Experimental investigation on coupling characteristics of principal and shear stress of wind turbine under dynamic change of wind direction

The wind direction misalignment problem significantly impacts the abnormal alteration in aerodynamic distribution, ultimately resulting in an abnormal stress response of wind turbines. In this study, an experimental method was employed to simulate dynamic wind changes. The study aimed to analyze the laws and mechanisms governing changes in principal and shear stress on wind turbine blades and towers under different wind dynamic change angles. The results revealed that variations in the initial tip speed ratio significantly influenced the stress experienced by the tower during dynamic changes in wind direction. The coupling effect of yaw and gyroscopic moments led to a transient increase in both principal and shear stresses in the wind turbine tower during the early stage of wind direction change. Due to inertia and aerodynamic deterioration, the principal and shear stress values of wind turbine blades and towers exhibited delayed changes. Notably, when the wind direction changed by 15° from the direction the turbine was facing, the principal stress fluctuations in the wind turbine tower and blade were 5.13 and 1.23 times higher, respectively. Therefore, when developing a small-angle yaw strategy, stress fluctuations should be comprehensively considered, in addition to power requirements.


Introduction
With the rapid consumption of fossil fuels, the world is actively developing renewable energy sources to replace traditional fossil fuels.Wind is one of the most efficient renewable energy sources.It has been widely used worldwide, with a new installed wind power capacity of 93.6 GW in 2021 and a cumulative installed capacity of 837GW, an increase of 12.4% by 2020 [1].
Owing to the frequent wind direction changes in nature, it is common for conventional wind turbine wind monitoring equipment to deviate from short-term wind direction changes [2].Owing to the delay time and low speed of the yaw and pitch systems, wind turbines often operate under unaligned wind conditions [3].This increases energy loss and structural fatigue, leading to inefficient operation and wind turbine damage.Therefore, exploring the mechanism of wind direction dynamics on the stress state of wind turbines can provide a new understanding of structural fatigue analysis, optimization analysis, and yawing strategies.
In previous studies [4,5], a comprehensive optimization of the wind turbine structure was performed using a coupled model of blades and towers.The results showed that the optimized design had a smaller mass and a larger power-generation capacity when the strength requirements were satisfied.However, the optimization effect may not be accurate because the operating conditions only consider extreme and average wind speeds in the IEC criteria without considering conditions such as wind direction changes.Studies [3,6] have examined the effects of rain and changing wind direction on wind turbine blade stress and aerodynamics by simulation, and the results showed that the conditions of wind and rain coupling would have significant effects on wind turbine blade stress and aerodynamics; however, the angle of wind direction change in this study was fixed and not the same as the actual wind dynamic changing conditions.Previous studies [7][8][9] have analyzed wind turbine blade integrity, progressive damage, and other characteristics by numerically calculating the wind turbine blade stress and other characteristics under extreme wind loads.The results showed that extreme wind loads can lead to structural buckling, which triggers structural bond position failure and severe structural damage.In contrast, the study analyzed only the wind turbine blade without considering the influence of the tower.In addition, extreme wind loads only considered the change in wind speed and not the change in wind direction.In previous studies [10,11], the stress characteristics of various composite blades were numerically investigated using different wind speeds and pitch angles.The results show that changing the pitch angle can improve the power output, and a blade with high elasticity can effectively reduce blade deformation.However, only wind speed and pitch angle changes were considered in this study, and the wind direction factor, which influences the power and blade deformation, was ignored.A study [12] used a fluid-solid coupling method to analyze the stresses in a wind turbine blade under rotor inclination and wind direction changes, showing that the wind direction change increases the yaw moment on the wind turbine blade.However, the study only examined the 5° wind direction change, which is a fixed wind direction change, and did not consider the speed of wind direction change; such conditions for the systematic analysis of the impact of wind direction change are not sufficient.
In another study [13], a fatigue stress analysis of wind-turbine tubular towers was performed while considering the effects of low stress, wind direction, and blade rotation.The results showed that factors such as wind direction and low stress have an apparent impact on the fatigue stress of wind turbines, and ignoring these factors will affect the judgment of fatigue life.Although the effect of wind direction change was considered in this study, the mechanism of the impact of wind direction change on fatigue stress was not discussed systematically.Previous studies [14][15][16] analyzed the dynamic stress and fatigue reliability of wind turbines under random wind loads.They examined the stresses and displacements in wind turbine blades' and towers' under random wind loads.The results show that the transfer of wind loads from the blades to the towers is amplified, and increasing the stiffness of the blades and towers can effectively mitigate such transfer characteristics.Using a fluid-solid coupling approach, extant studies [17,18] have analyzed the dynamic stresses in wind turbines under the atmospheric boundary layer, wind shear, and pulsating winds.The results showed that gravity significantly influences the tangential stresses in wind turbines and that the main form of vibration at the top of the tower is torsional vibration.A study has [19] analyzed the thrust and bending moments of wind turbines under atmospheric boundary layer conditions with high tip speed ratios and large yaw angles.The results showed that pitch and yaw operations could effectively regulate wind turbine loads.A simple analysis of the wind-induced fatigue characteristics of wind turbine towers under wind direction changes has been conducted [20].The results indicated that the maximum principal stress of the tower was concentrated at the bottom of the tower.The fatigue damage of the wind turbine tower was maximum when the wind speed was 7 m/s and the wind direction was 135°.However, this study did not analyze the law and mechanism of the effect of wind direction change on the stress change in wind turbine towers.
Offshore wind turbines are widely used because of their unique advantages.However, owing to their complex operating conditions, a series of simulations and experimental studies have been conducted by scholars worldwide [21], who examined the dynamic stresses of wind turbines under operating conditions such as wind-wave coupling [22], non-Gaussian incidence [23], and earthquakes [24,25] considering rigid-flexible coupling [26].However, the mechanism underlying the effect of wind direction changes on the dynamic stresses is yet to be elucidated.In contrast, wind direction changes can complicate the incident conditions, and the lack of relevant analysis may underestimate the dynamic stresses of wind turbines.
A previous study [27] has analyzed the structural dynamic stress of wind turbines by considering the wind load and earthquake load, and optimized the wind turbine structure.The results showed that the tower failed only when the wind speed reached 50 y of the wind load.The displacement of the top of the tower is maximum when a long-period earthquake occurs, and the tower is not only subjected to the load from the ground, but also to the load transmitted by the blade and nacelle through the link part.Therefore, only considering the extreme wind speed load without considering the wind direction change condition may underestimate the dynamic stress of the tower.
In summary, (1) studies on wind turbine blades and tower stresses have been widely conducted.
(2) The laws and mechanisms of wind direction variation on wind turbine blades and tower stresses have yet to be fully discussed when wind turbine blades and tower stresses are studied under different conditions.(3) The angles of wind direction change were fixed in studies on wind direction changes.(4) Most related studies have used numerical simulations that lack experimental support.Simultaneously, a change in wind direction results in an asymmetric force.In addition to the principal stress, the shear stress is also one of the main factors affecting the plastic deformation of the structure; therefore, the shear stress can also reflect the response condition of the wind turbine.
Considering the above facts, an experimental method for analyzing the influence law and mechanism of the coupling characteristics of the principal stress and shear stress of wind turbine blades and towers under wind direction change can provide a theoretical reference for structural optimization, fatigue life research, and yaw pitch strategy and deepen the understanding of the mechanism of the influence of complex wind conditions on the operational state response of wind turbines.
Based on the above analysis, this study builds an experimental platform for the dynamic change of wind direction to investigate the stresses in the blades and towers of wind turbine models under different wind direction change angles and systematically analyze their characteristics; the experiments are presented in Section 2, the results are presented and discussed in Section 3, and the conclusions, limitations of this study and suggestions for future research are given in the last section.

Experimental setups
A wind tunnel experiment was conducted on the stress of wind turbine blades and towers under dynamic wind direction changes, with a total length of 24 m and a circular opening section of 2 m in diameter, as shown in figure 1.The wind speed of the wind tunnel was calibrated by a Kanomax thermocline anemometer (range 0.01 m/s~30 m/s, accuracy ±3%), and the ambient temperature was measured by a digital thermometer with an accuracy of 0.1°C.The ambient temperature was kept within 25°C±1°C during the experiment.The air density during the experiment was 1.205 kg/m 3 .

Figure 1. Wind tunnel.
This experiment is based on the subject group's self-developed S-wing type three-blade horizontal axis wind turbine, with a rated speed of 601r/min, wind wheel diameter D=1400 mm, and hub height hhub=1500mm, in this hub height wind turbine can run in the center of the wind tunnel area, which is a more stable uniform incoming flow area, a wind turbine rated wind speed of 8 m/s, and a rated tip speed ratio of 5.5.The dynamic rotating platform designed by the group controls the wind turbine rotation and relative motion of the incoming wind to realize a dynamic change in the wind direction, where γ is the wind turbine rotation angle and can be expressed as the wind direction change angle.The modal knockdown experiment obtained the tower and blade vibration node positions.The points were laid out at positions 1 (0°), position 2 (90°), position 3 (180°), and 4 (270°) at the top of the tower and positions 5 (0°), position 6 (90°), position 7 (180°), and position 8 (270°) at the bottom.Experimental measurements were performed on the first airfoil section chord at the root and blade spreading to the aerodynamic centerline.Strain gauges were laid out on the pressure surface of the blade, and triaxial 45° strain gauges were laid out at the airfoil chord lengths 0.25c, 0.50c, 0.75c, and 0.90c, respectively, at 0.2R from the root; at the aerodynamic centerline at 0.2R, 0.39R, 0.53R, 0.67R, 0.75R, and 0.9R, as shown in figure 2. A servomotor drives the rotating platform, and the rotation angle, direction, and angular speed of the rotating platform are controlled by the control system through programming.Photoelectric sensors were installed on a rotating platform.The trigger signal can be sent to the synchronous acquisition system after the rotating platform begins to realize the synchronous acquisition of data.The stress test was performed using Donghua DH5902N (accuracy:0.3%)and DH5953G (accuracy:0.5%)equipment, as shown in figure 3. Before the experiment began, the wind speed was calibrated using a hot-wire anemometer, and the experiment began after the set wind speed was consistent with the actual wind speed.At the beginning of the experiment, the wind turbine ran against the incoming wind for some time.When the wind turbine operates stably, the wind direction changes, and the rotation signal triggers the synchronous acquisition system for data acquisition.When the wind turbine reaches the preset deflection angle, it maintains stable operation for a while and then returns and stops the experiment after returning to the right side.
The method proposed by Moffat was used for uncertainty analysis to reduce the influence of the test instrument on the test results [28,29].
Where Q is the physical quantity under study, δQ/Q is the uncertainty, x n is an independent variable, and δx n is the measurement accuracy for x n .According to this equation, the stress uncertainties of the wind turbine blades and towers in the experiment were 2.00% and 1.22%, respectively, which were within the experimentally allowed range.

Tower stress coupling characteristics analysis
3.1.1.Effect of wind speed on principal and shear stress in wind turbine tower.First, the effects of wind speed and tip speed ratio on the wind turbine tower stress were investigated by describing the wind turbine tower stress characteristics at different wind speeds and tip speed ratios under dynamic wind direction change conditions.The wind speeds were set to 7 m/s, 8 m/s, and 9 m/s, and the tip speed ratios were set to 5, 5.5, and 6.The principal and shear stress values at the top and bottom of the tower are shown in figure 4-figure 11 with a wind direction change angle of 30° and a wind direction change angular velocity of 1°/s.When the wind direction changed to 30°, it began to return after remaining at 30° for 30s.5, it is observed that the principal stress values at the top and bottom of the wind turbine tower decrease to different degrees with an increase in the wind direction change angle and are stable within 2 MPa (top of the tower) and 1-3 MPa interval (bottom of the tower) during wind direction angle maintenance.The fluctuations of the principal stress values at the top and bottom of the tower at 7 m/s wind speed are more apparent, and the magnitude of the principal stress is higher.With the increase in wind speed (8 m/s), the fluctuations of the principal stress values are not noticeable, and the magnitude is stable in the range of 1-2MPa, with a further increase in wind speed (9 m/s), the fluctuations of the principal stress values are further reduced, and there is no noticeable change in the magnitude, which indicates that when the wind direction changes and the available wind energy is insufficient, the effect of increasing wind speed on the principal stress of the wind turbine tower is minimal.During the wind direction change, the principal stress amplitude increases with the increase in wind speed, which is mainly because the principal stress increases with the rise in wind speed owing to the growth of aerodynamic load.The principal stress amplitude of tower top positions 1, 3, 5, and 7 is gradually larger than the principal stress amplitude of positions 2, 4, 6, and 8, reaching a maximum at a wind speed of 9 m/s.This is because with the increase in wind speed, the axial force on the stress-lifting effect becomes gradually apparent.In contrast, the impact of the nacelle and wind wheel centroid not coinciding with the tower axis on the stress distribution gradually diminishes.At this time, the tower was subjected to the maximum fatigue load.7. The magnitude of the tower shear stress was similar to that of the principal stress, and the fluctuation in the tower top shear stress was lower than that of the principal stress.The magnitude and fluctuation of the shear stress at the bottom of the tower are smaller than those of the principal stress.This is mainly because the tower can be regarded as a slender rod structure, and its length is much larger than the section height; therefore, the principal stress is larger than the shear stress.Because the shear stress, bending moment, and torque are related, the change in shear stress during the wind direction change indicates that the bending moment and torque also change significantly during this period, which is mainly due to the unbalanced aerodynamic force on the wind wheel caused by the wind direction deflection and the increase in yaw moment.These changes are transmitted to the tower through the link between the wind wheel and the tower to trigger changes in the bending moment and torque.

Effect of tip speed ratio on principal and shear stress in wind turbine tower.
As shown in figure 8-figure 9, the amplitude of the principal stress increases with an increase in the initial tip speed ratio.The amplitudes of the principal stress at the top of the tower at positions 1 and 3 and at the bottom of the tower at positions 5 and 7 were gradually greater than those at positions 2 and 4 and positions 6 and 8.During the maintenance period of the change in wind direction, the fluctuation in the principal stress decreased with an increase in the tip speed ratio, and the magnitude of the principal stress increased to different degrees.11, with an increase in the tip speed ratio, the trend of the shear stress is the same as that of the principal stress; the magnitude of the tower top shear stress is similar to that of the principal stress, and the fluctuation of the tower top shear stress is lower than that of the principal stress.The magnitude and fluctuation of the shear stress at the bottom of the tower were smaller than those of the principal stress.
Under the conditions of different wind speeds and tip speed ratios, the difference between the amplitudes of the principal stress and shear stress at the top of the tower is not apparent, mainly because the top of the tower is close to the wind wheel and nacelle, which is more obviously affected by the shear force brought about by the operation of the wind wheel and is subject to a small bending moment simultaneously.The above situation shows that the importance of the principal stress and shear stress on the top of the tower on the fatigue life of the tower is more consistent, and the effects of both the principal stress and shear stress must be considered when analyzing the fatigue life of the tower under wind direction change conditions.
By comparing the changes in the principal stress and shear stress amplitude during the maintenance of the wind direction change with different wind speeds and tip speed ratios, it was found that the change in the initial tip speed ratio had a more noticeable effect on the principal stress and shear stress amplitude of the tower than the increase in wind speed.This is because the wind direction deflection occurs, the wind power available to the wind wheel decreases When the wind direction deflects to 30 °, increasing the wind speed for the wind wheel available wind power gain is not apparent, so the effect of increasing the wind wheel speed is not as obvious as the effect brought by increasing the initial tip speed ratio, so increasing the initial tip speed ratio makes the wind wheel and nacelle transfer to the tower more obvious disturbance.

Effect of wind direction change angle on the principal and shear stress in the tower.
Select the wind speed 8m/s, tip speed ratio 5.5 conditions, analysis of principal and shear stresses in wind turbine towers at 15°, 30°, and 45° wind direction change angles, respectively, summarize the wind direction change angle on the wind turbine tower stress influence law, wind direction change angular velocity of 1°/s, when the wind direction change angle reached 15°, 30°, and 45° stay 30s and then start to return.13, with the increase of the wind changes angle, the principal stress value of the tower is reduced to different degrees, when the wind changes to a specified angle, the principal stress value of 15° is more significant than that of 30° and 45°, which is because the wind change angle of 15° is smaller and the aerodynamic deterioration is lower, so the principal stress value of the tower is higher.During the pre-wind change period, the asymmetric force exerted on the wind wheel by the deflecting wind causes an increase in the yaw and gyro moments, resulting in a transient increase in the principal stress value of the tower.During the maintenance of wind change, the stress value was the largest at the 15° wind change angle, and the stress values were smaller and similar at 30° and 45° wind change angles.During the maintenance of the 45° wind change angle, a fluctuation phenomenon appears, which may be due to the poor aerodynamic conditions when the wind change angle is 45°.and the unbalanced force transferred from the wind wheel to the tower triggers the fluctuation phenomenon of stress.As shown in figure 14-figure 15, the tower shear and principal stress values change similarly with different wind direction angles.The fluctuation in shear stress was weaker than that in principal stress.The magnitude of the shear stress at the top of the tower was similar to the principal stress value.The shear stress value at the bottom of the tower was smaller than the principal stress value, indicating that the relative increments in the shear strain at the top of the tower and the principal strain were not significantly different.In contrast, the relative increments in the shear strain at the bottom of the tower and principal strain were different, indicating that the shear stress value was smaller than the principal stress value.

Blade stress coupling characteristic analysis
As shown in figure 16, as the wind direction change angle increases, the blade root principal stress value decreases because of the wind direction deflection, and the wind wheel can use the wind energy reduction and aerodynamic deterioration; thus, the blade principal stress response decreases.Wind direction change angle for 15 °, the blade root principal stress value decline is not apparent, but fluctuations are more pronounced; because, at this time, the wind deflection angle is relatively small, aerodynamic force deterioration is not enough, and the distribution of force is not balanced.Observing the principal stress values of the blade root during the beginning of the wind direction change and wind direction change maintenance period revealed that the principal stress value is not in the wind direction change occurs immediately drop, and in the wind direction change stop immediately stop.Still, there is a delayed phenomenon, which is mainly due to the inertia at the beginning of the wind direction change, making the wind wheel rotational speed decline insufficient.The wind wheel still has a large centrifugal force, and aerodynamic force deterioration is also not sufficient, so the principal stress value exhibits a delayed decline.During the maintenance of the wind direction change, the

Maintain for 30s
Return aerodynamic deterioration is adequate, and the principal stress value of the wind wheel will continue to decrease and stabilize in a certain period owing to inertia; thus, the final state of the principal stress of the wind wheel is determined by both aerodynamic deterioration and wind wheel inertia.The large values of the principal stresses at blade-root positions 3 and 4 were mainly caused by the combined effect of the centrifugal load and axial thrust at these two positions, which were close to the section from the center.
U 0 =8m/s, λ=5.5, γ=30°, (c) U 0 =8m/s, λ=5.19, the shear stress amplitude of the wind turbine blade root and the spreading direction decreased as the wind direction change angle increased.In contrast, owing to aerodynamic deterioration and inertia, the shear stress had the same delayed decreasing effect as the principal stress in the initial wind direction change and maintenance period.The blade shear stress values are lower than the principal stress values, indicating that the shear force acting on the blade is lower than the axial force.At the same time, the distribution of the blade-spreading shear stress values during the wind direction change was more dispersed, indicating that the shear force acting on the spreading side of the blade was more dispersed.By comparing the wind turbine blade and tower stress changes during the maintenance of the wind direction change, it was found that the effect of the delayed blade stress drop caused by the inertial action of the wind turbine was not significant for the tower.

Characterization of stress fluctuations
To more clearly analyze the fluctuation characteristics of the wind turbine blades and tower stress during wind direction changes, the stress fluctuation coefficient was used as a reference to analyze the fluctuation characteristics of the wind turbine blade and tower stress, which is defined as follows: The position A represents the measured stress value, Q is the principal stress value, T is the shear stress value, Q 0 is the principal stress value when facing the wind direction, T 0 is the shear stress value when facing the wind direction, σA and  ̅ are the standard deviations and average value of the stress value, respectively, and  20, the fluctuation in the principal stress value increases with an increase in the angle of the wind direction change owing to the decrease in the principal stress value.The fluctuation at the 45° wind change angle was slightly smaller than that at the 30° wind change angle because of the slight increase in the principal stress value during the maintenance of the wind change, which attenuated the effect of the decrease in the principal stress value.The fluctuation in the principal stress value without a delay time was smaller than that with a delay time.The difference between the fluctuations of the 30° and 45° wind change angles without delay time is smaller than that of the issue with delay time, indicating that the change in the principal stress value does not stop after the wind change ends.The trend in the degree of fluctuation of the shear stress was similar to that of the principal stress.However, the degree of fluctuation in the shear stress value was slightly lower than that in the principal stress value.It can also be observed that even at a minimum wind change angle of 15°, the fluctuation of stress value is still 5.1 times (principal stress) and 4.8 times (shear stress) than that in the direction of the wind, indicating that the tower has a certain degree of stress fluctuation even at a small wind change angle.As shown in figure 21, with an increase in the wind direction change angle, the fluctuation of the wind turbine blade principal stress increases owing to the deterioration of the aerodynamic force caused by the wind direction offset, thus triggering the principal stress value down.The fluctuations without delay time were significantly lower than those with delay time, even lower than 1 at 15° wind change angle, which indicates that it is feasible to misalign the wind direction to the wind turbine by the control system, thus reducing the fatigue load and increasing the downstream wind turbine efficiency, but the delay effect of stress change should be considered.Otherwise, there may be an increase in the stress fluctuation and fatigue load at a later stage.When the wind direction change angle is 30° and 45° with delay time, the principal stress fluctuation is more significant than without delay time; this is due to the inertia effect mentioned above that the centrifugal load does not drop sufficiently after the wind wheel reaches the predetermined angle, during the wind direction change maintenance the wind wheel is subjected to continuous unfavorable aerodynamic conditions, the centrifugal load drops sufficiently leading to a constant decrease in the blade principal stress value and the overall fluctuation of the blade rises.The trend in the degree of fluctuation of the shear stress was similar to that of the principal stress.However, the degree of fluctuation of the shear stress value was significantly lower than that of the principal stress value in all cases.Comparing the stress fluctuations of the blade and tower, it was found that the stress fluctuations of the tower were more obvious than those of the blade, which indicates that the effect transmitted from the blade to the tower under the wind direction change condition had a certain amplification effect.

Conclusions
In this study, we investigated the impact of wind direction dynamic change angles on wind turbine blade and tower stress through a series of wind tunnel experiments.A two-dimensional rotating platform was utilized to simulate dynamic wind direction changes.Wind speeds of 7m/s, 8m/s, and 9m/s were selected, along with tip speed ratios of 5, 5.5, and 6.Wind dynamic change angles of 15°, 30°, and 45° were chosen, and the angular velocity of the dynamic wind direction change was set at 1°/s.We compared and analyzed the principal and shear stresses experienced by the wind turbine blades and tower.Furthermore, we assessed the relative fluctuation of stresses by using normalized stress fluctuation coefficients during the dynamic wind direction change process.Based on the results and discussions, the following conclusions were drawn: (1) The tower's principal stress and shear stress increased to varying degrees with higher wind speeds and tip speed ratios.The shear stress at the top of the tower did not significantly differ from the principal stress.Under different wind speeds and tip-speed ratios, the shear stress at the bottom of the tower is 40-65% lower than the principal stress.Particularly under the condition of a 7 m/s wind speed, the shear stress values at the bottom of the tower can be as much as 70-75% lower than the principal stress.The steady state of tower stress after the wind direction change was influenced more by the initial tip speed ratio than by the wind speed.
(2) The wind turbine blades and tower experienced a decrease in principal and shear stresses as the wind direction change angle increased.Due to the influence of yaw and gyroscopic moments, the tower's principal and shear stress values briefly increased during the initial wind direction change period.Due to the wind wheel inertia and aerodynamic deterioration, the delayed change of the principal and shear stresses of the wind turbine blades occurs during both the initial wind direction change and maintenance periods.This delay effect was particularly pronounced at wind change angles of 30° and 45°.The impact on the tower was less significant compared to the blades.
(3) As the wind direction change angle increases, stress fluctuations increase.The fluctuation in the principal stress and shear stress values of the wind turbine tower is 11.79 times and 11.03 times greater, respectively, compared to when facing directly into the wind.For the wind turbine blades, the fluctuation in the principal stress and shear stress values is 9 times and 6 times greater, respectively, compared to when facing directly into the wind.Stress value fluctuations with delay time are 30-50% (towers) and 50-70% (blades) higher than those without delay time.After the wind direction change, the principal and shear stresses of the wind turbine blades and tower continued to change for some time before stabilizing.Thus, when analyzing the fatigue load during the wind direction change process, the delay effect should be fully considered.
In addition to analyzing the effects of wind direction change on wind turbine stress, future research should delve into the wind vibration effect and the changes in the flow field caused by wind direction changes.This will help enhance our understanding of the wind turbine's dynamic response mechanism under wind direction changes.

Figure 2 .
Figure 2. Top view of the experimental section.

Figure 3 .
Figure 3. Schematic diagram of the experimental system.Before the experiment began, the wind speed was calibrated using a hot-wire anemometer, and the experiment began after the set wind speed was consistent with the actual wind speed.At the beginning of the experiment, the wind turbine ran against the incoming wind for some time.When the wind turbine operates stably, the wind direction changes, and the rotation signal triggers the synchronous acquisition system for data acquisition.When the wind turbine reaches the preset deflection angle, it maintains stable operation for a while and then returns and stops the experiment after returning to the right side.The method proposed by Moffat was used for uncertainty analysis to reduce the influence of the test instrument on the test results[28,29].

Figure 20 .
Figure 20.Stress fluctuations in the tower under different wind change angles, (a) U 0 =8m/s, λ=5.5, principal stress fluctuation, (b) U 0 =8m/s, λ=5.5, shear stress fluctuation.As shown in figure20, the fluctuation in the principal stress value increases with an increase in the angle of the wind direction change owing to the decrease in the principal stress value.The fluctuation at the 45° wind change angle was slightly smaller than that at the 30° wind change angle because of the slight increase in the principal stress value during the maintenance of the wind change, which attenuated the effect of the decrease in the principal stress value.The fluctuation in the principal stress value without a delay time was smaller than that with a delay time.The difference between the fluctuations of the 30° and 45° wind change angles without delay time is smaller than that of the issue with delay time, indicating that the change in the principal stress value does not stop after the wind change ends.The trend in the degree of fluctuation of the shear stress was similar to that of the principal stress.However, the degree of fluctuation in the shear stress value was slightly lower than that in the principal stress value.It can also be observed that even at a minimum wind change angle of 15°, the fluctuation of stress value is still 5.1 times (principal stress) and 4.8 times (shear stress) than that in the direction of the wind, indicating that the tower has a certain degree of stress fluctuation even at a small wind change angle.