Wind tunnel experimental study on the aerodynamic characteristics of straight-bladed vertical axis wind turbine

ABSTRACT

To investigate the effect of structural parameters on the aerodynamic characteristics of a Straight-Bladed Vertical Axis Wind Turbine (SB-VAWT), a 4-bladed SB-VAWT without an intermediate support shaft was designed to allow flexibility in changing structural parameters. Wind tunnel tests were conducted to measure the rotational speed, total lift, drag and torque of the wind turbine with different structural parameters at varying wind speeds. Based on the experimental design and optimisation, the wind turbine achieved the highest rotational speed and optimal power generation when the blades were installed in the forward direction at an installation angle of 10°, an installation radius of 160 mm, and a length of 600 mm. Under these optimal conditions, the speed and power generation characteristics of the wind turbine were tested at different wind speeds These results provide valuable insights for the design and application of similar wind turbines.

KEYWORDS:

• Straight-bladed vertical axis wind turbine
• wind tunnel
• asymmetric airfoil
• aerodynamic characteristics
• power generation characteristics

1. Introduction

The global energy shortage and environmental degradation have forced the world to seek and develop sustainable green energy in order to effectively achieve carbon neutrality or zero-emission goals. Wind energy, as a clean and readily available sustainable green energy source, has many advantages such as no pollution, small land occupation, and minimal negative impact on the environment. It provides an important solution to replace the use of fossil fuels and has garnered widespread attention worldwide (Rehman et al. 2023; Tong et al. 2023).

Wind power is currently the most mature technology with the most favourable conditions for large-scale development and commercial prospects in the field of sustainable green energy, as widely applied (Sun, Liu, and Peng 2023). Wind turbines are common devices used to capture and convert wind energy. They can be classified into two types: horizontal-axis wind turbines (HAWTs) and vertical-axis wind turbines (VAWTs), based on the orientation of their shaft relative to the wind direction (Azadani and Saleh 2022; Muzammil et al. 2017; Pietrykowski et al. 2023). HAWTs rotate with blades perpendicular to the incoming flow, causing the flow to interact with the blades only once before leaving the two-dimensional disc formed by the rotation of the blades. This results in consistent aerodynamic characteristics across different azimuth angles for each blade section. The analysis of relative motion and forces between the blades and the incoming flow is simplified. Furthermore, HAWTs can control blade pitch to maintain optimal angle of attack (AOA) and achieve higher energy conversion efficiency. Therefore, HAWTs are currently the primary form of large-scale wind power generation (Wang et al. 2022). VAWTs have long faced challenges in research and application due to their complex aerodynamics and insufficient foundational theory. During a single rotation cycle, the blades of these turbines cut through the wind field, resulting in the flow being interacted with twice by the same airfoil. This leads to significant variations in blade AOA, with alternating pressure and suction surfaces on the windward side. Additionally, the blades are influenced by complex upstream wake flows, often causing vortex shedding or reattachment phenomena. These distinctive features characterise VAWTs as large-scale, unsteady, three-dimensional structures (Tjiu et al. 2015; Zhang and Hu 2020). However, the lack of fundamental theories and the complexity of aerodynamic behavior pose numerous challenges in the research process, resulting in a prolonged stagnation in the study and practical application of VAWTs (Islam, Ting, and Fartaj 2008). Despite these challenges, VAWTs have several advantages, including the ability to operate without yawing into the wind, low center of gravity, simple structure, low cost, low aerodynamic noise, easy installation and maintenance, high safety, and adaptability to complex environments (Guevara, Rochester, and Vijayaraghavan 2021; Guo, Chen, and Tian 2022; Ni, Miao, and Li 2022). With the rise of small-scale distributed wind power generation and advancements in technology research and development, VAWTs have gradually become a research hotspot. Among these turbines, SB-VAWTs have gained increasing attention and research interest due to their regular blade shape, easy manufacturing, low cost, excellent aerodynamic characteristics, and significant engineering application value (Guevara, Rochester, and Vijayaraghavan 2021; Wang et al. 2018).

Currently, VAWTs are typically designed with intermediate support shafts and supporting systems, such as struts or stabilising rods, which are considered essential components for bearing loads (Li et al. 2015) . However, several other studies (Bai et al. 2021; Benmoussa and Páscoa 2023; Chen et al. 2023; Dai et al. 2022; Geng et al. 2022; He et al. 2021; Zhang and Qu 2021) tend to overlook the existence of support systems and oversimplify the impact of intermediate shafts and struts on the characteristics of wind turbines. This oversimplification inevitably leads to errors in research results. Therefore, many studies have focused on investigating the mutual influence between support shafts and the aerodynamic characteristics of VAWTs (Miao et al. 2023) . Zhang Yanfeng et al. (Zhang, Guo, and Zhu 2023) conducted CFD simulations on a SB-VAWT using the Reynolds-averaged Navier-Stokes (RANS) model with the SST k-ω turbulence model. They investigated the impact of blade support structures on the flow field distribution around the wind turbine. The study demonstrated that the complex flow separation phenomenon in the wind turbine is significantly affected by the blade supports. The rotational disturbance caused by the supports increases the turbulence intensity of the airflow within the rotor, leading to a decrease in the aerodynamic performance of the wind turbine, with a reduction of up to 47.5% in the maximum power coefficient. Huang Huilan et al. (Huang et al. 2022; Huang et al. 2023), through numerical simulation and experimental verification, investigated the influence of different diameters of enclosed cylinders on the aerodynamic performance of an H-type VAWT. They revealed that the presence of enclosed bodies of various diameters adversely affects the wind energy utilisation of the turbine, with a more significant impact observed as the diameter increases. In the analysis of unsteady aerodynamic characteristics of VAWTs, Lei Hang et al. (Lei 2019) found that omitting the modelling of the main shaft and support shaft in their numerical simulations resulted in a power coefficient computed by the model that was larger than the experimental value, with a maximum error of 9.03%. The study by Siddiqui et al. (Siddiqui, Durrani, and Akhtar 2015) indicated that neglecting the support system of a wind turbine during calculations led to a prediction error of 10–12% in the power coefficient.

In the study of SB-VAWTs, computational fluid dynamics (CFD) methods are commonly employed due to limitations in experimental conditions and costs (Li et al. 2023; Wilberforce and Alaswad 2023). This approach utilises CFD software equipped with either built-in turbulence models or custom models to calculate and obtain the flow field and aerodynamic characteristics of the wind turbine. However, since the software's development theory originates from HAWTs and involves numerous idealised assumptions and simplifications, coupled with the fact that VAWTs exhibit complex and dynamic three-dimensional structures prone to large separation and unsteady behaviour, the computational requirements are high, time-consuming, and the operating conditions are difficult to adjust flexibly. Additionally, the choice of turbulence model, discretization method for control equations, size of computational domain, grid partitioning, boundary conditions, and time step can all lead to significant discrepancies in the calculated results. Therefore, to verify the accuracy of the simulation, reliable wind tunnel tests are required to ultimately validate these results.

To eliminate the interference caused by the intermediate shafts and struts on the internal flow field of wind turbines, which adversely affects their performance, Wu Wanqiu et al. (Wu, Pan, and Lin 2021) designed a semi-cylindrical drag-type wind turbine without a central rotating axis. The structural advantages of this design are as follows: the exhaust gases passing through the staggered gaps between the blades can avoid impacting the central axis and generating noise or turbulent airflow that would affect the quality of energy absorption by the rotor, while simultaneously facilitating smoother airflow within the turbine, enhancing its ability to withstand high wind speeds. Based on these findings, this paper proposes a novel SB-VAWT without an intermediate support axis. By removing blade connectors and the intermediate support shaft, this design mitigates the influence of the support system on the aerodynamic characteristics of the wind turbine. This enables more accurate and convenient wind tunnel experimentation and computer fluid dynamics simulation calculations with this wind turbine. In this paper, different structural parameters of the wind turbine are varied, and the wind tunnel laboratory is used to test its aerodynamic characteristics under different wind speeds, thereby providing insights into the impact of these parameters. From this, we identify the optimal variable parameters and mounting configuration for the wind turbine and study its power generation performance under these optimal conditions. This provides a reference basis for the design and production of wind turbines.

2. Wind turbine designs

2.1. Design of the wind turbine test setup

A SB-VAWT without an intermediate support shaft consists of upper and lower end plates, four blades, a disc generator, and a motor support base, as shown in Figure 1. The lower end of the wind turbine is fixedly connected to the disc generator to form an integral structure, which is then fixed to the wind tunnel balance through the disc generator support base. Both ends of the blades are designed with connecting bolts that are fixed through mounting holes distributed around the circumferences of the end plates. Therefore, through the structural combination of the upper and lower end plates and the blades, a stable frame support structure can be formed without the additional support of the intermediate support shaft and blade struts. This simplifies the structure of the wind turbine, reduces the number of components, and eliminates the need to account for the influence of the intermediate support shaft on the internal airflow of the wind turbine during research and analysis. Additionally, the existence of the upper and lower end plates can also reduce the tip vortex bypassing flow at both ends of the blades (Chen et al. 2023; Gim and Lee 2013; Tang et al. 2023; Zuo and Kang 2015), thus improving the wind turbine performance (Ung et al. 2022).

Figure 1. Wind Tunnel Test Setup, Key Dimensions, and Installation Connection Method.

2.2. Design of wind turbine structural parameters

2.2.1. Selection of airfoil

The airfoil profile directly determines the wind energy conversion efficiency, blade cost, and wind turbine load. According to reference (Song et al. 2018), a wind turbine with curved asymmetric airfoil blades can obtain a larger torque in the windward direction at the same wind speed and enter the lift state at a smaller tip speed ratio. This can provide a higher lift coefficient and lower drag coefficient, resulting in a higher wind energy conversion efficiency. Additionally, the design of the asymmetric airfoil blade with curvature can reduce the blade vibration, lower the noise generated when the wind turbine rotates, and improve the stability of the wind turbine. Moreover, the larger thickness of the airfoil can increase the lift-to-drag ratio, widen the AOA range of the high lift-to-drag ratio, and effectively improve the separation flow characteristics of the airfoil. Based on the above considerations, the commonly used thick airfoils such as NACA0018, NACA0021, and NACA0024, known for high torque and low tip speed ratios for VAWTs, were chosen as the basis for the design and drawing of the asymmetric airfoil blades with curvature for experimental use. With the help of the open-source wind turbine analysis software QBlade developed by the Hermann Föttinger Institute of Technical University of Berlin, blades using curved asymmetrical airfoils for experimental purposes were designed and drawn (Altmimi et al. 2021; Francis, Ajayi, and Ojo 2021), as shown in Figure 2. The lift coefficient curve (Figure 3(a)) and lift-to-drag ratio curve (Figure 3(b)) of the newly designed airfoil were compared in QBlade software. The results showed that within the same common AOA range, the new airfoil design had the highest lift-to-drag ratio and a good lift coefficient. This could improve the wind energy utilisation rate obtained by the wind turbine. Therefore, this airfoil profile was selected as the airfoil for the wind turbine test, and a wind turbine device was manufactured accordingly.

Figure 2. The designed airfoil with curvature (green coordinate line).

Figure 3. Comparison curves of lift coefficient (a) and lift-to-drag ratio variation (b) for the experimental blade (the red curve represents the airfoil used in the experiment).

2.2.3. Selection of blade installation angle

This paper defines the blade installation angle as the angle between the chord line of the blade and the tangent line at the radius of the upper and lower end plate mounting holes. It is specified that the positive direction is clockwise and the negative direction is counterclockwise. The blade installation angle can be adjusted flexibly on the end plate, as depicted in Figure 4(a). By adjusting the blade installation angle, the variation range of the AOA during operation can be reduced, ensuring that the AOA remains within a reasonable range and improving the aerodynamic performance of the wind turbine. Yang et al. (Yang et al. 2018) studied the effect of blade installation angle on the power performance of a SB-VAWT through CFD simulations and wind tunnel tests. They found that a wind turbine with an installation angle of −6° achieved the maximum rated power coefficient. Sun et al. (Sun et al. 2021) improved the power performance of a VAWT by optimising the installation angle. They found that an installation angle of −4° yielded the best power performance, with average power coefficients for the 5-blade turbine and 3-blade turbine increasing by 5.89 and 5.14 times, respectively, compared to a 0° installation angle. Reference (Yang and Xi 2017) utilised unsteady Reynolds-averaged Navier-Stokes (URANS) equations and k-ω SST turbulence model, and simulated the unsteady three-dimensional flow field of an H-type VAWT using CFD analysis software CFX. The study focused on investigating the impact of blade installation angle on the aerodynamic performance of the H-type VAWT. The results showed that the performance of the wind turbine can be improved by changing the installation angle when the relative thickness of the blade airfoil is small or under high tip speed ratio (TSR) conditions. To compare the characteristics of wind turbines within commonly used installation angle ranges and larger installation angle ranges, this experiment selected installation angles of 30°, 25°, 20°, 15°, 14°, 12°, 10°, 8°, 6°, 4°, 2°, 0°, −2°, −4°, −6°, and −8° for testing, and analyzed the influence of different installation angles on the characteristics of the wind turbine through experimental data analysis.

Figure 4. The variable initial installation angle of the blades (a), as well as the forward (b) and reverse (c) blade installation configurations.

This article further defines the forward installation method as having the concave side of the blade facing inward, and the reverse installation method as having the concave side facing outward, as depicted in Figure 4(b) and Figure 4(c) respectively. These definitions are employed to analyze the impacts of forward and reverse blade installation on wind turbine characteristics.

2.2.4. Selection of installation radius

The selection of the installation radius for wind turbines plays a crucial role in determining the rotor diameter and the potential wind energy utilisation, thus significantly influencing the performance and economics of the wind turbine. When designing a wind turbine, various factors such as wind resources, turbine performance, and economics considerations need to be taken into account to determine the appropriate blade installation radius that can achieve optimal power generation efficiency. Generally, a larger blade installation radius results in a larger rotor diameter, enabling a broader range of wind energy capture and consequently generating more electricity. However, increasing the blade installation radius also leads to higher costs as it requires larger blades and stronger tower structures to support the expanded rotor. Hence, in wind turbine design, a balance must be achieved between economy, performance, and reliability to determine the optimal blade installation radius. In this study, by considering the cross-sectional area of the wind tunnel test section, the measurement range of the measurement system, and the size of the wind turbine model, a comparative test was conducted using installation radii of 190 and 160 mm at different wind speeds to investigate the impact of different installation radii on wind turbine performance.

2.2.5. Selection of blade length

Variations in blade length can significantly impact the sweep area of the wind turbine. To investigate the influence of different blade lengths on the performance of the wind turbine, this experiment was conducted based on the previous design of asymmetric airfoils. Specifically, three sets of blades, measuring 500 mm, 600 mm, and 700 mm in length with a chord length of 110 mm, were manufactured for comparative testing. The physical appearance of the blades of different length is illustrated in Figure 5.

Figure 5. Physical image of blades with different lengths.

3. Wind tunnel test equipment and test plan

3.1. Wind tunnel

The wind tunnel used in the experiment was a closed-loop reflux wind tunnel at the Wind Tunnel Laboratory of Shanghai Maritime University, as shown in Figure 6 (a). The rated power of the wind tunnel dynamic fan is 132 kW, driven by a variable frequency motor. The test wind speed is manually adjusted to an accuracy of 0.01 m/s. The wind speed in the wind tunnel is measured by a pitot tube and fed back into the control system to achieve closed-loop control of the wind speed. It can easily and accurately control and adjust the test wind speed continuously between 1 m/s and 40 m/s. To ensure the reliability and accuracy of experimental data, the wind tunnel boasted high airflow stability, turbulence control, and uniformity. The fluctuation range of airflow stability is ≤±0.365%, the turbulence level is ≤0.275%, and the airflow non-uniformity is ≤±0.28%(Zhang and Hu 2021). These excellent performance indicators guaranteed the stability and uniformity of the airflow within the wind tunnel, thereby providing a dependable environment for conducting precise wind tunnel experiments.

Figure 6. The closed-loop wind tunnel at Shanghai Maritime University (a), and external six-component force balance device (b).

The wind tunnel test section used in this experiment was 6 m long, 1.4 m wide, and 2 m high, with a cross-sectional area of 2.8 m². The maximum windward area of the device used in the wind tunnel test was 0.266 m², and the degree of blockage of the wind tunnel was approximately 9.5%. In order to eliminate the pressure difference between the inside and outside of the wind tunnel caused by gas flow inside the tunnel, the wind tunnel was designed and constructed with a barometric pressure compensating slot behind the test section of the wind tunnel, as shown in Figure 6(a), and the cross section of the wind tunnel was gradually enlarged to reduce the wind speed behind the test section, restore normal air pressure, and more effectively pass through the power fan again. The primary goal of this study is to assess the aerodynamic performance of the wind turbine in relation to force, torque, and rotational speed across varying wind speed conditions. By providing different wind speed conditions in the wind tunnel, the performance of the wind turbine under different conditions can be compared and analyzed. However, it's important to note that this study did not involve precise flow field analysis or airflow diffusion research. The wind tunnel walls remained consistent across different operating conditions, and the external environment conditions were also kept constant. Therefore, the testing conditions met the criteria for conducting comparative tests under uniform external environment for wind turbines with differing structural parameters.

The lift, drag and torque applied to the wind turbine were measured using an external six-component force balance mounted on the turntable, as shown in Figure 6(b) (Zhang and Hu 2023). The balance has a measuring range of 0–60 N for force and 0–120 Nm for torque, with an accuracy of 0.1 N/0.1 Nm. The turntable is controlled by a servo motor and the turntable angle can be precisely adjusted to change the initial azimuth angle of the wind turbine within the range of −10° to 370° with an accuracy of 0.1°. During this experiment, the turntable remained stationary at the initial 0° position throughout the test, ensuring that the force coordinate system of the balance aligned with the flow field coordinate system in the wind tunnel. Consequently, there was no need for coordinate transformation of the force measurement from the balance. Figure 7 depicts schematic diagrams of the force and torque coordinate system of the balance. To obtain the lift, drag, and horizontal torque of the wind turbine within the airflow, only the forces and torques in the horizontal plane of the force balance were considered, without accounting for forces in the vertical direction. As the coordinate system of the force balance aligns with the flow field coordinate system of the wind tunnel, the lift force F_L perpendicular to the incoming flow direction is equivalent to F_Z, and the drag force F_d along the incoming flow direction is equivalent to F_X. The six-channel data measured by the balance were acquired by two NI data acquisition cards from National Instruments (China) Instrumentation Co., Ltd, model: cDAQ-9181, with an acquisition frequency of 5 KHz. The data were stored in the data acquisition and processing computer. The data processing computer processed the data every 5 s using the data processing software designed by the manufacturer according to the balance calibration formula. The processed data were then averaged and output as a dataset. Each working condition was tested for a minimum of 3 min, resulting in at least 30 sets of output data. The data acquisition and processing computer was calibrated automatically to ensure the accuracy of the measured values. Subsequently, the average values were derived to determine the force and torque in three directions. Prior to each measurement, tension tests were conducted on the test apparatus at 0 degrees and 90 degrees azimuth angles using a tension sensor to verify the accuracy of the data acquisition. Tension tests were also conducted along the tangential direction to calculate the generated horizontal torque. Through comparison, it was confirmed that the values directly measured by the balance were accurate. During wind tunnel measurements, the initial values in a windless state were measured first. Then, the wind tunnel was operated at the specified wind speed for measurement. By subtracting the initial values, accurate measurements at the set wind speed were obtained, thus eliminating measurement disturbances caused by initial installation and the weight of the test apparatus. These measurement and processing methods effectively eliminate measurement and random errors, ensuring the accuracy of data acquisition in terms of experimental means and methods. This ensures the acquisition of reliable steady-state experimental data for further analysis and research.

Figure 7. Balance force measurement coordinate system in wind tunnel at 0-degree azimuth angle.

3.2. Other testing equipment

In this test, a non-contact digital tachometer model DT-2234B manufactured by Guangzhou Yuanhengtong Technology Co., Ltd. is used to measure the speed of the wind turbine. The tachometer boasts high precision and high resolution, with a speed measurement range of 2.5–99999 rpm and a resolution of 0.1 rpm. During measurement, the photoelectric sensor emits a light beam that strikes the reflective sticker on the rotating component, and the speed of the rotating part can be obtained from the reflection of the sticker.

In addition, a 100 W permanent magnet disc generator manufactured by Guangzhou Hongying Energy Co., Ltd. was selected. The disc generator has a simple and compact structure, small size and high torque density. Especially for disc-type permanent magnet motors with two external rotors and no stator iron core, it effectively eliminates cogging torque and stator iron losses, has low starting torque and high efficiency. The wind turbine can be directly mounted on the outer rotor, resulting in a simple and reliable system suitable for use as a vertical axis direct drive wind turbine. During the wind turbine test, the wind turbine drives the disc generator into rotation, causing the rotor magnetic poles of the disc generator to generate a moving magnetic field in the air gap. This magnetic field interacts with the three-phase winding to produce symmetrical three-phase currents. These currents are subsequently rectified to DC by an MDS60A three-phase rectifier manufactured by Shanghai Shangzheng Rectifier Co., Ltd. through an unregulated rectifier bridge circuit. Finally, the voltage and current are measured across a 10-Ohm shunt resistor using a digital multimeter to determine the generated power.

3.3. Experimental setup

The VAWT with an asymmetric airfoil blade design and no intermediate support shaft was tested in the wind tunnel laboratory at Shanghai Maritime University. The tests encompassed force testing, rotational speed testing, and power generation characteristic testing. Each experiment focused on varying a single structural parameter to determine its optimal form through comparative tests. The optimal form was subsequently utilised in comparative tests for other structural parameters, ultimately obtaining the best combination of all structural parameters. The experimental setup involved the following steps:

1. Study the change rule of force and rotational speed of VAWT at 5 m/s, 7.5 m/s, 10 m/s, 12.5 m/s wind speed under different blade installation methods, compare and analyze the influence of different blade installation methods on the aerodynamic performance of the wind turbine, and obtain the optimal blade installation method.

2. Study the influence of different blade installation angles on the aerodynamic performance of the wind turbine by analyzing force and rotational speed variations at various wind speeds. Comparative analysis was conducted to determine the optimal blade installation angle.

3. Investigate the impact of different wind wheel radii on the aerodynamic characteristics of the wind turbine by studying force and rotational speed variations at installation radii of 190 and 160 mm under various wind speed conditions. Comparative analysis was conducted to determine the optimal installation radius.

4. Analyze the aerodynamic performance of the wind turbine by studying force and rotational speed variations under different blade lengths of 500, 600, and 700 mm at various wind speeds. Comparative analysis was conducted to determine the optimal blade length.

5. Utilisation of the findings from the aforementioned experiments to analyze the wind power generation characteristics by connecting a resistive load under the optimal combination conditions.

4. Experimental data and analysis

4.1. Analysis of the influence of different installation methods of blades on aerodynamic characteristics

Under the same initial installation and structural parameters such as blade installation angle of 0°, installation radius of 190 mm, and blade length of 500 mm, the rotational speed, lift, drag, and torque of the wind turbine were measured for two different installation modes of VAWT blades, forward and reverse installation.

Figure 8 illustrates the gradual variation of wind turbine rotational speed with wind speed under forward and reverse blade installations. It can be observed that the wind turbine rotational speed increases approximately linearly with wind speed for both forward and reverse blade installations, and the greater the wind speed, the greater the wind turbine rotational speed. Under identical initial installation and structural parameters, at the same wind speed, the wind turbine rotational speed is higher in the case of forward installation compared to reverse installation. Because the blade has an asymmetrical airfoil, when the blade is installed in the forward direction, most parts of the wind turbine blade are inside the circular path of rotation, and when installed in the reverse direction, most parts of the wind turbine blade are outside the circular path of rotation. Therefore, during rotation, the disturbance of the airflow caused by the forward installation of the blade is smaller than that caused by the reverse installation of the blade, resulting in lower air resistance. Thus, under the same external flow conditions, the rotational speed of the wind turbine with the blades installed in the forward direction is higher than that of the wind turbine with the blades installed in the reverse direction. As the wind speed increases, the difference in wind turbine rotational speeds between forward and reverse blade installations becomes larger, indicating that the forward installation method is more effective in capturing and harnessing wind energy, thereby increasing the rotational speed of the wind turbine.

Figure 8. The curve of wind turbine rotational speed with wind speed variation under forward and reverse blade installations.

Figure 9 shows the data curves of lift and drag of the wind turbine at different wind speeds for both forward and reverse mounting of the wind turbine blades. As can be seen from Figure 9, with the increase of wind speed, the absolute values of lift and drag of the wind turbine increase for both forward and reverse mounting. It is worth noting that the direction of the lift force on the wind turbine is opposite for the blade forward mounted condition and reverse mounted condition. As can be seen from Figure 9(a), when the wind speed is lower than 10 m/s, the absolute value of the lift force in the forward mounted condition is greater than that in the reverse mounted condition. However, at a wind speed of 12.5 m/s, the absolute value of lift is greater in the reverse installation compared to the forward installation. Furthermore, as indicated in Figure 9(b), the direction of drag is the same for both forward and reverse installations, with slightly higher drag in the forward installation. Based on the analysis of Figure 8, it can be inferred that at the same wind speed, the rotational speed of the wind turbine is higher in the case of forward installation, which results in more pronounced airflow resistance and increased drag. During the rotation of the wind turbine, significant wind resistance is encountered, with the drag being approximately 8–10 times greater than the lift. The lateral lift is relatively weak, and its direction depends on the blade installation direction. At high wind speeds, the lift in reverse installation exceeds that in forward installation. However, in this case, the generated lift is not the lift of the blade profile, but rather the lateral force acting on the entire apparatus perpendicular to the incoming flow. This force leads to lateral displacement and vibration of the wind turbine in a direction perpendicular to the flow, negatively impacting the structural stability and fatigue life of the wind turbine.

Figure 9. The lift variation curve (a) and the drag variation curve (b) of the wind turbine under different wind speeds for both forward and reverse blade installations.

Figure 10 shows the variation of torque with wind speed for wind turbines in both forward and reverse blade mounting modes. The Figure indicates that the torque directions are opposite in the forward and reverse installation modes. In the forward installation mode, the wind turbine rotates counter-clockwise, while in the reverse installation mode it rotates clockwise, consistent with the phenomenon observed in the experiment. According to Figure 8, it can be observed that under the condition of reverse blade installation, at a wind speed of 5 m/s, the wind turbine's rotational speed is relatively low, indicating that it is in a just-starting state. Before the wind turbine starts, it will undergo slight back and forth movement in both clockwise and counterclockwise directions until it eventually continues to rotate consistently in one direction. Therefore, there may be a period of time during the measurement where the torque is negative. As the wind speed increases, the occurrence of negative torque diminishes, and the positive rotational speed of the reverse installation increases. Moreover, as the wind speed increases, the average torque of the wind turbine in the reverse installation mode gradually increases. However, within the measured range of wind speeds, the absolute value of the torque in the forward mounting mode is larger and shows less fluctuation. This indicates that the forward installation of the blades can provide greater torque and more stable operation of the wind turbine.

Figure 10. the torque variation curves of a wind turbine under different wind speeds for both the forward and reverse blade installation modes.

Based on the above experimental results, the wind turbine in the forward blade mounting mode has several advantages. Firstly, the wind turbine in the forward installation mode has a higher rotational speed, indicating that the blades can rotate faster at the same wind speed. Secondly, the forward mounting mode results in greater drag on the wind turbine, suggesting a more efficient conversion of wind energy. Furthermore, the forward installation mode generates less lateral force, which reduces the lateral displacement and vibration of the wind turbine and improves its structural stability. Finally, the forward mounting mode generates more torque, which is essential for efficient wind energy conversion. Therefore, wind turbines with forward mounted blades are able to harness wind energy more effectively and have a superior advantage in terms of operational stability.

4.2. Analysis of the effect of different installation angles on aerodynamic characteristics

Under the conditions of a VAWT with forward-installed blades, a 190 mm installation radius, and a 500 mm blade length, the wind turbine's rotational speed, lift, drag, and torque were tested at different blade installation angles to study the effect of different blade installation angles on the performance of the wind turbine.

Figure 11 illustrates the variation in the rotational speed of a wind turbine at different installation angles and wind speeds. At a wind speed of 5 m/s, the highest rotational speed is attained with an installation angle of 0°. It is evident that the rotational speeds at negative installation angles consistently exceed those at positive angles. As the installation angle increases, the rotational speed gradually decreases. In the case of low wind speeds, a wind turbine with forward-mounted blades features a negative blade installation angle, orienting the concave surface of the blade toward the windward side. This configuration enhances the obstruction of the blade to the airflow, generating a larger torque for start-up. As the installation angle transitions from negative to positive, the concave surface of the blade gradually retracts inside the rotor, reducing the obstruction. With further increases in the positive angle, the concave surface of the blade shifts more towards the leeward side, leading to a reduction in the rotational speed of the wind turbine at low wind speeds. This indicates that negative installation angles result in higher rotational speeds in the low wind speed range. At wind speeds of 7.5 m/s, 10 m/s and 12.5 m/s, the maximum rotational speed is achieved with an installation angle of 10°. As the installation angle transitions from negative to positive, there is a tendency for the rotational speed to first increase and then decrease. When the wind speed exceeds 7.5 m/s, the rotation of the wind turbine is no longer primarily influenced by the resistance torque. The faster rotational speed of the blades leads to increased lift, resulting in a larger torque, which becomes the primary source of torque. However, the forward installation angle cannot infinitely increase; it requires a suitable installation angle to achieve a broader range of optimal attack angles that can generate high torque. Therefore, once the optimal installation angle is surpassed, the rotational speed of the wind turbine decreases. Additionally, under high-speed rotation conditions, a corresponding reduction in wind resistance is necessary, leading to a markedly different pattern of change compared to low wind speeds. This implies the presence of an optimum installation angle, deviation from which significantly reduces the wind turbine's speed. Empirically, the optimal wind turbine speed varies with wind speed and installation angle conditions. Negative installation angles contribute to higher rotational speeds in the low wind speed range. while an installation angle of approximately 10° yields the highest rotational speed at higher wind speeds.

Figure 11. the curve of wind turbine rotational speed variation with different installation angles at various wind speeds.

The lift and drag data of the wind turbine at different installation angles and wind speeds are shown in Figure 12(a) and Figure 12(b) respectively. It can be observed that as the wind speed increases, both the drag and lift of the wind turbine at different installation angles increase proportionally. The minimum lift of the wind turbine is observed at an installation angle of 8–10°, indicating a minimum lateral force acting on the wind turbine. The lowest drag is observed at an installation angle of 8°. Combining the results from Figure 11, it can be concluded that in the range of higher wind turbine speeds, specifically at an installation angle of 8–10°, the wind turbine exhibits minimal lateral force and drag, resulting in more stable operation.

Figure 12. The variation curves of lift (a) and drag (b) of the wind turbine with different installation angles at various wind speeds.

The variation of the torque of the wind turbine with different installation angles at different wind speeds is shown in Figure 13. From the figure, since all the blades are installed in the forward direction, the torque directions are all negative, which is consistent with the observed regularity of forward blade installation. As the wind speed increases, the absolute value of the torque generally increases with the increase in wind speed at different installation angles. However, the torque varies significantly with different installation angles. Within the range of installation angles 0°−17°, the torque fluctuates most dramatically and both the maximum and minimum torques occur within this range. Outside this range, the absolute value of the torque fluctuation decreases and the torque values remain at a lower level. Specifically, at wind speeds of 5 m/s and 10 m/s, the maximum absolute torque occurs at 0°installation angle, while at 7.5 m/s and 12.5 m/s, the maximum absolute torque is measured at 10°installation angle.

Figure 13. the curve of the variation of wind turbine torque with different installation angles at various wind speeds.

By analyzing the combined data of wind turbine speed, lift, drag and torque measured at different installation angles under different wind speeds, the optimal installation angle is determined to be 10°. At this installation angle, the wind turbine exhibits characteristics such as low lateral force, low drag, stable operation and a high absolute value of torque.

4.3. Analysis of the influence of different installation radii on aerodynamic characteristics

Under the conditions of forward installation of VAWT blades, an installation angle of 10° and a blade length of 500 mm, the rotational speed, lift, drag and torque of the wind turbine were measured for installation radii of 160 mm and 190 mm.

As shown in Figure 14, the rotational speed of wind turbines with varying installation radii gradually varies with wind speed. The curve in the figure demonstrates that an increase in wind speed corresponds to a proportional increase in the rotational speed of the wind turbine. It is noteworthy that, within the tested range of wind speeds, the wind turbine with an installation radius of 160 mm consistently exhibits a higher rotational speed compared to the wind turbine with an installation radius of 190 mm.

Figure 14. The comparative diagram of the rotational speed of wind turbines with two different installation radii under various wind speeds.

Figure 15(a) and Figure 15(b) present the lift and drag data for wind turbines with installation radii of 160 mm and 190 mm, respectively. Analysis of Figure 15(a) reveals that the magnitude of lift increases with higher wind speeds. In other words, as the wind speed increases, so does the lift generated by the wind turbine. Furthermore, a larger rotor radius leads to greater lift, resulting in increased lateral force on the rotor. It is worth noting that wind turbines with larger rotor radii are more susceptible to oscillation, especially at high wind speeds, due to the amplified lateral forces they experience. This oscillation negatively impacts the stability and fatigue life of the structure.

Figure 15. The comparative diagram of lift and drag for wind turbines with two different installation radii.

Figure 15(b) illustrates that the resistance of the wind turbine escalates rapidly as the wind speed rises. Additionally, an increase in installation radius corresponds to an increase in drag. However, it is crucial to acknowledge that the disparity in drag caused by variations in installation radius is not substantial and not easily discernible. The primary factor influencing drag is the size of the windward area of the turbine.

The results of processing the torque data for wind turbines with two different installation radii are depicted in Figure 16. In the case of forward installation, the torque is represented by a negative value (the positive or negative sign only denotes the direction). With an increase in wind speed, the absolute value of the torque exhibits an upward trend, and the magnitude of this increase is significant. Furthermore, the absolute value of the torque generally surpasses that of the wind turbine with a 190 mm installation radius when comparing it to the wind turbine with a 160 mm installation radius. Based on the analysis of the torque data, it can be inferred that wind turbines with a 160 mm installation radius generate higher torque and therefore exhibit better performance.

Figure 16. The comparative diagram of the change in torque of wind turbines with two different installation radii as a function of wind speed.

The experiments described above reveal that when the installation radius is 160 mm, wind turbines exhibit higher rotational speed, lower drag, lower lift, and higher torque in the high wind speed range. These results suggest that wind turbines with a 160 mm installation radius possess superior load characteristics and optimal rotational performance.

4.4. Analysis of the impact of different blade lengths on aerodynamic characteristics

Under the parameter conditions of forward installation of VAWT blades, installation radius of 160 mm, and installation angle of 10°, the wind turbine rotational speed, lift, drag, and torque were tested for blades of different lengths (500 mm, 600 mm, 700 mm) to explore the impact of different blade lengths on wind turbine aerodynamic characteristics.

Figure 17 shows the curve of wind turbine rotational speed as a function of wind speed for wind turbines with blades of length 500, 600, and 700 mm installed. It can be seen that the trend of wind turbine rotational speed changing with wind speed is roughly the same for all three blade lengths. At low and high wind speeds, the wind turbine with a blade length of 600 mm has the highest rotational speed, while at medium wind speeds, the wind turbine with a blade length of 700 mm has the highest rotational speed. The lengths of the blades may vary, but the structural form of the wind turbine and the operational state of the blades during rotation remain the same, resulting in no significant differences in aerodynamic forces. It is worth noting that the rotational speed differences among the different blade lengths are not significant at different wind speeds.

Figure 17. The comparative diagram of wind turbine rotational speed at different wind speeds for different blade lengths.

The lift and drag data of wind turbines with different blade lengths are shown in Figures 18(a) and (b). Figure 18(a) shows that the lift of wind turbines with different blade lengths increases with increasing wind speed. For a blade length of 600 mm, the wind turbine has a significantly higher lift compared to wind turbines with blade lengths of 500 and 700 mm. When the wind speed is less than 7.5 m/s, the absolute value of the lift for the 700 mm blade is greater than that of the 500 mm blade, and in the wind speed range above 7.5 m/s, the lift of the 700 mm blade is still greater than that of the 500 mm blade. On the other hand, Figure 18(b) shows that as the blade length increases, the area of the turbine exposed to the wind increases, resulting in an increase in drag. As the wind speed increases, the drag curve accelerates and expands proportionally to the wind speed. Between the blade lengths of 600 and 500 mm, the increase in drag caused by the increase in turbine area exposed to the wind is significantly greater than the increase in drag between the blade lengths of 700 and 600 mm. The increase in drag is proportional to the rate of increase in the area of the wind turbine exposed to the wind. Wind turbine drag depends mainly on the increase of the wind turbine area exposed to the wind.

Figure 18. The curves of wind turbine lift (a) and drag (b) with wind speed for installation of blades with different lengths.

The torque data of the wind turbine with different blade lengths is shown in Figure 19. When a 700 mm blade is installed, the wind turbine torque is significantly lower compared to the other two blade lengths. At low wind speeds, the wind turbine torque with the 500 mm blade installed is slightly higher than that with the 600 mm blade installed, but the difference is not significant. At high wind speeds, however, the torque of the turbine with the 600 mm blade length is greater than that of the turbine with the 500 mm blade length.

Figure 19. the comparison diagram of torque variations with wind speed for wind turbines with different blade lengths.

The above results indicate that the installation of different blade lengths leads to variations in torque. Among them, the 500 and 600 mm blade lengths exhibit higher torque values with minimal difference. Across the entire range of wind speeds, the installation of a 600 mm blade length yields the best performance.

5. Analysis of the characteristics and efficiency of wind turbine power generation

After analyzing the impact of various structural parameters on the aerodynamic characteristics of the wind turbine, it was determined that the wind turbine with a 600 mm blade length, forward installation, 160 mm installation radius, and a 10° installation angle exhibited the highest speed, the largest torque and the lowest lateral force at identical wind speed. Consequently, these installation conditions were chosen for the wind power generation experiment, during which a 10 Ω pure resistance load was incorporated to measure the voltage–current data of the wind turbine at different wind speeds, allowing for analysis of power generation characteristics and efficiency.

5.1. Analysis of wind turbine power generation characteristics

During the test, the wind tunnel airflow was first adjusted to 8 m/s. After the wind turbine speed stabilised, the speed, torque, voltage and current of the fixed resistance load were measured and recorded. The wind tunnel airflow was then gradually increased in 0.2 m/s increments and the above steps were repeated until the wind speed reached 14 m/s.

Figure 20 shows the correlation between the wind turbine speed and the wind speed under different conditions, specifically with a 10 Ω load and under open circuit conditions. It is evident that the turbine speed is notably reduced when the load is applied at the same wind speed. In the presence of a load, the wind turbine speed demonstrates a gradual initial rise with increasing wind speed. However, at a critical wind speed of 13 m/s, the wind turbine speed experiences a sudden and significant surge, transitioning from low to high speed, before returning to a slower growth trajectory.

Figure 20. The comparison curve of wind turbine speed with and without a 10 Ω load at different wind speeds.

The voltage and current data of the fixed resistance load were measured under the optimal installation configuration of the VAWT blade, and the results are shown in Figures 21(a) and (b). As the voltage and current generated during wind turbine operation are intricately linked to the rotational speed, it is expected that the curves of these three variables exhibit similar patterns.

Figure 21. The Variation curves of fixed resistance load voltage (A) and current (B) with wind speed at different wind speeds.

The sudden increase phenomenon observed in Figures 20 and 21 indicates significant changes in the performance of the wind turbine and generator at certain wind speeds. This occurrence can be attributed to the fact that when the wind speed corresponds to the abrupt transition in the speed of the wind turbine, the torque increases but the power generation efficiency of the pancake generator remains relatively low. As a result, the electromagnetic torque remains small, causing the wind turbine to experience greater acceleration and a rapid surge in speed. As the rotational speed of the wind turbine blades increases, the corresponding tip speed ratio also increases, causing the aerodynamic characteristics to develop in a more favourable direction. This further reinforces the increase in rotational speed. However, as the speed continues to rise, the efficiency of the generator also improves, triggering an immediate change in voltage and current for the resistive load Consequently, there is an increase in the electromagnetic torque. Therefore, when the wind speed exceeds a critical value, the wind turbine rapidly adapts to a new equilibrium state and continues to operate with a gradually increasing trend in wind speed.

Figure 22 shows the torque curves for both unloaded and loaded states at various wind speeds. It is evident that the torque in the unloaded state is significantly higher than in the loaded state, and the torque difference between these two states becomes more pronounced as the wind speed increases. In the loaded state of the wind turbine, the conversion of shaft power into electrical energy results in a reduction of the output torque compared to the unloaded state. This is because in the unloaded state, the rotating wind turbine experiences relatively less resistance and does not need to drive a load, allowing for a higher proportion of energy to be transformed into shaft power output. However, once a load is introduced, as in the loaded state, a portion of the shaft power is converted into electrical energy consumed by the load, resulting in a relative decrease in the mechanical power output. As the wind speed increases, the torque difference between these two states widens further. This phenomenon is attributed to the increased energy requirement for driving the load as the wind speed escalates. With the conversion of a portion of energy into electrical energy output in the loaded state, the available shaft power for torque output decreases, resulting in an amplified magnitude of the measured torque reduction.

Figure 22. The torque variation curves of a wind turbine with a resistive load and an unloaded condition at different wind speeds.

5.2. Analysis of mechanical-to-electrical energy conversion efficiency in wind turbines

The electrical generation efficiency of the generator is defined as the ratio of the power consumed by the resistance to the mechanical power transmitted to the generator by the rotating shaft of the wind turbine.

Figure 23 illustrates the variations in power output and electrical conversion efficiency of a wind turbine at different speeds. As the rotational speed increases, the power output of the wind turbine gradually increases, accompanied by an improvement in energy conversion efficiency. However, a notable observation is that when the wind speed reaches a certain threshold, there is a sudden surge in the rotational speed, leading to a sharp increase in both power output and efficiency. Once the wind speed exceeds 13 m/s and the rotational speed exceeds 112 rpm, surpassing the turning point, the conversion efficiency becomes relatively high and can exceed 50%. In particular, at a wind speed of 14 m/s and a speed of 210.4 rpm, the conversion efficiency can reach an impressive 55.9% and continues to rise. This phenomenon highlights the significant impact of the generator’s speed on the efficiency of converting mechanical energy into electrical energy. In order to achieve a higher efficiency of electrical generation, it is crucial to maintain the generator within a higher speed range. This ensures that the wind turbine operates at an optimal speed, maximising the conversion of mechanical energy into electrical energy.

Figure 23. The variations in power output and electrical generation efficiency of a wind turbine device at different rotational speeds.

According to the law of conservation of energy, the total amount of energy is conserved during the energy conversion process. A wind turbine serves as a device designed to harness wind energy and transform the kinetic energy of the moving air into mechanical energy within the wind turbine(Wang et al. 2020). This mechanical energy propels the connected disc generator, ultimately converting the wind energy into electrical energy output. In most studies, the wind energy conversion efficiency of a wind turbine refers to the efficiency of converting wind energy into mechanical energy. However, it is essential to consider certain factors that limit the overall efficiency of this conversion process. According to the Betz limit, the maximum efficiency of converting wind energy into mechanical energy cannot exceed 59.3%. In practical operation, wind turbine generators experience energy losses in various forms such as vibrating energy, sound energy, resistance from wind rotation, mechanical friction, and so on. Furthermore, there are additional losses stemming from the generator itself, including iron and copper consumption, mechanical losses and stray losses, which result in the inability to fully convert the extracted mechanical energy from the wind into electrical energy. Additionally, as the wind turbine needs to maintain its own rotation, a portion of the energy cannot be converted into electrical energy output.

6. Conclusion

1. When installed in the forward direction at varying wind speeds, the blades designed in this paper exhibited higher rotational speed, lower lateral lift, higher torque, superior structural stability, and increased utilisation efficiency of wind energy compared to their performance when installed in the reverse direction.

2. Wind turbine blades are optimised for a specific installation angle, where high rotation speed, low lateral force, and minimal drag are achieved. Deviating from this optimal angle results in increased rotation speed and lateral force in an unfavourable direction.

3. Wind turbines with smaller radii demonstrate slightly higher rotation speeds and lower drag under the same wind speed, albeit with negligible impact. Conversely, larger blade radii lead to increased lateral force, potentially causing vibration at high wind speeds, which is detrimental to structural stability and fatigue life.

4. As wind speed increases, the rotation speed of the wind turbine experiences gradual linear growth. However, under load resistance, the rotation speed significantly decreases compared to the no-load condition. Upon reaching a certain wind speed threshold, the rotation speed of the wind turbine undergoes a sudden increase, followed by a gradual rise. Operational load affects the wind turbine, resulting in lower rotational speed and torque compared to the no-load state, with a specific threshold for sudden acceleration.

5. The electrical power output of the wind turbine steadily increases with the speed increases, and the energy conversion efficiency also gradually improves as the speed increases. The generator has an optimum efficiency conversion speed and must be operated stably within this speed range to achieve the best conversion efficiency.

7. Future work

This paper investigates the rotational, force and power generation characteristics of a vertical axis wind turbine without an intermediate support shaft under dynamic conditions. The influence of varying a single structural parameter on the wind turbine characteristics is studied to understand the impact of parameter changes. There are several aspects that can be further investigated in future studies.

The various influencing parameters in this paper can be further extended to form a rich set of coupled variables, such as aspect ratio, solidity and tip speed ratio, to study the aerodynamic characteristics under the condition of multi-parameter coupling and dimensionless parameter changes. Further optimisation of the best match between wind turbine and generator through theory and experiment is needed to establish an optimal design matching theory. A comparative study of different airfoil profiles under the optimal ratio state in terms of power generation efficiency is required to identify the most suitable airfoil profile and understand the influence of different airfoil parameters. In addition, it is necessary to study the power generation characteristics of the wind turbine and the overspeed protection characteristics of the generator beyond its rated speed in a wider range of wind speeds in order to conduct comprehensive experiments for practical engineering applications.

Author contributions

Conceptualisation, H.Z. and Y.H.; methodology, H.Z.; validation, H.Z. and Y.H.; formal analysis, H.Z.; resources, H.Z. and Y.H.; data curation, H.Z.; writing – original draft preparation, H.Z.; writing – review and editing, H.Z. and Y.H.; visualisation, H.Z.; supervision, Y.H.; project administration, Y.H.; funding acquisition, H.Z. and Y.H. All authors have contributed significantly.

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Disclosure statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Additional information

Funding

This work was supported by the Science & Technology Commission of Shanghai Municipality and Shanghai Engineering Research Center of Ship Intelligent Maintenance and Energy Efficiency under Grant 20DZ2252300.