Study on the repair parameters for trailing‐edge bonding failure of wind turbine blade in service

A numerical analysis method of trailing edge deboning is proposed in this paper. Using this method, multiple repair parameters can be quantified by analyzing aerodynamic responses and structural characteristics of the trailing edge. This method can be applied to three types of trailing edge, including blunt trailing edge, transitional trailing edge, and pointed trailing edge. In this study, the repair parameters are divided into two types, including the internal parameters that can affect the bonding strength and the external parameters that can affect the stiffness and aerodynamic shape. The main research steps are as follows: First, a repair structure shell‐body model was developed. Second, static tensile tests were carried out using 49 specimens, covering two lap joint types and seven bonding thicknesses. Finally, nine different repaired trailing edge models were developed using Ansys/Fluent for each two two‐dimensional airfoil. A 30–40 m section of a 71 m blade was used to develop a three‐dimensional (3D) rotating model with the repaired trailing edge. The simulation results show that the two internal parameters, overlap length and the slope of adhesive joints, are the key to improving the bonding performance of the pointed trailing edge. In addition, the bonding thickness range of 1–10 mm is proved by the experiment results and numerical analysis to be sufficient for good bonding performance. Besides this, the influence of the repair height on the aerodynamic pressure distribution and lift coefficient is much greater than the repair width, and the torque and power of the repaired 3D blade model are 1.91% higher than that of the original blade. This should further help provide an effective theoretical basis for determining the repair plan for a wind turbine blade.


| INTRODUCTION
Although designs and maintenance plans of wind turbines have improved a lot, major components such as blades, gearboxes, and generators still have relatively high failure rates. 1 Failure of a wind turbine due to failure of the blades represents 19.4% of a total of 1028 wind turbine failures, 2 and the contribution of rotor issues to the total downtime of a wind turbine ranges between 8% and 20%. 3 Wind turbine blades are multipart, high-aspect-ratio, thin-walled structures made of glass-fiber or carbon-fiber composite. Many subcomponents of which a blade is comprised are produced separately and connected with each other via adhesive bonding in most manufacturing processes. 4 These bonding connections destroy the integrity of the blade and become a weak link, especially the trailing edge joints which are notoriously vulnerable to damage ( Figure 1). 5 Trailing edge bonding area that has not reached the expected lifetime leads to downtime, maintenance, and even worse blade replacement, resulting in considerable operation and maintenance costs. 6 Continuous increase of blade length leads to large thickness, blunt trailing edge, and large closed chamber structure which are suspected to initiate bonding failure of the adhesive trailing edge joints. 7 Thus, repair design is an important technique to ensure the lifetime of blades. 8 The performance degradation and repair of wind turbine blades in service is a multiscale problem in which mechanical model, stress analysis, and repair design should be comprehensively considered. 9 Determination of main connection parameters that affect the bonding performance of the trailing edge is an important prerequisite for repair parameter design, of which the essential purpose is to restore the bonding state. The failure mechanism of the trailing edge bonding was studied via the theoretical model of the trailing edge bonding connection to capture the repair parameters for bonding quality improvement. Thereafter, the influence of the quantitative design of the repair parameters on the performance of the trailing edge bonding connection can be evaluated. 10 This method is very important to guide the implementation of the trailing edge bonding failure repair of the blades in service. 11 Many scholars [12][13][14][15][16] studied the trailing edge bonding failure with the finite element method. The complex boundary conditions and material property parameters in three-dimensional (3D) stress field analysis make it very difficult to solve the overall control equation for predicting bonding performance. 10 One-dimensional (1D) method is simplified too much that only considers the stiffness in the bonding direction. So, many adhesive bonding studies are based on the two-dimensional (2D) stress analysis method. 17 Theoretical model of the scarf adhesive joints is used to calculate the shear stress of the bond line in each direction, which makes it convenient to evaluate the bonding connection state 18 and determine whether bonding repair parameters are reasonable. [19][20][21][22] Currently, models mainly used are the pointed trailing edge that is directly bonded. [23][24][25] However, with the increase in blade length, nearly half of the spanwise blade has a relatively thick trailing edge that cannot be bonded directly. Prefabricated parts need to be designed to control the bonding quality. There is less research on the analysis model considering both large thickness trailing edge and pointed trailing edge forms, which hinders the applicability of repair parameter design to multiple kinds of the trailing edge.
Recently, researchers have found that the repair parameters have profound influences on the adhesion performance of the trailing edge. Shohag and Hamel 26 determined that the main parameters affecting the adhesion performance of the trailing edge of the blade in service are the surface treatment, appropriate materials selection, and the fracture toughness of adhesives. Banea 27 and canales 28 determined that bonding performance is mainly affected by bonding thickness, joint configuration, and bonding properties, and an accurate test of adhesive thickness needs to be carried out. 29,30 Patch thickness, 31 patch shape, 32 and patch design 33 affect the bonding strength, and also change the aerodynamic shape of the repair part, which make them important repair parameters that affect the aerodynamic responses. Djelall et al. 34,35 and Etetemadi et al. 36,37 found that damage caused a significant decrease in lift drag ratio and pressure coefficient. However, the F I G U R E 1 The trailing edge debonding of wind turbine blade in service.
research on the influence of damage repair on aerodynamic characteristics of blades is much less than that on aircraft. 38,39 Yuan 40 conducted numerical simulation on the aerodynamic flow field of a repaired airfoil with different thicknesses but did not quantitatively analyze the influence of repair design on the aerodynamic response.
This paper presented a numerical method for analyzing the influence of the quantitative design of multiple repair parameters on bonding strength and aerodynamic characteristics of an in-service blade with repaired debonding trailing edges. This method was efficient and suitable for both large thickness trailing edge and pointed trailing edge. Based on the adhesive joints model of trailing edge, 41 the repair parameters were divided two categories, the internal parameters that affected the bonding strength and the external parameters that affected the stiffness and aerodynamic shape of the bonded structure. The structural and aerodynamic analysis models were developed, respectively, and the static tensile tests of single lap and double lap specimens with different bonding thicknesses were carried out to determine the influence of the multiple repair parameters on the bonding shear stress, aerodynamic lift, and pressure distribution. This would further provide an effective theoretical basis for determining the selection of repair parameters and quantitative design for the trailing edge debonding failure of the wind turbine blade in service.
2 | ADHESIVE JOINTS MODEL AND REPAIR PARAMETERS

| Adhesive joints model of trailing edge
Loads of wind turbine blade were based on the principal axes coordinate system (Figure 2A), the positive z-axis followed the local deflected neutral axis at each blade station towards the blade tip, the positive y-axis was defined by the principal axis orientation, and the positive x-axis was orthogonal to the y and z and followed the right-hand rule. The origin of the axes was on the neutral axis at each local deflected blade station. The bonding area at the trailing edge of the blade provided edgewise stiffness. It mainly bore the action of edgewise moment (Mx) and axial force (Fz). At this point, both the edgewise moment (Mx) and the axial force (Fz) had the stretching effect on the trailing edge.
The structure, layering, and shape of the trailing edge of the wind turbine blade shown in Figure 2B together affected the bonding performance of the trailing edge. Figure 2C showed the lay-up of the trailing edge of the pressure side (PS), and two sides of the adhesive bonded parts in Figure 2D were composed of different layers. At this point, the trailing edge adhesives could be regarded as the scarf adhesive joints model ( Figure 2E). The edgewise moment and the axial force on the trailing edge were equivalent to the uniaxial tensile load P along 2 were thickness, the fiber directional elastic model, and allowable stress of the thin and thick end of adhesively bonded parts, respectively. α, angle between the section-cross chord and the principal axis; τ av , bonding average shear stress; τ p , bonding shear stress; γ γ / p e , bonding strain ratio; θ, angle of adhesive joints; P, tensile load; Fx, flapwise force; Fy, edgewise force; Fz, axial force; Mx, edgewise moment; My, flapwise moment; Mz, torsional moment; G, bonding hear modulus; h, bonding thickness; l, length of adhesive overlap. the blade spanwise (z-axis). However, the effect of Mx on the trailing edge was much higher than that of Fz.
As shown in Figure 2D,E, the adhesive bonding of the trailing edge and structure of PS and SS, respectively corresponded to the bond line (red area) and adhesively bonded parts (blue area). The coordinate system of the scarf adhesive joints model in Figure 2E was the same as that of the structural analysis model in Figure 2A-D. However, the global Z-direction in Figure 2E needed to be rotated by −π/2. In this way, the parameters of material and geometrics of the scarf adhesive joints model could be demonstrated in detail.
Comparing the scarf adhesive joints model ( Figure 2E) and analysis model for trailing edge adhesive joints ( Figure 2D), in the case of the following conditions, the layering design, material properties, and loading mode of the two models were the same, the two models' calculated shear stress of bond line along the elastic segment of the adhesive overlap length tended to be the same. In particular, the authors used the scarf adhesive joints model as a qualitative analytical solution means to investigate the bonding strength as a function of the scarf joint geometry and material parameters rather than a direct model representation of the trailing edge detail.
It is assumed that failure first occurs at the thin end of the adhesively bonded part, and the max length of adhesive overlap is: The "transition overlap length" of the scarf adhesive joints l*: When  l l*, the adhesive layer can be regarded as elastic-plastic material in adhesive strength analysis (i.e., τ τ l / = 1.0 av p ). At this time, the maximum load-bearing capacity of the bond line is: When   l l l * max , iteratively solve for Ψ by Equation (6): We use Ψ to calculate τ τ / av p by Equation (7): Then, the maximum load-bearing capacity of the bond line is: The joints efficiency is: Consequently, based on the scarf adhesive joints model, the repair parameters should ensure the bonding strength recovery and provide enough stiffness for the adhesively bonded part to improve the joint efficiency.

| Repair parameters of bonding failure
To determine the debonding repair parameters of three types of the trailing edge, a commercial 71 m blade (B71 for short) was used as a reference blade. The aerodynamic profile of the B71 blade as shown in Figure 3A. The red rectangle denoted ( Figure 3B) the blunt trailing edge (BTE) from the blade root to the maximum chord, and the blue rectangle denoted ( Figure 3B) the transitional trailing edge (TTE) of the blade. These two trailing edge types were also referred to as large thickness trailing edge (LTE) in the aerodynamic analysis in this paper. The prefabricated flange and filler were designed to assist the bonding of BTE and TTE to achieve the desired bonding thickness. The other span locations were pointed trailing edge (PTE) that could be bonded directly ( Figure 3D). To study the influence of the multiple repair parameters on the debonding repair of three trailing edge types, the debonding repair parameters of the trailing edge were divided into the internal parameters (length of adhesive overlap, slope of adhesive joints, and bonding thickness) that affected the bonding strength and the external parameters (width and height of outer reinforcing layer) that improved the stiffness of the adhesively bonded parts.
Figures 3B-D showed the repair parameters of three trailing edge types. RE_N represented each repair parameter. RE_1 and RE_3 represented the length of adhesive overlap of PS and bonding thickness, respectively, the values of which directly affected the bearing capacity of the bond line. RE_2 characterized the slope of the adhesive joints ( Figure 3C), and represented the inclination degree of the front of the adhesive joints from PS to SS. The slope value was the ratio of the PS overlap length to the difference value of both sides' overlap length. RE_4 and RE_5 represented repair weight and repair heigh of the outer reinforcing layer (ORL), which could significantly improve the local stiffness of adhesively bonded parts, but those could also cause the local shape of the trailing edge to deviate from the original aerodynamic shape. In particular, the bonding thickness of PTE and the slope of the adhesive joints of LTE could not be controlled in advance and were not introduced into the corresponding repair parameter as variables, respectively.

| Structural repair model and repair parameters
The DU airfoil was used to design the B71. The lift coefficient distribution of different airfoil thicknesses is shown in Figure 4A. The aerodynamic data of each airfoil was listed in Table 1, and the high lift coefficient and lift-drag ratio indicated the good aerodynamic performance of the blades. Figure 4B illustrated the material distribution and structural design of B71, which showed different specifications of fiber, core, and F I G U R E 4 B71 model. (A) Lift coefficient distribution of B71 airfoil; (B) material distribution and structural design. Among them, the Y-axis of the blade section coordinate system was the chord length direction from the leading edge to the trailing edge, the Z-axis was from the blade root to the blade tip, and the X-axis was perpendicular to the Y-axis.
adhesive bonding used in the spar, UD type, sandwich, and bonding area. The fiber-reinforced composite material and core material Balsa were modeled by 2D orthogonal anisotropic composite material, core material PVC, and structural adhesive were considered isotropic materials, and the material properties were shown in Table 2.
According to GH bladed, assuming that the wind speed distribution follows the Rayleigh distribution model and the annual average wind speed was 7.5 m/s, the equivalent fatigue loads with cycle number 1E+08 (m = 4-14) were calculated. The loads were based on the principal axes coordinate system. Because the trailing edge mainly provided edgewise stiffness, therefore, the maximum edgewise moment of m = 4 and m = 14 were taken as the analytical load. The equivalent fatigue load distribution along the blade spanwise is shown in Figure 5.
As shown in Figure 6A, the six degrees of freedom of all nodes at the blade root were constrained by fixed. Multipoint constraint (MPC) was used to simulate equivalent fatigue loading in each blade cross-section ( Figure 6B). The rigid bar element (RBE3) was used to distribute the concentrated bending moment of the master node to the slave node ( Figure 6C). The master node was on the neutral center at each local deflected blade station, and the slave node was the spar cap node. Thus, a loading approach could be realized that corresponded to the equivalent fatigue load.
In this paper, R15m, R27m, and R50m cross-section models of B71 were used to establish three types of Patran was used to establish the structural models with R = 15 m ( Figure 7A), R = 27 m ( Figure 7B), and R = 50 m ( Figure 7C), including layering sequence, layer angle, and ply thickness. To truly reflect the blade trailing edge structure, the spar cap and trailing edge UD were established as UD tape, and the damage expansion was not considered. Therefore, Biax and Triax interfacial layers between the unidirectional layer, which improve the damage tolerance, were not added.
To study the repair performance, repair parameters were introduced into the analysis model of BTE, TTE, and PTE as variables. Based on the repair parameter requirements that could be achieved by field repair technology in aerial operation, the variation range of repair parameters was formulated, which was listed in Table 3. The first value in brackets represented the initial value of the variable, the second value represented the maximum value, and the third value represented the variable increment, and "+" represented the minimum  increment. The repair width and repair height of ORL represented by RE_4 and RE_5 were defined in detail in Section 3.2 of this paper. The APDL program of MSC.Patran was applied to create a high-precision shell-body blade trailing edge debonding repair model including structure, material, boundary, loading conditions, and repair parameters. According to Saint-Venant's principle, the stresses far from the loading side of the structural model could be regarded as unaffected by boundary conditions. Therefore, as shown in Figure 8A-C, the solid element of bonding adhesive of the blade cross-section at midstretch length was regarded as the research object. The shear stresses txz and tyz were extracted ( Figure 8D,E), which determined the shear failure of the bond line. Where τ XZ and τ YZ are the shear stress components along the thickness direction, and τ shear is the allowable shear strength of the adhesive bonding (determined by test or standard 42 ). The root mean square of shear stress combined by stress vectors τ XZ and τ YZ is:

| Aerodynamic repair model and repair parameters
Based on LTE airfoil DU-300 ( Figure 9A) and PTE airfoil DU-210 ( Figure 9B) of B71, ORL was laid to SS and PS respectively, the repair width was expressed as a percentage of ORL laying width projected to chord. Therefore, the repair height, repair width, and repair length of the ORL led to a slight deviation of the local shape of the trailing edge. The DU-300 and DU-210 airfoils were designed with nine different trailing edge repair models, which were marked by DU airfoil-repair width-repair height, respectively. Table 4 indicated that the repair width and repair height variations are slightly different from the settings in each repair model. Furthermore, to verify the accuracy of the calculation method, the computational mesh was introduced to the DU-300 airfoil. As shown in Figure 10, a C-type mesh of DU-300 airfoil was used to ensure the orthogonality between mesh and airfoil surface. The mesh thickness of the first layer in the boundary layer was set as 10-5c to meet the requirement that y+ should be less than 1. 40 layers of mesh were set in the boundary layer along the surface normal direction, of which the mesh height growth rate was 1.1. The farfield boundary was set at a distance of 10c from the airfoil. The upper and lower boundary and front boundary of the C-type mesh were the speed inlet, and the rear boundary was the pressure outlet. The mesh independence test was calculated according to the performance of the airfoil, and the total number of grids was finally determined to be 90,000.
The governing equation was the conserved unsteady incompressible Reynolds average Navier-Stokes equation, and the turbulence model was the shear stress transport model, which is a good linear vortex-viscous model and had high accuracy in the simulation of both boundary layer flow and separation flow. 43 γ-Re θ transition model proposed by Menter   44 Multiple transition mechanisms such as natural transition, cross transition, and separate flow transition were considered, 45,46 and the SIMPLE algorithm was used to solve the governing equation. First-order difference scheme was adopted for the initial field pressure, momentum and k, ω all the, second-order upwind scheme for the stable pressure, and the QUICK scheme for the rest of the terms. The pressure distribution of DU300 airfoil with α = 10°a nd α = 15°was calculated by setting Reynolds number 2E6, as shown in Figure 11.
According to the experimental data on the aerodynamic performance of thick airfoil (DU-300 airfoil with 30% thickness) published by the Wind Energy of the Delft University of Technology, 47 the pressure distributions with the Angle of attack (AOA) of 10.293°and 15.216°were extracted. Compared with the numerical simulation results of the DU-300 airfoil, the pressure distributions were in good agreement with the experimental data (Figure 12), and the deviation rate was within 2%. Therefore, the numerical simulation method of aerodynamic analysis adopted in this paper could accurately simulate the aerodynamic characteristics.

| Experimental study on bonding thickness
To study the effect of bonding thickness on the bonding performance, an experimental study with the bonding thickness of 0.2-20 mm was carried out. In this paper, the dimension design, preparation, and testing process of bonding thickness specimens were strictly based on the tensile shear strength test standard of adhesive joints. 29,30 We selected EUL1200 (0) EP-600E7 (CTG) and Hexion Epoxy Resin LR235 (Hexion) to prepare laminates. The unidirectional epoxy laminates with a thickness of 2-4 mm were prepared by vacuum infusion process. After curing, the unidirectional laminates were cut into a 100 mm × 25 mm sample and a 50 mm × 25 mm sample.
The adhesive was Ashland BP6200 and the curing agent was M-50 which were mixed with a ratio of 100: 45 ± 5. The bonding specimen was fully mixed using the static mixing machine (Heydrich all-in-one machine VIA45K) along the crisscross sealed mixing pipe path. Thus, the speed gradient of the laminar motion was increased to realize the "division, displacement, and rejoin" mixing process. It could minimize the bubbles and voids introduced in the mixing process. In the repair of trailing edge debonding for the blade in service, manual mixing was used to stir the mixture thoroughly, and then let it stand for a while to ensure that the bubble content could not cause a significant decrease in bonding strength.
When the bonding thickness was 0.2 mm, the size of the single lap specimen was shown in Figure 13A. When the bonding was not less than 0.5mm, the size of the double laps specimen was shown in Figure 14A. The adhesive bonding with different thicknesses was evenly applied to the overlap area of the unidirectional samples by hand layup and cured at 80°C for 8 h. Distance between two laminates is precisely controlled by the standard thickness cushion block had realized the target adhesive thickness. As shown in Figures 13B and 14B, there were no less than five effective specimens of each bonding thickness for both the single lap and double lap joints.
There were seven groups of bonding thicknesses (0.2, 0.5, 1, 5, 10, 15, and 20 mm) in the bonding thickness test, and eight specimens were prepared for each group. Seven specimens were fractured during loading, and the final effective specimens were 49. A universal testing machine (GoTech) with a 200 kN load cell was used for the tensile test, the loading method was shown in Figure 15A, one side of the specimens was fixed and the other side was loaded with displacement tensile load. All specimens were tested at room temperature with the crosshead speed held constant at 1 mm/min until failed. When the specimen failed, the corresponding load-displacement curve and failure location of the specimen were recorded.
The shear failure stress: where P bond was the failure load, and S was the failure area. As shown in Figure 15B, the load corresponding to the moment when the curve showed rapid force decline was the failure load. Accordingly, the failure area was calculated according to the shear failure location of the specimen. For the single lap joint specimens ( Figure 16A), the failure area was the overlap area. For the double lap joint specimens ( Figure 16B), the failure area was calculated according to the final shear failure location of the joint area. The test results of the effective specimens were counted, and the shear stress characteristic values of bond lines with different bonding thicknesses were calculated 42 : (13) where X was the arithmetic mean value; V was the dispersion coefficient (V = S/X, S was the standard variance); N was the number of specimens.
As shown in Figure 17, the ideal bonding thickness should be less than 1 mm. Otherwise, the bonding performance would decrease rapidly with the increase of the bonding thickness. But this was not easy to achieve in the actual manufacturing process. When the bonding thickness was 1-10 mm, the bonding performance also decreases rapidly with the increase of the bonding thickness. However, the effect of bonding thickness on bonding properties decreased gradually. When the bonding thickness was larger than 10 mm, the effect of increasing the bonding thickness on the bonding properties became less obvious. Therefore, the bonding thickness of 1-10 mm was not only easy to achieve, but also had a relatively obvious effect on the bonding performance.

| Length of adhesive overlap
The calculated results indicated that the sensitivity of adhesive overlap length was higher in PTE than in BTE and TTE. Figure 18 given the PTE, in two equivalent fatigue loading conditions, the length of adhesive overlap increased from 180 to 800 mm, and the shear stress of the bond line decreased gradually. Especially when the overlap length was greater than 260 mm, the shear stress attenuation rate of the bond line increases rapidly. But for BTE and TTE, the bearing capacity of the bond line did not increase obviously with the increase of the length of adhesive overlap, only the width and depth of the elastic zone of the bond line increased.

| Slope of the adhesive joints
The front of the adhesive joints of the trailing edge was the stress singularity of the elastic structure. Poor adhesive joints were easy to introduce initial bonding defects, which might evolve into large crack surfaces with the increase in blade service time. Many scholars pointed out that the slope of the adhesive joints could improve the force transmission path between the adhesively bonded parts and the bond line. 13,48,49 However, there were few studies on the influence of the slope value of the adhesive joints on the bonding strength. As shown in Figure 19A, the slope could be effectively quantified. The smaller the slope value, the flatter the front of the adhesive joints. Therefore, the influence of slope on bonding performance could be analyzed concretely and quantitatively.
In this paper, we demonstrated that for the PTE, as shown in Figure 19B, the shear stress of the bond line significantly increased with the increase of the slope of the adhesive joints, and the growth rate was similar under both load cases. These results indicated that the slope of the adhesive joints had a certain influence on the bonding strength of the PTE. Therefore, the slope of the adhesive joints was gentle, which could effectively relieve the stress concentration at the front of the adhesive joints and significantly reduce the bonding shear stress.

| Bonding thickness
The simulation results of the effect of bonding thickness on the bonding shear stress were shown in Figure 20. All analytical models showed an inflection point at the bonding thickness of 10 mm. One notable exception was that when the bonding thickness of the BTE and TTE was more than 10 mm, the growth rate of shear stress of the bond line tended to be gentle, and the influence of bonding thickness on shear stress was weakened. Furthermore, since the bonding thickness was affected by the bonding type, layering, and shape, it was difficult to give a clear optimal thickness value. The excessive thickness of the bond line might lead to more bubbles and other bonding defects, which would affect the bonding fatigue performance. At present, the restriction of bonding thickness on the trailing edge of blade design was basically given by tolerance, which was 6 ± 4 mm. Therefore, based on the bonding thickness test, bonding thickness tolerance of blade design, and numerical analysis results, we proposed that the bonding thickness of 1-10 mm could achieve the optimal bonding quality.

| Outer reinforcing layer
The outer reinforcement layer could improve the local stiffness of the bonding area of the trailing edge. With the increase in the width and thickness of the outer reinforcement layer, the adhesive bearing capacity of the trailing edge could be effectively improved. The structural repair model in this study realized the qualitative analysis of the influence of the outer reinforcement layer on bonding performance. For the three types of trailing edge, when four biaxial outer reinforcement layers with a width of 200 mm were laid at the trailing edge, the maximum value for the root mean square of shear stress declined by 3.6%. However, the width and thickness of the outer reinforcement layer had a more profound effect on the change of the shape of the trailing edge. In this paper, CFD simulation analysis was carried out to further analyze the influence of the slight deviation of the local shape of the trailing edge caused by the outer reinforcing layer on the aerodynamic characteristics.

| AERODYNAMIC RESPONSES ANALYSIS OF EXTERNAL REPAIR PARAMETERS
For the 2D airfoil, the model was calculated in extreme turbulent wind conditions (1.3Y000V08 load case) of the B71 wind model, the wind speed was 8 m/s, and the wind direction was 0°. Ansys/Fluent was used for aerodynamic analysis. Table 5 showed that the lift and drag characteristics of the trailing edge repair models were closely related to the repair width and repair height. These findings suggested that the lift coefficient (C l ) of repaired LTE was generally higher than the original airfoil in the whole angle of attack (AOA), and the lift-drag ratio (C l /C d ) was also slightly improved. Compared with the original airfoil, the C l and C l /C d of the LTE models 300-15-6 and 300-20-6 were increased by about 7% and 1.5%, respectively. For PTE, the C l /C d of the repaired model decreased compared with the original airfoil, especially in the models of large repair width and repair height. Figure 21 showed the pressure distribution comparison of the LTE airfoil at α = 14°. As shown in Figure 21A, the pressure distribution on the SS of the repair model with 20% repair width was significantly increased, and the envelope area of aerodynamic pressure was larger than that of the repair model with 15% and 10% repair width. In Figure 21B, near the stall AOA, the aerodynamic pressure distribution on the suction side (SS) and PS caused by different repair widths was basically chordwise identical. There was no local configuration surge on the trailing edge repair surface, and would not cause an abrupt change in the aerodynamic responses. Figure 22 showed the C l of 2 and 6 mm repair heights with different repair widths of LTE, respectively. the C l of 20% and 15% repair width were basically the same in the whole AOA (Figure 22A), and C l varied by only 0.2%, also showed a similar variation in Figure 22B, with only slight changes at high angles of attack. This study verified that the C l changed little due to the aerodynamic shape deviation caused by the repair width. Figure 23 illustrated that the influence of repair height on aerodynamic pressure distribution fluctuated greatly. Both repair widths could be seen, with the repair width of 10% and 20%, respectively at the stall AOA of LTE, with the increase of the repair height, the envelope area of the aerodynamic pressure distribution gradually increased. One notable feature was that compared with the repair width, the effect of increasing repair height on airfoil aerodynamic responses fluctuated greatly. Figure 24 showed the repair model stalled near AOA of 14°. With the increase of repair height, C l increased in the range from small AOA to stall AOA. From the stall AOA to the high AOA, the repair height had little effect on the lift, which was quite different from the C l distribution caused by repair width. That further explained that aerodynamic responses of airfoil were more sensitive to the repair height at small AOA, which could also be verified by Figure 25. At α = 14°, the aerodynamic pressure distribution on the SS caused by repair height fluctuated greatly along the chord.

| Influence of repair height
The above findings implied that for the LTE and PTE, the influence of aerodynamic configuration deviation caused by repair height change was far greater than that caused by repair width change. Similarly, from small AOA to stall AOA, with the increase of the repair height, the pressure distribution on the SS bulged higher, and the lift coefficient increased.

| Influence of repair length
In this paper, based on the transition region between LTE and PTE of full-size B71 ( Figure 26A), the repair length of 10 m trailing edge with a spanwise of 30-40 m was selected as the 3D rotating blade trailing edge repair model ( Figure 26B). The outer reinforcement layer with 20% repair width and 6 mm repair height was laid on both SS and PS ( Figure 26C). At the end of the ORL, the chamfering slope along the spanwise was 1:50, and the chord direction was 1:10, which could realize the smooth transition of the shape of the trailing edge repair. Compared with the original aerodynamic shape, the slight deviation of the local shape of the repaired blade within 10 m along the spanwise did not show many mutations ( Figure 26D).
For the 3D rotating blade, the calculation condition of the B71 blade model was wind speed of 7 m/s, rotor speed of 13.618 rpm, hub radius of 2 m, and a pitch angle of 0°. With the increase in grid density, the total number of grid cells increased from 5 to 18 million. The results showed that grid density had a certain effect on power. When the total number of grid cells reached 18 million, the convergence of blade aerodynamic responses was very good, and the difference in calculated results was within 1%. Based on the grid sensitivity test results, hexahedron was selected for the B71 blade and periodic boundary conditions were adopted. The number of grids for repaired blades was 20.16 million (Figure 27).
Based on the SST k-ω turbulence model, the 3D incompressible Reynolds mean equation was used to solve the aerodynamic performance. In the spanwise 33 and 37 m cross-sections, the aerodynamic pressure in the repaired zone of the SS was slightly increased, but the aerodynamic pressure on the PS was basically unchanged, and the aerodynamic pressure in the unrepaired zone was basically unchanged ( Figure 28A,B). The circumferential force was obtained according to the pressure distribution and the point coordinates of the airfoil along the airfoil circumference. The torque of each cross-section was obtained by multiplying the circumferential force with the distance from the section to the blade root. The calculation results showed that the torque of 33 and 37 m cross-section was increased by 0.06% and 0.31%, respectively. The repair led to a slight increase in the envelope area of pressure distribution on the SS of the cross-section, resulting in a slight increase in aerodynamic lift. Although a single cross-section had no significant effect on the torque, as all discrete crosssections of the repaired blade accumulated to the root, which resulted in a 1.91% increase in the torque and power of the repaired model with 30-40 m length of the trailing edge compared with the original blade.

| CONCLUSION
In this paper, a numerical method was carried out for analysing the influence of the quantitative design of multiple repair parameters on bonding strength and aerodynamic characteristics of an in-service blade with repaired debonding trailing edge. This method was efficient and suitable for blunt trailing edge, transition trailing edge, and pointed trailing edge.
1. Based on the scarf adhesive joints model, the debonding repair parameters of the trailing edge were divided into internal parameters (length of adhesive overlap, slope of adhesive joints, and bonding thickness) that affected the bonding strength and external parameters (width and height of outer reinforcing layer) that improved the stiffness of the adhesively bonded parts. 2. A high-precision shell-body blade trailing edge debonding repair model including structure, material, boundary, loading conditions, and repair parameters was created. Static tensile tests were carried out on 49 specimens with seven groups of bonding thicknesses. The effect of repair parameters on bonding strength was analyzed.
• For the pointed trailing edge, the length of adhesive overlap and the slope of the adhesive joints were the main repair parameters. Especially when the overlap length was greater than 260 mm, the shear failure resistance of the trailing edge was significantly improved.
• The slope of the adhesive joints was gentle, which could effectively relieve the stress concentration at the front of the adhesive joints and significantly reduce the bonding shear stress. • Based on the bonding thickness test, bonding thickness tolerance of blade design, and numerical analysis results, the bonding thickness of 1-10 mm could achieve the optimal bonding quality. • The outer reinforcement layer could significantly improve the shear resistance of the trailing edge but caused a slight deviation in the local shape. 3. Two-dimensional airfoil with nine groups of each of two trailing edge types and a 3D rotating blade repaired model was designed for the slight deviation of the local trailing edge caused by the repair width, repair height, and repair length, and were carried out aerodynamic responses analysis.
• Lift and drag characteristics of the trailing edge repaired models were closely related to the repair width and repair height. • The influence of repair height on aerodynamic responses was much greater than that of the repair width. • With the increase of the repair height, the envelope area of the aerodynamic pressure distribution gradually increased, and C l increased in the range from small AOA to stall AOA. • The torque and power of the 3D rotation blade with repaired 30-40 m length of trailing edge increased by 1.91% compared with the original blade.