The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade

Transcription

1 Journal of Applied Science and Engineering, Vol. 21, No. 1, pp (2018) DOI: /jase _21(1).0013 The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade Yi-Ren Wang 1 *, Chi Tang 1 and Chien-Chih Chiu 2 1 Department of Aerospace Engineering, Tamkang University, Tamsui, Taiwan 25137, R.O.C. 2 China Airlines, Da-Yuan Dist. Taoyuan City, Taiwan 33758, R.O.C. Abstract This research studied a dynamic wake and blade interacted wind turbine. The finite state dynamic wake theory was applied. The effects of the wake and the configuration of the modern trailing-edge-flap (TEF) on the wind turbine blade were analyzed. The lift and the stress distribution on the blade were performed by using semi-analytic and numerical wake theory (The finite state wake theory) and the combination with APDL (ANSYS Parametric Design Language) and FORTRAN code. The effects of TEFs, considering their span-wise lengths and index angles on wind turbine blades, were fully discussed. The thrusts and root stresses on the wind turbine blade were also presented. The wake effect of a 5MW turbine blade was verified by an existed numerical result. The present research showed that with identical shape and material of blades, installing TEF could increase the lift (thrust), while no significant rise in stress are produced at the root section of the blade. Key Words: Blade Element Theory, Dynamic Wake, Fluid-structure Interaction, Trailing Edge Flap (TEF) 1. Introduction *Corresponding author @mail.tku.edu.tw Attention to the reduction of greenhouse gas (GHG) emissions is paid due to the emergence of greenhouse effect and extreme weathers, developments in renewable energy have thus sprung up. Wind power generation has become one of the keys in energy development. In consideration of the cost-effectiveness in large-scale power generations, the majority of wind turbines is the threebladed horizontal axis wind turbines. For the horizontal axis wind turbine, there have been designs to install Trailing-Edge-Flap (TEF) on it in recent years [1 3]. TEFs adjust the angle of pitch of the blades, in order to achieve optimum efficiency while the turbine blades are in different speeds and directions of winds. Compare to those without TEF installations, blades with TEFs could simplify the complexity of the overall mechanism and reduce the cost of follow-up maintenance. In addition, while analyzing a blade, its aerodynamic phenomena affecting other blades caused by vibrations should be considered at the same time. Thus, the unsteady flow field is one of the factors that must be considered. Furthermore, wake effect, an important factor in aerodynamics should also be considered. Wake effect causes induced flow, this induced flow will affect the accuracy of the actual results [4,5]. As a result, a complete simulation of wind turbine blades should include the coupling of structural dynamic analysis and the unsteady aerodynamics system aforementioned. For the structural dynamic analysis, numerous typical studies regarding nonlinear or composite rotating blades have been discussed thoroughly. For example, the study of nonlinear effects on rotor blades developed by Hodges [6] is often used by researchers studying rotor dynamics. In the literature of Peters [7], it combined the dynamic wake theory with Hodges [6] nonlinear equations of mo-

2 106 Yi-Ren Wang et al. tion of the composite structure and results in the reduction of errors in lag damping. Crespo da Silva [8] referred that the nonlinear resonance in lag-motion is a field worth investigating. The nonlinear equations of motion for rotor blade proposed by Crespo Da Silva and Hodges is also widely adopted. Pai et al. [9,10] used the virtual local rotation method to derive the highly nonlinear equations for the composite rotor blade and had been proved to be accurate for the simulation of high stress or displacement. Compared to using the transmission mechanism to change the pitch angle of the rotor blade, by utilizing piezoelectric materials implant to drive the trailing edge control surface, we can eliminate the weight of the transmission mechanism and at the same time achieve the same control effectiveness. It is a revolutionary technology in the Higher Harmonic Control (HHC) [11 13], and it is also one of the fields researchers are actively involved in. Fulton and Ormiston [11] analyzed the effect of lift on rotating blade caused by different kinds of the Trailing-Edge Elevon (TEE) with the experimental method. While Nikki and Chopra [12] investigated a series of experimental analysis on the manipulations of the Trailing Edge Flap (TEF). Kurdila et al. [13] continued Fulton s [11] concept, utilizing the idea of the control compensator to construct a set of nonlinear model of off-line test and analyze the responses of the nonlinear actuator to the TEF with the theoretical method. For general studies in the integration of turbine blade, Chou et al. [14] researched the blade of a 1KW power generation turbine. They used the finite element analysis on the composite laminated blade by applying the blade element theory. They found that composite laminates could improve the endurance of stress on the blade under the effect of wind and at the same time reduce the problem of fatigue failure of the blade under long-term high forces and high stresses. Bergami [15] studied the power generation of the NREL 5-MW wind turbine. He used the blade element method to calculate the coefficients of lift, drag and torque the turbine blade endures during the turbulence, wind shear and flapping motion from the atmosphere. Jonkman et al. [16] documented the specifications of the NREL offshore 5-MW baseline wind turbine - including the aerodynamic and structural system properties and the background of its development. Siddiqui et al. [17] investigated the wake dynamics behind an NREL 5MW HAWT turbine in near and far wake regions operating under different tip-speed-ratio and turbulence intensities. For the application of TEF, Wang and Chang [18] considered the effect of TEF on the rotating blade and the induced flow. By changing index angle and position of TEF, they found that the farther the TEF is from the root of the blade, the higher the lift and torque will be. At the same time, they examined the overall effect of altering TEF s chord location and length on the blade. The applications of smart materials and piezoelectric materials on TEF are growing in diversity. Mac Gaunaa et al. [1] made a thorough introduction to the study of TEF on wind turbine blades from 2003 to They manipulated the TEF by changing the value of voltage through the piezoelectric materials. They also studied the algorithm of the control. With the control system, the TEF will deflect to a specific angle to change the aerodynamics on the blade. As a result, the endured force on the root of the blade will decrease. Madsen et al. [2] proposed a study of controllable TEF with a type of rubber material installed on the blade, it cited the conclusion of Anderson et al. s [3] research. They calculated that in the scenario of turbulence, the installment of TEF on a 5 MW wind turbine blade could decrease 37% of fatigue load in the flap-wise direction. Madsen et al. [2] manufactured a NACA0015 TEF with a chord length of 15 cm and a wingspan of 30 cm. They placed the TEF on a 1 m long blade and test the change of bending under pressure at different chordwise positions. From the studies above, it is observable that the installment of TEF is a trend in designing turbine blades nowadays. This study will make use of FORTRAN to combine the ANSYS finite element analysis program to analyze the system of blades. We used the ANSYS to construct the structure of the wind turbine blade (including the structure of 1KW and 5MW wind turbine), and import the program of FORTRAN. We combined aerodynamics and wake theory by ANSYS APDL, in order to analyze the change of thrust and force endured at root corresponding to the fluid-structure interaction in the TEF-installed wind turbine. 2. Wake Theory This paper aims to investigate the effect of wake on

3 The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade 107 the TEF installed wind turbine blade. Therefore, the wake theory used by this paper will be introduced at the beginning. 2.1 Finite State Wake Theory The finite state wake theory [19,20] is derived from Prandtl s acceleration function. The pressure distribution function could be presented with the Legendre function and the Fourier series: (4) (1) and Among them, j > r, andj + r are odd numbers,,, are the coordinates functions of the elliptic coordinates. 2 It is noted that =0, 1 r on the rotor blade rotating plane, r is the radial coordinate (normalized by blade length) and is the azimuthal angle. P r r j and Q j are respectively the function of the first kind and second kind of the associated Legendre function, wherec j r and D r j are the coefficient functions. From these definitions, the equation of the pressure field of the wind turbine rotating plane could be derived as: where (5) (2) (6) where j rc and j rs are called the coefficient of pressure expansion, is the pressure distribution function and satisfies the Laplace s equation. By using the inducedflow theory, we can get the expression of induced velocity ( i )as: (3) r r The coefficient functions j and j are induced flow states of the model (state variables of wake), and the r polynomial j ( r )can be chosen as Legendre functions. The matrix form of the finite state inflow equation can be expressed as (7) The matrices [A]and[B] provide for coupling between radial inflow distributions of any given harmonic. They are simple integrals of the Legendre functions (P r j )and r of the assumed functions ( j ( r )).[ L ] is the matrix of induced flow influence coefficients (wake influence coefficients). The closed form of these matrices can be found in [19] and [20]. Those inflow forcing functions on the right-hand side of Eqs. (4) and (5) are defined as: (8) (9)

4 108 Yi-Ren Wang et al. for cosine part, and (10) for sine part, and L q is the q th blade lift per unit span of the blade. Generally, induced velocity is obtained by grid generation and numerical methods. However, the process is too complicated, it takes a huge amount of CPU time for problems of fluid-structure coupling. The constant induced velocity assumption could also be roughly obtained by combining momentum theory and blade element theory, but it is unable to accurately estimate the aerodynamic forces under fluid-structure coupling condition. The biggest advantage of finite state wake theory is that the dynamic wake equations is in closed form, it is beneficial for combining blade structural dynamics to obtain the induced velocity while fluid structure coupling. The process of calculation is as follows: First select the structural equation of the blade motion, such as the general beam vibration equations or composite beam equations. This study uses ANSYS to simulate the motion of the blade structure. The aerodynamic force (L q ) on the blade varies due to the motion and deformation of the rotor structure; this aerodynamic forcing function could be simulated by the general aerodynamic theory. It should be noted that due to the concept of fluid-structure coupling, factors of the effects in lift caused by induced velocity and motion of the blade should be included in L q. We can use blade element theory to solve for the simple L q function. By substituting L q into Eqs. (18 20) and then into Eqs. (4 and 5), we are able to couple it with the structural equation of the blade motion. Furthermore, we could obtain the induced velocity by solving the simultaneous equations. Once we solve for the induced velocity, the lifts, deformations and forces on the blade could be obtained. 2.2 The Advanced Finite State Wake Theory The finite state wake theory could be revised and enhanced by the following methods. First, in equation (4) and (5), the elements in each matrix must take infinite harmonic modes to get the exact solution. The number of harmonic modes taken would affect the time of calculation. Therefore, reference [20] has studied that it only takes 4 harmonic modes and 4 mode shape functions to achieve the allowable accuracy. However, after striking out the higher harmonics, the truncation error will differ along with the number of the harmonic mode. This will lead to higher truncation error in the higher harmonics functions, where deficient harmonic modes will be not accurate enough. Therefore, once a fixed harmonic mode is chosen, the higher harmonic mode should take fewer mode functions to increase accuracy. This phenomenon is mentioned in [20], the literature provided a harmonic mode and what corresponding orders the mode function should take. Thus this article will make use of this method of improvement to enhance the accuracy of finite state wake theory. 3. Fluid-structure Coupling Analysis of Turbine Blades We will use a rectangular blade to demonstrate how to construct turbine blade structure by ANSYS APDL, and calculate the aerodynamics and wake dynamic forces by the programming of FORTRAN. 3.1 Aerodynamic Forcing Function The calculation of material, structure, deformation, and stress of turbine blade in this study is mainly by ANSYS. To explain the process of analysis, we take a rectangular blade for example. The blade data is shown in Table 1. To formulate the lift forcing function (L q )on the right-hand side of the wake equations (Eqs. (4, 5)), we assume a small angle of attack and no stall on the rotor plane. Since we desire induced flow normal to the airfoil surface, the most logical assumption is to use lift normal to the airfoil (circulatory only) surface as the wake forcing function [21], (11) where is the air density, a is the slope of lift curve, c is the blade chord, is the blade rotating speed, r repre- Table 1. Materials properties Material Young s Modulus (Gpa) Density (kg/m 3 ) Poisson ratio Aluminum 6061-T

5 The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade 109 sents the blade radial state, U 0 is the wind speed, denotes the blade twist angle and v i is the induced velocity. It is noted that the dimensional value in Eq. (11) can be non-dimensionalized by 2 R 4. We then substitute equation (11) into our wake forcing functions (Eqs. (8 10)) to obtain the wake equations. By wake equations (Eqs. (4, 5)) and lift function (Eq. (11)), we can coordinate with ANSYS to use different materials and shapes of turbine blades. By each iteration, we obtain different blade twist angles and deformations under different induced velocity and lift force. Then by substituting it into Eqs. (11 and 4, 5) to get the next value of fluid-structure coupling, until it converges. Please see Figure 1 for the process. Figure 2, the horizontal axis represents the span-wise state points on the blade, and the vertical axis represents lift. We can observe from Figure 2 that lift converges to its final value for each state point. The post-process and display of ANSYS show that the maximum deformation of the rotor blade happens on the wingtip (see Figure 3), the maximum twist angle happens on the blade root (see Figure 4). Through Von Mises stress (see Figure 5 and Figure 6) we can observe that the maximum stress on the blade surface is 5.69 Mpa. At this time, due to the deformation on the blade, the wing upper surface structure is subject to the compressive stress and the opposite bottom surface is subject to the tensile stress. From the following results of the processes, we are able to verify that 3.2 Rectangular Blade and APDL Verification By coupling ANSYS and FORTRAN to iterate the value of the lift to converge, we can obtain the distribution of lift of the rectangular blade (see Figure 2). The rectangular blade was made of 6061 aluminum alloy and the upwind speed was 3 m/sec for the wind turbine. In Figure 2. Lift curve of the rectangular blade. Figure 1. Flow chart of wake-structural coupling analysis. Figure 3. Blade deformation diagram.

6 110 Yi-Ren Wang et al. our numerical calculations by using ANSYS and FOR- TRAN are viable. Figure 4. Spanwise twist angle diagram. 4. Results and Discussion By the aforementioned theories and the programming of APDL, this section will discuss the aerodynamic characteristic on the 1KW blade and the 5MW blade, respectively. The effect of wake dynamics and TEF on the turbine blade will be summarized at the end of this section. 4.1 Verification of the Blade-wake Coupling on a 1KW Blade This section takes Chou s [14] 1KW wind turbine blade structure as the benchmark in order to observe the distribution of stress. On the left of Figure 7 is the stress distribution of Chou s [14] blade, on the right is the stress distribution of this study. We can find in Figure 7 that the maximum stress distributes in the center section in both cases. The different result in maximum stress between Chou s [14] and ours is because our 1KW turbine blade is to be a homogeneous metallic material, while Chou s [14] blade is to be a multilayer composite. However, the consideration of material is not the objective of our study. This section is mainly to verify the tendency of blade stress in this study is consistent with Chou s [14] result. 4.2 Verification of the Blade-wake Coupling on a 5MW Blade This section uses the 5MW turbine blade of Lee et al. [22] as the main structure to verify the wake effect. We Figure 5. Von-mises stress on blade upper surface. Figure 6. Von-mises stress on blade bottom surface. Figure 7. Comparison of stress distribution of 1KW blade.

7 The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade 111 combine its blade shape and structure with the dynamic wake, and compared it with the lift distribution results from Lee et al. Figures 8 and 9 are cases under wind speeds 9 m/s and 11.5 m/s, respectively. In the two figures, lines with square marks are the lift curve from Lee et al., lines with inverted triangle marks represent the lift curve from this study without considering wake and lines with diamond marks represent the lift curve of this study with wake considered. Instead of using complicated modified strip theory, we employed a simple lifting theory [21]. The lift distribution away from the blade tip for a larger blade chord and twist angle cannot be exactly included in the current aerodynamic model. However, the value of maximum lift agrees with the results from Lee et al. [22] very well with no wake effect. Since induced velocity will increase due to wake effect, therefore, it causes lift (thrust) to decrease. Our present result matches this phenomenon shown in Figures 8 and The Analysis of Dynamic Wake Coupling of a 5MW Blade with TEF This section uses the 5MW turbine blade with the TEF as the main structure. We consider the following parameters: TEF mid-span located on R/4 of the blade, TEF index angle fixed at 10 degrees and TEF with wingspan of R/10, R/8, and R/6 respectively. The effect of wake and TEF span on deformation and stress of blade will be discussed The Effect of Wake We use ANSYS to analyze whether considering wake effect, the stress distribution on the blade. Figure 10 and Figure 11 are the stress distribution graphs with TEF mid-span located on R/4 on the blade, TEF index angle fixed at 10 degrees and TEF with the wingspan of R/6. Figure 8. Lift certified chart of the 5MW blade under 9 m/s wind. Figure 10. Stress distribution of TEF span R/6 without wake. Figure 9. Lift certified chart of the 5MW blade under 11.5 m/s wind. Figure 11. Stress distribution of TEF span R/6 with wake.

8 112 Yi-Ren Wang et al. The detailed data of other combinations is as Table 2. From Table 2, we can see that maximum stress and deformation of blade increase along with the increasing of TEF span (R/10~R/6). This is due to the increased lift from the increased TEF. Moreover, we can observe that regardless of how long the TEF span is, if the wake is considered, its stress or deformation are lesser than those without wake considered. The reason is that wake causes induced flow to increase, therefore decreasing lift and reduce the force on the blade. With the case in Table 2, by using ANSYS to calculate the stress distribution whether considering wake. The maximum stress dropped by 7.5%, thus we can see the effect of the wake The Effect of Fluid-structure Coupling To determine the effect of fluid-structure coupling, we use the 5MW turbine blade from Lee et al. [22] as the main structure and consider the effect of wake and TEF. We use TEF with mid-span at R/4, length of R/10 and index angle fixed at 10 degrees. Using different iteration times to record its lift, deformation and stress to observe the process of dynamic wake-structural coupling, see Table 3. From Table 3, we find that after given the initial lift (regardless N/W (no wake effect) or W/W (with wake effect)), the values will converge at about the fifth iteration. Where lift, stress and deformation decrease. This study also verifies that iteration must be satisfied in the fluid-structure analysis The Effect of TEF Under the consideration of wake, to understand the effect of TEF on the 5MW turbine blade, we consider two cases. One without TEF, the other with TEF installed. The TEF mid-span is at R/4, with R/6 length and index angle set at 30 degrees. With the same parameters, as seen in Figure 12, the lift curve of the turbine blade with TEF installed is slightly larger. From Figure 13 we observe that both maximum stresses occur at blade root, and no significant changes in overall stress in both cases. It can be seen that in consideration of wake effect, turbine blades with TEF installed could increase lift, but at the same time would not increase too much load on the root of the blade The Effects of TEF and Wake on the Blade To comprehensively analyze the installment of TEF on the 5MW wind turbine blade, we set TEF mid-span at Figure 12. Lift curve of blade with/without TEF. Table 2. Structural analysis of different TEF span TEF span R/10 TEF span R/8 TEF span R/6 Max stress (Mpa) Max Disp. (m) Max stress (Mpa) Max Disp. (m) Max stress (Mpa) Max Disp. (m) No wake With wake Table 3. Blade-wake coupling iteration data Iteration Lift (N, N/W) Lift (N, W/W) Disp l. (m) Stress (Mpa)

9 The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade 113 R/4 and change different index angles (10,20 and 30 ) and TEF spans (R/10, R/8 and R/6). By comparing the maximum lift (W/W and N/W), stress and deformation of this blade respectively, we can investigate the effect of TEF on the aerodynamic and structure of a turbine blade. Table 4 is the results of iteration from the aforementioned parameters using the combination of ANSYS APDL and FORTRAN respectively, with wake and fluid-structure coupling considered. Figure 14 is the schematic diagram of the position, length, width and index angle of the TEF. In Table 4 we displayed the data by different TEF span, and each TEF span is subdivided into different index angle. From Table 4 we find that with fixed TEF span, the maximum lift will increase when the index angle increases, both (N/W) and (W/W) performed the same trend. At the same time, the maximum deformation and stress will also increase when the maximum lift increases. If we fix the index angle, its maximum lift will increase when the length of TEF span increases. Similarly, the maximum deformation and maximum stress will also increase. We can find from the analysis of this section and section that with wake considered, the installation of TEF could increase lift and would not cause significant load in stress at the blade root, thus making it a better choice. 5. Conclusions This study had successfully completed the coupled structure of dynamic wake and wind turbine blade with TEF. This structure will be used to simulate under different parameters, the effect of wind turbine blade with TEF and dynamic wake effect, and by mutual iteration to convergence between FORTRAN of APDL and ANSYS to simulate the effect of fluid-structure coupling. We take the 5MW wind turbine blade with TEF installed as the main object, analyze the effect of TEF s index angle and span on the thrust of overall blade structure and force at the root of the blade and made the conclusion as follows: (1) This study successfully combined FORTRAN program by APDL on the analysis of fluid-structure coupling. It is shown from the results of iteration to convergence every time that both lift and deformation of the blade exists significant differences from the initial values, this is what could not be done by the open loop aerodynamic analysis. (2) The larger the index angle of TEF installed on the wind turbine blade, whether consider wake or not, Figure 13. Stress distribution of blade with/without TEF. Figure 14. Schematic diagram of blade with TEF. Table 4. Effects of different TEF parameters on the blade TEF span R/10 TEF span R/8 TEF span R/6 Index angle ( ) Lift (N, N/W) Lift (N, W/W) Max. Displ. (m) Max. stress (Mpa)

10 114 Yi-Ren Wang et al. will increase its lift. With the same index angles, the longer the TEF span, the larger the lift will be on the wind turbine blade. (3) Finite state wake theory is a method that is easy to couple with other structures and aerodynamic theory, it does not require complex calculations to preliminarily estimate wake. In general, the wake will result in the increase of induced flow and therefore causes the decrease in thrust of the blade. (4) Under the condition of same shape and material of blade, by installing TEF, in addition to the increased lift, there is no significant trend of increase in stress at the root of the blade, thus making it a better choice. References [1] Mac Gaunaa, Peter B., Anderson, Christian D. and Bak, Thomas Buhl, Adaptive Trailing Edge Flap - Recent Development within Smart Blades, Proc. of 2010 Wind Turbine Blade Workshop, Albuquerque, NM, Aeroelastic Design Program Wind Energy Division, Risø DTU (2010). [2] Aagaard Madsen, H., Andersen, P. B., Løgstrup Andersen, T., Bak, C., Buhl, T. and Li, N., The Potentials of the Controllable Rubber Trailing Edge Flap (CRTEF), EWEC 2010 Proceedings online, European Wind Energy Association (EWEA) (2010). doi: /S (01) [3] Andersen, P. B., Henriksen, L., Gaunaa, M., Bak, C. and Buhl, T., Deformable Trailing Edge Flaps for Modern Megawatt Wind Turbine Controllers Using Strain Gauge Sensors, Wind Energy, Vol. 13, No. 2 3, pp (2010). doi: /we.371 [4] Haans, W., Sant, T., van Kuik, G. and van Bussel, G., HAWT Near-wake Aerodynamics, Part I: Axial Flow Conditions, Wind Energy, Vol. 11, No. 3, pp (2008). doi: /we.262 [5] Bontekoning, M. P. C., Perez-Moreno, S., Ummels, B. C. and Zaaijer, M. B., Analysis of the Reduced Wake Effect for Available Wind Power Calculation During Curtailment, Proc. of IOP Wake Conf. Series: Journal of Physics: Conf. Series 854, 11 pages (2017). doi: / /854/1/ [6] Hodges, D. H., Crespo da Silva, M. R. M. and Peters, D. A., Nonlinear Effects in the Static and Dynamic Behavior of Beams and Rotor Blades, Vertica, Vol. 12, pp (1988). [7] Peters, D. A. and Johnson, M. J., Finite-state Airloads for Deformable Airfoils on Fixed and Rotating Wings, Aeroelasticity and Fluid-Structure Interaction Prob - lems, ASME, AD-Vol. 44, pp (1994). [8] Crespo de Silva, M. R. M., A Comprehensive Analysis of the Dynamics of a Helicopter Rotor Blade, International Journal of Solids and Structures, Vol. 35, No. 7 8, pp (1998). doi: /S (97) [9] Pai, P. F. and Palazotto, A. N., Large-deformation Analysis of Flexible Beams, International Journal of Solids and Structures, Vol. 33, No. 9, pp (1996). doi: / (95) [10] Pai, P. F., Anderson, T. J. and Weather, E. A., Largedeformation Tests and Total-lagrangian Finite-element Analysis of Flexible Beams, International Journal of Solids and Structures, Vol. 37, No. 21, pp (2000). doi: /S (99) [11] Fulton, M. V. and Ormiston, R. A., Hover Testing of a Small-scale Rotor with On-blade Elevons, Journal of the American Helicopter Society, Vol. 46, No. 2, pp (2001). doi: /JAHS [12] Nikhil, A. K. and Chopra, I., Open-loop Hover Testing of a Smart Rotor Model, AIAA Journal, Vol. 40, No. 8, pp (2002). doi: / [13] Kurdila, A. J., Li, J., Strganac, T. and Webb, G., Nonlinear Control Methodologies for Hysteresis in PZT Actuated On-blade Elevons, Journal of Aerospace Engineering, Vol. 16, No. 4, pp (2003). doi: /(ASCE) (2003)16:4(167) [14] Chou, K.C., Development of Blade & Tower Structure and Monitoring System for the 1KW Wind Turbine, Master Thesis, Department of Aeronautics & Astronautics, National Cheng Kung University (2011). [15] Bergami, L., Adaptive Trailing Edge Flaps for Active Load Reduction, Wind Energy Division, Ris DTU- National Laboratory for Sustainable Energy, Proc. of the 7th Ph.D. Seminar on Wind Energy in Europe, Delft, Netherlands (2011). [16] Jonkman, J., Butterfield, S., Musial, W. and Scott, G., Definition of a 5-MW Reference Wind Turbine for Offshore System Development, National Renewable Energy Laboratory Technical Report, NREL/TP-500-

11 The Effects of Wake Dynamics and Trailing Edge Flap on Wind Turbine Blade (2009). [17] M., Siddiqui, M. S., Rasheed, A., Tabib, M. and Kvamsdal, T., Numerical Analysis of NREL 5MW Wind Turbine: a Study towards a Better Understanding of Wake Characteristic and Torque Generation Mechanism, Proc. of the Science of Making Torque from Wind (TORQUE 2016), Journal of Physics: Conf. Series 753, 10 pages (2016). doi: / /753/3/ [18] Wang, Y. R. and Chang, Y. S., The Effects of an Onblade Trailing Edge Flap on Rotor Dynamics in Hover, Journal of Aeronautics, Astronautics and Aviation, Series A, Vol. 43, No. 4, pp (2011). [19] Peters, D. A. and He, C. J., Comparison of Measured Induced Velocities with Results from a Closed Form Finite State Wake Model in Forward Flight, Proc. of the 45th Annual National Forum of the American Helicopter Society, Boston, Massachusetts, May (1989). doi: /JAHS [20] Wang, Y.-R. and Peters, D. A., The Lifting Rotor Inflow Mode Shapes and Blade Flapping Vibration System Eigen-analysis, Computer Methods in Applied Mechanics and Engineering, Vol. 134, No. 1 2, pp (1996). doi: / (96) [21] Johnson, W., Helicopter Theory, Princeton University Press, Princeton (1980). [22] Lee, J. W., Lee, J. S., Han, J. H. and Shin, H. K., Aeroelastic Analysis of Wind Turbine Blades Based on Modified Strip Theory, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 110, pp (2012). doi: /j.jweia Manuscript Received: Jul. 24, 2017 Accepted: Dec. 1, 2017

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