Research on Aerodynamic Performance of Asynchronous-Hybrid Dual-Rotor Vertical-Axis Wind Turbines

Abstract

This study analyzes the performance degradation of traditional hybrid wind turbines under high blade-tip-speed ratio conditions and proposes solutions through two-dimensional Computational Fluid Dynamics (CFD) simulations. It also introduces the design of two innovative asynchronous-hybrid dual-rotor wind turbines. The results indicate a remarkable 98.5% enhancement in torque performance at low blade-tip-speed ratios with the hybrid wind turbine model. However, as the blade-tip-speed ratio increases, it leads to negative torque generation within the inner rotor of the conventional design, resulting in a reduction of the power coefficient by up to 13.1%. The introduction of the new wind turbine design addresses this challenge by eliminating negative torque at high blade-tip-speed ratios through adjustments in the inner rotor’s operating range. This modification not only rectifies the negative torque issue but also enhances the performance of the outer rotor in the leeward region, consequently boosting the overall power coefficient. Moreover, the optimized inner rotor configuration effectively disrupts and shortens the wake length by 16.7%, with this effect intensifying as the rotational speed increases. This optimization is pivotal for enhancing the efficiency of multi-machine operations within wind farms.

1. Introduction

Conventional fossil fuel energy sources are already stretched to the limit, and carbon dioxide emissions are increasing rapidly [1]. Therefore, the utilization of clean and low-cost renewable energy sources appears to be urgent [2]. Wind energy, as a renewable energy source, is abundant and non-polluting and has become the focus of global research [3,4]. Horizontal and vertical-axis wind turbines are the two main ways to utilize wind energy [5].

The lift-type Darrieus wind turbine, which has attracted much attention among vertical-axis wind turbines, suffers from the drawbacks of low starting torque and difficulty in self-starting [6]. In order to improve its starting performance, Huang [7] designed a hybrid wind turbine with dual Darrieus rotors, which effectively achieved the design purpose. Ahmad [8] replaced the internal Darrieus airfoil with an asymmetric airfoil based on this design, which improved the power coefficient and self-starting capability. During the following year, Ahmad [9] realized a positive static torque coefficient at all angles by adopting a leading-edge serrated structure at the leading edge based on the principle of bionics. Cao Yu [10], however, studied the structure from the perspective of a coaxial-reversing wind turbine and determined that the structure can effectively improve the aerodynamic and stability performance of vertical-axis wind turbines.

The vertical-axis wind turbine with higher starting torque is the drag-type wind turbine, the most representative of which is the Savonius vertical-axis wind turbine, but it has lower power generation efficiency [11]. Therefore, in order to better improve the starting torque of the lift-type wind turbine, Sun [12] used the Savonius rotor to replace the Darrieus rotor inside the hybrid wind turbine, so that the inner and outer rotors rotate together under the action of the wind. This mechanism provides a higher starting torque than the conventional Darrieus wind turbine. When the Savonius wind turbine blades are moved away from the rotor axis, the starting torque increases, but the overall power coefficient decreases and vice versa. For this reason, Zhang [13] systematically analyzed the combined effect of pitch angle, mounting angle, overlap ratio and diameter ratio on hybrid wind turbines based on Taguchi’s method and designed an optimal structure. Hosseini [14] changed the Savonius blades to a Bach shape, which was realized to operate over a wide range of operating conditions, while maintaining high efficiency. Liu [15] modified the internal Savonius rotor designed with three height levels to improve self-starting performance by adjusting the angles between each level. Chegini [16] added multiple deflectors to a hybrid-shaft wind turbine, which resulted in improved wind turbine efficiencies at both the minimum and optimum blade-tip-speed ratios.

As mentioned earlier, in order to overcome the drawbacks of lift-type wind turbines, scholars often choose to modify the rotor shape or flow field. However, these modifications are usually complex and costly, and may pose challenges to the array layout of the wind turbine. In addition, it is rare to find hybrid-shaft wind turbines with rotors capable of rotating separately. Therefore, this thesis presents an improved asynchronous-hybrid dual-rotor vertical-axis wind turbine with as few modifications as possible. The design aims to improve the performance parameters of the vertical-axis wind turbine through the dynamic combination of the operating ranges of the twin rotors, thus filling the research gap and demonstrating its uniqueness among the existing hybrid wind turbines.

2. Research Modeling and Numerical Validation

2.1. Geometric Models

This paper focuses on the aerodynamic performance parameters of the Darrieus-Savonius hybrid wind turbine, and the solution region is shown in Figure 1. It has a total of three sub-domains, called stationary region, rotating region 1 and rotating region 2, where the rotating region 1 is used as the rotating domain of the outer rotor with an outer diameter of 3 R and an inner diameter of 0.9 R; the rotating region 2 is used as the rotating domain of the inner rotor with a diameter of 0.9 R. The inner rotor diameter is set to 0.3 times the diameter of the wind turbine, according to the data provided by Zhang [13]. The blades of the outer and inner rotor are named blade 1, blade 2, blade 3, S1 and S2, according to the direction of rotation, starting from 0° azimuthal angle. Their dimensions are sourced from Marco Raciti Castelli et al. [17] and Heejeon Im et al. [18], respectively. The specific geometrical parameters of the wind turbine rotor can be obtained from

Table 1. Geometrical specifications of wind turbines.

Specifications	Darrieus	Savonius
Blade profile	NACA0021	-
Turbine diameter [m]	1.03	0.309
Blade chord [m]	0.0858	-
Overlap ratio [m]	-	0.0281
Number of blades	3	2
Solidity ratio	0.25	-

.

2.2. Theoretical Equations

The numerical simulation in this study is based on the continuity equation and momentum equation (N-S equation) to calculate the various performance parameters of the wind turbine. The equation is as follows [19]:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla ·(\rho \overrightarrow{v})=0$$

(1)

$${\displaystyle \frac{\partial \rho \overrightarrow{v}}{\partial t}}+\nabla ·(\rho \overrightarrow{v}\times \overrightarrow{v})=-\nabla P+\nabla \overrightarrow{\tau }+\rho \overrightarrow{f}$$

(2)

Equations (1) and (2) are the Navier–Stokes equations, where $\rho$ is the fluid density, $t$ is time, $\overrightarrow{v}$ is the velocity vector, $P$ is the surface pressure, $\overrightarrow{\tau }$ is the surface stress vector, and $\overrightarrow{f}$ is the volumetric force vector per unit mass.

For the turbulence modeling in this study, the shear stress transfer (SST) k ω model was used with the following transport equations [20]:

$${\displaystyle \frac{\partial }{\partial t}}(\rho k)+{\displaystyle \frac{\partial }{\partial x_i}}(\rho k{v}_i)={\displaystyle \frac{\partial }{\partial x_j}}({\Gamma }_k{\displaystyle \frac{\partial k}{\partial x_j}})+G_k-Y_k+S_k+G_b$$

(3)

$${\displaystyle \frac{\partial }{\partial t}}(\rho \omega )+{\displaystyle \frac{\partial }{\partial x_i}}(\rho \omega v_i)={\displaystyle \frac{\partial }{\partial x_j}}({\Gamma }_{\omega }{\displaystyle \frac{\partial \omega }{\partial x_j}})+G_{\omega }-Y_{\omega }+D_{\omega }+S_{\omega }+G_{\omega b}$$

(4)

Equation (3) is the equation for turbulent kinetic energy (k), and Equation (4) is the equation for specific dissipation rate (ω). Here, $G_k$ represents the production of turbulent kinetic energy due to the mean velocity gradient, and $G_{\omega }$ represents the generation of ω. The terms ${\Gamma }_k$ and ${\Gamma }_{\omega }$ represent the effective diffusivity of k and ω, respectively, while $Y_k$ and $Y_{\omega }$ represent the dissipation of k and ω due to turbulence. The term $D_{\omega }$ represents the cross-diffusion term, and the terms $S_k$ and $S_{\omega }$ are the user-defined source terms. Terms $G_b$ and $G_{\omega b}$ account for the influence of buoyancy effects.

According to the SST model, the turbulent viscosity is defined by Equation (5):

$${\mu }_t={\displaystyle \frac{\rho k}{\omega }}{\displaystyle \frac{1}{\max \left[\frac{1}{a^{*}},\frac{S{F}_2}{a_1\omega }\right]}}$$

(5)

where S denotes the magnitude of the strain rate, and the coefficient a* suppresses turbulent viscosity, resulting in a low Reynolds number correction. F₂ is then given by Equation (6):

$$F_2=\tanh \left\{{\max }^2\left[2{\displaystyle \frac{\sqrt{k}}{0.09\omega y}},{\displaystyle \frac{500\mu }{\rho y^2\omega }}\right]\right\}$$

(6)

where y denotes the distance to the next surface.

The tip-speed ratio is an important dimensionless parameter in the design of wind turbine blades, which represents the ratio of the linear velocity at the tip of the blade to the incoming wind speed, and is generally expressed as $\lambda$, defined by Equation (7) [21]

$$\lambda ={\displaystyle \frac{\omega R}{U_{\infty }}}$$

(7)

where $\omega$ is the angular velocity of the wind turbine rotation in units of $\mathrm{rad}·{\mathrm{s}}^{-1}$, $R$ is the radius of the wind turbine in units of $\mathrm{m}$, and $U_{\infty }$ is the incoming wind speed in units of $\mathrm{m}·{\mathrm{s}}^{-1}$.

The moment coefficient and the power coefficient are important aerodynamic performance parameters of wind turbines and are denoted by $C_m$ and $C_p$, respectively [22]:

$$C_m={\displaystyle \frac{M}{0.5\rho AR{U}_{\infty }^2}}$$

(8)

$$C_p={\displaystyle \frac{\omega T}{0.5\rho A{U}_{\infty }^3}}=\lambda C_m$$

(9)

where $M$ is the torque of the wind turbine in units of $\mathrm{N}·\mathrm{m}$, $A$ is the swept area of the wind turbine in units of ${\mathrm{m}}^2$, and $R$ is the radius of the wind turbine in units of $\mathrm{m}$.

2.3. Mesh Generation

In numerical simulation of wind turbines, more accurate calculation results can be obtained by using 3D simulation [23]. However, 2D simulation can also be used for simulation when the wind turbine blade has a high spreading ratio. The 2D simulation can be considered as a 3D simulation of a wind turbine blade with a high spreading ratio [15]. Although this may lose some of the effects of the blade-tip vortices, according to previous studies [24,25] and the author’s simulation results, 2D simulation can predict the performance of the wind turbine well and can reduce the computational burden. Therefore, this study chooses to use 2D simulation for numerical simulation of wind turbine.

In this study, Grid 3, shown in Figure 2, is used to discretize the computational domain. This process was performed interactively with ICEM via ANSYS 2022 R1 Mesh and subsequently validated through mesh analysis. In order to capture the details of the high velocity gradients in the air flow on the blade surface, special attention needs to be paid to the mesh of the blade surface. By setting up an expansion layer to enclose the blade surface, the boundary layer flow can be better resolved, thus improving the accuracy of the simulation.

2.4. Solver Settings

The numerical simulation process is achieved with the help of Ansys Fluent 2022 R1. For the solution of the transient problem, a second-order accurate numerical method is used.

For the 2D CFD model, the following assumptions are made:

The blade support arm and the connecting strut to the wind turbine tower are ignored in the modeling process, and the effect of frictional resistance is ignored. Heat transfer effects are neglected, and any external volumetric forces, such as gravity or electromagnetic forces, are not considered. The air is assumed to conform to the ideal gas law. The flow field proceeds in a plane, and the flow variations perpendicular to this plane are neglected. Since the Mach number M (defined as $M={\displaystyle \frac{\lambda U_{\infty }}{343}}$) of the wind turbine in the simulation is always lower than 0.3, the airflow is considered as incompressible flow [26]. A pressure-based solver was used to solve the continuity and momentum equations. The SST k-ω model was chosen as the turbulence model. The SST k-ω model is used in the near-wall region to improve the accuracy of the near-wall simulation, while the k-ε model is used in the free shear flow region to take advantage of its advantageous property of being far from the wall in the free flow [27]. Meanwhile, the results obtained by previous authors using this turbulence model are in good agreement with the experimental data [28,29]. The vertical-axis wind turbine rotates at a uniform speed and is implemented using a slip mesh approach, which has the advantage of model simplification, avoidance of the negative volume problem, smaller computational errors, and applicability to non-stationary problems. The boundary conditions are shown in Figure 1, with a uniform wind speed of 9 m/s at the inlet and a pressure of 0 Pa at the outlet. Symmetric boundary conditions were used at the sides of the solution domain to avoid reflections [30]. A no-slip wall was chosen as the boundary condition on the blade surface to capture the flow behavior between the wind turbine blade and the air more accurately. Data transfer and calculations were performed between different regions using a grid intersection interface. Reference values were set to facilitate the acquisition of numerical simulation results. Fluent was able to automatically recognize the reference values and calculate and output the accurate torque coefficients by using Equation (8). The Reynolds number is 6.4 × 10⁵ [5].

For the solution methodology, the SIMPLE algorithm was used for pressure-velocity coupling, and second-order windward discretization formats were used for pressure, momentum, turbulent kinetic energy and specific dissipation rate, respectively [31]. The time discretization format used Second Order Implicit, with the absolute standard for all residuals set to 1 × 10⁻⁵ and 30 iterations at each time step to ensure convergence.

2.5. Convergence Criterion

Convergence assessment is required to ensure that the calculation results are accurate. The wind turbine was rotated for multiple revolutions, and Equation (9) was set up in Fluent to monitor the power coefficient Cp [32]. When the power coefficient satisfies the convergence condition of Equation (10), the wind turbine is rotated for 5 additional revolutions to eliminate the effect of chance.

$$ConvergenceCriterion={\displaystyle \frac{\left(C{p}_{(ave,n+1)}-C{p}_{(ave,n)}\right)}{C{p}_{(ave,n)}}}<1\%$$

(10)

According to the results in Figure 3, the difference between the power coefficient Cp(ave,8) for the 8th rotation and Cp(ave,7) for the 7th rotation is 0.902%, which satisfies the convergence criterion of Equation (10). Subsequently, the wind turbine went through 5 more rotations to control the convergence error to 0.341%, and the final converged solution was obtained.

2.6. Grid Independence Verification

Table 2. Grid size parameters.

Grid Features	Grid 1	Grid 2	Grid 3	Grid 4
Blade surface grid length [m]	1.264 × 10−4	9.481 × 10−5	6.320 × 10−5	3.792 × 10−5
Height of the first grid layer on the blade surface [m]	3.941 × 10−5	3.153 × 10−5	1.892 × 10−5	1.419 × 10−5
Boundary layer growth rate	1.1	1.08	1.05	1.03
Number of boundary layers	12	15	23	30
Overall growth rate	1.2	1.15	1.1	1.08
Minimum orthogonal mass	0.701	0.713	0.716	0.714
Maximum skewness	0.497	0.470	0.468	0.454
Number of grids	123,989	201,628	477,501	1,194,387
Blade 1 average moment coefficient	0.0367	0.0410	0.0462	0.0457

shows the specific parameters of the meshes, with four uniformly refined 2D meshes used. The minimum orthogonal mass of all these grid models is greater than 0.7, and the maximum skewness is less than 0.5, so they have good grid quality. Figure 4 shows the variation of moment coefficient, with the azimuthal angle for a single blade of a wind turbine in one revolution at a tip-speed ratio of 2.64. From the figure, it can be seen that the moment coefficient curves of Grid 3 and Grid 4 are almost the same, with only slight differences at the azimuth angles of 195° to 249°. On the other hand, Grid 1 and Grid 2 are significantly different from Grid 3 and Grid 4 at the azimuth angles of 78°~171°. It was found that the number of meshes in Grid 4 increased by 150%, compared to Grid 3, but the average moment coefficient only changed by 1.08%. Therefore, the size of Grid 3 was chosen as the discretization standard for all models in this study to save computational resources while maintaining the desired accuracy.

$y^{+}$ is a dimensionless number that describes the roughness and fineness of the mesh profile inside the boundary layer. In this study, the SST k-ω turbulence model was used, so the $y^{+}$ value should be less than 1 [33]. Figure 5 illustrates the distribution of $y^{+}$ values based on Grid 3. From the figure, it can be seen that only the maximum $y^{+}$ value of Blade 1 is close to 1.07, while the maximum $y^{+}$ values of the other two blades are less than 1. In addition, the overall $y^{+}$ distribution on the right-hand side shows that only 0.843% of the $y^{+}$ values are larger than 1. This further verifies that the sizing of Grid 3 meets the simulation requirements.

2.7. Validation of Time-Step Independence

In wind turbine simulations, the time step is often set based on the time increment of the wind turbine azimuth. Figure 6 illustrates the relationship between the instantaneous torque coefficient, rate coefficient and azimuth angle for one blade during one revolution in the turbine at TSR = 2.64. It can be observed from the figure that there is a significant change in the instantaneous torque coefficient when reducing Δθ from 1° to 0.5°. However, further reduction of the time step has no significant effect on the CFD results. Therefore, Δθ = 0.5° was chosen as the time step in this study to strike a balance between computational costs and the accuracy of the results.

2.8. Model Validation

As verified in the previous section, the grid model in this study achieves the desired accuracy while controlling computational costs. However, the simulation model still needs to be compared with specific experimental data and other simulation results to evaluate its advantages and disadvantages. The comparison of the results in Figure 7 leads to the following conclusions:

• When observing the simulation results of this study alongside the experimental and simulation results of Raciti Castelli et al. [17], it is clear that the trends of the curves are generally similar. However, the trend of their next year’s simulation data [34] differs somewhat from the experiments.
• The simulation results of this study are numerically closer to the experimental values, compared to Raciti Castelli et al.’s data, while maintaining a similar trend. Specifically, the values align more closely with experimental data at low- and medium-leaf-tip-speed ratios, with only a slightly larger error at high ratios, compared to Raciti Castelli et al.’s later simulation data [34]. The advantageous simulation results in this study are mainly due to optimizations in the choice of turbulence model, grid resolution, time step, wind turbine revolutions and boundary conditions.
• It is noted that the numerical simulation results in this study are slightly higher than the experimental data, which is attributed to the model simplification of blade support arms and the neglect of mechanical friction losses. Additionally, the 2D simulation does not account for losses due to blade-tip vortices and 3D vortices, nor does it consider the 3D effects of fluid flow [35].
• Furthermore, the experimental data may also be affected by measurement error and uncertainty. The absence of data on turbulence intensity, which was not provided in the experiment, could further increase the discrepancy between the simulation and experimental results.

In conclusion, based on the discussion of the above results, the model in this study is capable of making reasonable predictions of the performance of vertical-axis wind turbines.

3. Results and Discussion

3.1. Conventional-Hybrid Wind Turbines

The hybrid vertical-axis wind turbine uses Savonius blades as the inner rotor to provide starting torque and Darrieus-type blades as the outer rotor to maintain power coefficient at high blade-tip-speed ratios. Figure 8 shows the performance comparison between the Darrieus-type wind turbine and the hybrid wind turbine at different blade-tip-speed ratios. It can be observed that the hybrid wind turbine enhances the power coefficient by up to 98.5% with respect to the Darrieus wind turbine at low blade-tip-speed ratios. According to Equation (9), this can be explained as an improvement in the torque coefficient. This enhancement is due to the drag-type blades of the inner rotor. However, at high blade-tip-speed ratios, the power coefficient of the hybrid wind turbine is reduced by up to 13.1%. This is because at high blade-tip-speed ratios, the drag of the inner rotor impedes the rotation of the hybrid-shaft wind turbine. Figure 9 illustrates the contribution of the inner and outer rotors to the power coefficient in the hybrid-shaft wind turbine, where the bar graph indicates the effect of the inner rotor. Since the inner rotor diameter is set to be 0.3 times the diameter of the hybrid wind turbine, it can be calculated that the inner rotor plays a role between 0.432 and 0.99 of the blade-tip-speed ratio.

In Figure 9, it can be observed that in hybrid wind turbines, the outer rotor plays a major role in the overall power coefficient, while the inner rotor has a lower power coefficient. For most of the tip-speed ratios, the inner rotor has a positive effect on the overall performance, but as the tip-speed ratio approaches 3, the efficiency of the inner rotor is almost zero. As the tip-speed ratio increases further, the inner rotor may even negatively affect the overall power coefficient. There are several reasons for this phenomenon.

First, the inner rotor has a small swept area of only 9% of the overall area.

Second, there is a mismatch between the operating ranges of the inner and outer rotors. In a conventional-hybrid wind turbine, the inner and outer rotors rotate simultaneously. Figure 10 demonstrates the variation of the torque coefficient of the blades with the azimuthal angle in one rotation cycle of the hybrid wind turbine when the blade-tip-speed ratio is 3.3. It can be observed that at the current blade-tip-speed ratio, the thrust of the inner rotor decreases and presents negative torque coefficients in the azimuthal angle ranges from 0° to 75°, from 150° to 261° and from 330° to 360°. This accounts for 60% of a rotation cycle, and the magnitude of the negative values is significantly greater than the magnitude of the positive values, resulting in a decrease in the overall power coefficient factor.

Thirdly, as the tip-speed ratio of the wind turbine increases, the rotational speed of the inner and outer rotors is accelerated, and their dynamic realism increases, which has a greater impact on the downstream blades, leading to a decrease in efficiency.

For hybrid wind turbines, the inner rotor diameter is too large to affect the operation of the downstream outer rotor blades, but if the inner rotor diameter is reduced, the starting torque is reduced. Therefore, the operating range of the inner rotor of a hybrid wind turbine needs to be varied to improve the overall performance while keeping the wind turbine dimensions the same. Two solutions are proposed below: the clutched-hybrid wind turbine and the differential-hybrid wind turbine.

3.2. Clutched-Hybrid Wind Turbine

The structure of the clutched-hybrid wind turbine is shown in Figure 11. Figure 11a shows an overall schematic diagram, with the red dashed line box indicating the clutching device. In Figure 11b, the clutching device has not yet functioned, the red wire frame shows the counterweight block, and the angle between the clutching device and the support arm of the blade is 45°. When the stationary wind turbine is affected by the incoming wind, the inner rotor starts to rotate due to resistance. The clutching device drives the outer rotor to rotate, and at the same time, the angle decreases under the effect of centrifugal force. When the outer rotor reaches the freewheeling speed, as shown in Figure 11c, the angle reaches the freewheeling angle, and the inner and outer rotors separate. By controlling the mass of the counterweight, the clutching speed can be adjusted, so that the tip-speed ratios of the inner and outer rotors can be controlled separately to keep them in the appropriate operating range. The blade-tip-speed ratio of the inner rotor is controlled near the peak of the inner rotor’s gain in the conventional-hybrid wind turbine. At this point, the power coefficient curve of the clutched-hybrid wind turbine, at a blade-tip-speed ratio of 2.64 is shown in Figure 12.

It is evident from Figure 12 that the power coefficient of the adjusted clutched-hybrid wind turbine is higher than that of the conventional-hybrid wind turbine at TSR = 0.792. The peak value of this occurs around the inner rotor blade-tip-speed ratio of 0.504, which enhances the Cp by 4.89%, as compared to that of the conventional-hybrid wind turbine. Therefore, this value is chosen as a constant value for the blade-tip-speed ratio of the inner rotor. Figure 13 demonstrates the difference in performance between the clutched-hybrid wind turbine and the conventional-hybrid wind turbine at this blade-tip-speed ratio. It is evident that the power coefficient of the clutched-hybrid wind turbine is the same as that of the conventional-hybrid wind turbine until the blade-tip-speed ratio of 1.68, which is due to the speed matching of the inner and outer rotors. However, at all other points, the power coefficient of the clutched-hybrid wind turbine is higher than that of the conventional-hybrid wind turbine, with a maximum improvement of 18.43%.

Figure 14a demonstrates the torque coefficient of the inner rotor of the clutched-hybrid wind turbine at different TSRs, and Figure 14b shows the torque coefficient of the conventional-type inner rotor. After introducing the data of the conventional-type inner rotor, the range of the torque coefficient had to be adjusted to show the torque coefficient of the conventional-type inner rotor. The comparison shows that the trend of the inner rotor torque coefficients with the azimuthal angle for the clutched-hybrid wind turbine at different TSRs is roughly the same as that of the conventional type, and that the torque coefficients of the inner rotor of the clutched-hybrid wind turbine gradually decrease with the gradual increase in the TSR of the whole turbine. However, the difference between the two is that the torque coefficient of the inner rotor of the clutched-hybrid wind turbine is overall greater than 0 at different TSRs, which helps the operation of the wind turbine. In contrast, the conventional-type inner rotor presents a negative torque coefficient over a wide range, hindering the operation of the wind turbine.

In order to understand the reason for the variation in the torque coefficient, Figure 15 shows the pressure fields of the inner rotor of the clutched-hybrid wind turbine and the conventional-hybrid wind turbine at different azimuth angles. Since the torque coefficient of the inner rotor shows periodicity, and the period is 180° in the azimuthal angle, only the variations in the pressure fields maps for 0°, 45°, 90° and 135° azimuthal angles are analyzed. Focusing on Figure 15a,b it is obvious that, due to the difference in the inner rotor tip-speed ratio, the conventional-type inner rotor has a wide range of negative pressure areas around the blades. At azimuth angles from 0° to 45°, the pressure at the convex side of the S1 blade is significantly larger than that at the concave side, and even the pressure gradient experienced by the blade on the conventional-type inner rotor is larger, which makes both S1 blades hinder the rotation of the blade. Meanwhile, the pressure at the concave surface of the S2 blade of the clutched-hybrid wind turbine is greater than the pressure at the convex surface, which indicates that a positive torque is generated on the blade in favor of the blade rotation. In contrast, the pressure at the concave surface of the S2 blade of the conventional-type inner rotor remains less than the pressure at the convex surface, which makes its total torque at 0° azimuth negative. From 90° to 135°, the pressure at the concave side of both S1 blades is greater than the pressure at the convex side, creating a pressure gradient that contributes to the rotation of the blades, with the clutched-hybrid wind turbine generating a greater pressure gradient. In contrast, the pressure on both sides of the S2 blade is similar and even produces a pressure gradient against the direction of rotation. At these two azimuthal angles, it is mainly the S1 blade that generates the torque required for the rotation of the inner rotor. As a result, the torque coefficients of the inner rotor of the clutched-hybrid wind turbine are all greater than those of the conventional type, thanks to the control of the inner rotor blade’s tip-speed ratio.

The same analysis can be applied to Figure 15a,c, where it can be argued that for the inner rotor of the clutched-hybrid wind turbine, the torque coefficient at TSR = 2.04 is greater than the torque coefficient at TSR = 3.30. The specific reason for this is that as the TSR increases, the range of the low pressure side action of the outer rotor increases, causing the pressure gradient on the inner rotor blades to decrease in favor of the direction of rotation of the blades, causing the inner rotor torque coefficient to decrease.

3.3. Differential-Hybrid Wind Turbines

The overall structure of the differential-hybrid wind turbine is shown in Figure 16, where the outer rotor and inner rotor are connected to the gear ring and the planetary carrier, respectively, and the sun wheel is fixed immovably on the shaft body. At this time, the inner rotor is the input and the outer rotor is the output, forming a speed-up structure with a transmission ratio between 0.5 and 1. Thus the blade-tip-speed ratio of the inner rotor is between 0.5 and 1 times that of a conventional-hybrid wind turbine. Figure 17 shows the power coefficient of the wind turbine operating at the optimum operating point, with different transmission ratios, where a transmission ratio of 1 represents a conventional-hybrid wind turbine. It can be seen that by reducing the speed of the inner rotor, it can operate in a better range. When the transmission ratio is 0.7, i.e., the tip-speed ratio of the inner rotor is 0.554, the maximum improvement in the power coefficient, compared to the conventional-hybrid wind turbine, is 6.38%.

Extending this ratio to the full operating range of the wind turbine and comparing it to the two hybrid wind turbines mentioned earlier yields Figure 18, from which it can be seen that, although the differential-hybrid wind turbine outperforms the conventional-hybrid wind turbine over essentially the entire operating range, it only outperforms the clutched-hybrid wind turbine near the point of the optimum blade-tip-speed ratio. This is due to the fact that the inner rotor of a clutched-hybrid wind turbine fixes a single operating range, so that it operates only at the optimum point as much as possible. In contrast, a differential-hybrid wind turbine translates the entire operating range of the inner rotor, so that the optimum point of its operating range matches that of the outer rotor.

Figure 19 demonstrates the variation of the single blade torque coefficient with the azimuth angle for the outer rotor of the hybrid wind turbine and the Darrieus wind turbine for TSR = 3.30. From the figure, it can be seen that the presence of the inner rotor has a large impact on the torque coefficient trend of the outer rotor, as shown near 90° azimuth and between 190° and 350°. At low tip-speed ratios, the presence of the inner rotor has a lagging effect on the performance of the outer rotor. At this time, in the windward zone, the variation of the inner rotor speed has almost no effect on the outer rotor. However, in the leeward zone, the presence of the inner rotor helps to reduce the stall range of the outer rotor and improve the performance of the outer rotor in the second half of the revolution.

Figure 20 shows the velocity fields between the Darrieus wind turbine and the differential-hybrid wind turbine between 65° and 90° azimuths for TSR = 1.44. It can be observed that the velocities around the blades of the Darrieus wind turbine are higher than those of the hybrid wind turbine at each azimuthal angle, which is particularly noticeable on the high-speed side. This is due to the fact that the presence of the inner rotor creates a low velocity region inside the wind turbine, which delays the flow separation. At high tip-speed ratios, the hysteresis effect of the inner rotor diminishes because, as the tip-speed ratio increases, the relative velocity of the inner rotor to the outer rotor decreases, and the effect then diminishes. It can also be seen that, when the operating range of the inner rotor changes, the outer rotor blades are almost unaffected by the inner rotor speed in the windward region. However, when the blades operate into the leeward region, especially when the outer rotor is in the wake region of the inner rotor, the performance of the blades is greatly affected.

Continuing to explore the reasons for the differences in the curves, Figure 21 shows the pressure distributions for the Darrieus wind turbine and the differential-hybrid wind turbine at the 90° azimuth angle, as depicted in Figure 19c. The hybrid wind turbine’s curves essentially overlap at this point, so only the differential-hybrid wind turbine was chosen for comparison. At this point, the upstream of the blades of the outer rotor is only affected by the incoming wind, so the pressure distribution on the high pressure side is the same. The difference occurs on the low pressure side, where the inner rotor of the hybrid wind turbine develops a high pressure in the windward region, which causes the pressure in the leeward region of the neighboring outer rotor blade to increase and the low pressure region to decrease. As a result, the pressure gradient on the outer rotor blades is lower than that of the Darrieus wind turbine, and the torque decreases.

The blades of a hybrid wind turbine are susceptible to the effects of the inner rotor wake when the blades run into the leeward zone. As Figure 22a demonstrates, the vortex distribution of different wind turbines at an azimuth angle of 270°, depicted in Figure 19c, two shedding vortices are thrown out from the upper and lower positions when the inner rotor rotates, which will affect the downstream outer rotor blades. At this time, the outer rotor blades are affected by the shedding vortices, and the torque coefficient decreases to the lowest point. In addition, the shedding vortices generated by the inner rotor will also disturb the tail vortex of the outer rotor. Continuing to look at Figure 22b, the blades are affected by the shedding vortex, just as they enter the low speed range of the inner rotor wake field, when the torque will remain low. However, the inner rotor of different types of hybrid wind turbines is at different operating points, and the degree of reduction experienced by the outer rotor blades varies. Observing Figure 22c, the inner rotor of the conventional-hybrid wind turbine generates the strongest turbulence kinetic energy, which makes the evolution of turbulent motions downstream of the inner rotor more intense, and the development of these turbulence structures directly affects the aerodynamic performance of the outer rotor blade in the leeward region. In contrast, the inner rotor of the differential-hybrid wind turbine generates the weakest turbulence kinetic energy, which somewhat weakens the inhomogeneous turbulence caused by the inner rotor and makes the load distribution on the outer rotor blade less affected by the inner rotor. The specific reason is that the new hybrid wind turbines change the working range of the inner rotor, which lowers the blade-tip-speed ratio, weakens the wake region, strengthens the torque performance of the outer rotor in the wake region and improves the power coefficient of the outer rotor. When the blade reaches a 300° azimuth, it starts to leave the wake region of the inner rotor, and the torque is gradually restored.

3.4. Wake Conditions

The wake flow has an important influence on the array layout of vertical-axis wind turbines. This section focuses on the wake flow of different types of wind turbines at the point of optimal blade-tip-speed ratio. Figure 23 illustrates the velocity losses of different wind turbines at locations immediately downstream of the rotor. At 2.5 m downstream, the hybrid wind turbine experiences less lateral velocity loss but has a larger flow direction impact, which increases with decreasing inner rotor speed. When the position reaches 5 m downstream, the hybrid wind turbine is still exhibits less lateral velocity loss, but the streamwise velocity loss is significantly compared to the Darrieus wind turbine. In addition, the degree of wake loss decreases as the inner rotor speed increases. The reduced lateral and streamwise velocity losses imply faster energy recovery in the wake stream, allowing for a tighter wind turbine array layout.

Figure 24 illustrates the normalized profiles of wake velocity in the x-direction for different wind turbines. The specific data show that the clutched-hybrid wind turbine and the Darrieus wind turbine recovered the incoming wind speed at 18 m downstream of the wind turbine. However, the conventional-hybrid wind turbine and the differential-hybrid wind turbine essentially recovered the free incoming wind speed at 15 m downstream of the wind turbine, shortening the wake by 16.7%. At 10 m downstream, the hybrid wind turbine had recovered more than 80% of its wake velocity, while the Darrieus wind turbine, at the same location, had only recovered 70% of its wake velocity. If each wind turbine is connected in series at the wake recovery, the Darrieus wind turbine has a power coefficient per unit length of 2.03% (defined as $C_{pL}={\displaystyle \frac{C_p}{L}}$, where L is the wake recovery length). The power coefficients per unit length for the conventional-hybrid wind turbine, the disjointed-hybrid wind turbine and the differential-hybrid wind turbine are 2.16%, 1.89% and 2.29%, respectively. Among them, the power coefficients per unit length of both conventional-hybrid wind turbine and differential-hybrid wind turbine are higher than that of the Darrieus wind turbine, so it is easy to achieve a higher overall power coefficient with the series connection compared to the Darrieus wind turbine.

The wake velocity fields plot presented in Figure 25a shows that the velocity loss is more pronounced in the wake region of the hybrid wind turbine compared to the Darrieus wind turbine, but accordingly, the wake of the hybrid wind turbine disappears more quickly. Further observation of the fields diagrams reveals that the sharp increase in velocity loss begins at the inner rotor of the hybrid shaft, which results in the wake being destroyed more quickly and recovering in a shorter distance. The comparison of hybrid wind turbines reveals that the clutched-hybrid wind turbine has the longest wake region, while the differential-hybrid wind turbine and the conventional-hybrid wind turbine have similar lengths of wake regions. This indicates that the wake flow recovery distance is inversely related to the rotational speed of the inner rotor. Figure 25b illustrates the vortex distribution for different wind turbines, and the magnitude and range of vortices are also similar to the pattern of the velocity wake. In hybrid turbines, the faster the rotational speed of the inner rotor, the greater the intensity of the vortex generated, which is conducive to disrupting the tail vortex of the outer rotor, thus leading to faster dissipation of vortex in the wake, which in turn helps in the disruption and reconstruction of the wake, and reduces the impact on the downstream wind turbine. Therefore, Figure 25 further validates these conclusions by showing the distribution of the wake streams for different wind turbines.

4. Conclusions

In this study, the CFD-calculated values of the wind turbine were first compared with the experimental data, and the results showed that the reliability of the present CFD model is high, and the trend is in line with previous simulations, with smaller errors. Secondly, a hybrid design to improve the self-starting capability of Darrieus vertical-axis wind turbine was proposed in this paper and its performance was analyzed. Finally, to address the shortcomings of this design, a new asynchronous-hybrid vertical-axis wind turbine was further proposed, and two implementations were designed and analyzed for power coefficients, torque variations and wake flow. The following are the conclusions drawn from this study:

• At low impeller tip-speed ratios, the presence of the inner rotor causes the outer rotor performance to lag, improving the performance of the outer rotor in the leeward zone and increasing the torque coefficient of the vertical-axis wind turbine by a maximum of 98.5%. However, the hysteresis effect gradually disappears as the blade-tip-speed ratio increases. At high blade-tip-speed ratios, the excessive speed of the inner rotor leads to reduced thrust and affects the downstream blades, resulting in a maximum reduction of 13.1% in the power coefficient.
• Asynchronous-hybrid vertical-axis wind turbines can solve the problem of performance degradation of conventional synchronous hybrid generators at high blade-tip-speed ratios. Appropriately lowering the inner rotor speed can enhance the performance of the outer rotor blades in the leeward zone and match the optimal operating points of the inner and outer rotors.
• The performance of the inner rotor can be improved, and the negative torque it produces can be eliminated by fixing the tip-speed ratio of the inner rotor at 0.504 by using a clutched-hybrid wind turbine. This change can lead to an increase in the power coefficient to varying degrees, with a maximum increase of 18.43% and a peak increase of 4.89%.
• The use of a differential-hybrid wind turbine, controlling the inner rotor speed to be 0.7 times the outer rotor speed, can increase the peak power coefficient by 6.38%. Although the other operating points are slightly lower than those of the differential-hybrid wind turbine, they are still higher than those of the conventional type.
• At the same overall blade-tip-speed ratio, the presence of the inner rotor, while it will increase speed loss at the downstream proximal end of the wind turbine, will help to disrupt and rebuild the wake, reduce the wake impact area, and return the downstream area to free wind speed more quickly. This degree will also be strengthened with the increase in the inner rotor speed, which helps the array layout of wind turbines.

Therefore, the differential-hybrid wind turbine is the best way to realize an asynchronous-hybrid vertical-axis wind turbine. It has a simpler design and installation, shorter wake recovery distances, no need for additional control of the inner rotor, and lower usage and maintenance costs compared to the clutched-hybrid wind turbine. These advantages are sufficient to compensate for the performance loss at other blade-tip-speed ratios. However, in this study, only a single wind turbine was investigated, without changing the incoming wind conditions or investigating a specific wind turbine layout. Therefore, further work is needed to explore different types of incoming winds and their effects on different turbine layouts.