Optimization of the Energy Capture Performance of the Lift-Drag Hybrid Vertical-Axis Wind Turbine Based on the Taguchi Experimental Method and CFD Simulation

: In order to improve the energy capture performance of vertical axis lift wind turbines in a low wind speed environment, the drag wind turbine is employed to couple with the design of existing vertical axis lift wind turbines. In contrast to the existing literature, in this work, a computational model is proposed that can simulate the interaction between the turbine and the ﬂuid. The effects of pitch angle ( β ), installation angle ( θ ), overlap ratio ( ε ) and diameter ratio (DL) on the energy capture performance of hybrid vertical axis wind turbines are systematically analyzed based on Taguchi and CFD methods. The results show that under the optimized parameter combination, the peak energy capture coefﬁcient of the lift-drag hybrid wind turbine can be increased to 0.2328, compared with 0.0309 and 0.0287 of the pure lift and drag turbine, respectively. In addition, the result of the prototype test show that the optimized hybrid wind turbine not only has a better-starting performance but also has 2.0 times the output power of that of the lift wind turbine.


Introduction
Increasing the proportion of clean energy in the energy consumption structure, reducing greenhouse gas emissions, and responding to the call of the Paris Agreement is of great significance for the survival of all humanity [1]. In the process of clean energy research, wind energy resources with clean, pollution-free, and renewable characteristics have attracted increasing attention in recent years [2,3]. According to their different rotational shaft arrangements, wind energy capture machinery can be divided into horizontal axis wind turbines (HAWTs) and vertical axis wind turbines (VAWTs) [4][5][6][7][8]. Until now, the HAWT has been the main model in the wind turbine market due to its higher efficiency in capturing wind energy. However, in the urban environment with variable wind direction, obvious turbulence effect, low wind speed, and requirements for noise emission, the VAWT has more advantages [9][10][11][12].
Conventional VAWTs can be divided into two types, namely, Darrieus and Savonius. It is generally believed that the Darrieus wind turbine has a high wind energy capture efficiency at a high tip speed ratio, while its stall is serious at a low tip speed ratio, leading to reduced energy capture performance and even self-start failure [13][14][15]. To improve the self-starting ability of the Darrieus-type wind turbine, many methods have been carried out, such as modifying the airfoil of the blade, increasing the solidity of the wind turbine, adding auxiliary wind-catching devices, and using active and passive pitching angle mechanisms to inhibit the stall of the blade. Sridhar studied the impact of diffusers on the aerodynamic performance of wind turbines [1]. They found that diffusers can improve the performance of wind turbines, and wind turbines with slotted diffusers have the highest and lowest performance. Afterward, they also studied the aerodynamic performance of wind turbines with tubercles [16] and found that this structure can effectively control the dynamic stall of wind turbines and reduce their noise emissions. Tong analyzed the impact of chord-todiameter ratio on the aerodynamic performance of straight blade wind turbines [7]. The analysis results showed that when the chord length is fixed, the optimal chord-to-diameter ratio is 8%, while when the diameter is fixed, the optimal range of chord to diameter ratio is 10-13%. In addition to the methods mentioned above to improve the performance of wind turbines, the hybrid turbine design is prevailing due to its manufacturing-friendly, simple control system and excellent energy capture performance at low wind speed [17]. Therefore, the combined design of the Savonius and Darrieus wind turbines can improve the energy capture performance of the Darrieus wind turbines, especially in a low wind speed environment. Fang Feng designed a VAWT with a combination of lift and drag and studied in detail the impact of blade number changes on the performance of the VAWT through a combination of CFD simulation and experiments [18]. The research results indicate that the lift-drag hybrid wind turbine with three blades has the best static starting characteristics. Bhuyan and Biswas studied the aerodynamic performance of the Darrieus-Savonius hybrid wind turbine, and the experimental results showed that the designed hybrid wind turbine has self-start capability at all azimuth angles [19]. Ghosh analyzed the aerodynamic performance of the Darrieus-Savonius hybrid wind turbine with three blades by numerical calculation and concluded that under any TSR, Savonius installed under Darrieus would have higher energy capture power than that installed above it [20]. Sahim investigated the influence of radius ratio on the aerodynamic performance of Darrieus-Savonius hybrid wind turbines and found that the larger the radius ratio, the lower the power coefficient [21]. Asadi and Hassanzadeh investigated the influence of installation angles on the performance of hybrid wind turbines under different tip speed ratios [22]. The results showed that the influence of installation angle on the performance of hybrid wind turbines is related to the incoming wind speed and the tip-to-speed ratio (TSR). When TSR = 1.5 and 2.5, the hybrid wind turbine with a 45 • installation angle has a higher power coefficient. Gupta conducted wind tunnel experiments to study the aerodynamic performance of the Savonius 2-blade and Darrieus 3-blade hybrid wind turbines with overlap ratios of 16% and 20%. The experimental results showed that the energy capture efficiency of hybrid wind turbines could reach 25% when the overlap ratio is 20% [23]. Subsequently, they also compared the aerodynamic performance of the 3-blade Savonius and 3-blade Darrieus hybrid wind turbines with different overlap ratios and concluded that hybrid wind turbines have better energy capture performance under the condition of no overlap ratio [24]. Liang analyzed the influence of radius ratio and installation angle on start-up performance and energy capture efficiency of hybrid wind turbine [25]. The results showed that the start torque of the optimized hybrid wind turbine is less than 0.1 N·M at a wind speed of 2 m/s.
The aforementioned studies conclude that the lift-drag hybrid wind turbine has better energy capture performance at low wind speeds. Nevertheless, it is noted that these studies carry out the aerodynamics simulation of the wind turbine by fixing its rotational angular velocity without considering the interaction between the wind turbine blade and the fluid flow and the influence of the coupling between various parameters of the lift-drag hybrid wind turbine on the aerodynamic performance of the turbine. Therefore, the aerodynamic performance of the hybrid wind turbine has not been fully understood. This paper develops a set of calculation programs that can effectively solve the interaction between a wind turbine and fluid flow and combine the Taguchi test method to optimize the aerodynamic performance of the hybrid wind turbine. Finally, a detailed comparison between the lift and the drag-dominant wind turbine is summarised for the performance study of the optimized hybrid wind turbine; a detailed comparison will be made between the lift wind turbine and the drag wind turbine. The findings of this study provide theoretical guidance for the development of hybrid wind turbines that can achieve improved energy capture efficiency and self-starting performance in their design.

Physical Model Description
The model of the lift-drag hybrid wind turbine studied in this paper is shown in Figure 1, consisting of a three-bladed straight Darrieus rotor and a three-bladed semicircle Savonius rotor. Where β is the pitch angle of the Darrieus wind turbine, D L is the radius ratio of the hybrid wind turbine, θ is the installation angle of the Savonius wind turbine relative to the Darrieus wind turbine, and ε is the overlap ratio of the Savonius wind turbine. ε and D L can be defined as follows: where d is the diameter of the Savonius rotor, R D is the rotation radius of the Darrieus rotor, and S is the radius from the outer edge of the Savonius blade to the center of the rotating shaft. In the subsequent analysis, except for the pitch angle, other characteristic parameters of the three-blade Darrieus turbine are fixed, and the specific values are shown in Table 1. theoretical guidance for the development of hybrid wind turbines that can achieve improved energy capture efficiency and self-starting performance in their design.

Physical Model Description
The model of the lift-drag hybrid wind turbine studied in this paper is shown in Figure 1, consisting of a three-bladed straight Darrieus rotor and a three-bladed semicircle Savonius rotor. Where β is the pitch angle of the Darrieus wind turbine, DL is the radius ratio of the hybrid wind turbine, θ is the installation angle of the Savonius wind turbine relative to the Darrieus wind turbine, and ε is the overlap ratio of the Savonius wind turbine. ε and DL can be defined as follows: where d is the diameter of the Savonius rotor, RD is the rotation radius of the Darrieus rotor, and S is the radius from the outer edge of the Savonius blade to the center of the rotating shaft. In the subsequent analysis, except for the pitch angle, other characteristic parameters of the three-blade Darrieus turbine are fixed, and the specific values are shown in Table 1.

Calculation Model of the Interaction between Hybrid Turbine and Fluid
In this paper, the fluid flow at low wind speeds (specifically, at a wind speed of 6 m/s) was studied, with the governing equation of the hybrid wind turbine's flow field being the incompressible turbulent Navier-Stokes equation: where u i and u j are the velocity vector, P is the pressure, ρ is the wind density, µ is the hydrodynamic viscosity, −ρu i u j is the Reynolds stresses, k v and µ t are the turbulent kinetic energy and turbulent viscosity, δ ij is the kronecker function. The Fluent fluid solver is used to solve the governing Equation (3). According to the research on the Darrieus wind turbine studied by Sun [26], the S-A turbulence model can effectively capture the flow field of the wind-induced motion of VAWT. Therefore, this paper adopts the S-A turbulence model to solve the governing equation.
In order to realize the passive rotation of a hybrid wind turbine on the basis of a Fluent fluid solver, the governing equation of wind turbine rotation is coupled with a Fluent solver through UDF, and the specific solution process is shown in Figure 2.

Calculation Model of the Interaction between Hybrid Turbine and Fluid
In this paper, the fluid flow at low wind speeds (specifically, at a wind speed of 6 m/s) was studied, with the governing equation of the hybrid wind turbine's flow field being the incompressible turbulent Navier-Stokes equation: where ui and uj are the velocity vector, P is the pressure, ρ is the wind density, µ is the hydrodynamic viscosity, − is the Reynolds stresses, kv and µt are the turbulent kinetic energy and turbulent viscosity, δij is the kronecker function.
The Fluent fluid solver is used to solve the governing Equation (3). According to the research on the Darrieus wind turbine studied by Sun [26], the S-A turbulence model can effectively capture the flow field of the wind-induced motion of VAWT. Therefore, this paper adopts the S-A turbulence model to solve the governing equation.
In order to realize the passive rotation of a hybrid wind turbine on the basis of a Fluent fluid solver, the governing equation of wind turbine rotation is coupled with a Fluent solver through UDF, and the specific solution process is shown in Figure 2.  where I is the moment of inertia, is the angular acceleration, is the aerodynamic torque received by the wind turbine, is the electromagnetic resistance torque and mechanical friction torque of the wind turbine. In this study, it is assumed that there is a linear relationship between and : The governing equation of passive rotation of a lift-drag hybrid wind turbine can be derived from Newton's second law: where I is the moment of inertia, ..
θ is the angular acceleration, M wind is the aerodynamic torque received by the wind turbine, M f riction is the electromagnetic resistance torque and mechanical friction torque of the wind turbine. In this study, it is assumed that there is a linear relationship between M f riction and .
θ: Thus, the governing Equation (4) can be rewritten as: On the other hand, the second derivative term in the governing Equation (6) can be solved by the central difference method: ..
In addition, the governing Equation (7) can be rewritten as: where ∆t is the time step, t − ∆t, ∆t, t + ∆t is the time of the corresponding moment. Moreover, the value of k, which measures the frictional resistance, is fixed at 0.0043 kg·m 2 /s in this paper. This value serves to reflect the inhibiting effect of frictional resistance on the operation of wind turbines. The specific value of friction resistance needs to be measured through experiments. With aerodynamic torque M wind and angular velocity θ, the power generated by the wind turbine and the energy capture coefficient can be calculated: Since the wind energy capture coefficient changes with azimuth angle in a rotation period, in order to compare the aerodynamic performance of different wind turbines, researchers use the average wind energy capture coefficient in a stable rotation period as the evaluation index of wind turbine performance:

Computing Domain and Grid Generation
The flow field of the hybrid wind turbine is simplified as a rectangle calculation domain. Figure 3 shows the shape, size, and setting of boundary conditions of the whole computational domain. The distances from the left and right boundaries of the calculation domain to the center of the rotating shaft of the hybrid wind turbine are set as 5D and 20D, respectively, and the distances from the upper and lower boundaries to the center of the rotating shaft are set as 12.5D. According to the results of Bouhal [27], when the boundary of the calculation domain is set to the above size, a further increase in the calculation domain will have a small impact on the numerical calculation results.
In order to capture the details of fluid flow around the blade of the hybrid wind turbine, the computational domain is divided into two parts: the stationary domain and the rotating domain. Hybrid wind turbine blades are in the rotation domain. During the passive rotation of the wind turbine, the grid in the rotation domain remains unchanged and rotates with the passive rotation of the wind turbine. The grid reconstruction is limited to the interface between the stationary domain and the rotation domain. The left boundary of the calculation domain is set as the velocity inlet boundary condition, the wind speed is set to 6 m/s, and the turbulence intensity is set to 5%. The right side of the calculation domain is set as the pressure outlet boundary condition, and the static pressure value is set as 0. To reduce the influence of the blockage effect on simulation results, the upper and lower boundaries of the calculation domain are set as symmetric boundary conditions [28]. The blade surface is set as a non-slip interface. In order to better capture the details of fluid flow around the blade, 15 layers of the boundary layer are set on the near wall of the blade to ensure that the Y + value is below 1 (which is based on the NASA y + calculator http://www.pointwise.com/yplus/URL (accessed on 27 June 2022)).
Sustainability 2023, 15, x FOR PEER REVIEW 6 of 21 set as 0. To reduce the influence of the blockage effect on simulation results, the upper and lower boundaries of the calculation domain are set as symmetric boundary conditions [28]. The blade surface is set as a non-slip interface. In order to better capture the details of fluid flow around the blade, 15 layers of the boundary layer are set on the near wall of the blade to ensure that the Y + value is below 1 (which is based on the NASA y + calculator http://www.pointwise.com/yplus/URL (accessed on 27 June 2022)).

Mesh Density Verification
To analyze the influence of grid density variation on the numerical calculation results, three different grid systems are used to calculate the flow field of the lift-drag hybrid wind turbine. The specific division methods of different grid systems are shown in Table  2. Figure 4 shows the curve of the angular velocity of the hybrid wind turbine calculated by three different grid systems. It can be found from the figure that the time-dependent curve of angular velocity calculated by grid system two and grid system 3 is almost identical, while the time-dependent curve of angular velocity calculated by grid system 1 and grid system 3 is obviously different. Therefore, grid system two is used as the grid system for subsequent numerical analysis.

Mesh Density Verification
To analyze the influence of grid density variation on the numerical calculation results, three different grid systems are used to calculate the flow field of the lift-drag hybrid wind turbine. The specific division methods of different grid systems are shown in Table 2. Figure 4 shows the curve of the angular velocity of the hybrid wind turbine calculated by three different grid systems. It can be found from the figure that the time-dependent curve of angular velocity calculated by grid system two and grid system 3 is almost identical, while the time-dependent curve of angular velocity calculated by grid system 1 and grid system 3 is obviously different. Therefore, grid system two is used as the grid system for subsequent numerical analysis.

Verifying the Time Step
To analyze the influence of time steps on the numerical simulation results, three-time steps ∆t = 0.0003 s, ∆t = 0.00015 s, ∆t = 0.0001 s are used for the numerical calculation of the hybrid wind turbine, and the results are shown in Figure 5. As can be seen in Figure 5 that the torque curve calculated by the three-time steps has a similar change trend with time, while the torque curve calculated by ∆t = 0.0003 s and ∆t = 0.0001 s have an obvious difference when the azimuth angle is 60° and 300°.The torque curves calculated by ∆t = 0.00015 s and ∆t = 0.0001 s almost coincide in the whole rotation period. Therefore, in the subsequent numerical analysis, the time step is fixed at ∆t = 0.00015 s.

Model Verification
In order to verify whether the developed calculation program can effectively simulate the interaction between a hybrid wind turbine and fluid flow, the same wind turbine model as Rainbird [29] is established in this work, and the specific model settings are shown in Table 3.

Verifying the Time Step
To analyze the influence of time steps on the numerical simulation results, three-time steps ∆t = 0.0003 s, ∆t = 0.00015 s, ∆t = 0.0001 s are used for the numerical calculation of the hybrid wind turbine, and the results are shown in Figure 5. As can be seen in Figure 5 that the torque curve calculated by the three-time steps has a similar change trend with time, while the torque curve calculated by ∆t = 0.0003 s and ∆t = 0.0001 s have an obvious difference when the azimuth angle is 60 • and 300 • .The torque curves calculated by ∆t = 0.00015 s and ∆t = 0.0001 s almost coincide in the whole rotation period. Therefore, in the subsequent numerical analysis, the time step is fixed at ∆t = 0.00015 s.

Verifying the Time Step
To analyze the influence of time steps on the numerical simulation results, three-time steps ∆t = 0.0003 s, ∆t = 0.00015 s, ∆t = 0.0001 s are used for the numerical calculation of the hybrid wind turbine, and the results are shown in Figure 5. As can be seen in Figure 5 that the torque curve calculated by the three-time steps has a similar change trend with time, while the torque curve calculated by ∆t = 0.0003 s and ∆t = 0.0001 s have an obvious difference when the azimuth angle is 60° and 300°.The torque curves calculated by ∆t = 0.00015 s and ∆t = 0.0001 s almost coincide in the whole rotation period. Therefore, in the subsequent numerical analysis, the time step is fixed at ∆t = 0.00015 s.

Model Verification
In order to verify whether the developed calculation program can effectively simulate the interaction between a hybrid wind turbine and fluid flow, the same wind turbine model as Rainbird [29] is established in this work, and the specific model settings are shown in Table 3.

Model Verification
In order to verify whether the developed calculation program can effectively simulate the interaction between a hybrid wind turbine and fluid flow, the same wind turbine model as Rainbird [29] is established in this work, and the specific model settings are shown in Table 3.   Figure 6 shows the comparison of the current CFD calculation results, the experimental and numerical results from Rainbird [29] and Hill [30]. The dimensionless time axis t * (t * = t/T) is used in the figure, where T is the time when the wind turbine reaches the stable speed. It can be seen from Figure 6 that the current CFD model can accurately predict the wind turbine start-up process. The difference between the predicted results and the experimental results is due to the neglect of the 3D effect, mechanical friction loss and other factors in the 2D simulation [29].   Figure 6 shows the comparison of the current CFD calculation results, the experimental and numerical results from Rainbird [29] and Hill [30]. The dimensionless time axis * ( * = / )is used in the figure, where T is the time when the wind turbine reaches the stable speed. It can be seen from Figure 6 that the current CFD model can accurately predict the wind turbine start-up process. The difference between the predicted results and the experimental results is due to the neglect of the 3D effect, mechanical friction loss and other factors in the 2D simulation [29].  [29] and Hill et al. [30]).

Taguchi Experimental Design and Its Results Analyzing
The Taguchi test method is an optimal design method that can obtain the ideal experimental effect with the least number of tests [31]. In this paper, the effects of pitch angle, installation angle, overlap ratio and diameter ratio on the aerodynamic performance of lift-drag hybrid wind turbine are systematically studied by combining CFD and Taguchi test. Five levels of the above four factors are selected. Table 4 shows the value of each factor level. Based on the characteristic parameters in Table 4, the designed Taguchi test is shown in Table 5.

Taguchi Experimental Design and Its Results Analyzing
The Taguchi test method is an optimal design method that can obtain the ideal experimental effect with the least number of tests [31]. In this paper, the effects of pitch angle, installation angle, overlap ratio and diameter ratio on the aerodynamic performance of lift-drag hybrid wind turbine are systematically studied by combining CFD and Taguchi test. Five levels of the above four factors are selected. Table 4 shows the value of each factor level. Based on the characteristic parameters in Table 4, the designed Taguchi test is shown in Table 5.  In the Taguchi test, the signal-to-noise ratio is the core index to analyze and evaluate the scheme, and its definition is given by: S/N = −10 log 10 1 In this study, η in the formula represents the average wind energy capture coefficient. The SNR models can be divided into the larger-the-better model, the smaller-the-better model and the nominal-the-better model. In this paper, the average wind energy capture coefficient of wind turbines is taken as the index to measure the optimal design, which conforms to the larger-the-better model. Table 6 shows the average wind energy capture coefficient and the signal-to-noise ratio of the hybrid wind turbine under different combinations of parameters obtained by CFD calculation. The sixth test group can be found to have the largest SNR, the value is 15.94, and the 23rd test group has the smallest SNR, the value is −100. What needs to be explained here is that the CFD calculation results of the 23rd group of tests show that the wind turbine cannot start itself, and the wind turbine shows an oscillation trend after a little rotation, which indicates that the hybrid wind turbine under this parameter combination does not have the capacity of capturing energy. In order to facilitate the analysis, the average wind energy capture coefficient is set to 0.00001%.  In addition, the Taguchi test method can also predict the degree of influence of each factor on the energy capture efficiency of the wind turbine. The degree of influence of each parameter on the energy capture efficiency is determined by M j , which depends on the difference between the maximum average SNR and the minimum average SNR of each factor: where G ji represents the average SNR of each parameter at the level of I = 1, 2, 3, 4 and 5, the average SNR of each feature parameter at different levels and the degree of influence of each parameter are shown in Table 7.  Figure 7 shows the average SNR for each factor level. It can be seen from Figure 7 that the average SNR of β and ε first increases with increasing levels and then decreases after reaching the maximum value. However, the average SNR of θ and D L shows a trend of first decreasing, then increasing and finally decreasing. Figure 8 shows the variation M j with different parameters. It can be found from Figure 8 that the degree of influence of each factor on wind turbine energy capture efficiency is: β > ε > D L > θ, which indicates that the pitch angle has the greatest effect on the aerodynamic performance of hybrid wind turbines, while the installation angle has the least effect. after reaching the maximum value. However, the average SNR of θ and shows a trend of first decreasing, then increasing and finally decreasing.

Analysis of the Intra-Navigation Mechanism of the Influence of Different Combinations of the Parameters on the Aerodynamic Performance of Hybrid Wind Turbines
According to the analysis above, it is found that the hybrid wind turbine has the best performance under the sixth test condition, with an average energy capture coefficient of 6.35%, while the pure lift wind turbine and the Savonius wind turbine with the same parameters have an average energy capture coefficient of 0.73% and 1.62%, respectively. To explore the intrinsic mechanism of the improvement of the energy-capturing performance of the hybrid wind turbine, a detailed comparison of the aerodynamic performance of the

Analysis of the Intra-Navigation Mechanism of the Influence of Different Combinations of the Parameters on the Aerodynamic Performance of Hybrid Wind Turbines
According to the analysis above, it is found that the hybrid wind turbine has the best performance under the sixth test condition, with an average energy capture coefficient of 6.35%, while the pure lift wind turbine and the Savonius wind turbine with the same parameters have an average energy capture coefficient of 0.73% and 1.62%, respectively. To explore the intrinsic mechanism of the improvement of the energy-capturing performance of the hybrid wind turbine, a detailed comparison of the aerodynamic performance of the

Analysis of the Intra-Navigation Mechanism of the Influence of Different Combinations of the Parameters on the Aerodynamic Performance of Hybrid Wind Turbines
According to the analysis above, it is found that the hybrid wind turbine has the best performance under the sixth test condition, with an average energy capture coefficient of 6.35%, while the pure lift wind turbine and the Savonius wind turbine with the same parameters have an average energy capture coefficient of 0.73% and 1.62%, respectively. To explore the intrinsic mechanism of the improvement of the energy-capturing performance of the hybrid wind turbine, a detailed comparison of the aerodynamic performance of the hybrid wind turbine with the lift and drag wind turbines will be carried out in the following. Figure 9 shows the curve of angular velocity change of the optimized hybrid wind turbine, the lift wind turbine, and the drag wind turbine under the same conditions. It can be seen from Figure 9 that in the starting phase, the angular speeds of hybrid wind turbines and drag wind turbines both increase rapidly, and both generate similar angular accelerations, indicating that the hybrid wind turbine inherits the starting performance of drag wind turbines at low wind speeds. In addition, it can also be found that the stable angular velocity of the hybrid wind turbine reaches 33.58 rad/s, which is much higher than the 11.57 rad/s of the lift wind turbine and 17.28 rad/s of the drag wind turbine. In summary, it can be found that the hybrid wind turbine not only improves the starting performance of the wind turbine but also can achieve greater stable speed. Figure 9 shows the curve of angular velocity change of the optimized hybrid wind turbine, the lift wind turbine, and the drag wind turbine under the same conditions. It can be seen from Figure 9 that in the starting phase, the angular speeds of hybrid wind turbines and drag wind turbines both increase rapidly, and both generate similar angular accelerations, indicating that the hybrid wind turbine inherits the starting performance of drag wind turbines at low wind speeds. In addition, it can also be found that the stable angular velocity of the hybrid wind turbine reaches 33.58 rad/s, which is much higher than the 11.57 rad/s of the lift wind turbine and 17.28 rad/s of the drag wind turbine. In summary, it can be found that the hybrid wind turbine not only improves the starting performance of the wind turbine but also can achieve greater stable speed. In order to explore the cause of this phenomenon, Figure 10 shows the torque change curve of a hybrid wind turbine, lift wind turbine and drag wind turbine in a stable period. It can be seen from Figure 10 that the hybrid wind turbine can generate the largest amplitude of aerodynamic torque, followed by the lift wind turbine and the drag wind turbine. Among them, the peak torque of the hybrid wind turbine reached 0.540 N·m, which is about 2.56 times the peak torque of 0.211 N·m for the pure lift wind turbine and 4.09 times the peak torque of 0.132 N·m for the drag wind turbine. It can also be found that the torque generated by the hybrid wind turbine in the azimuth angles of 3.361°-57.6°, 123.4°-177.3° and 243.4°-297.4° is not only less than that of the pure lift wind turbine but also negative in most of the range, which is very unfavorable for the start of the wind turbine. However, in other azimuths, the torque generated by hybrid wind turbines is much higher than that generated by pure lift wind turbines and drag wind turbines. On the contrary, it can be found that the drag wind turbine generates positive torque at all azimuths, which indicates that the drag wind turbine has a starting ability at any azimuths. On the basis of the above analysis, it can be concluded that although the hybrid wind turbine generates negative torque at some azimuth angles, it generates a greater average torque throughout the rotation cycle, which makes the wind turbine have a greater angular acceleration. In order to explore the cause of this phenomenon, Figure 10 shows the torque change curve of a hybrid wind turbine, lift wind turbine and drag wind turbine in a stable period. It can be seen from Figure 10 that the hybrid wind turbine can generate the largest amplitude of aerodynamic torque, followed by the lift wind turbine and the drag wind turbine. Among them, the peak torque of the hybrid wind turbine reached 0.540 N·m, which is about 2.56 times the peak torque of 0.211 N·m for the pure lift wind turbine and 4.09 times the peak torque of 0.132 N·m for the drag wind turbine. It can also be found that the torque generated by the hybrid wind turbine in the azimuth angles of 3.361 • -57.6 • , 123.4 • -177.3 • and 243.4 • -297.4 • is not only less than that of the pure lift wind turbine but also negative in most of the range, which is very unfavorable for the start of the wind turbine. However, in other azimuths, the torque generated by hybrid wind turbines is much higher than that generated by pure lift wind turbines and drag wind turbines. On the contrary, it can be found that the drag wind turbine generates positive torque at all azimuths, which indicates that the drag wind turbine has a starting ability at any azimuths. On the basis of the above analysis, it can be concluded that although the hybrid wind turbine generates negative torque at some azimuth angles, it generates a greater average torque throughout the rotation cycle, which makes the wind turbine have a greater angular acceleration. Figure 11 shows the change curve of the wind energy utilization coefficient of the hybrid wind turbine, the lift wind turbine and the drag wind turbine in a stable rotation cycle. It can be seen from Figure 11 that the trend change in the wind energy utilization coefficient is basically the same as that of the torque curve. The maximum wind energy utilization coefficient of the hybrid wind turbine can be as high as 0.2327 in some azimuths, which is much higher than 0.0309 for a lift wind turbine and 0.0287 for a drag wind turbine. However, the hybrid wind turbine also produces a large negative wind energy utilization coefficient in other azimuths, so the overall wind energy utilization coefficient is not high. Although the wind energy utilization coefficient of the drag-type wind turbine is positive at all azimuths, the value of the wind energy utilization coefficient is too small, resulting in its average value in a stable period being lower than that of the hybrid wind turbine. Furthermore, although the maximum value of the wind energy utilization coefficient of the drag wind turbine is smaller than that of the lift wind turbine, the average wind energy utilization coefficient of the drag wind turbine is greater than that of the lift wind turbine because the lift wind turbine has a negative wind energy utilization coefficient at some azimuth angles. In general, the average value of the wind energy utilization coefficient generated by hybrid wind turbines is higher.  Figure 11 shows the change curve of the wind energy utilization coefficient of the hybrid wind turbine, the lift wind turbine and the drag wind turbine in a stable rotation cycle. It can be seen from Figure 11 that the trend change in the wind energy utilization coefficient is basically the same as that of the torque curve. The maximum wind energy utilization coefficient of the hybrid wind turbine can be as high as 0.2327 in some azimuths, which is much higher than 0.0309 for a lift wind turbine and 0.0287 for a drag wind turbine. However, the hybrid wind turbine also produces a large negative wind energy utilization coefficient in other azimuths, so the overall wind energy utilization coefficient is not high. Although the wind energy utilization coefficient of the drag-type wind turbine is positive at all azimuths, the value of the wind energy utilization coefficient is too small resulting in its average value in a stable period being lower than that of the hybrid wind turbine. Furthermore, although the maximum value of the wind energy utilization coefficient of the drag wind turbine is smaller than that of the lift wind turbine, the average wind energy utilization coefficient of the drag wind turbine is greater than that of the lift wind turbine because the lift wind turbine has a negative wind energy utilization coefficient at some azimuth angles. In general, the average value of the wind energy utilization coefficient generated by hybrid wind turbines is higher.   Figure 11 shows the change curve of the wind energy utilization coefficient of the hybrid wind turbine, the lift wind turbine and the drag wind turbine in a stable rotation cycle. It can be seen from Figure 11 that the trend change in the wind energy utilization coefficient is basically the same as that of the torque curve. The maximum wind energy utilization coefficient of the hybrid wind turbine can be as high as 0.2327 in some azimuths, which is much higher than 0.0309 for a lift wind turbine and 0.0287 for a drag wind turbine. However, the hybrid wind turbine also produces a large negative wind energy utilization coefficient in other azimuths, so the overall wind energy utilization coefficient is not high. Although the wind energy utilization coefficient of the drag-type wind turbine is positive at all azimuths, the value of the wind energy utilization coefficient is too small, resulting in its average value in a stable period being lower than that of the hybrid wind turbine. Furthermore, although the maximum value of the wind energy utilization coefficient of the drag wind turbine is smaller than that of the lift wind turbine, the average wind energy utilization coefficient of the drag wind turbine is greater than that of the lift wind turbine because the lift wind turbine has a negative wind energy utilization coefficient at some azimuth angles. In general, the average value of the wind energy utilization coefficient generated by hybrid wind turbines is higher.

Comparative Analysis of Pressure Cloud Images
The pressure cloud diagram of a hybrid wind turbine, pure lift wind turbine and drag wind turbine is shown in Figure 12. Comparing the lift-type wind turbine with the hybrid-type wind turbine, it can be found that at the 0 • azimuth angle, the lift-type wind turbine has a positive pressure area due to the leading edge of blade 1, and the existence of this positive pressure area hinders the self-starting of the wind turbine. In contrast to the hybrid wind turbine, blade 1, blade 2, and blade 3 of the lift-type wind turbine have a larger positive pressure area and lower negative pressure area, resulting in greater starting torque. At the 24 • azimuth angle, the pressure center of the leading edge of blade 1 of the hybrid wind turbine is closer to the lower part of the airfoil. Although there is a larger negative pressure area in the abdomen of blade 2, it still has a negative impact on the wind turbine, which has been verified in Figure 10. At an azimuth angle of 48 • , there is little difference between the maximum positive pressure intensity generated by the lift wind turbine and the hybrid wind turbine at the leading edge of blade 1, but a lower negative pressure area is generated at the back of blade 1 of the hybrid wind turbine. At the azimuth angles of 72 • and 96 • , it can be seen that due to the existence of the pitch angle, the area of the high-pressure area in front of blade 1 of the hybrid wind turbine is larger, and the negative pressure area in the back is lower. In addition, it can be seen that the pressure distribution of blade 3 and blade 1 of a hybrid wind turbine is symmetrical, and a larger low-pressure area is generated outside blade 3. Although the performance of a hybrid wind turbine is worse than that of a pure lift wind turbine in some azimuth angles, it has better performance on the whole.
angles of 72° and 96°, it can be seen that due to the existence of the pitch angle, the area of the high-pressure area in front of blade 1 of the hybrid wind turbine is larger, and the negative pressure area in the back is lower. In addition, it can be seen that the pressure distribution of blade 3 and blade 1 of a hybrid wind turbine is symmetrical, and a larger low-pressure area is generated outside blade 3. Although the performance of a hybrid wind turbine is worse than that of a pure lift wind turbine in some azimuth angles, it has better performance on the whole.
Similarly, comparing the hybrid wind turbine with the drag wind turbine, it can be found that the drag wind turbine has a larger positive pressure area on the convex surface of the return blade, and there is an obvious strong pressure center in the positive pressure area. In addition, it can also be found that the pressure center has not changed in general during the rotation of the wind turbine, which has been hindering the rotation of the wind turbine. Looking back at the pressure distribution near the drag blade of the hybrid wind turbine, it can be found that, with the rotation of the wind turbine, the positive pressure area on the convex surface of the returning blade 1 at 0° azimuth angle first gradually decreases and then slowly increases, and the maximum pressure in the positive pressure area also shows a trend of decreasing first and then increasing. Furthermore, at azimuth angles of 0°, 24°, 72° and 96°, the negative pressure generated by the concave surface of return blade 2 and blade 3 of the hybrid wind turbine is significantly smaller.  Similarly, comparing the hybrid wind turbine with the drag wind turbine, it can be found that the drag wind turbine has a larger positive pressure area on the convex surface of the return blade, and there is an obvious strong pressure center in the positive pressure area. In addition, it can also be found that the pressure center has not changed in general during the rotation of the wind turbine, which has been hindering the rotation of the wind turbine. Looking back at the pressure distribution near the drag blade of the hybrid wind turbine, it can be found that, with the rotation of the wind turbine, the positive pressure area on the convex surface of the returning blade 1 at 0 • azimuth angle first gradually decreases and then slowly increases, and the maximum pressure in the positive pressure area also shows a trend of decreasing first and then increasing. Furthermore, at azimuth angles of 0 • , 24 • , 72 • and 96 • , the negative pressure generated by the concave surface of return blade 2 and blade 3 of the hybrid wind turbine is significantly smaller.
In summary, it can be found that the hybrid wind turbine performs better than the lift wind turbine in a larger azimuth range; Compared to the drag type wind turbine, the drag type wind turbine inside the hybrid wind turbine produces a smaller resistance torque.

Comparative Analysis of Flow Field Structure
In order to directly observe the difference in flow field changes between hybrid wind turbine, lift wind turbine and drag wind turbine, vorticity cloud charts of three wind turbines are drawn, as shown in Figure 13. It can be seen from Figure 13 that compared to the pure lift wind turbine, due to the existence of a drag wind turbine, the vortex on the surface of the outer lift wind turbine blade of the hybrid wind turbine is obviously suppressed. In the upwind area, the existence of a Savonius rotor improves the starting performance of the wind turbine, makes the wind turbine reach a higher tip speed ratio, and suppresses the vortex shedding phenomenon. In the downwind area, the shedding vortex of the Savonius blade interacts with the Darrieus blade, making the vortex cling to the surface of the outer lift wind turbine blade and improving the performance of the outer lift wind turbine blade in the downwind area. This is the internal reason why the hybrid wind turbine has better aerodynamic performance than the pure lift wind turbine.

Comparative Analysis of Flow Field Structure
In order to directly observe the difference in flow field changes between hybrid wind turbine, lift wind turbine and drag wind turbine, vorticity cloud charts of three wind turbines are drawn, as shown in Figure 13. It can be seen from Figure 13 that compared to the pure lift wind turbine, due to the existence of a drag wind turbine, the vortex on the surface of the outer lift wind turbine blade of the hybrid wind turbine is obviously suppressed. In the upwind area, the existence of a Savonius rotor improves the starting performance of the wind turbine, makes the wind turbine reach a higher tip speed ratio, and suppresses the vortex shedding phenomenon. In the downwind area, the shedding vortex of the Savonius blade interacts with the Darrieus blade, making the vortex cling to the surface of the outer lift wind turbine blade and improving the performance of the outer lift wind turbine blade in the downwind area. This is the internal reason why the hybrid wind turbine has better aerodynamic performance than the pure lift wind turbine. It can also be found from Figure 13 that, compared to the drag wind turbine, although a very complex vortex is generated inside the hybrid type wind turbine due to the existence of the overlap ratio, the vorticity generated inside the drag wind turbine is stronger, and the stronger separate vortex results in greater energy loss. In addition, at 0°, 24° and 48° azimuths, the concave surface of the return blade of the drag wind turbine also generates more separate vortex, and the wake generated by the drag wind turbine returning to the blade tip is closer to the rear blade, which has a greater impact on the rear blade. The hybrid wind turbine generates less vorticity inside, and the vorticity generated on the concave surface of the returning blade is less, and the wake on the return blade is farther away from the rear blade. These three phenomena cause the hybrid wind turbine to perform better than the single-drag wind turbine. It can also be found from Figure 13 that, compared to the drag wind turbine, although a very complex vortex is generated inside the hybrid type wind turbine due to the existence of the overlap ratio, the vorticity generated inside the drag wind turbine is stronger, and the stronger separate vortex results in greater energy loss. In addition, at 0 • , 24 • and 48 • azimuths, the concave surface of the return blade of the drag wind turbine also generates more separate vortex, and the wake generated by the drag wind turbine returning to the blade tip is closer to the rear blade, which has a greater impact on the rear blade. The hybrid wind turbine generates less vorticity inside, and the vorticity generated on the concave surface of the returning blade is less, and the wake on the return blade is farther away from the rear blade. These three phenomena cause the hybrid wind turbine to perform better than the single-drag wind turbine.
In summary, thanks to hybrid design, the hybrid wind turbine has achieved a higher tip speed ratio, the vortex shedding on the surface of the external lift blade of the hybrid wind turbine has been restrained, and the performance of the lifting blade in the downwind area has been improved; In the same way, the drag blades of hybrid wind turbines generate less vortex inside, and the shedding vortex has less influence on the returning blades. This is the reason why the hybrid wind turbine has better performance.

Experimental Setup
To verify that the hybrid wind turbine optimized by the Taguchi test has better aerodynamic performance, based on the above analysis, a prototype of the hybrid wind turbine and a prototype of the pure lift wind turbine are made using 3D printing technology, as shown in Figure 14. The experiment test for the prototype is carried out at a wind speed of 6 m/s. The prototype lift blades are made of resin, the main supporting parts are made of aluminum alloy, and the drag blades and other connecting parts are made of PLA. To reduce the mass, some hollow treatment was carried out on the blades. During the experiment, the support is connected at 1/2 chord length of the lifting blade. It should be noted that due to the limitation of experimental conditions, the incoming flow cannot be uniform. Therefore, the wind speed at four points on the upper, lower, left and right of the plane where the rotor axis of the wind turbine prototype is located was measured. The measurement results show that the maximum wind speed is 6.2 m/s, the minimum wind speed is 5.8 m/s, and the degree of incoming flow fluctuation is ±3.3%.

Experimental Setup
To verify that the hybrid wind turbine optimized by the Taguchi test has better aerodynamic performance, based on the above analysis, a prototype of the hybrid wind turbine and a prototype of the pure lift wind turbine are made using 3D printing technology, as shown in Figure 14. The experiment test for the prototype is carried out at a wind speed of 6 m/s. The prototype lift blades are made of resin, the main supporting parts are made of aluminum alloy, and the drag blades and other connecting parts are made of PLA. To reduce the mass, some hollow treatment was carried out on the blades. During the experiment, the support is connected at 1/2 chord length of the lifting blade. It should be noted that due to the limitation of experimental conditions, the incoming flow cannot be uniform. Therefore, the wind speed at four points on the upper, lower, left and right of the plane where the rotor axis of the wind turbine prototype is located was measured. The measurement results show that the maximum wind speed is 6.2 m/s, the minimum wind speed is 5.8 m/s, and the degree of incoming flow fluctuation is ±3.3%. The self-made experimental platform is used to test the pure-lift wind turbine and hybrid wind turbine. The experimental platform, wind source and test device are shown in Figure 15. To obtain the output power of the wind turbine, connect the 10 kΩload resistance to the output terminal of the self-made electromagnetic generator, and measure its output voltage with an oscilloscope. After obtaining the voltage at both ends of the load resistance, first, obtain the equivalent voltage [32] of the rotor output through the trapezoidal formula (see formula (14)). Thus, the output power of the wind turbine can be calculated using the formula = ⁄ . The self-made experimental platform is used to test the pure-lift wind turbine and hybrid wind turbine. The experimental platform, wind source and test device are shown in Figure 15. To obtain the output power of the wind turbine, connect the 10 kΩload resistance to the output terminal of the self-made electromagnetic generator, and measure its output voltage with an oscilloscope. After obtaining the voltage at both ends of the load resistance, first, obtain the equivalent voltage [32] of the rotor output through the trapezoidal formula (see Formula (14)). Thus, the output power of the wind turbine can be calculated using the formula P = U 2 /R.

Analysis of Experimental Results
In order to ensure the reliability and repeatability of the experiment, five experiments were conducted in each case. Table 8 shows the results of each experiment and the average data from five experiments. For comparison purposes, the experimental results of the pure lift wind turbine prototype (left) are also given in Table 8. It can be seen from Table 8 that the average power generated by the hybrid wind turbine (right) is 0.111 W, about 2.0 times the average power of the conventional pure-lift wind turbine of 0.056 W.
To explore the reason why hybrid wind turbines generate large power, Figure 16 shows the equivalent voltage values of two wind turbines considered. It can be seen from Figure 16 that the equivalent voltage generated by the hybrid wind turbine is greater than that of the pure lift wind turbine. Because the load resistance is certain, the output power of the hybrid wind turbine is greater than that of the pure lift wind turbine. Figure 17 shows the measured results of the average speed of different wind turbines. It can be seen in Figure 17 that during the initial startup, the hybrid wind turbine generated a higher angular acceleration and also a higher angular velocity when the turbine reached a stable passive rotation. This is consistent with the simulation results above.

Analysis of Experimental Results
In order to ensure the reliability and repeatability of the experiment, five experiments were conducted in each case. Table 8 shows the results of each experiment and the average data from five experiments. For comparison purposes, the experimental results of the pure lift wind turbine prototype (left) are also given in Table 8. It can be seen from Table 8 that the average power generated by the hybrid wind turbine (right) is 0.111 W, about 2.0 times the average power of the conventional pure-lift wind turbine of 0.056 W. angular acceleration and also a higher angular velocity when the turbine reached a stable passive rotation. This is consistent with the simulation results above.

Conclusions
Unlike the existing research literature, the passive rotation governing equation of the wind turbine is coupled with the Fluent solver through UDF, and the interaction between the wind turbine and the fluid is considered in the numerical calculation in this work. The effects of pitch angle (β), installation angle (θ), overlap ratio (ε) and diameter ratio (DL)on the energy capture performance of the hybrid vertical axis wind turbine are systematically analyzed by the Taguchi test and the CFD method, and the optimization parameters of the hybrid wind turbine are determined. In order to explore the performance improvement mechanism of the optimized hybrid wind turbine, a detailed comparative analysis