Numerical Investigation of Wake Characteristics for Scaled 20 kW Wind Turbine Models with Various Size Factors

Abstract

Wind energy is essential for sustainable energy development, providing a clean and reliable energy source through the wind turbine. However, the vortices and turbulence generated as wind passes through turbines reduce wind speed and increase turbulence, leading to significant power losses for downstream turbines in wind farms. This study investigates wake characteristics in wind turbines by examining the effects of different scale ratios on wake dynamics, using both experimental and numerical approaches, utilizing scaled-down models of the Aeolos H-20 kW turbine at scales of 1:33, 1:50, and 1:67. The experimental component involved wind tunnel tests in an open-circuit tunnel with adjustable wind speeds and controlled turbulence intensity. Additionally, Computational Fluid Dynamics (CFD) simulations were conducted using STAR-CCM+ (Version 15.06.02) to numerically analyze the wake characteristics. Prior to the simulation, a convergence test was performed by varying grid density and y+ values to establish optimized simulation settings essential for accurately capturing wake dynamics. The results were validated against experimental data, reinforcing the reliability of the simulations. Despite minor inconsistencies in areas affected by tower and nacelle interference, the overall results strongly support the methodology’s effectiveness. The discrepancies between the experimental results and CFD simulations underscore the limitations of the rigid body assumption, which does not fully account for the deformation observed in the experiment.

1. Introduction

Energy is fundamental to economic growth and social development. The rapid population increase, rising incomes, technology-driven lifestyles, and modernized living standards are major factors driving the escalating demand for electricity in the current decade. Meeting these high energy requirements presents significant challenges to the power sector, which must adapt to the increasing strain on resources and infrastructure. Recently, there has been an unparalleled effort to hasten the shift towards renewable energy sources. Among these, renewable energy, especially wind technologies, is set to lead the growth in electricity demand in the near future, offering a sustainable solution to our energy needs while addressing environmental concerns and reducing reliance on fossil fuels.

As countries strive to meet their climate goals and reduce reliance on fossil fuels, wind energy is emerging as a cornerstone of sustainable development, providing a reliable and clean source of power for future generations. According to the International Energy Agency, renewable sources are projected to account for 98% of the 2518 TWh of additional electricity generation between 2022 and 2025 [1]. The Global Wind Energy Council (GWEC) anticipates a significant surge in wind capacity, with an estimated 680 GW expected to be added globally from 2023 to 2027, including 130 GW in offshore installations as shown in Figure 1 [2]. Wind power continues to maintain a competitive edge in terms of pricing across most countries, even without factoring in potential future carbon pricing mechanisms or other impacts. The growing emphasis on renewable energy is not just a trend but a necessity for sustainable development. Wind energy, with its vast potential and decreasing costs, stands out as a key player in this transition. As we move forward, the role of wind power in our energy landscape will only become more critical, driving us towards a cleaner and more sustainable future.

Wind energy converters, also known as wind turbines, are devices that convert the kinetic energy of the wind into mechanical energy. This mechanical energy is then transformed into electrical energy through a generator. As the wind passes through the turbine, energy is harnessed, generating vortices and turbulence. These wakes result in a reduction in wind speed and an increase in turbulence intensity, impacting the downstream flow field [3]. Consequently, the power output of wind turbines located further downstream in the wind farm decreases. This wake effect has been found to be the largest contributor to various power losses in wind farms [4]. Wakes are typically classified into two regions based on their spatial distribution: the near wake and the far wake. The near wake spans up to approximately 1–2 times the blade diameter and is relatively influenced by turbine geometry and operating conditions. Beyond this range lies the far wake, which extends beyond two times the blade diameter. Within the 2–4 times wake region, factors such as terrain, turbulence characteristics, and wake models play a significant role. In the four times wake zone, the reduction in wind speed occurs at a slower rate [5,6].

Extensive research has been undertaken to optimize power generation by considering wake effects when sitting wind turbines within wind farms, along with strategies to mitigate adverse effects on downstream turbines [6,7]. These studies encompass both experimental and numerical approaches. For precise analysis, it is crucial to cross-validate numerical analysis findings with experimental results. While many wind tunnel experiments investigate wake patterns using full-scale models, a significant portion of these studies [8,9,10,11,12,13] rely on a single scale model, overlooking correlations across models of varying scale ratios. This gap in research hampers our understanding of the interrelations among different scale models. In order to improve the accuracy of wake predictions using scaled-down models, comprehensive research is necessary. This includes comparative and correlation analyses between wakes generated by actual wind turbines and those simulated in wind tunnel experiments with scaled-down models. However, wind tunnel experiments face challenges in accurately verifying turbine-generated wakes, often due to a lack of clear comparison standards for experimental results [8,10,12]. Park et al. (2023) conducted an experimental study on small-type wind turbines with different scale models to check the correlation between actual small wind turbines and scaled-down models [11]. Achieving precise analyses requires the cross-referencing and validation of numerical analysis outcomes with experimental results. This is particularly important in wind turbine studies, where turbulence modeling poses significant challenges. Limited research has been presented in numerical studies due to the lack of sufficient validation of turbulence modeling, as highlighted by Kang S.H. et al. (2017) [6]. Ahn et al. (2023) conducted a numerical study of wind tunnel tests and wake verification for small-scale wind turbines [13]. However, similar to other cases of numerical analysis, the research remains constrained by the lack of comprehensive validation of turbulence models.

This study is driven by the need to improve the wake characteristics, particularly by examining how different scale ratios influence wake dynamics. To achieve this goal, the research combines both experimental and numerical approaches. Three different scaled-down models of the Aeolos H-20 kW turbine, with scales of 1:33, 1:50, and 1:67, were used, ensuring geometric, tip speed ratio (TSR), and Reynolds number similarity to accurately represent the turbine’s behavior. The experimental component involved wind tunnel tests in an open-circuit wind tunnel equipped with 96 high-flow DC fans, allowing for a wide range of adjustable wind speeds and controlled turbulence intensity. On the numerical side, Computational Fluid Dynamics (CFD) simulations were conducted using STAR-CCM+ software (Version 15.06.02), focusing on detailed boundary layer analysis through Menter’s SST k-ω model. Prior to the primary analysis, a convergence test using the NREL 5 MW wind turbine model was performed to establish the optimal mesh grid, comparing Y+ values to assess wake performance and refining the grid, particularly in the wake region, to ensure accurate measurement of wind flow dynamics. These preparatory steps were crucial for enhancing the reliability and accuracy of the simulations, aligning them closely with experimental data. The simulation results were validated against experimental observations, ensuring their robustness and accuracy. This comprehensive approach not only deepens the understanding of how different scale ratios affect wake behavior but also highlights the importance of grid density and Y+ values in capturing complex aerodynamic phenomena. The findings contribute to the development of more precise modeling techniques, ultimately improving predictions of wind turbine performance and aiding in the design of more efficient turbines.

2. Experimental Investigation on Wake Characteristics

2.1. Design and Development of Scaled 20 kW Wind Turbine Model

The scaled models utilized in the experiment were developed in reference to the Aeolos H- 20 kW wind turbine, which is situated at Kunsan National University. This wind turbine is an upwind type with three blades, a rotor rotation diameter of 10 m, and a hub height of 24 m. The rated wind speed is 11.5 m/s, the rated rotation speed is 125 rpm, and the tip speed ratio (TSR) is 5.7.

In the experiment utilizing a scaled wind turbine model, it is essential to examine the principles of geometric similarity, tip speed ratio (TSR) similarity, and Reynolds number similarity. To match the geometric similarity of the scale model, the shape of the 20 kW wind turbine blade was secured through 3D scanning, while the hub, nacelle, and tower were secured through specification tables and actual measurements. To analyze the wake correlation according to the scale ratio of the 20 kW wind turbine scale model, three scale models with different scale ratios were used. Minimizing the influence of cross-section closure effects during wind tunnel experiments requires maintaining the closure rate below 10%, with an ideal target of under 5%. Consequently, the maximum size of the scale model was set to 1:33 of the 20 kW wind turbine, resulting in a rotation diameter of 0.3 m and a closure rate of 4.9%. The remaining scale models are 1:50 and 1:67, with rotation diameters of 0.2 m and 0.15 m and closure rates of 2.2% and 1.2%, respectively. Detailed information on the blade shape, airfoil at each cross-section, and wind turbine configuration is presented in Figure 2 and

Table 1. Normalized wind turbine blade and shape size.

Category (Symbol)	Scale (-)	1:33 (m)	1:50 (m)	1:67 (m)
Main blade diameter (D1)	1.0D	0.3	0.2	0.15
Rotor diameter (D2)	-	0.04	0.026	0.026
Nacelle height (L1)	0.13D	0.04	0.026	0.02
Rotor length (W1)	0.10D	0.03	0.02	0.015
Nacelle length (W2)	0.18D	0.055	0.036	0.027
Blockage ratio	-	4.9%	2.2%	1.2%

, while the shape of the produced scale model is illustrated in Figure 3.

In order to match the TSR, which is a function of the inflow speed and wind turbine blade tip speed, the rotational speed of the blade must increase according to the size of the scale model, as shown in Equation (1). In this study, due to the limitation of controlling the TSR solely with the wind speed of the wind tunnel, TSR similarity was achieved by increasing the rotational speed of the blade through the attachment of a DC motor to the nacelle and the supply of power from an external source.

$$\mathrm{TSR}={\displaystyle \frac{R\omega }{V_{\infty }}}$$

(1)

where R denotes rotor diameter, ω denotes rotor speed, and V_∞ denotes inflow wind speed.

The utilization of a scaled model that satisfies the principles of Reynolds number similarity, as outlined in Equation (2), requires an increase in the wind speed proportional to the size of the model. Alternatively, fluids with a high viscosity coefficient, such as water, can be employed. However, precisely matching Reynolds number similarity poses a significant challenge in practical applications. Despite this, it is widely acknowledged that the influence of Reynolds number on the wake is not substantial, as evidenced by previous studies [14,15,16]. Consequently, the effect of Reynolds number was disregarded in the present study.

$$Re={\displaystyle \frac{\rho V_{R}c}{\mu }}$$

(2)

where ρ denotes air density, V_R denotes relative wind speed, c denotes chord length, and μ denotes viscosity.

2.2. Wind Tunnel Experimental Setup

In this research investigation, the researchers developed a laboratory-scale wind tunnel to conduct scaled-down experiments on turbine models, as shown in Figure 4. This wind tunnel deviates from the conventional design, featuring an open-circuit configuration [17,18], where the airflow generated by the 96 high-flow DC fans in the blowing section is directly connected to the test section and then exhausted to the outside environment, differing from typical wind tunnels that incorporate a diffusion section and stagnation room. This design allows for a more streamlined and efficient flow of air through the system. A screen was attached at the location where the blower unit and the test unit are connected to control the turbulence intensity. This screen was designed with a detachable and attachable structure to accommodate indoor installation conditions, making it more versatile and adaptable to different experimental setups. The wind speed within the wind tunnel can be adjusted from a minimum of 0.9 m/s to a maximum of 6.7 m/s, in increments of approximately 0.2 m/s, using Pulse-Width Modulation (PWM) control. This wide range of wind speeds allows the researchers to simulate a variety of atmospheric conditions and test the performance of the turbine models under different wind speeds. According to previous research, under the maximum wind speed condition of the wind tunnel, the average wind speed within the test section was 6.7 m/s, with the turbulence intensity confirmed to be 1.83% on average and the spatial deviation measured at 0.117 m/s [19]. The dimensions of the wind tunnel test section are 0.985 m (H) × 1.47 m (W) × 2.56 m (L), providing a sizable and well-defined space for the placement and observation of the scaled-down turbine models.

2.3. Results and Analysis of Wake Characteristics

Figure 5 illustrate the measurement points in the x-z and y-z planes, with Figure 5a showing points along the vertical axis (Z/D) and Figure 5b showing points along the horizontal axis (Y/D), both at the downstream separation distance (X/D) and relative to the rotor centerline. The maximum separation distance is determined by the length (L) of the experimental wind tunnel for each scale. As shown in Figure 6, the maximum separation distances are 4D for the 1:33 scale, 6D for the 1:50 scale, and 8D for the 1:67 scale. Observation points for each scale model are measured at 1D intervals. The experimental results demonstrate the wake profile for the x-z plane and the x-y plane, centered on the rotor, for the 1:33, 1:50, and 1:67 scale models, as depicted in Figure 7, Figure 8 and Figure 9, respectively. Figure 7a, Figure 8a and Figure 9a represent the wake distribution in the x-z plane, Figure 7b, Figure 8b and Figure 9b illustrate the wake distribution in the x-y plane. These profiles offer a comprehensive understanding of the wake behavior in different planes, providing insights into the vertical and horizontal spread of the wake at various scales. The impact of scale-down ratios on wake characteristics can be more thoroughly comprehended by analyzing these wake profiles, which is essential for optimizing wind turbine designs and enhancing the accuracy of numerical simulations.

For the 1:33 scale model, the wake was measured from 1D to 4D, as depicted in Figure 7a,b. The non-dimensional wake at 1D from the rotor center gradually recovered to a velocity ratio (V_m/V_inf) of 0.69 and further to 0.78 at 4D, indicating a consistent recovery of the wake over the measured distance. Figure 8a,b show the normalized horizontally and vertically wake of the 1:50 scale model, respectively. The wake was measured from 1D to 6D, resulting in similar wake recovery behavior was observed from 1D to 4D, with the wake gradually recovering to a velocity ratio of 0.85 at 6D, the furthest point measured. For the 1:67 scale model, shown in Figure 9a,b, the wake was measured from 1D to 8D, and the model demonstrated wake recovery behavior similar to the 1:33 and 1:50 models, with the wake gradually recovering to a velocity ratio of 0.92 at 8D. The consistent recovery pattern across different scale models highlights the reliability of the measurements and the effectiveness of the scaling method in capturing wake dynamics. To investigate the wake recovery and flow characteristics for each scale model, the normalized separation was examined for three distinct scale models: 1:33, 1:50, and 1:67. The wake shapes are depicted in both the x-z plane and the x-y plane, as shown in Figure 10a,b, respectively, extending backward from the center of the rotor for each scale model.

3. Numerical Simulation

3.1. Grid System Convergence Test

The commercial software Star-CCM+ (Version 15.06.02) was employed to compare the trailing data derived from both the scale model trailing experiment and the numerical simulation of a 20 kW wind turbine. This comparison aimed to enhance the accuracy and reliability of the simulation results. For verification purposes, the present study utilized a 5 MW terrestrial wind turbine designed by the National Renewable Energy Laboratory (NREL). This choice was driven by the need to develop a high-resolution grid that could effectively represent the downstream flow characteristics of the scale model 20 kW wind turbine. The NREL 5 MW wind turbine is a well-established model in research and development, offering extensive data that ensures robust verification.

The NREL 5 MW wind turbine, widely used in research, features a rotor diameter of 126 m, a tilt angle of 5 degrees, a precone angle of 2.5 degrees, and a hub height of 90 m, as depicted in Figure 11. It is designed to operate at an optimal rotational speed of 12.1 rpm when the wind speed reaches its rated value of 11.4 m/s. The availability of diverse and detailed data for this turbine model makes it exceptionally suitable for verification tasks, ensuring that the high-resolution grid developed is both accurate and reliable. This comprehensive verification process underscores the effectiveness of using the NREL 5 MW wind turbine as a benchmark for enhancing the simulation accuracy of smaller scale models, such as the 20 kW wind turbine in this study.

The NREL 5 MW wind tunnel for numerical simulation was designed as depicted in Figure 12, with reference to Zhang (2018) [21]. This design serves as a critical framework for accurately modeling the aerodynamic behavior of wind turbines under various conditions. An important aspect of this simulation is the rotation analysis method of wind turbine blades, which employs a technique allowing the periodic rotation of the rotational area within the implicit unsteady analysis. This is achieved using the Sliding Moving Mesh (SMM) approach, enabling more precise and dynamic simulation results.

The analysis model is governed by the classical Navier–Stokes equations, which are formulated as

$$\nabla ·v=0$$

(3)

$${\displaystyle \frac{{\mathsf{\partial }}_v}{{\mathsf{\partial }}_t}}+v·\nabla v=-{\displaystyle \frac{1}{\rho }}\nabla p+\mathsf{\nu }{\nabla }^{2}v$$

(4)

where v is the velocity vector, ρ is the fluid density, p is the pressure, and ν is the kinematic viscosity. These equations are solved numerically using the finite volume method, with the following assumptions: incompressible flow, constant fluid properties, and a steady-state solution. The turbulence model employed is Menter’s Shear Stress Transport (SST) k-ω model, which is a hybrid model that combines the advantages of the k-ω and k-ε models. The SST k-ω model is formulated as

$${\displaystyle \frac{{\mathsf{\partial }}_k}{{\mathsf{\partial }}_t}}+U_j{\displaystyle \frac{{\mathsf{\partial }}_k}{{\mathsf{\partial }}_{x_j}}}=P_k-\beta \ast k\omega +{\displaystyle \frac{\mathsf{\partial }}{{\mathsf{\partial }}_{x_j}}}\left[\left(\mathsf{\nu }+{\displaystyle \frac{{\mathsf{\nu }}_t}{{\sigma }_k}}\right){\displaystyle \frac{{\mathsf{\partial }}_k}{{\mathsf{\partial }}_{x_j}}}\right]$$

(5)

$${\displaystyle \frac{{\mathsf{\partial }}_{\omega }}{{\mathsf{\partial }}_t}}+U_j{\displaystyle \frac{{\mathsf{\partial }}_{\omega }}{{\mathsf{\partial }}_{x_j}}}=\alpha \left({\displaystyle \frac{S^2}{\omega }}\right)-\beta {\omega }^2+{\displaystyle \frac{\mathsf{\partial }}{{\mathsf{\partial }}_{x_j}}}\left[\left(\mathsf{\nu }+{\displaystyle \frac{{\mathsf{\nu }}_t}{{\sigma }_{\omega }}}\right){\displaystyle \frac{{\mathsf{\partial }}_{\omega }}{{\mathsf{\partial }}_{x_j}}}\right]$$

(6)

where k is the turbulent kinetic energy, ω is the specific dissipation rate, and ν_t is the turbulent viscosity. The model constants α, β, ∂_k, and ∂_ω are set to their default values as recommended by Menter [22]. The Menter’s SST (Shear Stress Transport) k-ω model (Equations (5) and (6)) was employed for its dual advantages. The k-ω model excels at accurately capturing near-wall flows, which are essential for detailed boundary layer analysis. Concurrently, the k-ε model effectively represents regions outside the boundary layer, ensuring comprehensive coverage of the entire flow field. The SST k-ω model offers a robust and accurate framework for modeling the intricate aerodynamic characteristics of centrifugal compressors by incorporating these inherent capabilities [23,24].

3.1.1. Investigation of y+ Value Impact

In this study, we conducted a detailed analysis to evaluate the thrust effect of the NREL 5 MW wind turbine, focusing on the influence of different y+ values in relation to the blade surface grid density to select the optimal grid number. Specifically, we compared the thrust performance wake characteristics of the turbine at y+ values of 1, 30, and 100. The y+ parameter is a non-dimensional value crucial in characterizing the behavior of the boundary layer, especially near the turbine blades, and it plays a significant role in the accuracy of CFD simulations. This study involves minimizing the turbine grid to include a large number of background grids. To achieve this, the impact of varying y+ values on the wake structure and overall performance of the wind turbine was systematically examined. The study systematically examined the effects of varying the y+ values on the wake structure and overall performance of the wind turbine. The objective was to gain a comprehensive understanding of how each y+ value influences these critical aspects of the wind turbine’s behavior. A y+ value of 1 ensures a fine near-wall mesh, capturing intricate flow details close to the blade surface. In contrast, y+ values of 30 and 100 offer a coarser mesh, which might simplify computations but could potentially overlook critical near-wall phenomena. Through this comparative approach, our study provides comprehensive insights into optimizing y+ settings for accurately predicting wake effects and enhancing the performance assessment of the NREL 5 MW wind turbine.

The initial prismatic layer thickness and the aggregate prismatic layer thickness for each blade segment of the wind turbine blade, as depicted in Figure 13, are defined in accordance with the subsequent equations (Equations (7)–(9)). These parameters are crucial in the meshing process, ensuring that the boundary layer is accurately represented. The first prism layer thickness refers to the initial layer of cells adjacent to the blade surface, capturing the fine details of boundary layer flow and resolving near-wall phenomena. The total prism layer thickness encompasses all the prism layers, extending from the blade surface into the flow field, adequately covering the entire boundary layer region. The precise specification of the thicknesses for each blade section ensures that the computational mesh accurately models the intricate interactions between the airflow and the blade, thereby enhancing the overall fidelity of the simulation and resulting in more reliable predictions of the wind turbine’s aerodynamic characteristics and performance.

$${\displaystyle \frac{y+}{FLT}}={\displaystyle \frac{0.487U}{\nu \ln \left(0.06R{e}_C\right)}}$$

(7)

$$R{e}_C={\displaystyle \frac{UC}{\nu }}$$

(8)

$${\displaystyle \frac{\delta }{C}}={\displaystyle \frac{0.16}{{{Re}_C}^{1/7}}}$$

(9)

where y+ denotes distance from non-dimension walls, FLT denotes first prism layer thickness, U denotes linear velocity, ν denotes kinematic viscosity, Re_C denotes blade chord-based Reynolds number, and δ denotes prism layer total thickness.

In order to enhance the grid utilized, a comparative analysis of thrust outcomes determined is conducted by the quantity of blade surface grids. Three types of tests were conducted, comparing thrust as a function of the total number of grids in the rotor (rotation) area by adjusting the number of blade surface grids, as illustrated in Figure 14. The boundary layer grid was set based on a y+ value of 30, with the main parameter being the total number of grids in the rotation area, which varies according to the blade surface size. The results are summarized in

Table 2. Thrust values for the NREL 5 MW wind turbine based on blade surface grid resolution.

Grid Resolution	Total Number of Elements in Rotor Region	Average Thrust (kN)	Error Rate (%)
Coarse	1.65 × 106	713.2	4.01
Medium	3.13 × 106	730.6	1.67
Fine	6.94 × 106	740.9	0.28

. While the coarse grid effectively reduces the number of grids, it results in a significant error rate. Conversely, the fine grid greatly reduces the error rate but requires a substantially larger number of grids.

In the previously explained comparative analysis with varying grid resolutions, including coarse, medium, and fine, we compared the y+ values 1, 30, 100 based on the medium grid to obtain the optimal value with a smaller grid. We observed that the total prism layer thickness in certain sections of the wind turbine blade, such as the blade tip, was smaller than the first prism layer thickness. To address this discrepancy, we applied a scaling factor of ten times the total thickness when creating the grid for numerical simulations. This adjustment ensured that the mesh could adequately capture the complex flow dynamics near critical areas of the blade. Additionally, the number of prism layers was carefully adjusted based on the y+ values to optimize the accuracy of the simulation. For each y+ value, we tailored the layer count to ensure a fine resolution near the wall while maintaining computational efficiency, achieving a more precise representation of the boundary layer and better predicting the aerodynamic performance of the wind turbine, as illustrated in Figure 15 and Figure 16. The analysis was performed at a rated wind speed of 11.4 m/s of NREL 5 MW wind turbine, and the time step was set to 0.0138 s, with the rotor rotating by about 1 degree.

The comparison of the y+ grid on the blade surface, in relation to the delicacy of the wake expression through the Q-criterion and the thrust, is presented in Figure 17, as per the findings of Weiyang et al. (2022) [19]. Furthermore, Figure 18 illustrates that the y+1 and y+100 values similarly depict the wake characteristics associated with the blade’s y+ parameter. When observing the wake from an oblique angle, it is evident that y+1 exhibits a more complex internal flow, despite the resemblance in the shape of the blade tip. In addition, the thrust is different, as shown in

Table 3. The thrust table of the NREL 5 MW wind turbine according to y+ (Range: 132.1902 s~133.8876 s).

Y+ Value	Total Number of Elements in Rotor Region	Range (kN)		Average (kN)	Error Rate (%)
		Min.	Max.
Y+ 1	4.81 × 106	729.9	748.1	743.4	0.05
Y+ 30	3.13 × 106	719.4	735.4	730.6	1.67
Y+ 100	2.37 × 106	721.2	737.4	732.9	1.36

and Figure 19. The thrust matures during the 134 s simulation time, in which the wind turbine rotates about 27 times. The range shown in the table is the range of the time the turbine rotates about 120 degrees, and the error rates for each y+ are compared according to the average within the range. The error rates were low in the order of y+1, y+100, and y+30.

3.1.2. Grid Generation for the Wake Flow Representation behind the Turbine

To accurately measure the wake flow, it is crucial to effectively generate a wind tunnel grid capable of capturing the wake produced by the rotation of a wind turbine, behind the wind turbine. This investigation contrasted diverse grid shapes utilized for the scale-down model analysis with the NREL 5 MW wind turbine model. The comparison emphasized grids that not only separate the blade tip area and the inner area but also incorporated the tower and nacelle for a comprehensive analysis. Figure 20 illustrates various grid configurations, each with a distinct approach to capturing the complex flow dynamics around the turbine. There are four different configurations, denoted as (a), (b), (c), and (d), with grid counts of 9.53 million, 9.58 million, 9.35 million, and 10.34 million, respectively. Despite the variations in grid design, the total number of cells remained relatively consistent across all configurations. This consistency enabled a fair evaluation of how each grid shape influenced the accuracy of the wake flow measurements. By examining these detailed grid structures, the simulation aimed to determine the most efficient grid design for capturing the complex vortices and wake effects generated by the wind turbine.

The comparison of various grid configurations was carried out in a similar manner to the y+ comparison, with the wake shape being analyzed at a q-criterion of 0.01/s², as shown in Figure 21 and Figure 22. In the comparison of grid generation without subdivision, grid configuration (a), which featured a refined grid in the inner area, demonstrated a higher grid density than grid configuration (b), which featured a refined grid in the blade tip area. Furthermore, grid configuration (a) also offered a more detailed representation of the wake shape, indicating that inner flow dynamics significantly influence the tip flow. In the grid configuration with subdivision, grid configuration (d), which featured a dense grid on the blade tip area, produced a clearer wake representation compared to grid configuration (c), which featured a fine grid in the inner area. Grid configuration (d) successfully captured sections that were otherwise distorted or not represented at all in the other configurations. This finding highlights the importance of concentrating grid density at the blade tip to accurately capture dynamics of the wake and suggests that interactions between inner and tip flows are crucial for precise wake modeling.

In order to verify whether the previously applied grid configurations generate valid results for the 20 kW scale model, the wake analysis domain of the wind turbine was configured by scaling the rotor diameter and hub height ratio with reference to the NREL 5 MW turbine. As shown in Figure 23, only grid configuration (c) and (d) are considered for the analysis due to their refinement compared to grid configuration (a) and (b). The analyses were performed for 19.2 s under analysis conditions of a rated wind speed of 11.5 m/s, 125 rpm, and a time step of 0.01333 s, the time it takes for the blade to rotate 10 degrees. The results of Q-criterion 1.0/s² are shown in Figure 24. Similar to the NREL 5 MW turbine, the regions missed due to hub concentration were captured, and additional vortices in the far wake were also identified.

3.2. CFD Simulation for Various 20 kW Scaled Wind Turbine Model

In this study, various scaled-down models of a 20 kW wind turbine (1:33, 1:67, and 1:50) were simulated using STAR-CCM+ software (Version 15.06.02) to investigate the characteristics of the wake. The y+ value and the grid configuration were established based on a prior convergence test. The results indicate that, for small-scale wind turbines, the y+ value should be maintained below 1 (y+ < 1). The grid configurations of these three distinct models are shown in Figure 25. The simulation conditions, outlined in

Table 4. Numerical setup for the simulation of scaled-down wind turbine models.

Scale (Units)	1:33 (m)	1:50 (m)	1:67 (m)
Rotor diameter (mm)	300	200	150
Inflow wind (m/s)	6.7
RPM	2431.3	3647.9	4862.5
Time step (s)	1.03 × 10−3	6.85 × 10−4	5.14 × 104
Total mesh (-)	143.5 × 106	153.6 × 106	169.4 × 106
Measurement section	1D–4D	1D–6D	1D–8D

, the wind speed was fixed to match the tip speed ratio (TSR), with the RPM increasing as the scale-down ratio increased. Due to the varying amounts of rotation for each scale-down ratio, a time step was set to ensure that each model rotated 15 degrees. This uniform rotation angle allowed for a consistent analysis of wind speed across different scale-down ratios, ensuring comparable results and an accurate assessment of aerodynamic performance.

The simulation averaged the wind speed measurement data from 1 s to 5 s, as it was deemed convergent and more practical than analyzing a 60 s duration as conducted in the experiment. In this study, the tower and nacelle were neglected. Consequently, only the distance from each rotor center was shown. Figure 26 and Figure 27 illustrate the wake growth by separation distance for each ratio of scaled-down models. This approach ensured that the data collected was consistent and reliable for evaluating the wake dynamics at different scales. From the side view, it is shown that as the scale-down ratio increases, the wind speed at the blade tip position decreases compared to the wind speed at the rotor center due to the influence of the tower and nacelle. This observation suggests that even without considering the tower and nacelle in the grid, capturing the wake at a close distance becomes challenging as the scale-down ratio increases. The reduced wind speed at the blade tip indicates the need for more refined grid designs to accurately simulate the wake dynamics in scaled-down models. This insight is crucial for improving the accuracy of simulations and enhancing the understanding of aerodynamic performance in different scaling scenarios.

Figure 28 and Figure 29 illustrate the wake distribution by scale-down ratio for each separation distance. These figures provide a detailed view of how the wake evolves as the distance from the rotor increases for different scaled-down models. Notably, the wake distributions for the 1:50 and 1:67 scales successfully captured the lowest wind speed at the center of the rotor from a separation distance of 3D away from the rotor. This finding highlights the ability of these specific scale models to accurately represent the core wake region, where the wind speed is significantly reduced due to the rotor’s influence. This detailed wake distribution analysis underscores the importance of selecting appropriate scale-down ratios for accurate wake modeling. The effectiveness of the 1:50 and 1:67 scales in capturing the wake characteristics suggests that these scales are particularly well-suited for studying the aerodynamic effects at different distances from the rotor. This insight is crucial for improving the fidelity of wind turbine simulations, leading to better predictions of performance and more efficient turbine designs.

4. Result and Discussion

Figure 30 and Figure 31 illustrate the comparison of the experimental results and numerical simulation according to the separation distance for all three different scale-down wind turbine models. At positions where the interference between the tower and the nacelle is significant, the discrepancies between the interpretation and experimental data are also large. However, in other areas, the results show similar trends, indicating a good agreement between the experiments and the numerical interpretations. This suggests that while the tower and nacelle interference possess challenges in accurately capturing wake behavior, the overall methodology remains effective for other parts.

The specific numerical values and error rates of the experimental and analytical results are shown in

Table 5. Experimental data (EXP) for 1:33 scale at various measure points.

Measure Point		1D	2D	3D	4D
0.0D		0.6871	0.7309	0.7561	0.7752
Side	0.5D	0.9552	0.9570	0.9486	0.9443
	1.0D	1.0114	1.0124	1.0091	1.0155
Top	0.5D	0.9959	0.9873	0.9896	0.9910
	1.0D	1.013	1.010	1.011	1.017

,

Table 6. Computational Fluid Dynamics (CFD) for 1:33 scale at various measure points.

Measure Point		1D	2D	3D	4D
0.0D		0.5144	0.6564	0.6247	0.6657
Side	0.5D	0.9627	0.9724	0.9906	0.9868
	1.0D	1.0284	1.0295	1.0309	1.0328
Top	0.5D	0.9824	0.9853	0.9929	1.0026
	1.0D	1.0270	1.0290	1.0300	1.0320

,

Table 7. Experimental data (EXP) for 1:50 scale at various measure points.

Measure Point		1D	2D	3D	4D	5D	6D
0.0D		0.7132	0.7597	0.7752	0.7907	0.8217	0.8527
Side	0.5D	0.9740	0.9527	0.9509	0.9496	0.9483	0.9576
	1.0D	1.0120	1.0089	1.0066	1.0036	1.0094	1.0115
Top	0.5D	0.9384	0.9378	0.9409	0.9345	0.9417	0.9374
	1.0D	1.0158	1.0144	1.0166	1.0103	1.0107	1.0111

,

Table 8. Computational Fluid Dynamics (CFD) for 1:50 scale at various measure points.

Measure Point		1D	2D	3D	4D	5D	6D
0.0D		0.6982	0.6885	0.7043	0.7415	0.7629	0.7726
Side	0.5D	0.9765	0.9799	0.9822	0.9920	0.9972	1.0025
	1.0D	1.0239	1.0231	1.0233	1.0241	1.0252	1.0266
Top	0.5D	0.9769	0.9946	1.0004	1.0055	1.0081	1.0126
	1.0D	1.0240	1.0236	1.0235	1.0242	1.0253	1.0264

,

Table 9. Experimental data (EXP) for 1:67 scale at various measure points.

Measure Point		1D	2D	3D	4D	5D	6D	7D	8D
0.0D		0.7369	0.7590	0.8086	0.8385	0.8539	0.8976	0.8935	0.9213
Side	0.5D	1.0089	0.9574	1.0003	0.9989	0.9721	0.9916	0.9780	1.0019
	1.0D	1.0078	0.9979	0.9946	0.9959	0.9782	0.9969	0.9914	0.9940
Top	0.5D	0.9728	0.9729	0.9946	0.9976	0.9884	0.9995	0.9841	0.9958
	1.0D	0.9989	0.9983	0.9981	1.0121	1.0033	1.0297	1.0088	1.0255

and

Table 10. Computational Fluid Dynamics (CFD) for 1:67 scale at various measure points.

Measure Point		1D	2D	3D	4D	5D	6D	7D	8D
0.0D		0.7649	0.7007	0.6951	0.7324	0.7678	0.7867	0.8020	0.8068
Side	0.5D	0.9675	0.9694	0.9791	0.9862	0.9926	0.9961	1.0005	1.0028
	1.0D	1.0204	1.0194	1.0192	1.0196	1.0204	1.0212	1.0222	1.0231
Top	0.5D	0.9667	0.9810	0.9911	0.9906	0.9993	0.9973	1.0040	1.0057
	1.0D	1.0208	1.0200	1.0196	1.0198	1.0204	1.0212	1.0221	1.0231

. As indicated in the tables, high error rates are commonly observed at the 0.0D to −1.0D (Z/D) positions, which correspond to the hub/nacelle and tower locations, across all reduction ratios in the side view. In the top view, stable values are generally observed except at the hub/nacelle position; however, the 1:50 scale showed a high error rate at the +0.5D (Y/D) position, which is in the direction of rotation. Additionally, in the experiment, a lower trend was observed at the +0.5D (Y/D) position compared to the −0.5D position in the 1:33 and 1:50 scales, but this phenomenon was not consistently captured in the analysis. For the 1:33 scale (Table 5 and Table 6), the dimensionless wake at the rotor center was 0.51 at 1D, 0.66 at 2D, 0.62 at 3D, and 0.67 at 4D, showing a gradual recovery trend similar to the experimental results. However, the wake recovery tendencies for the 1:50 (Table 7 and Table 8) and 1:67 (Table 9 and Table 10) scales differed from the experiment. In the 1:50 scale, the wake recovered to 0.70, 0.69, 0.70, 0.74, 0.76, and 0.77 depending on the separation distance, while in the 1:67 scale, it recovered to 0.76, 0.70, 0.70, 0.73, 0.77, 0.79, 0.80, and 0.81, showing a decrease in the near wake and an increase in the far wake. These results highlight the importance of accurately modeling the grid system around the hub, as inappropriate grid configurations for the hub/nacelle and tower led to inaccurate flow separation. The analysis and calculations at the 1.0D location did not yield significant results in comparison to other high-speed wind turbine analyses.

The error rates between the experiment and the simulation in the rotor areas of 0.5D and 1.0D for each model were compared by separation distance, as shown in Figure 32 and Figure 33. Data from the sides, where interference with the tower and nacelle occurred, were excluded, and the top view data were averaged from both sides for comparison with the experimental data. Figure 32 shows that the error rate for the 1:33 and 1:50 scale-down models increased with separation distance, exceeding the uncertainty range at separation distances of 3D and 4D when observed from the side view. Conversely, the 1:67 scale-down model showed a fluctuating error rate at the 1D position, indicating variations in capturing the blade tip’s dynamics. At the 1.0D position, the error rates for both the 1:33 and 1:50 scale-down models remained within the uncertainty range, while the 1:67 scale model exceeded the uncertainty at a separation distance of 5D. This suggests that the 1:67 scale model, being relatively more extreme, likely deforms during rotation. In the experiment, the wind turbine is a flexible body, while the simulation model is rigid, leading to errors due to the inability to account for deformation. In Figure 33, it is shown that the 1:50 scale model only exceeded the margin of error at the 0.5D position, which corresponds to the blade tip location, when viewed from the top perspective. This comprehensive analysis highlights the challenges in accurately simulating the flexible nature of wind turbine blades, particularly in more extreme scale-down models, and underscores the need for more advanced modeling techniques that can account for structural deformations.

The error rates for the 0.5D and 1.0D positions according to scale ratios are presented in

Table 11. Error rate comparison at 0.5D position according to scale ratio.

Scale	1:33 Scale		1:50 Scale		1:67 Scale		MU (%)
X/D	Side	Top	Side	Top	Side	Top
1	0.8	1.8	0.3	4.2	4.1	0.9	3.54
2	1.6	2.4	2.9	6.1	1.2	2.0
3	4.4	2.9	3.3	6.4	2.1	1.9
4	4.5	3.3	4.5	7.7	1.3	2.3
5	-	-	5.2	7.1	2.1	1.8
6	-	-	4.7	8.0	0.5	2.5
7	-	-	-	-	2.3	2.1
8	-	-	-	-	0.1	1.4

and

Table 12. Error rate comparison at 1.0D position according to scale ratio.

Scale	1:33 Scale		1:50 Scale		1:67 Scale		MU (%)
X/D	Side	Top	Side	Top	Side	Top
1	1.7	1.5	1.2	2.1	1.3	2.2	3.54
2	1.7	1.9	1.4	2.4	2.2	2.2
3	2.2	1.8	1.7	2.4	2.5	2.2
4	1.7	1.5	2.0	2.3	2.4	1.2
5	-	-	1.6	2.0	4.3	1.7
6	-	-	1.5	1.9	2.4	0.8
7	-	-	-	-	3.1	1.3
8	-	-	-	-	2.9	0.7

. The 1:67 scale model appears to have relatively stable error rates within the measurement uncertainty (MU) compared to the other scale models. The influence of the wake is not significant at the 1.0D position for all scale ratios, but a discrepancy occurs between the experimental and analytical results at 0.5D. Specifically, in the 1:67 scale model, the non-dimensional velocity consistently showed values close to 1.0 due to deformation at the 0.5D position (blade tip) during the experiment, leading to inaccurate results.

Figure 34 and Figure 35 show the non-dimensional velocities of the experiment and numerical simulation were compared according to the separation distance (X/D) at the lateral Z/D = +0.5 position. This position is presumed to be minimally affected by the tower and nacelle. In the experiment, the non-dimensional speed of the 1:67 scale model exhibited considerable fluctuations, as previously predicted, in contrast to the other scale ratios. For the 1:33 and 1:50 scales, the non-dimensional speed tended to decrease. Conversely, the analysis results were divergent from this observation. In the simulations assuming a rigid body, the 1:67 scale model demonstrated a similar increasing trend in non-dimensional speed as the 1:33 and 1:50 scales. Therefore, while the experimental results exhibited a decreasing trend in non-dimensional speed, the numerical analysis showed an increasing trend. This discrepancy is believed to be due to differences in the consideration of the tower and nacelle and the weak deformation of the rotor in the experimental setup, which were not accounted for in the rigid body assumptions of the numerical analysis.

5. Conclusions

This study investigates wake characteristics in wind turbines by examining the impact of different scale ratios using both experimental and numerical methods. The wind turbine models analyzed were scaled versions of the Aeolos H-20 kW turbine at 1:33, 1:50, and 1:67. The experimental component included wind tunnel tests conducted in an open-circuit tunnel with adjustable wind speeds and controlled turbulence intensity. Computational Fluid Dynamics (CFD) simulations were performed using STAR-CCM+ (Version 15.06.02) to numerically analyze the wake characteristics. A convergence test, involving variations in grid density and Y+ values, was conducted to optimize the simulation settings, which were crucial for accurately capturing wake dynamics. The simulation results were validated against experimental data to ensure the reliability of the numerical analysis.

In the experiment, the 1:33 scale model, with wake measurements taken from 1D to 4D, showed a gradual recovery in the non-dimensional wake velocity ratio (V_m/V_inf), increasing from 0.69 at 1D to 0.78 at 4D. Similarly, the 1:50 scale model, measured from 1D to 6D, displayed improved recovery, with the wake velocity ratio rising from 0.69 at 1D to 0.85 at 6D. The 1:67 scale model exhibited the most significant recovery, with the wake velocity ratio increasing from 0.69 at 1D to 0.92 at 8D. This consistent recovery pattern across different scale models underscores the reliability of the measurements and confirms the effectiveness of the scaling method in accurately capturing wake dynamics.

From the CFD simulations, the 1:33 scale model showed a gradual recovery in the non-dimensional wake velocity ratio at the rotor center, with values increasing from 0.51 at 1D to 0.67 at 4D, closely mirroring the experimental results. However, the wake recovery tendencies for the 1:50 and 1:67 scales diverged from the experimental outcomes. For the 1:50 scale, the wake recovery varied, with values of 0.70, 0.69, 0.70, 0.74, 0.76, and 0.77 at 1D to 6D separation distances, respectively. The 1:67 scale showed a decrease in near-wake recovery and an increase in far-wake recovery, with values progressing from 0.76 at 1D to 0.81 at 8D.

The CFD simulation results showed differences from the experimental results only at the hub/nacelle and tower positions. However, the 1:50 scale showed a slightly high error rate at the +0.5D (Y/D) position, which is in the direction of rotation. The error rates between the experiment and simulation in the rotor areas at 0.5D and 1.0D for each model were compared according to separation distance for all scale models. The results from the side view observation show that the error rate for the 1:33 and 1:50 scale models followed a similar trend, while the 1:67 scale model showed a fluctuating error rate. However, the 1:67 scale model appears to have relatively stable error rates within the measurement uncertainty (MU) compared to the other scale models. This suggests that the 1:67 scale model, being relatively more extreme, likely deforms during rotation. In the experiment, the wind turbine behaves as a flexible body, while the simulation model assumes rigidity, leading to errors due to the inability to account for deformation. From the top view, all scale models remained within the measurement uncertainty, except for the 1:50 scale model at the 0.5D position, which corresponds to the blade tip location. Fluctuating error rates at the 1D position were noticed in both side and top view observations.

Overall, the study highlights the consistent recovery patterns observed across different scale models, validating the effectiveness of the scaling method in capturing wake dynamics. However, the discrepancies between experimental results and CFD simulations, particularly in the 1:50 and 1:67 scales, underscore the limitations of current simulation practices. The rigid body assumption in simulations does not fully account for the deformation observed in the more extreme 1:67 scale model, leading to errors. This emphasizes the need for advanced modeling techniques that incorporate the flexible nature of wind turbine blades. Enhancing simulation accuracy through refined grid designs and better accounting for structural deformations is crucial for improving aerodynamic performance predictions and advancing the design of more efficient, sustainable wind turbines.