A method for predicting aerodynamic damping of single degree of freedom vibration of a wind turbine blade

Abstract

The present application relates to the technical field of wind turbine aerodynamic damping prediction, and discloses a kind of wind turbine blade single degree of freedom vibration aerodynamic damping prediction method, comprising the following steps: obtaining the different airfoil of blade, selecting standard airfoil control section, according to the structure geometric parameter distribution relationship of blade with spanwise position, the local angle of attack and mass ratio of standard airfoil control section are calculated;Standard airfoil control section is modeled by reduced order modeling method, and the coupled system is obtained, while the structural modal damping of the coupled system under different wind direction angles and reduced frequencies is obtained, to obtain the aerodynamic damping of standard airfoil control section, and the aerodynamic damping of the remaining airfoil control section is obtained by interpolation method;The modal shape and modal frequency of the coupled system are obtained, the aerodynamic damping of each airfoil is calculated, and the modal superposition method is used for superposition to obtain the aerodynamic damping of the blade;The method improves the aerodynamic damping prediction accuracy of wind turbine blade.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wind turbine aeroelastic instability prediction, and particularly relates to a wind turbine blade single degree of freedom vibration aerodynamic damping prediction method. BACKGROUND

[0002] With the large-scale and lightweight design of wind turbines, blades gradually develop in the direction of long and soft; at the same time, wind turbine blades are often in complex inflow conditions, and are prone to aeroelastic instability phenomenon coupled with structure. For the aeroelastic system of the blade, when the aerodynamic damping is negative, the system is unstable, that is, the aeroelastic instability phenomenon occurs. Therefore, the aerodynamic damping of the blade needs to be accurately calculated and predicted to avoid the aeroelastic instability of the wind turbine blade and ultimately cause structural damage.

[0003] In the early stage of wind turbine airfoil design, a simple and fast evaluation method is needed to simply evaluate the aeroelastic characteristics of the blade. The methods such as test and computational fluid dynamics-computational structural mechanics coupling simulation are too time-consuming and are not conducive to the current industry's demand for rapid design. Under this background, the aerodynamic damping calculation method based on quasi-steady aerodynamic force is generally used in actual engineering to quickly evaluate the aerodynamic damping of the airfoil or blade. This classical aerodynamic damping calculation method ignores the unsteady characteristics of the flow due to the quasi-steady assumption, and the error is large when the wind direction angle is large. SUMMARY

[0004] In view of the above problems in the prior art, the present application provides a wind turbine blade single degree of freedom vibration aerodynamic damping prediction method, which is used to solve the problems of large error in calculating the aerodynamic damping of the wind turbine blade and long time consumption in the prior art.

[0005] In order to achieve the above-mentioned application purposes, the technical scheme adopted by the present application is as follows:

[0006] A wind turbine blade single degree of freedom vibration aerodynamic damping prediction method, comprising the following steps:

[0007] S1, the wind turbine blade is divided into elements, different airfoils are obtained, and standard airfoil control sections and remaining airfoil control sections are selected, the local angle of attack and the mass ratio of the standard airfoil control sections are obtained according to the structural geometric parameter distribution relationship of the wind turbine blade with the spanwise position;

[0008] S2, the selected standard airfoil control section is modeled by a single degree of freedom reduced order model method, the coupled system is obtained by coupling the aerodynamic force state equation and the structural motion equation, the structural modal damping of the coupled system under different wind direction angles and reduced frequencies is obtained, the aerodynamic damping of the standard airfoil control section is obtained, and the aerodynamic damping of the remaining airfoil control section is obtained by interpolation method;

[0009] S3, according to the structural motion equation of the wind turbine blade, and based on the structural finite element analysis method, the modal shape and the modal frequency of the coupling system are obtained, and the aerodynamic damping of each airfoil is calculated, the modal superposition method is used to superimpose the aerodynamic damping of each airfoil, and the aerodynamic damping of the wind turbine blade is obtained.

[0010] The present application has the following beneficial effects:

[0011] 1. The present application provides a kind of wind turbine blade single degree of freedom vibration aerodynamic damping prediction method, using reduced order model method to the standard airfoil control section of wind turbine blade is modeled, to analyze the aeroelastic characteristics of wind turbine blade, the state equation and output equation of coupling system are obtained, the characteristic root of coupling system can be obtained by solving state equation and output equation, using characteristic root instead of traditional quasi-constant method aerodynamic damping, make full consideration flow non-steady characteristics, improve the precision and aerodynamic damping calculation efficiency of coupling system;

[0012] 2. Based on structural finite element analysis method, the modal shape and the modal frequency of the coupling system are obtained, the logarithmic decrement of wind turbine blade is calculated, so as to obtain the aerodynamic damping of each airfoil, finally the aerodynamic damping of each airfoil is superimposed by using modal superposition method, the aerodynamic damping of wind turbine blade is obtained, the calculation precision of aerodynamic damping is improved. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 It is the flow chart of the wind turbine blade single degree of freedom vibration aerodynamic damping prediction method provided by the present application.

[0014] Figure 2 It is the schematic diagram of chord length and pitch angle distribution along the spanwise position of wind turbine blade.

[0015] Figure 3 It is the local angle of attack distribution schematic diagram of standard airfoil control section at different spanwise positions under two different wind direction angles.

[0016] Figure 4 It is the schematic diagram of the realization principle of aerodynamic force reduced order model method.

[0017] Figure 5 It is the schematic diagram of displacement signal amplitude variation with time of equal amplitude scanning signal in embodiment.

[0018] Figure 6 It is the schematic diagram of equal amplitude scanning signal reduction frequency variation with power spectrum amplitude in embodiment.

[0019] Figure 7 It is the schematic diagram of the comparison between the aerodynamic force calculated by aerodynamic force reduced order model and the aerodynamic force calculated by computational fluid dynamics method under 168° wind direction angle in embodiment.

[0020] Figure 8 Root locus of the eigenvalue of the coupled system under the wind direction angle of 168° in the embodiment with the variation of the structural reduced frequency;

[0021] Figure 9 Schematic diagram of the real part of the structural modal eigenvalue with the variation of the structural reduced frequency under different damping ratios;

[0022] Figure 10 Schematic diagram of the variation of the modal frequency of the coupled system with the structural reduced frequency under different wind direction angles;

[0023] Figure 11 Schematic diagram of the instability region of the coupled system obtained by the aerodynamic force reduced order model method and the computational fluid dynamics-computational structural mechanics coupled simulation;

[0024] Figure 12 Schematic diagram of the comparison between the calculated aerodynamic negative damping of the wind turbine blade and the experimental instability region when the reduced frequency is 0.06;

[0025] Figure 13 Schematic diagram of the distribution of the calculated aerodynamic negative damping of the wind turbine blade with the wind direction angle and the reduced frequency. DETAILED DESCRIPTION

[0026] The specific embodiments of the present application are described below to facilitate the understanding of the present application for those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application defined and determined by the appended claims, and all the inventions utilizing the concept of the present application are within the scope of protection.

[0027] As shown in Figure 1 , a method for predicting the aerodynamic damping of a single degree of freedom vibration of a wind turbine blade, comprising the following steps S1-S3:

[0028] S1, dividing the wind turbine blade into blade elements, obtaining different airfoils, selecting standard airfoil control sections and remaining airfoil control sections, and obtaining the local angle of attack and mass ratio of the standard airfoil control sections according to the distribution relationship of the structural geometric parameters of the wind turbine blade with the spanwise position.

[0029] In the embodiment, according to the design requirements of a certain type of wind turbine blade studied by wind tunnel test, the entire wind turbine blade is stretched according to a certain rule by different standard airfoils, and the thickness and distribution of part of the airfoils of the experimental wind turbine blade are selected as shown in Table 1:

[0030] Table 1 Thickness and distribution of part of the airfoils of the experimental wind turbine blade

[0031]

[0032] It can be found from Table 1 that there are six airfoils excluding the root circle, and the airfoil thickness decreases in turn, and the lowest is 18%. Five airfoils in Table 1 are selected as standard airfoil control sections for experiments. According to the structural geometric parameters of the wind turbine blade such as chord length, pitch angle, and mass distribution with the spanwise position, the local angle of attack of the selected standard airfoil control section and the mass ratio are obtained.

[0033] Specifically, step S1 specifically includes S11-S13:

[0034] S11, the wind turbine blade is divided into elements, different airfoils of the wind turbine blade are obtained, and part of the airfoils of the wind turbine blade are selected as standard airfoil control sections, and the remaining airfoils are selected as remaining airfoil control sections.

[0035] S12, according to the chord length and pitch angle distribution with the spanwise position of the wind turbine blade, the local angle of attack of the standard airfoil control section and the remaining airfoil control section under different wind direction angles is obtained.

[0036] In this embodiment, Figure 2 The chord length and pitch angle distribution with the spanwise position of the wind turbine blade is given, wherein Figure 2 The abscissa is the spanwise position, the ordinate on the left of the figure is the chord length, the ordinate on the right of the figure is the pitch angle, the solid line is the chord length, and the dashed line is the pitch angle; therefore, according to the chord length and the spanwise position distribution relationship, the pitch angle distribution with the spanwise position, the local angle of attack of the airfoil under different wind direction angles can be obtained; Figure 3 The local angle of attack of the airfoil of the wind turbine blade at different spanwise positions under two different wind direction angles, i.e., the wind direction angle of the root circle is 156° and 180°, is given in Table 1, wherein Figure 3 The abscissa is the spanwise position, the ordinate on the left of the figure is the local angle of attack distribution under the 180° wind direction angle, the ordinate on the right of the figure is the local angle of attack distribution under the 156° wind direction angle, the solid line is the local angle of attack under the 156° wind direction angle, and the dashed line is the local angle of attack under the 180° wind direction angle; from Figure 3 It can also be found from Table 1 that under the 156° wind direction angle, the local angle of attack of most of the wind turbine blade is less than 170° and greater than 160°; under the 180° wind direction angle, the local angle of attack of the upper half near the tip is greater than 190°; wherein the local angle of attack is defined as the angle between the airfoil chord line and the incoming flow, and since there is a twist angle between the sections in the actual wind turbine blade, the local angle of attack of each section is different.

[0037] S13, according to the mass distribution of the standard airfoil control section and the chord length distribution relationship, the mass of the standard airfoil control section is obtained, and the mass ratio of the standard airfoil control section is obtained by comparing the air mass contained by the cylinder with the chord length at the standard control airfoil section as the diameter.

[0038] In this embodiment, according to the mass distribution of the standard airfoil control section, the mass ratio of each standard airfoil control section can be obtained, as shown in Table 2:

[0039] Table 2 is a mass ratio table of different standard airfoil control sections

[0040]

[0041] In Table 2, 5 of the 6 airfoils in Table 1 are randomly selected as standard airfoil control sections, and the mass ratio of each standard airfoil control section is obtained according to the mass distribution relationship of each standard airfoil control section in the wind turbine blade.

[0042] S2, the selected standard airfoil control section is modeled by single degree of freedom reduced order model method, the coupled system is obtained by coupling the aerodynamic force state equation and the structure motion equation, and the structure modal damping of the coupled system under different wind direction angles and reduced frequencies is obtained, the aerodynamic damping of the standard airfoil control section is obtained, and the aerodynamic damping of the remaining airfoil control section is obtained by interpolation method.

[0043] In this embodiment, the above selected 5 standard airfoil control sections are modeled by single degree of freedom aerodynamic force reduced order model method. As shown in Figure 4 , the implementation process of aerodynamic force reduced order model method is shown in Figure 4 , first, the computational fluid dynamics method is used to obtain high-precision generalized aerodynamic force load data of 5 standard airfoil control sections under the designed generalized displacement motion signal; second, the high-precision generalized aerodynamic force load data obtained is modeled by aerodynamic force reduced order model, so as to realize the aeroelastic analysis of the wind turbine blade. In the modeling and analysis process, the used generalized displacement motion signal, i.e. training signal, is equal amplitude scanning signal. Figure 5 The displacement signal amplitude variation process of equal amplitude scanning signal with time is shown in Figure 5 , the horizontal coordinate is time (dimensionless), and the vertical coordinate is the displacement signal amplitude of equal amplitude scanning signal; Figure 6 The frequency of equal amplitude scanning signal is analyzed by using fast Fourier analysis method to obtain the variation process of reduced frequency with power spectrum amplitude, wherein Figure 6 , the horizontal coordinate is reduced frequency, and the vertical coordinate is power spectrum amplitude; from Figure 6It can be found that the amplitude of the equal amplitude scanning signal is 0.004 times the chord length, and the structural motion under the signal has a structural reduction frequency range of 0-1.2, which covers the structural reduction frequency range of 0.05-0.5 of a conventional wind turbine blade, meeting the modeling requirements. In addition, the results of the aerodynamic force calculated by the aerodynamic force reduction model obtained by the modeling method of the application under the wind direction angle of 168° are shown, and the results of the aerodynamic force calculated by the existing technology computational fluid dynamics method, as shown in Figure 7 , Figure 7 The horizontal coordinate is time (second), and the vertical coordinate is the lift coefficient. The solid line is the computational fluid dynamics method, and the dot is the reduction model. Figure 7 It can be seen from the

[0044] Specifically, step S2 specifically includes S21-S23:

[0045] S21, the single-degree-of-freedom reduction model method is used to model the selected standard airfoil control section, and the specific process is:

[0046] First, the computational fluid dynamics method is used to obtain high-precision generalized aerodynamic force load data and displacement of the standard airfoil control section under the designed generalized displacement motion signal.

[0047] Second, the aerodynamic force reduction model method is used to identify the parameters of the high-precision generalized aerodynamic force load data and displacement, to obtain the aerodynamic force state equation and the structural motion equation. By coupling the aerodynamic force state equation and the structural motion equation, the coupled system and the state equation and the output equation of the coupled system are obtained.

[0048] In this embodiment, the high-precision generalized aerodynamic force load data and displacement obtained by the computational fluid dynamics method are identified by the aerodynamic force reduction model method, so as to obtain the aerodynamic force reduction model, and further realize the aeroelastic analysis of the standard airfoil control section. The specific analysis process is:

[0049] Specifically, the aerodynamic force reduction model method is used to identify the parameters of the high-precision generalized aerodynamic force load data and displacement, to obtain the aerodynamic force state equation and the structural motion equation. By coupling the aerodynamic force state equation and the structural motion equation, the coupled system and the state equation and the output equation of the coupled system are obtained. The specific process is:

[0050] The output vector model of the aerodynamic force is established, that is:

[0051]

[0052] Wherein, represents the first The output vector at time t, , This indicates the delay order between the output and the input. Indicates the output of the first A matrix of coefficients to be identified with delay orders, Indicates the input number of the first... A matrix of coefficients to be identified with delay orders, Indicates the first The output vector at time step 1 Indicates the first The input vector at time t, Indicates the first Zero-mean white noise at time step.

[0053] In this embodiment, the output vector Aerodynamic force, input vector Refers to the displacement of aerodynamic forces; the delay order of the output. Delay order of the input , used to characterize the former Step output and previous The input step contributes to the aerodynamic force at the current moment; therefore, the delay order reflects the non-fixed-length characteristic of the aerodynamic force. Furthermore, after obtaining the input and output vector data, the least squares method can be used to solve the contradictory equations, thereby determining the matrix to be identified. and Furthermore, to facilitate fluid-structure interaction analysis, the output vector model is transformed into a state-space model, as shown below:

[0054] Define a state vector to transform the aerodynamic output vector model into a state-space model, i.e.:

[0055]

[0056] in, Indicates the first The state vector at time t, Indicates the first The output vector at time step 1 Indicates the first The input vector at time t, Indicates the first The input vector at time t, This indicates transpose.

[0057] Discretizing the state-space model yields discrete aerodynamic state equations, namely:

[0058]

[0059] in, Indicates the first The state vector at time t, , , , Let represent matrices consisting of the coefficients to be identified in the state space of the discrete system. Indicates the first The input vector at time step 1.

[0060] In this embodiment, , , , The calculation formula is as follows:

[0061] ,in , , , These represent the 1st, 2nd, and 3rd outputs, respectively. , The coefficients to be identified for the delay order. Represents the identity matrix. , , , These represent the 1st, 2nd, and 3rd inputs, respectively. , The coefficients to be identified for the delay order.

[0062] ,in This represents the input coefficient to be identified at the 0th delay order.

[0063] .

[0064] .

[0065] Furthermore, in order to couple the discrete aerodynamic state equations with the structural motion equations, a bilinear transformation of the discrete aerodynamic state equations is required, as follows:

[0066] By performing a bilinear transformation on the discrete aerodynamic state equations, we obtain the continuous aerodynamic state equations, namely:

[0067]

[0068] in, Indicates time, Indicates the first The aerodynamic state vector in continuous space at time t. Indicates the first The output vector at time step 1 , , , denote the matrix composed of the system to be identified under continuous state space, respectively, denote the state vector at the time, denote the input vector at the time.

[0069] Therefore, the whole process of obtaining the continuous aerodynamic force state equation is the modeling process of the aerodynamic force reduced order model method, that is, after completing the parameter identification, the continuous aerodynamic force state equation, i.e. the aerodynamic force state space model, can be obtained, so that the stability characteristics of the flow can be solved by solving the eigenvalues of .

[0070] Define the structural motion equation, that is:

[0071]

[0072] wherein, denote the derivative of the structural motion state vector of the aeroelasticity under continuous space at the time, denote the structural motion state vector of the aeroelasticity under continuous space at the time, , , , denote the coefficient matrix of the structural motion equation under continuous space, respectively, denote the dynamic pressure, denote the modal displacement output at the time, denote the modal displacement output at the time, denote the aerodynamic force vector corresponding to the structural motion state vector of the aeroelasticity under continuous space at the time.

[0073]

[0074]

[0075] wherein, denote the derivative of the state vector of the coupled system at the time, denote the coupled system, denote the state vector of the coupled system at the time, denote the modal displacement output of the coupled system at the time.

[0076] In this embodiment, the structural motion equations are coupled with the continuous aerodynamic state equations to obtain the state equations and output equations of the coupled system. Therefore, the state equations and output equations of the coupled system construct a unified fluid-structure interaction analysis model based on a reduced-order aerodynamic model, transforming the stability problem of the coupled system into an eigenvalue problem of solving a matrix. The eigenvalues ​​can be expressed as... ,in Indicates the real part, The imaginary part represents the modal angular frequency (which is 2 times the modal characteristic frequency). The real part represents the modal growth rate (times), and the real part represents the modal growth rate (times). ) or modal decay rate, i.e., logarithmic decay rate ( This refers to the aerodynamic damping term. Furthermore, here... The symbol is a mathematical symbol representing an imaginary number. Therefore, the aerodynamic order reduction model method can obtain the eigenvalue locus of the coupled system, specifically as follows: Figure 8 As shown, the root locus process of the characteristic roots of the coupled system as a function of the structural reduction frequency is illustrated at a wind angle of 168°. Figure 8 The solid lines with circles represent flow modes, and the solid lines with squares represent structural modes. The horizontal axis represents the real part of the characteristic roots, indicating the mode growth rate; a value greater than 0 indicates mode instability. The vertical axis represents the imaginary part of the characteristic roots, indicating the mode response frequency. Therefore, the root locus diagrams of the coupled system under different wind angles and different structural reduction frequencies can be obtained using the aerodynamic order reduction model method. The real part of the characteristic roots represents the damping of the structural modes in the coupled system. The damping of the structural modes in the coupled system consists of structural damping and aerodynamic damping. Figure 9 The paper illustrates the variation of the real part of the modal eigenvalues ​​of a structure with varying damping ratios and the structure's shrinkage frequency, where the parameters... The damping ratio is given, and the gray area represents the modal instability process; therefore, it is determined by... Figure 9 It is known that structural damping does not change the coupling degree between structural modes and flow modes, but it shifts the structural mode branches to the left, thereby reducing the instability structural shrinkage frequency boundary of the structural modes in the coupled system. Therefore, when modeling using the aerodynamic order reduction model method, the structural damping can be set to 0, and the resulting damping value of the structural modes in the coupled system is the aerodynamic damping value of the airfoil.

[0077] In summary, based on the calculated local angle of attack of the standard airfoil control sections under different wind angles, the distribution of local angle of attack of the standard airfoil control sections at different blade spanwise positions under the same incoming wind angle can be determined. Therefore, a reduced-order aerodynamic model is used to model the selected standard airfoil control sections within a certain angle of attack range. Based on the local angle of attack of the standard airfoil control sections, the aerodynamic damping of each standard airfoil control section under each wind angle is obtained. Using the obtained aerodynamic damping of the standard airfoil control sections, the aerodynamic damping of the remaining airfoil control sections can be obtained through trispline interpolation, as detailed below:

[0078] S22, according to the coupling system, the selected standard airfoil control section is analyzed by the local angle of attack range reduction model method, the structural modal damping of the coupling system under different wind direction angles and reduced frequencies is obtained, and the aerodynamic damping of the standard airfoil control section is obtained.

[0079] In this embodiment, the standard airfoil control section is selected to be analyzed in the range of 164°-198° wind direction angle based on the aerodynamic force reduction model method, as shown in Figure 10 , Figure 10 The change process of the modal frequency of the coupling system with the structural reduced frequency is shown in Figure 10 , and the instability range of the standard airfoil control section under the windward condition of the trailing edge is obtained. The real part of the characteristic value represents the aerodynamic negative damping. When the real part of the characteristic value is greater than 0, the structure is unstable.

[0080] In addition, as shown in Figure 11 , Figure 11 The instability region of the coupling system obtained by the aerodynamic force reduction model method and the computational fluid dynamics-computational structural mechanics coupling simulation is shown, Figure 11 , where the horizontal coordinate is the wind direction angle and the vertical coordinate is the reduced frequency. The black dotted line is the instability boundary obtained by the computational fluid dynamics-computational structural mechanics coupling simulation. From Figure 11 , it can be seen that in the two stall wind direction angle ranges near 180° (near 165° and near 195°), aerodynamic elastic instability will occur. When the structural reduced frequency is 0.1, the two instability wind direction angle ranges are 164°-168° and 192°-196°, respectively, verifying the effectiveness and accuracy of the present application, and the prediction result is better.

[0081] S23, according to the aerodynamic damping of the standard airfoil control section, the remaining airfoil control sections are interpolated by using the cubic spline interpolation method, and the aerodynamic damping of the remaining airfoil control sections is obtained.

[0082] S3, according to the structural motion equation of the wind turbine blade, and based on the structural finite element analysis method, the modal shape and modal frequency of the coupling system are obtained, and the aerodynamic damping of each airfoil is calculated. The modal superposition method is used to superimpose the aerodynamic damping of each airfoil, and the aerodynamic damping of the wind turbine blade is obtained.

[0083] Specifically, step S3 specifically includes S31-S32:

[0084] S31, the structural motion equation of the wind turbine blade is obtained, and the structural finite element analysis method is used to solve, and the modal shape and modal frequency of the coupling system are obtained.

[0085] wherein the structural motion equation of the wind turbine blade is:

[0086]

[0087] wherein, denotes the spanwise position length of the wind turbine blade, denotes the displacement of the wind turbine blade at the spanwise position length at the time t, denotes the first-order derivative of the displacement of the wind turbine blade at the spanwise position length at the time t, denotes the second-order derivative of the displacement of the wind turbine blade at the spanwise position length at the time t, denotes the mass matrix of the wind turbine blade at the spanwise position length at the time t, denotes the damping matrix of the wind turbine blade at the spanwise position length at the time t, denotes the stiffness matrix of the wind turbine blade at the spanwise position length at the time t, denotes the external force received by the wind turbine blade at the spanwise position length at the time t.

[0088] Specifically, the step S31 specifically comprises S311-S312:

[0089] S311, assuming that the structural damping of the coupled system is 0, the motion of the coupled system is simple harmonic motion, then:

[0090]

[0091] wherein, denotes the modal shape at the spanwise position length of the wind turbine blade, denotes the modal frequency, denotes the cosine function. S312, substituting

[0092] into the structural motion equation of the wind turbine blade, then:

[0093] ;

[0094] solving , the modal shape and the modal frequency of the coupled system are obtained.

[0095] ​​​​​S32, calculating the aerodynamic damping of different airfoils based on the modal shape and the modal frequency of the coupled system, superimposing the aerodynamic damping of different airfoils by using the modal superposition method to obtain the aerodynamic damping of the wind turbine blade.

[0096] Specifically, the step S32 specifically comprises S321-S328:

[0097] S321, defining the modal mass and the modal stiffness of the wind turbine blade, that is:

[0098]

[0099] Wherein, represents the modal mass of the wind turbine blade, represents the modal stiffness of the wind turbine blade, represents the total length of the wind turbine blade, represents the integral function.

[0100] S322, defining the modal damping of the wind turbine blade, and discretely converting the defined modal damping of the wind turbine blade to obtain the discrete modal damping of the wind turbine blade, that is:

[0101]

[0102] Wherein, represents the modal damping of the wind turbine blade, represents the discrete modal damping of the wind turbine blade, represents the number of airfoils divided by the wind turbine blade, represents the modal shape of the th airfoil, represents the spanwise length of the th airfoil, represents the damping matrix of the th airfoil.

[0103] S323, calculating the damping ratio of the wind turbine blade according to the modal mass of the wind turbine blade, the discrete modal damping of the wind turbine blade and the modal frequency of the coupled system, that is:

[0104]

[0105] Wherein, represents the damping ratio of the wind turbine blade.

[0106] S324, calculating the logarithmic decrement of the wind turbine blade according to the damping ratio of the wind turbine blade, that is:

[0107]

[0108] Wherein, This represents the logarithmic decay rate of wind turbine blades. Represents a constant.

[0109] When the damping ratio of the wind turbine blades When less than 1, .

[0110] S325, according to , as well as The logarithmic decay rate of the discrete wind turbine blades is obtained, i.e.:

[0111]

[0112] in, This represents the logarithmic decay rate of a discrete wind turbine blade. This represents the natural frequency of the structural mode.

[0113] S326. Define the modal damping effect of wind turbine blades, namely:

[0114]

[0115] in, The first blade of a wind turbine Modal damping effect of an airfoil.

[0116] S327, will Substitution Then we have:

[0117] .

[0118] according to Calculate the first Damping matrix of each airfoil , obtained the Aerodynamic damping of each airfoil .

[0119] S328, According to the obtained number Aerodynamic damping of each airfoil The aerodynamic damping of the wind turbine blades was obtained by superimposing modal data using the modal superposition method.

[0120] In this embodiment, the structural motion equations of the wind turbine blade are solved using the structural finite element method to obtain the modal shape and modal frequency of the coupled system. Based on the modal shape and modal frequency, the aerodynamic damping of different airfoils is calculated. The aerodynamic damping of different airfoils is then superimposed using the modal superposition method to obtain the aerodynamic damping of the wind turbine blade. This method improves the calculation accuracy of the aerodynamic damping of the wind turbine blade.

[0121] in, Figure 12The paper demonstrates the variation of aerodynamic negative damping of a wind turbine blade with wind direction angle at a reduction frequency of 0.06. Figure 12 The horizontal axis represents the wind direction angle (based on the incoming wind direction angle of the blade root circle), and the vertical axis represents the negative aerodynamic damping. When it is greater than 0, it indicates structural instability. Here, when the aerodynamic damping is negative, it will destroy stability, therefore... Figure 12 When aerodynamic negative damping is positive, it means that the aerodynamic damping is negative. From Figure 12 As can be seen, when the reduction frequency is 0.06, the instability range calculated by the aerodynamic damping method for the wind turbine blades in this embodiment shows good agreement with the experimental results for the instability range near a wind direction angle of 156°, while the prediction results for the instability range near a wind direction angle of 180° deviate from the experimental results by 1°~2°. Meanwhile, in Figure 3 The diagram shows the local angle of attack at other locations on the blade when the wind direction angle based on the blade root circle is 156° and 180°. Figure 3 It can be seen that at a wind angle of 156°, the local angle of attack for most of the blade is between 160° and less than 170°; at a wind angle of 180°, the local angle of attack for the upper part near the blade tip is greater than 190°. These angle-of-attack regions are related to... Figure 12 The two unstable regions in the airfoil overlap, so it is believed that the instability of the blade is caused by part of the airfoil section entering the unstable angle of attack range.

[0122] like Figure 13 As shown, Figure 13 The calculation process of the aerodynamic negative damping distribution of wind turbine blades with wind direction angle and reduction frequency is shown. Figure 13 The horizontal axis represents the wind direction angle (based on the incoming wind direction angle of the blade root circle), and the vertical axis represents the reduction frequency. The black area represents aerodynamic negative damping greater than 0, indicating structural instability. From... Figure 13 It can be observed that within the instability range near wind angles of 156° and 180°, the wind turbine blades enter the instability region when the damping frequency is less than 0.2. Furthermore, a relatively large range of instability damping frequencies exists when the wind angle is approximately 152°. This is because when the blade wind angle is less than 152° or greater than 185°, the local angle of attack of the control section on the blade exceeds the range of angles of attack suitable for aerodynamic damping modeling using a reduced-order modeling methods. The aerodynamic damping here is obtained through interpolation using an interpolation function.

[0123] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0124] Those skilled in the art will appreciate that the embodiments described herein are presented for purposes of illustration and that the inventive principles are not limited to these particular embodiments. Other variations and modifications can be made to the embodiments without departing from the spirit and scope of the inventive principles.

Claims

1. A method for predicting aerodynamic damping of single-degree-of-freedom vibration of wind turbine blades, characterized in that, Includes the following steps: S1. Divide the wind turbine blades into blade elements, obtain different airfoils, and select the standard airfoil control section and the remaining airfoil control section. Based on the distribution relationship of the structural geometric parameters of the wind turbine blades with the spanwise position, obtain the local angle of attack and mass ratio of the standard airfoil control section. Specifically, step S1 includes: S11. Divide the wind turbine blades into blade elements, obtain different airfoils of the wind turbine blades, select some airfoils of the wind turbine blades as standard airfoil control sections, and the remaining airfoils as residual airfoil control sections. S12. Based on the relationship between the chord length and pitch angle of the wind turbine blades and their spanwise position, the local angle of attack of the standard airfoil control section and the remaining airfoil control section under different wind direction angles is obtained. S13. Based on the relationship between the mass distribution and chord length distribution of the standard airfoil control section, the mass of the standard airfoil control section is obtained, and the mass ratio of the standard airfoil control section is obtained by comparing the mass of the standard airfoil control section with the mass of air contained in a cylinder whose diameter is the chord length at the standard airfoil control section. S2. Model the selected standard airfoil control section using a single-degree-of-freedom reduced-order model method. By coupling the aerodynamic state equation and the structural motion equation, obtain the coupled system. At the same time, obtain the structural modal damping of the coupled system under different wind angles and reduction frequencies to obtain the aerodynamic damping of the standard airfoil control section. Use interpolation to obtain the aerodynamic damping of the remaining airfoil control sections. Specifically, step S2 includes: S21. Model the selected standard airfoil control section using a single-degree-of-freedom reduced-order model method. The specific process is as follows: First, computational fluid dynamics methods are used to obtain high-precision generalized aerodynamic load data and displacement of the standard airfoil control section under the designed generalized displacement motion signal; Secondly, the aerodynamic order reduction model method is used to identify parameters of high-precision generalized aerodynamic load data and displacement, and the aerodynamic state equation and structural motion equation are obtained. By coupling the aerodynamic state equation and structural motion equation, the state equation and output equation of the coupled system are obtained. S22. Based on the coupled system, the selected standard airfoil control section is analyzed using a reduced-order model method within the local angle of attack range. The structural modal damping of the coupled system under different wind angles and reduced frequencies is obtained, and the aerodynamic damping of the standard airfoil control section is obtained. S23. Based on the aerodynamic damping of the standard airfoil control section, the remaining airfoil control section is interpolated using the cubic spline interpolation method to obtain the aerodynamic damping of the remaining airfoil control section. S3. Based on the structural motion equations of the wind turbine blades and using the structural finite element analysis method, the modal characteristics of the coupled system are obtained. The airfoil and its modal frequencies are determined, and the aerodynamic damping of each airfoil is calculated. The aerodynamic damping of each airfoil is then superimposed using the modal superposition method to obtain the aerodynamic damping of the wind turbine blade. Specifically, step S3 includes: S31. Obtain the structural motion equations of the wind turbine blades and solve them using the structural finite element analysis method to obtain the modal shape and modal frequency of the coupled system. The structural motion equations of the wind turbine blades are as follows: in, Indicates the spanwise length of a wind turbine blade. Indicates the first Wind turbine blade spanwise position length Displacement at that point Indicates the first Wind turbine blade spanwise position length Take the first derivative of the displacement at that point. Indicates the first Wind turbine blade spanwise position length Take the second derivative of the displacement at that point. Indicates the spanwise length of a wind turbine blade The mass matrix at that location, Indicates the spanwise length of a wind turbine blade The damping matrix at that point, Indicates the spanwise length of a wind turbine blade Stiffness matrix at that location, Indicates the first Wind turbine blade spanwise position length The external force acting on the point; S32. Based on the modal shape and modal frequency of the coupled system, calculate the aerodynamic damping of different airfoils, and use the modal superposition method to superimpose the aerodynamic damping of different airfoils to obtain the aerodynamic damping of the wind turbine blade.

2. The aerodynamic damping prediction method for single-degree-of-freedom vibration of wind turbine blades according to claim 1, characterized in that, The aerodynamic order reduction model method is used to identify parameters of high-precision generalized aerodynamic load data and displacements, resulting in aerodynamic state equations and structural motion equations. The specific process of coupling the aerodynamic state equations and structural motion equations to obtain the state equations and output equations of the coupled system is as follows: Establish the output vector model of aerodynamic force, namely: in, Indicates the first The output vector at time t, , This indicates the delay order between the output and the input. Indicates the output of the first A matrix of coefficients to be identified with delay orders, Indicates the input number of the first... A matrix of coefficients to be identified with delay orders, Indicates the first The output vector at time t, Indicates the first The input vector at time t, Indicates the first Zero-mean white noise at any given time; Define a state vector to transform the aerodynamic output vector model into a state-space model, i.e.: in, Indicates the first The state vector at time t, Indicates the first The output vector at time t, Indicates the first The input vector at time t, Indicates the first The input vector at time t, Indicates transpose; Discretizing the state-space model yields discrete aerodynamic state equations, namely: in, Indicates the first The state vector at time t, , , , Let represent matrices consisting of the coefficients to be identified in the state space of the discrete system. Indicates the first The input vector at time step; By performing a bilinear transformation on the discrete aerodynamic state equations, we obtain the continuous aerodynamic state equations, namely: in, Indicates time, Indicates the first The aerodynamic state vector in continuous space at time t. Indicates the first The output vector at time t, , , , Let represent matrices composed of the coefficients to be identified in the continuous state space. Indicates the first The state vector at time t, Indicates the first The input vector at time step; Define the equations of motion for the structure, namely: in, Indicates the first The derivative of the aeroelastic structural motion state vector in continuous space at any given time. Indicates the first The aeroelastic structural motion state vector in continuous space at any given time. , , , Let represent the coefficient matrices of the structural motion equations in continuous space. Indicates dynamic pressure. Indicates the first The modal displacement output at time t. Indicates the first The aerodynamic force vector corresponding to the aeroelastic structural motion state vector in continuous space at any given time. By coupling the structural motion equations with the continuous aerodynamic state equations, we obtain the state equations and output equations of the coupled system, namely: in, Indicates the first The derivative of the state vector of the coupled system at time t. Indicates a coupled system. Indicates the first The state vector of the coupled system at time t. Indicates the first The modal displacement output of the time-coupled system.

3. The aerodynamic damping prediction method for single-degree-of-freedom vibration of wind turbine blades according to claim 2, characterized in that, Step S31 specifically includes: S311. Assuming the structural damping of the coupled system is 0, the motion of the coupled system is simple harmonic motion, then: in, Indicates the spanwise length of a wind turbine blade Modal shape at the location, The modal frequency is represented by cos(), and the cosine function is represented by cos(). S312, will Substituting the equations of motion for the wind turbine blades, we get: ； right Solving the problem yields the modal shapes of the coupled system. With modal frequency .

4. The aerodynamic damping prediction method for single-degree-of-freedom vibration of wind turbine blades according to claim 3, characterized in that, Step S32 specifically includes: S321. Define the modal mass and modal stiffness of wind turbine blades, namely: in, This indicates the modal quality of the wind turbine blade. This represents the modal stiffness of the wind turbine blade. Indicates wind turbine blades Total length of the film Represents an integral function; S322. Define the modal damping of the wind turbine blade. Perform a discretization transformation on the defined modal damping of the wind turbine blade to obtain the discrete modal damping of the wind turbine blade, i.e.: in, This represents the modal damping of the wind turbine blade. This represents the modal damping of a discrete wind turbine blade. This indicates the number of airfoils that divide a wind turbine blade. Indicates the first The modal shape of an airfoil, Indicates the first A wing-shaped span length, Indicates the first Damping matrix of each airfoil; S323. Based on the modal mass of the wind turbine blade, the modal damping of the discrete wind turbine blade, and the modal frequencies of the coupled system, calculate the damping ratio of the wind turbine blade, i.e.: in, This indicates the damping ratio of the wind turbine blades; S324. Based on the damping ratio of the wind turbine blades, calculate the logarithmic attenuation rate of the wind turbine blades, i.e.: in, This represents the logarithmic decay rate of wind turbine blades. Represents a constant; When the damping ratio of the wind turbine blades When less than 1, ; S325, according to , as well as The logarithmic decay rate of the discrete wind turbine blades is obtained, i.e.: in, This represents the logarithmic decay rate of a discrete wind turbine blade. Represents the natural frequencies of structural modes; S326. Define the modal damping effect of wind turbine blades, namely: in, The first blade of a wind turbine The modal damping effect of an airfoil; S327, will Substitution Then we have: ; according to Calculate the first Damping matrix of each airfoil , obtained the Aerodynamic damping of each airfoil ; S328, According to the obtained number Aerodynamic damping of each airfoil The aerodynamic damping of the wind turbine blades was obtained by superimposing modal data using the modal superposition method.

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