Optimum design of morphing flaps for improving horizontal axis wind turbine performance

This study presents a conceptual design of optimum deformable blades as a function of wind speed. In this design, at any speed of wind flow, the blade sections have their optimal shape. Accordingly, the wind turbine performance will increase at different speeds. The WindPACT 1.5‐MW wind turbine is used as the base turbine, which has three different sections at the root, middle, and tip of the blade. The proposed deformation method, due to its simplicity, is suitable for the use of actuators. Different deflection angles are obtained at various wind speeds for each section through a controllable flap deformation method. The blade element momentum theory is used to calculate the performance of the morphing flaps. The results of this design are then validated by computational fluid dynamics (CFD) simulations using three‐dimensional Reynolds averaged Navier–Stokes equations together with the k–w turbulence model. The CFD results show that using optimum flap angles between 2° and 8° in the root, middle, and tip parts of the blade leads to a promising power increase of about 1.2%, 3.7%, and 13.5% at wind speeds of 4, 8, and 11.5 m/s.


| INTRODUCTION
Today, improving the design and performance of wind turbine systems has become particularly important with the increasing requirement for energy production. In this regard, one aspect studied by researchers is the optimal design of wind turbine blades in which the design of blade sections plays an important role. In the case of the optimal blade section design, different objective functions are usually considered as a single objective or multiobjective based on wind turbine size and weather conditions. These target functions can include wind turbine blade performance in terms of aerodynamics, structure and stability, acoustics, or economics. 1,2 Therefore, wind turbine manufacturers try to offer different ideas to increase aerodynamic power, reduce unstable structural loads, increase the life of wind turbine components and reduce the need for maintenance.
In the development of wind energy technology, the desire to access more power generation and increase the blade diameter has added new constraints to the large wind turbine design. Deformable blades can be a suitable solution as they can adapt the blade geometry under the flow characteristics and rapid response due to slight deformation of the blade surface. This design should include simplicity, aerodynamic efficiency, a control system, and less weight. Owing to their continuous aerodynamic profiles and lightweight, they are a suitable tool to increase wind turbine efficiency, control forces, and prevent aerodynamic stalls. Also, they require less energy and equipment than conventional hinged flaps. 3 Extensive research has been conducted on using smart blade technology in wind turbines. 4 Besides the aerodynamic point of view, morphing technology should be justified in terms of structure, weight, and energy required for movement. Deformable structures have also been used to increase the lift-to-drag ratio and aerodynamic efficiency of wind turbine airfoils. [5][6][7] The morphing blades have indicated noticeable performance in reducing structural loads. The effect of the flap on reducing unstable loads has been presented in Cavens et al., 8 Karakalas et al., 9 and Zhang et al. 10 For a 10-MW horizontal axis wind turbine, Karkalas et al. used morphing flaps added at the trailing edge (TE) to reduce fatigue and torque at the blade root by 27.6% and 7.4%, respectively, while its required energy was estimated at 0.22% of annual energy production (AEP). 9 Wang et al. considered two controllable twists at the root and tip of the National Renewable Energy Laboratory (NREL) phase VI wind turbine blade and significantly improved the annual production capacity at two constant speeds by 24.5% and 69.7%. 11 Nejadkhaki et al. designed an adaptive wind turbine with variable twist angle distribution at different wind speeds. [12][13][14] In this study, discrete deformation along the blade of a 20-kW wind turbine is suggested, as each section has its rigidity and the proposed control strategy is that, at medium and high wind speeds, the control mechanisms put the blades in the preselected optimal position. Alejandro Franco et al. increased the power coefficient of a kW wind turbine by 10% employing a set of variable camber National Advisory Committee for Aeronautics airfoils at the speed range of 4-11 m/s. 15,16 However, their design needs complicated structures for camber varying. Macphee and Beyene carried out an experimental study that led to increase the power coefficient by 32% using a small morphing blade with more curvature at the TE of a kW wind turbine. 17 Barlas et al. used a hinged flap at the TE of a 10-MW wind turbine, and their objective function was to reduce weight and increase AEP. In their study, using active hinged flaps, there was double the fatigue reduction potential compared with the original blade, while the increment in AEP was approximately 1%. 18 It has also been shown that in vertical axis wind turbines, the use of morphing blades increases the pressure coefficient and delays the separation of the flow. 19,20 McWilliam et al. used a morphing flap on a constant length in their aeroelastic optimization of the 10-MW wind turbine blade and investigated its effect on each speed compared with the baseline blade. The flap they added to the reference blade increased the AEP by 0.51%, while the contribution of aeroelastic optimization was above 10%. In their optimization, blade length, thickness, chord, and twist angle were among the design variables. 21 Aerodynamic control using deformable blades, especially from the TE, is done through various systems, such as shape memory alloys, microtabes, and fishbone structures. 22 The idea of deformability is applied for better performance of a device in different working conditions, while most designs are optimized for only one given condition. Therefore, to develop the design of smart blades, since wind turbines produce various power from cut-in speed to rated speed, the central focus of this study is to increase power in this range of wind speed, especially at rated speed. The researches show that using active deformable blades can significantly increase power, or reduce structural loads, and cause better wind turbine stability. The primary purpose of this study is to provide a conceptual design using a deformable blade idea to increase the aerodynamic power of wind turbine blades. According to the researches so far, no study has been carried out for designing the optimum shape of the flaps at different blade sections of a MW wind turbine in various wind speeds for increasing the power efficiency. In the current study, a controllable morphing flap strategy is used to enhance the power efficiency of the turbine blade and the optimum arrangements of these flaps at different blade sections and different wind speeds are presented. Thus, wind turbine blades remain at their best performance geometry even when the wind speed is changing. For this purpose, the blade element momentum (BEM) theory is used to investigate the performance of this idea and finally, the accuracy of the results is confirmed using computational fluid dynamics (CFD) simulations.

| Morphing airfoil deformation
In this work, the deformation is applied only at the 20% rear part of the blade section. The method of the airfoil deformation as a morphing flap is shown in Figure 1.
This deformation can be used in actuators and optimization due to its variables. A polynomial function defines the surface geometry of the deformed airfoil. In this method, the blade section deformation occurs through its midline movement so that the x-coordinates of the airfoil surface points and the corresponding thickness of each point do not change. 23 Thus, in each x-coordinate, the new y-coordinates of surface points, y new , resulting from the deformation by η, are obtained from the following relation: η is the deflection of the midline at each x-coordinate in the y-direction. The transformation function must be continuous at the beginning of the transformation (i.e., ξ = 0) and at the end (i.e., ξ = 1). The following quadratic function satisfies this requirement: By writing the above equation for the TE of the airfoil, its parameters are defined in turn. ξ is the nondimensional distance in the x-direction, which is defined as x TE and x 0 indicate the chord length and the starting positions of the TE deformation, respectively. In Equation (2), if θ is considered as the deformation angle, α is a constant, which is defined as In this study, the TE deformation is considered in the last 20% of the chord that is similarly used in the root, middle, and tip sections of the blade.

| Reference wind turbine characteristics
For this study, the WindPACT 1.5-MW wind turbine is selected as the reference wind turbine, and its geometric characteristics and operating conditions are given in Tables 1 and 2. The reference wind turbine is schematically shown in Figure 2. According to the technical report of this turbine designer (NREL), the airfoils forming the root section up to the tip of the blade are S818, S825, and S826, respectively, which are asymmetric and truncated.  The performance of this wind turbine and its other geometric specifications designed by NREL is shown in Figure 3. To remain at the optimum tip speed ratio (TSR = 7), this turbine is pitch control type. It has different rotational speeds and blade pitch angles at different wind speeds, which are shown in Figure 3. The Eppler design and analysis code was used for aerodynamic coefficients calculation by NREL as indicated in Rinker and Dykes. 24

| BEM theory
The BEM theory is used in the present study for fast calculation of power generated by wind turbine when different blade sections are utilized. This theory has shown its efficiency, computational time saving, and reasonable results in numerous studies. 25 The blade is divided into elements in this theory, and each is analyzed separately. Tables of lift and drag coefficients of the sections are required by this theory that can be provided experimentally or numerically at different angles of attack, to calculate the aerodynamic forces. It is clear that the accuracy of this theory is increased by using experimental or high accurate numerical data. 26 Important details of this theory are explained in Ingram. 27 In brief, BEM theory comprises two parts: the momentum theory and the blade element. The idea of stream tubes, which defined the wind flow around the rotor, is the basis of the momentum theory. It is assumed that there is no radial dependency and the forces from the blade on the flow are constant in each annular element, which corresponds to a rotor with a limited number of blades when the stream tubes are discretized into N annular elements. It was discovered that the axial and tangential induction factors (a a , ′) must be correctly evaluated for the model to behave well. This can be done if the lift and drag coefficients are estimated accurately. In this theory, F I G U R E 2 Schematic of the reference wind turbine (WindPACT 1.5 MW).
F I G U R E 3 Steady-state behavior for the WindPACT 1.5-MW model. 24 TSR, tip speed ratio.
there are four key equations: two express the axial force and torque obtained by considering the blade forces and the other two includes, the momentum theory of axial thrust and torque regarding the flow parameters. By combining and equalizing these equations, the following relations are obtained: In these equations σ′ is called solidity, and λ r is the radial TSR. The presence of vortices at the tip of the blade causes a waste of energy. In these equations, which are used to wind turbine design, this phenomenon is considered by applying the tip loss correction factor (Q). As a result of an iterative loop, the induction factors are obtained, and then the blade forces are calculated (the torque and the axial force). The total power generated of the rotor can be obtained as where r h is the radius of the rotor hub. Ω is the angular velocity, and dT is the torque differential at each element. As mentioned, the classic BEM theory needs modifications to have reasonable results. For example, this theory does not consider the effect of vortex shedding on the velocity field at the hub and blade tip. This phenomenon, especially at the tip of the blade, severely affects the aerodynamic performance; therefore, the Prantel correction coefficients should be considered. This correction is also used in open-source codes, such as Aerodyn. Also, the momentum theory does not consider the high induction factors, so the Glauert correction factor should be used in this case. In this study, Xfoil was used to calculate the aerodynamic coefficients of airfoils without flaps and with flaps. It should be noted that the validation of the BEM theory results is presented in Section 3, together with the CFD simulation results.

| CFD ANALYSIS
The computational fluid dynamic simulations in this study are based on solving the incompressible and steady-state computation of the Reynolds averaged Navier-Stokes equations using the K-Omega SST turbulence model. 28 The coupled method is used to combine velocity-pressure, and the second-order accurate method is applied to discretize the equations. The geometry modeling, grid generation, and numerical method validation is presented in this section.

| Geometry modeling and grid generation
In this study, the computational domain boundaries are located at a 120°sector of an incomplete cone, the blade is placed 90 m from the upstream flow inlet, and the downstream flow outlet is set at 340 m distance from the blade, as shown in Figure 4. The small radius of the cone is 120 m, and its large radius is 240 m. To reduce the calculation cost, the two side faces of the incomplete cone are set as the periodic boundary condition. The tetrahedral mesh type and a hexahedral prism layer are used to form the computational domain. The mesh size on the blade surface is about 0.05 m. The number of prism layers is 20, and its first layer thickness is 4.8E −06 m, which is consistent with the requirement of near-wall models to capture boundary layer changes with the Y+ values on the blade surface to be around 1. The growth rate of the prism layer is 1.35. Also, a wake refinement distance is considered using a sphere with a radius of 40 m around the blade. An overview of the computational domain and the different parts of the computational grid is shown in Figure 4.
In the computational modeling of the wind turbine, to get accurate results and speed up the computation, a high-quality mesh is required. Different grid sizes are used for the mesh independence study. Figure 5 represents the result of the three-dimensional (3D) mesh study through the power coefficient (Cp) parameter at 6 m/s. The maximum Cp deviation between the medium and fine grids is 0.5%, thus the medium grid with 5.8E +6 cells is used for calculations.
As shown in Figure 6, the structured mesh type is used for two-dimensional (2D) simulations, and the appropriate size of mesh around one section of the blade is obtained based on the grid study of the 3D mesh. The size of the domain is large enough to observe the flow changes; its inlet and outlet are at 12.5 * chord and 20 * chord away from the airfoil, respectively. The first layer thickness of mesh is set to 8.41E −6 , and the number of nodes on the airfoil surface is 350. Similar to the 3D simulation, the incompressible steady-state Reynolds averaged Navier-Stokes equations are solved together with the K-Omega SST turbulence model. The coupled method is used to combine velocity-pressure, and the accuracy of discretization is of the second order.

| Validation of numerical solution method
In this study, the validation of numerical methods is performed in two steps. In the first step, the aerodynamic coefficients of the 2D blade-forming airfoil S825 are compared with the experimentally measured coefficients in Somers 29 in Re = 3 × 10 6 . In the second step, the 3D simulated results of compact turbine are compared with the results of Wang et al. 28 The generated power is obtained by multiplying the torque obtained from CFD to the rotational speed corresponding to each wind speed. As shown in Figure 7, the lift and drag coefficients of the blade middle airfoil (S825) obtained by CFD are in acceptable agreement with the corresponding experimental data in Re = 1.0E +6 . Figure 8 shows the generated power at different wind speeds obtained from 3D CFD results in comparison with those of Wang et al. 28 Also, in this figure, the comparison of the current BEM results with these results can be seen. Figure 9 shows the final angle of attack of all three blade-forming airfoils and blade elements from the BEM theory. As can be seen from this figure, the final attack angle of the main elements along the blade is in the range of −3°to 7°, in which the CFD results have good agreement with experimental data due to linear behavior of aerodynamic coefficients. According to Figure 3, the TSR of 4 and 8 m/s are equal and greater than the TSR of 11.5 m/s. Therefore, as shown in Figure 9, the final angles of attack along the blade at these two speeds (4 and 8 m/s) obtained from the BEM theory are equal, and greater than the corresponding angles of attack at 11.5 m/s speed. Therefore, at this speed (11.5 m/s) the flap can effectively increases the local angle of attack on the airfoil surface and leads to a better increase in the lift.

F I G U R E 4 Computational grid and boundary conditions.
F I G U R E 5 Three-dimensional mesh independence study.

| RESULTS
As mentioned before, this study aims to identify the optimal arrangement of deformable flaps at different wind speeds to increase the blade output power. For this purpose, in the first step the effect of individual flap angles at each section of the blade on output power is F I G U R E 6 The 136,000 structured cells on S825 for Re = 3 × 10 6 .  calculated using BEM theory. The possible optimum arrangement is then obtained by combining the best flap angles of each blade section at a specific wind speed. Finally, the accurate performance of these arrangements is validated by CFD method.

| Optimum arrangement of morphing blades from BEM theory
The optimum arrangement of morphing flaps is obtained by examining the effect of each flap at the specific blade elements (root, middle, and tip) at different wind speeds using BEM theory. Thus, the optimum flap angle that maximizes the power increment at each wind speed and blade element is achieved. The results are shown in Figure 10.
It should be noted that, in Figure 10, the positive flap angle is to move the TE down. As shown in this figure, the negative flap angles do not indicate any power improvement, while some positive flap angles increase the total blade power at various wind speeds. Also, it can be concluded from this figure that the effect of the flap on the root section of the blade is normally higher than that of the middle and tip parts of the blade. This result is similar to other studies using the gurney flap in the root section of the blade. 30 The optimal arrangement of flaps for root, middle, and tip elements of the blade at wind speeds is summarized in Table 3. It can be assumed that simultaneous employment of optimum flaps at different blade elements will result in the best power improvement. The examination of this assumption is also shown in Table 3 for the baseline blade and the morphing blade. The power increase at wind speeds of 4 and 8 m/s is about 0.2% and 2.03%, while it increases by 10% at the rated speed.
Also, Figure 10 shows that the effect of the flap is more significant at the rated speed of 11.5 m/s. According to Figure 9, the final angle of attack at rated speed is lower than those of the lower speeds. Thus, the flap shows a better effect at this speed due to locally increasing the angle of attack on the airfoil surface which leads to better aerodynamic performance and more lift at this speed.
On the basis of Table 3, to use optimum flaps simultaneously, there are three arrangements of flaps at different wind speeds. In Figure 11, the optimal arrangement of flaps is drawn at the most dominant wind speed for which the wind turbine is designed. In this figure, it is specified how the deformations of the flaps along the blade looks like.

| Three-dimensional CFD results
A set of 3D simulations is carried out for initial blade and the blade with optimum flaps at different wind speeds to evaluate the results using BEM theory. Table 4 shows the power output from the baseline blade and optimum morphing blade via CFD. The agreement between CFD and BEM results is acceptable. The power gain of the morphing blade is estimated by the CFD and BEM methods to be 13.5% and 10%, respectively, at the rated speed, which is significant for wind turbines. Also, in Table 4, the CFD results are reported at two other speeds (i.e., 4 and 8 m/s), for which the BEM results were previously obtained. As expected from the BEM results in Table 3, the power improvement from CFD calculations using the morphing flap is lower than that of in the rated speed. On the basis of Figure 10, at rated wind speed, the 2°flap at the root, 8°flap in the middle, and 6°flap at the tip had the best performance among other flap angles.
As indicated in Figure 2, the reference blade consists of three sections with different airfoils. A cut is made in the middle of each section, and under the rated working condition, the pressure contours of the initial and morphed blade sections have been shown in Figure 12 T A B L E 3 The best flap angles and their power output at different wind speeds using BEM theory.
The best flap angle at root (°) 2 2 2 The best flap angle at middle (°) 0 2 8 The best flap angle at tip (°) 0 at r/R = 0.28, 0.60, and 0.96, respectively. As can be seen, in all blade sections due to the presence of morphing flaps, the pressure has increased in the pressure side of the airfoil, while it has decreased in the suction side. Consequently, the pressure difference on the morphing airfoil is more than that of the primary airfoil which causes more lift force produced. Also, this figure clearly shows that the pressure difference (or loading of the blade) is more severe in the tip and middle sections than that of the root section which usually needs further structural investigations. In Figure 13, the distribution of aerodynamic efficiency factor (L/D) along the baseline blade and optimum morphing blade is compared. As shown, this value is improved along the optimized blade compared with the baseline blade, especially at the middle and tip regions.
At the rated wind speed, the surface pressure contours of the suction sides are compared in Figure 14. According to this figure, while there is no significant pressure difference between baseline and morphing blades in the root part, but from the middle part, the pressure distribution difference increases and continues to the tip of the blade. Figure 15 shows the corresponding pressure distribution on the pressure side. Again, in the root part, there is no significant difference between the baseline and morphing pressure distributions. However, in the middle and tip sections of the blade the pressure has increased. Altogether, this figure indicates higher pressure on the pressure side of the optimized blade surface compared with the baseline blade, especially in the spanwise direction, close to the tip section. These make improved blade power generation as a result.

| CONCLUSIONS
This research focused on optimum design of a morphing blade technology to increase the power output of a megawatt wind turbine. This idea is defined by placing  In the present study, it can be concluded that at low wind speeds, the wind turbine operation is less sensitive to flap deformation. So that the average value of power increment due to flap in each part of the root, middle, and tip is 0.2%, 1.7%, and 0% at low wind speeds, respectively. Then, the improvement in power due to the flaps increases as the wind speed increases up to the rated speed. The flap deformations are such that the blade power is significantly improved as a result of using the positive flaps at the TE of the root, middle, and tip of the blade by 7.6%, 6.6%, and 2.3%, respectively. Finally, by combining the best arrangement of morphing flaps in all three parts of the blade length, an increase in power was observed compared with the flaps used singly. There is about a 10% gain in power generation at rated speed.
Despite the increase in power due to morphing blades, a comprehensive study of other important aspects of optimal design is required for the practical application of this design, including how the system is constructed and fatigue and stress analysis during flap deformation. In addition, providing a set of flap arrangements for each wind speed and optimization algorithm with design constraints is a future interest. The starting point of deformation and the amount of vertical displacement affect the blade performance and should be optimized to cost reduction and power increase.