity and turbulence integral scale at the inlet is used to generate random inlet turbulence, the average wind speed and turbulence intensity at the inlet are set to 4m / s and 5%, respectively, the turbulence integral scale is 0.05m, and the Reynolds number is 3300.

[0101] The flow domain grid is discretized using a hybrid grid division scheme of inner and outer domains: the non-structural grid is used for the inner domain near the wall surface of the tower model to adapt to the local irregular surface of the tower, and the structural grid is used for the outer domain away from the model. The Interface boundary condition provided by the FLUENT software is used for data exchange between the structural grid and the non-structural grid. The boundary layer surrounds the model, and thus the height of the first unit and the dimensionless wall distance are 0.003r hThe near-wall y+ value is about 35-85, which is suitable for the wall function of large eddy simulation. The tetrahedral mesh is generated with a growth ratio of 1.1, and the total number of meshes reaches 6 million. The mesh distribution of the whole computational domain and the region near the tower model is shown in FIG. 1. Since the mesh generation method is consistent under different eccentricity ratios, only the mesh distribution of the M1 model is given here. The purpose of the higher density of the near-wall region is to reduce the need for a large number of elements in the whole region and to provide better resolution for capturing any key aerodynamic flow trends in the wake region. Figure 9

[0102] The pressure implicit split operator (PISO) algorithm is used in the numerical simulation calculation, the second-order implicit format is selected for time discretization, and the second-order central format is selected for spatial discretization. Since large eddy simulation belongs to a high Reynolds number model, when analyzing low Reynolds number flow in the near-wall region, a wall-adaptive local eddy viscosity model WALE is selected for the sub-grid scale model SGS. Considering the high performance requirements of large eddy simulation on computers, 18-core parallel computing is used. When the Courant number is generally between 0 and 5, the numerical stability is better, and the required calculation time is reduced. In order to meet the Courant condition CFL, the time step is set to Δt = 0.0003s in this embodiment.

[0103] In this embodiment, dimensionless data coefficients are used to discuss the results for simplicity and effectiveness. The definition is as follows:

[0104] Pressure coefficient C p Expression:

[0105]

[0106] Original aerodynamic three-force coefficient expression:

[0107]

[0108] Original correlation coefficient expression:

[0109]

[0110] wherein C p represents a pressure coefficient, P represents the static pressure of the model surface, P0 represents the reference pressure (0 Pa) of the model surface; Cor(m, r) represents a correlation coefficient, m and r are variables, for example, a force coefficient; Cov(m, r) is the covariance of m and r; σ m represents the standard deviation of variable m, σ r represents the standard deviation of variable r; θ m represents the time history of variable m in the x, y, or z direction, θ r represents the time history of variable r in the x, y, or z direction, ​denotes the time history average of the variable m in the x, y or z direction, denotes the time history average of the variable r in the x, y or z direction.

[0111] To verify the sufficiency of the grid resolution, three types of grids, i.e. coarse, medium and fine grids, were tested before determining the final grid scheme. The corresponding simulation results are given in Table 2. The results show that the accuracy of the numerical calculation can be improved with the increase of the number of grid cells, especially from the coarse grid to the medium grid. However, when the grid changes from the medium type to the fine type, the improvement is no longer obvious. It is worth noting that the difference between the drag coefficient obtained from the medium grid case and the wind tunnel test is less than 3%, while the lift coefficient and the torque coefficient differ greatly between the numerical results and the experimental results but are still less than 10%. Therefore, the medium grid type with a total of 5.96 million cells is adopted in this embodiment, which meets the accuracy while greatly reducing the calculation cost.

[0112] Table 2 Grid independence verification results

[0113]

[0114] This embodiment performs a high-frequency balance force HFFB test on a standard T-shaped tower model in the wind tunnel laboratory of Tianjin Water Research Institute as shown in Figure 3 . The tower model is made of steel. A high-frequency six-component force moment sensor is used to measure the time history of the model's along-wind resistance, cross-wind lift and torque around the central axis. The wind-induced vibration response of the structure can be calculated according to the random vibration theory by combining the three-component time history data of the T-shaped tower with the structural dynamic characteristics. The sampling frequency and duration are set to 1000 Hz and 60 s, respectively. The high-frequency balance force wind tunnel laboratory and the T-shaped tower model are shown in Figure 3 . Among them, the T-shaped tower model M1, the T-shaped tower model M3 and the T-shaped tower model M6 have the same size as the numerical simulation in Table 1. The test wind field is uniform flow, and the wind speed at the top of the T-shaped tower model is 4.0 m / s.

[0115] To verify the correctness of the numerical simulation model size, the same model parameters and wind field parameters as the wind tunnel test are set, and the relative errors of the aerodynamic three-component force coefficients of the whole tower model obtained by numerical simulation and wind tunnel are shown in Table 3.

[0116] Table 3 Relative error of whole aerodynamic three-component force coefficients obtained by numerical simulation and wind tunnel

[0117]

[0118]

[0119] As can be seen from Table 3, the overall drag coefficient, the lift coefficient and the torque coefficient obtained by numerical calculation show acceptable consistency with the experimental results. The lift coefficient and the torque coefficient have certain differences, mainly due to the complex flow conditions on the side and leeward surfaces. Although there are differences, the maximum relative error of individual points is still less than 10%, and Huang et al. also reported similar phenomena. The drag coefficient has relatively better fitness. The numerical model for large eddy simulation in this embodiment can reasonably explain the wind effect.

[0120] Table 4 compares the overall drag coefficient, the lift coefficient and the torque coefficient under different eccentricity ratios.

[0121] Table 4 Overall three-component force under different eccentricity ratios

[0122]

[0123] As can be seen from Table 4, the aerodynamic eccentricity has a significant effect on the torque coefficient, which is caused by the imbalance of the instantaneous wind pressure distribution on the surface of the tower caused by structural eccentricity. In addition, a larger eccentricity ratio will result in a greater increase in the torque of the tower. Specifically, when the eccentricity ratio increases from 0.50 to 0.55, the average overall torque coefficient of the tower increases by 0.0078; when the eccentricity ratio increases from 0.7 to 0.75, the average overall torque coefficient of the tower increases by 0.0107. When the wind flows through the tower, the uneven pressure formed on its surface and the vortex shedding in the wake cause the existence of lateral lift and torsional moment. With the increase of 50% in the eccentricity ratio, the average torque increases by 99.7%, and the average lift shows a fluctuating trend, and the average lift coefficient is equal when the eccentricity ratio is 0.5 and 0.75. The fluctuation components of the overall lift and torque of the tower increase by 16.32% and 99.50%, respectively. However, for the drag coefficient, the maximum change rate of the average drag coefficient is 0.18%, and the maximum change rate of the drag fluctuation component is 0.2%. In summary, the increase of the eccentricity ratio has an effect on the average and fluctuation of the lift and torque, among which the effect on the torque is the largest, but the effect on the drag is smaller.

[0124] The continuous time series values of the overall aerodynamic three-component force obtained by numerical simulation in this embodiment, and the absolute values of the correlation coefficients of the aerodynamic three-component force obtained according to formula (14) change with the eccentricity ratio, as shown in Figure 4 . Among them, m, r represents any two forces in the overall tower aerodynamic three-component force. The correlation between the drag, the lift and the torque increases roughly with the increase of the eccentricity ratio. The correlation between the drag and the lift changes rapidly at the eccentricity ratio of 0.60, but overall shows an accelerating trend. With the increase of the eccentricity ratio, the correlation between the drag and the torque and the correlation between the lift and the torque both accelerate, which is related to the increase in the change range of the torque coefficient at high eccentricity ratio.

[0125] The mean pressure distribution on the windward side of the structure with different eccentricity ratios is shown in Figure 5 Due to the same way of generating the inlet wind speed by using the uniform turbulence inlet of the numerical simulation software FLUENT, the pressure distribution on the windward side is generally similar. The stagnation point on the windward side is located at the position of 0.967H, which is basically on the same horizontal line as the central axis of the cross column. When affected by the eccentricity ratio, the symmetry of the windward pressure distribution of the vertical column changes, in addition, with the increase of the eccentricity ratio, the wind pressure on the right end of the cross column is strengthened, and the area becomes more concentrated with the increase of the eccentricity ratio, which may cause larger local wind pressure on the surface of the eccentric structure of the general structure, thereby causing larger structural wind-induced response.

[0126] The aerodynamic eccentricity has a certain influence on the pressure distribution on the leeward side of the model, as shown in Figure 6 Specifically, compared with the M1 model, the suction effect in the height range of about 3 / 4H to H on the upper end of the vertical column of the remaining models is enhanced, and the negative pressure on the leeward side becomes larger, for example, the peak pressure coefficient of the M4 model increases by 7.5%. In addition, the increase of the eccentricity ratio from 0.5 (non-eccentric) to 0.65 significantly changes the distribution of the local negative pressure area on the leeward side. It gradually changes from the symmetrical distribution of the M1 model to disorder, which may cause a certain wind pressure difference and affect the distribution of the structural aerodynamic force.

[0127] In order to explain the reason for the change of aerodynamic force under different eccentricity ratios, the flow field and vortex structure are further observed. This embodiment only selects three typical working conditions M1, M4 and M6 for regularity analysis, and the time-averaged velocity contour on the horizontal plane at different heights of M1, M4 and M6 is shown in Figure 8 It is obvious that the eccentricity ratio changes the flow lines and vortex structure around the tower to a great extent. Specifically, for the M1 model, as shown in Figure 8 (a1)-(a3), the shear layer separates uniformly on both sides of the tower at each height, thereby generating symmetrical vortex shedding along the flow direction. However, M1, M4 and M6 models appear different degrees of flow separation and reattachment on the horizontal plane at different heights. The asymmetric recirculation zone tends to tilt towards the long arm of the cross column and extend downstream, changing the wind speed and direction of the flow field, which directly leads to the increase of the negative pressure on the leeward side of the upper end of the vertical column of the eccentric model. In addition, there is no great change on the windward side, but the stagnation point on the leeward side is the red dot in Figure 8 (c3), which is close to the side of the long arm of the cross column. Under the action of fluctuating wind load, the changes of flow characteristics caused by aerodynamic eccentricity directly lead to the increase of the overall torque of the tower. The separation bubble under the M4 model is no longer symmetrical, as shown by the red box in Figure 8 (b2). The separation bubble on the right side becomes flatter and closer to the tower wall, as shown in Figure 8The red dotted ellipse in (b3) shows this. This asymmetric distribution of streamlines on both sides of the tower will amplify the wind-induced response in the crosswind direction. In addition, as the eccentricity increases, the difference in the side shear layer bubbles becomes more obvious. For example, Figure 8 As shown in (c3), the bubble beneath the M6 ​​model reattaches and moves backward, occurring on the leeward side near the long arm of the column. In contrast, the detached shear layer toward the short arm of the column becomes flatter and is about to be immersed in the deviating wake. Bubble attachment can change the wind pressure distribution at the attachment location; more bubbles attach, greater partial pressure. This can explain the sudden changes in the mean and root mean square pressure coefficients on the leeward side.

[0128] It is obvious that when the model has aerodynamic eccentricity, the wake area will deviate from the centerline of the tower. In this embodiment, the deviation angle α is used to evaluate the effect of eccentricity on the deviation of the wake area at different heights, which is defined as the angle between the red line and the black dashed line. The red line represents the development direction of the wake area, connecting the stagnation point near the windward side and the end of the wake flow; while the pink dashed line represents the center axis of the tower column. Figure 8 As can be seen, because the eccentric horizontal column is primarily located at the tower's top, α in the wake region at different heights increases with increasing tower height. Specifically, for the M4 model, α increases by 5.9° and 6.6° for height increases of 0.33H and 0.47H, respectively. This indicates that the aerodynamic eccentricity of the horizontal column affects the vertical column, and the effect on α gradually decreases from the top to the bottom. Furthermore, because the lateral scale of the horizontal column is much larger than that of the vertical column, it is easy to observe that α is the largest at the height of the horizontal column compared to other heights.

[0129] For the M6 ​​model, vortices at different heights are more complex than those in other models, particularly at z = 0.967H, the location of the tower column. This is the fundamental reason why increasing eccentricity promotes the overall lift and torque pulsation components of the model. Furthermore, this variation accelerates with increasing eccentricity. Furthermore, this phenomenon suggests that the tower column imparts a "twisting extensibility" to the wake wind field in the vertical direction. This can be explained by the fact that the wake deviation angle is not only determined by the oncoming wind direction at the same height, but also by the deviation of the wake at adjacent heights. One possible explanation for this "twisting extensibility" is that structural eccentricity can enhance momentum exchange and greater vertical correlation compared to symmetrical structures. Therefore, the extensibility of the tower column exacerbates the torsional response, posing a risk to tall structures such as T-shaped towers.

[0130] For the central vertical plane basin, such as Figure 7It is shown that the aerodynamic eccentricity has little effect on the flow field in front of the model, for example, the streamlines upstream of the model and on the top are almost unchanged. In addition, the effect on the wake region far away from the cross column structure is small, but it is obvious that the closer to the cross column position, the greater the effect on the vortex pattern and distribution in the near wake region. With the change of the eccentricity ratio, the large-scale vortex in this region derives more small-scale vortices, and the small-scale eddies gradually approach the leeward surface of the model. These phenomena may lead to greater correlation in the vertical direction near the cross column and different pressure distribution on the leeward surface, and affect the downwind resistance of the eccentric structure.

[0131] The vortex structure is visualized by Q-criterion to further compare the instantaneous flow characteristics and analyze the change of turbulent kinetic energy. As shown in Figure 10 and Figure 11 , under the influence of the eccentricity ratio, the flow region near the structure has the characteristics of non-uniformity, small-scale fragments, downstream deflection and distortion. These different fluid-structure interactions are the potential physical mechanisms for generating irregular wind pressure distribution and asymmetric aerodynamic force. 1. The asymmetric vortex on both sides of the cross column enhances the conical vortex structure at the top of the vertical column, as shown by the black ellipses in Figure 10 (a), (c), (e), (f), the enhanced vortex structure at the top leads to the change of wind pressure on the top of the tower on the leeward surface; 2. The large-scale vortex structure is decomposed into small-scale vortices, especially in the wake region near the vertical column, see blue ellipses; 3. The vortex in the direction of the cross column not only extends downstream to the far wake, but also deflects to the right, which is also the direction of the torque force, see Figure 11 and Figure 11 (f) black ellipses.

[0132] According to the random vibration theory, the cross power spectral density S Fi (x1, x2; f) of the aerodynamic three-component forces at different heights can be calculated by the following expression:

[0133] S Fi (x1, x2; f) = F i (x1)F i (x2)S Fi '(f)Cor Fi (x1, x2) (1)

[0134]

[0135] where x1, x2 represent the coordinates of two points in the space of the tower vertical column or cross column, x1 takes the relative height of the vertical column, and x2 takes the relative width of the cross column; f represents the frequency, F i (x1) represents the aerodynamic force at x1, F i (x2) represents the aerodynamic force at x2, and Cor Fi(x1, x2) denotes the correlation coefficient, S Fi (f) represents the dimensionless overall tower aerodynamic force triad spectrum, S Fi (f) denotes the aerodynamic force triad auto-power spectral density function under wind load, denotes the root mean square aerodynamic force triad.

[0136] In this embodiment, the nonlinear least squares method NLSM is used to establish the calculation formula (2) on the basis of the numerical simulation results.

[0137] The overall triad time history of the T-shaped tower model under different eccentricity ratios is subjected to fast Fourier transform to obtain the corresponding aerodynamic force power spectrum. The overall lift and torque power spectrum of the tower remains consistent in a large range. With the increase of frequency, the overall lift power spectrum of the tower gradually becomes similar to the overall drag power spectrum in the high frequency band, becomes more gentle, and the amplitude is increasingly close to the overall drag power spectrum in the high frequency band. Therefore, the triad correlation increases with the increase of eccentricity ratio, as shown in Figure 4 Through nonlinear fitting of the numerical simulation results, the normalization formula of the overall force spectrum of the T-shaped tower model is as follows:

[0138]

[0139] wherein ε it denotes the function of eccentricity e, χ t , δ t , denotes the calculation parameter, e denotes the eccentricity; i = 1, 2, 3; t = 1, 2, 3, 4, 5. The calculation parameter is determined according to the numerical simulation results, as shown in Table 5.

[0140] Table 5 for calculating parameters

[0141]

[0142] The comparison of the overall tower aerodynamic triad force spectrum of the models M1-M6 by the proposed formula and the numerical simulation results is shown in Figure 12 . The results show that the overall tower aerodynamic triad force spectrum array determined by the formula is in good agreement with the numerical simulation results, indicating that the formula provides a reasonable prediction for the aerodynamic triad force power spectrum of the T-shaped tower. It is worth noting that the flow in the atmospheric boundary layer is not simulated here, so the power spectrum cannot be directly applied to evaluate the wind effect of the actual tower, and further improvement is needed, which is also part of the future research plan.

[0143] The polynomial expression shown in equation (5) is used to fit the aerodynamic force coefficients of the T-shaped tower with the relative height z / H, the relative width y / B, and the eccentricity e as independent variables, wherein a i , bi and c i are the parameters involved in the equation; y and z are the vertical coordinate z and the horizontal coordinate y of the geometric center of the nth tower section. The nonlinear least squares method (NLSM) is then used to fit the parameters based on the eccentricity, as shown in Table 6.

[0144] C Fij =θ ij1 +θ ij2 (x j )+θ ij3 (x j ) 2 (5)

[0145]

[0146] θ ijg =a i +b i e+c i e 2 , g=1,2,3 (7)

[0147] Among them, C Fij represents the aerodynamic three-force coefficient in the j direction; z / H represents the relative height of the vertical column, y / B represents the relative width of the horizontal column; a i 、b i 、c i ,θ ijg Represents the calculation parameters, y represents the horizontal coordinate of the geometric center of the nth section in the vertical direction of the tower, and z represents the vertical coordinate of the geometric center of the nth section in the horizontal direction of the tower.

[0148] Table 6 is used to calculate the parameter C i ′(z)

[0149]

[0150] In order to verify the above empirical formula, the relative errors between the numerical simulation results and the formula calculation results are less than 5%, thus verifying the applicability of the proposed formula.

[0151] The correlation coefficient is defined as shown in formula (14). According to the characteristics of the target T-shaped tower model in this embodiment, the horizontal columns and vertical columns are studied separately, where the vertical columns mainly consider the vertical correlation and the horizontal columns mainly consider their horizontal correlation.

[0152] Depend on Figure 13The distribution of the correlation coefficients of the M1 model shows that the vertical correlation coefficients are almost between 0.1 and 0.9. For the vertical and horizontal columns of the model, the vertical correlation coefficients (with the top of the vertical column as the reference point) and the horizontal correlation coefficients (with the right end of the horizontal column as the reference point) gradually decrease with the increase of the distance between two points, and finally tend to be flat. According to the values of the test and numerical simulation results of the embodiment, a new expression of the vertical and horizontal correlation coefficients as a function of the eccentricity is established, as follows:

[0153] Cor Fij = C r1 x exp(-C r2 x)x = |x1-x2| / H (8)

[0154] wherein, Cor Fij represents the correlation coefficient, C r1 and C r2 represent the coefficients varying with the eccentricity, and exp represents the exponential function with e as the base;

[0155] C ru = A u +B u e+C u e 2 +D u e 3 , u = 1, 2 (9)

[0156] wherein, A u , B u , C u , and D u represent the calculation parameters.

[0157] wherein, the values of the correlation parameters of Cr1 are shown in Table 7, and the values of the correlation parameters of Cr2 are shown in Table 8.

[0158] Table 7 Values of the correlation parameters of Cr1

[0159]

[0160] Table 8 Values of the correlation parameters of Cr2

[0161]

[0162]

[0163] Since the fitting methods of different T-shaped tower models are the same, only the fitting results of the aerodynamic three-force coefficients of the vertical and horizontal columns of the M1 model are given, as follows: Figure 13The correlation coefficient calculated by this expression is in good agreement with the test results, although there are some differences between the predicted and measured values. In general, the proposed formula can effectively describe the variation of the correlation coefficient with the eccentricity ratio.

[0164] To evaluate the reliability of the T-shaped tower under wind excitation, it is a key problem to obtain a specific expression of the predicted wind load. The kth order generalized force spectrum can provide wind load excitation at different frequencies, and accurate establishment of the mathematical model of the T-shaped tower aerodynamic load is helpful to predict the behavior and response of the system, so on the basis of the above nonlinear fitting, according to the random vibration theory, the kth order generalized force spectrum is obtained as follows:

[0165]

[0166] wherein, represents the kth order generalized force spectrum, represents the kth order mode shape at x1 position, represents the kth order mode shape at x2 position; the integral tower aerodynamic three forces are respectively drag force, lift force and torque.

[0167] When formula (1) is substituted into formula (11) and combined with formula (12), the kth order generalized force spectrum is simplified as follows:

[0168] The simplified formula of the kth order generalized force spectrum, i.e. the calculation formula of the generalized wind load power spectrum, is as follows:

[0169]

[0170] wherein, represents the aerodynamic force coefficient at x1 in j direction, represents the aerodynamic force coefficient at x2 in j direction, A(x1) represents the front surface area of the measurement layer at x1, A(x2) represents the front surface area of the measurement layer at x2, and D represents the model thickness in the direction parallel to the wind.

[0171] The calculation formula of the generalized displacement power spectrum is as follows:

[0172]

[0173] wherein, represents the power spectrum of the generalized displacement, H k represents the kth order frequency response function of the tower, f k represents the kth order frequency of the tower, ζ k represents the damping ratio of the kth order mode shape.

[0174] The calculation formula of the generalized displacement standard deviation is as follows:

[0175]

[0176] where σ denotes the standard deviation of the generalized displacement.

[0177] The peak displacement is calculated as follows:

[0178]

[0179] where g s = 2.5, denotes the k-th mode shape at x, M k * denotes the generalized mass of the k-th mode shape.

[0180]

[0181] where m(x) denotes the mass at x.

[0182] In summary, (1) the increase of the eccentricity ratio has an effect on the average value and fluctuation component of the lift and torque, and has a significant effect on the torque, but the effect on the drag can be ignored. The aerodynamic eccentricity significantly changes the distribution of the negative pressure area on the leeward surface, which causes a certain wind pressure difference and thus affects the distribution of the structural aerodynamic force.

[0183] (2) The aerodynamic eccentricity greatly changes the streamline and vortex structure around the tower. The asymmetric recirculation zone tends to tilt towards the direction of the long arm of the cross column and extend downstream, and these changes in flow characteristics caused by aerodynamic eccentricity directly lead to the enhancement of the overall torque of the tower. The cross column of the tower makes the wake wind field have a "twisted extension" at the height of the vertical column. Compared with the symmetric structure, the aerodynamic eccentricity can enhance the momentum exchange and greater correlation in the vertical direction, thus intensifying the torsional response, and with the increase of the eccentricity ratio, the influence between the adjacent heights of the vertical column direction is more significant, resulting in greater correlation. The vortex in the cross column direction not only extends downstream to the far wake, but also deflects to the right side, which twists around the direction of the torque force, which is the reason for the amplification of the lateral and torsional responses under the aerodynamic eccentricity.

[0184] (3) With the increase of the eccentricity ratio, the aerodynamic three-component force power spectrum decreases gently in the low frequency band and changes greatly in the high frequency band, especially the overall lift power spectrum. With the increase of the eccentricity ratio, the overall lift power spectrum and the overall drag power spectrum gradually become similar and tend to be flat, which is closely related to the increase of the three-component force correlation with the increase of the eccentricity ratio. Based on the random vibration theory, the normalized formula of the overall force spectrum of the T-shaped tower is obtained through the nonlinear fitting of the numerical simulation results.

[0185] (4) The aerodynamic eccentricity will enhance the correlation between the three directions of downwind, crosswind and torsion, so we will analyze the aerodynamic three-component force coupling characteristics and coupling principle of T-shaped tower from the three-component generalized force spectrum next, and provide a more effective method for the analysis of aerodynamic force characteristics of high-rise structures based on the above research ideas and results.

[0186] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Various modifications and changes can be made by those skilled in the art based on the spirit and principles of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for predicting three-dimensional aerodynamic forces of a cross-armed asymmetric tower, characterized in that, The method comprises the following steps: Step 1: constructing a T-shaped tower model, setting the parameter values of the vertical column height H, the vertical column radius r, the horizontal column length L, the horizontal column radius r, and the horizontal column long side L' of the T-shaped tower model, the eccentricity e is defined as the ratio of the horizontal column long side L' to the horizontal column length L s h h h h h ​​​​​​ Step 2: segmenting the T-shaped tower model, determining the windward area of each measuring layer and the wind speed at each height; Step 3: determining the frequency f of the T-shaped tower according to the stiffness, elastic modulus and density of the T-shaped tower building material, and obtaining the mutual power spectral density of the aerodynamic three-component force of the T-shaped tower model according to the dimensionless integral tower aerodynamic three-component force spectrum, the correlation coefficient and the aerodynamic force at each position; Step 4a: obtaining the aerodynamic three-component force power spectral density of the T-shaped tower model according to the frequency f, the eccentricity e and the numerical simulation result; Step 4b: calculating the aerodynamic three-component force coefficient of the T-shaped tower model according to the relative height z / H of the vertical column, the relative width y / B of the horizontal column and the eccentricity e; Step 4c: calculating the correlation coefficient of the T-shaped tower model according to the eccentricity e; Step 5: obtaining the generalized wind load power spectrum according to the aerodynamic force coefficient, the front area of the measuring layer at each position, the model thickness and the kth order vibration mode at each position; Step 6: obtaining the power spectrum of the generalized displacement according to the generalized wind load power spectrum and the frequency response function; Step 7: obtaining the standard deviation of the generalized displacement according to the power spectrum of the generalized displacement; Step 8: obtaining the peak displacement x according to the standard deviation of the generalized displacement, the peak factor and the vibration mode; Step 9: comparing the peak displacement x with the specification displacement, and when the peak displacement x is less than the specification displacement, entering step 11; otherwise, entering step 10; Step 10: by adjusting the parameter value of the lateral column long side L' h and thus the value of the eccentricity e, go to Step 4a; Step 11: Determine the erection scheme of the physical T-shaped tower according to the parameter values of the column height H, column radius r s , cross column length L h , cross column radius r h , and cross column long side L' h , and erect the physical T-shaped tower.

2. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 1, characterized in that: In the step 1, the tower body in the T-shaped tower model is a T-shaped tower structure composed of two cylinders, wherein the horizontal column is installed on the top of the vertical column.

3. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 1, characterized in that: In the step 3, the mutual power spectral density of the aerodynamic three-component force is calculated according to the following formula: S Fi (x1,x2;f) = F i (x1) F i (x2) S Fi '(f) Cor Fi (x1,x2) (1) where x1, x2 represent the coordinates of two points in the tower column or cross column space, x1 takes the relative height of the column, x2 takes the relative width of the cross column; f represents the frequency, F i (x1) represents the aerodynamic force at x1, F i (x2) represents the aerodynamic force at x2, Cor Fi (x1, x2) represents the correlation coefficient, S Fi ′(f) represents the dimensionless integral tower aerodynamic three-force spectrum, S Fi (f) represents the aerodynamic three-force self-power spectral density function under wind load, represents the root mean square aerodynamic three-force.

4. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 3, characterized in that: In the step 4a, the aerodynamic three-component force power spectral density formula is as follows: where ε it is a function of the eccentricity e, χ t , δ t , is a calculated parameter, e is the eccentricity; i = 1, 2, 3, i = 1 represents the model drag, i = 2 represents the model lift, i = 3 represents the model torque; t = 1, 2, 3, 4, 5; S Fi (f) is the auto-power spectral density function of the aerodynamic three-force under wind load, is the root mean square aerodynamic three-force.

5. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 1, characterized in that: In the step 4b, the aerodynamic three-component force coefficient calculation formula is as follows: C Fij = θ ij1 + θ ij2 (x j ) + θ ij3 (x j ) 2 (5) θ ijg = a i + b i e + c i e 2 , g = 1, 2, 3 (7) wherein C Fij represents the aerodynamic three-force coefficient in j direction; j = 1, 2, j = 1 represents the vertical direction, i.e. the direction in which the vertical column extends, j = 2 represents the horizontal direction, i.e. the direction in which the horizontal column extends; z / H represents the relative height of the vertical column, y / B represents the relative width of the horizontal column; a i , b i , c i , θ ijg represents the calculation parameter, y represents the transverse coordinate of the geometric center of the nth section in the vertical direction of the tower, and z represents the vertical coordinate of the geometric center of the nth section in the horizontal direction of the tower.

6. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 5, characterized in that: In the step 4c, the correlation coefficient calculation formula is as follows: Cor Fij = C r1 x exp(-C r2 x j ) (8) wherein Cor Fij represents a correlation coefficient, C r1 , C r2 represents a coefficient varying with eccentricity, and exp represents an exponential function with base e; C ru = A u + B u e + C u e 2 + D u e 3 , u = 1,2 (9) wherein A u , B u , C u , D u denote calculation parameters.

7. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 1, characterized in that: In the step 5, the generalized wind load power spectrum calculation formula is as follows: wherein, Cj(x1) represents the aerodynamic force coefficient at x1 in the j direction, Cj(x2) represents the aerodynamic force coefficient at x2 in the j direction, A(x1) represents the front surface area of the measurement layer at x1, A(x2) represents the front surface area of the measurement layer at x2, and D represents the model thickness in the direction parallel to the wind; φk(x1) represents the kth mode shape at the x1 position, φk(x2) represents the kth mode shape at the x2 position; r represents the correlation coefficient; U Hn Un represents the average wind speed at the nth height; Cj represents the root mean square aerodynamic three-force.

8. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 1, characterized in that: In step 6, the calculation formula of the power spectrum of the generalized displacement is as follows: wherein, P(k) represents the power spectrum of the generalized displacement, H k (if) represents the tower kth order frequency response function, f k represents the tower kth order frequency, ζ k represents the kth mode shape damping ratio; M k * represents the kth mode shape generalized mass.

9. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 7, characterized in that: In step 7, the calculation formula of the standard deviation of the generalized displacement is as follows: where σ denotes the generalized displacement standard deviation; denotes the power spectrum of the generalized displacement; M k * denotes the generalized mass of the kth mode; U H is the wind speed at the tower top position height; denotes the aerodynamic force coefficient at xl in j direction; denotes the aerodynamic force coefficient at x2 in j direction; A(xl) denotes the measurement layer frontal area at xl, A(x2) denotes the measurement layer frontal area at x2, and D denotes the model thickness in the direction parallel to the wind; S Fi (f) denotes the aerodynamic three-component force self-power spectral density function under the wind load; denotes the root mean square aerodynamic three-component force; denotes the kth mode at xl position, denotes the kth mode at x2 position; denotes the correlation coefficient; H k (if) denotes the tower kth frequency response function; and p denotes the density of air.

10. The method of predicting three-dimensional aerodynamic forces on an asymmetrical tower of a horizontal arm according to claim 9, characterized in that: In step 8, the calculation formula of the peak displacement is as follows: where g s = 2.5, denotes the kth mode of vibration at x, M k * denotes the generalized mass of the kth mode of vibration; σ denotes the standard deviation of the generalized displacement; Wherein, m(x) represents the mass at x.

Images