Design,simulation,and experimental evaluation of a novel three-stage coaxial counter-rotating wind turbine

Abstract

This paper presents the design, aerodynamic simulation, and experimental validation of a novel three-stage horizontal-axis wind turbine (HAWT) with coaxial and independently rotating rotors. Building on the dual-rotor architecture widely studied in recent years, the proposed configuration introduces a third rotor with a larger radius (120–125% compared to the first two rotors) to harness the remaining wind energy passing through upstream stages. The rotors rotate in opposite directions to increase the relative velocity of magnetic field interaction, thereby improving electrical generation efficiency. The aerodynamic behavior of the turbine was analyzed using XFlow software with the Lattice-Boltzmann Method (LBM), enabling large eddy simulations (LES) on an octree mesh to capture flow interactions and wake effects. The optimized blade geometry and spacing were determined through simulation, focusing on maximizing energy extraction at low to moderate wind speeds (3–9 m/s). A 3D-printed experimental prototype was developed using GOE222 airfoil profiles and tested in a controlled wind tunnel environment. The test setup allowed selective activation of one, two, or all three rotor stages to isolate and compare their respective power outputs. Results demonstrated that the three-stage turbine consistently outperformed both single-stage and dual-stage configurations. Notably, power output increased by 30%–94% compared to the two-stage design, and up to 703% compared to the single-stage model at lower wind speeds. This study demonstrates the significant potential of multi-stage, counter-rotating turbines in small and medium-scale applications, offering a viable path toward higher efficiency and improved energy harvesting from wind resources.

Keywords

multi-stage wind turbine counter-rotating rotor aerodynamic simulation Lattice-Boltzmann method small-scale wind energy systems

Introduction

In the context of the growing demand for developing more efficient wind energy harvesting solutions, multi-stage wind turbines have emerged as a promising research direction aimed at improving power coefficients and optimizing investment costs, especially at small and medium scales. Both international and domestic studies have approached this topic from multiple perspectives: model design, numerical simulation using CFD, wind tunnel experiments, aerodynamic theory, as well as structural and transmission system analysis. The two most commonly studied configurations are (1) multi-rotor turbines mounted on the same plane, and (2) multi-rotor turbines with coaxial alignment.

The initial designs by Lagerwey Wind (1995) and the NASA research project (2010) demonstrated certain technical effectiveness; however, they encountered difficulties in synchronization control and speed reduction under strong wind conditions. Unidirectional coaxial turbines are considered advantageous in terms of mechanical stability and power generation efficiency, owing to the use of high-speed generators. Nevertheless, the extended shaft length poses challenges regarding structural durability and control under stormy conditions (Nguyen et al., 2022a).

Another noteworthy configuration is the counter-rotating dual-rotor wind turbine, intended to utilize the residual energy from the front rotor. The benefits of this configuration can be further enhanced through innovative drivetrains, such as those using counter-rotating electric generators to improve overall system efficiency (Saulescu et al., 2021). The transmission system may employ either shared gear mechanisms or two independent generators. However, such studies are often limited by structural complexity and challenges in electrical output synchronization. Recently, the invention by the Bakanov group (Bakanov, 2018, 2019) with the ИнС-В-1000 model, which applies a clutch mechanism to control rotor speed, represents an effort to realize the dual-rotor turbine concept. Nonetheless, the claimed power efficiency of 100% is inconsistent with established aerodynamic principles and the theoretical Betz limit, highlighting the need for rigorous, independently validated performance data for such designs. Several other patents registered in the United States (US Patents, 2009, 2013, 2016) have not been practically applied due to their reliance on planetary gearsets, which entail significant losses and are unsuitable for low-power systems.

Regarding experimental and CFD-based studies, Jung et al. (2005) conducted tests on a 30 kW dual-rotor wind turbine. Lucia-Andreea Mitulet et al. (2020) reported an average power increase of 40% compared to single-stage turbines in the wind speed range of 5.5–10 m/s. Recent numerical investigations have also explored various DRWT configurations, including those with different rotor sizes, confirming their potential to significantly increase the power coefficient (Wang et al., 2022). Santhana Kumar et al. (2021) performed tests on scaled models and compared them to CFD results. However, for turbines with novel drive structures, there remains a lack of comprehensive wind tunnel experimental data.

In terms of numerical simulation, high-fidelity methods like large eddy simulation (LES), often coupled with an actuator line model (ALM), have become a standard approach for analyzing the complex aerodynamics and wake characteristics of dual-rotor turbines (Bai et al., 2023; Zhao et al., 2023). Li et al. (2021) employed the LBM-LES method to analyze the effects of blade pitch and rotor spacing. Rosenberg et al. (2020) used the RANS model, which was later validated by LES. The study by Yin et al. (2022) constructed a detailed CFD model based on theoretical foundations, while Mohamed et al. (2021) simulated a dual-rotor wind turbine with a diffuser-augmented design.

Theoretical investigations have primarily employed linear momentum theory. Newman (1986) were the first to propose an aerodynamic model for dual-rotor turbines, establishing a maximum efficiency of 64%, exceeding the Betz limit of 59.3%. This theoretical gain is supported by modern simulations showing that while DRWTs create a large initial wake deficit, they also exhibit a faster wake velocity recovery, which is crucial for improving performance (Bai et al., 2023; Zhao et al., 2023). Subsequent researchers, such as Chantharasenawong et al. (2016) and Agrawal (2017), refined the model by distinguishing the axial induction factors of the inner and outer streamtubes, while assuming atmospheric pressure recovery between the rotors. Their models predict a maximum power coefficient of up to 81.4%. Sundararaju et al. (2017) further extended the model by incorporating realistic factors such as rotor diameter ratio, inter-rotor spacing, and tip-speed ratio. They concluded that maximum efficiency of 81.4% is achieved when the spacing between rotors equals 2.8 times the rotor diameter. Yin et al. (2022) applied the Blade Element Momentum (BEM) theory to analyze in detail the aerodynamic interactions between the two rotor stages. They constructed a model incorporating axial and tangential interference factors, extending the applicability of BEM to straight-blade configurations.

In Vietnam, research on dual-rotor wind turbines remains relatively novel. Notable publications include Nguyen and Ngo (2021), who patented a coaxial turbine model with independent rotation; Nguyen et al. (2022b), who investigated a horizontal-axis dual-rotor turbine with coaxial and independent operation, which demonstrated significantly higher energy harvesting capability than conventional single-rotor designs; Le and Nguyen (2022), who applied blade element theory to simulate and calculate the performance of a dual-rotor turbine; Le et al. (2023), who presented experimental results and CFD simulations of a small-scale dual-rotor turbine, confirming its superior performance at low wind speeds; and Le et al. (2024), who studied the influence of rotor spacing on the electrical output at various wind speeds for both aerodynamic and straight-profile blades.

While existing studies on dual-rotor counter-rotating turbines have primarily focused on enhancing power coefficients, often demonstrating significant gains, practical implementations can face challenges. These may include increased mechanical complexity, the need for sophisticated synchronization mechanisms when using shared gearing, and potential long-term reliability concerns, which have been noted as a limiting factor for some counter-rotating designs. The novel three-stage coaxial wind turbine configuration proposed herein, featuring independently rotating rotors and direct-drive transmission for each stage, aims not only to further augment energy capture by harnessing residual wind energy with a specifically sized third rotor but also seeks to address some of these operational concerns. This is achieved by potentially reducing mechanical complexity compared to geared multi-rotor systems, thereby offering a pathway to improved robustness alongside increased efficiency.

All the aforementioned studies focus exclusively on dual-rotor turbines. No prior study has investigated a three-stage rotor configuration. However, empirical findings from studies (Le et al., 2023, 2024; Le and Nguyen, 2022; Nguyen and Ngo, 2021; Nguyen et al., 2022b) indicate that substantial residual wind energy remains after the second rotor stage, which could be further harnessed with the addition of a third rotor. Therefore, the present research is dedicated to studying a novel invention—a three-stage coaxial wind turbine with independently rotating rotors.

To further elucidate the uniqueness of the proposed configuration, Table 1 summarizes and compares the key features of this three-stage system against existing wind turbine technologies. The comparison shows that while dual-rotor counter-rotating systems have improved efficiency over single-rotor turbines, our three-stage configuration targets a higher level of optimization by actively harnessing the expanded streamtube and enhancing the electromagnetic induction effect—an approach that has not been comprehensively explored before.

Table 1.

Comparative analysis of wind turbine configurations.

Feature	Conventional single-rotor	Dual-rotor (counter-rotating, geared)	Dual-rotor (counter-rotating, independent)	Proposed three-stage independent counter-rotating
Energy Capture	Single swept area	Recovers rotational energy in wake	Recovers rotational energy in wake	Recovers rotational energy AND captures energy from expanded streamtube
Generator	Single, standard speed	Often complex, shared gearbox	Two independent generators	Three independent generators, counter-rotating electrical components
Mechanical Complexity	Low	High (gearbox, synchronization)	Moderate (two systems)	Moderate (direct-drive, no gears)
Key Innovation	N/A	Wake energy recovery	Electrical synchronization challenges	Third, larger rotor for expanded flow & enhanced electromagnetic induction

General structural design of the three-stage wind turbine

The three-stage wind turbine is structured as follows:

The turbine consists of three distinct blade stages arranged coaxially. The first and second blade stages share identical blade dimensions, while the third blade stage is larger than the first and second stages.

Each blade stage is directly connected to a separate rotor. Specifically, the first and second blade stages are attached to rotors equipped with wound coils, while the third blade stage is coupled with a rotor containing permanent magnets.

Slip rings are installed on the first and second rotors to transmit the generated current from the coils to the external circuit via carbon brushes, directing the electricity to the end-use point.

The first and second blade stages rotate in the same direction, whereas the third blade stage rotates in the opposite direction relative to the first and second stages (Figure 1).

Figure 1.

General structure of the three-stage wind turbine.

Aerodynamic simulation

The aerodynamic simulation of the three-stage wind turbine can be conducted using specialized software such as Ansys Fluent, employing the URANS model, or Simulia XFlow, which utilizes particle-based simulation methods. The Lattice-Boltzmann Method (LBM) is the core approach adopted by XFlow for implementing particle-based simulations. This method employs an Octree mesh structure, which can be conceptualized as a system of cubic cells where each level of refinement halves the edge length of the preceding cube, effectively reducing the volume by a factor of eight. This mesh structure is automatically generated within XFlow, and when combined with the LBM, it enables Large Eddy Simulation (LES) with relatively low computational cost.

The computational domain was established extending 5 rotor diameters (D, based on the front rotor diameter) upstream and 15D downstream from the turbine, with a lateral dimension of 5D from the turbine centerline to minimize blockage effects. A uniform velocity inlet boundary condition, corresponding to the experimental wind speeds (3–9 m/s), was applied at the domain’s entrance, while a pressure outlet condition was set at the exit. The outer boundaries of the domain were treated as slip walls. A no-slip boundary condition was applied to all blade surfaces and rotating shafts. The Lattice-Boltzmann Method, combined with Large Eddy Simulation (LES) utilizing the Wall-Adapting Local Eddy-viscosity (WALE) sub-grid scale model, was chosen for its robustness in handling the inherently transient and complex vortical interactions between the multiple, independently rotating stages. Each of the three rotor stages was modeled within its own rotating reference frame, with appropriate interface conditions to ensure continuity of flow variables across the frame boundaries, accurately simulating their independent rotational speeds and, for the third stage, its counter-rotating motion.

The simulation was considered converged when the scaled residuals for velocity and pressure components dropped below 1 × 10⁻⁴ and key performance metrics, such as the aerodynamic torque on each rotor, reached a quasi-steady state with fluctuations of less than 2% over 500 consecutive time steps. A mesh independence study, similar to the one performed for the front rotor (Figure 2), was also conducted for the rear rotor, confirming that a 0.02 m resolution in the blade region provided a balance of accuracy and computational cost. For the inflow boundary condition, a uniform velocity profile was used without introducing turbulence intensity. This approach was intentionally chosen to isolate and clearly identify the aerodynamic effects originating purely from the multi-stage, counter-rotating interactions, which is the primary focus of this novel design. We acknowledge this as a simplification, and the influence of realistic atmospheric turbulence intensity will be a key variable in our future high-fidelity studies.

Figure 2.

Assessment of mesh convergence capability.

A notable limitation of XFlow is its inherently transient simulation approach—meaning that it always operates in dynamic simulation mode. As a result, in scenarios where the system requires a long time to reach steady-state conditions, the computational resources required may become significantly higher.

In this study, the primary aerodynamic concept for the three-stage wind turbine is to exploit the expansion of the streamtube after it passes through the first two rotor stages, allowing the third rotor to intercept the expanded flow. This concept is illustrated in Figure 3.

Figure 3.

Illustration of streamtubes passing through blade stages.

The red streamtube passes over the leading edge of the front blade stage, while the black streamtube passes over the leading edge of the middle blade stage.

The primary objective of this section is to use XFlow to propose a preliminary design for the dimensions of the third blade stage. Detailed simulations and power calculations for the three-stage wind turbine will be addressed in subsequent sections.

The main implementation steps are as follows:

1. Simplify the geometric model and import it into the simulation software.

2. Define boundary conditions and computational domain parameters.

3. Configure the mesh settings.

4. Set up monitoring variables.

5. Post-process and analyze the results.

In Step 1, the geometry of the three-stage wind turbine used in the simulation can be summarized by the parameter table below. Notably, the front and middle blade stages rotate in the opposite direction to the rear blade stage.

The dimension of the rear blade stage reported in Table 2 is only a preliminary, relative value; its exact size will be determined once the XFlow simulations have been completed.

Table 2.

Geometric parameters of the three-stage wind turbine.

Parameters	Unit	Values
Airfoil profile	X	GOE222, for all three blade stages
Front blade stage diameter	m	2.970
Middle blade stage diameter	m	2.970
Rear blade stage diameter (assumed)	m	4.000
Reference radius of the rear blade stage	m	1.500
Distance between the front and middle blade stages	m	0.715
Distance between the rear and middle blade stages	m	0.340
Blade pitch angle	degree	8.5

From a theoretical standpoint, exploiting the expansion of the red streamtube in Figure 2 does provide a basis for sizing the rear blade stage, yet several indeterminacies remain (Figure 4):

• The flow at the blade tip is fundamentally vortical and highly turbulent, making it difficult to quantify precisely.

• The result is strongly dependent on variables such as the inter-stage spacing and the individual dimensions of each blade stage.

Figure 4.

Geometric model of the three-stage wind turbine in XFlow, with blade roots removed for simplification.

In Step 2, the operation of the three-stage wind turbine will be examined under a range of inlet wind speeds: 5, 6, 7, 8, and 9 m/s. These values were selected to approximate expected real-world operating conditions while also generalizing the simulation problem.

A tip-speed ratio (TSR) of 4.5 is assigned to each blade stage, from which the corresponding rotational speeds are derived as presented in the following table:

In Step 3, the mesh size was selected based on a trade-off between computational cost and simulation accuracy. Initially, the mesh near the blade region was set to 0.08 m, then gradually refined to 0.04 m, 0.02 m, and finally 0.01 m.

Figure 2 illustrates the axial thrust force (F_x) acting on the front blade stage at 10 s under a wind speed of 7 m/s. From the results, it is evident that the simulation has converged at a mesh size of 0.02 m. The value of F_x at 0.02 m differs by only 0.6% compared to that obtained at 0.01 m. Therefore, to balance computational efficiency and accuracy, the mesh size of 0.02 m was selected.

The mesh size selected for the wake region is 0.04 m. The background mesh size is selected as 0.08 m. The mesh structure generated in Xflow is illustrated in the figure (Figure 5).

Figure 5.

Computational mesh in Xflow software.

In Step 4, a series of simulation result monitoring points (probe or sensor objects in Xflow) will be configured to track the desired quantities over time (Figure 6):

• Probes are configured to estimate axial velocity at the measurement plane, thereby allowing the application of the mass conservation equation to quantify the streamtube expansion.

• Sensors are configured to measure the tangential wind velocity (V_z) at the position just before the plane of rotor 3. The transition point from a non-zero V_z value to V_z = 0 is the desired location: the intersection between the outer streamtube—passing over the tip of the first rotor—and the plane of the third rotor at a specific position.

Figure 6.

Computation points configured in Xflow.

After completing Steps 1 through 4, the following key results were obtained:

• The intersection point between the outer streamtube (red in Figure 3) and the rotor plane of the rear blade stage is presented in the table below:

It can be observed that this intersection position depends on multiple variables: the incoming free-stream wind speed, the rotational speed, and the dimensions of the blade stages. However, for the purposes of preliminary design—and to fully utilize the streamtube expansion from the front blade stage—it is reasonable to select an increase ratio of approximately 125% relative to the reference radius of the rear blade stage. In the XFlow simulation results, it was found that at a wind speed of V = 5 m/s, this ratio is approximately 120%. However, at lower wind speeds, such as 4 or 3 m/s, the ratio may reach around 125%.

• Representative streamlines:

The simulated streamlines (Figure 7) and vorticity contours (Figure 8) provide crucial insights into the inter-stage aerodynamic interactions. The expansion of the streamtube past the first two co-rotating stages, as quantified in Table 3, is clearly visualized, creating an enlarged area of influence for the third, larger-diameter rotor. Figure 8 reveals the complex wake structures shed from each blade stage. Notably, the counter-rotation of the third stage appears to interact with the incoming wakes from the upstream rotors, potentially modifying the downstream wake recovery characteristics and influencing the energy extraction of the final stage. The Lattice-Boltzmann Method with LES (Figure 2, Figure 5) effectively captures these intricate flow interactions, including tip vortices and inter-rotor flow accelerations or decelerations, which are fundamental to understanding the performance benefits of this three-stage design.

Figure 7.

Representative streamlines at a free-stream wind speed of 7 m/s, shown as vectors.

Figure 8.

Wake interaction of the three-stage wind turbine at a free-stream wind speed of 7 m/s.

Table 3.

Simulation setup parameters.

Wind speed (m/s)	Rotational speed (RPM)
Wind speed (m/s)	Front stage	Middle stage	Rear stage
5	144.68	144.68	107.43
6	173.62	173.62	128.91
7	202.56	202.56	150.40
8	231.50	231.50	171.89
9	260.43	260.43	193.37

The power output of the three-stage wind turbine is shown in the graph in Figure 9.

Figure 9.

Power curve of the three-stage wind turbine in this study.

The above conclusions are consistent with the preliminary investigation regarding the sizing of the rear blade stage of the three-stage wind turbine. However, further theoretical studies may need to be conducted and used for comparison with the simulation results obtained from XFlow software.

Operating principle of the invented three-stage wind turbine

Based on the above simulation results, the operating principle of the turbine is described as follows. The three-stage wind turbine consists of three blade stages mounted coaxially. The first and second blade stages have identical blade dimensions, while the third blade stage has a radius equal to 120% of the radius of the first and second stages. The three blade stages are connected to three separate rotors. The first and second blade stages are attached to rotors containing wound coils, while the third blade stage is attached to a rotor containing magnets.

When wind blows into the turbine, the tail vane helps align the entire turbine directly into the wind flow. The first and second blade stages rotate in the same direction, driving the two coil rotors to rotate in the same direction. The third blade stage rotates in the opposite direction, causing the magnet rotor to rotate counter to the first two. The electricity generated is transmitted through slip rings and brushes to the end-use system.

The enhanced electrical generation efficiency stems directly from the counter-rotating design of the electrical components. As illustrated in the simplified schematic in Figure 10, the coil assemblies, driven by the first two blade stages, rotate in one direction, while the magnet assemblies, driven by the third blade stage, rotate in the opposite direction. This counter-rotation dramatically increases the relative speed between the magnetic field and the conductors, leading to a higher rate of change of magnetic flux $(\frac{{d ϕ}_{B}}{d t})$ and thus a greater induced voltage.

Figure 10.

Conceptual schematic of the counter-rotating electrical generation principle.

The system uses direct-drive transmission to reduce friction losses, thereby improving the efficiency of the turbine. The main structure consists of three separate rotors rotating independently, with each blade stage directly mounted to its respective rotor. The turbine is equipped with three wind vanes to further support directional control of the turbine.

Detailed structure of the three-stage wind turbine

As shown in Figure 11, the three-stage coaxial independently rotating wind turbine consists of the following components:

Figure 11.

Detailed structure of the three-stage coaxial independently rotating wind turbine.

As detailed in Figure 11, the first (1) and second (2) blade stages drive rotors (11 and 12, respectively) which contain wound coils. These coil rotors rotate around magnet cores (13 and 14) that are mechanically coupled to the shaft (15) of the third blade stage (3), which carries permanent magnets. Since the first two-stages rotate in one direction and the third stage (carrying the magnets) rotates in the opposite direction, the relative angular velocity between the coil assemblies (on rotors 11 and 12) and their respective magnet cores (13 and 14) is significantly increased compared to a conventional single-rotor generator or a co-rotating multi-rotor system. This heightened relative speed directly amplifies the rate of change of magnetic flux through the coils, leading to a higher induced electromotive force (voltage) and consequently greater power output for a given wind condition, as per Faraday’s Law of Induction.

The main rotating frame 22 comprises a flange and a cylindrical tube, designed to be mounted at both ends with bearings 35 and 36. It is fastened to the column 34 using bolts and functions to support the entire turbine structure while allowing it to rotate around the column to align properly with the wind direction (Figure 12).

Figure 12.

Rotating frame.

The main rotating shaft assembly 37 consists of a steel shaft and a cylindrical tube. The steel shaft is designed to be mounted onto the main rotating frame 22 through two bearings, 35 and 36, and is secured in place with bolt 28. A slip ring and brush assembly 27 is mounted beneath it. The cylindrical tube is designed to be fitted with bearings 20 and 21 at both ends (Figure 13).

Figure 13.

Main rotating shaft assembly.

The turbine shaft 15 is made of steel and is designed to mount the rear blade stage 3 via the blade disc 6, secured by bolt 30. The shaft 15 is equipped with two magnet cores 13 and 14. The entire turbine shaft is mounted onto the main rotating shaft assembly 37 via two bearings, 20 and 21, and is fixed in place by bolt 29. This assembly also serves as the rear rotor (Figure 14).

Figure 14.

Turbine Shaft.

The front rotor 11 consists of laminated electrical steel sheets wound with copper wire. The front rotor is mounted to housing 7, which is enclosed by two covers: cover 4 and cover 9. Cover 4 functions both as a protective cap and as a blade disc to mount the front blade stage 1. Cover 9 is fitted with a slip ring assembly 25 to transmit electrical output from the front rotor to the outside. Bearings 16 and 17 are installed on covers 4 and 9, allowing the front rotor to rotate around the turbine shaft 15 and magnet core 13 (Figure 15).

Figure 15.

Front rotor of the turbine.

The middle rotor 12 consists of laminated electrical steel sheets wound with copper wire. The middle rotor is mounted to housing 8, which is enclosed by two covers: cover 5 and cover 10. Cover 5 serves both as a protective cap and as a blade disc for mounting the middle blade stage 2. Cover 10 is fitted with a slip ring assembly 26 to transmit electrical output from the middle rotor to the outside. Bearings 18 and 19 are installed on covers 5 and 10, allowing the middle rotor to rotate around the turbine shaft 15 and magnet core 14 (Figure 16).

Figure 16.

Middle rotor of the turbine.

Two brush assemblies 23 and 24 are mounted on the main rotating shaft assembly 37, each consisting of three brushes, to collect electrical output from slip rings 25 and 26 and transmit it to the slip ring and brush assembly 27, which delivers electricity to the end-use point.

The front nose cone 31 is attached to cover 4 to optimize airflow into the turbine and reduce aerodynamic drag.

The middle housing shell 32 includes wind vanes that assist in directional control of the turbine and protect internal components (Figure 17).

Figure 17.

Middle housing of the turbine.

The rear housing 32 is mounted to cover 5 and functions to create a unified turbine body, enhancing its appearance and protecting internal components. The rear nose cone 33 is attached to the blade disc 6, contributing to the turbine’s structural continuity and uniformity.

Experimentation and results

Experiment

A prototype of the three-stage wind turbine was designed based on the new invention proposed in this study and fabricated for experimental purposes. The turbine blades with a straight airfoil profile of type GOE222 were manufactured and used for testing. In this experiment, the blades were 3D-printed using PLA (Polylactic Acid) material.

The experiments were conducted in a controlled laboratory environment using an open-jet wind stream generated by an electric fan (2000W, D = 800 mm). The fan speed was precisely regulated using a frequency inverter to achieve the desired wind speeds at the turbine’s location. Wind speed measurements were taken using a calibrated UniT anemometer positioned 0.5 m upstream of the first rotor stage, with uniformity across the rotor swept area verified prior to testing. A schematic of the open-jet wind tunnel setup is provided in Figure 18. The turbine’s frontal area resulted in a blockage ratio of approximately 8% within the effective jet area, which was considered to have a minor, uncorrected influence for these comparative tests. All measuring instruments, including the VOM meters and the anemometer, were calibrated according to manufacturer specifications prior to the experiments.

Figure 18.

A schematic of the open-jet wind tunnel (in dimension in meters).

Figure 19 illustrates the experimental model of the coaxial, independently rotating three-stage wind turbine invented in this study.

Figure 19.

Experimental three-stage turbine model.

Since the three stages of the turbine rotate independently, one or two stages can be selectively stopped during the experiment in order to measure the power output of the remaining operating blade stages. In other words, this model allows for power measurements of one-stage, two-stage, or full three-stage turbine configurations, thereby enabling comparative assessment of their performance under identical experimental conditions. This selective activation was achieved by mechanically decoupling and braking the non-operational stage(s) at their respective shafts, ensuring minimal aerodynamic interference with the active stage(s). This setup thereby enabled a direct comparative assessment of their performance under near-identical inflow conditions.

The measurement devices, as shown in Figure 20, include the following:

• UniT VOM meter for measuring voltage in the range of 0–60 V, with an accuracy of 0.01%

• KAWEETS brand VOM meter for measuring current in the range of 0–60 A, with an accuracy of 0.1%

• UniT wind speed meter with a measurement range of 0–30 m/s, accuracy 0.01%

Figure 20.

Measuring equipment used during the experiment.

The first and second blade stages each have a diameter of 500 mm, while the third blade stage has a diameter of 620 mm; each stage consists of three blades. Experiments were conducted at wind speeds of 3 m/s, 4 m/s, 5 m/s, 6 m/s, 7 m/s, and 8 m/s. The load used in the experiments was LED bulbs. While it is acknowledged that LED bulbs constitute a non-linear, non-purely resistive load, their use was deemed appropriate for this study’s primary objective: to evaluate the relative performance gains between the one-, two-, and three-stage configurations under identical operating conditions. The LED bank provided a consistent, stable, and easily replicable load across all test runs, thereby ensuring the validity of the reported percentage improvements (e.g., Table 4). For future work aimed at determining absolute turbine efficiency and the power coefficient (C_p), a calibrated, purely resistive load bank will be utilized. The output power of the wind turbine was calculated using the formula P = U × I (W), where U (V) and I (A) are the voltage and current measured during the experiment, respectively.

Table 4.

Power output of single-stage, two-stage, and three-stage wind turbines.

Wind speed	Single-stage turbine	Two-stage turbine	Three-stage turbine	Δ₂₋₁	Δ₃₋₂	Δ₃₋₁
(m/s)	W	W	W	(%)	(%)	(%)
3	0	0.3418	0.4671	–	37%	–
4	0.0023	0.5135	0.6685	–	30%	–
5	0.3253	1.3495	2.6135	315%	94%	703%
6	1.6588	2.5607	4.7176	54%	84%	184%
7	2.3778	4.3336	6.216	82%	43%	161%
8	3.8339	5.4789	9.3432	43%	71%	144%

An uncertainty analysis for the calculated power (P = U × I), based on the specified accuracies of the voltage (0.01%) and current (0.1%) meters and observed fluctuations during measurements, indicated an overall experimental uncertainty in power output of approximately ±2% for most test conditions.

Results

Table 4 and Figure 21 present the experimental results of the power output of the wind turbine with one-stage, two-stage, and three-stage blade configurations. The data in the table and figure clearly show that the power output from the two-stage and three-stage turbines is consistently higher than that of the single-stage and two-stage configurations across the tested wind speed range.

Figure 21.

Experimental results of single-stage, two-stage, and three-stage wind turbines.

For example, as shown in Table 4, the percentage increase in power output of the three-stage turbine compared to the two-stage configuration ranges from 30% to 94%. The increase in power output of the three-stage and two-stage turbines relative to the single-stage model is even more substantial, particularly at lower wind speeds.

Further analysis of the data in Table 4 allows for an estimation of the incremental power contribution of each stage, assuming “Single-stage Turbine” primarily represents the performance of the first stage, and “Two-stage Turbine” represents the combined output of the first and second stages. For instance, at a wind speed of 5 m/s, the single-stage output is 0.33 W. The two-stage configuration yields 1.35 W, suggesting an incremental contribution of approximately 1.02 W from the second stage. The three-stage configuration produces 2.61 W, indicating that the third stage contributes an additional 1.26 W. This demonstrates the substantial energy harvesting capability of the second and particularly the third stage, which benefits from its larger diameter designed to capture the expanded streamtube and the modified inflow conditions created by the upstream rotors.

In Figure 21, the mathematical curve with a high coefficient of determination (R²) demonstrates that the experimental data conform well to the theoretical cubic relationship between wind speed and power output. This confirms the accuracy of the experimental results.

The superior performance of the three-stage configuration is strongly supported by the design principle of capturing the expanded streamtube. The XFlow simulations (Table 5) indicated an optimal radius for the third blade stage to be approximately 120–125% of the preceding stages. The experimental prototype was constructed based on this finding, with its third stage diameter (620 mm) being 124% of the first two stages (500 mm each). The substantial power augmentation observed experimentally, particularly the 30%–94% increase over the two-stage design and up to 703% over the single-stage model at 5 m/s, validates this simulation-guided design approach and underscores the effectiveness of the third stage in harnessing otherwise uncaptured wind energy.

Table 5.

Results of streamtube expansion positions on the rotor plane of the rear blade stage.

	Range of tangential velocity at the third blade stage
Radius (m)	1.6	1.65	1.7	1.75	1.8	1.85
Increase ratio relative to the reference radius of the rear blade stage	107%	110%	113%	117%	120%	123%
V (m/s)
5	>0	>0	>0	>0	x	∼0
6	>0	>0	>0	>0	x	∼0
7	>0	>0	>0	x	∼0	∼0
8	>0	>0	>0	x	∼0	∼0
9	>0	>0	>0	x	∼0	∼0

To facilitate a standardized comparison of aerodynamic efficiency, the power coefficient (C_p) was calculated for each configuration. It is important to note that these C_p values are based on the final measured electrical power output, and thus account for all cumulative aerodynamic, mechanical, and electrical losses inherent in the lab-scale experimental prototype. As such, these values are not intended for direct comparison against the theoretical Betz limit or the performance of optimized commercial turbines. Instead, their primary value lies in the direct, relative comparison between the one-, two-, and three-stage configurations under identical, non-ideal conditions. The results, presented in Table 6, clearly demonstrate the superior relative performance of the novel three-stage design.

Table 6.

Calculated power coefficient (C_p).

Wind speed	Single-stage turbine	Two-stage turbine	Three-stage turbine
3	0.00	0.11	0.15
4	0.00	0.09	0.07
5	0.02	0.09	0.18
6	0.07	0.10	0.19
7	0.06	0.11	0.16
8	0.06	0.09	0.16

Conclusions

This study presented a novel approach to improving wind energy harvesting efficiency through the design, simulation, and experimental validation of a three-stage coaxial wind turbine with independently rotating rotors. Building upon the promising results from dual-rotor configurations, the research team developed and fabricated a three-stage turbine model, in which the first two blade stages have identical dimensions while the third stage features an expanded radius to effectively capture the expanded streamtube flow. Simulations conducted using XFlow helped determine optimal aerodynamic parameters, particularly indicating that the radius of the third blade stage should be approximately 120–125% of the preceding stages to maximize the remaining airflow utilization.

In the experimental setup, the model allowed flexible deactivation of one or two blade stages, enabling individual evaluation of one-stage, two-stage, and three-stage configurations under the same physical conditions and ensuring consistency for comparison. Results showed a significant increase in power output with the number of blade stages. Specifically, the three-stage turbine achieved a 30% to 94% increase in power output compared to the two-stage design, and an even greater improvement compared to the single-stage configuration—particularly at lower wind speeds. The resulting power curve followed the theoretical cubic relationship with wind speed, confirming the accuracy of the experimental model.

The structural design featuring three independently rotating rotors with direct-drive transmission not only minimizes mechanical losses but also enhances the magnetic flux cutting rate, thereby increasing voltage and output power. The coaxial mechanical layout, combined with counter-rotating blade stages, takes advantage of aerodynamic vortex characteristics and inter-stage interaction effects.

These findings provide a scientifically and practically important foundation for the development of higher-efficiency small- and medium-scale wind turbines. It is acknowledged that multi-rotor, counter-rotating systems can introduce complex vibrational dynamics. While the experimental prototype, fabricated with high-precision bearings and dynamically balanced, did not exhibit significant vibrations within the tested operational range, a comprehensive structural analysis represents a critical next step. Future work should involve detailed modal analysis using finite element methods (FEM) and experimental vibration measurements to ensure long-term reliability and facilitate the scaling-up of the design. Moreover, the results open a new pathway for more effectively exploiting the residual wind energy following each rotor stage—a potential-rich area that remains largely untapped.

Footnotes

ORCID iD

The Bao Nguyen

Author contributions

Le Đang Huy: Conceptualization, Methodology, Software (CFD Simulation), Validation (Experimental), Writing – Original Draft.; Ngo Van Minh: Conceptualization, Resources, Project Administration.; Nguyen The Bao: Conceptualization, Supervision, Funding Acquisition, Writing – Review & Editing.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was funded by the Ho Chi Minh City Department of Science and Technology under grant number KHCN2024030289.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author, Dr Nguyen The Bao, upon reasonable request.*

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