*3.3. Topology Optimization Results of Internal Configuration of Wind Turbine Blade*

Figure 4 exhibits the topology optimization results of the wind turbine blade. The outer shell of the blade was completely retained (Figure 4a), and in the internal configuration appeared obvious strip-shaped "gap" and "hole" regions along the axial direction of the blade (Figure 4b), which indicated several webs should be set in these regions. Furthermore, from the left and right enlarged views, some vertical webs should be retained in order to improve the bending resistance. Figure 4c shows the specific internal views cut from 12 various locations from the root to the tip of blade. More obviously, some web-like structures were retained though the topology optimization design.

Based on the aforesaid analysis, the preliminary design of the webs inside the blade in accordance with the topology optimization (Figure 4b,c) was subsequently carried out, see Figure 5. Taking into account seven cross-sections at different locations along the axis direction, the internal web structure of the blade from the root to tip generally changes from the single-web mode to twin-web mode and then to the single-web mode (Figure 5a,b), respectively. However, there are some discontinuous regions among the transition regions of webs, see Figure 5a. Consequently, we proposed to connect the discontinuous region " <sup>1</sup> " by using a twin-web structure and also arranging the twin-web structure in the region " <sup>2</sup> ", but other regions were filled by the single-web structure. Four webs were reversely designed and the specific sizes of the web cross-sections were determined by the seven cross-sections shown in Figure 5b, in which the corresponding locations along the blade were at 6.70, 17.13, 28.18, 50.28, 56.69, 70.30 and 74.71%, respectively. Ultimately, according

to the dimensions of the different cross-sections shown in Figure 5b, the first generation turbine blade inspired by topology optimization was constructed by Boolean operation between the designed web structures and blade boundary, see Figure 5c. The corresponding finite element model of the blade is exhibited in Figure 5c.

**Figure 4.** Topology optimization results of the wind turbine blade. (**a**) External shell structure. Inset: the enlarged left and right views. (**b**) Retained materials in the internal blade. (**c**) Cross-section views at different axis locations.

#### *3.4. Validation of Performance Indexes for the First Generation Wind Turbine Blade*

The designed first generation wind turbine blade was firstly validified in the DLC-1 case (Table 2) to ensure the feasibility of the reverse design structure. If it was a feasible solution, the design was further validified in the DLC-2 and DLC-3 cases. Otherwise, the aforesaid design strategy was repeated until all the work cases were satisfied.

Figure 6 and Table 5 show the simulation results of the first generation wind turbine blade in the DLC-1 case. From Figure 6a and Table 5, the stress levels in the X direction were the largest, resulting from the waving force (i.e., wind speed incoming flow direction). The maximum tensile and compressive stresses were 45.56 and 49.72 MPa, which are less than the corresponding allowable stress of GFRP. The maximum tensile and compressive stresses in the Y direction were 27.49 and 16.76 MPa, and the values in the Z direction were 17.66 and 12.72 MPa, respectively. The aforementioned stress values were within the allowable stress ranges. Moreover, the maximum displacement of the blade tip was 4.38 m, which was also less than 9 m. Thus, the overall stress and displacement indexes met the design requirements. Figure 6b illustrates the stress contours of the web of the first generation blade. The stresses in the X, Y and Z directions were less than the overall stresses, indicating that the reverse designed web structure satisfied the stress requirements. Figure 6c exhibits the local stress contours of the web in the X, Y and Z directions. It can be seen that the high stress levels were concentrated at the web notch location, which was

due to the discontinuity of the designed web. Likewise, all the local stresses were within the requirements of stress. Based on the above-mentioned results, the preliminary design of the first generation turbine blade driven by the topology optimization was reasonable, but the blade is prone to fatigue damage in the long-term service. Thus, the fatigue life should be also considered as an important evaluation index of safety. Figure 6d and Table 5 demonstrate the fatigue life results in the X, Y and Z directions. The minimum fatigue lives in the X and Y directions were 1.27 × <sup>10</sup><sup>9</sup> and 6.45 × 108, both of which meet the fatigue life requirements. However, from Figure 6d, the fatigue life levels at the discontinuous location of the web were considerably lower. The minimum fatigue life in the Z direction was 8.97 × 107, which does not meet the requirement. Therefore, the first generation blade structure at the local position should be further modified. In this work, we directly connected the middle discontinuous region using a web structure and the second generation wind turbine blade was generated, see Figure 6e.

**Figure 5.** Reverse design of the wind turbine blade. (**a**) Turbine blade with the optimal internal structure. (**b**) Reverse design of turbine blade inspired by the topology optimization. (**c**) First generation turbine blade.

**Figure 6.** Validation of performance indexes for the first generation wind turbine blade in the DLC-1 case. (**a**) Stress and deformation contours of overall turbine blade. (**b**) Stress contours of internal structure. (**c**) Stress contours of localized regions of internal structure. (**d**) Fatigue life contours of whole turbine blade (**e**) The second generation design of the wind turbine blade.

**Table 5.** Simulation results of the first generation wind turbine blade in the DLC-1 case.


Figure 7 shows the simulation results of the second generation wind turbine blade in the DLC-1, 2 and 3 cases. Table 6 compared results of performance indexes between the first and second generation wind turbine blades in the DLC-1 case. Compared with the performance indexes of the first generation blade in the DLC-1 case, the overall maximum tensile stress of the blade in the X direction was slightly changed, but the maximum compressive stress in the Y direction was reduced by 18.79%. It is worth noting that the maximum localized tensile and compressive stresses of the web in the Z direction were remarkably decreased by 97.05 and 95.17%, respectively. Furthermore, the maximum displacement of the blade tip was 4.03 m, which was also reduced by 7.99%. All the stress and displacement indexes met the design requirements. Importantly, after connecting the discontinuous region by the additional web, the minimal fatigue life of the web was 2.25 × <sup>10</sup>8, significantly improved by 150.84%, which achieved the requirement of fatigue life.

In addition, the overall stress contours of the second blade in the X, Y and Z directions were similar to those of the first blade (Figure 7a,b). The stress levels in the X direction were higher than those in the Y and Z directions. From Figure 7c, the stress levels at the local region in three directions were relatively uniform, indicating that the stress concentration had been accommodated by adding additional web structure in this region. Furthermore, the maximum tensile stresses were still less than the allowable ones. In summary, the design strategy for the internal structure of the second generation wind turbine blade is

a feasible solution. In the following discussion, the performance indexes of the blade are further evaluated in the DLC-2 and DLC-3 cases.

**Figure 7.** Validation of performance indexes for the second generation wind turbine blade in the DLC-1, DLC-2 and DLC-3 cases. (**a**,**e**,**i**) Stress and deformation contours of whole turbine blade. (**b**,**f**,**j**) Stress contours of internal structure. (**c**,**g**,**k**) Stress contours of localized regions of internal structure. (**d**,**h**,**l**) Fatigue life contours of whole turbine blade.

Figure 7 and Table 7 exhibit the validation results of the second blade in the X, Y and Z directions in the DLC-2 case. The overall stress distribution contours of the blade in the X, Y and Z directions were totally consistent with those of the first blade, and the maximum tensile and compressive stresses meet the stress requirements. The maximum displacement was only 1.18 m, which also meets the design allowable value. Compared to the performance indexes of the first blade, the stress and deformation responses of the second blade were relatively lower. It should be noted that the wind turbine obtained an additional torque in this case, and the outer part of the blade had a negative angle of attack which to some extent counteracted the internal lift. Although the turbine operated at a higher wind speed, the aerodynamic load acting at the blade tip was weaker than that in the DLC-1 case. Additionally, the minimal fatigue life also achieved the design requirement. Consequently, all the performance indexes of the second turbine blade met the design requirements, confirming that it was also a feasible solution in the DLC-2 case. In addition, Figure 7 and Table 7 also show the validation results of the second blade in the X, Y and Z directions in the DLC-3 case. In this case, the wind turbine was suffering from typhoon conditions, and the blade was in the down pitch stop state. The maximum displacement of blade tip was 2.28 m and the minimum fatigue life was 3.90 × 108, both of which met the design requirements. Furthermore, it can be seen from the stress contours that the middle stress levels in the X direction were slightly higher, giving an indication of stress concentration in the region. However, those in the Y and Z directions were relatively uniform. All the stress indexes were within the requirements. Therefore, the second turbine blade was also a feasible design in the DLC-3 case.

**Table 6.** Compared results of performance indexes between the first and second generation wind turbine blades in the DLC-1 case.


**Table 7.** Simulation results of the second generation wind turbine blade in the DLC-1, 2 and 3 cases. Unit in stress: MPa, in displacement of tip: m.


Note: "Disp" means displacement. "TS" and "CS" mean tensile stress, compressive stress.

In summary, a novel turbine blade with the optimal web structure guided by the topology optimization was accomplished.

#### **4. Discussion**

#### *4.1. Comparison of Performance Indexes between the Novel and Reference Turbine Blades*

Table 8 lists the compared results of the performance indexes between the novel and reference turbine blades. Overall, the stress levels of the novel blade were lower than those of the reference blade. Note: a positive value in Table 8 represents the increase in performance index. The displacement values of the novel blade in various load cases were larger than those of the reference blade, indicating that a more flexible blade was obtained in this work. Importantly, the weight of the novel blade was reduced by 9.88% relative to the reference blade, which is a significant benefit in decreasing the cost of turbine blades. Therefore, the novel wind turbine blade driven by topology optimization in this work has predictably better power efficiency than the reference blade without the loss of load-bearing capacity.

**Table 8.** Compared results of performance indexes between the novel and reference turbine blades. Unit in stress: MPa, in displacement of tip: m, in overall weight: kg.


Note: "Dir.", "Ref." and "Nov." mean "Direction", "Reference" and "Novel", respectively.

*4.2. Modal Analysis of the Novel Wind Turbine Blade*

As the decrease of blade weight, the vibration problem of the novel wind turbine blade should be discussed to further identify the dynamic properties. In this work, the modal analysis was also carried out based on the novel blade, see Figure 8 and Table 9. It can be seen from Figure 8, the first six orders of the novel turbine blade include: first order waving vibration, second order pendulum vibration, third order waving vibration, fourth order waving vibration, fifth order waving vibration and sixth waving pendulum, which are similar to those of the reference blade. The vibration types of the blade are mainly dominated by waving and pendulum vibrations. Moreover, from Table 9, it can be seen that the first six order frequencies were well in agreement with those of the reference blade, indicating that the designed internal layout is reasonable.

**Figure 8.** Vibration types of the novel and reference turbine blades.


**Table 9.** Comparison of frequency between the novel and reference turbine blades.

#### *4.3. Full Life Cycle Assessment of the Novel Wind Turbine Blade*

The service life of a wind turbine is generally more than 20 years. During long-term service, wind turbine blades are always subjected to complex aerodynamic loads induced by wind, with the result that it is very susceptible to fatigue damage and failure. Hence, to ensure the long-term service safety, a full life-cycle assessment of the novel wind turbine blade should be discussed in this work. According to the wind speed data of a full year in Guangdong Province, the wind speed range from 5–25 m/s was considered in this work, see Table 10. The statistical duration of wind speed in an hour can be obtained through the Weibull distribution, see Table S3, SI. Based on the finite element analysis given in Section 3, the stress responses of the novel blade were obtained, see Table 10. Considering the S-N curve of GFRP used as the shell composite material (Table S4, SI), the fatigue lives of turbine blades corresponding to the wind speed were calculated though the Goodman curve, see Table 10. Afterwards, the fatigue damage with respect to each wind speed was obtained via the ratio of stress range in the Weibull distribution and the related fatigue life (Table 10). Finally, the full life of the novel blade over 20 years was evaluated based on the linear P-M accumulative damage theory, viz:

$$\begin{array}{l} Y = \frac{N}{N' \times \omega \times 60} = \frac{1/(\sum\_{i} \gamma\_{i}/N\_{i})}{N' \times \omega \times 60} \\\ = \frac{1/(\frac{0.197}{1.70 \times 10^{8}} + \frac{0.15}{1.60 \times 10^{8}} + \frac{0.101}{1.05 \times 10^{8}} + \frac{0.061}{1.08 \times 10^{8}})}{7250 \times 12.1 \times 60} = 21.9 \text{ Year} \end{array} \tag{7}$$

where *Y* is the full life; *ω* is the rated speed of turbine blade, taken as 12.1 RPM (Table 2); *N* is the sum of duration of wind speed in hours; *γ<sup>i</sup>* is the stress range Weibull distribution; *Ni* is the fatigue life corresponding to wind speed. Consequently, the full life over the 20 years is 21.9 years, which meets the design requirement of 20 years.


**Table 10.** Wind speed distribution and fatigue damage in a year.

#### **5. Conclusions**

This work develops an innovative multi-web internal layout for the offshore wind turbine blade in accordance with the variable density topology optimization method, which theoretically answers the proposed scientific issues about how many webs need to be used inside the blade and where the related webs should be laid out. The following conclusions can be summarized as follows:


**Supplementary Materials:** The following supporting information can be downloaded at: https://www. mdpi.com/article/10.3390/jmse10101487/s1, Figure S1: *y*<sup>+</sup> values for evaluating the mesh quality under the different wind speeds; Figure S2: Illustration of the relationship between the amount of element and torque; Table S1: Distributed blade aerodynamic properties in NREL 5 MW wind turbine blade; Table S2: Mesh independence analysis; Table S3: Statistic duration of wind speed in hour; Table S4: S-N data of GFRP.

**Author Contributions:** J.S.: writing—original draft, reviewing, project administration and supervision; J.C.: writing—original draft, reviewing and validation; Y.W.: review, editing and validation; L.L.: conceptualization and supervision. All authors have read and agreed to the published version of the manuscript.

**Funding:** The support for this research has been provided by the National Natural Science Foundation of China (Grant No. 51905350), the Shenzhen Science and Technology Program (Grant No. KQTD20200820113004005), Shenzhen Key Laboratory of Structure Safety and Health Monitoring of Marine Infrastructures (Grant No. ZDSYS20201020162400001) and the National Natural Science Foundation of Guangdong Province (Grant No. 2022A1515011499) are gratefully acknowledged.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

#### **References**

