- Email: [email protected]
Large-eddy simulation and wind-tunnel measurement of aerodynamics and aeroacoustics of a horizontal-axis wind turbine
Renewable Energy 77 (2015) 351e362
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Large-eddy simulation and wind-tunnel measurement of aerodynamics and aeroacoustics of a horizontal-axis wind turbine Kun Luo a, b, *, Sanxia Zhang b, Zhiying Gao a, c, Jianwen Wang a, c, Liru Zhang a, c, Renyu Yuan b, Jianren Fan b, Kefa Cen b a b c
School of Energy and Power Engineering, Inner Mongolia University of Technology, Huhhot 010051, China State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China Key Laboratory of Wind and Solar Power Energy Utilization Technology Ministry of Education and Inner Mongolia Construction, Huhhot 010051, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 May 2014 Accepted 8 December 2014 Available online
Large-eddy simulation of the whole three-dimensional vortex dynamics and noise radiation around a horizontal-axis wind turbine has been studied and analyzed together with wind-tunnel experimental measurement. A computational framework that takes into account of the true shape of the wind turbine blade geometry for calculating the aerodynamics and aeroacoustics is developed and validated against the experimental data. The LES results generally agree well with the experimental data in terms of both the aerodynamics and aeroacoustics statistics. The formation and development of the complex threedimensional wake vortexes are captured and analyzed, and the aerodynamic noise is further studied based on the flow field using the FWeH method. It is found that noise generation and acoustic radiation are closely associated with the generation and evolution of these vortex structures. The blade tip region is the main resource area of the aero-noise and the acoustic radiation intensity of the rotor decreases rapidly downstream. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Large-eddy simulation Wind-tunnel measurement Horizontal-axis wind turbine Aerodynamics Aeroacoustics
1. Introduction The aerodynamic research and wake flow analysis for wind turbines have contributed a lot to the success of modern wind energy utilization [1e3], and technologies for wind energy conversion have significantly advanced during the past few decades. The Horizontal-Axis Wind Turbine (HAWT) is the least expensive and clean way to make use of the wind power. As the interaction between the wind and the blade influences the efficiency, the design and development of more efficient and reliable wind turbines rely heavily on accurate prediction of aerodynamic behaviors and can benefit significantly from a good knowledge of parameters related to the wake [4,5]. However, some environmental and social problems still remain unsolved, and the wind turbine noise becomes the most serious issue among them [6]. The wind turbine noise, especially the aerodynamic noise is even hindering the global use of the wind turbine. It is thus very important to understand the noise source mechanisms, depending on the rotor
* Corresponding author. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China. Tel./fax: þ86 571 87951764. E-mail address: [email protected] (K. Luo). http://dx.doi.org/10.1016/j.renene.2014.12.024 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
aerodynamic characteristics and the operating conditions for a wide range of the rotor's frequency spectrum [7,8]. Methods of different levels of complexity to investigate the aerodynamic and aeroacoustic behaviors of a wind turbine rotor have been developed. These methods include the Blade Element Momentum (BEM) theory, the wind tunnel experiment, the field experiment and the computational fluid dynamics (CFD) [1]. The BEM theory that proposed by Glauert is the most classical approach for the aerodynamic design of wind turbine [9]. However, it requires adding a number of amendments to the project [10]. The BEM theory occupies fewer resources in the calculation and it would be relatively more rapid, but it cannot get the details of the blade surface pressure distribution, and cannot provide accurate aerodynamic load data for the structural analysis of wind turbine blades. On the contrary, CFD simulation is a cheap and efficient way to provide valuable quantitative insight into the aerodynamic and aeroacoustic behaviors of flow around wind turbine. It has helped the industry become more efficient and productive and has enabled new designs and levels of efficiency not possible before [11,12]. CFD modeling and experiment have both advantages and disadvantages. They can be complementary to each other and one can expect more effective understanding of the phenomenon. The CFD
352
K. Luo et al. / Renewable Energy 77 (2015) 351e362
method is useful to utilize as an efficient tool for the wind turbine and can complement experimental data that is difficult to measure. It is also possible to obtain useful CFD results based on verification and validation by the experimental results. Moreover, the verified model can be used to deliver correct results for any arbitrary condition without considering the limitations of experimental equipment, measurement errors and problems with measurement systems. For CFD simulations, the Reynolds-averaged NaviereStokes simulation (RANS), the large-eddy simulation (LES), and the direct numerical simulation (DNS) are three commonly used approaches with different accuracies. The RANS approach, especially the k-ε turbulence model, is traditionally used with the advantages of robustness, economy, and reasonable accuracy for a wide range of turbulent flows. DNS solves the NaviereStokes equations without any closure model, but is not feasible for practical engineering problems involving high Reynolds number flows because of high demand of computational resources. LES is developed as an intermediate approach between DNS and RANS. The general idea is that the large, non-universal scales of the flow are computed explicitly, while the small scales are modeled [13]. LES has been proven to be a successful approach to simulate unsteady flows around airfoils [14], but only recently have there been some efforts to apply LES to simulate wind turbine wakes [15e17]. It is more accurate than RANS and requires substantially finer meshes than those typically use the k-ε turbulence model. So time-accurate LES solver can capture the noise-generating region well and hence becomes a very promising method for predicting noise. Although there have been some aerodynamic studies of wind turbine by means of LES or experimental measurement independently, it is still difficult to fully calculate both the noise source and its propagation to the far-field, and as yet no detailed and open experimental data for wind turbine noise is available for model validation. In the present work, both the aerodynamic and aeroacoustic characteristic of a horizontal-axis wind turbine is studied with the LES and wind tunnel experiment. The main objective is to develop a LES framework for simulations of aerodynamics and aeroacoustics around a horizontal-axis wind turbine and improve the fundamental understanding of turbulenceenoise interaction. The wind turbine used in the simulation is exactly the same as the real model measured in the Key Laboratory of Renewable Energy in Inner Mongolia University of Technology for LES validations.
Fig. 1. B1/K2 wind tunnel and the wind turbine.
the wind blade rotational plane is vertical to the inlet flow direction. Fig. 2 shows the planes illuminated by the laser light sheet. They are vertical to the wind turbine rotation axis. In the PIV results, the coordinates of the blade tip is (224.1 mm, 57.4 mm). The size of the PIV picture is 257.34 mm 190.38 mm and the resolution is 1200 1600 pixels [20]. PIV measurement accuracy depends on the accuracy of the measurement of the particle displacement and the control accuracy of the time interval of two images. In the monitoring of wind speed during the present experimental process, the velocity uncertainty is about 5%. 2.2. Acoustic radiation measurement The acoustic radiation test is conducted in the same section of the wind tunnel with the same wind turbine. Acoustic analysis requires detailed records of sound information. The microphone
2. Wind tunnel experiment 2.1. PIV measurement Particle image velocimetry (PIV) is an advanced non-contact flow measurement technology that became applicable in the late 1990s [18]. It has been applied to explore research of wind turbine wakes [19]. In the present work, PIV measurement of a fixed area in the near wake of a horizontal-axis wind turbine has been done in the Key Laboratory of Renewable Energy in Inner Mongolia University of Technology. The experiment is conducted in the open section of the wind tunnel using the phase-locked periodic sampling method. The B1/ K2 wind tunnel used in the experiment is shown in Fig. 1, together with the wind turbine and the CCD camera. The diameter of the open test section of the wind tunnel is 2.04 m and the maximum steady wind speed is 20 m/s. The wind turbine model is a NACA4415 horizontal-axis wind turbine with three blades. Its blade has a diameter of D ¼ 1.4 m and the rated wind speed is 8 m/s. The rated tip-speed ratio l is 5 and the rated power is 100 W in this case. The tail is removed in order to achieve stable experimental conditions. The wind turbine is fixed to the system to ensure that
Fig. 2. PIV testing sketch.
K. Luo et al. / Renewable Energy 77 (2015) 351e362
353
can transfer the sound pressure into the electrical signal that can be recognized by the computer. MP201 microphone is applied in the experiment as shown in Fig. 3. Background noise is measured before the experiment to remove its influence. To ensure the reliability of the acoustic test, two different measuring-point arrangements are applied. In the first arrangement, the measuring-point is located in the horizontal and vertical lines of the central plane which is vertical to the rotational plane, as shown in Fig. 4(a). The tip of one blade is located in the point o. The distance between two points along one line is 10 cm. There are 10 points in the horizontal line and 14 points in the vertical line. In the second arrangement, the frequency signal is measured along the corresponding test line as shown in Fig. 4(b). Each line has 14 points and there is 10 cm distance between each point.
where D is the fluid domain, and G is the filter function that determines the scale of the resolved eddies. For incompressible flows, filtering the NaviereStokes equations, one obtains
3. Large-eddy simulations
sij ≡ m
3.1. Flow configuration
3.2. Mathematical models 3.2.1. The LES approach In LES, large eddies are resolved directly, while small eddies are modeled. The governing equations employed for LES are obtained by filtering the time-dependent NaviereStokes equations in either wave-number space or physical space. A filtered variable (denoted by an overbar) is defined by
Z
fðx0 ÞGðx; x0 Þdx0
D
(2)
and
v v v ðrui Þ þ rui uj ¼ vt vxj vxj
vsij m vxj
!
vp vtij vxj vxj
(3)
where sij is the stress tensor due to molecular viscosity defined by
"
vui vuj þ vxj vxi
!#
2 vu m l dij 3 vxl
(4)
and tij is the subgrid-scale stress defined by
To simulate the experimental wind turbine as real as possible, the flow configuration and computation domain are taken exactly the same as that in the experiments, as shown in Fig. 5. The axial distance is 7.68 m which is the length from the exit of the wind tunnel to the end of the room. The horizontal and vertical length is 5.1 m and 5.3 m, respectively. The wind turbine is placed in the middle of the horizontal line across the rotational plane. The origin of the coordinate axes is in the middle of the blades, which is 1.71 m from the ground and 0.78 m from the exit of the wind tunnel. The left and right wall, the roof and the ground are set to be the wall boundary condition.
fðxÞ ¼
vr v þ ðrui Þ ¼ 0 vt vxi
(1)
tij ≡rui uj rui uj
(5)
The subgrid-scale stresses resulting from the filtering operation are unknown, and require modeling. They can be modeled as [21]:
1 tij tkk dij ¼ 2mt Sij 3
(6)
where mt is the subgrid-scale turbulent viscosity. The isotropic part of the subgrid-scale stresses tkk is not modeled, but added to the filtered static pressure term. Sij is the rate-of-strain tensor for the resolved scale defined by
1 vui vuj Sij ≡ þ 2 vxj vxi
! (7)
In the SmagorinskyeLilly model, the eddy-viscosity is modeled by
mt ¼ rL2s S
(8)
qffiffiffiffiffiffiffiffiffiffiffiffiffi where Ls is the mixing length for subgrid scales and S≡ 2Sij Sji .Ls is computed using
Ls ¼ min kd; Cs V 1=3
(9)
n constant, d is the distance to the closest where k is the von K arma wall, Cs is the Smagorinsky constant, and V is the volume of the computational cell. 3.2.2. The Ffowcs Williams and Hawkings model The Ffowcs Williams and Hawkings (FWeH) equation is essentially an inhomogeneous wave equation that can be derived by manipulating the continuity equation and the NaviereStokes equations. The FWeH equation can be written as [22]:
1 v2 p0 v2 V2 p 0 ¼ Tij Hðf Þ 2 2 vx vx a0 vt i j v
Pij nj þ rui ðun vn Þ dðf Þ vxi v þ f½r0 vn þ rðun vn Þdðf Þg vt
where
Fig. 3. The microphone for measurement of noise.
ui ¼ fluid velocity component in the xi direction un ¼ fluid velocity component normal to the surface f ¼ 0
(10)
354
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 4. Measuring-point arrangements for noise measurement. (a) The first measuring-point arrangement (b) The second measuring-point arrangement.
vi ¼ surface velocity components in the xi direction vn ¼ surface velocity component normal to the surface d(f) ¼ Dirac delta function H(f) ¼ Heaviside function 0
Pij ¼ pdij m
0
p is the sound pressure at the far field (p ¼ pp0).f ¼ 0 denotes a mathematical surface introduced to “embed” the exterior flow problem (f > 0) in an unbounded space, which facilitates the use of generalized function theory and the free-space Green function to obtain the solution. The surface (f ¼ 0) corresponds to the source (emission) surface, and can be made coincident with a body (impermeable) surface or a permeable surface off the body surface. nj is the unit normal vector pointing toward the exterior region (f > 0),a0 is the far-field sound speed, and Tij is the Lighthill stress tensor, defined as
" # vui vuj 2 vuk þ dij vxj vxi 3 vxk
(12)
The free-stream quantities are denoted by the subscript 0. The solution to Equation (10) is obtained using the free-space Green function (d(g)/4pr). The complete solution consists of surface integrals and volume integrals. The surface integrals represent the contributions from monopole and dipole acoustic sources and partially from quadrupole sources, whereas the volume integrals represent quadrupole (volume) sources in the region outside the source surface. In this wind turbine case, the flow is low subsonic and the source surface encloses the source region, and the contribution of the volume integrals becomes small. So the volume integrals are dropped. Thus, we have
! ! ! p0 ð x ; tÞ ¼ p0T ð x ; tÞ þ p0L ð x ; tÞ Tij ¼ rui uj þ Pij a20 ðr r0 Þdij
(11)
Pij is the compressive stress tensor. For a Stokesian fluid, this is given by
(13)
where
3 2 r0 U_ n þ Un_ ! 4 5dS 4pp0T ð x ; tÞ ¼ rð1 Mr Þ2 f ¼0 o n Z "r Un r M_ r þ a Mr M 2 # 0 0 þ dS r 2 ð1 Mr Þ3 Z
(14)
f ¼0
! 4pp0L ð x ; tÞ
1 ¼ a0 þ
Z " f ¼0
1 a0
L_r
#
Z "
Lr LM
#
dS þ dS rð1 Mr Þ2 r 2 ð1 Mr Þ2 f ¼0 o n Z "L_r r M_ r þ a Mr M 2 # 0 dS r 2 ð1 Mr Þ2
f ¼0
(15) where
Ui ¼ vi þ Fig. 5. Flow configuration and computational domain.
r ðu vi Þ r0 i
(16)
K. Luo et al. / Renewable Energy 77 (2015) 351e362
355
The various subscripted quantities appearing in Equations (14) and (15) are the inner products of a vector and a unit vector ! c ! implied by the subscript. For instance, Lr ¼ L $ r ¼ Li ri and ! ! ! ! Un ¼ U $ n ¼ Ui ni , where r and n denote the unit vectors in the radiation and wallenormal directions, respectively. The dot over a variable denotes source-time differentiation of that variable.
experiment. The averaged wind velocity coming out of the wind tunnel is about 8 m/s, and the angular-velocity of the wind turbine blade is 545 rpm. The computational domain is divided into two parts: the internal rotating field and the external relatively stationary flow field. The interfaces are set to transfer data between the rotational and stationary parts. Coupled problems between the two parts have a great influence on the accuracy of numerical simulation. In the present study, the sliding mesh model is used to account for the rotation of the blades. The computational domain is discretized by about 2.86 million cells. Finer mesh is used on the whole rotor surface and gradually coarsens as the distance from the blades increases. It has been checked that the quality of the mesh meets the needs of the LES calculation. Another mesh of about 6 million cells is also tested and it is found that there is no obvious difference, which means that 2.86 million cells are enough for the present LES simulation.
3.3. Numerical details
4. Results and analysis
The flow around wind turbines, even in very large ones, is still essentially incompressible with Mach numbers based on blade tip speed almost never exceeding 0.25, which justifies the use of incompressible fluid solvers for most wind turbines. In the present work, an incompressible Navier Stokes solver is applied. The LES SmagorinskyeLilly model is used for the simulation. The PRESTO (PREssure STaggering Option) scheme [21] and the bounded central differencing format are used for the pressure and momentum discretization, respectively. The Pressure-Implicit with Splitting of Operators (PISO) [21] is used for the pressureevelocity coupling, and the second order implicit scheme is used for time integration. The no-slip boundary condition is applied for the wall boundary condition. To approach the experimental conditions, the inlet flow velocity is described by
4.1. Aerodynamic characteristics
b j þ rui ðun vn Þ Li ¼ Pij n
(17)
! ! p0T ð x ; tÞ and p0L ð x ; tÞ are referred to as thickness and loading terms, respectively. The square brackets in Equations (14) and (15) denote that the kernels of the integrals are computed at the corresponding retarded times (t), defined as follows, given the observer time (t), and the distance to the observer (r),
t¼t
r a0
Uin ¼ Uc þ
(18)
Uj Uc y þ H=2 y H=2 tanh tanh 2d 2d 2
(19)
where Uc and Uj represent the co-flow and the mean inflow velocity respectively. H is the entrance diameter of 2.04 m. d ¼ 0.05H. This prescribed inlet velocity profile is shown in Fig. 6. When y is greater than H/2, the speed is set to be zero. Furthermore, a turbulence intensity of 4% is imposed on the inflow according to the
Fig. 6. Inlet velocity profile.
4.1.1. Comparisons between LES and PIV In order to demonstrate the reliability of the aerodynamic simulations, comparisons between the LES results and the PIV experimental data have been conducted in this section. By observing the vertical plane which contains the PIV measuring field, the similarities can be found between the LES results and the PIV experimental data, as shown in Fig. 7. Fig. 7(b) displays the velocity magnitude contours of the tip vortexes in the shooting area of the experiment, and Fig. 7(a) displays the results of the LES in the vertical plane, in which the shooting area is marked roughly. The same tip vortex region has been found in both the LES and the experimental results. The speed in the increased area is higher than the inlet speed in the exit of the wind tunnel, and the maximum value exceeded 18 m/s. While the speed of the decreased area is lower than the inlet speed, with a minimum value close to 0 m/s. We further quantitatively compare the LES results with the experimental data. Take the first tip vortex core (shown in Fig. 7(b)) in the downstream of the wind turbine as a reference point to observe the instantaneous distribution of the axial and radial velocity. The distribution of the axial velocity U of the line which goes through the point and parallel to the z-axis is shown in Fig. 8(a), with the axial velocity U as abscissa and the observation point as yaxis. Y is the vertical distance from the viewpoint to the rotational axis. R is the radius of the wind rotor. Y/R represents the relative position. The range of the observation point is 0.94e1.13Y/R. The yaxis value 1 corresponds to the maximum circumferential position of the rotor rotating surface (the position of the blade tip). It is clear that the LES results are in good agreement with the experiment data. Outward from the central wake region, As the Y/R increases, the loss of axial velocity increases and reaches an extreme value near the tip (Y/R ¼ 0.98). Within a short distance across the tip (Y/ R ¼ 1.01), the axial velocity reaches the extreme value in the increased area. The two extreme points are symmetrical about the reference point selected. As the Y/R value continues to increase, the speed obtained becomes lower, and there is a trend towards integration with the mainstream. The distribution of the radial velocity along the line which goes through the point and parallel to the xaxis is shown in Fig. 8(b). X is the horizontal distance from the viewpoint to the rotational plane. There are two extreme points symmetrical about the reference point selected which is similar to Fig. 8(a). As the X/R value continues to reduce, the loss of speed increases, and tends to be steady with only small fluctuations. As mentioned above, the speed increase and decrease are attributed to
356
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 7. Velocity magnitude contour of the tip vortexes. (a) LES results (b) PIV results.
the tip vortex inducement. In the tip vortex induced region, the impact on the structure of the wake is dominated by the axial velocity while the radial velocity effect is relatively small. The mean velocity has also been compared for further validation. As the phase-locked periodic sampling method has been used in the PIV experiment, we use the same averaging method in our simulation for velocity statistics. Fig. 9 shows the comparison of the mean velocity in the pictured area with a phase angle of 100 . It can be seen that the distribution of the PIV mean velocity is consistent with that of the LES. The same tip vortex region has been found in both the LES and the PIV experiment results. In the tip vortex induced region, a symmetrical region of velocity magnitude is formed. Because of the presence of fluid viscosity, the tip vortex rotation increases and reduces the speed of these regions. The above comparisons between LES and PIV demonstrate that the present LES framework is reliable and lays a solid foundation for further study. 4.1.2. Vortex structures The blade rotation region is the work area of the wind turbine, and the air flow pattern in it is very complex. As the tip vortex, the attached vortex, the vortex behind the tower and the center vortex phenomena are formed in the rotation region, the analysis of the
flow characteristic in the rotation region is necessary. The circumferential distribution of the physical field near the upstream of the wind turbine obviously has a cycle symmetry phenomenon. Fig. 10 shows the different vortices in the wind turbine flow field identified by l2 criteria [23]. After the attached vortex, which distribute along the blade span, fall off the rim of the blade, it rapidly curled into the vortex surface. Meanwhile, the tip vortex is generated by the pressure difference between the suction side and pressure side of the blade tip and moved downstream, forming the near wake structure which has a concentrated vortex form. The near-wake structure is characterized by the tip vortex. Fig. 11 shows some details of the entire flow field through the velocity magnitude and vector in the horizontal and vertical planes. Fig. 11(a) and (b) shows the velocity magnitude contours in the horizontal plane (z ¼ 0 plane through the centerline) and the vertical plane (y ¼ 0 plane through the centerline), respectively. The maximum speed that appears at the tip of the blade could be 42 m/ s. The scale range has been reduced to 0e10 m/s in order to facilitate observation. The movement of the tip vortex can induce axial velocity at the blade, which will affect the airflow speed in front of the turbine, as shown in Fig. 11(a) and (b). Due to the momentum loss and vortex inducement, velocity of the internal flow field in the downstream of the wind turbine has been reduced (with the largest
Fig. 8. Velocity distribution along the x and z-axis passing through the reference point. (a) Axial velocity U profiles (b) Radial velocity V profiles.
K. Luo et al. / Renewable Energy 77 (2015) 351e362
357
Fig. 9. Comparison of mean velocity between PIV and LES. (a)Mean experiment-u velocity. (b)Mean simulation-u velocity. (c)Mean experiment-v velocity. (d)Mean simulation-v velocity.
Fig. 10. Vortices in the near wake of the wind turbine.
reduction at the centerline at hub height), while the velocity of the external flow field increased. The speed change region extends into the upstream of the wind blades, forming a large velocity gradient region around the wind turbine. However the speed contour expands gradually, which indicates that the flow takes a long time to revert to its original velocity after passing through the wind turbine. The complex unsteady wake structure includes the central wake region, the outside mainstream region, and the tip vortex induced region. This is usually looked upon as the “wake” behind the wind turbine, and the effect of the wake is still noticeable even in the far wake. In fact the flow of the wind turbine wake is a typical turbulent flow dominated by the vortex flow. Wake region of the wind turbine can be divided into the near wake and the far wake. In the near wake the vortex line changes obviously and the wind speed decreases, while in the far wake, the center wake vortex is visible and the tip vortex is gradually dissipated to be steady. These structural features of the near wake flow field are the basis of the horizontal axis wind turbine aerodynamic performance design and characteristics prediction [24]. In Fig. 11(a) and (b) the spiral tubular vortex generated by the blade tip (the tip vortex as shown in Fig. 10) can be observed, so as
358
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 11. Distribution of velocity magnitude and vector at different planes. (a) Velocity magnitude in the horizontal plane, (b) Velocity magnitude in the vertical plane, (c) Velocity vector in the horizontal plane, (d) Velocity vector in the rotational plane.
the position of the vortex core. The tip vortex is generated from the tip region and then fell off. As the blades continue to rotate, the tip vortexes move downstream. The energy is gradually dissipated and the vorticity magnitude is reduced in the moving process. The vortex concentrated area gradually disappears and a series of vortex structures appear after the wind turbine. In addition, the distribution of the velocity contours is almost axisymmetric at z ¼ 0 plane, however, it's non-axisymmetric at y ¼ 0 plane, which is caused by the influence of the support structure of wind turbine and the ground. So we should be informed that the effects of the nacelle, the turbine tower and the ground condition on the turbulent flow need to be considered when operating the wind farm. Fig. 11(c) and (d) display the magnified velocity vector, in which the velocity magnitude and direction near the blade can be seen more clearly. These are important areas that affect the flow structure in the downstream. The three-dimensional effect of the blade, the differential pressure effect of the pressure surface and the suction side on the tip separated flow, and the air flow motion of rotating in a circular generated by the blades can be seen in Fig. 11(c) and (d). And with these causes the flow continues to spread downstream with concentrated vortex, forming the complex unsteady wake structure mentioned above. The three regions in the near wake can be identified from their different speeds and directions. The maximum speed can be found in the blade tip and the air flow changes its direction around the tip blade. The trail flow of the rotational blade can be seen obviously. It is rotating in the clockwise direction and has relatively high wind speed in the windward side. Between the three blades the value of velocity increased from the blade root to the blade tip. But this order is not
clear near the blade surface. Meanwhile, there is a tendency of separating from the tip in the spanwise direction, which is the characteristic of a three-dimensional rotating flow. Fig. 12(a) shows the mean velocity in the center vertical lines across the wake at x ¼ eR, 0.5R, 2R and 9R. The line x ¼ R represents the inlet condition. It can be seen that the section plane gradually expands and the center area has the maximum speed loss. The second maximum speed loss is in the blade tip (z/R ¼ ±1) where the tip vortex generates. The lines are almost symmetric except the x ¼ 0.5R line that is non-uniform in the lower part because of the influence of the turbine tower. Fig. 12(b) shows the mean velocity in the horizontal lines through the wake at z ¼ 0, R, 1.45R, R, and 1.45R. Each line displays the velocity distribution in and around the rotation area. The z ¼ ±1.45R lines are near the outer boundary of the exit wind tunnel. They reach the maximum velocity around x/R ¼ 1, and then reduce downstream. The lower one z ¼ 1.45R line reduces more than the upper one. The velocity is relatively lower near the center line (line z ¼ 0). The center line and the z ¼ ±R lines all have a velocity increase in the region of x ¼ 2e5R while the z ¼ ±1.45R lines decrease. Combining with Fig. 11, it can be concluded that the tip vortex area forms, moves downstream and dissipates with the evolution of time. The more it moves downstream, the more disturbance and stronger fluctuations the tip vortex receives. 4.1.3. Pressure distribution The above analysis indicates that the tip blade is the important area for producing energy. The energy that the wind turbine can get is closely related to the pressure distribution and change on the
K. Luo et al. / Renewable Energy 77 (2015) 351e362
359
Fig. 12. Mean velocity magnitude in different lines. (a) Center vertical lines across the wake, (b) Center horizontal lines through the wake.
blade surface. Fig. 13 presents the pressure and suction surface respectively. On the pressure surface the pressure magnitude increases from root to tip of the blade and reaches the maximum value at the tip. In the suction side, it's just the opposite. The maximum positive pressure and maximum negative pressure both appear at the tip blade which results in the maximum differential pressure at the tip. Additionally, the pressure is different even on the two sides of the same tip surface. The windward side of both the two surfaces obtain larger aerodynamic load. The higher the differential pressure, the more energy converted, if only the blade is strong enough. The main concern point of improving wind turbine performance and reducing noise should be laid in the tip area. Improving the structure of the tip region, reforming the flow condition, suppressing vortex intensity and increasing the pressure difference between the pressure surface and the suction surface will increase the power output and at the same time reducing wind turbine noise [25]. 4.2. Aeroacoustic characteristics 4.2.1. Comparisons between LES and measurement After the flow field being fully developed, the Ffowcs-Williams & Hawkings model is applied for aero-noise simulation. Based on
transient flow simulation results, time variation of acoustic pressure is calculated. The results will be compared with the experiment data in the form of sound pressure level (SPL). In the first arrangement, the measuring-points are shown in Fig. 4(a), and the results are shown in Fig. 14, which contain the comparison of SPL between the LES results and the experimental data at x ¼ 10 cm, x ¼ 40 cm and y ¼ 20 cm, y ¼ 20 cm lines. The LES results are generally consistent with the experimental data. They have the same trend and the LES results are a little higher than the experiment data in certain region. The region near the blade has higher sound pressure level with the highest value of about 120 dB. It can be seen from the complete data that the region which is marked in Fig. 15 has relatively high SPL value, and the blade tip region is the main resource area of the aero-noise. In the second arrangement, the measuring-points are shown in Fig. 4(b), and the comparisons of SPL between the present LES result and experimental data in the four different test lines are shown in Fig. 16. As can be seen from the figure the distributions of the sound pressure level along different lines obtained by LES generally agree well with those of the experimental data. With the increase of the test line angle, the sound pressure level decreases at the points close to the blade tip. The main resource area of the acoustic radiation is identified around the wind turbine. In each test
Fig. 13. The pressure and suction surface of the blades. (a) The pressure surface, (b) The suction surface.
360
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 14. Comparisons of SPL between LES results and experimental data for the first arrangement. (a) Comparison of SPL at x ¼ 10(cm), (b) Comparison of SPL at x ¼ 40(cm), (c) Comparison of SPL at y ¼ 20(cm), (d) Comparison of SPL at y ¼ 20(cm).
line, the first measuring point close to the wind turbine has the highest SPL value. As a result of the masking effect of the rotating blade and the diffraction of the sound when across the wind turbine, the acoustic radiation intensity of the rotor reduces rapidly with the test point moves downstream. It cannot be ignored that there are some small differences between the LES and experimental results. The small fluctuations in the flow and rotational speed are inevitable in the experimental measurements because vibration, deformation and the vortex shedding position are always fluctuating during wind turbine operation. Furthermore, there is background noise in the experiment and the influence of the wind tunnel aerodynamic noise is estimated in the analysis. 4.2.2. Vortex-noise relationship To further explore the relationship between vortex dynamics and aeroacoustic distribution, the distribution of acoustic noise and the related region of vortices are illustrated in Fig. 17. To facilitate observation, the SPL value at different points around the wind rotor in the LES is processed into contour, as shown in Fig. 17(a). The yaxis represents the rotating plane and the x-axis stands for the axis of rotation. It is clear that the region near the blade has high SPL value which is in accordance with Fig. 15, and the value increases from the center point to the blade tip. This region is interestingly distributed between the central vortex and the tip vortex,
indicating that vortex structures have significant effect on aeroacoustic noise. The sound pressure level decreases fast along the center line in the area near the blade because of the impact of the motor. However, a little far away from the blade it decreases slower
Fig. 15. Schematic diagram of noise generation region.
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 16. Comparison of the sound pressure level in the second arrangement. (a) 0 testing line, (b) 15 testing line, (c) 30 testing line, (d) 45 testing line.
Fig. 17. The contour of the acoustic noise and the related region of vortices. (a) The contour of the acoustic noise, (b) The vortices in the related region.
361
362
K. Luo et al. / Renewable Energy 77 (2015) 351e362
in the center line direction, caused by the impact of the central vortices near the motor as shown in Fig. 17(b). In the tip vortex moving direction, the SPL value also decreases slower, which shows that the radiation of the aerodynamic noise is influenced by the movement of the tip vortex. The maximum SPL value appears in the area between the tip and root of the blade, and is closer to the tip. One may conclude that both the tip vortex and the vortex near the motor generate the noise, and the influence of the blade tip is more significant. The tip vortex can be regarded as a main reason that not only reduces the output power, but also increases the aerodynamic noise and the fatigue loads. 5. Conclusions Three-dimensional vortex dynamics and aeroacoustic characteristics around a horizontal-axis wind turbine have been investigated by LES and wind-tunnel measurement. In general, the LES results are in good agreement with the experimental data, indicating that the present models and methodology are capable of accurately reproducing near wake characteristics (including velocity, pressure and vortices) and noise generation of the wind turbine. The near wake has complex vortex structures, including the tip vortex, the attached vortex, the vortex behind the tower and the center vortex structures which can be well captured by the LES. Noise generation and acoustic radiation are closely associated with the generation and evolution of these vortex structures, and both of them are influenced by the periodic rotation of the wind turbine. The blade tip region is the main resource area of the aero-noise and the acoustic radiation intensity of the rotor decreases rapidly with the test point moves downstream. These results indicate that more attentions should be paid to the tip area to improve wind turbine performance and reduce noise. Acknowledgments This work is financially supported by the Inner Mongolia Autonomous Region Open Major Basic Research Project (Grant No. 20120905) and the National Natural Science Foundation of China (Grant No. 51366010). We are grateful to that. References [1] Hu Danmei, Tian Jie, Du Zhaohui. Measurement and analysis of wake behind horizontally orientated air turbines. J Power Eng 2006;26(5):751e60. [2] Hu Danmei, Hua Ouyang, Du Zhaohui. An experimental study of the wake structure of a model horizontal-axis wind turbine. Acta Energiae Solaris Sin 2006;27(6):606e12.
[3] Krogstad Per-Åge, Eriksen Pål Egil. “Blind test” calculations of the performance and wake development for a model wind turbine. Renew Energy 2013;50: 325e33. [4] Whale J, Anderson CG, Bareiss R, Wagner S. An experimental and numerical study of the vortex structure in the wake of a wind turbine. J Wind Eng Ind Aerodynamics 2000;84(1):1e21. [5] Daichin, Kang Wen, Zhao Li-li. PIV measurements of the near-wake flow of an airfoil above a free surface. J Hydrodynamics 2007;19(4):482e7. [6] Johansson L. Summary of IEA topical expert meeting on noise immission. 2000. [7] Brentner Kenneth S, Farassat F. Modeling aerodynamically generated sound of helicopter rotors. Prog Aerosp Sci 2003;39(2e3):83e120. [8] Fragias AP, Spyropoulos AI, Margaris DP, Papanikas DG. Coupled aerodynamic and aeroacoustic numerical model for helicopter main rotor blades. In: Proceedings of the fourth GRACM congress on computational mechanics, vol. 2; 2002. p. 643e50. Patras-Greece [II]. [9] Martin Hansen OL. Aerodynamics of wind turbines. In: Earthscan in the UK and USA. 2nd ed. 2008. [10] Larsen JW, Nielsen SRK, Krenk S. Dynamic stall model for wind turbine airfoils. J Fluids Struct 2007;23:959e82. [11] Wang Ji-feng, Piechna Janusz, Müller Norbert. A novel design of composite water turbine using CFD. J Hydrodynamics 2012;24(1):11e6. [12] Saavedra-Moreno B, Salcedo-Sanz S, Paniagua-Tineo A, Prieto L, PortillaFigueras A. Seeding evolutionary algorithms with heuristics for optimal wind turbines positioning in wind farms. Renew Energy 2011;36:2838e44. -Agel Fernando, Wu Yu Ting, Lu Hao, Conzemius Robert J. Large-eddy [13] Porte simulation of atmospheric boundary layer flow through wind turbines and wind farms. J Wind Eng Ind Aerodyn 2011;99:154e68. [14] LESFOIL: large eddy simulation of flow around a high lift airfoil. In: €hlich J, Leschziner MA, Mellen C, Rodi W, editors. Davidson L, Cokljat D, Fro Notes on numerical fluid mechanics, vol. 83. Springer Verlag; 2003. -Agel Fernando. Large-eddy simulation of wind-turbine [15] Wu Yu-Ting, Porte wakes: evaluation of turbine parametrisations. Boundary Layer Meteorol 2011;138:345e66. [16] Rolland S, Newton W, Williams AJ, Croft TN, Gethin DT, Cross M. Simulations technique for the design of a vertical axis wind turbine device with experimental validation. Appl Energy 2013;111:1195e203. [17] Mo Jang-Oh, Choudhry Amanullah, Arjomandi Maziar, Lee Young-Ho. Large eddy simulation of the wind turbine wake characteristics in the numerical wind tunnel model. J Wind Eng Ind Aerodyn 2013;112:11e24. [18] Adrian RJ. Twenty years of particle image velocimetry. Exp Fluids 2005;39(2): 159e69. [19] Grant I, Mo M, Pan X, Parkin P, Powell J, Reinecke H, et al. An experimental and numerical study of the vortex filaments in the wake of an operational horizontal-axis wind turbine. J Wind Eng Ind Aerodyn 2000;85(2):177e89. [20] Gao Zhiying, Wang Jianwen, Dong Xueqing, Zhang Liru. Experimental study of the near wake flow field structure of the horizontal axis wind turbine. Acta Energiae Solaris Sin 2011;32(6):897e900 [in Chinese]. [21] FLUENT 6.3 documentation. USA: Fluent Inc; 2006. [22] Ffowcs-Williams JE, Hawkings DL. Sound generation by turbulence and surfaces in arbitrary motion. Philos Trans R Soc Lond A 1969;264(1151): 321e42. [23] Jeong J, Hussain F. On the identification of a vortex. J Fluid Mech 1995;285: 69e94. [24] Ebert PR, Wood DH. The near wake of a model horizontal-axis wind turbine-I. Experimental arrangements and initial results. Renew Energy 1997;12(3): 225e43. [25] Wang Jianwen, Jia Ruibo, Wu Keqi. Numerical simulation of dynamic amplification characteristics of wind turbine with winglets in the blade tip. Acta Energiae Solaris Sin 2007;28(1):55e61 [in Chinese].
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Large-eddy simulation and wind-tunnel measurement of aerodynamics and aeroacoustics of a horizontal-axis wind turbine Kun Luo a, b, *, Sanxia Zhang b, Zhiying Gao a, c, Jianwen Wang a, c, Liru Zhang a, c, Renyu Yuan b, Jianren Fan b, Kefa Cen b a b c
School of Energy and Power Engineering, Inner Mongolia University of Technology, Huhhot 010051, China State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China Key Laboratory of Wind and Solar Power Energy Utilization Technology Ministry of Education and Inner Mongolia Construction, Huhhot 010051, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 May 2014 Accepted 8 December 2014 Available online
Large-eddy simulation of the whole three-dimensional vortex dynamics and noise radiation around a horizontal-axis wind turbine has been studied and analyzed together with wind-tunnel experimental measurement. A computational framework that takes into account of the true shape of the wind turbine blade geometry for calculating the aerodynamics and aeroacoustics is developed and validated against the experimental data. The LES results generally agree well with the experimental data in terms of both the aerodynamics and aeroacoustics statistics. The formation and development of the complex threedimensional wake vortexes are captured and analyzed, and the aerodynamic noise is further studied based on the flow field using the FWeH method. It is found that noise generation and acoustic radiation are closely associated with the generation and evolution of these vortex structures. The blade tip region is the main resource area of the aero-noise and the acoustic radiation intensity of the rotor decreases rapidly downstream. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Large-eddy simulation Wind-tunnel measurement Horizontal-axis wind turbine Aerodynamics Aeroacoustics
1. Introduction The aerodynamic research and wake flow analysis for wind turbines have contributed a lot to the success of modern wind energy utilization [1e3], and technologies for wind energy conversion have significantly advanced during the past few decades. The Horizontal-Axis Wind Turbine (HAWT) is the least expensive and clean way to make use of the wind power. As the interaction between the wind and the blade influences the efficiency, the design and development of more efficient and reliable wind turbines rely heavily on accurate prediction of aerodynamic behaviors and can benefit significantly from a good knowledge of parameters related to the wake [4,5]. However, some environmental and social problems still remain unsolved, and the wind turbine noise becomes the most serious issue among them [6]. The wind turbine noise, especially the aerodynamic noise is even hindering the global use of the wind turbine. It is thus very important to understand the noise source mechanisms, depending on the rotor
* Corresponding author. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou 310027, China. Tel./fax: þ86 571 87951764. E-mail address: [email protected] (K. Luo). http://dx.doi.org/10.1016/j.renene.2014.12.024 0960-1481/© 2014 Elsevier Ltd. All rights reserved.
aerodynamic characteristics and the operating conditions for a wide range of the rotor's frequency spectrum [7,8]. Methods of different levels of complexity to investigate the aerodynamic and aeroacoustic behaviors of a wind turbine rotor have been developed. These methods include the Blade Element Momentum (BEM) theory, the wind tunnel experiment, the field experiment and the computational fluid dynamics (CFD) [1]. The BEM theory that proposed by Glauert is the most classical approach for the aerodynamic design of wind turbine [9]. However, it requires adding a number of amendments to the project [10]. The BEM theory occupies fewer resources in the calculation and it would be relatively more rapid, but it cannot get the details of the blade surface pressure distribution, and cannot provide accurate aerodynamic load data for the structural analysis of wind turbine blades. On the contrary, CFD simulation is a cheap and efficient way to provide valuable quantitative insight into the aerodynamic and aeroacoustic behaviors of flow around wind turbine. It has helped the industry become more efficient and productive and has enabled new designs and levels of efficiency not possible before [11,12]. CFD modeling and experiment have both advantages and disadvantages. They can be complementary to each other and one can expect more effective understanding of the phenomenon. The CFD
352
K. Luo et al. / Renewable Energy 77 (2015) 351e362
method is useful to utilize as an efficient tool for the wind turbine and can complement experimental data that is difficult to measure. It is also possible to obtain useful CFD results based on verification and validation by the experimental results. Moreover, the verified model can be used to deliver correct results for any arbitrary condition without considering the limitations of experimental equipment, measurement errors and problems with measurement systems. For CFD simulations, the Reynolds-averaged NaviereStokes simulation (RANS), the large-eddy simulation (LES), and the direct numerical simulation (DNS) are three commonly used approaches with different accuracies. The RANS approach, especially the k-ε turbulence model, is traditionally used with the advantages of robustness, economy, and reasonable accuracy for a wide range of turbulent flows. DNS solves the NaviereStokes equations without any closure model, but is not feasible for practical engineering problems involving high Reynolds number flows because of high demand of computational resources. LES is developed as an intermediate approach between DNS and RANS. The general idea is that the large, non-universal scales of the flow are computed explicitly, while the small scales are modeled [13]. LES has been proven to be a successful approach to simulate unsteady flows around airfoils [14], but only recently have there been some efforts to apply LES to simulate wind turbine wakes [15e17]. It is more accurate than RANS and requires substantially finer meshes than those typically use the k-ε turbulence model. So time-accurate LES solver can capture the noise-generating region well and hence becomes a very promising method for predicting noise. Although there have been some aerodynamic studies of wind turbine by means of LES or experimental measurement independently, it is still difficult to fully calculate both the noise source and its propagation to the far-field, and as yet no detailed and open experimental data for wind turbine noise is available for model validation. In the present work, both the aerodynamic and aeroacoustic characteristic of a horizontal-axis wind turbine is studied with the LES and wind tunnel experiment. The main objective is to develop a LES framework for simulations of aerodynamics and aeroacoustics around a horizontal-axis wind turbine and improve the fundamental understanding of turbulenceenoise interaction. The wind turbine used in the simulation is exactly the same as the real model measured in the Key Laboratory of Renewable Energy in Inner Mongolia University of Technology for LES validations.
Fig. 1. B1/K2 wind tunnel and the wind turbine.
the wind blade rotational plane is vertical to the inlet flow direction. Fig. 2 shows the planes illuminated by the laser light sheet. They are vertical to the wind turbine rotation axis. In the PIV results, the coordinates of the blade tip is (224.1 mm, 57.4 mm). The size of the PIV picture is 257.34 mm 190.38 mm and the resolution is 1200 1600 pixels [20]. PIV measurement accuracy depends on the accuracy of the measurement of the particle displacement and the control accuracy of the time interval of two images. In the monitoring of wind speed during the present experimental process, the velocity uncertainty is about 5%. 2.2. Acoustic radiation measurement The acoustic radiation test is conducted in the same section of the wind tunnel with the same wind turbine. Acoustic analysis requires detailed records of sound information. The microphone
2. Wind tunnel experiment 2.1. PIV measurement Particle image velocimetry (PIV) is an advanced non-contact flow measurement technology that became applicable in the late 1990s [18]. It has been applied to explore research of wind turbine wakes [19]. In the present work, PIV measurement of a fixed area in the near wake of a horizontal-axis wind turbine has been done in the Key Laboratory of Renewable Energy in Inner Mongolia University of Technology. The experiment is conducted in the open section of the wind tunnel using the phase-locked periodic sampling method. The B1/ K2 wind tunnel used in the experiment is shown in Fig. 1, together with the wind turbine and the CCD camera. The diameter of the open test section of the wind tunnel is 2.04 m and the maximum steady wind speed is 20 m/s. The wind turbine model is a NACA4415 horizontal-axis wind turbine with three blades. Its blade has a diameter of D ¼ 1.4 m and the rated wind speed is 8 m/s. The rated tip-speed ratio l is 5 and the rated power is 100 W in this case. The tail is removed in order to achieve stable experimental conditions. The wind turbine is fixed to the system to ensure that
Fig. 2. PIV testing sketch.
K. Luo et al. / Renewable Energy 77 (2015) 351e362
353
can transfer the sound pressure into the electrical signal that can be recognized by the computer. MP201 microphone is applied in the experiment as shown in Fig. 3. Background noise is measured before the experiment to remove its influence. To ensure the reliability of the acoustic test, two different measuring-point arrangements are applied. In the first arrangement, the measuring-point is located in the horizontal and vertical lines of the central plane which is vertical to the rotational plane, as shown in Fig. 4(a). The tip of one blade is located in the point o. The distance between two points along one line is 10 cm. There are 10 points in the horizontal line and 14 points in the vertical line. In the second arrangement, the frequency signal is measured along the corresponding test line as shown in Fig. 4(b). Each line has 14 points and there is 10 cm distance between each point.
where D is the fluid domain, and G is the filter function that determines the scale of the resolved eddies. For incompressible flows, filtering the NaviereStokes equations, one obtains
3. Large-eddy simulations
sij ≡ m
3.1. Flow configuration
3.2. Mathematical models 3.2.1. The LES approach In LES, large eddies are resolved directly, while small eddies are modeled. The governing equations employed for LES are obtained by filtering the time-dependent NaviereStokes equations in either wave-number space or physical space. A filtered variable (denoted by an overbar) is defined by
Z
fðx0 ÞGðx; x0 Þdx0
D
(2)
and
v v v ðrui Þ þ rui uj ¼ vt vxj vxj
vsij m vxj
!
vp vtij vxj vxj
(3)
where sij is the stress tensor due to molecular viscosity defined by
"
vui vuj þ vxj vxi
!#
2 vu m l dij 3 vxl
(4)
and tij is the subgrid-scale stress defined by
To simulate the experimental wind turbine as real as possible, the flow configuration and computation domain are taken exactly the same as that in the experiments, as shown in Fig. 5. The axial distance is 7.68 m which is the length from the exit of the wind tunnel to the end of the room. The horizontal and vertical length is 5.1 m and 5.3 m, respectively. The wind turbine is placed in the middle of the horizontal line across the rotational plane. The origin of the coordinate axes is in the middle of the blades, which is 1.71 m from the ground and 0.78 m from the exit of the wind tunnel. The left and right wall, the roof and the ground are set to be the wall boundary condition.
fðxÞ ¼
vr v þ ðrui Þ ¼ 0 vt vxi
(1)
tij ≡rui uj rui uj
(5)
The subgrid-scale stresses resulting from the filtering operation are unknown, and require modeling. They can be modeled as [21]:
1 tij tkk dij ¼ 2mt Sij 3
(6)
where mt is the subgrid-scale turbulent viscosity. The isotropic part of the subgrid-scale stresses tkk is not modeled, but added to the filtered static pressure term. Sij is the rate-of-strain tensor for the resolved scale defined by
1 vui vuj Sij ≡ þ 2 vxj vxi
! (7)
In the SmagorinskyeLilly model, the eddy-viscosity is modeled by
mt ¼ rL2s S
(8)
qffiffiffiffiffiffiffiffiffiffiffiffiffi where Ls is the mixing length for subgrid scales and S≡ 2Sij Sji .Ls is computed using
Ls ¼ min kd; Cs V 1=3
(9)
n constant, d is the distance to the closest where k is the von K arma wall, Cs is the Smagorinsky constant, and V is the volume of the computational cell. 3.2.2. The Ffowcs Williams and Hawkings model The Ffowcs Williams and Hawkings (FWeH) equation is essentially an inhomogeneous wave equation that can be derived by manipulating the continuity equation and the NaviereStokes equations. The FWeH equation can be written as [22]:
1 v2 p0 v2 V2 p 0 ¼ Tij Hðf Þ 2 2 vx vx a0 vt i j v
Pij nj þ rui ðun vn Þ dðf Þ vxi v þ f½r0 vn þ rðun vn Þdðf Þg vt
where
Fig. 3. The microphone for measurement of noise.
ui ¼ fluid velocity component in the xi direction un ¼ fluid velocity component normal to the surface f ¼ 0
(10)
354
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 4. Measuring-point arrangements for noise measurement. (a) The first measuring-point arrangement (b) The second measuring-point arrangement.
vi ¼ surface velocity components in the xi direction vn ¼ surface velocity component normal to the surface d(f) ¼ Dirac delta function H(f) ¼ Heaviside function 0
Pij ¼ pdij m
0
p is the sound pressure at the far field (p ¼ pp0).f ¼ 0 denotes a mathematical surface introduced to “embed” the exterior flow problem (f > 0) in an unbounded space, which facilitates the use of generalized function theory and the free-space Green function to obtain the solution. The surface (f ¼ 0) corresponds to the source (emission) surface, and can be made coincident with a body (impermeable) surface or a permeable surface off the body surface. nj is the unit normal vector pointing toward the exterior region (f > 0),a0 is the far-field sound speed, and Tij is the Lighthill stress tensor, defined as
" # vui vuj 2 vuk þ dij vxj vxi 3 vxk
(12)
The free-stream quantities are denoted by the subscript 0. The solution to Equation (10) is obtained using the free-space Green function (d(g)/4pr). The complete solution consists of surface integrals and volume integrals. The surface integrals represent the contributions from monopole and dipole acoustic sources and partially from quadrupole sources, whereas the volume integrals represent quadrupole (volume) sources in the region outside the source surface. In this wind turbine case, the flow is low subsonic and the source surface encloses the source region, and the contribution of the volume integrals becomes small. So the volume integrals are dropped. Thus, we have
! ! ! p0 ð x ; tÞ ¼ p0T ð x ; tÞ þ p0L ð x ; tÞ Tij ¼ rui uj þ Pij a20 ðr r0 Þdij
(11)
Pij is the compressive stress tensor. For a Stokesian fluid, this is given by
(13)
where
3 2 r0 U_ n þ Un_ ! 4 5dS 4pp0T ð x ; tÞ ¼ rð1 Mr Þ2 f ¼0 o n Z "r Un r M_ r þ a Mr M 2 # 0 0 þ dS r 2 ð1 Mr Þ3 Z
(14)
f ¼0
! 4pp0L ð x ; tÞ
1 ¼ a0 þ
Z " f ¼0
1 a0
L_r
#
Z "
Lr LM
#
dS þ dS rð1 Mr Þ2 r 2 ð1 Mr Þ2 f ¼0 o n Z "L_r r M_ r þ a Mr M 2 # 0 dS r 2 ð1 Mr Þ2
f ¼0
(15) where
Ui ¼ vi þ Fig. 5. Flow configuration and computational domain.
r ðu vi Þ r0 i
(16)
K. Luo et al. / Renewable Energy 77 (2015) 351e362
355
The various subscripted quantities appearing in Equations (14) and (15) are the inner products of a vector and a unit vector ! c ! implied by the subscript. For instance, Lr ¼ L $ r ¼ Li ri and ! ! ! ! Un ¼ U $ n ¼ Ui ni , where r and n denote the unit vectors in the radiation and wallenormal directions, respectively. The dot over a variable denotes source-time differentiation of that variable.
experiment. The averaged wind velocity coming out of the wind tunnel is about 8 m/s, and the angular-velocity of the wind turbine blade is 545 rpm. The computational domain is divided into two parts: the internal rotating field and the external relatively stationary flow field. The interfaces are set to transfer data between the rotational and stationary parts. Coupled problems between the two parts have a great influence on the accuracy of numerical simulation. In the present study, the sliding mesh model is used to account for the rotation of the blades. The computational domain is discretized by about 2.86 million cells. Finer mesh is used on the whole rotor surface and gradually coarsens as the distance from the blades increases. It has been checked that the quality of the mesh meets the needs of the LES calculation. Another mesh of about 6 million cells is also tested and it is found that there is no obvious difference, which means that 2.86 million cells are enough for the present LES simulation.
3.3. Numerical details
4. Results and analysis
The flow around wind turbines, even in very large ones, is still essentially incompressible with Mach numbers based on blade tip speed almost never exceeding 0.25, which justifies the use of incompressible fluid solvers for most wind turbines. In the present work, an incompressible Navier Stokes solver is applied. The LES SmagorinskyeLilly model is used for the simulation. The PRESTO (PREssure STaggering Option) scheme [21] and the bounded central differencing format are used for the pressure and momentum discretization, respectively. The Pressure-Implicit with Splitting of Operators (PISO) [21] is used for the pressureevelocity coupling, and the second order implicit scheme is used for time integration. The no-slip boundary condition is applied for the wall boundary condition. To approach the experimental conditions, the inlet flow velocity is described by
4.1. Aerodynamic characteristics
b j þ rui ðun vn Þ Li ¼ Pij n
(17)
! ! p0T ð x ; tÞ and p0L ð x ; tÞ are referred to as thickness and loading terms, respectively. The square brackets in Equations (14) and (15) denote that the kernels of the integrals are computed at the corresponding retarded times (t), defined as follows, given the observer time (t), and the distance to the observer (r),
t¼t
r a0
Uin ¼ Uc þ
(18)
Uj Uc y þ H=2 y H=2 tanh tanh 2d 2d 2
(19)
where Uc and Uj represent the co-flow and the mean inflow velocity respectively. H is the entrance diameter of 2.04 m. d ¼ 0.05H. This prescribed inlet velocity profile is shown in Fig. 6. When y is greater than H/2, the speed is set to be zero. Furthermore, a turbulence intensity of 4% is imposed on the inflow according to the
Fig. 6. Inlet velocity profile.
4.1.1. Comparisons between LES and PIV In order to demonstrate the reliability of the aerodynamic simulations, comparisons between the LES results and the PIV experimental data have been conducted in this section. By observing the vertical plane which contains the PIV measuring field, the similarities can be found between the LES results and the PIV experimental data, as shown in Fig. 7. Fig. 7(b) displays the velocity magnitude contours of the tip vortexes in the shooting area of the experiment, and Fig. 7(a) displays the results of the LES in the vertical plane, in which the shooting area is marked roughly. The same tip vortex region has been found in both the LES and the experimental results. The speed in the increased area is higher than the inlet speed in the exit of the wind tunnel, and the maximum value exceeded 18 m/s. While the speed of the decreased area is lower than the inlet speed, with a minimum value close to 0 m/s. We further quantitatively compare the LES results with the experimental data. Take the first tip vortex core (shown in Fig. 7(b)) in the downstream of the wind turbine as a reference point to observe the instantaneous distribution of the axial and radial velocity. The distribution of the axial velocity U of the line which goes through the point and parallel to the z-axis is shown in Fig. 8(a), with the axial velocity U as abscissa and the observation point as yaxis. Y is the vertical distance from the viewpoint to the rotational axis. R is the radius of the wind rotor. Y/R represents the relative position. The range of the observation point is 0.94e1.13Y/R. The yaxis value 1 corresponds to the maximum circumferential position of the rotor rotating surface (the position of the blade tip). It is clear that the LES results are in good agreement with the experiment data. Outward from the central wake region, As the Y/R increases, the loss of axial velocity increases and reaches an extreme value near the tip (Y/R ¼ 0.98). Within a short distance across the tip (Y/ R ¼ 1.01), the axial velocity reaches the extreme value in the increased area. The two extreme points are symmetrical about the reference point selected. As the Y/R value continues to increase, the speed obtained becomes lower, and there is a trend towards integration with the mainstream. The distribution of the radial velocity along the line which goes through the point and parallel to the xaxis is shown in Fig. 8(b). X is the horizontal distance from the viewpoint to the rotational plane. There are two extreme points symmetrical about the reference point selected which is similar to Fig. 8(a). As the X/R value continues to reduce, the loss of speed increases, and tends to be steady with only small fluctuations. As mentioned above, the speed increase and decrease are attributed to
356
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 7. Velocity magnitude contour of the tip vortexes. (a) LES results (b) PIV results.
the tip vortex inducement. In the tip vortex induced region, the impact on the structure of the wake is dominated by the axial velocity while the radial velocity effect is relatively small. The mean velocity has also been compared for further validation. As the phase-locked periodic sampling method has been used in the PIV experiment, we use the same averaging method in our simulation for velocity statistics. Fig. 9 shows the comparison of the mean velocity in the pictured area with a phase angle of 100 . It can be seen that the distribution of the PIV mean velocity is consistent with that of the LES. The same tip vortex region has been found in both the LES and the PIV experiment results. In the tip vortex induced region, a symmetrical region of velocity magnitude is formed. Because of the presence of fluid viscosity, the tip vortex rotation increases and reduces the speed of these regions. The above comparisons between LES and PIV demonstrate that the present LES framework is reliable and lays a solid foundation for further study. 4.1.2. Vortex structures The blade rotation region is the work area of the wind turbine, and the air flow pattern in it is very complex. As the tip vortex, the attached vortex, the vortex behind the tower and the center vortex phenomena are formed in the rotation region, the analysis of the
flow characteristic in the rotation region is necessary. The circumferential distribution of the physical field near the upstream of the wind turbine obviously has a cycle symmetry phenomenon. Fig. 10 shows the different vortices in the wind turbine flow field identified by l2 criteria [23]. After the attached vortex, which distribute along the blade span, fall off the rim of the blade, it rapidly curled into the vortex surface. Meanwhile, the tip vortex is generated by the pressure difference between the suction side and pressure side of the blade tip and moved downstream, forming the near wake structure which has a concentrated vortex form. The near-wake structure is characterized by the tip vortex. Fig. 11 shows some details of the entire flow field through the velocity magnitude and vector in the horizontal and vertical planes. Fig. 11(a) and (b) shows the velocity magnitude contours in the horizontal plane (z ¼ 0 plane through the centerline) and the vertical plane (y ¼ 0 plane through the centerline), respectively. The maximum speed that appears at the tip of the blade could be 42 m/ s. The scale range has been reduced to 0e10 m/s in order to facilitate observation. The movement of the tip vortex can induce axial velocity at the blade, which will affect the airflow speed in front of the turbine, as shown in Fig. 11(a) and (b). Due to the momentum loss and vortex inducement, velocity of the internal flow field in the downstream of the wind turbine has been reduced (with the largest
Fig. 8. Velocity distribution along the x and z-axis passing through the reference point. (a) Axial velocity U profiles (b) Radial velocity V profiles.
K. Luo et al. / Renewable Energy 77 (2015) 351e362
357
Fig. 9. Comparison of mean velocity between PIV and LES. (a)Mean experiment-u velocity. (b)Mean simulation-u velocity. (c)Mean experiment-v velocity. (d)Mean simulation-v velocity.
Fig. 10. Vortices in the near wake of the wind turbine.
reduction at the centerline at hub height), while the velocity of the external flow field increased. The speed change region extends into the upstream of the wind blades, forming a large velocity gradient region around the wind turbine. However the speed contour expands gradually, which indicates that the flow takes a long time to revert to its original velocity after passing through the wind turbine. The complex unsteady wake structure includes the central wake region, the outside mainstream region, and the tip vortex induced region. This is usually looked upon as the “wake” behind the wind turbine, and the effect of the wake is still noticeable even in the far wake. In fact the flow of the wind turbine wake is a typical turbulent flow dominated by the vortex flow. Wake region of the wind turbine can be divided into the near wake and the far wake. In the near wake the vortex line changes obviously and the wind speed decreases, while in the far wake, the center wake vortex is visible and the tip vortex is gradually dissipated to be steady. These structural features of the near wake flow field are the basis of the horizontal axis wind turbine aerodynamic performance design and characteristics prediction [24]. In Fig. 11(a) and (b) the spiral tubular vortex generated by the blade tip (the tip vortex as shown in Fig. 10) can be observed, so as
358
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 11. Distribution of velocity magnitude and vector at different planes. (a) Velocity magnitude in the horizontal plane, (b) Velocity magnitude in the vertical plane, (c) Velocity vector in the horizontal plane, (d) Velocity vector in the rotational plane.
the position of the vortex core. The tip vortex is generated from the tip region and then fell off. As the blades continue to rotate, the tip vortexes move downstream. The energy is gradually dissipated and the vorticity magnitude is reduced in the moving process. The vortex concentrated area gradually disappears and a series of vortex structures appear after the wind turbine. In addition, the distribution of the velocity contours is almost axisymmetric at z ¼ 0 plane, however, it's non-axisymmetric at y ¼ 0 plane, which is caused by the influence of the support structure of wind turbine and the ground. So we should be informed that the effects of the nacelle, the turbine tower and the ground condition on the turbulent flow need to be considered when operating the wind farm. Fig. 11(c) and (d) display the magnified velocity vector, in which the velocity magnitude and direction near the blade can be seen more clearly. These are important areas that affect the flow structure in the downstream. The three-dimensional effect of the blade, the differential pressure effect of the pressure surface and the suction side on the tip separated flow, and the air flow motion of rotating in a circular generated by the blades can be seen in Fig. 11(c) and (d). And with these causes the flow continues to spread downstream with concentrated vortex, forming the complex unsteady wake structure mentioned above. The three regions in the near wake can be identified from their different speeds and directions. The maximum speed can be found in the blade tip and the air flow changes its direction around the tip blade. The trail flow of the rotational blade can be seen obviously. It is rotating in the clockwise direction and has relatively high wind speed in the windward side. Between the three blades the value of velocity increased from the blade root to the blade tip. But this order is not
clear near the blade surface. Meanwhile, there is a tendency of separating from the tip in the spanwise direction, which is the characteristic of a three-dimensional rotating flow. Fig. 12(a) shows the mean velocity in the center vertical lines across the wake at x ¼ eR, 0.5R, 2R and 9R. The line x ¼ R represents the inlet condition. It can be seen that the section plane gradually expands and the center area has the maximum speed loss. The second maximum speed loss is in the blade tip (z/R ¼ ±1) where the tip vortex generates. The lines are almost symmetric except the x ¼ 0.5R line that is non-uniform in the lower part because of the influence of the turbine tower. Fig. 12(b) shows the mean velocity in the horizontal lines through the wake at z ¼ 0, R, 1.45R, R, and 1.45R. Each line displays the velocity distribution in and around the rotation area. The z ¼ ±1.45R lines are near the outer boundary of the exit wind tunnel. They reach the maximum velocity around x/R ¼ 1, and then reduce downstream. The lower one z ¼ 1.45R line reduces more than the upper one. The velocity is relatively lower near the center line (line z ¼ 0). The center line and the z ¼ ±R lines all have a velocity increase in the region of x ¼ 2e5R while the z ¼ ±1.45R lines decrease. Combining with Fig. 11, it can be concluded that the tip vortex area forms, moves downstream and dissipates with the evolution of time. The more it moves downstream, the more disturbance and stronger fluctuations the tip vortex receives. 4.1.3. Pressure distribution The above analysis indicates that the tip blade is the important area for producing energy. The energy that the wind turbine can get is closely related to the pressure distribution and change on the
K. Luo et al. / Renewable Energy 77 (2015) 351e362
359
Fig. 12. Mean velocity magnitude in different lines. (a) Center vertical lines across the wake, (b) Center horizontal lines through the wake.
blade surface. Fig. 13 presents the pressure and suction surface respectively. On the pressure surface the pressure magnitude increases from root to tip of the blade and reaches the maximum value at the tip. In the suction side, it's just the opposite. The maximum positive pressure and maximum negative pressure both appear at the tip blade which results in the maximum differential pressure at the tip. Additionally, the pressure is different even on the two sides of the same tip surface. The windward side of both the two surfaces obtain larger aerodynamic load. The higher the differential pressure, the more energy converted, if only the blade is strong enough. The main concern point of improving wind turbine performance and reducing noise should be laid in the tip area. Improving the structure of the tip region, reforming the flow condition, suppressing vortex intensity and increasing the pressure difference between the pressure surface and the suction surface will increase the power output and at the same time reducing wind turbine noise [25]. 4.2. Aeroacoustic characteristics 4.2.1. Comparisons between LES and measurement After the flow field being fully developed, the Ffowcs-Williams & Hawkings model is applied for aero-noise simulation. Based on
transient flow simulation results, time variation of acoustic pressure is calculated. The results will be compared with the experiment data in the form of sound pressure level (SPL). In the first arrangement, the measuring-points are shown in Fig. 4(a), and the results are shown in Fig. 14, which contain the comparison of SPL between the LES results and the experimental data at x ¼ 10 cm, x ¼ 40 cm and y ¼ 20 cm, y ¼ 20 cm lines. The LES results are generally consistent with the experimental data. They have the same trend and the LES results are a little higher than the experiment data in certain region. The region near the blade has higher sound pressure level with the highest value of about 120 dB. It can be seen from the complete data that the region which is marked in Fig. 15 has relatively high SPL value, and the blade tip region is the main resource area of the aero-noise. In the second arrangement, the measuring-points are shown in Fig. 4(b), and the comparisons of SPL between the present LES result and experimental data in the four different test lines are shown in Fig. 16. As can be seen from the figure the distributions of the sound pressure level along different lines obtained by LES generally agree well with those of the experimental data. With the increase of the test line angle, the sound pressure level decreases at the points close to the blade tip. The main resource area of the acoustic radiation is identified around the wind turbine. In each test
Fig. 13. The pressure and suction surface of the blades. (a) The pressure surface, (b) The suction surface.
360
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 14. Comparisons of SPL between LES results and experimental data for the first arrangement. (a) Comparison of SPL at x ¼ 10(cm), (b) Comparison of SPL at x ¼ 40(cm), (c) Comparison of SPL at y ¼ 20(cm), (d) Comparison of SPL at y ¼ 20(cm).
line, the first measuring point close to the wind turbine has the highest SPL value. As a result of the masking effect of the rotating blade and the diffraction of the sound when across the wind turbine, the acoustic radiation intensity of the rotor reduces rapidly with the test point moves downstream. It cannot be ignored that there are some small differences between the LES and experimental results. The small fluctuations in the flow and rotational speed are inevitable in the experimental measurements because vibration, deformation and the vortex shedding position are always fluctuating during wind turbine operation. Furthermore, there is background noise in the experiment and the influence of the wind tunnel aerodynamic noise is estimated in the analysis. 4.2.2. Vortex-noise relationship To further explore the relationship between vortex dynamics and aeroacoustic distribution, the distribution of acoustic noise and the related region of vortices are illustrated in Fig. 17. To facilitate observation, the SPL value at different points around the wind rotor in the LES is processed into contour, as shown in Fig. 17(a). The yaxis represents the rotating plane and the x-axis stands for the axis of rotation. It is clear that the region near the blade has high SPL value which is in accordance with Fig. 15, and the value increases from the center point to the blade tip. This region is interestingly distributed between the central vortex and the tip vortex,
indicating that vortex structures have significant effect on aeroacoustic noise. The sound pressure level decreases fast along the center line in the area near the blade because of the impact of the motor. However, a little far away from the blade it decreases slower
Fig. 15. Schematic diagram of noise generation region.
K. Luo et al. / Renewable Energy 77 (2015) 351e362
Fig. 16. Comparison of the sound pressure level in the second arrangement. (a) 0 testing line, (b) 15 testing line, (c) 30 testing line, (d) 45 testing line.
Fig. 17. The contour of the acoustic noise and the related region of vortices. (a) The contour of the acoustic noise, (b) The vortices in the related region.
361
362
K. Luo et al. / Renewable Energy 77 (2015) 351e362
in the center line direction, caused by the impact of the central vortices near the motor as shown in Fig. 17(b). In the tip vortex moving direction, the SPL value also decreases slower, which shows that the radiation of the aerodynamic noise is influenced by the movement of the tip vortex. The maximum SPL value appears in the area between the tip and root of the blade, and is closer to the tip. One may conclude that both the tip vortex and the vortex near the motor generate the noise, and the influence of the blade tip is more significant. The tip vortex can be regarded as a main reason that not only reduces the output power, but also increases the aerodynamic noise and the fatigue loads. 5. Conclusions Three-dimensional vortex dynamics and aeroacoustic characteristics around a horizontal-axis wind turbine have been investigated by LES and wind-tunnel measurement. In general, the LES results are in good agreement with the experimental data, indicating that the present models and methodology are capable of accurately reproducing near wake characteristics (including velocity, pressure and vortices) and noise generation of the wind turbine. The near wake has complex vortex structures, including the tip vortex, the attached vortex, the vortex behind the tower and the center vortex structures which can be well captured by the LES. Noise generation and acoustic radiation are closely associated with the generation and evolution of these vortex structures, and both of them are influenced by the periodic rotation of the wind turbine. The blade tip region is the main resource area of the aero-noise and the acoustic radiation intensity of the rotor decreases rapidly with the test point moves downstream. These results indicate that more attentions should be paid to the tip area to improve wind turbine performance and reduce noise. Acknowledgments This work is financially supported by the Inner Mongolia Autonomous Region Open Major Basic Research Project (Grant No. 20120905) and the National Natural Science Foundation of China (Grant No. 51366010). We are grateful to that. References [1] Hu Danmei, Tian Jie, Du Zhaohui. Measurement and analysis of wake behind horizontally orientated air turbines. J Power Eng 2006;26(5):751e60. [2] Hu Danmei, Hua Ouyang, Du Zhaohui. An experimental study of the wake structure of a model horizontal-axis wind turbine. Acta Energiae Solaris Sin 2006;27(6):606e12.
[3] Krogstad Per-Åge, Eriksen Pål Egil. “Blind test” calculations of the performance and wake development for a model wind turbine. Renew Energy 2013;50: 325e33. [4] Whale J, Anderson CG, Bareiss R, Wagner S. An experimental and numerical study of the vortex structure in the wake of a wind turbine. J Wind Eng Ind Aerodynamics 2000;84(1):1e21. [5] Daichin, Kang Wen, Zhao Li-li. PIV measurements of the near-wake flow of an airfoil above a free surface. J Hydrodynamics 2007;19(4):482e7. [6] Johansson L. Summary of IEA topical expert meeting on noise immission. 2000. [7] Brentner Kenneth S, Farassat F. Modeling aerodynamically generated sound of helicopter rotors. Prog Aerosp Sci 2003;39(2e3):83e120. [8] Fragias AP, Spyropoulos AI, Margaris DP, Papanikas DG. Coupled aerodynamic and aeroacoustic numerical model for helicopter main rotor blades. In: Proceedings of the fourth GRACM congress on computational mechanics, vol. 2; 2002. p. 643e50. Patras-Greece [II]. [9] Martin Hansen OL. Aerodynamics of wind turbines. In: Earthscan in the UK and USA. 2nd ed. 2008. [10] Larsen JW, Nielsen SRK, Krenk S. Dynamic stall model for wind turbine airfoils. J Fluids Struct 2007;23:959e82. [11] Wang Ji-feng, Piechna Janusz, Müller Norbert. A novel design of composite water turbine using CFD. J Hydrodynamics 2012;24(1):11e6. [12] Saavedra-Moreno B, Salcedo-Sanz S, Paniagua-Tineo A, Prieto L, PortillaFigueras A. Seeding evolutionary algorithms with heuristics for optimal wind turbines positioning in wind farms. Renew Energy 2011;36:2838e44. -Agel Fernando, Wu Yu Ting, Lu Hao, Conzemius Robert J. Large-eddy [13] Porte simulation of atmospheric boundary layer flow through wind turbines and wind farms. J Wind Eng Ind Aerodyn 2011;99:154e68. [14] LESFOIL: large eddy simulation of flow around a high lift airfoil. In: €hlich J, Leschziner MA, Mellen C, Rodi W, editors. Davidson L, Cokljat D, Fro Notes on numerical fluid mechanics, vol. 83. Springer Verlag; 2003. -Agel Fernando. Large-eddy simulation of wind-turbine [15] Wu Yu-Ting, Porte wakes: evaluation of turbine parametrisations. Boundary Layer Meteorol 2011;138:345e66. [16] Rolland S, Newton W, Williams AJ, Croft TN, Gethin DT, Cross M. Simulations technique for the design of a vertical axis wind turbine device with experimental validation. Appl Energy 2013;111:1195e203. [17] Mo Jang-Oh, Choudhry Amanullah, Arjomandi Maziar, Lee Young-Ho. Large eddy simulation of the wind turbine wake characteristics in the numerical wind tunnel model. J Wind Eng Ind Aerodyn 2013;112:11e24. [18] Adrian RJ. Twenty years of particle image velocimetry. Exp Fluids 2005;39(2): 159e69. [19] Grant I, Mo M, Pan X, Parkin P, Powell J, Reinecke H, et al. An experimental and numerical study of the vortex filaments in the wake of an operational horizontal-axis wind turbine. J Wind Eng Ind Aerodyn 2000;85(2):177e89. [20] Gao Zhiying, Wang Jianwen, Dong Xueqing, Zhang Liru. Experimental study of the near wake flow field structure of the horizontal axis wind turbine. Acta Energiae Solaris Sin 2011;32(6):897e900 [in Chinese]. [21] FLUENT 6.3 documentation. USA: Fluent Inc; 2006. [22] Ffowcs-Williams JE, Hawkings DL. Sound generation by turbulence and surfaces in arbitrary motion. Philos Trans R Soc Lond A 1969;264(1151): 321e42. [23] Jeong J, Hussain F. On the identification of a vortex. J Fluid Mech 1995;285: 69e94. [24] Ebert PR, Wood DH. The near wake of a model horizontal-axis wind turbine-I. Experimental arrangements and initial results. Renew Energy 1997;12(3): 225e43. [25] Wang Jianwen, Jia Ruibo, Wu Keqi. Numerical simulation of dynamic amplification characteristics of wind turbine with winglets in the blade tip. Acta Energiae Solaris Sin 2007;28(1):55e61 [in Chinese].