Aerodynamic Optimization of Trailing-Edge-Serrations for a Wind Turbine Blade Using Taguchi Modified Additive Model

Abstract

For the rotor, achieving relatively high aerodynamic performance in specific wind conditions is a long-term goal. Inspired by the remarkable flight characteristics of owls, an optimal trailing edge serration design is investigated and proposed for a wind turbine rotor blade. Fluid flow interaction with the proposed serrations is explored for different wind conditions. The result is supported by subsequent validation with three-dimensional numerical tools. The present work employs a statistical-numerical method to predict and optimize the shape of the serrations for maximum aerodynamic improvement. The optimal combination is found using the Taguchi method with three factors: Amplitude, wavelength, and serration thickness. The viability of the solution on an application is assessed using the Weibull distribution of wind in three selected regions. Results show that the presence of serration is capable of improving the annual power generation in all the investigated cities by up to 12%. The rated speed is also shifted from 10 m/s to 8 m/s for most configurations. Additionally, all configurations show similar trends for the instantaneous torque, where an increase is observed in pre-rated speed, whereas a decrease is noticed in the post-rated speed region. A look at the flow field pattern for the optimal design in comparison with the clean blade shows that the modified blade is able to generate more lift in the pre-stall region, while for the post-stall region, early separation and increased wake dominate the flow.

1. Introduction

Today, the potential and characteristics of wind energy have already been thoroughly investigated in several nations worldwide. The International Energy Agency’s (IEA)’s 2019 report on Morocco highlights the ambitious energy transition of the country to renewable energy sources. Wind energy is anticipated to be the second most common method of electricity generation after hydro-power.

The many difficulties this sector faces are not obscured by the success of wind turbines as a source of green and renewable energy [1,2]. Grasping and evaluating the operation of wind turbines requires a thorough understanding of wind dynamics. Additionally, the location has a big impact on the frequency and speed of the wind. In order to determine the performance of wind, the statistical features of the wind speeds at the location of installation of the wind farm must be considered. Indeed, the market value of wind power declines during periods of heavy winds, and the exchange price for wind power tends to be near zero on windy days as the amount of wind power in the energy system increase [3,4]. Modern wind turbine blades have increased in size by a factor of 100 versus a drop in energy by a factor of 5 in the past 30 years. This rise comes at a cost for the companies. Due to the size, the blade geometry must be created during the design phase while considering both aerodynamic and acoustic requirements. The future of wind turbines should be focused more on the improvement of these machines for better power output in unfavorable conditions.

A potential solution to improve existing wind turbines is the addition of flow-control devices to the rotor blades. Flow control devices can effectively prevent or delay flow separation and suppress turbulence resulting in improved aerodynamic and aeroacoustics performance, load reduction, fluctuation suppression, and ultimately increased wind turbine power output [5,6,7,8,9,10,11,12,13,14,15].

Through learning from its miraculous nature, researchers and engineers have proposed techniques that have revolutionized modern machinery [10,16]. Birds, in particular, have inspired human flight since the early days of flight machine development and continue to inspire the aerospace industry on different levels. Owls have been extensively researched as potential star raptors, and it was discovered that the owl’s exceptional ability to fly is mostly due to its distinctive feather structure. Particle Image Velocimetry (PIV) experiments [17,18] of owl-like surfaces have demonstrated its ability to delay the transition, reduce the separation bubble and decay the vortical structures along the wing. To understand the unique morphological characteristics and the biological mechanisms of the owl’s flight, Bachmann et al. [19] compared the wing of a barn owl to that of a pigeon with an emphasis on the distinctive features of the owl’s feathers, both on a macroscopic and microscopic level. They reported that owl feathers had some characteristic features, such as serrations at the leading edge of the wing, fringes at the edges of each feather, and a velvet-like dorsal surface. This study also pointed out the notably larger area of owl wings compared to pigeons with the same body mass, allowing the owl to generate enough lift to glide at a relatively low speed. The wings of owls are significantly different from those of all other groups of birds in terms of the intricate pattern and surface roughness. Typically, the feathers of an owl have directional textures, velvet-like surfaces, leading edge combs, and trailing edge fringes.

Extensive literature [19,20,21,22,23,24,25,26,27] detailing the owl wing morphological structure in general and trailing edge shapes in particular is available. Figure 1 shows the placement of serrations and fringes on a sample feather. Serrations are found on some of the primary feathers of an owl, especially towards the tip of the feather. At the same time, thin fringes can be found on the trailing edge of each primary feather. The thickness of the feather decreases towards the end of the fringes. These fringes reveal variations in size and direction within a single feather as well as between many feathers on a single wing. From the base of the feather toward the tip, the length of the fringed region often decreased.

Investigation into the aerodynamic effect of these distinct owl wings features [18,22,28,29,30] has shown that serrations cause the flow near the wing leading edge to turn toward the wingtip forming a stationary leading edge vortex that delays separation and producing non-linear lift on the outer half of the owl’s wing. Additionally, they discovered that transition was moved upward over the wing as a result of the separation bubble’s size being reduced on the velvet surface that mimicked down feathers. Finally, as the flow passes over the wing and sheds in the trailing edge, the fringes result in a smoother lower wing reducing the sharp edges and allowing for the decay of the vortical structures.

Inspired by the owl wing, serrated trailing edges are rising in popularity. Industries have adopted these shapes as they are rather simple to manufacture, and their installation and maintenance costs are plausible. The fundamental reason this control device has gained so much traction is the ability to retrofit already-running wind turbines to comply with noise laws. Saw-tooth serrations and sinusoidal serrations are the two main types of bio-inspired simulation of the owl wing serrations [16]. In general, there are two ways to apply trailing edge serrations: either cutting forms directly from the sharp trailing edge or adding thin serrated flat plate inserts to the current trailing edge. The ability to trail edge serration to reduce the airfoil tonal noise is confirmed through a large existing literature [31,32,33,34,35,36,37,38,39].

Gharali et al. [40] looked into the impact of a dynamic serrated airfoil. Unlike researchers who tested static serrated airfoils, the dynamic serrated airfoil is exposed to angles of attack that oscillate sharply, which is typical behavior for a wind turbine when working in the field. The primary conclusions of their research are that lift values for the serrated case increased closer to the dynamic stall angle, from 18.5 to 19.5 degrees, while lift values for the unserrated case generally remained consistent with the original airfoil at low angles of attack.

More recently, Zhou et al. [35] tested trailing edge serrations on two airfoil profiles and drew a theoretically derived optimum for the amplitude, the wavelength, and the flap angle. The obtained optimal configuration was tested on a full-scale wind turbine on terrain where it was found that the trailing edge serrations increased the annual power output by less than 0.7%. Overall, a carefully thought-out configuration of the serrations is possible to significantly reduce the loss of the aerodynamic efficiency and power generation of a wind turbine in particular operating conditions.

The focus of this research is to obtain an optimum configuration of serrations for the application of wind turbines. Even less work dives into the effect of these serrations on the aerodynamics and, eventually, the power generated by the wind turbine. This work is a detailed numerical study of the aerodynamic performance of different trailing edge serrations configurations on a sample horizontal axis wind turbine. An optimal configuration is sought to obtain the best results for the particular conditions of the National Renewable Energy Laboratory (NREL) phase VI wind turbine blade. Three-dimensional simulations of the clean blade and the modified blade with the trailing edge serrations are carried out. The results are finally used to derive an optimum configuration. The primary goal of this research is to use a mix of Computational fluid dynamics (CFD) and Taguchi methodologies to comprehend how a horizontal wind turbine’s trailing edge serration parameters interact with one another under various flow conditions.

2. Methodology

2.1. Flow Control Model

In order to concentrate the efforts on a set number of parameters, this research introduces trailing edge saw tooth serration on the NREL phase VI wind turbine. Finally, a constant flap angle of 5° is selected, as shown in Figure 2. In literature [41,42], it appears that the lower the flap angle, the better the performance. A preliminary investigation of the effect of the flap angle has been conducted by the authors, and the results confirm that for higher flap angles, the torque generation drops significantly. This is in agreement with the natural fringes of the owl. Indeed, the fringes on an owl wing’s trailing edge are parallel to the flow direction. Maintaining small flap angles is important in ensuring the good functioning of the serrations. Moreover, Figure 3 shows the serration amplitude and the wavelength. These parameters are a function of the tip chord.

2.2. Taguchi Method Plan of Experiments

Genichi Taguchi created a statistical method to improve the quality of numerous products [43]. The application of parameter design, which focuses on finding the parameter (factor) settings that create the optimum levels of a quality characteristic (performance measure) with the least amount of fluctuation, is the main element of Taguchi’s approaches. A potent technique for creating goods that perform consistently and optimally under many circumstances is the use of Taguchi designs.

The first step in planning the Taguchi method is to define the objective function. Ideally, this function will be used as a benchmark to compare the effectiveness of the parameter combination tested. Secondly, a proper set of orthogonal arrays that depend on the factors and levels tested is built to perform the minimum number of experiments allowing us to derive the optimum. Finally, the Signal noise (S/N) ratio is analyzed to define the optimum design.

As indicated by the quality method of Taguchi [44], when evaluating characteristics that become better as their value increases, the loss function is calculated with Equation (1):

$$L\left(y\right)=k\left(\frac{1}{y^2}\right)$$

(1)

where k is the quality loss coefficient, and y is the measured output. We derive the Signal to Noise function from the loss function with Equation (2):

$$SN=-10\log \left[\left(\frac{1}{y^2}\right)\right]$$

(2)

Evaluating the power output of a wind turbine is critical as the main function of a wind turbine is to generate power. For our application, the characteristic parameter of a wind turbine is the power coefficient in Equation (3), representing the ratio of the power extracted by the wind turbine relative to the energy available in the wind.

$$C_p=\frac{P}{\frac{1}{2}\rho V_{\infty }^{3}A}$$

(3)

where the wind turbine power P = Tω, T is the torque, ω is the wind turbine rotational speed, V∞ is the free-stream velocity, and A is the rotor swept area.

Here Taguchi’s loss Function (4) and signal-to-noise ratio (SN) (5) can be written as follows:

$$L\left(y\right)=k\left(\frac{1}{C_p{}^2}\right)$$

(4)

$$SN=-10\log \left[\frac{1}{C_p{}^2}\right]$$

(5)

The second step in Taguchi’s method is to define the noise factors and testing conditions. In other words, we identify factors that affect performance and which are crucial, difficult to control, or expensive to control. For horizontal-axis wind turbines, different geometric variables in the blade designs can be described as factors, and various parameter values for each factor are referred to as levels. The goal here is to investigate the optimal design for the trailing edge to maintain good power output. The three factors used in this work are the wavelength λ, the amplitude A, and the thickness t of the serration plate. For each factor, the levels are selected based on previous investigations [16,41,45]. Keeping in mind that the efficiency of serration for noise reduction increases with higher amplitudes and lower wavelength [46,47], a design that also appears in owl wings, three levels have been from the range that has already been shown to improve turbine performance. The design parameters and their levels are detailed in

Table 1. Taguchi design parameters and factor levels.

Factors	Level 1	Level 2	Level 3
Wavelength (λ)	2.5% ctip	5% ctip	7.5% ctip
Amplitude (A)	10% ctip	15% ctip	20% ctip
Thickness (t)	0.32% ctip	0.49% ctip	0.65% ctip

.

Finally, the quality characteristics were defined to be observed and optimized, and the matrix of experiments was to be conducted. Taguchi uses orthogonal arrays contracted from the knowledge of the number of factors and levels, where every factor and its corresponding are considered equally. When using the Taguchi approach, the orthogonal array will be essential in determining the importance of components and their chosen levels. It offers a collection of minimum tests that result in optimal design factors.

Based on the degrees of freedom technique, the necessary minimum for a problem with four elements and three levels for each factor is 3⁴ (81) tests to equally cover all the factors and levels. In our case, we will adopt the common Orthogonal array L₉ (3⁴). The analysis can be completed with just nine tests since only three factors, and three levels are considered in the current investigation.

Table 2. L₉ orthogonal array.

Experiments	Wavelength (λ)	Amplitude (A)	Thickness (t)
T1	1	1	1
T2	1	2	2
T3	1	3	3
T4	2	1	2
T5	2	2	3
T6	2	3	1
T7	3	1	3
T8	3	2	1
T9	3	3	2

shows the L₉ orthogonal array used in this work. As can be seen, in Table 2, nine different wind turbine blade designs are necessary to conduct the nine experiments denoted T1 to T9.

2.3. Weibull Wind Distribution

To determine whether a location is suitable for the construction and administration of wind energy facilities, the statistical features of the wind speeds at that location must be considered. The power output is a function of V. Therefore, the loss function is calculated using Equation (6):

$$L=k{(C_p\left(V\right)-C_{pmax}\left(V\right))}^2$$

(6)

To evaluate the optimum serration configurations of the nine performed tests, we will evaluate the potential yearly power generation in different regions.

Since wind speed is a random variable, probability density functions may be computed by looking at how it changes over time. For the accurate evaluation of that site’s potential wind energy, wind data collected from that location should be thoroughly investigated and interpreted. The potential for wind energy in a given area depends on the wind’s speed and its availability for how long. Various probability density functions have been used to characterize the frequency distributions of wind speed, with the Weibull distribution being the most used [48,49,50].

In order to calculate the wind power density, the Weibull distribution Function (7) is used to represent wind performance [51].

$$f\left(V\right)=\left(\frac{K}{C}\right){\left(\frac{V}{C}\right)}^{K-1}{e}^{-{\left(\frac{V}{C}\right)}^k}$$

(7)

where K and C are, respectively, the shape and scale parameters of the Weibull function.

For one test case, the yearly generated torque, and subsequently power, is the sum of the expected torques in different wind speeds with the probability of occurrence of these wind speeds in one area for one year. The resulting torque for each case is finally calculated using Equation (8):

$$T={\displaystyle \sum }_i^{j}f\left(V_i\right)\times T_i$$

(8)

with “i” indicating the cut-in speeds of the wind turbine and “j” the cut-off speed.

Morocco has favorable conditions for wind power plants, with 17 regions chosen as ideal for installing wind farms [52]; several studies have estimated and investigated wind distribution in different potential regions [48,53,54].

Three representative cities of the wind regions of Morocco have been selected to evaluate the viability of the proposed optimal condition relative to the potential region for installation. The southern coastal city of Dakhla is selected to represent region 1 in Morocco’s reference wind map. Representing region 2 is the city of Laayoune, and region 3 will be depicted using Essaouira. Weibull’s distribution for the three cities is available in the literature [48]. The latter conducted measurements for five years in six cities and used the least squares (graphical method), Maximum likelihood, and Wind Atlas Analysis and Application Program (WAsP) methods to find an appropriate estimation of the Weibull parameters.

Table 3. Weibull parameters for the chosen regions [48].

Region	Weibull K	Weibull C	Mean Wind Speed (m/s)
Dakhla	4.35	8.62	7.85
Laayoun	3.45	8.17	7.35
Essaouira	2.64	6.71	5.96

summarizes the findings of Allouhi et al. [48] that will be used as a deciding factor for the selection of the optimal trailing edge serration design.

3. Numerical Setup and Model Validation

3.1. Physical Model

This study uses the NREL phase VI wind turbine with 19.8 KW. The lengthy experimental program produced a comprehensive data set detailing different configurations and their aerodynamic performance, printed in numerous NREL reports [55,56,57,58,59].

The blade of the NREL phase VI wind turbine has a linear chord distribution and a nonlinear twist distribution. It has a 5.029 m blade radius and a 12.192 m tower height. The blades are installed with a tip pitch angle of 3° and a fixed yaw angle of 0°. All the cases are run with constant density ρ = 1.24 Kg/m³.

The detailed geometrical specifications of this twisted and tapered blade can be found in the open literature [60].

Table 4. NREL phase VI wind turbine parameters.

Parameter	Value
Blades number	2
Blade radius	5.029 m
Minimum chord	0.35 m
Blades rotational speed	72 RPM
Direction of rotation	Counter-clockwise

provides a list of the design and operational parameters of the baseline NREL phase VI wind turbine, and

Table 5. Test cases used for the NREL phase VI wind turbine.

Cases	Wind Speed (m/s)	TSR	Pitch Angle (Degree)
S05	5	7.58	3°
S06	6	6.32	3°
S07	7	5.42	3°
S08	8	4.74	3°
S09	9	4.21	3°
S10	10	3.79	3°
S13	13	2.92	3°
S15	15	2.59	3°
S18	20	2.08	3°
S21	21	1.78	3°

details the test cases considered for this work. Here forth, the baseline geometry will be named the clean blade.

In order to analyze the effect of trailing edge serrations on a fully rotating wind turbine, the NREL phase VI wind turbine rotor blade geometry is retained for the body of the modified blade. The modified geometry comprises a serration plate in the trailing edge between 50% of the blade radius to 100% of the blade radius. In this area, the twist angles vary between 3.425° and −1.815°. As detailed in Section 1, the serration wavelength (λ), serration plate thickness (t), and serration amplitude (H) are the three primary geometrical parameters related to a saw-tooth serration. These parameters are varied with respect to the constant tip chord length of ctip = 0.35 m. Figure 4a shows a planar view of a sample configuration of the modified blade with trailing edge serrations. A distance of 0.5 mm exists between the serration and the blade tip. As mentioned in Section 1, an angle of 5° exists between the serration and the chord line at the position of occurrence of the serration. Figure 4b shows the computational domain and boundary conditions.

ANSYS Fluent is used to do the three-dimensional Computational Fluid Dynamics (CFD) study. Ten wind speeds covering the range between 5 m/s and 21 m/s were investigated for the clean blade and all variants of the modified blade.

Although high wind speeds (more than 15 m/s) are often characterized by unsteady phenomena, the unsteady behavior of localized vortices has very little bearing on the overall aerodynamic performance of wind turbine blades [61]. The analysis is consequently conducted using stable Reynolds Averaged Navier-Stokes (RANS) Equations with the k-ω SST turbulence model, where convergence is obtained for all the simulations with an error of 10⁻⁴.

3.2. Mesh Topology and Grid Independence Investigation

A rotating frame technique is employed in the current study to account for the relative motion of the rotor and stationary geometry components. For all the tested geometries in this work, the employed grid is an unstructured tetrahedral mesh. The computational grid is displayed in a magnified cross-sectional image for both the clean Figure 5a and the modified Figure 5b blades. A detailed description of the adopted grids for the clean blade and the T1 case of the modified blade. The T1 was selected among the test cases for the complicated geometry at high wavelength and low thickness.

Table 6. Details of grid topology used are used for the clean and the modified blades.

Case	Total Grid Elements (106)	Total Grid Nodes (106)	Blade Face	Blade Face Size	Serration Band Faces	Interior Fluid Body Faces
Clean	9.98	1.77	441,308	0.005	-	19,651,385
T1	37.39	6.60	824,839	0.005	429,735	74,046,431

presents details of the adopted topologies.

To ensure a grid-independent solution, the number of mesh elements is varied, and six grid topologies are adopted by monitoring the torque value in comparison with the expected experimental value. Ideally, grid independence should be verified for each geometry and flow condition. In order to lower the number of required computations to cover all conditions, sample wind speeds representing the linear power curve and the highly turbulent part are selected.

Table 7. Grid independence of an unstructured mesh.

	Clean Blade: At 7 m/s		Clean Blade: At 13 m/s		Modified Blade: Case T1 at 13 m/s
	Elements (106)	Torque (N.m)	Elements (106)	Torque (N.m)	Elements (106)	Torque (N.m)
Extremely Coarse	0.92	350.9	3.12	583.76	10.10	298.3
Coarse	1.11	368.49	5.12	590.69	11.29	258.3
medium	1.45	399.21	6.92	601.94	15.43	233.13
Fine	2.73	414.80	9.98	642.41	27.60	238.10
Finer	3.27	418.25	10.83	644.08	37.39	237.80
Extremely fine	9.98	414.80	12.34	642.10	39.63	236.30

shows the grid independence for a wind speed of 7 m/s and 13 m/s for the clean blade, and 13 m/s for the modified case T1. An unstructured mesh topology has been used for all the cases.

The variation between the finer meshes can be ignored, while the variation between coarser and medium meshes is more noticeable. Finally, the selected grid is the fine mesh composed of about 9.98 million grid elements. The fine grid is enough to predict the torque according to this mesh independence study. The selected grid is composed of about 9.98 million grid elements. The fine grid is enough to predict the torque according to this mesh independence study.

3.3. Numerical Model Validation

The experimental results of the NREL phase VI wind turbine tests carried out by NASA Ames Research Centre are used for validation of the numerical model intended to be used in this work. The same numerical setup that was previously presented is used for all wind speeds. This wind turbine has been extensively studied by the authors in previous works [8,62], and the two-dimensional and three-dimensional flow field characteristics have been analyzed as a preliminary study for future control applications. As shown in Figure 6a,b, the numerical method used in this work is able to closely predict the experimental torque and thrust values for the investigated range of wind speeds.

4. Results and Discussion

4.1. Torque

The power coefficient was previously selected as the objective function for the Taguchi design of the experiment. The power P is a function of the torque such that:

$$P=\omega T$$

(9)

where ω is the rotational speed of the wind turbine in RPM and T is the torque in N.m.

The main focus of this study is to assess the effect of trailing edge serrations on the power generation of a horizontal axis wind turbine and derive an optimum for the region of operation of the machine. The instantaneous torque is calculated from the simulation for eight different wind speeds at each configuration, resulting in a total of 72 simulation cases.

Figure 7 displays the instantaneous torque generation for all the cases described in the Taguchi L9 design of the experiment in comparison with the available experimental data for the clean blade.

As observed in Figure 7, the presence of the serrations maintains the overall trend of the torque versus wind speed plot. The configurations in all their form on the modified blade result in a shift of the rated wind speed. There is a clear decrease in the rated power in the new rated wind speed. In the post-stall region, the modified blade generates significantly higher torque. When the wind speed is between 5 m/s and the rated wind speed, there is an increase in power production. It implies that when the control method is left unchanged, serrations only increase power output when the wind speed is less than the rated speed.

4.2. Annual Power Generation

As mentioned in Section 1, the results will be evaluated with respect to the expected power generation in a region having regard for the yearly wind distribution in that particular region.

Because it can create more electricity before attaining V = 10 m/s, which is the rated wind speed for this wind turbine, the modified blade’s annual power output is larger than that of the wind turbine with the clean blade. Essaouira’s region sees an improvement of up to 11%, as shown in

Table 8. Comparison of the yearly power generation and SN ratios for all experiments at three different cities.

Cases	Laayoune			Essaouira			Dakhla
	Yearly Power (kW)	Improvement%	SN Ratio	Yearly Power (kW)	Improvement%	SN Ratio	Yearly Power (kW)	Improvement%	SN Ratio
Clean	5.93	-	-	4.72	-	-	6.79	-	-
T1	6.33	6.71	16.03	5.09	7.92	13.07	7.12	4.86	17.05
T2	6.49	9.45	16.25	5.17	9.55	13.17	7.34	8.08	17.31
T3	6.31	6.39	16.00	5.13	8.78	13.01	7.10	4.56	17.02
T4	6.54	10.21	16.31	5.27	11.66	13.23	7.38	8.75	17.37
T5	6.41	8.14	16.14	5.13	8.80	13.07	7.25	6.74	17.20
T6	6.65	12.09	16.45	5.38	14.10	13.35	7.50	10.50	17.50
T7	6.21	4.64	15.86	5.03	6.66	12.94	6.97	2.60	16.86
T8	6.21	4.65	15.86	5.01	6.30	12.84	6.99	2.94	16.89
T9	6.48	9.32	16.24	5.16	9.45	13.14	7.32	7.78	17.29

. It means that the usage of trailing edge serrations does not necessarily result in a decrease in the aerodynamic performance of the blade or the power output of the wind turbine.

Based on the results displayed in Table 8, the mean SN ratio is calculated by averaging the value of SN of a factor at one level. For instance, the mean value of the SN ratio for wavelength at level one is the average of the SN ratios of the configurations where this same factor has a level 1 (T1, T2, and T3). Figure 8 shows the mean SN ratios for the three factors considered in this study at the three levels described in Table 1. In this case, as explained by Taguchi’s quality method [43], the larger the SN ratio, the better. Increased scattering in the mean SN can also indicate the most influencing factors. In our case, for all the considered cities, the wavelength factor has the highest impact on power generation. Indeed, the serration wavelength appears in different studies [45,63] as the main parameter for more noise reduction.

Based on the results of Figure 8, the combination of wavelength level 2, amplitude level 3, and thickness level 2 is the optimum for this blade’s performance through the Taguchi method.

Since this combination is not part of the L9 design of the experiment, this can be found in the L27 full design of the experiment for a three-level three-factor test.

4.3. Additive Model Results

Applying the additive model is utilized to determine the estimated SN ratios for each of the 27 combinations of components and levels in an L27 based on the L9.

The additive model [44] estimation of the SN ratio can be achieved by using the Equation:

$${\eta }_e\left({\lambda }_i,A_j,t_k\right)=\mu +x_i+y_j+z_k+e$$

(10)

where $x_i={\mu }_{{\lambda }_i}-\mu ,y_j={\mu }_{A_j}-\mu ,z_k={\mu }_{t_k}-\mu$, µ is the mean SN ratio for all the tests achieved in the used orthogonal array, ${\mu }_{{\lambda }_1}$, ${\mu }_{A_j}$ and ${\mu }_{t_k}$ are the mean SN ratio for all the tests for a particular factor (i.e., λ = wavelength, A = amplitude, t = thickness). Finally, e is a negligible error.

Using the SN ratio of the minimum orthogonal array L9 described in Table 8, the SN ratio of the corresponding extended L27 Orthogonal array is shown in

Table A1. Estimated SN ratio for the three cities using the additive model.

Experiment	Wavelength	Amplitude	Thickness	Estimated S/N–Laayoune	Estimated S/N–Essaouira	Estimated S/N–Dakhla
T1	1	1	1	16.02	14.18	17.04
T2	1	1	2	16.17	14.24	17.21
T3	1	1	3	15.90	14.07	16.92
T4	1	2	1	16.03	14.14	17.08
T5	1	2	2	16.19	14.20	17.25
T6	1	2	3	15.92	14.03	16.96
T7	1	3	1	16.18	14.34	17.22
T8	1	3	2	16.33	14.40	17.39
T9	1	3	3	16.07	14.23	17.10
T10	2	1	1	16.23	14.39	17.26
T11	2	1	2	16.38	14.46	17.44
T12	2	1	3	16.11	14.29	17.15
T13	2	2	1	16.24	14.35	17.31
T14	2	2	2	16.40	14.42	17.48
T15	2	2	3	16.13	14.25	17.19
T16	2	3	1	16.39	14.55	17.45
T17	2	3	2	16.54	14.62	17.62
T18	2	3	3	16.28	14.45	17.33
T19	3	1	1	15.91	14.07	16.92
T20	3	1	2	16.06	14.14	17.09
T21	3	1	3	15.79	13.97	16.80
T22	3	2	1	15.93	14.03	16.96
T23	3	2	2	16.08	14.10	17.14
T24	3	2	3	15.81	13.93	16.84
T25	3	3	1	16.07	14.23	17.10
T26	3	3	2	16.23	14.30	17.27
T27	3	3	3	15.96	14.13	16.98

. Case T17 in the additive model agrees with the prediction of Figure 8 for all cities. This recommendation led to a simulation that combined the levels of factors in T16. For wavelength level 2, amplitude level 3, and thickness level 2 in modified blade serration designs, the yearly power outcome in Laayoune, Essaouira, and Dakhla, respectively, is 5.30 kW, 3.46 kW, and 6.14 kW. However, the L9 tested cases in Table 8 show that there’s a combination (case T6: wavelength 2, amplitude 3, thickness 1) that yields higher power generation in all three cities. It is clear that even though the additive model provides the best direction to improve power performance, the ideal condition was not accurately forecasted. This approach performs exceptionally well in problems with no-interaction components, as was already mentioned. However, this model is unable to make an accurate forecast for the best design if any interactions between the components were chosen.

4.4. Modified Additive Model Results

In order to account for the contributions from the interactions of any two elements, the additive model is modified by the addition of new terms. The new SN ratio is calculated such that the contribution of the interaction between two factors (i.e., Wavelength and amplitude) is expressed by Equation (11):

$${\eta }^{\prime }\left({\lambda }_i,A_j\right)=\left({\mu }_{{\lambda }_i{A}_j}-\mu \right)-x_i-y_j$$

(11)

where ${\mu }_{{\lambda }_i{A}_j}$ is the mean SN ratio of the cases containing the wavelength and the amplitude factors. Equation (12) is finally used to compute the estimated SN ratio while taking into account the contributions from the interactions of each two of the three considered factors:

$${\eta }_e\left({\lambda }_i,A_j,t_k\right)=\mu +x_i+y_j+z_k+{\eta }^{\prime }\left({\lambda }_i,A_j\right)+{\eta }^{\prime }\left({\lambda }_i,t_k\right)+{\eta }^{\prime }\left(A_j,t_k\right)+e$$

(12)

Table A2. Estimated SN ratios using the modified additive model.

Experiment	Wavelength	Amplitude	Thickness	Estimated S/N–Laayoune	Estimated S/N–Essaouira	Estimated S/N–Dakhla
T1	1	1	1	15.94	13.99	16.95
T2	1	1	2	16.29	14.35	17.35
T3	1	1	3	15.85	14.06	16.85
T4	1	2	1	15.97	14.03	17.01
T5	1	2	2	16.43	14.36	17.52
T6	1	2	3	16.34	14.41	17.41
T7	1	3	1	16.17	14.38	17.20
T8	1	3	2	16.02	14.09	17.07
T9	1	3	3	15.80	14.14	16.81
T10	2	1	1	16.43	14.55	17.49
T11	2	1	2	16.42	14.60	17.49
T12	2	1	3	16.07	14.14	17.12
T13	2	2	1	16.08	14.24	17.12
T14	2	2	2	16.17	14.25	17.23
T15	2	2	3	16.17	14.13	17.26
T16	2	3	1	16.84	15.06	17.90
T17	2	3	2	16.33	14.45	17.37
T18	2	3	3	16.19	14.34	17.24
T19	3	1	1	15.71	13.86	16.71
T20	3	1	2	16.21	14.35	17.25
T21	3	1	3	15.65	13.89	16.61
T22	3	2	1	15.52	13.74	16.54
T23	3	2	2	16.14	14.19	17.19
T24	3	2	3	15.92	14.08	16.94
T25	3	3	1	16.35	14.41	17.42
T26	3	3	2	16.36	14.24	17.42
T27	3	3	3	16.00	14.13	17.02

shows the full L27 array with the estimated SN ratios using the modified additive model. The modified model predicts T16 as the optimum. Looking back at the results of the Taguchi L9 and the verification case T17 from the additive model, it is clear that the modified model estimate is indeed the optimum. The combination T16 in Table A2 is similar to T6 in Table 8, which yields the highest yearly power output in all investigated cities.

4.5. Flow Field Investigation

In an attempt to shed light on the mechanisms behind the improvement due to the optimum solution, the flow characteristics of this configuration are studied. Through Taguchi’s modified additive model, we identified experiment T16 as the optimum solution. This model leads to a mean improvement of 12% in yearly generated power.

In order to understand the reason for the high torque production for wind speeds lower than the rated wind speed (V = 10 m/s), the coefficient of lift distribution over the wind turbine radius is evaluated. In theory, sawtooth-shaped serrations with edges angled less than 45° to the direction of the mean flow should be used to obtain the best performance [35,64]. The serration extends the chord line and allows for more lift generation. As can be observed from Figure 9, the lift generated by the modified blade at the position of the serration is higher than the lift generated by the clean blade. Indeed, in our case, the serrations were placed above the 50% radial position corresponding to 2.5 m. This agrees well with the findings of Zhou et al. [35], who also observed an increase in lift coefficient over the real wind turbine in the region of trailing edge serrations.

Torque comparison has shown a decrease in performance in the post-stall region (V > 10 m/s). Indeed, in this region, the blade is fully stalled, and the flow is separated from root to tip. The case of V = 10 m/s is further examined as a sample for the region of performance decay, and instantaneous limiting streamlines are shown in Figure 9. For the clean blade, the flow is attached throughout the blade. At a wind speed of V = 10 m/s, the pressure stays low on the suction side, and the blade provides consistent lift. A separation line appears for the T6 modified blade, which explains the decay in power generation in the region of V > 10 m/s. Separation results in lower lift and higher drag, which in consequence, leads to lower torque. Despite the increase in lift generation for V < 10 m/s, as shown in Figure 9, the serrations clearly encourage separation in the post-stall region (V > 10 m/s), as shown in Figure 10.

4.6. Effect of the Unsteady Behavior

A stable RANS method was used to produce the numerical results shown above. Even with stall inflows, the steady RANS technique ought to be able to capture the primary physical structures over wind turbine blades. Unavoidably, a steady computation will not include the unstable interactions between the vortical structures (such as stretching, bending, and shedding of the leading-edge vortices, etc.). Even with stall inflows, the steady RANS technique ought to be able to capture the primary physical structures over wind turbine blades. Therefore, to assess the effect of unsteadiness, an Unsteady Reynolds Averaged Navier Stokes (URANS) formula is used for the baseline blade and the obtained optimum T6 in this section for a sample wind speed of V = 10 m/s. A second-order implicit-time stepping method (dual-time stepping method) is used in the URANS simulation with the grid system described in Section 3. The time step is set to 2.3 × 10⁻³.

Figure 11 illustrates a clear comparison of the ear wall vertical structure for the clean blade and the T6 modified blade at λ2 = 0.03. The unsteady results present a clear unsteady behavior of the blade. The difference between the near-wall vortex system over the modified bade is noticeable in comparison with the clean bade. With the presence of the serrations at the trailing edge of the modified blade, the flow leaves the trailing edge originating from the pressure side and moving upwards. The clean blade shows conventional flow behavior at the trailing edge, in which the flow curls in the trailing edge from bottom to top. Additionally, the flow over the serrated blade predicted the presence of the serration at the trailing edge, and vortices are distributed equally over the upper surface. The serration will then act as a vortex generator in this region.

Vortices are generated at the edges of each serration, as shown in Figure 12, and curl around the upper surfaces of the serrations in a counter-rotating manner. This is due to the opening of the serrations where the flow is pushed through the serrations at minimum amplitude and curled towards the suction side, whereas, for the clean blade, the flow exits tangentially at the trailing edge. This is due to the opening of the serrations where the flow is pushed through the serrations at minimum amplitude and curled towards the suction side, whereas, for the clean blade, the flow exits tangentially at the trailing edge. Generally, the level of vorticity generated at the trailing edge (Figure 13) for the serrated blade is higher in magnitude in the area of serrations. Consequently, the roll-up around the blade tip appears to be enlarged.

Figure 14 displays the evolvement of the unsteady vortices over the modified blade for case T6 at a wind speed of V = 10 m/s within a period of T = 8.28 s. the vortices quickly develop on the leading edge of the blade and meet with the vortices generated at the trailing edge to be shed in the wake. Above t = 3.321 s, almost nothing changes as the vortices continue to be shed away from the rotation axis. However, the tip vortices continue to grow due to the shedding of the trailing edge vortices. It can be concluded that vorticity distribution over the upper surface of the blade after a given period (t = 3.321 s) shows no change with time. Qualitatively, the shape of the vortices remains unchanged. This explains the ability to capture the main flow phenomena using steady-state conditions.

5. Conclusions

The present work highlights the impact of trailing-edge serrations on horizontal wind turbine aerodynamics through a CFD investigated on a 3D wind turbine blade. To evaluate the impact of different trailing edge saw tooth serration designs on the performance of the wind turbine, the Taguchi experimental design is employed, and the annual output power is measured using Weibull’s distributions of three selected cities. The optimal design is tested and validated for the selected regions through the Modified additive Taguchi model. The purpose of this study is to shed light on the aerodynamic capability of trailing edge serration for further improvement of the design approaches used in horizontal axis wind turbines. The major findings of the present work can be summarized as follows:

• The Taguchi-modified additive model coupled with CFD is effective in estimating the interactions between the factors and deriving the optimal design for the horizontal axis wind turbines.
• The optimal design predicted by the Taguchi model and the modified additive model is the trailing edge serration of wavelength is equal to 5% tip chord line, the amplitude of 20% chord line, and serration plate thickness of 1 mm.
• The optimum design was found to be consistent for the three different regions.
• The instantaneous torque of the modified wind turbine results in a shift of the rated wind speed from 10 m/s on the clean blade to 8 m/s for a majority of the configurations.
• The instantaneous torque increases pre-rated wind speed and decreases post-rated wing speed for all configurations.
• In the post-stall region, the serrations result in an increased wake and advancement of the separation towards the leading edge.

The results obtained in this study show that with an optimal design, the serration can increase performance in certain important regions. In addition, the evaluation of the performance of these wind turbines should be conducted in a manner that accounts for the terrain, as specific instantaneous parameters of the wind turbine are not enough. Further studies in this area can cover the mechanical aspect and aero-acoustic impact of the trailing edge serrations, as well as the correlation between acoustic emission, power generation, and aerodynamic forces in the improvement of an overall wind turbine performance.