CFD-Driven Design Optimization of Corrugated-Flange Diffuser-Integrated Wind Turbines for Enhanced Performance

Abstract

In the global shift toward sustainable energy, enhancing the efficiency of renewable energy systems plays a pivotal role in advancing the Sustainable Development Goals. This study focuses on optimizing the design of a corrugated-flange diffuser integrated with a wind turbine to enhance its performance, particularly in low-wind conditions. While most previous research has examined wind farm performance at high wind speeds, the challenge of effective power extraction at low wind speeds remains largely unresolved. The potential of diffusers to enhance wind turbine efficiency under low-wind conditions has received limited investigation, with most prior studies focusing solely on empty diffuser configurations without turbine integration. In addition, the influence of flange geometry on diffuser performance remains largely unexplored. In this study, parametric analyses were conducted to identify the optimal diffuser design, followed by comparative performance evaluations of configurations with and without turbine integration, using computational fluid dynamics (CFD) simulations. The results show that integrating a turbine with the optimized corrugated-flange diffuser increased flow velocity by 67.85%, achieving an average of approximately 14 m/s around the blade region. In comparison, the optimized corrugated-flange diffuser alone increased flow velocity by 44%, from 4.5 m/s to 8.036 m/s. These findings highlight the potential of optimized diffuser designs to enhance small-scale wind turbine performance in low-wind conditions.

1. Introduction

In today’s world, the global transition to renewable energy has become essential due to the depletion of fossil fuel resources and the increasing effects of climate change. This shift aims to protect the environment, promote economic development, and enhance public health. Wind energy ranks among the most rapidly expanding renewable energy sources worldwide [1,2]. According to the European Union report [3], by 2050, wind energy is projected to generate more electricity than any other technology in regions with high renewable energy potential. Furthermore, the Global Wind Energy Council’s 2025 report states that wind power added 117 GW of new capacity in 2024, maintaining the same trend seen in 2023 and bringing the total global installed capacity to 1136 GW. The report also projects that capacity will rise to 139 GW in 2025, with nearly 1000 GW of new wind installations expected by the end of 2030 [4]. Moreover, people in each country work to improve their living standards, which leads to an increase in energy demand. However, renewable energy faces several challenges, one of the main ones being the high upfront investment required, which contributes to overall higher energy costs. According to the Renewable Finance from 2023 [5], the world invested $1.3 trillion in renewable transition technologies in 2022. In addition, the 2024 report [6] estimates that increasing global power capacity to over 11,000 gigawatts will require a total investment of approximately $31.5 trillion between 2024 and 2030.

Hence, for attaining the optimum power output of wind turbines with less cost, numerous prior studies have investigated methods for enhancing the efficiency of wind turbines, with particular attention given to the optimization of critical structural components. Researchers have examined the application of advanced blade materials [7], wind turbine control systems for robust performance [8], modifications to blade geometry [9,10], and improvements in the design configurations of the rotor and tower systems. These elements are consistently identified in the literature as key contributors to the overall performance enhancement of wind energy conversion systems.

For a considerable amount of time, large-scale wind energy has been researched in regions with strong winds. However, as a viable and less expensive endeavor in wind energy harvesting, the issue of small-scale wind turbine systems producing less electricity at small wind speeds remained unresolved. Wind turbine power output is proportional to the cube of wind speed, so wind acceleration before the blade’s rotor plane significantly influences the power generated by wind farms [11]. The faster the wind moves across the rotor surface, the more power is generated.

As researchers continue to address the challenges of low wind speeds and high costs, the idea of using diffusers in wind turbine designs has recently gained increasing attention, even though it is challenging for wind turbines to produce power output in low-wind-speed areas. Currently, many researchers are researching diffusers to integrate with wind turbines to achieve greater power optimization, as reported in [12,13,14,15]. They are attempting to prove that the diffuser can be the best way for wind turbine optimization at low wind speeds.

Bontempo et al. [16] studied the influence of coupled and uncoupled diffusers on wind turbines using NACA airfoil profiles for the diffuser design. Their study involved CFD simulations to analyze the parametric influence of nozzle and diffuser configurations on turbine performance. The results demonstrated that wind turbines equipped with diffusers achieved a higher power coefficient compared to those without diffusers. The authors concluded that integrating a wind turbine equipped with a diffuser is an effective strategy to enhance overall performance. The CFD findings were validated using two sets of experimental data from the existing literature.

Seifi Davari et al. [17] conducted a study comparing the aerodynamic performance of NACA and Selig airfoil shapes at a Reynolds number of 40,673. The analysis was performed over a tip speed ratio (TSR) range from 0 to 2.5, with increments of 0.5. Among the evaluated profiles, the modified NACA 0015 airfoil demonstrated the highest aerodynamic performance and is applicable to vertical-axis wind turbines operating under low wind speed conditions.

The work in [14] investigated key design parameters affecting the performance of HAWTs in the case of low wind speeds using CFD. Their study focused on turbine blade geometry, blade inclination, and the use of confusor-diffuser (nozzle-diffuser) shaped casings. They examined different casing designs, including circular, rectangular, and hybrid combinations, and compared them to a baseline case with an empty diffuser. The results showed that optimizing blade shape led to a 35% increase in power output, while adjusting blade inclination contributed a 16% improvement compared to the original configuration. Additionally, the use of a confusor-diffuser structure to accelerate airflow resulted in a 21% power increase with an extended diffuser length.

Sridhar et al. [18] performed a study employing 3D CFD analysis to evaluate the aerodynamic characteristics of slotted versus non-slotted diffusers in wind turbine applications. Their results showed that the slotted diffuser significantly outperformed the non-slotted version, with efficiency improvements of 27.4% and 46.8% compared to turbines without diffusers.

Various studies have analyzed the impact of different duct configurations, such as straight and curved types [19], curved diffusers [20], variations in diffuser length and area ratio [21,22], and the addition of a flange. In all these cases, the wind turbines equipped with these modifications consistently demonstrated higher power output compared to conventional bare turbines, as reported in references [19,20,21,22].

Previous research has shown that flow-concentrating devices—such as cylindrical ducts [23,24], nozzles and nozzle-diffuser systems [12,15,25], and diffusers [16,18,19,20,21,26,27,28,29]—can improve wind energy performance by increasing the mass flow rate at the rotor section. This enhancement of wind speed at the rotor is especially important for small-scale wind turbines operating under low wind conditions.

The literature has primarily focused on computational parametric studies of diffusers in isolation, without incorporating wind turbines, as referenced in [15,30,31,32,33,34]. In contrast, this study presents a novel investigation into the effects of incorporating a corrugated-flange diffuser, offering a fresh perspective not previously explored in the literature for optimizing the power output of turbines.

To analyze this concept, the flange on the diffuser requires enhanced structural stiffness, particularly in applications where minimizing the pressure drop is critical. Corrugated steel roofing, featuring alternating ridges and valleys, provides increased strength and reduced weight while efficiently guiding water flow. Inspired by this geometry, the corrugated shape was designed to direct airflow over the surface rather than along the flow line, aiming to reduce pressure at the flange exit. The airflow behavior over these corrugated surfaces was analyzed and served as the basis for the present study. In this work, this additional flange is referred to as the corrugated flange. Furthermore, it uniquely integrates an optimized diffuser design with a wind turbine system to rigorously evaluate their combined performance, highlighting potential advancements in turbine efficiency and flow dynamics. Wind turbines with and without a diffuser were compared and analyzed through CFD and validated against prior experimental data at a low wind speed of 4.5 m/s. The main optimum diffuser parameters were identified in terms of the optimum velocity attained and the power it extracts. In general, this research investigates how an optimized diffuser can amplify wind speed to significantly boost power output at the rotor of a small-scale wind turbine. The primary contribution of this work is the optimization of diffuser configurations for wind turbine applications in low-wind-speed regions. The main novelty of this study lies in the use of a corrugated-flange diffuser and its integration with the wind turbine to enhance power output.

To outline the processes that led to these findings, the paper is organized as follows: Section 2 discusses the materials and methods employed in the study. Section 2.1 provides an overview of the theoretical background and turbine–diffuser modeling, while Section 2.2 offers a detailed account of the CFD approach used in the simulations. Section 2.3 describes the mathematical modeling and setup procedures applied in the CFD analysis. Section 2.4 presents the mesh independence test, while Section 2.5 discusses the validation of results. Section 3 presents the results, along with an in-depth discussion. Finally, Section 4 concludes the study and outlines potential directions for future research.

2. Materials and Methods

2.1. Theoretical Background and Turbine–Diffuser Modeling

The study’s methodology is generally outlined in Figure 1. According to the theory of aerodynamic behavior of wind turbines, focusing on energy extraction processes without referencing specific turbine designs determines the Power coefficient ($C_P$), as given in Equation (1) [35,36].

$${\mathrm{C}}_{\mathrm{P}}={\displaystyle \frac{P_{out}}{P_{Av}}}={\displaystyle \frac{P_{out}}{{\frac{1}{2}{\rho \mathrm{A}}_{\mathrm{d}}{\mathrm{U}}_{\infty }}^3}}$$

(1)

where $\rho$ is the air density, ${\mathrm{A}}_{\mathrm{d}}$ is the diffuser exit area, and ${\mathrm{U}}_{\infty }$ is the free-stream wind velocity.

P_out denotes the power extracted by the turbine, and P_av represents the available wind power across the rotor area.

Theoretical analyses have established that an optimum of 59.3% of the wind’s kinetic energy can be changed into mechanical power by a wind turbine rotor, a constraint known as the Betz limit [35,36].

However, various studies have investigated the integration of diffusers with wind turbines to enhance energy capture. Under such conditions, Equation (1) is no longer applicable, as it was originally formulated for bare wind turbine systems. The assumption of a larger diffuser diameter was made to account for the Betz limit.

The mathematical formulation of wind turbine power output is expressed as follows:

$$P={\displaystyle \frac{1}{2}}{V}^2{\displaystyle \frac{dm}{dt}}={\displaystyle \frac{1}{2}}{V}^2\left(\rho AV\right)={\displaystyle \frac{1}{2}}\rho A{V}^3$$

(2)

As expressed in Equation (2), the wind turbine’s power output is influenced by the air density, the rotor’s swept area (A), and the wind speed (V).

Additionally, the performance improvement of a diffuser-integrated wind turbine is largely influenced by the shape and geometry of the diffuser, the blade airfoil design, and the wind conditions at the installation site. Therefore, this study primarily focuses on increasing wind speed to enhance power output, which follows a cubic relationship.

To design the wind turbine, the NACA 0012 symmetric airfoil was chosen due to its high lift-to-drag ratio, low drag, and favorable stall characteristics [26,36]. The average ambient parameters, a temperature of 21.3 °C, and a pressure of 82 kPa are considered. At this temperature, the air density ($\rho$) is approximately 0.97 kg/m³, and the dynamic viscosity (μ_∞) is 1.825 × 10⁻⁵ kg/(m∙s). A structural rigidity equivalent to 15% of the wind turbine’s diameter was assumed to estimate the average chord ($C_{avg}$) length as ref. in [37], giving $C_{avg}$ = 15% × Dr = 0.108 m, based on a rotor diameter (Dr) of 0.7 m.

To find the optimum angle of attack for the modeling of the blade, the Reynolds number (Re) $={\displaystyle \frac{\rho V{C}_{avg}}{{\mu }_{\infty }}}$ was initially $25\times {10}^5$. Assuming free-stream velocity, Re was updated to 1 × 10⁵. According to airfoiltools.com, the NACA 0012 airfoil achieves its highest lift-to-drag ratio at a 7.5° angle of attack for Re up to 1 × 10⁶. At low Re for NACA 0012 profiles, the best optimum ${\displaystyle \frac{C_l}{C_d}}$ was obtained at $7°$ as studied in [38]. Therefore, it is logical that the maximum angle of attack of $7.5°$ was used in this study, where angles of attack were measured in radians [36]. Hence, since NACA 0012 is an asymmetrical airfoil, the lift coefficient can be defined as in Equation (3) [36].

$$C_l=2\pi \alpha$$

(3)

The angle of attack $\alpha =7.5°=7.5°\times {\displaystyle \frac{\pi }{180°}}$

Then lift coefficient $C_l=2\pi \alpha =2\pi \times 7.5°\times {\displaystyle \frac{\pi }{180°}}\cong 0.83$

As referenced in the work of [36], a tip speed ratio (TSR) between 3 and 5 is considered optimal for a diffuser-integrated wind turbine. For the current study, a TSR ($\lambda )$ value of 3 was considered. The angular velocity (ω) can be calculated following the method described in [22], as given by Equation (4), for the inlet wind speed (u) and a rotor radius (R) of 350 mm.

$$\lambda ={\displaystyle \frac{R\omega }{u}}$$

(4)

Blade element theory assumes the absence of aerodynamic interaction among elements and neglects radial flow. Lift and drag on each element represent the blade forces, as indicated in [36]. For this analysis, the blade is segmented into ten elements, as illustrated in [36]. The relative wind angle (φ), chord length (C), and tip speed ratio for each NACA0012 section are determined as in Equations (5)–(7) [36] and listed in

Table 1. Normalized blade distribution parameters and angle variation for Betz-optimal blade design.

$\frac{\mathit{r}}{\mathit{R}}$	r (mm)	C (mm)	$\frac{\mathit{C}}{\mathit{R}}$	(${\mathit{\theta }}_{\mathit{T}}$)	($\mathit{\phi }$)	${\mathit{\theta }}_{\mathit{p}}=\mathit{\phi }-\mathit{\alpha }$
0.1	35	188.3	0.538	45.54	53.13	45.63
0.2	70	130.57	0.373	26.1	33.69	26.19
0.3	105	95.6	0.273	16.372	23.962	16.462
0.4	140	74.41	0.212	10.84	18.43	10.93
0.5	175	60.64	0.173	7.34	14.93	7.43
0.6	210	51.02	0.145	4.93	12.52	5.02
0.7	245	44.02	0.125	3.19	10.78	3.28
0.8	280	38.68	0.11	1.87	9.46	1.96
0.9	315	34.46	0.098	0.83	8.42	0.92
1	350	31.09	0.088	0	7.59	0.09

Where ${\theta }_T$ is twist angle, $\phi$ is relative wind angle, and ${\theta }_p$ is section pitch angle. The units for ${\theta }_T$, $\phi ,$ and ${\theta }_p$ are in degrees.

. The blade twist angle at the tip (θ_po) was set to zero.

$$\phi ={\tan }^{-1}\left({\displaystyle \frac{2}{3{\lambda }_r}}\right)$$

(5)

$$\mathrm{C}={\displaystyle \frac{8\pi r\sin \phi }{3B{C}_1{\lambda }_r}}$$

(6)

$$\mathrm{C}={\displaystyle \frac{8\pi r\sin \phi }{3B{C}_1{\lambda }_r}}$$

(7)

where ${\theta }_{p,o}$ is the blade pitch angle at the tip. The sum of the section pitch angle and the angle of attack equals the relative wind angle, as indicated in Equation (8).

$$\phi ={\theta }_{\mathrm{p}}+\alpha$$

(8)

${\theta }_{p_{tip}}$ $={\phi }_{at tip}-\alpha =7.59°-7.5°=0.09°$ and the same pattern of calculation is used for the next successive airfoil up to the 10th end.

For modeling the NACA 0012 airfoil, the blade’s profile and coordinates were obtained from the NASA-endorsed airfoil database using the Selig-format data file, as referenced at [39]. The coordinates are provided in Appendix A.

The choice of material plays a crucial role in the design and performance of wind turbine blades. GFRP is preferred in modern manufacturing for its strength-to-weight advantage and lower cost, as noted in [40]. The 3D blade, modeled in SolidWorks 2021 using the NACA 0012 profile, is presented in Figure 2 and Figure 3a.

For diffuser modeling, an inlet diameter of 720 mm, a length of 1.25D, and a wall thickness of 5 mm were selected, based on experimental data from previous studies [41]. The diffuser opening angle (β) is defined as the angle between the horizontal line and the top or bottom surface of the diffuser. The inlet diameter of the diffuser (D) refers to the diameter at the diffuser’s inlet tip. The flange angle (∅), flange length (L), and flange height (H) are shown in Figure 4b. The difference between the diffuser and the flange is depicted in Figure 5.

The corrugated flange is illustrated in two dimensions in Figure 4c. The design parameters of this flange, as indicated in Figure 4c, are summarized in

Table 2. Corrugated-flange design parameters.

Dimensions	Values	Flange Types
A1	0.025D	Corrugated flange
R1 = R2 = R3	(0.0347D) × 6
C	(0.0139D) × 2
A2	0.039D
Total Length(L)	0.3D	Both corrugated and flat

.

Rotor diameter (Dr) indicates the diameter of the wind turbine blades, which are designed to be shorter than the inlet diameter of the diffuser to allow the wind turbine to be placed inside the diffuser. In designing the wind turbine inside the diffuser, the space between the rotor blade tip and the diffuser wall was assumed to be 0.01 m, based on the experimental work mentioned in [41].

The following diffuser models were considered for the optimization of diffuser parameters, and the simulation work for each case was thoroughly studied and compared. Moreover, the performance of the wind turbine integrated with the diffuser, as shown in Figure 3, was investigated.

This study investigates three cases:

• Case I. Effect of opening angle for flat-flange diffuser and normal (no flange) diffuser comparison, as illustrated in Figure 6.
• Case II. This case examines the performance differences among three diffuser flange configurations: a corrugated-flange diffuser (Figure 7), a flat-flange diffuser, and a diffuser without a flange (both illustrated in Figure 6).
• Case III. Performance analysis of a wind turbine integrated with a corrugated-flange diffuser, as illustrated in Figure 3b.
• Case IV. Evaluation of the inlet guide’s influence when integrated with the corrugated-flange diffuser (refer to Figure 8).
• Case V. Comparative performance analysis between a standalone wind turbine and a wind turbine integrated with the optimized diffuser configuration (see Figure 3).

2.2. Methods in CFD Analysis

Computational fluid dynamics (CFD) was applied in the current work, as it offers significant advantages over experimental prototyping [22]. Experimental testing is often too expensive, less scalable and flexible, and does not provide a detailed visualization of fluid flow. However, CFD can overcome all these limitations. The method used in the CFD analysis is illustrated in Figure 1.

In the CFD computation, mesh quality and mesh independence testing are key criteria to ensure the accuracy of the results. Mesh features were evaluated, as shown in Figure 9. According to the findings in [42], a skewness value approaching zero—within the range of 0 to 0.95—can yield accurate simulation results. The corrugated-flange diffuser combined with the wind turbine exhibited an average skewness of 0.26348, which falls well within the 0 to 0.95 range documented by [42]. Being relatively close to zero within this range indicates that the mesh is well constructed and suitable for accurate simulation.

Figure 9a–e illustrate the overall geometry and enclosure for the case of a wind turbine integrated with a corrugated-flange diffuser meshing. Part a shows the full geometry, while parts b through e present the meshing characteristics of various components, including the enclosure, face of enclosure, diffuser, rotating zone, and wind turbines. Specifically, parts c and d highlight the detailed mesh configuration of the corrugated-flange diffuser integrated with the wind turbine, along with the surrounding enclosure. Parts d and c provide a side view of the entire enclosure, with the diffuser and wind turbine integrated and positioned at the center. Part e shows the isometric zoomed mesh view.

A hybrid meshing approach was used for the simulations of the corrugated-flange diffuser integrated with the wind turbine. While structured meshes are often favored in wind turbine analyses for their precision and computational efficiency, creating them across the entire domain is difficult when dealing with complex geometries. In this work, structured meshes were applied in regions distant from the turbine–diffuser assembly, whereas unstructured meshes were utilized in the intricate areas surrounding the turbine.

To ensure an accurate representation of aerodynamic behavior, face-sizing controls and inflation layers were applied along the blade surfaces to effectively capture near-wall flow characteristics across different simulations.

2.3. Mathematical Modeling and Setup of CFD Analysis

In this study, a steady-state flow simulation was employed due to its computational efficiency and suitability for modeling stable, time-invariant flow conditions (as illustrated in Figure 10). Compared to steady-state analysis, unsteady flow simulations are significantly more time-consuming and less efficient, as noted in [43,44].

This study utilized a pressure-based solver, consistent with the approach outlined in [45], where the selection is justified by the treatment of incompressible and compressible flows through density variation. Turbulence was characterized by a Reynolds number of 2.174 × 10⁵ associated with an inlet wind velocity of 4.5 m/s, which substantially surpasses the critical threshold of 2300. For accurate modeling of near-wall flow behavior, simulation was performed using the k-ω SST turbulence model, as recommended in [14,22,38,45]. In CFD, fluid dynamics are modeled through the application of numerical techniques and numerical algorithms applied to solve the governing equations. The stress tensor and enthalpy are formulated in Equations (12) and (13), which also integrate the momentum Equation (10), energy Equation (11), and continuity Equation (9). Although turbulent flows are common in both natural and industrial systems, simulating them computationally is expensive due to their chaotic and unpredictable nature. In computational fluid dynamics (CFD), turbulent flows can be modeled using a range of approaches, such as Reynolds-Averaged Navier–Stokes (RANS) equation-based models, Detached Eddy Simulation (DES), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS). RANS models, widely used in practical engineering applications, play a crucial role in managing the transfer of averaged flow quantities between turbulence models while minimizing computational costs. All these approaches were compared in [46]. In the present study, the Reynolds-Averaged Navier–Stokes (RANS) model was employed.

Continuity Equation

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial }{\partial xi}}\left(\rho ui\right)=0$$

(9)

where $\rho$ is the fluid density, t is time, ${\displaystyle \frac{\partial }{\partial t}}$ denotes the partial derivative with respect to time, u is velocity, and $ui$ and $uj$ are the velocity components in the i^th and j^th directions, respectively.

Momentum Equation

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial }{\partial xi}}\left(\rho ui\right)=0$$

(10)

For $p$, it is the pressure, and ${\tau }_{ij}$ represents the viscous stress tensor components in the ith and jth directions.

Energy equation

$${\displaystyle \frac{\partial }{\partial t}}\left[\rho \left(h+{{\displaystyle \frac{1}{2}}{u}_i}^2\right)\right]+{\displaystyle \frac{\partial }{\partial x_j}}\left[\rho u_j\left(h+{{\displaystyle \frac{1}{2}}{u}_i}^2\right)\right]={\displaystyle \frac{\partial p}{\partial t}}+{\displaystyle \frac{\partial }{\partial x_j}}\left(u_i{\tau }_{ij}+\lambda {\displaystyle \frac{\partial T}{\partial x_j}}\right)$$

(11)

The stress tensor and enthalpy (h) are defined by the following formulas:

$${\tau }_{ij}=\mu \left({\displaystyle \frac{\partial u_i}{\partial x_j}}+{\displaystyle \frac{\partial u_i}{\partial x_i}}\right)-{\displaystyle \frac{2}{3}}\mu {\displaystyle \frac{\partial u_i}{\partial x_i}}{\delta }_{ij}$$

(12)

$$h=C_{P}T$$

(13)

C_P represents the specific heat capacity, T is the temperature, and μ denotes the dynamic viscosity of the fluid.

The SST k-ω model uses two equations: one for turbulent kinetic energy (k) and one for specific dissipation rate (ω).

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho K\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho K{u}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left({\Gamma }_K{\displaystyle \frac{\partial k}{\partial x_j}}\right)+{}_G{}^{~}K-Y_k+S_k$$

(14)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho \omega \right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho \omega u_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left({\Gamma }_{\omega }{\displaystyle \frac{\partial \omega }{\partial x_j}}\right)+G_{\omega }-Y_{\omega }+D_{\omega }+S_k$$

(15)

where ${\Gamma }_K$ and ${\Gamma }_{\omega }$ represent the effective diffusivity of k and ω, respectively; $G_{\omega }$ denotes the generation of ω due to turbulence production; $Y_k$ and $Y_k$ represent the dissipation of ω and $k$ caused by turbulence; $S_k$ is the source term; and ${}_G{}^{~}K$ corresponds to the production of turbulent kinetic energy.

The fluid domain used air, and the solid diffuser used aluminum. Power output was determined using multiple reference methods for frame motion [22]. For all the walls, a no-slip boundary condition was assumed. A computational domain with a diameter of 11.89D and a length of 15.27D was defined, where D represents the inlet diffuser diameter of 0.72 m.

The present simulation employed inlet and outlet boundary conditions, with walls enclosing the domain circumferentially. A turbulence intensity of 5% and a viscosity ratio of 10 were specified at both the inlet and outlet boundaries for the given geometry. This approach follows the same trend reported in previous studies [22,46]. The computational domain was analyzed under two primary scenarios: one involving a corrugated diffuser integrated with a wind turbine, and the other focusing on the parametric optimization of an empty diffuser.

The simulation employed a SIMPLE algorithm for pressure–velocity coupling, alongside second-order upwind schemes for turbulent kinetic energy, discretizing momentum, and specific dissipation rate. A least-squares cell-based gradient method was applied for gradient calculations. Furthermore, hybrid initialization was used to promote improved convergence of the solution with a residual set to 10⁻⁶.

2.4. Grid Independent Test

The mesh independence test is crucial for accurate results in CFD simulation, as inaccurate results can be obtained if the grid is not properly generated. The standard grid-independent test involves increasing resolution and repeating the simulation until the results become constant or independent of grid size [22]. The finest mesh provides more accurate results and faster convergence, but it requires more computational time and cost. The mesh test was conducted for the diffuser corrugated flange to verify the start of the simulation. The mesh independent test was carried out at the exit of the diffuser for different mesh sizes, as indicated in Figure 11.

The finer mesh, with 2,966,385 elements and 5,079,434 elements, yields nearly identical pressure coefficients (Cp), and then the finest mesh of 12,696,230 elements produces the same Cp, with 5,079,434 elements. Hence, to reduce computational time and resources, the mesh size of 5,079,434 elements was considered for the current work.

2.5. Result Validation

This section validates the current simulation results by comparing them with the experimental data reported by Ohya et al. [47]. The comparison is based on a configuration with an L/D ratio of 1.5, an opening angle of 4, a diameter D of 200 mm, and an inlet velocity of 5 m/s—consistent with the conditions in the Ohya et al. study. The present simulation, conducted using the k-omega turbulence model with an enclosure length of 11 m and a diameter of 10 m, shows close agreement with the experimental observations. As illustrated in Figure 12, the non-dimensional velocity (U/U_in) is plotted against the non-dimensional length (X/L) along the central streamline. The deviation between the simulation and experimental data remains within 3% in the optimal region, which serves as the primary focus of this study. Although the simulated velocities are slightly lower than those reported in [47], the overall agreement is strong, supporting the validity of the current model. In the simulation, the flow exhibits turbulence immediately downstream of the diffuser exit but gradually returns to a stable state as it progresses into the freestream region due to the 11 m enclosure length used in the setup. The differences observed are likely due to the inherent assumptions within the mathematical model, especially its steady-state nature, which limits its ability to fully represent the dynamic variations encountered in real-world conditions. Furthermore, factors like surface roughness, which are difficult to model accurately, may also play a role in these differences.

Interestingly, the simulation slightly underpredicts the velocity compared to the experimental data, which may prove beneficial; this conservative estimate suggests that actual performance in a full-scale experimental setup could exceed predictions, as indicated in Figure 12.

3. Results and Discussion

The following section presents a comprehensive analysis of the results and discussion based on the evaluation of optimal diffuser configurations aimed at enhancing wind turbine performance. The outcomes of the five case studies (Case I to Case V), as outlined in Section 2.1, are systematically examined. This investigation focuses on the aerodynamic efficiency of a wind turbine integrated with an optimized corrugated-flange diffuser. To ensure greater accuracy and better capture of flow behavior, a three-dimensional model of the turbine was employed to account for asymmetrical flow characteristics. A key innovation of this study lies in the introduction and evaluation of the corrugated-flange design, which is compared against the conventional flat flange configuration referenced in previous works [13,15,32,48,49,50,51]. Moreover, the performance of the proposed configuration integrated with the wind turbine was analyzed and compared to that of a standalone (bare) wind turbine. In general, this study conducts a parametric analysis of various diffuser models to evaluate their impact on the performance of diffuser-integrated horizontal-axis wind turbines (DIHWTs).

3.1. Effect of Opening Angle on the Performance of Flat-Flange and No-Flange Diffusers for Wind Turbine Applications

In general, this study conducts a parametric analysis of various diffuser models to evaluate their impact on the performance of diffuser-integrated horizontal-axis wind turbines (DIHWTs).

This case study examines how variations in the diffuser opening angle influence the aerodynamic performance of configurations with flat flanges and without flanges, as introduced in Case I (Section 2.1) and depicted in Figure 6. The investigation considers opening angles ranging from 0° to 16° applied to diffusers equipped with a constant flange length of 0.3D. For the flat-flange design, a fixed flange angle of 15° was used throughout the analysis.

In contrast, previous studies [11,15,52] did not examine the opening angle in the case of diffusers with flanges but instead studied the diffuser opening angle separately and considered it randomly. In the current study, we observed from the comparison shown in Figure 13 and Figure 14 that the optimal diffuser opening angle for wind turbine applications may vary depending on the diffuser type. The optimal opening angle is 8° for the diffuser without a flange and 4° for the diffuser with a flat flange, as shown in Figure 13 and Figure 14, respectively. It is also well known that adding a flange at the diffuser exit, as shown in Figure 15, generates turbulence that causes flow separation and generates a low-pressure zone at the diffuser’s outlet. This low pressure draws velocity toward the flange and into the diffuser flow, resulting in a maximum velocity inside the diffuser. Therefore, it is recommended to study the effect of opening angle across all diffuser types and shapes.

As clearly shown in Figure 14, the velocity inside the diffuser reaches its maximum for the flat-flange diffuser at an angle of four degrees. The velocity increases progressively from 0° to 4°, then decreases up to 16°, indicating that positioning the diffuser at around four degrees optimizes the internal velocity. This is critical for maximizing the wind turbine’s power output, given the cubic relationship between wind velocity and power generation.

As illustrated in Figure 13 and Figure 14, the opening angle varies depending on the type of diffuser used. In Figure 13, the diffuser incorporates a flange at the exit, as shown in the model presented in Figure 16. The presence of the flange induces additional turbulence at the outlet, which results in a reduction in exit velocity. This turbulence enhances the entrainment of surrounding airflow into the diffuser, thereby increasing the intake velocity compared to a conventional diffuser without a flange. Consequently, the velocity profile reaches its peak at a smaller opening angle, specifically at 4°, earlier than in the case of the diffuser without a flange.

In contrast, Figure 14 depicts a diffuser without a flange, as represented by the model in Figure 6b. Due to the absence of the flange and its associated aerodynamic advantages, the velocity profile reaches its maximum at a larger opening angle of 8°.

These findings suggest that the optimal opening angle is not a fixed parameter but is highly dependent on the diffuser configuration. Therefore, determining a universal optimum opening angle for wind turbine applications is impractical without considering the specific diffuser design. While the investigation of empty diffuser configurations provides valuable insights into the aerodynamic behavior and shape optimization, it is more appropriate to evaluate these parameters with wind turbines integrated within the diffuser system to obtain more application-relevant results.

3.2. Effect of Diffuser Flange Type (Corrugated Flange, Flat Flange, and No Flange)

This section analyzes the performance variations among the three configurations described in Case II of Section 2.1, as illustrated in Figure 6 and Figure 7. The comparison is based primarily on the pressure coefficient and velocity contour to evaluate aerodynamic effectiveness. As ref. in [53,54], the pressure coefficient, $Cp$, is defined by Equation (16), as the pressure difference divided by the dynamic pressure.

$$C_P={\displaystyle \frac{P_X-P_{\infty }}{{\frac{1}{2}\rho U_{\infty }}^2}}$$

(16)

$U_{\infty }$ represents the free-stream velocity, and $P_X$ and $P_{\infty }$ denote the static pressure at an arbitrary point and the free-stream pressure, respectively.

As presented in Figure 15, the pressure coefficients for the flat, corrugated, and no-flange configurations are plotted.

As indicated in Figure 15, the pressure remains constant for the corrugated flange from the enclosure inlet to around the entrance of the diffuser. After that point, it decreases and becomes lower than in both the flat-flange and the no-flange model. All three models—flat flange, corrugated flange, and no flange—have the same overall dimensions, but they differ in shape, with the no-flange model lacking a flange section entirely.

The pressure coefficient (Cp) for the corrugated flange is lower than for both of the others. This is due to the pressure drop created at the exit by the corrugated shape, which also causes a noticeable velocity increase in the inlet section. However, the pressure returns to the freestream level slightly earlier than in the flat flange configuration, as revealed in Figure 15.

Hence, the corrugated flange produces the lowest pressure coefficient between 0 and 0.5 m along the length, with the minimum occurring at 0.2420 m from the entrance of the diffuser.

The diffuser without a flange exhibited a higher pressure coefficient compared to the other two configurations. Among the flanged designs, the corrugated-flange diffuser demonstrated superior flow characteristics, yielding a more favorable velocity contour than the flat-flange counterpart, as shown in Figure 17.

3.3. Performance Investigation of Corrugated-Flange Diffuser Integrated with Wind Turbine

This part of the study evaluates the performance characteristics associated with Case III, corresponding to the configuration shown in Figure 3b. As shown at the exit section of the diffuser near the corrugated flange, flow separation occurs, leading to the formation of a recirculation zone, as illustrated in Figure 18 and Figure 19. In this region, the velocity drops below zero, which is clearly visible in the velocity contour in Figure 18. Figure 19 displays the turbulent kinetic energy contours and streamlines of flow at the diffuser exit with the corrugated flange. The visualization confirms that flow separation takes place at the flange’s exit edge. This localized turbulence contributes to a further pressure drop, which accelerates the airflow toward the diffuser’s intersection. As a result, the internal flow velocity increases, potentially enhancing the wind turbine performance. Consequently, a higher inlet velocity is observed in the diffuser with the corrugated flange than the flat flange, as shown in Figure 18 when compared to Figure 16.

Moreover, as indicated in Figure 19, the flow enters from the left toward the diffuser configuration. In the inlet section, when wind enters the diffuser, the maximum turbulent kinetic energy—ranging from 2.49 m²/s² to 2.90 m²/s²—occurs near the wall. This distribution reflects the velocity increase around the inlet, given the proportional relationship between turbulent kinetic energy and velocity, as also observed in Figure 18 for the same configuration. The observed increase is primarily due to greater pressure reduction at the exit section, which is a beneficial effect of the corrugated design.

As clearly illustrated in Figure 18 at location A*, the effects of the corrugated flange at the diffuser exit section under non-dimensional velocity conditions are presented. Furthermore, Figure 20 highlights the differences in pressure coefficient between the corrugated and flat flanges along the y-axis at the exit section.

According to Figure 18, in the exit section of the diffuser—from the bottom to the top or vice versa, marked as A*—the pressure coefficient for the corrugated flange is significantly lower than that of the flat flange, as indicated in Figure 20. This suggests that the velocity in the corrugated flange section is higher, particularly within the diffuser’s internal flow.

Consequently, incorporating a corrugated flange leads to improved diffuser performance, making it more suitable for wind turbine applications compared to the flat flange commonly used in earlier studies [32,47,49,50,51]. El-Zahaby et al. [50] examined the influence of flange angle on diffuser efficiency for the wind turbine systems and identified 15 degrees as the optimal flat flange angle. When this optimal angle was applied to the corrugated flange, it demonstrated superior performance over the flat configuration, as illustrated in Figure 17, Figure 18, Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24, Figure 25 and Figure 26.

After determining the optimal flange shape, a full-scale simulation was conducted on the complete geometry—specifically, the corrugated flange diffuser integrated with a horizontal-axis wind turbine. The integrated system was analyzed under two conditions: one with a stationary frame and the other with a moving frame motion. As illustrated in Figure 21, the velocity contour corresponds to the stationary wind turbine case. In comparison, Figure 22 and Figure 23 present the results for the rotating frame simulation at an angular velocity of 38.57 rad/s, corresponding to a tip speed ratio of 3, as calculated from Equation (4). In the rotating frame case, the flow is inherently asymmetric, leading to slight variations in the velocity contour above and below the central axis—an expected outcome. Conversely, in the stationary case shown in Figure 21, the velocity distribution remains symmetric since there is no frame motion. Figure 22 and Figure 23 also reveal increased turbulence in the upper region of the corrugated flange. This occurs because the extracted results lie along the Z–X plane, where the turbine blade overlaps with the upper section, leading to increased disturbance and turbulence in that region during rotation.

3.4. Comparison of the Effect of with and Without Inlet Guide of Diffuser on Performance of Diffuser Integrated with Wind Turbine

This section examines the effect of an inlet guide on the performance of a diffuser to determine whether it contributes to increased airflow velocity for wind turbine applications, as indicated in Case IV of Figure 8. A comparison was made between a diffuser equipped with an inlet guide of 0.1D length and one without the guide. As illustrated in Figure 17 and Figure 24, the velocity distribution in both configurations remains nearly the same, suggesting that the inlet guide has a negligible impact under the given conditions.

The case with the inlet guide, as shown in Figure 24, exhibits a similar velocity distribution to the configuration without the guide. Furthermore, as observed in Figure 17, the velocity contour for the case without the inlet guide ranges from 5.74 m/s to 6.88 m/s, extending from the inlet through to the end of the corrugated flange. In contrast, the configuration with the inlet guide does not maintain this velocity range across the full length of the diffuser. Therefore, the addition of the inlet guide does not significantly enhance diffuser performance for wind turbine applications. Its primary function appears to be directing airflow toward the diffuser; however, this may also result in increased pressure near the tip of the inlet guide, as indicated by the contours along the top and bottom walls.

3.5. Comparison of Corrugated-Flange Diffuser-Integrated Wind Turbine with the Bare Wind Turbine (Normal Wind Turbine)

In this subtopic, the corrugated-flange diffuser-integrated wind turbine (IWT) was simulated, and its performance was compared to that of a bare wind turbine using the same enclosure, turbine diameter, angular velocity (or tip speed ratio), and inlet velocity. Figure 25 indicates that the corrugated-flange diffuser-IWT produces a much lower pressure coefficient compared to the wind turbine without a diffuser. In these low-pressure regions, the velocity inside the diffuser equipped with a turbine increases significantly, enhancing the turbine’s performance. This simulation was conducted at an optimal distance of 0.242 m from the diffuser inlet, where the velocity reaches its maximum for the corrugated-flange diffuser-IWT configuration. An angular velocity of 38.57 rad/s (368.51 rpm) was applied in the simulation, calculated using Equation (4) of this paper and based on the methodology described in [22]. This condition was applied to both the standalone wind turbine and the configuration integrated with a diffuser. The resulting torque values obtained were 0.127 N·m for the bare turbine and 0.942445 N·m for the corrugated-flange diffuser-IWT on the wall of the wind turbine. The power extracted in each case was calculated as follows:

$$P_{out}=Torque \left[\mathrm{N}.\mathrm{m}\right] \times Rotational velocity \left[\mathrm{rad}/\mathrm{s}\right]$$

$P_{out}=0.942445 \left[\mathrm{N}.\mathrm{m}\right] \times 38.57 \left[\mathrm{rad}/\mathrm{s}\right]=36.34$ W for the corrugated-flange diffuser-integrated wind turbine. For the bare wind turbine, the output power of 4.89 W was obtained from an available power of 21.47 W.

Available power of the wind turbine:

$P_{av }={\displaystyle \frac{1}{2}}\rho \left[\pi \left(r^2\right){\left(U\right)}^3\right]=0.5\times 1.225\times \pi \left({0.35}^2\right){\left(4.5\right)}^3=21.4688 \mathrm{W}$. For $U=4.5{\displaystyle \frac{m}{s}}$ and a diameter of 700 mm of the wind turbine.

Available power for the case of a corrugated-flange-integrated wind turbine:

$$P_{av }={\displaystyle \frac{1}{2}}\rho \left[\pi {\left({\displaystyle \frac{D_O}{2}}+H\right)}^2{\left(U\right)}^3\right]={\displaystyle \frac{1}{2}}\times 1.225\times \left[\pi {\left({\displaystyle \frac{0.42294}{2}}+0.2087\right)}^2{\left(4.5\right)}^3\right]=69.35\mathrm{W}.$$

The diffuser has an outer diameter, including the flange height, of 422.94 mm and an inlet diameter of 720 mm, with a 4° opening angle and a length of 900 mm. The flange, oriented vertically as indicated in Figure 4c, has a height of 208.7 mm, corresponding to a length of 0.3D and a flange angle of 15°. Integrating this corrugated-flange diffuser with the wind turbine resulted in a power coefficient of 0.524. This represents a significant improvement compared to a free-standing turbine of equivalent diameter, which is primarily attributed to the accelerated flow within the diffuser and the recovery of blade tip speed losses.

Figure 25 illustrates and compares the pressure coefficients for both the bare wind turbine (BWT) and the corrugated-flange diffuser-integrated wind turbine (CFDIWT). Based on Bernoulli’s principle, where pressure and velocity are inversely related, the CFDIWT exhibits a lower (negative) pressure coefficient. This indicates that the pressure at this point is below the reference level, corresponding to a peak in wind velocity as indicated in Figure 26. This pressure drop in the diffuser region is attributed to the acceleration of airflow within the diffuser’s central area. At the inlet, both turbine types experience similar pressure levels. However, as the flow progresses through the system, the pressure in the diffuser decreases and then rises again at the outlet, matching the inlet pressure.

As shown in Figure 27, the velocity and pressure contours for the bare wind turbine reveal that, at an inflow velocity of 4.5 m/s, the airflow is primarily concentrated near the blade tip. In contrast, Figure 22 demonstrates that the use of a corrugated-flange diffuser shifts the velocity concentration toward the central region of the blade, enhancing the interaction between the wind and blade surface and thereby improving rotational efficiency and power generation.

In

Table 3. Comparison of previous studies with the current work.

Comparison	${\mathit{U}}_{\mathit{i}\mathit{n}}$	${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}$	Type of Diffuser	Increment in Wind Speed	Power Factor
Hamid et al. [30]	5	7.5	Split diffuser profile	0.5	3.38
Bekele and Bogale, [11]	5	7.69	Diffuser with flat flange	0.53.8	3.64
Parsa and Maftouni, [55]	8	12		0.5	3.38
Lokesharun et al. [56]	5	7.62		0.524	3.54
Current work	4.5	8.04	Diffuser with corrugated flange	0.78	5.69

, $U_{in}$ denotes the inlet free-stream wind speed, while $U_{max}$ indicates the maximum velocity attained in meters per second. In this comparison, diffuser simulations were conducted independently of the wind turbine, revealing that the proposed corrugated flange configuration effectively enhanced the flow region within the diffuser, thereby improving its suitability for wind turbine applications.

As presented in

Table 4. Performance comparison of the present study with previous studies in the case of diffuser-integrated wind turbine applications.

Authors	${\mathit{C}}_{\mathit{P}}$		${\mathit{U}}_{\mathit{i}\mathit{n}}$ (m/s)	Type of Diffuser
	Based on Rotor Area	Based on Outer Diameter of Diffuser
Kanya and Visser [57]	1	-	5.5	Airfoil diffuser profile with curved flange
Jafari and Kosasih [22]	-	0.31	10	Normal diffuser without flange
This research	1.69	0.524	4.5	Diffuser with corrugated flange

, the power coefficient ($C_P$) from the present study is compared with values reported in previous works. In the referenced studies, ($C_P$) was evaluated in two ways: (i) based on the rotor area of a bare wind turbine [57] and (ii) by comparing the extracted power from a diffuser-integrated turbine with that of a free turbine having a rotor diameter equal to the diffuser’s outer diameter, as in [22]. In both evaluations, the current corrugated-flange design demonstrated superior performance compared to both the curved flange and the no-flange configurations.

3.6. Effect of Turbulent Structures for Corrugated-Flange Diffuser Integrated with Wind Turbine

This subsection presents the velocity vectors showing flow from the left toward the diffuser, with magnitudes indicated in Figure 28a,b. Figure 28a illustrates the overall flow field, while Figure 28b focuses on the local flow around the corrugated flange, as highlighted in Figure 28a for the CFDIWT case. The velocity contours in Figure 22 reveal increased turbulence above the flow center, which is confirmed by the vectors in Figure 28a,b. Notably, the flow follows the corrugated geometry of the flange, creating recirculation zones that locally reduce velocity at the exit section while accelerating the main flow toward the diffuser inlet by mitigating pressure losses, thereby highlighting the impact of the corrugated design on overall flow behavior.

3.7. Discussion

The results of the parametric analysis on diffuser opening angles indicate that the optimal angle is not a universal constant but varies significantly with the specific diffuser configuration. As such, defining a single optimum opening angle for wind turbine applications is impractical without accounting for the design characteristics of the diffuser. Although studies on empty diffuser setups offer useful insights into aerodynamic performance and shape optimization, evaluating these parameters in conjunction with integrated wind turbines yields results that are more relevant to practical applications.

Moreover, the corrugated-flange design was inspired by the geometry of corrugated steel roofing, which efficiently channels water during rainfall. The airflow behavior over the surface of these corrugated sections was studied and used as the basis for the analysis in the current work. This configuration proves especially effective in applications where pressure drop is a concern, offering significantly better performance compared to flat flange designs. Overall, the corrugated-flange diffuser without a wind turbine exhibited a 44% increase in velocity, reaching 8.036 m/s, as illustrated in Figure 17. In comparison, the configuration with a wind turbine achieved a 67.85% velocity enhancement, yielding an optimal average flow velocity of approximately 14 m/s around the blade region, as depicted in Figure 22.

4. Conclusions

This study investigated the aerodynamic performance of a horizontal-axis wind turbine integrated with a corrugated-flange diffuser, complemented by a parametric analysis of diffuser configurations both with and without the rotor. The results reveal that the corrugated-flange geometry substantially improves turbine efficiency by enhancing mass flow and promoting a favorable pressure reduction at the diffuser exit, thereby promoting greater airflow into the diffuser.

The corrugated-flange diffuser-integrated turbine achieved a high-power coefficient of 0.524, corresponding to the optimal diffuser diameter and marking a significant improvement over the bare turbine configuration. These findings highlight the potential of corrugated-flange diffusers as an effective passive augmentation strategy for small- to medium-scale wind energy systems, particularly in low-wind-speed environments.

In the present study, a steady-state approach was employed to reduce computational cost and time by assuming time-independent flow conditions. However, this simplification restricts the ability to fully capture transient flow phenomena and complex interactions within the corrugated-flange diffuser–wind turbine system. Future research should include unsteady flow simulations to capture transient interactions between the corrugated-flange diffuser geometry and the turbine, providing deeper insights into aerodynamic performance under realistic conditions across different tip speed ratios. While this study utilized the k–ω SST model, future work should compare LES and hybrid turbulence models with the k–ω SST model to investigate flow phenomena within the diffuser–turbine system.

Furthermore, to facilitate practical implementation, subsequent research should include comprehensive experimental measurements and full-scale field validations. Future work will also explore methods for detecting blade damage in diffuser-integrated wind turbine systems. This research will combine insights from CFD simulations with machine learning- and statistics-based fault detection algorithms, applied to Supervisory Control and Data Acquisition (SCADA) data, such as [58,59,60]. The outcome will be the development of novel hybrid approaches capable of delivering a more reliable and accurate detection of blade damage.