CFD Investigation on the aerodynamic characteristics of a small-sized wind turbine of NREL PHASE VI operating with a stall-regulated method

Transcription

1 Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 DOI /s CFD Investigation on the aerodynamic characteristics of a small-sized wind turbine of NREL PHASE VI operating with a stall-regulated method Jang-Oh MO 1 and Young-Ho LEE 2,* 1 School of Mechanical Engineering, The University of Adelaide, South Australia 5005, Austrailia 2 Division of Mechanical and Energy-System Engineering, Korea Maritime University, Busan, , Korea (Manuscript Received January 24, 2011; Revised August 30, 2011; Accepted October 12, 2011) Abstract The objective of this investigation is to clearly understand the aerodynamic characteristics of a small-sized wind turbine of NREL Phase VI, operating with a stall-regulated method using CFD code. Based on this, it is possible to provide turbine designers with the aerodynamic design data to increase efficiency and improve performance in the design phase of future small-sized wind turbine blades. Moreover, a comparison was made between experimental datasets, in order to verify the reliability and validity of the analysis results. The first height in the normal direction from the surface of a rotor blade is about 0.2 mm, and the average value of y + is about 7 at 7 m/s. The domain is chosen to consist of only two hexahedral mesh regions, namely the interior region, including the wind turbine blade, and the external region excluding the rectangle. The total cell number of the numerical grid is about N g = Five different inflow velocities, in the range V in = m/s, are used for the rotor blade calculations. The calculated power coefficient is about 0.35 at a TSR of 5.41, corresponding to 7 m/s, and showed considerably good agreement with the experimental measurements, to within 0.08%. It was observed that the 3-D stall begins to generate near the blade root at a wind speed of 7 m/s. Therefore, root design approaches considering the appropriate selection of the angle of attack and the thickness are very important in order to generate the stall on the blade root. Through a clear understanding of aerodynamic characteristics of a small-sized NREL Phase VI wind turbine, it is expected that this useful aerodynamic data will be made available to designers as guidance in designing stall-regulated wind turbine blades in the development phase of small-sized wind turbine systems in the future. Keywords: CFD; A small-sized wind turbine; Aerodynamic characteristics; Stall-regulated method; Blade element momentum theory; Power coefficient; Pressure coefficient; 3-D stall; Separated flow; Stall angle; Surface streamlines; Tip speed ratio Introduction Owing to the potential severity of climate change as a result of global warming, every country in the world is taking an active interest in the development of renewable energy. In particular, the installation of wind power generation systems, which are economically feasible and environmentally friendly, has shown a sharp increase since the 1990s, with an annual average increase of 28% over the past five years. By 2020, wind power will generate about 1,200 GW, approximately 12% of the worldwide total energy production, and it is expected that capacity of 2,270 MW, corresponding to about 3% of the total capacity, will be introduced to the domestic market by 2012 [1]. The fundamental technological field in wind power system development is the blade. Once the basic design, including the This paper was recommended for publication in revised form by Associate Editor Jun Sang Park * Corresponding author. Tel.: , Fax.: address: lyh@hhu.ac.kr KSME & Springer 2012 capacity of the wind turbine and its operating wind speed, is finished, the blade development is the next stage. Development of a control system for the generator and gear box will then follow. For this reason, the major commercial wind power development companies and research institutes have made great efforts to develop unique blades; through this, the large scale-up and high efficiency of wind power generators has been realized. However, as there is no opportunity for independent blade development, this becomes an obstacle to the further activity in the wind power generation industry. Most blades for wind power generation require an optimized aerodynamic design, and new rotor blade designs must clearly understand the characteristics of the flow field in order to increase efficiency and improve performance. To obtain the optimum design parameters, it is necessary to study the characteristic results of the huge flow field and aerodynamic performance from reliable experiments. This is often difficult, owing to problems of cost and time. Moreover, full-scale measurements are often contaminated by varying wind speeds, changes in wind direction, etc. Therefore, various numerical

2 82 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 Table 1. Specification of the NREL Phase VI wind turbine. Number of blade Z 2 Rotor radius R m Rotational speed N 71.9 rpm Cut-in wind speed V c 6 m/s Rated power P r 19.8 kw Power regulation Stall Rotational direction CCW Global pitch angle 5 Fig. 1. Shape model of the NREL Phase VI wind turbine blade. analytic studies using the wake code, aero-elastic code, and CFD code have been attempted in order to understand the flow around the blade and the characteristics of efficient aerodynamic performance. Studies on full Navier-Stokes simulations of wind turbine rotors have been performed by Duque [2], Xu and Sankar [3, 4], Sørensen and Hansen [5], and Sørensen and Michelsen [6]. Additionally, a large number of rotor simulations have been performed by the helicopter community. The objective of this investigation is to clearly understand the aerodynamic characteristics of a small-sized wind turbine of NREL Phase VI, operating with a stall-regulated method using CFD code. Based on this, it is possible to provide turbine designers with the aerodynamic design data to increase efficiency and improve performance in the design phase of future small-sized wind turbine blades. Moreover, a comparison was made between experimental datasets, in order to verify the reliability and validity of the analysis results. 2. Computational methodologies 2.1 Specification of NREL Phase VI wind turbine Fig. 2. Twist angle of the NREL Phase VI wind turbine blade. NREL successfully completed an experimental test for a Phase VI wind turbine in a wind tunnel ( m) at NASA s Ames Research Center in May After this test, NREL revealed the experimental results and information on the shape of the test blade on their website, in order to verify the performance of commercial analytical codes developed around the world. Therefore, the present study adopts the blade shape used in the Phase VI tests as an analysis target for CFD simulation, because the NREL Phase VI blade shape can be accurately modeled using the released information, and reliable test results for the turbine can be easily obtained. The shape model of the Phase VI wind turbine blade (shown in Fig. 1) is controlled by a stall-regulated method, and produces a rated output power of 19.8 kw. The turbine blade diameter, rotational speed, and blade number is D = m, N = 71 rpm, and Z = 2, respectively. Detailed specifications of the turbine model are shown in Table 1. For the cases considered in the present study, the rotor cone angle is set at 0, and the blade pitch angle is set at 5. This rotates the blade tip chord line 5 towards feather, relative to the rotor plane, thus pointing the leading edge into the oncoming wind. The distribution of rotor blade twist angle from hub to tip is shown in Fig. 2. The twist angles are relative values to zero twist at the 0.75 span, and show negative values from 0.75 to 1 span. The blade shape of the Phase VI wind turbine consists of airfoil S809 from root to tip. This airfoil has a thickness of 21% of its chord length, and is designed to be less sensitive to the surface roughness at the leading edge of the wind turbine blade, in order to improve the turbine output power [7, 8]. 2.2 k-ω SST turbulence model In the present work, the turbulence in the boundary layer is modeled by the SST k-ω model. This model is chosen because of its very promising results for 2-D separated flows [9, 10]. The shear-stress transport (SST) k-ω model was developed by Menter [11, 12] to effectively blend the robust and accurate formation of the k-ω model in the near-wall region with the free-stream independence of the k-ε model in the far field. To achieve this, the k-ε model is converted into a k-ω formulation [12]. The equations for the turbulence model are solved after the momentum and pressure correction equations in every sub-iteration. All computations are performed assuming fully turbulent flow, excluding any laminar and transitional effects at the leading edge region of the rotor.

3 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 83 k ( ρk) + ( ρkui) = ( Γ k ) + G% k Yk + Sk (1) t x x x i j j ω ( ρω) + ( ρωui ) = ( Γ ) + G Y + D + S t x x x ω ω ω ω ω i j j (2) In these equations, G % k represents the generation of turbulent kinetic energy attributed to mean velocity gradients, G ω represents the generation of ω, Γ k and Γ ω represent the effective diffusivity of k and ω, respectively, Y k and Y ω represent the dissipation of k and ω attributed to turbulence, D ω represents the cross-diffusion term, and S k and S ω are user-defined source terms. The equations to which these symbols relate can be confirmed in more detail in Ref. [13]. The wall boundary conditions for the k equation in the k- ω models are treated in the same way as when enhanced wall treatments are used with k-ε models. This means that all boundary conditions for wall-function meshes will correspond to the wall function approach, while for fine meshes the appropriate low Reynolds number boundary conditions will be applied. In the ANSYS FLUENT solver, the value of ω at the wall is specified as + ω in the laminar sublayer is giv- The asymptotic value of en by where and. (3) where k S is the roughness height. In the logarithmic region, + the value of ω is which leads to the value of ω in the wall cell as (4) (5) (6) (7). (8) Fig. 3. Shape Configuration of the NREL Phase VI blade using GAMBT software. In the case of a wall cell being placed in the buffer region, ANSYS FLUENT will blend ω + between the logarithmic and laminar sublayer values. The meaning of these symbols can be confirmed in Ref. [13]. Numerous experiments have shown that the near-wall region can be largely subdivided into three layers, namely the viscous layer (to y + = 5), the buffer layer (to y + = 60), and the fully turbulent layer [14]. In this study, the first height in the normal direction from the surface of a rotor blade is about 0.2 mm, and the average value of y + is about 7 at 7 m/s, which is between the viscous and buffer layers. If y + exists within this range, it is possible to perform the rotor blade calculations. 2.3 Numerical method The geometrical model of the NREL Phase VI rotor blade was constructed using GAMBIT software, based on the shape data information [7, 8]. The twist angle is a maximum of at the root, and reduces to a minimum of at the tip in order to maximize aerodynamic performance. Each airfoil begins to attach from r/r = to the tip (Fig. 3). The original NREL S809 airfoil contains a sharp trailing edge, which is clearly not the case for the real blade. This feature also unnecessarily complicates the construction of the hexahedral grids. For this reason, it was replaced with a blunt trailing edge by cutting at 0.99c. The computational domain for the wind turbine blade is illustrated in Fig. 4. The domain is chosen to consist of only two hexahedral mesh regions, namely the interior region, including the wind turbine blade, and the external region excluding the rectangle, whose line is expressed in detail in Fig. 4. Only one of the two blades is explicitly modeled in the computations. The remaining blade is accounted for using periodic boundary conditions, exploiting the 180 symmetry of the two-bladed rotor. In the computational domain, a cylindrical cross-section with an area less than the actual tunnel cross-section ( m) is used, corresponding to a radius of 15.1 m. The calculation domain is defined by the reference length of the blade radius R, as shown in Fig. 5. A spatial resolution of 2.5R to the calculation

4 84 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 Table 2. Analysis conditions. Wind speed(v in ), m/s RPM ρ, kg/m 3 Case Case Case Case Case Case Fig. 4. Computational domain. Fig. 5. Surface grid on a rotor blade. Fig. 7. sketch on the stream of separated flow around rotor blade. 2.4 Flow patterns around rotor blade Fig. 6. Grid section at r/r=0.35 on a rotor blade. domain inlet, 3.5R to the downstream region, and 3.0R to the radial direction of the wind turbine model is applied. The surface grid is comprised solely of quad meshes. The 100 nodes on the upper and lower edges of each airfoil section were meshed in the chordwise direction and concentrated in the leading and trailing edge regions, and the 200 nodes in the spanwise direction, as shown in Fig. 6. In order to create boundary layers on the blade surface, 20 nodes were meshed in the O type block surrounding the rotor blade, with a spacing ratio of 1.1 in the normal direction and a first height of 0.2 mm. The total cell number of the numerical grid is about N g = , consisting of hexahedral grids over the total domain. For the boundary conditions, a velocity condition with a turbulent intensity of 3% is applied at the upstream boundary where the flow enters the cylindrical domain, and an ambient pressure condition is applied at the downstream point at which the flow leaves the cylindrical domain. Six different inflow velocities, in the range V in = m/s, are used for the rotor blade calculations. The analysis conditions are summarized in Table 2. The 3-D flow generated from a rotor blade on the actual wind turbine is quite complex. The flow that is branched out by separation at the root moves towards the tip, because of the influence of the centrifugal acceleration and the pressure gradient in the radial direction. The centrifugal acceleration can + be expressed as ω r. The pressure gradient in the radial direction changes according to the variation of the angle of attack on the airfoil in a given position, and according to the variation of the local velocity ratio (Tip speed ratio, R ω λ= ). The wind that is separated at the root and flows Vin in the radial direction of the blade passes the wind ( θ ) that flows on the surface of the blade, thus forcibly generating a 3- D separation on the surface of the blade, as shown in Fig. 7. At a certain point, the wind separates out in the θ direction. This airflow is also generated across the entire blade in both the leading and trailing edges of the airfoil [15, 16]. Although it is difficult to quantify the related data, the effect of this phenomenon is thought to be significant. 3. Results and discussion Fig. 8 represents the airfoil cross-section at radius r, having a local blade twist angle of β to the rotor s plane of rotation. The inflow wind speed V in in the rotor plane, and the tangen-

5 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 85 Fig. 8. Flow velocities and aerodynamic forces at a blade element. tial speed r ω at the radius of the blade cross-section, combine to give the local relative flow velocity, V r. Together with the airfoil chord line, this forms the aerodynamic angle of attack, α. The angle of attack is an aerodynamic parameter referring to the relative flow velocity. The blade pitch angle is a geometrical parameter referring to the plane of rotation. Blade element momentum theory is used to derive the axial and circumferential inflow factors, with the introduction of a tip loss factor to take into account the finite number of rotor blades. Therefore, the wind speed V in can be expressed as V in (1-a), owing to the aerodynamic interference among blades, where a is the axial inflow factor with a value of 1/3. This value is used in order to maximize the power coefficient at 0.593, called the Betz limit. The angle of attack can be calculated using Eq. (9) according to the axial and tangential velocities when the axial inflow factor is assumed to be 0. Owing to the global pitch angle, the axial inflow factor becomes much lower than 1/3; however, we cannot ascertain its exact value. Fig. 9. Experimental lift-to-drag ratios according to different Reynolds numbers of a S809 airfoil. (9) where 5 is a global pitch angle. In the process of the blade design, the rotor blade should be twisted in order to produce a maximum output power at an optimal angle of attack. This corresponds to a maximum liftto-drag ratio for the rated wind speed at each location, because the rotational speed linearly increases from root to tip. Therefore, it is important to confirm the performance characteristics of airfoils applied to a wind turbine blade. Fig. 9 shows experimental lift-to-drag ratios, according to different Reynolds numbers, of a S809 airfoil [8]. The lift-todrag ratio corresponding to 6.11 is approximately 55.4 at Re = As the Reynolds number rises to , the lift-todrag ratio increases up to a maximum of 89.58, corresponding to The important point is that the angle of attack corresponding to the maximum lift-to-drag ratio is in the vicinity of 6 regardless of the Reynolds number. The design angle of attack is generally at the point of maximum lift-to-drag ratio. Therefore, this fact will assist designers in performing the pitched-controlled or stall-regulated design of a rotor blade. In this study, the Reynolds number ranges from approximately Fig. 10. Surface streamlines on suction side (7 m/s, 10 m/s, 13 m/s, 15.1 m/s, 20.1 m/s and 25.1 ms from top to bottom) from root to tip for a wind speed of 7 m/s. Fig. 10 represents the streamline distributions on the suction side of the rotor blade at six different wind speeds (7 m/s, 10 m/s, 13.1 m/s, 15.1 m/s, 20.1 m/s, and 25.1 m/s) from top to bottom. It is observed that the stall phenomenon is initially generated on the blade root, because the effective angle of attack at the blade region for a wind speed of 7 m/s can be calculated from Eq. (9) as approximately This is higher than the stall angle of 9 mentioned in the 2-D S809 airfoil experiments [8], as shown in Fig. 11. However, near r/r = 0.6, corresponding to an angle of attack of approximately 10, an unseparated flow exists, unlike in the results of the 10 m/s wind speed. This is known as the stall delay phenomenon due to the rotation effect [17]. In a 7 m/s wind speed, the flow is

6 86 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 Fig. 11. Angle of attack distribution for various wind speeds. separated near the blade root, and then the radial flow is generated and moves to the spanwise section of approximately 0.35 because of the influence of the centrifugal acceleration and pressure gradient in the radial direction. Beyond that section, however, the attached flow is formed and stably passes along the blade surface. As the wind speed is increased, the streamlines on the blade surface develop very complicated flow patterns owing to the increasing angles of attack and radial flow in the θ direction It is confirmed that a 3-D stall separated from the blade root slowly generates and spreads toward the tip with the increasing wind speeds to keep the output power constant. The control of wind turbine systems with this flow phenomenon is called the stall-regulated method. In this study, the Phase VI wind turbine blade has a maximum thickness of 47% of chord length at r/r = 0.2 on the blade root, which is almost the shape of an ellipse. Thus, it is found that the root design on a blade is very important in allowing 3-D stall to slowly generate at a rated wind speed in wind turbines operating with a stall-controlled method. However, the root design with a pitch-controlled method should performed in such a way that the region of separated flow is decreased and the target output is increased. Figs. 12, 13, and 14 show a comparison of measured and calculated pressure coefficients on the spanwise sections r/r = 0.3, 0.47, 0.63, 0.80, and 0.95 for wind speeds of 7 m/s, 15.1 m/s, and 25 m/s, respectively [7, 8]. The pressure coefficient is defined by Eq. (10). (10) For the 7 m/s wind speed, a good agreement is found with the experimental data in Fig. 12 for all five spanwise sections, even though weak separated flow exists from r/r = 0 to r/r = 0.5, as shown in Fig. 10. It is widely known that the thickness around the blade root should be thick approximately to r/r = 0.25, from the viewpoint of the structural safety of the rotor blade, whereas, from an aerodynamic viewpoint, the thickness at r/r = (at the blade tip) should be thin for producing of the required output power. In the case of a 15.1 m/s wind speed (Fig. 13), it can be observed that the computation results are in comparatively good condition. At the point r/r = 0.3, the computed pressure distribution agrees well with the experimental results only on the pressure side. The agreement is not so good in the regions of the upper surface including the leading edge and trailing edge, where the pressure is over- or under-predicted over the forward and backward half at X/c = 0.5. The calculated pressure distributions at r/r = 0.47, 0.63, 0.80, and 0.95 show a little difference from the experimental results on the upper surface. For the highest wind speed of 25.1 m/s, the calculated results show comparatively good agreement with the measured results at r/r = 0.47, 0.63, and 0.95, but this is not the case for r/r = 0.3 and 0.8, as shown in Fig. 14. Although it is known that the SST k-ω model provides reasonable results for separated flows, in these cases, beyond expectation, the calculated results show comparatively good agreement with experiments even at the highest wind speed conditions, except for the regions of greatly separated flow on the blade root at r/r = 0.3 and the upper surface at r/r = 0.8. Generally, it is true that the SST k-ω turbulence model has an excellent prediction ability for wall characteristics, but there is a limitation to the accurate prediction of aerodynamic characteristics at extremely high angles of attack using the applied turbulence model. However, in this study, even at the two higher wind speed conditions, the calculated results agree wonderfully well with the experiments. Later, in regard to this matter, it is judged that additional investigation will be needed using the transition model developed by Ref. [18]. Fig. 15 shows the distribution of computed unit span torque divided into 10 sections for various wind speeds. At a wind speed of 7 m/s, the unit span torque at each location shows a linearly increasing tendency up to the point r/r = 0.85, and then suddenly drops off. It is known that the torque of a rotor blade is directly proportional to distance from the center of an object when the rotor blade is designed to be optimal. This phenomenon is related to tip vortices with very complex 3-D flow structures in the local cross flow along the trailing edge of the blade tip [19, 20]. Owing to these tip vortices, the pressure around the tip is decreased and the airflow changes its direction toward the optimal angle of attack, contrary to our initial design. It is also known that the shape of the blade tip has a strong influence on mechanical power. With increasing wind speeds, the partial torque at each location shows uneven distributions owing to the stall phenomenon with complex flow over the blade, and a negative partial torque is confirmed at the blade tip in conditions of 20.1 m/s and 25.1 m/s winds. Therefore, it is expected that this flow phenomenon will be able to keep the output power constant even in extreme situations. Table 3 shows the percentage ratio of partial torque to total torque. At 7 m/s, the partial torque from r/r = 0.35 to r/r = 0.85 is around 85.0% of all the torque generated from the rotor

7 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 87 (a) r/r = 0.3 (b) r/r = 0.47 (c) r/r = 0.63 (d) r/r = 0.8 (e) r/r = 0.95 Fig. 12. Comparison of measured and calculated pressure coefficient on the spanwise sections r/r=0.3, 0.47, 0.63, 0.80 and 0.95 for a wind speed of 7 m/s.

8 88 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 (a) r/r = 0.3 (b) r/r = 0.47 (c) r/r = 0.63 (d) r/r = 0.8 (e) r/r = 0.95 Fig. 13. Comparison of measured and calculated pressure coefficient on the spanwise sections r/r=0.3, 0.47, 0.63, 0.80 and 0.95 for a wind speed of 15.1 m/s.

9 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 89 (a) r/r = 0.3 (b) r/r = 0.47 (c) r/r = 0.63 (d) r/r = 0.8 (e) r/r = 0.95 Fig. 14. Comparison of measured and calculated pressure coefficient on the spanwise sections r/r=0.3, 0.47, 0.63, 0.80 and 0.95 for a wind speed of 25.1 m/s.

10 90 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 Table 3. Percentage ratio of partial torque to total torque. wind Percentage ratio of partial torque to total torque speed (V in ), m/s 7 3.7% 85.0% 11.3% 100.0% % 81.1% 14.3% 100.0% % 68.8% 24.0% 100.0% % 56.9% 23.1% 100.0% % 76.5% -4.3% 100.0% % 81.2% -3.1% 100.0% Fig. 16. Distribution of lift force to drag force ratio per unit span at r/r locations for various wind speeds. Fig. 15. Distribution of computed torque per unit span for various wind speeds. blade, while that from r/r = 0 to r/r = 0.35 accounts for just 3.7% of the total. This confirms that the partial torque generated in this region of the blade root has a weak effect on aerodynamic performance. With increasing wind speed, the proportion of the torque between r/r = 0.35 and r/r = 0.85 decreases up to the 15.1 m/s wind speed, and then begins to increase. The torque between r/r = 0.85 and 1.0 shows a negative value at wind speeds of 20.1 m/s and 25.1 m/s because of the strong separated flow limiting local power output. Generally, there are two methods of controlling the output power under stall control. The first approach is passive stall control, in which the fixed-blade pitch is chosen so that the turbine reaches its maximum or rated power at the desired wind speed. A wind turbine with this control suffers from the disadvantage of uncertainties in its post-stall aerodynamic behavior, which can result in inaccurate predictions of the power level and blade loading at the rated wind speed and above. The other approach is active stall control, which achieves power limitation above the rated wind speed by changing the blade pitch angle to a larger, so-called critical aerodynamic angle of attack. A significant advantage of this control is that the blade remains essentially stalled above the rated wind speed, so that gust slicing results in much smaller cyclic fluctuations in blade loads and output power [21]. Because the increasing wind speeds have the same effect as increasing the pitch angle in the negative direction, an appropriate angle of attack corresponding to the rated wind speed is very important in designing a small-sized wind turbine blade operating in the stallregulated method. Fig. 16 shows the distribution of lift force to drag force ratio per unit span at each r/r location for various wind speeds. This value is acquired by solving the simultaneous equations of Eqs. (11) and (12). The δq and δt can be easily calculated, rather than obtaining δl and δd due to the blade twist angle in the orthogonal coordinates system, as already explained in Fig. 8. For the 7 m/s wind speed, the ratio is 0.17 and at r/r = 0.05 and 0.85, respectively, corresponding to Reynolds numbers and The calculated values for a given Reynolds number and angle of attack are somewhat low compared with the 2-D experimental data. This is attributed to a limitation of the present fully turbulent models without transition effects, which have considerable difficulty in exactly predicting a drag force [22]. Therefore, these amplification errors in drag and lift forces cause the value to be inaccurately calculated. In addition, it is confirmed that the ratio decreases with increasing wind speeds over the entire region. This means that the δd increment is much larger than δl when the wind speed increases, owing to the stall phenomenon at wind speeds above 7 m/s. (11) (12) Fig. 17 compares the measured and computed shaft torques [7, 8]. The rotor blade used in this study adopts the stallregulated method, whose torque is regulated by stall generation throughout its range at wind speeds above 10 m/s. As shown by the comparison of these results, the torque does not increase from its value at a wind speed of 10 m/s, and is controlled in the range between 10 m/s and 25.1 m/s, thus gener-

11 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~ Conclusions Fig. 17. Comparison of measured and computed shaft torques. Fig. 18. Comparison of measured and computed power coefficient. ating the constant torque required for the output power. The computed and measured torques show a similar tendency, with an error range between a minimum of 0.08% and a maximum of 24.7%. Fig. 18 shows a comparison of the measured and computed power coefficients for various wind speeds [7, 8]. The power coefficient is defined by Eq. (13). The maximum achievable value of the power coefficient is 0.593, which is known as the Betz limit. To date, no wind turbine has been designed which is capable of exceeding this limit. The power coefficient of wind turbines currently in operation is lower than 0.593, and that of the recently commercialized small- or middle-sized wind turbine is around In the NREL Phase VI wind turbine, the calculated power coefficient is about 0.35 at a TSR of 5.41, corresponding to 7 m/s, and this agrees with the experimental results to within 0.08%. (13) (1) It was observed that the 3-D stall begins to generate near the blade root at a wind speed of 7 m/s. This is attributed to having a higher angle of attack than the stall angle of attack, and a maximum thickness of 47% of the chord length. Therefore, in the case of a stall-regulated method, it is judged that root design approaches considering the appropriate selection of the angle of attack and the thickness are very important in order to generate the stall on the blade root. (2) Through analysis of existing experimental data, the angle of attack corresponding to the maximum lift-to-drag ratio was found to be in the vicinity of 6, regardless of the Reynolds number. This fact will assist designers in performing the pitched-controlled or stall-regulated design of a rotor blade. The calculated lift force to drag force ratio for a given Reynolds number and angle of attack were somewhat low compared with the 2-D experimental data. This is attributed to a limitation of the present fully turbulent models without transition effect. (3) It was confirmed that 3-D stall that has separated from the blade root slowly generates and, as the wind increases, spreads toward the tip. This allows the rated output power to remain constant. This wind turbine system is controlled by a flow phenomenon called a stall-regulated method (4) The computed torque and power coefficients showed considerably good agreement with the experimental measurements, to within 0.08% at a TSR of 5.41, which corresponds to 7 m/s. (5) Through a clear understanding of aerodynamic characteristics of a small-sized NREL Phase VI wind turbine, it is expected that this useful aerodynamic data will be made available to designers as guidance in designing stall-regulated wind turbine blades in the development phase of small-sized wind turbine systems in the future. Acknowledgments This work is the outcome of a Manpower Development Program for Marine Energy by the Ministry of Land, Transport and Maritime Affairs (MLTM). Nomenclature β α θ c N g V in λ ω r R C P : Twist angle : Angle of attack : Flow angle : Local chord length : Grid number : Inflow wind speed : Tip speed ratio (TSR) : Rotational speed : Radial position : Radius of blade : Pressure coefficient

12 92 J.-O. Mo and Y.-H. Lee / Journal of Mechanical Science and Technology 26 (1) (2012) 81~92 P 0 P V r Ρ X References : Absolute pressure : Ambient pressure : Local Relative flow velocity : Dimensionless length : Length in chordwise direction [1] H. Erich, Wind turbines, Springer Verlag (2000) [2] E. P. N. Duque, C. P. van Dam and S. C. Hughes, Navier- Stokes simulations of the NREL combined experiment phase II rotor, AIAA Paper, (1999). [3] G. Xu and L. N. Sankar, Computational study of horizontal axis wind turbines, Journal of Solar Energy Eng, 122 (1) (2000) [4] G. Xu and L. N. Sankar, Effects of transition, turbulence and yaw on the performance of horizontal axis wind turbines, AIAA Paper, (2000). [5] N. N. Sorensen and M. O. L. Hansen, Rotor performance predictions using a Navier-Stokes method, AIAA Paper, (1998). [6] N. N. Sorensen and J. A. Michelsen, Aerodynamic predictions for the unsteady aerodynamics experiment Phase II rotor at the national renewable energy laboratory, AIAA Paper, (2000). [7] D. Simms, S. Schreck, M. Hand and L. J. Fingersh, NREL Unsteady aerodynamics experiment in the NASA-Ames wind tunnel: A Comparison of predictions to measurements, National Renewable Energy Laboratory, NREL/TP (2001). [8] M. M. Hand, D. A. Simms, L. J. Fingersh, D. W. Jager, J. R. Cotrell, S. Schreck and S. M. Larwood, Unsteady aerodynamics experiment phase VI: Wind tunnel test configurations and available data campaigns, National Renewable Energy Laboratory, NREL/TP , December (2001). [9] D. C. Wilcox, A half centry historical review of the k-ω model, AIAA Paper, (1991). [10] F. R. Menter, Performance of popular turbulence models for attached and separated adverse pressure gradient flows, AIAA Journal, 30 (1992) [11] F. R. Menter, Zonal two equation k-ω turbulence models for aerodynamic flows, AIAA Paper, (1993). [12] F. R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA Journal 32 (8) (1994) [13] ANSYS FLUENT 12.0 Theory Guide [14] D. C. Wilcox, Turbulence modeling for CFD, Second Edition (2000). [15] G. P. Corten, Inviscid stall model, Proceedings of EWEC, Denmark (2001) [16] B. S. Kim, J. H. Kim, Koji KIKUYAMA, P. P. J. O. M. van rooij and Y. H. Lee, 3-D numerical predictions of horizontal axis wind turbine power characteristics of the scaled delft university T40/500 model, the Fifth JSME-KSME Fluids Engineering Conference (2002) [17] S. P. Breton, Study of the stall delay phenomenon and of wind turbine blade dynamics using numerical approaches and NREL's wind tunnel tests, Doctoral thesis, June [18] F. R. Menter, R. Langtry and S. Völker, Transition modelling, for general purpose CFD codes, Flow Turbulence Combust, 77 (2006) [19] S. Wangner, R. Bareis and G. Guidati, Wind turbine noise, Springer-Verlag, Berlin (1996). [20] J. O. Mo and Y. H. Lee, Numerical simulation for prediction of aerodynamic noise characteristics on a HAWT of NREL Phase VI, Journal of Mechanical Science and Technology, 25 (5) (2011) [21] T. Burton, D. Sharpe, N. Jenkins and E. Bossanyi, Wind energy handbook. [22] C. L. Rumsey and R. T. Biedron, Computation of flow over a drag prediction workship wing/body transport configuration using CFL3D, Langley Research Center, NASA/TM , December (2001). Jang-Oh Mo is currently a visiting researcher at the University of Adelaide in Australia. He received his B.E, M.E degrees and Ph.D in Mechanical Engineering from the Korea Maritime University in 2001, 2003 and 2009, Korea. He worked as a CFD consulting engineer for 6 years from 2004 to 2009 in ANSYS KOREA branch (ATES Inc., Seoul, Korea). His research interests include wind farm optimal layout, design and aerodynamic noise of a wind turbine blade for an on and off-shore wind turbine blade. Young-Ho Lee received his B.E. and M.E. degrees from Korea Maritime University, Korea. He received his Ph.D in Engineering from the University of Tokyo, Japan. Dr. Lee is currently a Professor at the Division of Mechanical and Energy System, Korea Maritime University. His research interests include ocean energy, wind energy, small hydro power, fluid machinery, PIV, and CFD.